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1/” WM“

THE DEVELOPMENT OF NON-CONTACT AND NON-
DESTRUCTIVE EXPERIMENTAL TECHNIQUES CAPABLE
OF MEASURING THE THERMAL DIFFUSIVITY OF CVD
DIAMOND FILM.

Matthew J. White

A Thesis
Submitted to Michigan State University
in partial fulﬁllment of the requirements for
the degree of

MASTER OF SCIENCE

Depamnent of Mechanical Engineering

1 996

ABSTRACT

THE DEVELOPMENT OF NON-CONTACT AND NON-
DESTRUCTIVE EXPERIMENTAL TECHNIQUES CAPABLE
OF MEASURING THE THERMAL DIFFUSIVITY OF CVD
DIAMOND FILM.

By

Matthew J. White

A new optical, non-contact, and non-destructive experimental technique has been
developed. When used with existing analytical tools, this system is capable of estimating
the thermal diffusivity of thin ﬁlms. A signiﬁcant portion of this work is devoted to
establishing the general capabilities of the experimental components. The major
components include two infrared temperature measurement devices, a Q- Switched
Nd:YAG laser, instrumentation for laser beam diagnostics, and a data acquisition and
instrument control system.

Beyond the development, estimates for the thermal diﬂiisivity of copper, iron and
CVD diamond ﬁlm were obtained. In these experiments, the Nd:YAG laser was used to
perturb the thermal equilibrium of the sample and infrared thermography was used to
record the established temperature gradients. The method of least squares was used to
minimize the errors between the measured temperatures and the calculated temperatures

determined from a one dimensional quasi-steady state model.

to my family

iii

Acknowledgments

I would like to take this time to thank my co-advisors, Professor 1.]. McGrath and
Professor J.V. Beck. I feel they provided me with an excellent example of how to conduct
myselfas an engineer, a researcher, and most importantly as a person. I believe the skills I
developed under their guidance will help me successfully overcome any hurdles placed in
front of me in the future.

I would also like to thank colleagues such as Kevin Dowding, Heidi Relyea, Scott
Morris, and Dr. Moshen Shabana. Each of these individuals were always willing to take
the time to give a creative suggestion or if need be a meticulous explanation.

My thanks go out to Professor C.W. Somerton for his review of the present work.
Beyond Professor Somerton’s ability as instructor, his guidance over the past two years
was very helpful.

A special thanks goes out to my family. They always encouraged me to strive for
my goals and were willing to make the necessary sacriﬁces so I could be in a position to
obtain them. They may never realize the degree to which their support and
encouragement over the past few years was appreciated.

As I write this thesis I close the chapter on my days at Michigan State University.
M.S.U. has provided an environment in which I have had an opportunity to mature as a
person, meet some great people, and enjoy some good times. All this while obtaining a
high quality education. As I look back through all the good memories, however I leave

Michigan State with one regret. I believe a person can never have enough ﬁiends, and the

iv

way I conducted myself during recent stressﬁil periods seemingly cost me a great ﬁiend. I

hope some day she will forgive me.

Table of Contents

List of Tables
List of Figures

Nomenclature

Chapter

1 Introduction
1.1 Objectives
2 Background and Literature Review
2.1 CVD Diamond Films
2.2 Methods for Determining the Therrnophysical Properties
2.2.1 Standard Methods
2.2.2 Variations to Standard Methods for CVD Diamond Film
2.2.3 General Purpose System Development at M.S.U.
3 System Development and Component Description
3.1 Temperature Measurements
3.1.1 Infrared Imaging Radiometer
3.1.2 Infrared Point Detector
3 .2 Heating Source

3.2.1 Nd:YAG Laser

ix

xvii

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26

3O

31

39

45

45

3.2.2 Laser Diagnostic Equipment
3.2.2.1 Molectron Power/Energy Meter
3.2.2.2 High Speed Photodetector
3.2.2.3 Beam Proﬁling Techniques
3.3 Data Acquisition and Control
3.3.1 LabVIEW
3.3.2 The AT-MIOl6F Data Acquisition Board
3.3.3 The EISA-AZOOO Data Acquisition Board
3 .4 Miscellaneous Experimental Equipment
3.4.1 FOR.A Video Timer
Description of the Mathematical Model
4.] Mathematical Model
4.2 Parameter Estimation
Procedures and Results for One Dimensional Radial Experiments
5.] Sample Description and Sample Preparation
5.2 Experimental Setup and Measurement Techniques
5.3 Experimental Results for Veriﬁcation Materials
5.3.1 Experimental Results for Copper
5.3.2 Experimental Results for Iron
5.4 Experimental Results for CVD Diamond Film
5.4.1 Non-Uniform Thermal Properties of CVD Diamond Film
5.5 Experimental Uncertainty

5.6 Discussion of Experimental Results

vii

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103

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113

120

123

126

6 Summary and Conclusions 129

List of References

Appendices

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

Appendix G

Appendix H
Appendix I

Appendix J

Appendix K

135

Laser background

Calibration of IPPLUS for Infrared Temperature
Measurement

Spatial Calibration of IPPLUS for Infrared Temperature
Measurement

Laser Beam Diagnostics

Infrared Thermography used to Measure the
Temperature Distribution of Boron Doped Diamond
Films Heated with Joule Heating

Description of the LabVIEW VI Used to Externally
Trigger the Video Timer

NLIN Input File

NLIN, Non-Linear Sequential Estimation Program
NLIN Output File

A Listing of the Values for the Estimated Thermal
Diﬁiisivities

Fast Line Scan Testing

viii

Table 3.1

Table 5.1

Table 6.1

Table 6.2

List of Tables

Speciﬁcations of the ThorlAB DE T 2-SI high speed photodector.

Experimental Parameters, their estimated uncertainties and the
corresponding contributions to the uncertainty of the thermal

diﬁizsivity.

Ihe estimated thermal dlﬂusivity for experimental tests conducted
on copper and iron samples.

The estimated thermal drﬁ‘usivities for experimental tests conducted
on three C VD diamond samples.

122

132

133

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

List of Figures

The diamond cubic unit cell.

Scanning Electron Microscope (SEM) micrographs of diamond ﬁlms
with typical surface morphologies with (a. ) trigular shaped crystal
faces, (b. ) square shaped crystal faces, and (a) cauliﬂower-like
crystalline aggregates.

Thermal conductivity parallel (kg) and perpendicular (k j to the
surface of the ﬁlm.

Thermal conductivity of two diamond ﬁlms as measured by Morelli,
Beetz and Perry. The ﬁlms used in this experiment were created

using the hot ﬁlament assisted C VD method

Graebner, Muncha, Seibles, and Kammlott (1992) results for the
lhermal Conductivity parallel to the surface of the ﬁlm (kg). Yhe
diamond ﬁlms in this study were created using a microwave-plasma
C VD technique.

Schematic diagram of the experimental setup used by Graebner, Jin,
Herb, Kammlott, and Gardinier for determining the parallel thermal
conductivity.

Graebner, Jin, Herb, Kammlott, and Gardinier (1992) results for the
thermal conductivity parallel to the surface of the ﬁlm. Ihese
results show an increase in thermal conductivity by more than a
factor of two as the thickness is increased by a factor of ten.

Schematic representation of the experimental setup used by Albin,
Winfree, Crews to measure the thermal conductivity parallel to the
surface of the ﬁlm.

Schematic representation of the converging wave apparatus used by
Lu and Sivann for determining the thermal conductivity parallel to
the surface of the ﬁlm.

The experimental arrangement used by Graebner, Jin, Kammlott,
Bacon, and Seibles to measure the thermal conductivity

X

10

12

13

15

16

17

18

20

Figure 2.11

Figure 2.12

Figure 2.13

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

perpendicular to the surface of the ﬁlm.

Thermal conductivity measurements perpendicular to the surface of
the ﬁlm. In these test conducted by Graebner, Jin, Kammlott, Herb,
Wong, and Gradinier it is clear that k 1 increases with ﬁlm
thickness.

T )pical values for It. obtained by Petrovsky, Salnick, Mukhin, and
Spitsyn using the photothermal beam deﬂection technique.

A plot of the thermal conductivity as a function of ﬁlm thickness.
This plot illustrates the discrepancy in the estimated values among
separate research groups.

A generalized schematic representation of the newly developed
experimental setup.

A typical test conﬁguration for measuring the thermal diﬁusivity
parallel to the surface of the ﬁlm.

A apical experimental conﬁguration used to measure the thermal
conductivity perpendicular to the surface of the ﬁlm.

The Inﬁametrics Model 600L Inﬁared Imaging Radiometer.

The slit response function for the Inﬁametrics Radiometer with the
C lose-up and 3X lenses. These tests show that the imaging spatial
resolution is approximately 20 pm and the measurement spatial
resolution is approximately 67.5 m.

The slit response ﬁrnction for the Inﬁametrics Radiometer with no
external optics. This tests illustrates that at a working distance of
15 cm the imaging spatial resolution is approximately 65 m and
the measurement spatial resolution is approximately 335 pm.

A plot of the non-dimensional temperature as a function of gray
scale. This information is used to generate a calibration between
gray scale and temperature.

The EGd’cG Model J15D12 Inﬁ'ared Detector and PA -35 0
Preampliﬁer.

The comparison between response of the EG&G Infrared Detector
and temperature measured by the thermocouple.

22

23

24

27

27

28

31

35

35

37

38

39

Figure 3.10a A picture of the experimental setup used for transient temperature

W068 measurement

Figure 3.10b A schematic representation of the experimental setup used for

Figure 3.11

Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Figure 3.16

Figure 3.17

Figure 3.18

trcmsient surface measurement.

The output of the photodetector as a ﬁmction of scan number.
Since data was collected at 10 kHz, the information in the above plot
represents 2 seconds of heating.

Temperature as a function of scan number. This data was obtained
using the voltage to temperature calibration in Figure 3. 9.

Excel/Quantronix Model 1 1 7E Nd: YA G laser

(a. ) Laser power as a ﬁmction of lamp current. (b. ) A characteristic
representation of the beam proﬁle when operating the laser near
28.8 amps. At this current the thermal axis of the laser is aligned
with the mirrors and aperture in such a manner that a high quality
gaussicm shaped beam is established (c.) A characteristic
representation of the beam proﬁle with the laser ’s thermal axis
misaligned This distortion in beam quality occurs when operating
the laser at low lamp currents.

The required alignment of the beamsplitters to obtain a 50%
reduction in laser beam intensity.

The Galilean Beam Expander. Used in this case to magnify the
laser beam ’s diameter 8 times.

(a. ) The heating of a test specimen with laser passing through a beam
expander and a cylindrical lens. Temperature measurements are
made using the Inframetrics Model 600L inﬁared imaging
radiometer. (b. ) A schematic representation comparing the sample
thickness with the approximate beam thickness. (c.) Thermally
sensitive laser paper manufactured by KENTIX used to give a
general illustration of the size line generated with this optical
conﬁguration.

(a) The surface temperature distribution of the test specimen heated
along one surface with laser radiation spatially distributed as a line.
If the radiation intensity across the length of the line generated is
uniform, the surface temperatures parallel to the heated surface
should be relatively constant. As shown in (b. ) this is indeed the
case.

xii

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43

50

51

Figure 3.19

Figure 3.20

Figure 3.21

Figure 3.22

Figure 3.23

Figure 3.24

Figure 3.25

Figure 3.26

Figure 3.27
Figure 3.28

Figure 3.29

Figure 3.30

Figure 3.31

Figure 3.32

The Uniblitz electro—mechanical shutter and control driver. This
shutter system provides a means for mechanically chopping the
beam at various frequencies.

Beam intensity as a ﬁmction of time for the laser operating in a Q-
switch mode with a pulse repetition frequency of 5 OkHz. This
information is acquired with a high speed photodetector with output
connected to an oscilloscope.

T )pical performance curves for the Excel/Quantronix Nd: YAG laser
operating with a lamp current of 28.0 amps. This information was
acquired with a power/energy and photodector and is meant to
represent apical laser performance when operating in Q-switch
mode.

The Molectron EPM1000 Power/Energy Meter

The Molectron PowerA/LAX PM-10 thermopile probe. Thermopile
probes of this kind are primarily used to measure the output of
moderate to high power continuous wave (C m lasers.

The Molectron pyroelectronic probe. Pyroelectronic probes of this
kind are primarily used to measure the output of moderate to high
power q-switched or externally chopped lasers.

Lab VIEW Data Acquisition and Control program for EPM1000
Power/Energy Meter. This program allows for communication
through an analog BNC connection or through a RS-232 Serial
Port.

The bearnsplitter method of obtaining simultaneous heat ﬂux and
temperature information.

The ThorLAB high speed photodetector
Photodetector sensitivity as a ﬁrnction of wavelength.

Illustration of the external load used to convert the photo current
into a voltage.

The FOR.A V7633 Video Timer.

An example of the TIT. signal. This signal is used to remotely start
the VTG 33 video timer.

The wiring connections for external trigering of video timer.

52

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58

62

63

65

66

72

72

73

Figure 4.1

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Schematic representation of the test specimen.

(a) A dianond ﬁlm on silicon substrate placed in the ﬁeld of view of
the Inﬁanetrics Model 600L radiometer. (b. )A radiating bodies
placed behind the sample illustrating the eﬂects of measuring the
surface temperature of high tratsmissivity materials.

The copper (left) ard the iron (right) samples used in this
experiment. Each of the samples are 5.08 cm in diameter and have a
thickness of 100m.

The three C VD dianond ﬁlms measured in this study. Each of the
sanples have a diameter of 5. 08 cm. The average thicknesses of
sample AT#4, ST#192, ardST#120 are 370m, 370 ,um, and 240

pm respectively.

Schematic representation of the experimental setup used for
measuring the model thermal drﬂusivity of several thin circular
test samples.

The ORIEL X-Y positioner. This device can be moved to various
locations along the optical rail ard allows for micro-positioning of
specimen for bean alignment.

The output of the radiometer is used in conjunction with the IPPL US
image processing system to verify that the laser is properly aligned
in the center of the test specimen. Note the symmetry in gray level
(temperature) distribution.

The output of the radiometer is used in conjunction with the IPPL US
image processing system to illustrate that the bean is improperly
aligned Note the asymmetry in gray level (temperature) distribution.

The positioning of the photodetector with respect to the test sanple.

The ﬁont parel of a Lab WE W VI which is used to monitor the
response of the photodetector. When the progran senses that the
detector response has exceeded a preprogranmed trigger level it
initiates a data acquisition boad to send a TIT. low signal to
external connections on the ma parel of the video timer.

The response of the photodetector aid data acquisition boad used
to measure the execution time of the LabVIEW VI in Figure 5.9.
This V7 is responsible for externally triggering the video timer.

xiv

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87

88

89

90

93

94

95

96

97

98

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Figure 5.24

(a. ) A thermal image of a 5. 08 cm dianeter copper disk at 3. 00
seconds. The horizontal line across the center of the specimen
represents the line proﬁle function ﬁom the IPPL US intensity
aralysis toolbox. (b.) The output of the line proﬁle function Gray
scale intensity as a function of pixel number.

Temperature as a Function Pixel Number. This temperature
distribution was obtained using a calibration relating temperature
ard gray scale.

Measured ard calculated temperature distributions along a
horizontal line across the center of the copper sanple. This is
sanple has a dianeter of 5. 08 cm ard a thickness of 100m.

The distribution of residuals across the dianeter of the copper disk.

Sequential Estimation for the thermal diﬂusivity for the copper disk
using the non-linea' sequential estimation progran, NLIN.

A compa'ison between the estimated thermal diﬂusivities and the
published values.

Measured ard calculated temperature distributions along a
horizontal line across the center of the iron sanple. This is sanple
has a dianeter of 5. 08 cm and a thiclmess of 100 pm.

The distribution of residuals across the dianeter of the iron disk.

Sequential Estimation for the thermal drﬂusivity for the copper disk
using the non-linear sequential estimation program, NLIN.

A compa'ison between the estimated thermal diﬁ'usivities for iron
ard the published values.

The measured ard calculated temperature distributions with the
C. V.D. dianond ﬁlm sanple A T # 4.

The distribution of residuals across the dianeter of the C VD
dianond ﬁlm.

Sequential Estimation for the thermal drﬁirsivity for the iron sanple
using the non-linear sequential estimation progran, NLIN.

The experimental results for C VD dianond ﬁlm. (a) Sanple A T # 4,
(b.) Sanple ST#I92, (c.) Sanple ST#120.

XV

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111

113

114

115

116

Figure 5.26

Figure 5.27

Figure 5.28

Figure 5.29

Figure 5.30

A schematic representation of the cross section of the C VD diamond
ﬁlm. This representation illustrates the columnar microstruCture
responsible for the increasing grain size with distance for the
substrate surface. [Graebner et al, 1992]

The transient temperature distributions for two tests conducted on
dianond ﬁlm sanple A T # 4. This ﬁgure illustrates that using this
measurement procedure, the microstructural characteristics of the
growth and substrate surfaces do not contribute appreciable
differences in thermal transport.

T emperature ﬂuctuations at one speciﬁc location on a isothermal
ard constant temperature sample as a function of time. The
standard deviation of these ﬂuctuations we used to represent the
accuracy of the radiometer.

An inﬁared image of a ﬂat test specimen with two thin ﬁn attached
to the surface. This image is used to illustrate the blurring or
averaging phenomenon that causes systematic errors in the
measured temperatures

An illustration of the apparent temperature difference caused by the
additional of the icebath to the background of the right hand side of
the infrared image.

119

120

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126

127

t,‘r

r, r'
Bi

um

Nomenclature

Thermal Conductivity
Thermal Diﬁirsivity
Speciﬁc Heat
Emissivity
Transmissivity
Reﬂectivity

Mass Density
Temperature

Least Squares Funciton
Time

Eigenvalue

Cylindrical Coordinate
Estimate Parameter
Micron

Hertz

Heat Flux

Heat Generation

Sample Thickness

xvii

[W/m °C]
[mz/s]

[J/Kg K]

[kg/m3]

[°C]

[8601

[m]

[10*5 m]
[cycle/sec}
[W/m2]
[W/m3]
[m]

a, b Radial Distances [m]

T, Initial Temperature [°C]
Yj Measured Temperature [°C]
T,- Calculated Temperature [°C]
F o Fourier Number

Subscripts/ Superscripts

QS Quasi-Steady State
TR Transient Term
I Initial
j Indexing Constant
r,x,y,x Directions

Chapter 1

Introduction

Since the time Fourier so concisely set forth the principles of heat conduction, the
theoretical treatment of heat transmission through media has and will continue to be
important to many ﬁelds of science and engineering. The advent of the mechanical
refrigerator in the late 1920’s brought about a need for insulating materials and an
increased interest in thermal conductivity measurements. In the late 1930’s and early
1940’s an increased need to know the thermal conductivity of metals was in evidence and
further accelerated by nuclear energy and missile developments [Lucks, 1963]. The space
race in the late 1950’s and early 60’s brought about a considerable advancement in
parameter estimation as the design of reentry heat shields became a major issue [Beck,
1996]. The most recent impetus to this type of measurement is associate with the
emphasis on semi-conductors, heat sinks and high performance materials. Thermal

conductivity measurements are now being made over a wide spectrum of materials and

range of temperatures. Consequentially, many methods are now being used for these
measurements.

One material under scrutiny by the scientiﬁc world is diamond. Well known for
its aesthetic beauty and for its practical importance, diamond is a material which has
fascinated humankind since the early ages. Not only is it one of the rarest gem in the
world, but diamond is both harder and conducts heat better than any other known
substance. These two physical properties make diamond an excellent choice for many
technical applications, such as cutting, abrasion, protective coatings, and heat conduction,
to name a few. The use of diamond in such application has been hindered by the difﬁculty
and expense encountered by an experimentalist as he/ she tries to synthesize diamond in the
laboratory.

Over the past 15 years the situation has changed to a large degree as researchers
have explored new and innovative techniques to synthesize diamond ﬁlms. In particular,
a great deal of attention has been focused on growing diamond using far-ﬁom—equilibrium
thin growth techniques such as microwave or hot ﬁlament chemical vapor deposition
(CVD)[Jones, 1994]. This approach has been inviting since many applications,
particularly in the electronics industry, require thin ﬁlms. It is progress such as this that
will be responsible for transforming diamond ﬁ'om a rare jewel into a viable engineering
solution.

Before diamond can be used in thermal applications, it is important to gain a
complete understanding of how these ﬁlms conduct heat. A great deal of work has been
done which illustrates that the thermal conductivity of diamond ﬁlm is related to the ﬁlm

thickness, ambient temperature, amount of impurities, and growth techniques. This thesis

discusses the development of a new general purpose system capable of measuring the
thermal diffusivity of these ﬁlms. This system incorporates non-destructive and non-
contact experimental techniques with the analytical tools necessary for thermal physical

property estimation.

1. 1 Objectives

The objective of this research was the development of experimental methods and
the use of analytical tools which would allow for the thermal analysis of various materials
of manufacturing interest. The primary objective is to utilize these techniques to measure

the thermal diffusivity of diamond ﬁlms. In particular the objectives were:

1.) To develop the general capabilities of an experimental system capable of
measuring the thermophysical properties of thin ﬁlms. The components within
this system provide optical, non-contact, and non-destructive temperature

measurement and heating techniques.

2.) To demonstrate the utility of this system by measuring the thermal diffusivity of

three CVD diamond ﬁlms.

3.) To validate this newly developed system along with existing analytical tools by
determining the thermal diﬁirsivity of high purity copper and iron samples. These

materials were selected as veriﬁcation materials due to their well deﬁned thermal

properties.

Chapter 2

Background and Literature Review

Perhaps the area of greatest potential for diamond ﬁlms is in commercial and
military electronics [Herr 1993]. As electronic components becomes smaller and more
dense, temperature increases become a critical issue concerning their performance and
reliability. This issue currently limits the miniaturization of high-power electronic
systems. Because of their high thermal conductivity and large dielectric constant, diamond
materials are expected to successﬁrlly address the problem of local heat build-up. One
example for the passive use of diamond ﬁlms is the silicon on diamond (SOD) technology
which employs these ﬁlms as a direct substrate for the silicon micro-components
[Annamalai et al, 1993]. As diamond insulates the electronic circuits, heat is effectively
dissipated to the substrate (provided good contact between the circuits and diamond can

be established). Thin diamond ﬁlms have shown promising applications in radiation

detectors, ﬁeld effect transistors and sensors [Tamor and Aslam, 1994]. These
application potentials have propelled the development of diamond thin ﬁlm synthesis
techniques, but the direct applicability of diamond ﬁlms may be limited until a through

understanding of the thermophysical properties can be developed.

2. I - C VD Digmond Films

Diamond ﬁlms, like the gem, consists of carbon atoms bonded together in strong
sigma type covalent bonds. The atomic orbitals are sp3 and the bonds formed are very
strong. The carbon atoms are arranged in a tetrahedral formation resulting in the diamond

cubic unit cell seen in Figure 2.1.

 

 

 

 

 

 

 

Figure 2.1. The dianond cubic unit cell. [Herr 1993]
The structure of diamond gives rise to the extreme hardness with the ability to withstand
pressures over 900,000 lbsfrnz. The stiffness of the these unique molecular bonds also

contribute to the diamond’s high thermal conductivity [Herr 1993]. In nonmetallic

materials, heat conduction primarily occurs through a phonon transfer phenomenon. This
mechanism, which is dependent on the molecular vibrational energy and the amount of
defects and/or impurities, is most eﬁicient when atomic bonds are stiff and dampened
when bonds are elastic.

Through a process known as Chemical Vapor Deposition (CVD), polycrystalline
diamond ﬁlms can be deposited on a variety of substrates, including Si, SiC, WC, Ta, W,
Mo, and A1203. The two most commonly used CVD methods are the hot ﬁlament assisted
method and plasma enhanced microwave method. Recent variations of these methods
have resulted in steadily increased growth rates. However, Common in all techniques a
high supersaturation of atomic hydrogen is created along with a supersaturation of
carbonic species and a substrate temperature in the range of 600 C - 1000 C [Jones,
1994]. Other similarities include process parameters of gas pressure, the percentage of
hydrogen in the gas phase, and the resulting ﬁlm morphology. However, there are a
number of other speciﬁc process parameters which are considerably different from
technique to technique. These process parameters lead to differences in the energy
partitioning in the deposition process, the deposition efﬁciency, deposition rate, ﬁlm
purity, physical properties and ﬁlm uniformity to name just a few [Jones, 1994].

Regardless of the technique, the ﬁlm qualities are dependent on the deposition
conditions. Generally, a diamond ﬁlm grown on a non-diamond substrate will have a
highly faceted, large grained (>lum) ﬁlm morphology as shown in Figures 2.2(a) and
2.2(b). However, if the growth parameters are not optimized, especially the substrate
temperature and the methane concentration, the morphology becomes submicrocystalline

and cauliﬂower-like as shown in Figure 2.2(c) [Stoner et al, 1991].

 

    

(A

(0-)

Figure 2.2. Scanning Electron Microscope (SEM) micrographs of dianond ﬁlms with

typical surface morphologies with (a. ) trigular shaped crystal faces, (b. ) square shaped
crystal faces, and (c.) cauliﬂower-like crystalline aggregates [Stoner et al, 1991].

The extreme properties and application potential of diamond has spawned research
into the CVD process. Over the past few years this research has increased the quality of
the synthesized diamond ﬁlms. However, even when using the best CVD system one must
be aware that a certain amount of impurities and defects normally are present as a result of
this process. It is these impurities which have a major effect on the ﬁlm’s physical
properties. For example, Baba et al. (1991) reported that by increasing the methane
concentration from 1% to 5% the thermal conductivity decreased from 1200 W/mK to
200W/mK. This reduction was assumed to be the result of phonon scattering due to the
hydrogen impurity found in the ﬁlms. The thermal conductivity can also be severely
affected by structural defects in the ﬁlm. Grain boundaries can result in poor thermal
contact within the ﬁlm [Graebner et al, 1991]. Since CVD diamond ﬁlms are prone to
impurities and small defects, the application of such ﬁlms as heat sinks could be quite
restrictive without experimentally determining the thermal conductivity and relating it to

deposition technique [Herr, 1993].

gm 2. 2 - Methodsfor Determining Themqphzsical Properties
2.2.1 Stardard Methods

Generally, methods of determining the thermophysical characteristics of materials
are divided into three groups: steady state experiments, quasi-stationary methods, and
transient methods [Vorobei, 1986]. The American Society of Test and Materials (ASTM)
annual book of standards recommends two procedures for experimentally determining a
material’s thermophysical properties. The limitations of these methods are signiﬁcant and

can be observed by closely inspecting each method. The “ﬂash method” is cited as the

standard technique for determining the thermal diffusivity (ASTM 1995a). In practice this
method subjects one side of a small disk shaped sample to an energy pulse with a duration
on the order of milliseconds. Solid state lasers or ﬂash lamps are used to provide the
energy burst. The temperature rise on the opposite side of the sample is then recorded via
a pyrometer or thermocouple. A vacuum enclosure containing a resistive heater provides
environmental control. One dimensional heat transfer theory is applied and from the
measured temperature rise the diffusivity is determined. The main limitation of this
transient test procedure is that it only determines the thermal diffusivity in one location,
The standard method for determining the thermal conductivity is a guarded-
comparative-longitudinal heat ﬂow technique [ASTM, 1995b]. Typically, a heat source
and heat sink are applied at opposite ends of a composite rod system formed by rods of
know and unknown conductivities. Thermocouples are embedded inside the rods along
the longitudinal axis and the whole system is surrounded by insulating material and
auxiliary heaters to act as a one—dimensional heat ﬂow guard. Thermal conductivity, k, can
be calculated by the one-dimensional steady state Fourier equation under those conditions.
This technique is limited because it does not allow for in situ measurement and requires

the destructive insertion of thermocouples.

2. 2. 2 Variations to Stardard Methods ard Specigl Experiments for C VD Diamond Film
In both of the above standard tests, a heat source is used to perturb the thermal
equilibrium in the material of interest. The phenomenon of heat conduction attempts to

restore equilibrium by allowing heat to ﬂow down temperature gradients. By measuring

10

this temperature gradient and quantifying the amount of applied heat, the thermophysical
properties can be estimated [Herr, 1993]. Over the past several years, researchers have
used this idea to develop new experimental techniques and analytical tools to estimate the
thermal properties of CVD diamond ﬁlm.

The polycrystalline anisotropic nature of diamond ﬁlms also presents an
interesting problem. As with other anisotropic thermally conducting materials techniques
had to be developed which allowed for the determination of the thermal conductivity both

parallel (kn) and perpendicular (k i) to the surface of the ﬁlm.

 

 

 

 

 

 

Figure 2.3. Thermal conductivity parallel 0m) and perpendicular (k j to the surface of
the ﬁlm [Herr, I993].

The diﬁ‘erent experimental techniques used in these works can be divided into
three categories: surface instrumentation, non - contact temperature measurement, and
photothermal laser beam deﬂection. In the following pages different variations of these

experimental techniques will be discussed.

11

Surface Instrumentation

Thermocouples, therrnistors, and other surface instrumentation are commonly used
by researchers to detect and record the temperature distribution on the surface of diamond
ﬁlms. In 1988 Morelli, Beetz and Perry used a four probe thermocouple probe to estimate
the parallel thermal conductivity of diamond ﬁlms created using hot ﬁlament CVD as a
ﬁrnction of temperature. In this experiment two ﬁee standing diamond ﬁlms with lateral
dimensions of approximately 10 mm x 5 mm and thickness on the order of 15m were
tested. A thin ﬁlm heater was attached to one end of the ﬁlm and the temperature
distribution was recorded using type T thermocouples. Of crucial importance to this
experiment, was the minimization of heat loss due to convection and radiation. This was
accomplished by placing the experimental samples between two metal shrouds within a
vacuum. The heat input and temperature distribution were recorded at steady state and
the thermal conductivity of the two samples was determined as a ﬁmction of temperature.
The absolute uncertainty in their data (~15%) is determined by the accuracy to which the

ﬁlm thickness can measured. The results of their experiment are shown in Figure 2.4.

12

Thermal Conductivity as a Function of Temperature

Experimental Results From Morelli, Beetz, Perry
Thermal Conductivity Parallel to the Surface of the Film

 

 

 

 

 

 

 

 

September 1988
100
—-— Sonata #1 - Thiclmess- 13pm
--- SarrplonnThidmoaa new
10 ~
9‘
E
3 1
S.
x
0.1 ~
0.01 E
10 IM 1000

Temperature (K)

Figure 2.4. Thermal conductivity of two dianond ﬁlms as measured by Morelli, Beetz
ard Perry. The ﬁlms used in this experiment were created using the hot ﬁlanent assisted
C VD method

Baba, Aikawa, and Shohata (1991) studied the thermal diﬂirsivity parallel to the
surface of the ﬁlm. In this case, the diamond ﬁlms were grown on Si substrates by the
hot-ﬁlament CVD technique in gas mixtures of 1% to 5% methane concentration, and
measurements were made using a AC calorimetric method. In their experiment, one end
of the sample was periodically heated using a with a halogen lamp. The temperature at a

distance x ﬁom the heated area was monitored using a thermocouple directly attached to

ﬁlm’s surface The relation between the temperature and distance is given by the

following equation,

13

lanl = ln(q / 479(Cd)— ( nf / a)x (2.1)

where q is the heat quantity absorbed by the sample, f is the heating frequency and C, d,
and a are the speciﬁc heat, thickness, and thermal diffusivity of the sample respectively.
The thermal conductivity was extracted from the thermal diffusivity of the samples and
evaluated from the slope of Eqn 2.1 by varying x. Their results illustrate that the thermal
conductivity for diamond ﬁlms was dependent on the amount of hydrogen impurity
deposited ﬁ'om the methane gas mixture. For example, as the methane concentration
during the synthesis process is increased from 1% to 5%, the thermal conductivity
decreased from 1200 W/mK to 200 W/mK.

Graebner, Muncha, Seibles, and Karnmlott (1992) used a procedure similar to the
Morelli, Beetz and Perry method to determine that the diamond ﬁlm thermal conductivity
was inversely proportional to the growth rate. In their procedure the silicon
substrate was etched creating a 2 x 4 mm2 free standing window. The remaining silicon
substrate served as a rugged platform as well as a heat sink and reference temperature.
The ﬂow of heat from the thin foil heater in the center of this window was monitored with
thermocouples. The steady state temperature distribution was then compared with a
numerical simulation to extract a value for the thermal conductivity. The window
dimensions were chosen in an effort to minimize the effect of radiation. To predict the

inﬂuence of radiation they developed the following ratio,

km, ~ zae Wsz

2.2
k K1 ( )

cond

14

where km is the conductance along the ﬁlm of thickness t, km, is the effective
conductance due to radiation between the ﬁlm and its surroundings, or is the Stefan-
Boltzmann constant, a is the emissivity, T0 is the initial temperature, and x is the thermal
conductivity. For example, they were able to use Eqn 2.2 and determine that even under
non-ideal conditions (a = 1, To=3 00 K, t=2um, k=3 W/cm K) the effects of radiation could
be ignored if the proper width dimensions were selected. The results of their study are

shown in Figure 2.5.

Thermal Conductivity as a Function of Growth Rate

Experimental Results From Graebner, Mucha, Seibles, Kammlctt
Thermal Conductivity Parallel to the Surface of the Film

 

 

 

 

January 1992

7

c i o

5 O
S3 9 o
g 4 4 O
x Q C

3 .4

O
2 4 o
1 F I I I l
0.0 0.1 02 03 0.4 0.5 0.6
Growth Rate (um/h)

Figure 2. 5 Graebner, Muncha, Seibles, ard Kanmlott (1992) results for the Thermal
Conductivity parallel to the surface of the ﬁlm (kg). The dianond ﬁlms in this study were
created using a microwave-plasma C VD technique.

15

Later in 1992 Graebner, Jin, Herb, Karnmlott, and Gardinier introduced another
similar technique to determine the parallel thermal conductivity. This method employees
two thin-ﬁlm heaters evaporated directly onto each end of a bar shaped sample. The
temperatures between the heaters were monitored by a row of four ﬁne diameter
thermocouples attached to the surface with silver-epoxy. A schematic representation of
the experimental setup is shown in Figure 2.6. The tests were conducted on samples with
diﬁ‘erent thicknesses and the samples were placed in a vacuum where the effects of
radiation and convection could be avoided. From their test, Graebner, Jin, Herb,
Karnmlott, and Gardinier were able to show that the thermal conductivity of diamond was

a ﬁrnction of ﬁlm thickness. Their results are shown in Figure 2.7.

Thermocouples
/ 1 /1 Z 1 / 1

 

  

 

   

Thin Heaters

 

Figure 2.6. Schematic diagran of the experimental setup used by Graebner, Jin, Herb,
Kanmlott, ard Ga'dinier for determining the parallel thermal conductivity.

16

Thermal Conductivity as a Function of Thickness
Experimental Results From Grabner, Jin, Kammlctt. Herb, and Gardinier
Thermal Conductivity Parallel to the Surface of the Film
February 1992

 

2000
1000 -
1000 4 o
1400 l
1200 4 o

1000~ O

k (W/m °C)
§

1

 

 

 

o T T T ﬂ I I I
O 50 100 150 200 250 300 350 400

Film Thickness (m)

Figure 2. 7. Graebner, Jin, Herb, Kanmlott, ard Gardinier (1992) results for the thermal
conductivity parallel to the surface of the ﬁlm. These results show an increase in thermal
conductivity by more than a factor of two as the thickness is increased by a factor of ten.

Non - Contact Temperature Measurement

Non-contact infrared temperature measurement systems have been and continue to
be used by researchers to capture and record the temperature distribution necessary for
thermophysical property estimation.

Ono, Baba, Tunomoto and Nishikawa (1986) utilized a non-contact method to
determine the thermal conductivity parallel to the ﬁlm surface. Using a long diamond ﬁlm

sample suspended by heated supports in a vacuum, the temperature distribution along the

17

length was measured using infrared therrnography. The surface area of the samples
analyzed was 20 mm x 5 mm while the thicknesses varied between 7-30 mm.
Measurements were made between 100°C and 130°C on microwave plasma CVD
diamond. From the results of this study, the thermal conductivity of the diamond ﬁlms
was found to rapidly increase with decreasing concentration of methane. The highest
value for kg was approximately 1000 W/m K.

Another signiﬁcant study determining the kit of diamond ﬁlms using IR
thermography was done later by Albin, Winfree, Crews (1990). The thermal conductivity
was extracted from measurement of thermal diffusivity. Periodic heating was provided by
a 20W, 1.064 um Nd: YAG laser and the time dependent surface temperature was

measured by a 8-12 pm infrared camera. A diagram of the setup is shown in Figure 2.8.

Nd:YAG Laser .
Mirror

 

 

 

 

 

Sample IR Camera

 

 

 

 

I
Focusing I E

Mirror $

Output to
Image Processor

 

Figure 2.8. Schematic representation of the experimental setup used by Albin, Winfree,
Crews to measure the thermal conductivity parallel to the surface of the ﬁlm. '

18

Temperature measurements between 25-3 5°C were made on the back side of the
sample using the inﬁared camera. The camera scanned a single horizontal line which
passed through the center of the sample of the heating area. An image processor was used
to digitize 128 successive images. Each image was compressed into a single temperature
proﬁle resulting in a sampling rate of 1/30 of a second. The IR camera allowed for a
temperature resolution of less than 002°C and a spatial resolution of better than 1mm. In
this study kg for two samples of thickness 16 and 32 mm were determined to be 1350 and
1328 W/m K respectively. The major advantage of their technique is that the thermal
diﬂirsivity and thermal conductivity of diamond ﬁlms can be determined without special
sample preparation.

In 1992 Lu and Swann measured the in plane thermal conductivity of CVD

diamond ﬁlms using a converging wave technique. As shown in Figure 2.9 a 5 J/pulse ruby

Axicon Lens System

C Ruby Laser (
.V ,

 

 

 

 

 

 

1‘ ~ ”:1 HngTe Infrared DeteClor

Elihu-Amp

I iLock-InAmp

[:Elecmosoope

Figure 2. 9. Schematic representation of the converging wave apparatus used by Lu and
Swann for determining the thermal conductivity parallel to the surface of the ﬁlm.

 

 

19

laser was converted into a ring of light with a positive axicon (lens of conical cross
section) with an angle of 2°. The ring was focused onto the sample and heated in a sharp I
annular pattern. A HngTe detector was focused on the center of the back surface of the
sample. This detector was used to monitor the time required for the heat to travel from
the perimeter of the ring to the center of the sample.

For a thin sample (thickness << radius), the temperature at the center of the ring is

given by:
T: [E /4rrpCpat] exp(— R2 /4a t) (2.3)

where E is the energy absorbed per unit thickness, p is the density, Cp is the speciﬁc heat ,
or is the thermal diffusivity, t is the time, and R is the radius of the ring. The diﬁ‘usivity is
determined by:

a = R2 /4tm (2.4)
where tIn is the time needed to reach the maximum temperature at the center of the ring.
Based on this measured thermal diffusivity the thermal conductivity was extracted and
determined to be 1280 W/m K.

Lu and Swarm chose this technique because it could be used on samples of
varying and unknown thickness, is independent of laser power, and yields accurate
measurements in less than a minute.

While it is relatively straightforward to measure kl. using surface instrumentation

and non-contact inﬁared cameras, it is much more difﬁcult to measure k i due to the small

20

thermal resistance in this direction [ Graebner et a1. 1992 ]. For this reason high speed
infrared detectors are being used by many researchers for temperature acquisition.
Graebner, Jin, Kammlott, Bacon, and Seibles (1992) employed a non-contact
temperature acquisition method to determine the thermal conductivity perpendicular to the
surface of the ﬁlm (k i). Basically their procedure, shown in Figure 2.10 was similar to the
standard “laser ﬂash” discussed in Section 2.2.1. In this case, pulses of radiant energy
were used to heat one face of the sample and fast IR thermography was used to monitor

the arrival of the thermal response on the opposite face.

 

 

7) Mirror
< Nd:YAG Laser

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Attenuator
Sample
Infrared Detector Q )
\ Mirror
Germanium
Lenses

Figure 2. 10. The experimental arargement used by Graebner, Jin, Kanmlott, Bacon,
ard Seibles to measure the thermal conductivity perpendicular to the surface of the ﬁlm.

A Q—Switched Nd:YAG laser was used as the heat source. The sample was glued
with silver paste over a hole in a temperature-controlled copper plate. Germanium lenses

were used to collect thermal radiation from one side of the sample. Heat was conducted

21

laterally through the sample to thermal ground at its edges. The temperature rise on the
back surface and the rapid transient response were recorded by the data acquisition
system. An expression for the change in temperature with respect to time corresponding

to short heating pulses such as this was analytical determined by Parker et al. in 1961 as,

 

AT(t) = A[1+ 2i (—1)" exp[— "sz 04]] (2.5)

where A = q/pCpL and or = k i/pCp; q is the absorbed energy per unit area; L is the sample
thickness and or is the thermal diﬁiisivity. Eqn. 2.3 is used to solve a system of equations
where A and or are the unknown quantities. By solving for the thermal diﬂirsivity and
measuring both the thermal response and characteristic length of the ﬁlm (ﬁlm thickness),
the thermal conductivity, k i , was calculated assuming a value for pCp. Conductivities, k i,
of 800 and 1210 W/mK were found for two different samples with thicknesses of 234 and
144m respectively. When compared to k. measurements made on the same ﬁlms, it was
shown that the thermal conductivity through the thickness of the ﬁlm could be as much as
50% higher than the thermal conductivity parallel to the surface of the ﬁlm.

In January of 1993, Graebner, Jin, Karnmlott, Herb, Wong, and Gradinier utilized
the same setup to complete an in depth study on k i. In their study, several ﬁhns were
synthesized using similar deposition techniques and the results show that k r increases with

ﬁlm thickness. These results are shown in Figure 2.11.

22

Thermal Conductivity as a Function of Film Thickness
Experimertal Reauta From Graebner, Jin, Karnmlott, Hang, Herb, and Gardiner
Thermal Conductivity Perpendicular to the Surface of the Film
Jamery 1993

 

2200

raoo~ o
1000-
14004
moi

k (Wlm °C)

10004 O

 

 

 

Film Thickneu (pm)

Figure 2. 11. Thermal conductivity measurements perpendicular to the surface of the
ﬁlm. In these test conducted by Graebner, Jin, Kanmlott, Herb, Wong, ard Gradinier it
is clea' that k) increases with ﬁlm thickness.

Photothermal Bean Deﬂection:

The technique known as photothermal laser beam deﬂection was introduced by
Petrovsky, Salnick, Mukhin, and Spitsyn (1993). This is another of many alternate
methods of determining k. in diamond ﬁlms. This technique also know as the “mirage
effect” uses the assistance of two separate laser beams

One beam generates heat pulses within the sample producing heat pulses in the air
above the sample. The thermal pulse in the air results in an optical index of reﬁaction

gradient. The second beam passes through the established gradient and is deﬂected with

components both in plane and perpendicular to the plane of the sample. Since the heating

23

is periodic, the wavelength of these propagating waves can be detected. Because the
wavelength of these thermal waves depends on the frequency of the heating beam and on
the thermal properties, the thermal conductivity parallel to the surface of the ﬁlm can be

obtained. The experimental results of their study are shown in Figure 2.12.

Thermal Conductivity as a Function of Film Thickness

Experimental Results From Petrovsky, Salnick, and Mukhin
Thermd Conductivity Parallel to the Surface of the Film

 

 

 

 

 

June 1992
9
O
8 a
7 1
Films Deposited onSiliccn Stbstates

A 6 '1
‘9 Film Deposited onTungsten Substrate .
g 5 ‘
x 4 -

3‘ v

2 - O

1 I I I I I I I I

O 5 10 15 20 25 30 35 40 45

ﬁlm Thickness (um)

Figure 2. 12. Typical values for k, obtained by Petrovsky, Salnick, Mukhin, ard Spitsyn
using the photothermal bean deﬂection technique.

2. 2.3 Genera)! Purpose System Development at Michigar State University
Although there have been several studies concerning the thermophysical
properties of CVD diamond ﬁlms, there seems to be a large discrepancy between the

results of different research groups. This discrepancy can be illustrated by examining

24

Figure 2.13. The driving force behind this research is to develop a general purpose system
capable of measuring the thermophysical properties of diamond ﬁlms and other

manufacturing materials. Particular attention in this research is paid to thin ﬁlms.

Thermal Conductivity as a Function of Film Thickness

 

 

 

 

 

2500
A 211!) ~ 0
x
O
E
O
5 151) " .
e - -
> ' .
E .
.3 1CD 4 ll. 0
i: e
o
0 co .
g E!) 4 . 0
E
l- 1‘
O — - A
0 100 200 3]) 4(1) 5(1)
Film Thickness (um)
I Graebner er al. (1992)
e Graebner et al. (1%)
I Graebner eta! (1%2)
I Graebner et at. (192)
I Albin et at. (1%)
- Anthony etal. (1&1)
I Morrelli et al. (1%8)
I Babe etal.(1991)
A Graebner et al, (1%?)
A Potrovsky oral. (192)

 

 

 

Figure 2. 13. A plot of the thermal conductivity as a function of ﬁlm thiclmess. This plot
illustrates the discrepancy in the estimated values anong sepaate research groups.

In this newly developed system, the experimental equipment was selected to

provide ﬂexibility and a non-contact and non-destructive means of heating and

25

temperature measurement. For example, a solid state Nd:YAG laser was selected as the
heating source. This laser allows for variations in radiation intensity as well as spatial
distribution and temporal deposition of energy. Two infrared temperature measurement
systems were selected because of the challenge associated with the micro-structural size
and fast thermal response of diamond ﬁlms and other materials. Temperature measurement
systems such as these eliminate some of the problems associated with surface
instrumentation and provide a great deal of information in space and/or time.

In the following chapter, the experimental equipment comprising this newly
developed system will be discussed and characterized. In the chapters to follow, the
equipment is then used with existing analytical tools to determine the thermal diffusivity of
circular specimens. In this study, the thermal diffusivity of three CVD diamond ﬁlms with
average thicknesses between 240nm and 370m were measured. In order to validate the
experimental techniques, high purity and thermally well deﬁned copper and iron samples

were also measured.

Chapter 3

System Development and Component Description

In the areas of inverse heat conduction and parameter estimation, it is imperative
that experimental techniques are well understood. In general, most experimental
techniques used in these areas involve three processes. First, a heat source is used to
perturb the thermal equilibrium in the material of interest. Second, the phenomenon of
conductive heat transfer attempts to restore thermal equilibrium by ﬂowing heat down a
temperature gradient. Third, the temperature gradients are measured, the heat source
quantiﬁed, the data are analyzed based on a mathematical model, and the thermal
properties are estimated.

In order to assure accuracy in such experiments, the equipment must be thoroughly

characterized. As a result, this chapter is dedicated to a discussion of each of the

26

27

experimental components used in the development of this non-contact and non-destructive
system capable of measuring the thermal properties of various materials.

In order to avoid confusion and to give the reader a brief introduction into the use
of the experimental equipment, schematic representations of the overall system and two

typical test conﬁgurations are displayed in Figures 3.1, 3.2 and 3.3 respectively.

/— VIDEO TIMER

vroeo casserna raccoons:
0m ACMSITION LASER Pogﬁtgaﬁmt HETER
no IISIIILIBII 1’ SHUTTER comm.
cannot. &
moon 00000
D: E
N YAG LAS R \J 1 i ii i

\r i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3. I. A generalized schematic representation of the newly developed experimental
setup.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Nd:YAGLaaer
Kenmore
8m
mm cm
at“.
mum
MW
Bead
Viacom Vldeo‘nmar

 

 

 

 

 

 

 

 

Figure 3.2. A typical test conﬁguration for measuring the thermal drﬂusivity parallel to
the surface of the ﬁlm.

28

} Nd:YAG Laser F———‘\

 

 

 

 

Optics Computer

General Purpose
DAQ Board
_

High Speed
DAQ Board

 

   

 

 

l—..—.

Figure 3.3. A typical experimental conﬁguration used to measure the thermal
conductivity perpendicular to the surface of the ﬁlm.

In Figure 3.2, infrared therrnography is used to record the transient temperature
distributions along the surface as it is heated with the Nd:YAG laser. Since the output of
the IR camera is a video signal, digital indications of time are superimposed and the data is
recorded using a standard video timer and video cassette recorder. Since timing issues are
important, a photodetector, with a response proportional to the intensity of light, is used
to sense the presence of the laser. The response of the photodetector is monitored by a
general purpose data acquisition board programmed using LabVIEW. Once the response
of the photodetector increases beyond a preprograrnmed trigger level, a TTL low signal is
sent to the video timer and timing is initiated. Once the test is complete, the data are
analyzed using a general purpose image processing system

In Figure 3.3, transient temperature measurements at one point on the back

surface of the test sample are measured using an infrared detector. The data is collected

29

using a “fast data acquisition board” which has the ability to sample at lMHz. Once
again, the sample is energized using a Nd:YAG laser and the photodetector is .used to

sense the presence of the laser and initiate data collection.

3. 1 T empgrature Measurements

Experimentally, diamond ﬁlms and other similar materials are very challenging to
analyze thermally. Their microstructural size and rapid thermal response pose spatial and
temporal problems for experimental techniques utilizing surface mounted temperature
sensors such as thermocouples and resistive thermometers. In order to make surface
temperature measurements with these devices, small voids are commonly machined into
the sample for probe installation. The very presence of these probes, however, makes
these techniques intrusive and can affect the thermal behavior. These probes generally
have thermophysical properties different from those of the test specimen, and as a result
their response would be different than that of the substrate. That is, these probes can act
as a heat sink or source, thus measuring temperatures that would be signiﬁcantly different
than the temperatures that would have existed in the absence of the probes. For these
reasons optical, non-contact inﬁared techniques were implemented for temperature
acquisition [Form 1991].

Each of these inﬁared techniques obtain surface temperatures indirectly and rely
on the simple premise that all real objects in the universe exist at temperatures above
absolute zero. As a result, the atoms and molecules that compose the object are in
motion. These motions are constrained by interactions with other atoms and molecules;

therefore the elementary charges radiate electromagnetically. The magnitude of this

30

electromagnetic radiation increases with temperature and as a result the output of the
inﬁared detector focused onto the surface of the sample increases. In the following

subsections the two infrared temperature measurement systems used are discussed.

3. 1. 1 Inﬂaed Imaﬂng Radiometer

Infrared imaging provides a two-dimensional representation of surface temperature
variations across the target and hence it is a global technique as opposed to thermocouples
and resistance thermometers which only make point measurements. The technique is
totally non-intrusive and because of its non—destructive nature, repetitive surface
measurements are possible.

Inﬁ'ared irnagers sense temperature by detecting thermal radiation. Thermal
radiation is the radiation emitted by an object due to its temperature and covers the 0.3 to
50 micrometer spectral range of the electromagnetic spectrum. In general, IR irnagers are
available in the 2 to 5 or 8 to 12 micrometer range of the spectrum. The major
components of [R imaging system include a geranium optical lens system, a scanning
mechanism, a detector, an electronic signal processing unit, a control unit and a display
device.

The thermal radiation entering the scanner through a germanium window is
deﬂected by the horizontal and vertical scanning mirrors and is focused on a HngTe
detector. Motorized focus and zoom mechanisms are operated within the scanner by
remote control. “(ah the HngTe detector cooled by liquid nitrogen to approximately 77

K, detector noise is reduced and the maximum thermal sensitivity is obtained.

31

The low-level signal generated by the HngTe detector is processed, digitized,
reformatted and prepared for visual display by the video processor within control unit.
The result is a monochrome video signal which can be stored on a video cassette recorder.
The signal can also be processed on a image processing system to digitize the video signal,
calculate and display target absohrte temperatures, pseudo-color thermal images, and
apply image enhancement features.

In the development of this system, transient surface temperature measurements
were made utilizing an Inframetrics Model 600L inﬁ'ared imaging radiometer in
conjunction with an image processing system. The infrared system, shown in Figure 3.4,
allows for real-time thermal imaging of static and dynamic thermal events with user
deﬁned amounts of imaging averaging, temperature ranges, emissivity settings and ﬁelds

of view.

 

Figure 3.4. The Infranetrics Model 600L Infrared Imaging Radiometer.

32

Temporal Resolution:

The infrared scanner incorporates two independent electromechanical servos
(galvanometers) which perform horizontal and vertical scanning. Attached to these servos
are scanning mirrors contained in a sealed, evacuated module for increased efficiency. The
scanning rate of these mirrors controls the temporal resolution of the system. Horizontal
scanning is performed at the very high rate of 7866 Hz in a resonant sinusoidal mode.
Vertical scanning is performed in a sawtooth pattern at 60 Hz. These scanning
frequencies produce an output consistent with a standard interlaced television format. As a
result, in the normal operating mode infrared images of the radiometer’s entire ﬁeld of
view can be captured at 30 Hz.

The radiometer is also equipped with a high speed measurement mode known as
the fast line scan mode. This feature is designed to capture thermal events along a line
with a sampling rate of 7866 Hz. When conﬁgured in the fast line scan mode, the vertical
scanning galvanometer is stopped near the center of the radiometer’s ﬁeld of view. This
allows the horizontal galvanometer to scan the same line continuously. The video
processor within the control unit operates in it’s normal mode and continues to produce a
standard format video signal. The image output, however, appears different, in that it is no
longer a two-dimensional image. Instead, each line displayed from t0p to bottom on the

video image represents the same line in space, but at a different point in time.

33

Temperature Resolution:

The output of the infrared imaging system is a video format with 8 bits of
temperature resolution. The radiometer offers several temperature ranges which control
the temperature resolution. When operated in the smallest possible temperature span

(5°C), a maximum thermal resolution of 003°C is obtained.

Spatial Resolution:

The spatial resolution is a measure of the thermal imaging system’s ability to detect
and accurately measure the temperature of small objects. An ideal thermal irnager would
measure the true temperature even when it looks at an object which is very small
compared to the whole image. However, for a practical scanner, when the image of a
small object projected on the detector surface becomes smaller than the detector, the
detector will measure a combination of both the object and its background. Consequently
the measured temperature for a very small object is affected by its size. One would think
that is would be enough to make sure that the ideally projected image of the object is large
enough to ﬁll the whole detector. But the image of the detector is blurred by the optics.
Also the detector has a response time that affects the output for small objects.

One way to measure the spatial resolution is by placing a variable slit in front of a
large uniform blackbody radiator and to measure the modulation of the output signal as a
function of slit width (The Slit Response Function or SRF). The imaging spatial
resolution is normally speciﬁed by the manufacturer at a slit width that gives a 50% of full
modulation response. The 50% SRF value indicates the size of a small object which can

be resolved in the image. However, when it comes to temperature measurement a

34

modulation of 50% is not sufficient. The measurement spatial resolution is deﬁned at a slit
width which yields a response which is 95% of full modulation [Halmsten, 1991]

A specialized variable width slit has been created. The width of this slit is
controlled using a micro-positioner with a resolution of 1pm. A spatially uniform
blackbody heat source is viewed through the slit and used to create a measurable
temperature difference.

The radiometer was carefully focused on the jaws of the slit. The best focus is
assumed to occur when the edges of the slit become sharp and the maximum throughput
ﬁom the blackbody simulator is obtained. As the slit width was increased the output of
the radiometer was stored on a video cassette recorder. After the jaws of the slit were
Open to the point where 100% of the radiosity from the blackbody was measured, the test
was concluded and the stored data was processed using IPPLUS.

Three SRF tests have been completed. Two tests have been done with a
combination of the 3X and close-up lenses. Another test has been completed with no
external optics. The test results are shown in Figure 3.5 and Figure 3.6. The imaging
spatial resolution (IRS) of the system with the 3X and close-up lenses for both tests is
approximately 20pm and the temperature measurement spatial resolution (TMRS) is
approximately 67. Sum. These results compare well with the technical speciﬁcations given
by Inframetrics which state that the TMRS of the system is 100 pm. The IRS for the
radiometer with no external optics and with a working distance of 15 cm is 65 um and the

TMRS is 335 um.

35

Slit Response Function as a Function of Slit Width
June 22. 1996 - Close-Up Lens and 3X Lens - Working Distance I 5.3 inches

1.0

k

 

 

 

 

 

 

v

 

 

 

 

 

 

| o I ﬁo
0

0.9 1 . 0 ' I Test #1
A - Test82
5; 0.0 « a
1’” :
c 0.7 -
o O
3 , '
c 0.6 s
3 ~
LL ‘- ""9109
3 0.5 a Resolution:
c .4 SRF - 50%
a 0.4 ~ '0 /
I I
I: 0.3 - 8' Temperature Measurement
.— ° Resolution:
5 o 2 , 4' SRF - 95%

3
U

0.1 « I

0.0 '3" . r . .

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012

Slit Width (m)

Figure 3. 5. The slit response function for the Inframetrics Radiometer with the C lose-up
ard 3X lenses. These tests show that the imaging spatial resolution is approximately 20
pm ard the measurement spatial resolution is approximately 67. 5 pm.

Slit Response Function as a Function of Slit Width
June 22.1me-No External Optics-Working Distance ~ 150m

1.0

 

 

0.9 '1 a.

0.8 a

0.0 l .

0.5

 

0.4 4

03 q . {—— lmagrng Resolution
- SRF=5056

Slit Response Function (SRF)

0.2< ‘

0.1 i a

 

 

0.0 r 1

Temperature Meaerrement
0.7 -* Resolution:
SRF = 95%

 

T
O

 

 

I

T

T

0.00000 0.00005 0.00010 0.00015 0.00020 00th 000000 000035 0.00040 0.00045
SlithdtMm)

Figure 3. 6. The slit response function for the Infranetrics Radiometer with no external
optics. This tests illustrates that at a working distarce of 15 cm the imaging spatial
resolution is approximately 65 pm ard the measurement spatial resolution is

approximately 335 pm.

36

The simplest way to decrease the measurement errors due to small sized objects is
to decrease the distance between the object and the radiometer. This is illustrated by the
increase in spatial resolution that occurred due to the addition of external optics. A
feature that might seem helpﬁtl is the ZOOM function of the radiometer. The zoom
function decreases the amplitude of the scanning mirrors which only makes the ﬁeld of
view smaller. However, the instantaneous ﬁeld of view and the slit response function
remain the same as the optical magniﬁcation is not changed. Therefore, the zoom function

does not improve the spatial resolution.

Image Processing System:

The radiometer dissects the ﬁeld of view such that the thermal images produced
consist 365 horizontal and 280 vertical datum points. Therefore, in each thermal image
over 100,000 surface temperature measurement are made. The Image Pro Plus (IPPLUS)
image processing system is primarily used to capture and store thermal patterns and access
temperatures corresponding to any or all digitized picture elements (pixels) which make up
the thermal ﬁeld.

Temperature measurements are based on the gray scale intensity of each pixel.
The temperatures are calculated based on a calibration curve similar to that shown in
Figure 3.7. Since the output of the radiometer is an 8 bit format, the digitized gray scale

values will range from O to 255. Therefore, the temperature range of the radiometer is

37

broken up into 256 gray discrete gray levels. A detailed discussion of this calibration can

be found in Appendix B.

Calibration Curve For DOS Version of IPPLUS
Non-Dimensional Temperature as a Function of Gray Scale

 

 

 

 

 

 

 

 

June 24, 1996
1.0
.0
o
A 0.8 . a
3 '
. I
x O
E 0.6 4
E a
'T 0.4 «
1:: a
II I
C
I- e
0.2 4
- I AT = 10°C Calibration Data
0 0 AT = 20° C Calibration Data
0.0 . T r T T T
0 50 100 150 2(1) 250
Gray Scale Intensity (0-255)
Calibration Data AT = 10°C Calibration Data AT = 20°C
Temperature Span = 10°C Temperature Span = 20° C
Calibration Coefﬁcients: Calibration Coefﬁctenbt
lrtercept = 0021884604 Offset = 45531629774043
Slope = 3.821w18162e-3 Slope = 3.8237842677e-3
r ’=O.9979%1 219 r 3:0.9996157cn9

Figure 3. 7. A plot of the non-dimensional temperature as a junction of gray scale. This
information is used to generate a calibration between gray scale and temperature.
3. 1.; The EG&G Model J15D12 Infrared Point Detector

The EG&G Mercury Cadmium Telluride (HngTe) Model I 1 SD12 point detector,
shown in Figure 3.8, can also be used in temperature acquisition. The characteristic time

of this device is .5 usec. As a result of this rapid response, temperature measurements of

38

one point can be made at .2 MHz. This detector is designed for operation in the 2 to 12
um wavelength region with a peak response at 11pm.

This photoconductive detector is mounted on a metal dewar and operated at 77 K.
The actual detector is comprised of a thin layer (~ 10 to 20 pm) of HngTe with
metalized contact pads deﬁning the active area. Incident photons with energy greater than
the semiconductor band-gap energy, excite electrons into the conduction band, thereby
increasing the conductivity of the material [Dereniak and Crowe, 1993].

In order to sense the change in resistivity, a constant bias current is applied across
the 0.25mm square detector. The bias current is produced with either a low noise power
supply or a 15 volt battery applied across a resistor. As a result of this constant current,
the changes in detector resistance cause voltages ﬂuctuations which are applied by the PA-

350 preampliﬁer.

P,-\ 350 Preampliﬁer

and 15 Volt Battery

:‘.‘., D
as
.1321: ,
'l, l

The EG&G \lmlel .llSIHZ
Infrared Detector.

 

Figure 3. 8. The EG&G Model J15D12 Inﬁared Detector and PA-35 0 Preampliﬁer.
Initial tests have been completed using this temperature measurement system. The

output of PA-3 50 preampliﬁer can be displayed on a volt meter or acquired and collected

39

with a data acquisition system. Prior to such tests, a calibration must be done to ﬁnd a
relationship between the detector’s output and the surface temperature. In order to do so,
a resistive heater was attached to a aluminum disk. A thermocouple is mounted to the disk
for temperature measurements and a thin layer of black paint was added to improve the
surface emissivity. The radiation from this disk is focused onto the detector element using
two plane-convex lenses. As the power across the heater was gradually increased, the
response of thermocouple and inﬁ'ared detector were recorded simultaneously. The

relationship between the response of detector and thermocouple is shown in Figure 3 .9.

Detector Output as a Function of Temperature
Premlibration and Postcalibration

 

 

 

 

 

 

 

 

 

0.075
Preealibration
Preeal Linear Regression .
j - Coisvs Test2V
0.060 Postcal Linear Regression
£2
6‘
Z 0045 4
g-
3 0.0:!) -
0.015 «
0.“ “ r r r r r r r r r r r r r
20 30 40 50 60 70 80 90100110120130140150160
Temperature (°C)
Preealibration Postcalibration
Calibration Olive Calibration Curve
Intercept = 00120350698 Intercept = «00130564773
Slope = 5.0686549716e-4 Slope = 5.0764693133e-4
r ‘=0.9992957861 r ‘=O.9994696017

Figure 3. 9. The comparison between response of the EG&G Inﬁared Detector and
temperature measured by the thermocouple.

Also shown in Figure 3.9, the detector has a linear response to increases in
temperature. With knowledge of the response, transient temperature measurements along
a surface can be acquired. In this case a round aluminum sample with a diameter 635 mm
and a thickness of 100 um was energized with a Nd:YAG laser. Data was acquired at 10
kHz using a general purpose data acquisition board. The acquisition of data was initiated
when the response of a photodetector exceeded a soﬁware programmed trigger level. A
photograph and a schematic representation of the experimental setup are shown in Figure

3.10. A plot of the typical experimental results are shown in Figure 3.11.

Infrared Detect“ j

l «Chitin Lenses
' l
Aluminum Sample \
Photodetector ——

 

Figure 3. 10a. A picture of the experimental setup used for transient temperature surface
measurement

41

W: W
OUTPUT AMPlJFlED AND DATA
USED TO TRlGGE
COLLECTED WITH DATA A usmo~
0° DATA Acomsmon

BOARD.\

X , V; f lf/

 

W: /'

user) To FOCUS T .
HERMAL RADIATION ENERGIZED BY Nd:YAG
ONTO DETECTOR LASER

Figure 3.10b. A schematic representation of the experimental setup used for transient
surface measurement.

Detector Output as a Function of Sean Number
Alrmlnum sanple heated wlh 7.5 Watts of beer mciation
Data Ambition Rate - 10 kHz

 

Detector OLlpul (VOLTS)
p
8

 

 

 

Sean Mmbar

Figure 3.11. The output of the photodetector as a function of scan number. Since data
was collected at 10 kHz, the information in the above plot represents 2 seconds of
heating.

42

If the calibration data ﬁ'om Figure 3.9 is considered, the voltage output from the
detector can be related to the transient temperature measurements. A plot of these

transient temperature measurements is shown in Figure 3.12.

Temperature as a Function of Scan Number
Alummn sample heated wlh 7.5 was of laser radiation

 

 

 

 

Data Acquisition Rate-I told-t2

120

100«
6 80
L
5
g 00
a
E
O
I'- 40-1

204

0 e
o 5000 10000 15000 20000
ScanNumber

Figure 3. 12. Temperature as a ﬁmction of scan number. This data was obtained using
the voltage to temperature calibration in Figure 3. 9.

3. 2 Heating Source

Many types of heat sources are used by researchers interested in thermophysical
property estimation in order to perturb the thermal equilibrium of the test specimen. For
example, Graebner used resistive heaters in his study of the thermal conductivity parallel
to the surface of the ﬁlm [Graebner, 1992]. These heaters are easy to use and well
characterized, but are limited because they do not offer much mechanical ﬂexibility and
must be in direct contact with the test specimen. In this study a non-contact heat source

offering variability in the distribution of radiation spatially and with time was applied. The

43

following subsections describe this heating source and some of the instrumentation used

to quantify its characteristics.

3. 2. 1 Excel/QMonix Model 1 1 7E Nd: YAG Laser

As illustrated in the background review portion of Chapter 2 various types of
lasers are currently being used by many researchers interested in thermophysical property
estimation. The unique properties of laser make them very attractive. Along with their
exceptional monochromatic behavior and small amount of beam divergence, in most cases
lasers have the ability to deliver large amounts of power in a variety of spatial distributions
and with various temporal characteristics. For a more complete discussion pertaining to
some of the general properties of laser light, please see Appendix A.

In the development of this general purpose thermophysical property estimation
system the Excel/Quantronix Model 117E Nd:YAG laser, shown in Figure 3.13, was
chosen as the primary heating source. The ﬂexibility of operational modes oﬁ‘ered by this
type of laser was a signiﬁcant reason for its selection. Without the use of external optics
this laser produces a beam diameter of approximately 0.7 mm and has the ability to
deliver over 15.5 Watts of laser radiation to the surface of a variety of test samples. This
large amount of power carried in such a small beam diameter produces a very large power
density (4kW/cm2) and may not be desired in all situations. Several techniques can be

implemented to reduce the beam intensity.

 

Figure 3. I3. Excel/Quantronix Model I 1 7E Nd: YAG laser

One of the simplest methods for reducing the beams intensity is to lower the
pumping power of the laser. Although the laser power can be reduced signiﬁcantly using
this approach the beam quality is reduced at lower current levels. For example, with the
lamp current at 28.8 amps the thermal axis of the Nd:YAG Laser rod is aligned with
mirrors to produce a beam with a Gaussian Distribution (a laser operating in such a
manner is oﬁen said to be operating in its TEM.,0 mode). When the lamp current is
reduced thermal changes within the lamp housing affect the thermal axis producing a beam
of inferior quality. A beam of poor quality may be unstable or have cavities or high order
modes within the beam proﬁle. This variation in beam intensity and beam quality as a
function of lamp current is illustrated in Figure 3.14.

The data in Figure 3.14(a.) was measured using the Molectron Power/Energy
meter. In this case, the laser’s power was measured as the lamp current was varied. In
Figures 3.14(b.) and 3.14(c.) the beam proﬁle was obtained using a CCD camera in
conjunction with the Image Pro Plus (IPPLUS) image processing system. Figure 3.14 (b.)
is a characteristic representation of the beam proﬁle when operating the laser with a lamp
current near 28.8 amps. At this current the thermal axis of laser is aligned with the
mirrors and aperture in such a manner that high quality gaussian shaped beam is

established. When the lamp current is signiﬁcantly reduced or increased from 28.8 amps,

45

thermal changes within the lamp housing cause the laser’s thermal axis to be misaligned.
Under these conditions, cavities or modes are developed in the beam proﬁle as illustrated

in Figure 3.14(c.).

Laser Power as a Function of Lamp Current

 

 

 

 

81
a
g.
a:
s
8

\
.1" I .‘ .
$445533». 333‘

a“: O s

t
lit

\ e
:3:

'\
t

 

(h) (C-)

Figure 3.14. (a) Laser power as a function of lamp current. (b.) A characteristic
representation of the beam proﬁle when operating the laser near 28.8 amps. At this
current the thermal axis of the laser is aligned with the mirrors and aperture in such a
manner that a high quality gaussian shaped beam is established (c.) A characteristic
representation of the beam proﬁle with the laser ’s thermal axis misaligned This
distortion in beam quality occurs when operating the laser at low lamp currents.

47

Beamsplitters and partial reﬂectors provide another means for reducing the laser
beam intensity. Another method the laser intensity can be reduced is through the use of
partial reﬂectors or beamsplitters. These front surface reﬂectors, shown in Figure 3.15,
oﬁ‘er major reductions in beam intensity and surface qualities that will not signiﬁcantly
distort the bearn’s intensity proﬁle. These beamsplitters are wavelength (1.064 um) and
polarization (s—polarized) sensitive, When orientated at a 45° angle with respect to the

incoming laser, 50% of the beam is reﬂected and the remaining 50% is transmitted.

      
   
 

Reﬂected
Energy

Transmitted Energy

Figure 3.15. The required alignment of the beamsplitters to obtain a 50% reduction in
laser beam intensity.

The beam’s power density can also be reduced or increased by remapping the
beam’s spatial distribution. This is easily done through the use of external optics. For
example, Plano-convex and Plano-concave lenses can be used to create an optical system

oﬁen called a Galilean Beam expander. As illustrated in Figure 3.16 a plano-concave lens

48

with a focal length of 25.4mm is used to bend the parallel input rays of the laser away
from the optical axis so that they diverge away from one another. At the opposite end a
Plano-convex lens with a focal length of 200mm is used to collimate and straighten the
diverging rays. When orientated in such a manner, this optical system produces a beam

that is magniﬁed 8 times and the power density is reduced 64 times.

PLANO-CONCAVE LENS PLANO-CONVEX LENS
fin = -25.5 mm fout = 200 mm
12.7 mm Dia 25.4 mm Dia

 

 

 

r/
B

 

Beam Magniﬁcation ~ fm/fin

 

<————d= fm- Ifinl = 174.

Figure 3.16. The Galilean Beam Expander. Used in this case to magniﬁr the laser
beam ’s diameter 8 times.

The addition of a Plano-convex cylindrical lens to the end of the optical train
pictured in Figure 3.16 provides another example of how the laser radiation can be

redistributed. Depending on the orientation of this lens a horizontal or vertical line is

49

created at the focal length of the lens. Initial tests with this optical system illustrate that
the distribution across the length of this line is relatively constant. In Figure 3.17 a glass
test specimen with approximate lateral dimensions of 50.8 mm x 12.70 mm x 1.5875 mm
is heated along one edge with the laser passing through this optical system. A short time
after heating is initiated (~1 to 2 seconds) several temperature distributions parallel to the
heated surface are acquired using the output infrared radiometer. If the distribution of
radiation along the generated line is constant the surface temperatures along lines parallel

to heated surface would be constant. As shown in Figure 3.18 this is indeed the case.

50

Sample Width

T”

 

 

 

 

 

 

  

leI ~ 1/2

 

[INC-II:
Output-undoudllaotqe
humanly“

 

 

 

 

 

1 Beam Wdth

(a.) (b-)

‘v

 

(c.)
Figure 3.17. (a.)The heating of a test specimen with laser passing through a beam
expander and a cylindrical lens. Temperature measurements are made using the
Inframetrics Model 600L inﬁared imaging radiometer. (b. ) A schematic representation
comparing the sample thickness with the approximate beam thickness. (c.) Thermally
sensitive laser paper manufactured by KENTTX used to give a general illustration of the

size line generated with this optical conﬁguration.

TEMPERATURE
MEASUREMENTS
ALONG THESE
LINES

I.
>
m
m
:0
9
>
:I
O
z

 

Temperature as a Function of Pixel Orientation (side view)

110

 

‘W‘W’W‘rw

I I
.w-u‘.":’e‘.a_aeh.:fwn . - 5 . ’ﬁe - m e a a ale“

 

e
w .4 ’o.0‘0~‘..°,~"HM.0’.Ww~.e~'.~.e .'.~..e."e'.~'
I D .l O

a a e-a . 'I ' ' 'f -0. UNE’1
v.~.ee'.'ea .".:m °.'h-.A-.~a'*\~ - ..

LINE #2
UNE 83
LINE #4
UNE #5
UNE #0
UNE #7

Temperature (°C)
8

.00....

 

 

70 ‘ 'v"f"w""~ﬂ"'V'I'W'M'IU"UI'ﬁ""v:v'm'w""\".

 

w ‘b.-.gh‘e..e:w..."’".-'l~’\’%..-.‘--Iﬁn

 

 

 

(b.)

Figure 3.18. (a. ) The surface temperature distribution of the test specimen heated along
one surface with laser radiation spatially distributed as a line. If the radiation intensity
across the length of the line generated is uniform, the surface temperatures parallel to
the heated surface should be relatively constant. As shown in (b. ) this is indeed the case.

52

The variations possible for temporal radiation distribution is another advantage of
the Excel/Quantronix laser. Depending on the desired type of heating the laser can be
operated in a continuous wave (CW) mode or a Q-switched mode. In the CW mode the
laser’s output is very stable and its instability has been measured at less than 5% RMS.
This CW beam can be mechanically chopped at various frequencies using an external
shutter like that shown in Figure 3.19. This Uniblitz clectro-mechanical shutter and driver
can operate at frequencies up to 100 Hz and can be controlled externally with a standard
TTL signal. These signals have been generated with both a function generator and the
programmable data acquisition board capable of analog output. The use of this shutter
system is limited by electrical problems within the drive mechanism and as a result of the

low damage threshold of the shutter.

 

Figure 3.19. The Uniblitz electro-mecham'cal shutter and control driver. This shutter
system provides a means for mechanically chopping the beam at various frequencies.

53

The Q-switched mode oﬁ‘ers a very powerﬁil method for controlling the laser
intensity with time. Q-switching is a technique for obtaining short, intense bursts of
radiation from lasers. In order to understand Q-switching a “Q factor” must be introduced
to describe the properties of laser cavity. This Q factor characterizes the ability of the
cavity to store radiant energy. A high value of Q means that energy is stored well within
the cavity. A low value of Q means that energy present in the cavity will emerge rapidly.
For example, if the output mirror in the cavity is highly reﬂective, Q will be relatively high;
if the mirrors are of lower reﬂectivity, whatever energy is present in the cavity will emerge
rapidly through the mirrors, and Q will be low [Ready, 1987].

Consider a situation when the Q factor is high. During this period, lasing action is
not permitted and the arc lamp continues to pump optical energy to the laser rod. The
laser rod absorbs this optical energy and stores it much like a capacitor stores electrical
energy. When the Q-factor is switched to a lower value the stored energy within the rod
will be emitted in the form of a short pulse. Depending on the operating conditions of the
laser, the duration of the pulse is typically in the 50-500 nanosecond range. Since a large
amount of energy is released in a short period of time, the peak power of each pulse is
approximately 3000 times greater than the power generated by the laser when operating in
the continuous wave mode.

Q-switching with the Excel/Quantronix Laser is controlled by the Model 391 RP
(Repetition Frequency) Driver. The Electro-optic Q-switch acts like a high speed shutter
within the laser resonator and is used to control the beam emission. The built-in trigger
provides operation at Q-switch repetition rates between 100 Hz and 80 kHz. In Figure

3.20 time trace was recorded using the photodetector to illustrate the small bursts of

54

energy generated by the Q-switch driver operating at 50 kHz. In Figure 3.21 the peak
power, pulse width, pulse energy, and average power of these small bursts of energy are
quantiﬁed in a series of performance curves. The data in Figure 3.20 was measured with a
high speed photodetector and the output was displayed on an oscilloscope. The
performance curves in Figure 3.21 were measured with the Molectron Power/Energy

meter and the high speed photodetector.

 

P-ooc r1321 was; m
: i i: 5
............................ :.........:_ ...... 1.; ......... g .............................
: I: 2
.......;.........5 W. ................. 2; ...... g ......... : ....... , ..................
................ .,:. ...... ......... ....... i ......... i .......
j g 5‘ s i 5 2 2
- -r-r-r-!-i-i-r-i-I i-i-i-i-l-i-I-id -i-i-r-i+i-i-i- l-r-i-r-i-j-i-i-i -i-r-i-i-i- -l-l- r-
: a i = 2 5 2
. .e‘ 1
I3 4; '5
......... r.........i.........,........i;.........1.......1%.........r.........§.........z.........
2 I:
. 3 " i J‘
.................. ,...:E.T_.. .3.........5.........!.........:.........
: .3 i I;
1: :

 

 

 

Figure 3. 20. Beam intensity as a function of time for the laser operating in a Q-switch
mode with a pulse repetition frequency of 5 0kHz. This information is acquired with a
high speed photodetector with output connected to an oscilloscope.

 

 

 

 

 

 

 

 

 

 

lserPefanmsaFmdimd
QSMtchFreqrmo;
44 300 10 ~50
I
O
O .I I.
a IOU _ ._
3- 331 a . ‘ .‘ . .I . 8 Q
I. I
A. -
e ‘ 76 r3)
—4 El!) . . O
~22 v T O. -. ‘ g g
0 0 ._
E g o RIaerh "°° ‘ 43 F203
1- £15m 0 WM _' ° . a I
e Rhea” . A °
t MM 0 ‘.° *2 r 10
I Q .
I ‘3...
O
01 “Di I . I . .7 ::
. o . . .. ..... Mo ”’0
m T T T
01 1 10
MW”

Figure 3. 21. T )pical performance curves for the Excel/Quantronix Nd: YAG laser
operating with a lamp current of 28.0 amps. This information was acquired with a
power/energy and photodector and is meant to represent typical laser performance when
operating in Q-switch mode.
3. 2.2 Laser Diagnostic Equipment

Laser beam diagnostics include measurement of energy/power, intensity/beam
proﬁle, temporal/time dependence and measurements of beam diameter. These
measurements provide a complete understanding of the characteristics of the laser beam
and become important when attempting to optimize the laser for a particular application.
In the following subsections some of the initial steps towards developing these

measurement techniques are discussed. For a more thorough discussion the reader is

urged to read Appendix D.

3. 2. 2. 1 Molectron Power/EneLgy Meter
The microprocessor based EMPIOOO, shown in Figure 3.22, is a NIST calibrated,

single channel instrument capable of measuring energy, power, voltage, and frequency. It

56

is designed to measure the output of both pulsed and continuous-wave (CW) lasers and it

will operate with a variety of power and energy probes.

 

Figure 3. 22. The Molectron EPM1000 Power/Energy Meter

Two Opes of probes

A PowerMax thermopile probe, model NO. PMIO shown in Figure 3.23, is used
to measure voltage and power. The thermopile probe has an absorber disk deposited on a
ring of thermocouples. Incident radiation ﬁom the laser being tested heats a spot on the
disk, creating a temperature gradient between this region and the edge of the disk; heat

sinks maintain the edge of the disk at ambient temperature. The thermocouples convert

57

 

Figure 3. 23. The Molectron PawerMAX PM—10 thermopile probe. Thermopile probes
of this la'nd are primarily used to measure the output of moderate to high power
continuous wave (C m lasers.
the temperature gradient into an electronic signal that is then read by the meter. This
device is best suited for making steady-state measurements and is used to measure
primarily the output of moderate- to high power CW lasers throughout the ultraviolet and
infrared spectrum.

A pryoelectric probe, model NO. 125-112 shown in Figure 3.24, can be used to

make measurements of energy, power, volts and ﬁ'equency. This detector uses a crystal

with a permanent electronic polarization. As the crystal undergoes a

58

 

Figure 3. 24. The Molectron pyroelectronic probe. Pyroelectronic probes of this kind are
primwily used to measure the output of moderate to high power q-switched or externally
chopped lasers.

temperature change, the electronic polarization changes, generating a transient current
that is read by the EPMlOOO. The current is produced only when the temperature is
changing; once equilibrium is reached, no further current is produced. Consequentially,
this detector can only measure beams that inherently change with time. Such lasers
include pulsed lasers or artiﬁcially pulsed (chopped) CW lasers.

Pyroelectric detectors can be used with low- to high- energy pulsed lasers over the
entire UV and IR spectral range. Because the response speed of pyroelectric detectors is
slow as compared to the pulse length of most lasers, this type of detector is not useful for
performing highly accurate characterization of laser pulse shape. It is, however, quite

accurate for determining integrated pulse energy and peak power.

59

Measurement Errors

Both of the probes translate energy into an electrical signal and each has different
factors that affect accuracy, repeatability, and traceability. The thermopile meter detects
heat. As a result, any source of heat , whether it results from the beam being measured, or
the heat generated from the background, can inﬂuence the accuracy of the measurement
process. Errors can occur if there are extraneous heat sources in the ﬁeld of view of the
detector, if something directly changes the temperature of the measurement head itself, or
if something aﬂ‘ects the ability of the heat sink to dissipate heat.

The human body typically radiates about 100 Watts of power, which is well within
the measurement capabilities of the detector. Therefore a body or hand in the ﬁeld of
view of the detector during measurement can inﬂuence the results. Peripheral electronic
equipment, such as power supplies or oscilloscopes are sources of heat and are often
present on the optic table. They should be removed from the ﬁeld of view of the sensor
head. If need be however, the contribution of constant heat sources can be calculated and
removed ﬁom the instrument readings.

The sensor head should not be subjected to outside heat sources that could aﬂ‘ect
the temperature diﬁ‘erential between the beam and the heat sink. For example, a hand
placed on the sensor housing can inﬂuence measurements. Placing the measurement head
on the cool optical table and putting it back in place for measurement before it has had a
chance to equilibrate can also introduce errors

Location of the beam on the detector can have a signiﬁcant effect on the

measurement results. To achieve accuracy and repeatability to better than a fraction of a

percent, it is necessary to center the beam on the detector surface. Aligning the beam in
this manner allows for the most even ﬂow through the device.

For pyroelectric detectors, the most common source of error is damage to the
detector. Once the device has been damaged, it can no longer be relied on for accurate
temperature measurements. Under normal operating conditions the beam produced from
the Excel/Quantronix Model 117E Nd:YAG laser does not exceed the damage threshold
of the energy meter. Optics can used to focus the beam to a diameter as small as its
transverse wavelength. When operating in this mode the power density increases and

damage to the detector can result.

Example Measurements

As stated earlier the PowerMax thermopile detector is best suited for
measurement of CW lasers while the pyroelectronic detector can be used to measured Q-
switched and pulsed lasers. There are two separate electrical connections between the
sensor heads and EPMlOOO. The thermopile detector is connected to the 25 pin “smart
probe connector” and the pyroelectronic detector is connected to a BNC connector
labeled “pulse in.” The EPMl 000 automatically senses which of the two probes is present
during power up. For example, if the thermopile is connected to the smart probe
connection during the power up cycle the EPMIOOO is ready to display output in voltage
or power of a CW laser.

Some of the basic tests that have been conducted as part of this thesis included
measuring the power output as a function of lamp current and the characteristic

performance curves as shown previously in Figure 3.14 and Figure 3.21 respectively. In

61

conducting these tests the beam is aligned such that it strikes the center absorber disk and
the operating conditions of the laser are varied. The output of the probes at various
currents and Q-switch frequencies can be recorded manually or with an external computer
using the BNC output connection or the RS-232 serial port on the back panel of the
EPMlOOO.

In order to take advantage of the output features of the EPMIOOO a data
acquisition and control program was written using LabVIEW. This program, shown in
Figure 3.25, gives the user a choice of computer interface options. Ifthe BNC OUTPUT
button is selected the program acts simply as a data acquisition program. The output of
the EPMIOOO ranges between 0 and 2 VDC and is updated at a rate of 3 Hz. In this case,
the meaning of this output depends on the conﬁguration of the EPMIOOO. For example, if
the EPMIOOO is conﬁgured to measure power in the range of O to 30 Watts, a one volt
signal from the BNC OUTPUT corresponds to a laser power of 15 Watts. If the
operating conﬁguration of the meter matches the conditions on the front panel of the
LabVIEW program, the program will automatically convert the response to match the true
meaning of the detector’s output.

If higher data acquisition rates are desired, the SERIAL communication switch on
the LabVIEW program should be depressed before the program is activated. In this case,
a 9 pin serial cable is connected from the back panel of the EPMIOOO to the serial port
residing in the host Gateway 486-66 computer. Operating the LabVIEW program with the
RS-232 connection gives the user complete control of front panel options from a remote
location, allows for variations in the communication parameters(such as baud rate and

output format), and allows for the data to be updated at a relatively high rate of 100 Hz.

62

 

 

 

 

 

Figure 3. 25 Lab VIEW Data Acquisition and Control program for EPM1000
Power/Energy Meter. This program allows for communication through an analog BNC
connection or through a RS-232 Serial Port.

This program was developed to provide a means for acquiring information about
the laser’s performance. For example, this program could be used to monitor the stability
of the laser over a given period of time. The program could also be used to monitor the

laser’s power as it was being used to heat a surface. In this case, if a bearnsplitter was used

63

to split the beam such that a portion of the beam was projected onto the detector head
and the remaining portion of the beam was focused onto the test sample, information
regarding both the temperature and heat ﬂux could be obtained as a ﬁmction of time. The
main limitation of this experimental conﬁguration, shown in Figure 3.26, is the lack of
accurate information pertaining to the optical characteristics of the beamsplitter and

surface properties of the test specimen.

Power Meter

 

 

 

 

Infrared Camera Test Sample

 

 

 

 

 

Beamsplitter

Figure 3. 26. Ihe beamsplitter method of obtaining simultaneous heat ﬂux and
temperature information.

3. 3. 2. 2 IhorLab High Speed Photodetector
ThorLAB’s DETZ-SI high speed photodector, shown in Figure 3.27, consists of a
photo diode and internal 22.5 V battery enclosed in a rugged aluminum housing. A 8-32

tapped hole is provided on the base of the housing for easy mounting. The detector

covers a spectral range of 350 to 1100nm with rise times below lns. The speciﬁcations

of this device are shown in Table 3.1

 

Figure 3.27. The ThorLAB high speed photodetector.

 

 

 

 

 

 

 

 

 

Detector: Silicon PIN Housing: Black Anodized Alum.
Spectral Response: 350 - llOOnm Size: 0.75”xl.3”x2”

Peak Wavelength: 920nm e soum Output: BNC , DC—Coupled
Rise/Fall Time: Slns Bias: 22.5 VBattery

Diode Capacitance: 1.8 pF Mounting: 8-32 Tapped Hole
NEP: s x 10'“ W/(‘I-Iz‘m) Diode Socket: TO-S Anode Marked
Dark Current 2.5 nA Damage 'l‘hreahold: 0.5 I Ice:2 (10 ns purse)
Active Area Active Area linearity Limit: 1 mW

 

 

 

 

Table 3. 1. Speciﬁcations of the ThorLAB DE T2-SI high speed photodector.

 

65

The fast response time of this device and its high damage threshold make it a
versatile instrument in a laser environment. For example, the output of this device is
currently used to externally trigger instrumentation, LabVIEW data acquisition programs,
and to measure the temporal and spatial characteristics of the laser beam. .

The BNC output signal is the direct photo current out of the photo diode anode
and is a ﬁmction of the incident light power and wavelength. The sensitivity, 8(1), can be
read from Figure 3.28 to estimate the photo current to be expected based on the

wavelength of the laser of interest. (Nd:YAG - Wavelength = 1064 nm).

0.7

 

0.6 r

0.5 a

0.4 a

0.3 -

Sensitivity (NW)

0.2 i

0.1 4

 

 

0.0 V T T I
200 400 6G3 800 1000 1200

Wavelength (nm)

 

Figure 3. 28. Photodetector sensitivity as aﬁmction of wavelength.

This photo current is converted to a voltage by adding a external load resistance, RLOAD, as

shown in Figure 3.29.

BNC
Connection
m
\‘J *

 

R Measured
LOAD ‘ Voltage

 

Incident Q‘s...
laser VOMQG

radiation / 3538

ii , -

Figure 3. 29. Illustration of the external load used to convert the photo current into a
voltage.

 

 

 

 

 

 

The output voltage of the detector is derived as:

V0 = P * 5(1) * Rm (3.1)

The bandwidth, wa, and the rise time, TR are determined ﬁ'om the diode capacitance, C,,
and the load resistance, RLOAD:

fbw=1/(27r*R *Cj), T},=0.35/fbw (3,2)

LOAD

3. 3. 2. 3Beam Proﬁling

An intense study concerning beam proﬁling techniques is included in Appendix D.

67

3. 4 Data Acquisition and Instrument Control

The fundamental task of a data acquisition (DAQ) system is the measurement or
generation of physical signals. The typical components of a DAQ system include
transducers, signal conditioning accessories (if necessary), data acquisition boards,
application software, and a PC with a processing speed sumcient for the application.

For the most part, transducers sense physical phenomena and convert them into
electrical signals such as voltage or current. Signal conditioning accessories may be
necessary to amplify, isolate, and ﬁlter low-level signals allowing for accurate and safe
measurements. If the signal is conditioned properly plug-in data acquisition boards can be
used to digitize the signal. A data acquisition board can also be used to generate control
signals. Application software simpliﬁes the programming necessary for DAQ, allows for
data analysis, and data presentation. The PC in the DAQ system determines the overall
processing speed of the application. Therefore, applications requiring real-time processing
of high ﬁequency signals need a high speed processor possibly with an accompanying
coprocessor.

In the following subsections the major components of the newly developed data

acquisition system are discussed.

3. 4. I Lgb VIEW
Software plays a vital role in developing automated data acquisition and instrument
control systems. The selected software must span a broad range of functionality, from

device drivers for controlling speciﬁc hardware interfaces to application software

68

packages for developing complete systems. With this in mind, LabVIEW was chosen as
the software development system.

As shown previously in Figure 3.25, LabVIEW contains the necessary tools for
data acquisition and control, data analysis and data presentation, resulting in an integrated
system for developing instrumentation software.

LabVIEW is a graphical programming language which includes libraries of
functions and development tools designed speciﬁcally for data acquisition and instrument
control. LabVIEW programs are called Virtual Instruments (VI’s) because their
appearance and operation imitate actual instruments. However, the ﬂow and structure are
analogous to the ﬁmctions of other conventional programming languages.

There are basically two components to a LabVIEW program. The user interface
of a V1 is called the front panel. The ﬂoat panel can contain knobs, push buttons, graphs
and other control and indicator ﬁmctions. The V1 receives its instructions from a block
diagram. This block diagram is basically a wire diagram of a pictorial solution to a
programming problem. “Within the block diagram a variety of tools are available in the
form of subVIs. The tools within these subVIs may include the ﬁmction calls necessary
for communication with plug-in data acquisition boards or algorithms previously created
by the user or by the manufacturer. These subVIs allow for modular programming and as

a result complicated tasks can be divided into many simpler subtasks.

3.4.2 A M0-16FM1thi'pypose Data Acquisition Boa__r__c_l
The high performance AT-MIOl6F-5 data acquisition board has been used as a

primary source for general data acquisition and instrument control for this application. The

69

AT-MIOI6F-5, with its multifunction analog, digital and timing 110 can be used in many
applications for automation of machine and process control, level monitoring and control,
instrumentation, electronic testing, and various other ﬁanctions. The multichannel analog
input can be used for transient analysis or data logging. The two analog output channels
can be used for such functions as machine and process control and analog function
generation. The eight TTL compatible digital I/O lines can be used for such ﬁmctions as
machine and process control, interrnachine communication, and relay switching control
[Johnson 1993]. The three 16-bit counter/timers can be used for such ﬁmctions as pulse
or clock generation, timed control of laboratory equipment, and frequency, event, and
pulse width generation.

More speciﬁcally, the AT-MIO-16F board allows for 16 single ended or 8
differential ended inputs. The board’s analog to digital conversion (ADC) has a 12 bit
resolution and a 5 usec conversion speed. Both low-level and high-level signals can be
measured with this board using the software-programmable gain ampliﬁer to apply gains
of 0.5, l, 2, 5,10, 20, 50. National Instruments ensures ﬁlll accuracy at all gain setting
even at the maximum sampling rate of 200 ksamples/sec. The AT-MIOl6F-5 has a 2048
sample deep ﬁrst-in-ﬁrst out (FIFO) buffer for storing ADC results before transferring the
data to the computer memory through interrupts or DMA. The FIFO helps prevent
problems associated with so processor speed or data loss during data transfer delays such

as those that occur due to interrupt latencies.

70

3. 4.3 EISA -A 2000 H iglLSpeed Data Acquisition Boa_r_d

The EISA-A2000 board can be used to digitize signals resulting from high speed
events and is used when the data acquisition capabilities of the AT-MlO-16F are not
suﬁcient. It was incorporated into this system to be used with the EG&G IR detector for
through thickness ﬂash experiments. The EISA-A2000 can be used in the laboratory for
instrumentation waveform recording, and electronic test and measurement applications.
The fast, 12 bit resolution analog input makes the board useful for high-performance
signal analysis, transient analysis, pulse parameter measurement, and data logging. The
multichannel simultaneous ADC sampling is ideal for position and phase analysis of
multiple signals. Functions such as analog and digital triggering, pretrigger and posttrigger
modes, programmable AC/DC coupling are easily implemented through the use of
LabVIEW VI’s. Input to the various channels are made through a BNC adapter located
on the rear panel of the host Gateway 486-66 computer.

More speciﬁcally this data acquisition board contains a lMsamples/sec, 12 bit
resolution analog to digital expansion board for an EISA bus computer. The board has
four analog input channels, each with its own sample and hold circuitry. The board can
sample one channel at lMsamples/sec, two channels simultaneously at 500 ksamples/ sec,
and four channels at 250 ksamples/sec. Data acquisition from the input channels can be
started from software, digital triggers, or analog triggers.

As mentioned LabVIEW is used to conﬁgure the EISA-A2000 for A/D

conversion. By default the board is set to acquire data in an AC coupled mode. In this

71

mode the input channel range is :5 V peak AC with i 25 VDC offset. When conﬁgured
to acquire data in the DC coupled mode the input channel range of the board is 1r 5 V DC.

In order to work as an eﬁ‘ective tool for data acquisition the EISA-A2000 is
equipped with several trigger modes. In the pretrigger mode the EISA-A2000 acquires a
speciﬁed number of scans before and after it receives the trigger condition. In posttrigger
mode, the board acquires a speciﬁed number of scans after the trigger. In the posttrigger
mode with delay, the EISA-A2000 waits to acquire scans until a speciﬁed time interval
elapses after the trigger condition.

These trigger modes have two sources - analog and digital. The analog trigger
can be received from any one of the input channels or the ATRIG input on the I/O
connector. Analog trigger circuitry causes a trigger when selected input channel reach a
preprogrammed slope and level. A leading or trailing edge digital trigger can be received
from the DTRIG I/O connector input. In most situations a rising edge in the response of

the photodetector was used to trigger data acquisition.

3. 5 Miscellaneous Experimental Equipment
3.5.1 FORA Video Timer

The VTG-33 video timer, shown in Figure 3.30, is an all-electronic compact unit
which superimposes digital indications of time and date on standard RS-170 video events.
The crystal controlled IC circuitry provides a reliable and accurate time base indications
with a temporal resolution of 0.01 of a second.

This timer has an advantage over the unit (FOR.A 212) used in the past because its

remote capabilities allow for external triggering. A TTL low signal, shown in Figure 3 .3 1,

72

supplied to the remote control connector on the rear panel can be used as a trigger. The

connection pinouts for this for this external trigger are shown in Figure 3.32.

 

Figure 3. 30. The FOR.A VTG33 Video Timer.

V DROP IN VOLTAGE IS
TO ACTIVATE THE
~ 5 VOLTS VIDEO TIMER

 

~ 0 VOLTS

 

 

 

‘

time'

Figure 3.31. An example of the TIT. signal. This signal is used to remotely start the
VTG 33 video timer.

73

 

Figure 3. 32. The wiring connections for external triggering of video timer.

In this work the video timer was used to superimpose time indications onto the
output of the radiometer. The timing allowed for the temperature distributions to be
sampled at known times. The remote triggering capability oﬂ‘ered by this unit was

desirable because it allowed for an accurate means to initiate timing.

Chapter 4

Description of Mathematical Model

Along with well understood experimental components and measurement
techniques, inverse heat conduction and parameter estimation rely on the development of
accurate experimental models. A heat transfer model, previously developed by J.V. Beck
and F Breidenich in 1994, is used to describe samples used in the present experimental
setup such that the thermal behavior of the experiment can be predicted analytically.
\Vrthout such a model, the desired thermal properties can not be estimated and without an
accurate description ﬁ'om the model, any results are meaningless. Therefore, although
this description of the mathematical model is not original, it is included in this work for
completeness. Since there is a certain amount of error and uncertainty associated with

each experiment, the mathematical model can also be used to determine if a certain

74

75

experiment can be successﬁrl. This chapter is dedicated to a discussion of the experimental
model developed for estimating the thermal diffusivity parallel to the surface of the
material of interest. This one dimensional radial heat ﬂow model describes the

temperature distribution for transient and quasi steady state time periods.

4. 1 Mathematical Model

Conductive heat transfer can be described by the transport of energy in a medium
as the result of a temperature gradient. In nonmetallic solids, the physical mechanism for
this transport is the random activity between atoms and molecules. In a solid body with a

temperature gradient, Fourier’s Law is used to relate the heat ﬂux (q) to the temperature

U)

q(r,T) = —k(r,T)VT(r,T) (4.1)
where the k [W/m K] is the effective thermal conductivity of the material, the temperature
gradient VT [ c/m] is a vector normal to the isothermal surface and the heat ﬂux vector is
the heat ﬂow per unit time and unit area. The minus sign is inserted in accordance with
the second law of thermodynamics. For example, if heat ﬂows in a positive direction, the
temperature must decrease in that direction. For an isotropic , circular body, the two

components of q in the r and z direction are given by:

5T 5T
=—k —; =—k— 4.2
q, ,2 % Wk ( )

Using the conservation of energy and assuming that heat conduction is restricted

to the radial direction, the one dimensional heat conduction equation can be derived as

76

li£rﬂj+ﬁziﬂ (4.3)

rdr é’r k,6 a, é’t

The assumption of one dimensional heat ﬂow seems to be valid for thin ﬁlms as they are
relatively isothermal in the z direction during heating. Due to the present temperature
levels and the high thermal conductivity of the test specimens, the established model
assumes that there are negligible convective and radiative losses from the specimen to the
surroundings.

The ﬁrst term in equation (4.3) describes the net conductive heat ﬂux into the
control volume, the second term is the rate of effective internal heat generation within the
heated area and the right hand side of the equation represents the energy storage rate. In
the quasi-steady state, the energy storage rate is a constant and equation (4.3) will be used
in this case to derive a closed form algebraic expression for one of the two quasi-steady

state terms. The heat ﬂux q ( r) is qo for 0<r<a and zero is the area a<r<b, see Figure 4.1.

Heated Region

 

 

 

 

 

 

 

 

§IDE VIEW FR NT VIEW

Figure 4. 1 Schematic representation of the test specimen.

77

The Green’s ﬁmction solution for one dimensional radial heat ﬂow in a circular
disk with a natural boundary condition in the center and an insulated boundary condition
at the edge (r=b) is [Beck et al 1992]:

T (r,t)= Z’ i i g(r', t)GRo,(r,t

, r=o r'=0

 

 

r', r)2nr'dr'dr + T (4.4)

This formulation assumes that there are no convective or radiative losses and that
the source term g(r',1:) = q/8 [W/m3] is the continuous heat ﬂux generated by a laser in the
area (0<r<a) of the sample, where 8 is the thickness of the sample. The Green’s ﬁrnction

for the R02 case is

 

 

GR02 (r, t

 

' —
or :1)—

[1+ ; e‘ﬂmarlt-tl/b2 '10 (ﬂmrfljbgé:§ﬂmryb):l (4.5)

1
Jr b2
where J..(x) is the Bessel function of the ﬁrst kind of order zero and evaluated at x and
Bm’s are the eigenvalues of the eigencondition, J; (B...) = 0. The following paragraphs
describe the solution of equation (4.4) for times in transient and quasi-steady state. Since
values of the dimensionless time (at/b2) tend to be greater than 0.5 for all considered
materials at respective heating times, the main solution of interest in expected to be the
quasi-steady state, that is, a linearly increasing temperature with time. Thus, the

solutions of equation (4.5 ) can be expressed as a sum of the four following terms:

T (r.t)= 7;..(t)+TQS.(r)+Tm(r,t)+T. (4.6)
where TQSl(t) is the ﬁrst quasi-steady state term from the constant in equation (4.5),
TQ52(r) is the second quasi-steady state term from the inﬁnite series in equation (4.5),

Tm(r,t) is the transient state term from the inﬁnite series and T. is the initial temperature as

78

shown in equation (4.4). Here, TQs.(t) describes the linear dependence between
temperature and time and TQsz(r) contains the information about the spatial temperature

distribution during the quasi-steady state period.

Integrating the constant 1 in equation (4.5) and assuming that the heat ﬂux, q, is
the constant and uniform term qo in the region 0<r<a and zero in the region a<r<b, see

Figure 4.1. Under this assumption the quasi-steady state term becomes:

_ qoogta2

T t—
er() 5krb2

(4.7)

The second quasi-steady state term can be derived by substituting the inﬁnite series
into equation (4.4), leading to an inﬁnite sum that then would have to be integrated. On
the other hand a solution for T0520) can be found by substituting equation (4.6) and
equation (4.7) into equation (4.3) for both regions 0<r<a and a<r<b respectively. This
leads to a closed form algebraic expression for TQ32(r). The transient term, Tm(r,t)
disappears for the quasi-steady state solution. In order to make the solution more
computationally efﬁcient, the latter method is used. The term on the right side is a
constant determined from equation (3 .7):

Cziahsir) _ (1.02

a, at " aw
since 6TQsz(r) / 6t=0 and 6Tm(r,t) / at are neglected for the quasi-steady state. Solving

 

(4.8)

the differential equation (4.3) for 0<r<a, the general solution is obtained

QS,(r)=%(C-ki:5](rz -a’)+D,ln(r)+ D2, 0<r<a (4.9)

79

Using the boundary conditions at r = 0 of

TQS2 is ﬁnite as r —) O (4.10)

Yielding D1 = 0. Assume for a moment that the temperature at r = a is T..:

TQsz : 7:: (4.11)

Then the solution for 0<r<a is:
T (r)-1 C——q—‘1— (rz-a’)+T 0<r<a 412
Q” —4 k 5 ° ’ ( . )

For the region a<r<b, the volumetric energy generation term in equation (4.3) is zero.

Thus, the general solution for the differential equation is given by

TQS,(r)=%Cr2 + D3lnr+D4 (4.13)

Using the two boundary conditions

TQS2 (a) = T; (4.14)
and (4.14)
M = O (4.15)
dr no

the second quasi steady state term and for the non-heated region then becomes

80

r

TQS,(r)=C{%(r2 —a2)+%bzln(£)]+ T; a<r<b (4.16)

Equation (4.12) and (4.16) still contain the unknown T... The equation for heat
ﬂow continuity at boundary r=a for both solution, TQ32(0<r<a) and TQ31(a<r<b), equation

(3.17), can be used to determine C

dTQS,(O < r <a) ___ 077;”,(a < r<b)
5r 0‘ é’r

which was already known from equation (3.18). Hence the heat ﬂux continuity condition

 

 

 

 

0+ (4.17)

at the interface is satisﬁed.

C_ (1.02

_ 4.18
kﬁbz ( )

The task now is to determine T... At time zero the average temperature for T032 (r)

is zero or

b
ITQS,(r)27rrdr=O, t: 0 (4.19)

The quasi - steady temperature distribution integrated across the heated (0<r<a)
and non heated (a<r<b) areas add up to equal zero. Integrating the expression for TQ32(r)

from r=0 to a and from r=a to b respectively gives:

a b
ITLSAO < r < a)27rrdr+ [72mm < r < b)27rrdr= O (4.20)
no r=a

Solving for T. yields

81

               

 

a4 (a q, J 3Cb2 Ca: Cbz (4.21)
Since the experimental design is such that only temperature data in the non-heated region
is used for the estimation of on, the solution TQs(a<r<b) is the only one that needs to be
derived. Temperature measurements from the region O<r<b are omitted, because the
spatial power distribution of the heat source is not constant as assumed in the derivation of
the mathematical model. Hence, substituting equation (4.18) and (4.21) into (4.16) the

second term for the quasi-steady state temperature distribution for the non heated region

a(r_ +—1—J+-1-(ln(2)—2) , a<r<b (4.22)
4b2 2 2 r 4

becomes

     

 

TQsz

Now, a term for the last unknown, the temperature distribution for transient times

Tm has to be determined. The inﬁnite series in equation (4.5) has to to be integrated,
leading to a solution for T3 = TQs(r) + Tm(r,t). Already knowing the expression for

TQ32(r), only the term for Tm(r,t) is still of interest

82

7; = arqoa j i ie-ﬂzm"r(r—r)/b2 Jo(ﬂmrlb)Jo(ﬂmr'/b)2ﬂ,ridrrdt

k 67ml M ”:0 ":1 J: (16”) (4.23)

Integration over r’, using the substitution x=er’ lb equation (4.23) then reduces to

are. an, :1
.. 1309..)

dr (4.24)

 

 

Integrating equation (4.24) over time, the term

 

 

(4.25)

2ng i J'('B"' %) LLB" al- -"'”i]

T: l—e b2
‘ w ... 4.1/:0...) l

is obtained. The constant part (independent of time) in the eqn. (4.25) is equal to the
closed form algebraic expression T0520) (4.22) and therefore the exponential term must be

equal to Tm(r,t)

An analysis of eqn. (4.26) at various times using the physical properties and

 

 

dimensions of the copper, iron, and diamond samples shows that the ratio of Tm(r,t)/T(r,t)
is smaller than 1.0 percent. This result is expected since the characteristic sampling time
for each of the samples was selected based and their thermophysical properties such that

the dimensionless time (at/b2) was greater than 0.5. Based on this analysis, the transient

83

part of the solution is neglected, leading to the quasi-steady state solution for the

temperature distribution in the a<r<b region,

2 2 2
T(r,T)=£ a_t+ a (r—+—l—)+l[ln(§)—2) +T a<r<b (4.27)
k5 b2 4b2 a2 2 2 r 4

 

4. 2 Parameter Estimation

The ability to acquire temperature distributions along the surface of a sample and
predict this behavior with a mathematical model provides a great deal of data and insight
into the thermal behavior of the material. A third tool must be utilized to analyze this
information and estimate the desired thermophysical properties. This tool is parameter
estimation. As a discipline, parameter estimation provides the necessary algorithms to
estimate the constants that appear in mathematical models such as that in equation (4.27).
The present problem is an inverse problem because not all the constants in the
mathematical model are known. Using parameter estimation, these unknown constants
are estimated based on the temperature distribution. In this case, a nonlinear sequential
parameter estimation program called NLIN [Beck, 1994] is used to estimate the thermal
diﬂirsivity, I32, and the values for the laser effect term, 31: and the initial temperature, [33.

NLIN uses the method of least squares

S = inc. —T.]’ (4.28)

i=1

where N is the number of data points, Yj is the measured temperature and T5 is the
calculated temperature represented by (4.27). A simpliﬁed version of this equation is

repeated here for convenience,

2241:? +5.15%)+il'nlil-il]+ﬂs

where B. = qazlk.8, B2 = 0., and [33 = Tm...) . Using the method of least squares the NLIN

 

 

program simultaneously estimates I31. B2, and [33 to calculate T,- such that the error in S is
minimized. In order to minimize the error in S, NLIN uses the following system of

equations

 

 

 

-:—":= 2%[1’1 — 7}] :2 (4.30)
535:: zglg _ Ti] :2 (4.31)

0'33

85

NLIN not only ﬁts the mathematical model to the experimental data and
sequentially estimates the desired parameters, but it also calculates the experimental
residuals. These residuals are the differences between the measured and calculated
temperatures [Yj' j] and when analyzed provide information about the error within the
experiment. A hard copy of the NLIN program can be found in Appendix H. An NLIN

output ﬁle from an experiment conducted on a CVD diamond ﬁlm is given in Appendix I.

Chapter 5

Procedures and Results for One Dimensional
Radial Experiments

This chapter presents the experimental procedures and results for the measurement
of the thermal diffusivity of three different materials: iron, copper, and CVD diamond ﬁlm.
The following subsections describe the steps involved in sample preparation, experimental
setup, the procedures necessary for measuring the surface temperatures, and the

experimental uncertainty involved in the estimation of the thermal diffusivity.

5. 1 Sample Description and PrepaLation

Infrared temperature measurement systems respond to the sum of the radiation
emitted, reﬂected, and transmitted by and/or through the surface of interest. As a result,
inherent problems arise with IR systems when attempting to acquire accurate temperature
measurements of surfaces with variations in emissivity, high reﬂectivity and high

transmissivity. For example, in Figure 5.1(a.) a boron doped diamond ﬁlm on a silicon

87

substrate is placed in the ﬁeld of view of the IR camera. The surface of this specimen is
such that a uniform surface emissivity could be assumed and the specimen is non-
transparent in the visible spectrum. Although this diamond-silicon composite is relatively
thick (~300pm), it is transparent in 8 pm to 12 um range. As shown in Figure 5.1(b.) a
small radiating body (heated resisitor) was placed behind the specimen and caused an
apparent temperature difference across the surface of the sample. One of the common
methods used to eliminate problems like this and others resulting from variations in
surface emissivity and high reﬂectivity is to coat the sample with a thin coat of high

emissivity material.

 

  

j.

(b.)
Figure 5.1 (a.) A diamond ﬁlm on silicon substrate placed in the ﬁeld of view of the
Inﬁametrics Model 600L radiometer. (b. )A radiating bodies placed behind the sample

illustrating the eﬂects of measuring the surface temperature of high transmissivity
materials.

 

88

In this present work the thermal diﬂ‘usivities of copper, iron and CVD diamond
ﬁlms are measured. The copper and iron samples were purchased from the Goodfellow
Corporation and are guaranteed to have a purity of 99.999% of 99.79%, respectively.
The samples, shown in Figure 3.2, have a constant thickness of 500nm and a diameter of
5.08 cm. The surfaces of these samples are semi-polished and therefore have a high
reﬂectivity. This high reﬂectivity causes temperature measurement problems because
background sources operating at high temperature, such as power supplies or
oscilloscopes, may produce an artifactual apparent temperature differences across the
surface of a reﬂective test sample. Another problem arises because this high reﬂectivity is
associated with a low absorbtivity. Therefore, if it is of interest to maximize and/or
quantify the amount of laser radiation deposited onto the surface of the test specimen a
thin high absorbtivity material must be applied to the surface of the sample. In order to
eliminate these potential problems, a thin coat of high temperature resistant, high
emissivity black paint was added to each surface of the test samples. The emissvity of this

black paint was experimentally determined to be 0.96.

VERIFICATION MATERIALS

   

COPPER SAMPLE IRON SAMPLE

 

Figure 5. 2. The copper ﬂeft) and the iron (right) samples used in this emeriment. Each
of the samples are 5. 08 cm in diameter and have a thickness of 5 00pm.

89

Three freestanding CVD diamond ﬁlms, created using a microwave plasma
deposition process and shown in Figure 5.3, were studied in this experiment. These ﬁlms,
referred to as sample AT#4, ST#120, and ST#192, have average thicknesses of 370 pm,
370 um, and 240 um respectively (thickness variations are less than 15%), and diameters
of 5.08 cm. The surfaces of the samples are drastically different. The substrate or bottom
surface, where the crystalline growth was initiated, is smooth and highly reﬂective. The
growth or top surface is coarse and not very reﬂective. This rough surface appears to be
such that a uniform surface emissivity could not be assumed. Tests similar to that shown in
Figure 5.1 illustrate that the three specimen do not transmit radiation in 8 to 12 um range.
As with the copper and iron samples the potential measurement problems were eliminated

by adding a thin layer of black paint to each surface of the diamond samples.

 

SAMPLE ATM

   

SAMPLE ST#120 SAMPLE ST#192

 

Figure 5. 3. The three C VD diamond ﬁlms measured in this study. Each of the samples
have a diameter of 5. 08 cm. The average thicknesses of sample A T # 4, S T # 192, and
S T# 120 are 370,um, 370 pm, and 240 pm respectively.

5.2 Experiment Setup and Measurement Techniques

The experimental setup contains seven components: 1.) The Inﬁ'ametrics Model
600L Infrared Imaging Radiometer, 2.) a Excel/Quantronix Model 117E Nd:YAG Laser,
3.) a Thorlab’s high speed silicon photodetector, 4.) a PC based data acquisition system,
5.) FORA VTG33 Video Timer, 4.) a JVC video cassette recorder, and 7.) an image

processing system. A diagram of the data experimental setup is shown in Figure 5.4.

 

 

 

 

 

 

 

 

 

 

 

 

Nd:YAG Laser 1 .,
IR Camera
Sample
.. Oi I
Photodetector

 

 

 

 

Radium Output \.\ Computer
\
Y
iometer Output +
Tune Indication

General Purpose
DAQ Board

 

 

 

 

 

Video Recorder Video Timer

 

 

 

 

 

 

Figure 5. 4. Schematic representation of the experimental setup used for measuring the
parallel thermal diﬁiisivity of several thin circular test samples.

91

The theory and speciﬁcations of the major components are described in Chapter 3
and will not be repeated here. Instead, this section is devoted to a discussion on the
speciﬁc operating conditions and setup operations required for data acquisition.

The placement of the radiometer with respect to the sample is important. The
optical axis of the radiometer’s lens system must be centered on back of test specimen.
Poor alignment will cause spatial distortions and will effect the precision to which the
radial locations of individual temperature measurements are known. The distance of
between the radiometer and the test specimen is minimized. This acts to increase the
spatial resolution of the system and yields the maximum amount of temperature
information.

After the specimen and radiometer are in place, the radiometer settings are
adjusted and the system is prepared for data acquisition. Based on previous experimental
tests, the emissivity was of the black paint was determined to be approximately 0.96. The
camera’s thermal sensitivity was maximized by operating the radiometer in the smallest
possible temperature range. The temperature range setting in most cases was 10°C and is
dependent on the thermal behavior of the sample and the speciﬁc test conditions. The
image averaging mode of the radiometer was activated and four images were averaged in
real time. Image averaging is an attractive feature for two reasons. First, the signal-to-
noise ratio is increased by a factor of two and second the amount of data is compressed by
a factor of four.

The output of the radiometer is in RS-170 video format. As a result, the output is
passed through a standard video timer and digital indications of time and date are

superimposed onto each frame . In this format, the output could analyzed in real-time

92

using a general purpose image processing system or stored on conventional video
recording equipment for ﬁlture analysis.

The heating source for these experiments was the Nd:YAG laser. The laser was
operated in it continuous wave (CW) mode with various power levels depending on the
thermal physical properties of the test specimen. For example, the iron samples dissipate
heat much more slowly than the diamond samples. As a result, low power levels cause
signiﬁcant temperature increases in the center portion of these samples. As previously
mentioned, the temperature setting on the radiometer controls the thermal resolution of
the measured data. Since it is desirable to minimize the temperature resolution, the laser
power must be attenuated so saturation does not occur during the time period in which
data acquisition occurs. In general, the approximate power levels used to energize the
iron, copper, and diamond samples are 750 mW, 3.5 W, and 3.0 W respectively.

The alignment of the beam with respect to the center of the test specimen is
another key portion to the experimental setup. The mathematical model relies on the fact
that the heat source is concentrated on the center of the sample. Misalignment could
produce a non—symmetric temperature distrﬂaution or other erroneous results. This
alignment can be achieved in two ways. Course adjustments in alignment can be achieved
by physically moving the beam to different locations on the specimen. This is done by
adjusting the external mirrors which are used to deliver the beam to the optical table. Fine
adjustments are made by translating the sample and the radiometer to various locations
using an X-Y positioner manufactured by ORIEL (model #14901). This positioner,
shown in Figure 5.5, can be transferred along an optical rail and allows for micro-

positioning of the specimen.

93

 

Figure 5. 5. The ORIEL X-Y positioner. This device can be moved to various locations
along the optical rail and allows for micro-positioning of specimen for beam alignment.

In both cases,- the alignment can veriﬁed using the output ﬁ'om the radiometer in
conjunction with the IPPLUS image processing system. A sample with proper and

improper laser beam alignment are shown in Figures 5.6 and 5.7 respectively.

94

 

Radiometer Output - Illustrating Properly Aligned Beam
Gray Scale Intensity as a Function of Pixel Numer

 

\

 

 

 

220— [as
SE
200- 86
8a
3%
”0‘ I/J.’ g8
\
lul— J .
‘1.
a
“0 “E 197PbtebLeil 197 Pixels Right I
ofiheCorur oftheCerler '
120

 

 

Grey Scale Intensity (Linerly Proportional to Temperature)

0 25 so 75100125150175200225250275300325350375
Pixel Number Along the 5.08 cm Sample

(b-)
Figure 5.6. The output of the radiometer is used in conjunction with the IPPLUS image
processing system to verify that the laser is properly aligned in the center of the test
specimen. Note the symmetry in gray level (temperature) distribution.

95

 

Radiometer Output - Illustrating lmroperly Aligned Beam
Gray Scale Intensity as a Function of Pixel Numer

 

 

 

 

 

E
@200
O
‘2‘
3240- h
8 a
£220-
0
E
2200-
l C
a... g
5 4
ram 5
g a
g \
:10-r
— 211Pixedel leaner-nut
gm ant-Cater Aedhm
,, . . . . . . . . . 1 . . r 1 .
g o assorsmoizslsolrszoozzszsozrsaoomaeoars

Pixel NumberAlong the 5.08 cm Sample

(b.)
Figure 5. 7. The output of the radiometer is used in conjunction with the IPPLUS image
processing system to illustrate that the beam is improperly aligned Note the asymmetry
in gray level (temperature) distribution

96

\Vrth the beam properly aligned and the radiometer prepared to acquire data, the
photodetector must be positioned, the timing control system must be established. As
shown in Figure 5.8, the photodetector is positioned such that beam reﬂections from the
sample and the presence of the beam in general, causes an increase in the detector’s
output. A 1 MS) terminating resistor is added to the photodetector circuit. Even with
relatively low amounts of laser intensity a resistor of this size yields an appreciable

detector response ( ~ 3 to 6 volts ), and a characteristic time less than 4.0 us.

 

Figure 5. 8. The positioning of the photodetector with respect to the test sample.

The output of the photodector is connected to the one of the analog input channels
on the AT-MIO-16F data acquisition board. A LabVIEW VI, shown in Figure 5.9, is
used to monitor the response of the detector. When the detector output increases beyond
a preprogrammed voltage level, a TTL low signal is delivered from the data acquisition
board to the FORA video timer. This signal externally triggers the video timer and allows

for accurate digital indications of time to be superimposed onto the radiometer’s RS-170

97

formatted output. The speciﬁc operating instructions for this program and the proper

connections to the data acquisition board are discussed in detail in Appendix F.

 

Figure 5. 9. The ﬁont panel of a LabVIE W VI which is used to monitor the response of
the photodetector. When the program senses that the detector response has exceeded a
preprogrammed trigger level it initiates a data acquisition board to send a T'IZ low
signal to external connections on the rear panel of the video timer.

With any program in which timing issues are important, the execution time must be
measured. In this case, it is important to quantify the length of time necessary for the
LabVIEW program to recognize that there is an increase in photodetector response
beyond the preprogrammed trigger level, and respond by transferring a TTL low signal

ﬁom the DAQ board to the external connection on the rear panel of the video timer.

98

The delay time is measured by operating aligning the photodector and operating
the LabVIEW program as if an experiment was actually being conducted. In this case,
however, the output of the photodetector is split between channel 1 an input channel on an
oscilloscope and analog sent to a second channel on the oscilloscope instead of the
external connection of the video timer. When the internal electro-mechanical shutter
within the laser is opened the photodetector’s increase in response initiates the TTL low
signal and the delay time can be measured. This test was repeated several times with a
maximum delay time of 24m and a minimum delay time of 16ms. In Figure 5.10 the time

traces of three tests are illustrated indicating the minimum, average and maximum delay

 

 

 

 

 

 

 

 

times.

LS-OOV as-oov . 4202 2002/ m
l l OutpujtnomAT-MIo-lor
................... .l-_lusedteexremaﬂytuggcr

i i :: l thevideotimers g
n, - ~ “A -- ‘ 1 ";|....‘ ........ ......... ..........; .........
Threeséparatetectsinwhich : L/
elephotpdeteetor, ; 't...__.., e; .3 4;: TL:
wasmoriitored 5 E g -: l ‘
-I-I-l-l-i-l°l-l-I' -l~l-r-l- - -l-l-l-I-l-l-l:-l-ll-l:ll~l-l-I-l-l-l-l-I-l-l-l-l- -l-l-l-l- -I-l-l-l°
s s . :: I s s
......... It...l..
- f; ; gilli...i....; ......... 3T ...... - ..... T ..... T T...'. 1
——e: i I4——MlmmumDelay*1‘1me-16ms
......... lil. .,.
s s a a i i I = s s s
z : : : {i L : : ‘

 

 

11!: 46.00113 t2“: 0.000 a At = "focus I/At= 62. 50 Hz

Figure 5.10. The response of the photodetector and data acquisition board used to
measure the execution time of the Lab VIEW VT in Figure 5. 9. This V7 is responsible for
externally triggering the video timer.

The response time of the video timer after a TTL low signal is received is on the

order of nanoseconds [personal communication with FOR.A Corporation representatives].

99

Therefore, the most signiﬁcant portion of the delay between photodetector’s response
and the onset of timing is associated with program’s execution time. Even though this
delay is quite substantial, the 16 to 24 ms execution time does not cause problems
because the frame rate of the radiometer output is 33ms.

Now that the timing circuitry, radiometer and laser system are ready the actual
testing can begin. The procedure for acquiring temperature data with the infrared
radiometer can be divided into three main process: 1) capturing the thermal ﬁelds of the
sample on video tape while the sample is being energized, 2) using the image processor to
select images for the desired heating times and save the data to ﬁles, and 3) extracting the
surface temperatures for a desired area of the sample from the intensity-data ﬁles created
by the image processor.

As the sample is being energized by the laser the temperature changes with time
are captured and stored on video tape. Once the resulting thermal history of the sample is
stored on video tape, thermal images for three selected times during the quasi-steady state
heating period were captured using the IPPLUS image processing system.

The frozen images were analyzed using the line proﬁle ﬁrnction in the IPPLUS
analysis toolbox. Line proﬁle analysis allows the user to collect actual intensity or gray
scale values along lines with various lengths and in various orientations. This information
can then be saved to a ﬂoppy disk or to the computer’s hard drive. In these tests, the
positioning of this line is quite important. As shown in Figure 5.11, this line is positioned
horizontally across the center of the specimen and at a length corresponding to its

diameter.

 

Gray Scale Intensity as a Function of Pixel Number
Copper Sample Atler3 seconds of Healing

 

 

 

 

2°°' 1".
h. f t,
1.
g m .‘f x
g 140 J H
g .2..- I” ’
ﬂ. ‘8‘
1111-, o
l t
w 0 100 21'!) I!) 400
Pixel Number
(b.)

Figure 5.11. (a. ) A thermal image of a 5. 08 cm diameter copper disk at 3.00 seconds.
The horizontal line across the center of the specimen represents the line proﬁle ﬂmction
ﬁom the IPPL US intensity analysis toolbox. (b.) The output of the line proﬁle ﬁmction.
Gray scale intensity as a function of pixel number.

101

As mentioned in Chapter 3.1.1 and in Appendix B, a calibration can be used to
convert the gray scale distributions in Figure 5.1 1(b.) into the temperature distributions ill
Figure 5.12. This information is combined with temperature data from other heating times
and placed into an input ﬁle for the nonlinear sequential estimation program, NLIN. An
input ﬁle containing this temperature information is shown in Appendix G. It is this input

ﬁle that NLIN uses to ﬁnd an estimate of the thermal diﬂ‘usivity.

Temperature as a Function of Pixel Number
Copper Sample Alter 3 Seconrb of Healing

 

 

 

 

29
I"!
’ Q
\
g 2. “I x
E
8 f ~h‘
§ or: \
l- 27 -
l” :
S
26 ‘T T f
0 1CD 2CD 300 400
Pixel Nunber

Figure 5.12. Temperature as a Function Pixel Number. This temperature distribution
was obtained using a calibration relating temperature and gray scale.

5.3 Experimental Resyltsjor Veriﬁcation Materials
The copper and iron samples are measured in this study to verify the general test
procedures. The thermal properties of high purity copper and iron materials are well

deﬁned in a National Bureau of Standards Journal entitled “The Thermal Conductivity of

102

Selected Materials.” In this journal, Powell, Ho, an Liley state that the thermal
conductivites of high purity copper and iron at 300K are 397 W/mK and 80 W/mK
respectively. These recommended values are thought to be accurate to within :3 percent
at room temperature. The values of the thermal diﬂirsivities were extracted from the
thermal conductivites using the published pC, values (Copper pCp = 3.349 x 106 J/m3K ,
Iron pCp = 3.517 x 106 J/m3K)[Incropera and Dewitt, 1991]. Based on this calculation,
thermal diﬁ’usivities of the copper and iron were determined to be 115.94 x 1045 mZ/s and

22.74 x 10‘ mz/s respectively.

5. 3. I Experimenﬁtaﬂesultsfor Copper

Several tests were conducted on the copper sample. Variations in these tests were
used to see how effects such as natural convection and radiometer spatial resolution
inﬂuenced the experimental results. In the following paragraphs, a description of the
experimental results for a typical test is given and is followed by a summary of the results
for the copper sample.

The measured transient temperature distributions along a horizontal line across the
center of the copper sample aﬁer 3.0, 5.0, and 7.0 seconds of heating are shown in Figure
5.13. These times were selected to satisfy the quasi-steady state heating assumption.
Since the temperature data for the heated area (0<r<a), were not used in the development
of the mathematical model, the temperature distributions for the corresponding locations
are not represented in Figure 5.13. As illustrated by the linear temperature increases with
time at speciﬁc radial locations, these measured temperatures are characteristic of the

quasi-steady state heating period. The program NLIN uses these measured temperature

103

distributions along with the mathematical model in equation 4.30 to determine the
calculated temperatures. These calculated distributions are also plotted in Figure 5.13 as
green symbols. The curves for both measured and calculated temperature data, consist of
876 temperature values obtained at three different times and at 292 diﬁ‘erent radial

positions across the diameter of the disk.

Temperature as a Function of Radial Position
Copper Sample

 

Temperature (°C)
13

    

 

” _
27 _
‘ Measure Temperatures

 

 

26 ‘ . Calqhted Temperatures

 

-0.02 -0.01 0.00 0.01 0.02
Radial Position (m)

Figure 5.13. Measured and calculated temperature distributions along a horizontal line
across the center of the copper sample. This is sample has a diameter of 5. 08 cm and a
thickness of 5 00m.

The spatial distribution of the residuals for the three selected times are shown in

Figure 5.14. The residuals represent the differences between the temperatures measured

by the radiometer and the temperatures calculated NLIN. For this particular experiment,

the standard deviation of the residuals is 0.125°C compared to a temperature rise of 4.0°C

across the diameter of the disk.

Residuals as a Function of Radial Position

 

 

 

 

 

 

Copper Sample
°6 0 7
g 0 6 ‘ Residuals at 3 seconds
% ' l 0 Residualsat5 seconds
> 0-5 l . Residualsat? seconds
3 0.4 l
E o e o
a 0.3 - ° :9
3 . I e A‘
_ o O I I I
(.I) 0.2 ;’\n no.5 “=:- $15,: ..1,',' . ‘: ’
g 0-1“ ‘z I VI: : r ‘fl%“‘ zf:"
_ ‘ . 4 . 4' r
6 0.0 “ ‘ 9. [AR .‘ ‘ I i I I I
> 4‘; i‘ A o t '. “I #1. 10"...
_, A I A A. .
3'01 :~-- ‘*“T.‘3:‘ $‘I: ? ‘ ‘ A AI‘I“'I “
awn-t“ a . . .. .»
8 H. ' $ ‘ I ‘-
E413 J _- ' o _ -'
A
3 —o.4 l f
3 a.
g -o.5 l ‘
g -0.6 1
E 4) 7
8 . I I I l I
05 -0.02 -0.01 0.00 0.01 0.02

Radial Position (m)

Figure 5.14. The distribution of residuals across the diameter of the copper disk.

The residual pattern along the majority of the disk’s diameter is random. Such
patterns are characteristic of random rather than systematic errors. However, near the
center and along the edges of the test sample a trend does seem to exist. In these regions
the measured temperatures are consistently lower than the calculated temperatures
provided by the mathematical model (i.e. negative residuals). Trends such this result from

poor spatial resolution and will discussed further later in this chapter.

105

In general, Figure 5.15 illustrates the trend of sequential estimation. In this case of
the thermal diffusivity is estimated using NLIN. NLIN begins to estimate the desired
parameters based on initial guesses and one data observation. Then, another observation
is added to the previous set of data and the estimation process is repeated before the next
observation is added. The estimated values of parameters are very uncertain during the
ﬁrst 100 observations. However, as the number of observations are increased, the value
for the estimated parameter stabilizes. This stabilization in the estimated parameter is a
characteristic of sequential estimation and indicates that the observations accurately ﬁt the
proposed model.

More speciﬁcally, in the case of this test, the 876 radial temperature measurement
in Figure 5.13 are the observations. In Figure 5.15 the ﬁrst 292 data points represent the
sequential estimates based on the temperature distribution at 3 .0 seconds. The estimates
between 292 and 583 illustrate how the parameter changes as a result of adding the
information from the temperature distribution at 5.0 seconds. The estimates of 584 and
876 are the result of adding the temperature information captured at 7.0 seconds. At this
point, the estimated values are stable and the data is in good agreement with the thermal

model.

Sequential Estimate for Thermal Diffusivity
Copper Sample

O.(XD18

 

mzls)

O.CXI)16 -
0111314

0.00012 «
a. = 104.51 x 10" m’Is

    

0.(XD10 e
um ~
Om —
0.0mm ~

0.00002 —

 

 

0.00000 1 I 1 n
O 200 41) 600 8!)

Observation Number

 

Sequential Estimate for Thermal Diffusivity (a

Figure 5.15. Sequential Estimation for the thermal diﬂusivity for the copper disk using
the non-linear sequential estimation program, NLIN.

Aﬁer a series of 42 tests conducted on the copper the average thermal diﬁ‘usivity
was determined to be 100.297 x 1045 mz/s with a standard deviation of 2.91x10‘s mZ/s
(coeﬁicient of variation of 0.029). This value is 13.5 % less than the published value
reported by Powell, Ho, and Liley in their thermophysical property reference manual. A
plot illustrating the magnitude of the difference between the experimentally determined
and published thermal diffusivity is shown in Figure 5.16. A numerical listing of the

estimated values is presented in Appendix J.

107

The Estimated Thermal Diffusivities for Copper Sample

140
1301
120ﬁ
1101
100 ‘WW’.
90 4
80 ..
70 -
60 -
50 e
40 4
30 -
20 4
10 ~

 

Thermal Diffusivity , a ( x 10‘ m’Is)

 

 

 

0 I T f I

0 1o 20 30 40
Test Number

 

December 28, 1996 — Initial Tests on copper samples

March 16. 1996 — Distance between radiometer and sample is 13.0 cm
March 16, 1996 — Distance between radiometer and sample is 14.5 cm
March 16, 1996 — Distance between radiometer and sample is 16.0 cm
March 3, 1996 — Tests conducted with radiometer in 5° C range.

March 3. 1996 — Tests conducted with radiometer in 10° C range.
March 3, 1996 - Tests conducted with radiometer in 20° C range.
Published Thermal Diffusivity = 115.94 x 10‘ mzls [PowelL Liley, Ho]
Average Estimated Thermal Diffusivity = 100.29 x 10" m’ls

.IDCIOO

 

 

 

 

 

Figure 5. 16. A comparison between the estimated thermal diﬂusivities and the published
values.

108

5.3.2 rimental Results or Iran

The thermal diﬁiisivity of iron is approximately 6 times less than copper. The
quasi-steady state heating assumption is valid when the dimensionless time, atzlb, is
greater than 0. 5. Knowing this, and with knowledge of the published thermal diffusivity,
the ﬁrst sampling time should occur aﬁer 15 seconds of heating. As shown in Figure 5.17,

the selected sampling times for this experiment were 20.0, 30.0, and 40.0 seconds.

Temperature as a Funciton of Radial Position

 

 

 

 

 

 

 

 

Iron Sample
3‘ Curve (1) t = 20.0 eeee
Cave (2) t = 30.0 secs
Curve (3) t = 40.0 sees
33 -
32 - ‘l
8 i
L
2 31 e
3
8
8 30 -
.5.
,_ (3)
29 ‘ (2)
1
28 _ ( )
‘ Meewred Temperaqu
Calculated Temperatures
27 —T Y T T T
0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Radial Position (m)

Figure 5. 1 7. Measured and calculated temperature distributions along a horizontal line ,
across the center of the iron sample. Ihis is sample has a diameter of 5. 08 cm and a
thickness of 100 pm.

A signiﬁcant difference between the iron and copper tests was the magnitude of
the heat ﬂux. Under ideal conditions, it is best to operate the radiometer in the lowest

possible temperature span settings. This acts to minimize the temperature resolution, and

109

maximize the thermal sensitivity of the measurements. Since iron does not conduct heat as
well as copper, the temperature increases near the center of the specimen are such that the
instrument becomes saturated in low temperature span settings. This problem can be
eliminated by attenuating the laser such that the power input is reduced. In the case of
the iron sample, approximately 730 mW of laser radiation was used to heat the sample
during the 40 second period. This was reduced from 3.5 W used to energize the copper
sample during the 7.0 second heating time.

The spatial distribution of the residual values for this particular test is shown in
Figure 5.18. The standard deviation of the residual values is 0.0944, and the pattern is

characteristic of typical gaussian error distribution. As with the copper sample the errors

Residuals as a Function of Radial Position
Iron Sample

 

A Col5veCol6
0 ColSvsCol7
0.5- I Col5vsCol8

 

 

“if? '. 5" *3

 

 

Residual Values (Measued Values - Calculated Values)

 

 

-0.02 -0.01 0.00 0.01 0.02
Radial Position (m)

Figure 5. 18. The distribution of residuals across the diameter of the iron disk.

110

seem to be randomly distributed along most of the diameter, but there is a systematic
behavior near the center and along the edges of the sample.

The low residuals in this experiment are associated with a good ﬁt between the
measured data and the mathematical model. This can be visualized in the sequential
estimate. As shown in Figure 5.19, the estimate for the thermal diﬂiisivity is relatively
constant, even when a small number of observations are considered. In this case the

estimate for d. was 13.98 x 10*5 mz/s.

Sequential Estimate for Thennal Diffusivity
Iron Sanple

 

n =13.Qx 10‘ m’le

 

 

 

 

Sequential Estimate of Thermal Diffusivity (a, m’le)

 

4m '1
2m 7
am i i t t
o 200 am 600 800
Observation Number

Figure 5.19. Sequential Estimation for the thermal diffusivity for the copper disk using
the non-linear sequential estimation program, NLIN.

The average thermal diﬁ‘usivity for 15 experimental tests on the iron sample is
12.64 x 1045 mzls with a standard deviation of 1.34 x 10" m2/s (coeﬁicient of variation of
0.10163). This value is 44.4 % less than the published value given by value given by

Powell, Ho, and Liley in their thermophysical property reference manual. A plot

lll

illustrating the magnitude of the diﬁ‘erence between the experimentally determined and

published thermal diffusivity is shown in Figure 5.20.

Estimated Thermal Diffusivities for Iron Sample

 

28q

 

 

Thermal Diffusivity , a (x 10° mz/s)
3:
O
O
O
O
O
O

 

 

 

o T I T I T I T

0 2 4 6 8 10 12 14 16
Test Numbers

 

0 Estimated Values for lndvichld Tests
Average Estimated Thermal Diffusivity = 12.65 x 10" m’Is
— Published Thermal Diffusivity = 22.74 x 10‘ m’ls [Poweli. Liley, and Ho]

 

 

 

 

Figure 5. 20. A comparison between the estimated thermal dijﬁrsivities for iron and the
published values.
5.4 Mﬁmental Results for C VD Diamond Film

The CVD diamond samples were expected to higher thermal difﬁlsivities than the
veriﬁcation materials. Therefore, the gradients across the sample were low whereas the

absolute temperature rise with time was quite high. The laser had to be operated at

112

power levels which would provide signiﬁcant temperature differences between the center
and outer edges of the sample. Without such gradients, the signal to noise ratio of the IR
camera was not large enough to provide reliable results.

Since convection was neglected in the derivation of the mathematical model, high
temperature differences between the sample and the surroundings had to be avoided.
Evaluation of the heat ﬂow through the sample due to conduction and heat losses due to
convection for different temperature diﬁ‘erence levels showed that for the diamond
specimen an average temperature difference of 15 °C should not be exceeded. In this
case, heat loses due to convection amount to approximately 1% of the heat conduction
term. This problem can be totally eliminated if the temperature data is sampled at smaller
times. The high expected thermal diﬁ‘usivity of these ﬁlms allow for the dimensionless
time to be greater than 0.5 at times as early as 1.0 seconds. Therefore, in order to
minimize the effects of convection, while maximizing the temperature gradient within the
sample, the temperature distributions are sampled at 1.0, 2.0, and 3.0 seconds. These

temperature distributions are shown in Figure 5.21.

Temperature as a Function of Radial Position
Diamond Film Sample AT#4
32

 

314

iii
”K.

Temperature (°C)
'6’:

 

 

 

 

 

a
p
27 ~
26 ..
25 _.
A Measured Temperatures
Calculated Temperatures
24 l l I T T
-0.02 -0.01 0.0) 0.01 0.02

Radial Position (m)

Figure 5.21. The measured and calculated temperature distributions with the C. VB.
diamond ﬁlm sample A T # 4.

The spatial distribution of the residuals is shown in Figure 5.22. Similar to the
patterns in the veriﬁcation materials, the residuals for this test are unifomlly distributed
about zero over the majority of the disk. The standard deviation of these residual values is
0.0827°C compared to a relative temperature difference of 2°C across the surface of the

sample.

114

Residual Values as a Function of Radial Position
Diamond Film Sample - A114

 

0.7

064 ‘ Reﬁnisetteec
' - RedduelsatZeece

0.5 - Residueleataeece

0.4 4
0.3 -l
0.2 4
0.1 a
0.0 ~
«0.1 a
0.2 .
-O.3 -
«0.4 ~
0.5 -
-0.6 ~

0.7 r r r r ' r
-O.(B 0.02 0.01 0.00 0.01 OCR 0.03

Radial Position (m)

 

 

 

 

 

Residual Values (Measured Values - Calculated Values)

 

Figure 5. 22. The distribution of residuals across the diameter of the C W) diamond ﬁlm.

Figure 5.23 illustrates the sequential estimation for the thermal diﬁ‘usivity. This
estimate has a fairly constant value even when a small number of observations are
considered. Similar to the tests with the veriﬁcation materials, this stability in the
estimation proves that the measured temperature distributions are accurately modeled by
the mathematical model. In this case, the thermal diffusivity of diamond sample AT#4 was

determined to be 387.26 x 10‘ m2/s.

Sequenh‘al Estimste of Thermal lelusivity (a. . mzls)

Figure 5.23.. Sequential Estimation for the thermal diﬂitsivity for the iron sample using

0.0005 *

115

Sequential Estimate of Thermal Diffusivity
Diamond Sample - AT#4

 

a =- 38726 x 10" mzls

 

(We a

 

a
3

 

100 200 NO 400 500 000 700
Observation Number

the non-linear sequential estimation program, NLIN.

The reproducibility of the above test was veriﬁed by repeating the same test
several times. In this study, 14 tests were conducted on the diamond ﬁlm sample AT#4,
13 tests on sample ST#192, and 13 tests on sample ST#120. The averages and standard
deviations ofthese tests are 417.50 mz/s .t 23.211 x 10*5 mz/s, 475.29 i 19.86 x 10‘6 mz/s,

and 401.45 i 16.07 x 1045 mZ/s respectively. The variations of these tests are shown in

Figure 5.24 (a.), (b.), and (c.).

 

Thermal Diffusivity, a x 10° male

Thermal Diffusivity. a x 10" mzls

520

116

Estimated Thermal Diffusivities for Diamond Sample AT#4

 

 

 

Estimated Values for Individual Tests
Average Estinnbd Themal Dl'l'usivity a. = 417.” 1110‘6 mzls

 

 

 

 

 

 

I V T

4

T

5

r

6

Y Y ﬁr l

7 8 9 10
Test Nurrber

T

11

T

12 13 14 15

(a.)

Estimated Then'nal Diffusivity for Diamond Sample ST#192

 

 

320d

 

 

Em Values for Individual Tests

 

 

 

V T 1

2 3

‘l'

4

Y

5

7

 

—— Average em Thsnml Dlﬂusivity a. . 475.29 x 10‘ "1’1.

7 r 7 T T

6 7 8

Test Number

9 10 11 12 13 14

(b.)

117

Estimated Thermal Diffusivity for Diamond Sample ST#120

 

L

d

 

 

v Estimated Values for Individual Tests
-— Average Estimated Thermal Diffusiv'ty, a. = 401.45 x 10‘ mzls

¥_J_

 

 

Thermal lefuslVlty 01 x 10° mzla
§§§§§§§§§§§§
1
11

 

 

 

f Fl TiT

2 3 4 5 6 7 8 9 10 11 12 13
Test Number

A

(c.)

Figure 5. 24. The experimental results for C VD diamond ﬁlm. (a.) Sample A T# 4, (b.)
Sample ST#192, (c.) Sample ST#120.

If the estimated thermal diﬁ‘usivities are multiplied by the measured value of pCp
[pCp = 1.8981 x 106 J/m3 °C (Graebner, 1996)] the thermal conductivity of each of this
sample can be calculated. The calculated thermal diﬁiisivities for sample AT#4, ST#192,
and ST#IZO are 791.5077 W/mK, 902.14 W/mK, and 761.99 W/mK respectively.
These estimated themal conductivities are plotted as a function of thickness and

compared estimates by other researchers in Figure 5.25.

118

Themlal Conductivity as a Function of Film Thickness

 

 

 

 

 

2500
2&1) - s
§
5 .
O
s 15(1) 1 .
§ 1G1) . o
- I O O
E I s ° '
8 ~ ' t
.. '9 a
E 5°°‘ ' °
” bu
1'5 a;
0 100 200 300 400 500
Film Thickness (tun)
e Graebnaretal.(1992)
0 Graebnerelal. (1993)
e Graebner(4192)
0 Graebneretal.(1992)
I Albln(1990)
a Anthony(1991)
a Morrelli (1988)
I Baba(5l91)
A GraebnerU/QQ)
a Petrovsky(1992)
. Michigan State University (1996)

 

 

 

Figure 5.25 A plot of the estimated thermal conductivity as a ﬁmction of ﬁlm thickness.
This plot illustrates how the estimate at Michigan State University compare to estimates
ﬁom other research groups.

5. 4. 1. Non-Uniform Thermal Properties of C VD Diamond Film

CVD diamond ﬁlm grows in a columnar structure with a grain size which starts
out very small and typically increases with increasing ﬁlm thickness as grains with certain
orientations dominate [Graebner et al, 1992]. A schematic representation of a diamond
ﬁlm’s cross section in Figure 5.26 illustrates this columnar microstructure where the grain
size increases with the height above the substrate surface. This current technique involves

measuring the thermal conductivity according to the thermal transport in the plane of the

119

ﬁlm. To the extent that the heat heat-carrying phonons are scattered at grain boundaries,
a thermal conductivity gradient is expected. For example, in recent years J.E. Graebner
has done a signiﬁcant amount of work determining the sources of thermal resistance and
measuring the local thermal conductivity of CVD diamond ﬁlm as a function of height

above the substrate surface [Graebner et a1, 1992].

Growth Surface

 

 

Substrate Surface
Figure 5. 26. A schematic representation of the cross section of the C VD diamond ﬁlm.
This representation illustrates the columnar microstructure responsible for the increasing
grain size with distance for the substrate surface. [Graebner et al, 1992]

According to the results of Graebner, the thermal transport along the growth
surface is diﬂ‘erent than that of the substrate surface. The developed mathematical model
assumes that the temperature through the thickness of the ﬁlm is uniform. In order to test
the model the test procedure in Section 5.4 was repeated for individual tests with the
substrate and growth surfaces facing the radiometer.. Vlfrth the test specimen in these

orientations and the other experimental conditions constant, the temperature distributions

during the quasi-steady state heating period were acquired. These temperature

120

distributions, shown in Figure 5.27, illustrate that there is not a signiﬁcant difference in

thermal transport between the two conditions.

Temperature as a Function of Radial Position
Diamond Sample AT#4

32

 

Situation # 1 - Temperature measurements made along substrate surface.

31 Situation 5 2 - Temperature measurements made along growth surface.

30-
29-
28-

27‘

Temperature (°C)

   

1 Second

25-

24-

 

 

 

23 l f I l ‘1
-0.02 -0.01 0.00 0.01 0.02

Radial Position (m)

 

Situation # 1 - Temperature Distribution at 1 second
Situation # 1 - Temperature Distribution at 2 seconds
Situation 6 1 - Temperature Distribution at 3 seconds
Situation # 2 - Temperature Distribution at 1 second
Situation # 2 - Temperature Distribution at 2 seconds
Situation 5 2 - Temperature Distribution at 3 seconds

0 C D . I D

 

 

 

Figure 5.27. The transient temperature distributions for two tests conducted on diamond
ﬁlm sample AT #4. This ﬁgure illustrates that using this measurement procedure, the
microstructural characteristics of the growth and substrate surfaces do not contribute
appreciable diﬂ'erences in thermal transport.

As with the temperature distributions, little difference was found in the estimated

thermal diffusivity. Hence, the estimated thermal diffusivity using this measurement

technique seems to be insensitive to the sample’s orientation and any possible variations in

121

the thru-thickness direction. In 1991, Lu and Swan used their converging wave technique
and also found insigniﬁcant differences between the results when measuring the

temperature along the substrate and growth surfaces.

5. 5 Experimental Uncertaing

The experimental uncertainty is a measure of the accuracy of the method used in
determining the thermal diffusivity and accounts for uncertainties in quantities such as
temperature and radial position. It acts as a global uncertainty which is driven by the
precision with which all of the experimental parameters can be measured [Herr, 1993].
The uncertainty in the measurement of the thermal diffusivity is determined ﬁ'om the

expression,

mire”) {La Mei.) 4221,.) {an} .[e H (5.1)
ar é’r at as, da é’b

where the terms 601/61; are the sensitivity coeﬁicients determined from equation 4.27 and
the Ag terms are the estimated errors in the measurements. The experimental uncertainty
is calculated for the conditions employed when measuring the properties of the CVD
diamond ﬁlm. The experimental parameters, their uncertainties and their corresponding

contributions to the uncertainty of the thermal diffusivity are present in Table 5.1.

122

 

 

 

 

 

 

 

 

 

 

 

Experimental Parameter Estimated Uncertainty Contribution to the uncertainty
(i) in Parameter (Ag) in the thermal diffusivity (mZ/s)
a = 0.0005 m Constant with no uncertainty 0
Bering Diameter
b = 0.0254 m Constant with no uncertainty 0
Sample Diameter
[31 Estimated Value 0
Laser Effect Term
8;, Estimated Value 0
Initial Temperature
r = 0.0254 m Ar = 0.000282 at 3.2258 x 10‘6 m7/s
Radial Location
t = 2.0 s At = 0.0303 5 5.0545 x 10‘ m2/s
Time Indication
T(r,t) = 30 °C AT(r,t) = 0.11°C 35.48 x 10‘ mz/s
Radial Temperatures

 

Table 5. 1 Experimental Parameters, their estimated uncertainties and the corresponding
contributions to the uncertainty of the thermal diffusivity

The experimental parameters, “a” and “b”, correspond to the diameter of the
heated region and the sample diameter respectively. These parameters are constants
which are entered directly into the input ﬁle of the NLIN program and are ignored in this
uncertainty analysis. The parameters Br and B3 are estimated along with the thermal
diﬂ‘usivity and uncertainties in these values are ignored. The uncertainty in “1” results
ﬁom improper radiometer and sample alignment causing spatial distortions and was
determined to be 0.000282 m. Improper alignment causes errors in the assignment of
radial position to individual temperature measurements. This value was selected to
represent a worse case scenario in which the assigned radial position was off by 2 pixels
(i.e. 0.0508 m sample dissected into 360 datum points, each pixel represents 0.000141

m). The uncertainty in “t” is related to the timing resolution of the video timer and the

 

123

delay associated with the LabVIEW program used to externally initiate timing. Since the
frame rate of the radiometer’s output is 30 Hz, the uncertainty in “t” results from the delay
in the LabVIEW program causing the timer’s initiation to be delayed by one frame. Under
this worst case scenario, the uncertainty in “t” is 0.0303 seconds. The uncertainty in the
radial temperature measurements relies on the accuracy of the radiometer. The
radiometer’s accuracy was determined by analyzing a isothermal and constant temperature
disk. In this study, temperatures ﬂuctuations in time at speciﬁc locations were measured.
A typical plot of the temperature at one point as a function of time is shown in Figure
5.28. From a series of seven similar tests these ﬂuctuations produced an average standard
deviation of 0.11 °C. It is this value that is chosen to represent the accuracy of the
radiometer. Based on these initial tests, it is behaved that these ﬂuctuations are a strong
function of the operating conditions of the radiometer (i.e. the radiometer’s temperature

range and image average settings).

Temperatureatonepointasafunctionoftime

 

 

 

 

 

 

 

 

 

23.50
—AverageTempsratue=22.298°C
2325i 0 Individual Temperame Measuemerts
Standard Deviation = 0.109 °C
2300 1
8 22.75
2
0
g 2250 0
O
O " e. . A s ° . °
I- 22251 e . 0 v ' ° “ﬂ ' e
O . .
22.00 4
21.75 .
2150 T Y Y T Y T T T T T ’T I T 1' 7
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 0.5 7.0 75 8.0
Tine(sec)

Figure 5. 28. Temperature ﬂuctuations at one specific location on a isothermal and
constant temperature sample as a function of time. The standard deviation of these
ﬂuctuations are used to represent the accuracy of the radiometer.

124

By substituting the values presented in Table 5.1 into equation 5.1 the calculated
experimental uncertainty for the in plane thermal diffusivity of CVD diamond was
determined to be i17.47 x 10‘ mZ/s. Since this value is approximately equal to the
average standard deviation of the experimental results (oavgmge = 19.71 x 10‘3 mz/s) , it
can be assumed that the errors in the measured experimental parameters are accurately
modeled. The major contribution to the calculated uncertainty resulted from errors in
temperature measurement.

The diﬁ‘erence between the experimental uncertainty and the calculated uncertainty
for both the copper and iron samples were signiﬁcantly different. The major diﬁ‘erence in
the uncertainty model between the tests conducted on the diamond, iron and copper
samples results from the times at which the data was sampled. As the heating time is
increased, the effect of errors in the measured temperatures decreases while the eﬁ‘ect of
errors resulting from misrepresented radial positions are magniﬁed. In this case, the
calculated uncertainty for the copper and iron tests were determined to be 13.90 x 10'6
mz/s and 15.87 x 1045 mZ/s respectively. Although these uncertainties are signiﬁcantly
higher than the experimental uncertainty, it is interesting to note that the calculated
uncertainties closely approximate the measured uncertainty if errors in radial location are

ignored.

125

5. 6 Discussion QfExperimentcLl Rem

The experimental results using this measurement technique are not very
encouraging. Based on the tests conducted on the copper and iron veriﬁcation samples, it
is clear that the current procedure underestimates the thermal diffusivity.

The magnitude of the discrepancy seems to vary based on the thermal properties of
the test specimen. For the copper sample, there is a 15.2 % difference between the
experimental determined thermal diﬁilsivity and the published value. This diﬂ‘erence
between estimated thermal diffusivity and the published value is 44.4% on tests
conducted on the iron sample. The physical dimensions of the two samples are identical
and the experimental techniques vary only as a result of the material’s thermal diffusivity.
In order for the data to be sampled during the quasi-steady heating period, for example,
the sampling times and the amount of applied heat ﬂux must be changed based on the test
material.

The estimation process is driven by the measured temperatures. The accuracy of
the estimation depends on how accurately these temperatures are measured. It was
determined during this research that this accuracy is hindered by systematic errors caused
by the spatial resolution of the radiometer. This systematic error causes the data to be
“blurred or averaged ” about a speciﬁc region.

This averaging phenomenon can be illustrated by examining the infrared image in
Figure 5.29. In this Figure, a test specimen with two thin ﬁns attached to a ﬂat surface is
placed in the ﬁeld of view of the radiometer. The background temperature on the left
hand side of the infrared image corresponds to the ambient conditions within the

laboratory. To illustrate this blurring ﬁmction, an ice bath was placed on the right hand

126

side of the infrared image reducing the background temperature. Although the two ﬁns
are the exactly the same size, the addition of the ice bath causes an apparent difference in

their dimensions.

133-80 Dﬂiﬂﬂiﬂﬂiﬂﬂ

AMBIENT

ICE BATH
CONDITIONS AS BACK-
AS BACK- GROUND
GROUND

 

Figure 5. 29. An inﬁared image of a ﬂat test specimen with two thin ﬁn attached to the
surface. This image is used to illustrate the blurring or averaging phenomenon that
causes systematic errors in the measured temperatures

More signiﬁcantly, for the thermally diﬁirsivity tests recently conducted, the
averaging phenomenon causes an apparent temperature difference between the two ﬁns as
shown in Figure 5.30. Using the test conﬁguration described above, the temperature
distribution along the centerline of ﬁns is obtained and the inﬂuence of the ﬁns can be

visualized.

127

Temperature distribution along test specimen
with ice bath behind one ﬁn. In this case
radiometer is in the image mode.

 

 
     
   

 

 

 

 

 

30
LEFT FLAT PORTION RIGHT
OF TEST SPECIMEN
29 s
r
g 28 .1
2
3 .
g 27 .
O
E- lnﬂuence of Ice Bath °
0
I— 26 4 o
25 ~ s
O -
24 1 I I I I I
0 100 200 300 400 500 600
X Directions (pixels)

Figure 5. 30. An illustration of the apparent temperature difference caused by the
additional of the icebath to the background of the right hand side of the infrared image.
Problems such as those in Figures 5.29 and 5.30 are caused by the radiometer’s
spatial resolution. These problems also help to explain the discrepancies between the
estimated and published thermal diffusivities. It is clear that the averaging phenomenon
causes apparent temperature differences when the temperature of the surrounding area is
signiﬁcantly diﬁ‘erent from the measured location. Although the surrounding areas on the

test sample are not signiﬁcantly different than those at the measured location for the

128

thermal diﬁ‘usivity tests, they still have an inﬂuence. The inﬂuence of the surrounding
areas become more signiﬁcant as the temperature gradient along the diameter of the
sample increases. Based on this argument it seems logical that the temperature
measurement errors would have a larger inﬂuence on the estimated thermal diffusivity for
samples with smaller thermal diﬁ‘usivities.

In estimating the thermal diffusivity we depend on the imaging system to have a
very small spatial measurement resolution. The radiometer’s spatial resolution and the
tests conducted to measure it are discussed in detail in chapter 3.1.1. For example, in the
current experiments a 2 inch diameter sample is positioned such that the entire radiometer
ﬁeld of view is used. In this case, the radiometer is not conﬁgured with external optics
and positioned at a working distance approximately 15 cm from the sample. As the test is
being conducted the image is broken into many discrete points. These discrete points are
oﬁen called datum points or instantaneous ﬁeld of views (detector size projected on the
object). Each datum represents a location and local image intensity and is considered a
pixel. In one horizontal line scan there are 364 pixel locatibns. Therefore, for the 2 inch
sample a measurement spatial resolution of 140 um is required. As shown in Figure 3.6,
the slit response function for this resolution is approximately 70%. As a result, the
required resolution is such that details can be discerned, but accurate temperature

measurements can not be inferred.

Chapter 6

Summary and Conclusions

The goal of this research was divided into two main objectives. The ﬁrst objective
was to develop the capabilities of an experimental system that could be used to measure
the thermophysical properties of CVD diamond ﬁlm. The second objective was to
demonstrate the use of this utility. In this case, the newly developed experimental
techniques were combined with existing analytical tools to determine the thermal
diffusivity of copper, iron, and diamond samples. Although this research is driven the
measurement of CVD diamond ﬁlm, the copper and iron samples were measured validate
the experimental procedures.

The developed experimental system consists of a Nd:YAG laser, two inﬁared

temperature measurement systems, a data acquisition and instrument control system, and

129

130

laser diagnostic equipment. Together this system provides an optical, non-contact, and
non-destructive means of heating and temperature measurement.

As the heating source the Nd:YAG laser offers a great deal ﬂexibility. Without
the use of external optics, this laser produces a beam 0.7 mm in diameter with a maximum
power of 15.5 Watts (power density ~ 4kW/cm2) The laser’s power can be attenuated
optically using beamsplitters. These beamsplitters offer a 50% reduction in beam intensity
when orientated at a 45° angle incident to the incoming laser beam. Therefore, if both
beamsplitters are used the laser’s power can be reduce by 75%. Further optical
attenuation can be achieved through the use of neutral density ﬁlters. When using these
neutral density ﬁlters, however, care must be taken since they have a low and unknown
damage threshold.

Major reductions in laser power can also be achieved by adjusting the lamp
current. This method is not recommended since large reductions in lamp current (i.e.
greater that ~ 23 amps) cause thermal changes with the lamp housing and often cause
deterioration in the beam quality (i.e. cause high order modes in the beam proﬁle or
reductions in beam stability).

The spatial distribution of radiation is easily modiﬁed through the use of optical
components. Although the available optics only allow us to expand the beam, form a line
of uniform radiation, or focus the radiation to a point, the possible spatial distributions are
only limited by the imagination of the user.

Two methods are available for controlling the temporal distribution of radiation.
Internal Q-Switching allows for short, high intensity bursts of energy to be deposited

along the surface at rates between 100 Hz and 80kHz. Externally, the beam can be

131

chopped at rates as high a 100 Hz using the Uniblitz shutter system. The use of this
shutter is limited by electrical problems within the drive control and because of the low
damage threshold of the shutter.

In order to gain a thorough understanding of the characteristics of the laser beam
and optimize the laser for a particular application, laser beam diagnostic tools were
developed. These newly developed tools allow for the measurement of the beam’s
diameter, energy, power, proﬁle, and temporal dependence.

Temperature measurements can be made with two inﬁared measurement systems.
These systems offer a great deal of temperature information in time and/or space. The
Inframetric’s thermal imaging system has the ability to capture entire thermal events at 30
Hz or temperature distributions along one line at 8 kHz. The EG&G inﬁared point
detector has the ability to make temperature measurements of one point at 2 MHz.

Regardless of the measurement technique the data has to be processed. The
output of the thermal imaging system is a standard 8-bit video output, and for the ﬁrst
time it was demonstrated that a general image processing system (IPPLUS) could be used
to analyze the data.

Similar to other transducers, the output of the point detector is a voltage. This
output can be recorded using the newly developed data acquisition and instrument control
system. This system contains two data acquisition boards programmed with LabVIEW.
The AT-MIOI6F board has multiﬁlnctional analog, digital and timing I/O capabilities,
and allows for data at 8 differential input channels to be collected at a maximum rate of
200kHz . The EISA-A2000 board can be used to digitize signals resulting from high speed

events and is used when the data acquisition capabilities of the AT-MIO—16F are not

132

suﬂicient. The board can sample one channel at 1 MHz, two channels simultaneously at
500 kHz, and four channels at 250 kHz.

After the experimental components were characterized the utility of the system
was demonstrated. In these experiments, temperature measurements were made with the
infrared imaging system and the circular samples were energized in the center with the
Nd:YAG laser. The IPPLUS image processing system was used to capture thermal
events at times consistent with the quasi-steady state heating period. The temperature
distribution across the center of the sample was located and extracted with the image
processing system. This information was then used along with the non-linear sequential
estimation program, NLIN, to estimate the thermal diffusivity.

The test results on the copper and iron samples were quite discouraging. The
average experimentally determined thermal diffusivity and standard deviation for the
copper and iron samples are listed in Table 6.1. When compared to the published values,

it is clear that this experimental technique has tendency to underestimate the thermal

 

 

 

 

diﬂ’usivity.
Sample Number Average Standard Published Percent
Material of tests Estimated 0. Deviations a[m2/s] Difference
[ml/S] [ml/S]
Copper 42 100.297x10'6 2.91x10" 115.94x10*S 13.5 %
Iron 15 12.64x10'6 1.34x10'6 22.74x10*s 44.4 %

 

 

 

 

 

 

Table 6.1. The estimated thermal diﬂusivity for experimental tests conducted on copper
and iron samples.

As for CVD diamond, the average experimentally determined thermal diffusivity

and standard deviation for three samples are listed in Table 6.2.

 

133

 

 

 

 

Diamond Average Number Average Standard
Sample Sample of tests Estimated 0. Deviations
Thickness [ml/s] [mzls]
(um)
AT#4 370 14 417.50x10*S 23.211x10'6
ST#192 370 13 475.29x10'6 19.86x10'6
374120 240 13 401.45x10‘6 16.07x10'6

 

 

 

 

 

 

 

Table 6.2. The estimated thermal drﬂusivities for experimental tests conducted on three
C VD diamond samples.

If the estimated thermal diffusivity values are combined with published density and
speciﬁc heat values the thermal conductivity can be extracted [Graebner, 1996]. Based on
this calculation, the thermal conductivity values are 791.5077 W/mK, 902.14 W/mK, and
761.99 W/mK. A plot of these values as a ﬁrnction of thickness is shown in Figure 6.1.
Examination of this plot illustrates that these estimates seem to be lower than the
established trend. The most direct comparison between these estimates can be made wth
the results of Graebner. In this 1992 test, Graebner, Jin, Herb, Karnmlott, and Gardinier
determined that the thermal conductivity of a 355 pm thick diamond sample was
approximately 1500 W/rnK. Although the absolute accuracy of the Graebner estimate is
unknown, it seems to verify that our experimental technique may underestimate the

thermal diﬂ‘usivity for CVD diamond ﬁlms.

134

Thermal Conductivity as a Function of Film Thickness

 

25C!)

15nd.

10m~s0 0

Thermal Conductivity (chm K)
I

 

 

 

1' Y I

o 100 200 300 400 500
Film Thickness (tun)

 

O Graebner at at. (1992)
Graebner et at. (1993)
Graebner(4192)
Graebner et al. (1992)
Albin (1990)

Anthony (1991)
Morrelli (1988)
Baba(5l91)
Graebner(1l92)
Petrovsky(1992)
Michigan State University (1996)

.sesssa

 

 

 

Figure 6. 1. Thermal diﬂusivity as a function of ﬁlm thickness. This plot illustrates how
the estimates at Michigan State University compare to the estimates made by other
research groups.

135
List of References
Annamalai, N.K., Sawyer, J., Karulkar, P., Masyara, W., and Landstrass, M., ”Silicon-on-

Diamond Field-Effect Devices,” Proceedings of the 3“1 IUMRS International
Conference on Advanced Materials, Toyko, Japan, August 1993

Albin, S., Winfree, W.P., and Crews, B. Scott, “Thermal Diffusivity of Diamond Films
Using a Pulsed Laser Technique”, J. Electrochem. Soc, Vol. 137, 1990, No. 6.

Baba, K., Aikawa, Y., and Shohata, N., “Thermal Conductivity of Diamond Films” L
Appl. Phys. Vol. 69, 1991, No. 12.

Beck, J .V. “Parameter Estimation Concepts and Modeling: Flash Diﬂhsivity Application.”
June 1996

Beck, J.V., and Arnold, K.J., Piameter Estimation in Engineering and Science, John
Wiley and Sons, 1977.

Burleigh, D.D., Kuhns, DR, Cowell, SD, and Engel, J.E., "Thermographic
nondestructive testing of honeycomb composite structural parts of the Atlas space
launch vehicles.” Thermosense SPIE Volume 2245. pp. 152-163, June 1994.

Dereniak, E.L., Crowe, D.G., thical Radiation Detectors, John Wiley and Sons, 1993

136

Graebner, J.E., Jin, S. Karnmlott, G.W., Bacon. B., Seibles, L. and Banholzer,
W.,“AnisotrOpic Thermal Conductivity in Chemical Vapor Deposited Diamon .”,
J Appl Phys, Vol 72, 1992, No. 11

Graebner, J.E., Jin, S. Kammlott, G.W., Herb, J.A., and Gardinier, C.F., “Uncertainty
High Thermal conductivity in Diamond Films”, Appl Phys. Lett., Vol.. 60, 1992,
No. 13.

Graebner, J.E., Jin, S. Kammlott, G.W., Herb, J.A., and Gardinier, C.F., “Large
Anisotropic Thermal Conductivity in Synthetic Diamond Films”, Letters to
Nature Vol. 359, 1992, p. 401.

 

Graebner, J.E., Mucha, 1A., Siebles, L., and Karnmlott, G.W., “The Thermal
Conductivity of Chemical-Vapor-Deposited Diamond Films on Silicon”, J. Appl.
Phys, Vol. 71, 1992, No. 7.

Graebner J.E., Reiss, M.E., Seibles, L., Hartnett, T.M., Miller, R.P., Robinson, C.J.,
“Phonon scattering in chemical-vapor-deposited diamond”, The America
Physical Society. Vol. 50, 1994, No. 6.

Graebner J.E., “Measurements of the Speciﬁc Heat and Mass Density in CVD Diamond”
Diamond and Related Materials , April 12, 1996

Halmsten, P., and R. Houis, ”High resolution thermal scanning for hot strip mills."
Thermosense SPIE Volume 1313. pp. 322-331, June 1990.

137

Harnrelius, T.E., " Accurate temperature measurement in thermography. An overview of
relevant features, parameters and deﬁnitions" Thermosense SPIE Volume 1467.
pp. 448-457, June 1991.

Hecht, Jeﬂ‘, The Laser Guidebook, 2"" Edition, Tab Books, Blue Ridge Summit, PA
(1992).

Hey, Tony and Patrick Walters, The Quantum Universe. Cambridge University Press,
Cambridge, UK (1987).

Holst, Gerald 0, Testing and Evaluation of Infrared Imaging Systems, JCD Publishing
Co., Maitland, FL, 1993.

Incropera, F .P., and DeWitt, D.P., Introduction to Heat Transfer, 2'” edition, John Wiley
and Sons, 1990.

Jenkins, Francis and Harvey White, Fundamentals of Optics, 4‘h Edition, McGraw-Hill,
New York , NY (1976).

Koechner, Walter, _So_lid State Laser Engineering, 3'“ Edition, Springer-Verlag, New
York, NY (1992).

138

Morelli, D.T., Beetz, CR, and Pen'y, T.A., “Thermal Conductivity of Synthetic Diamond
Films”, The American Institute of Physics, Vol. 60, No. 6, September, 1988.

Powell, KW, Ho, C.Y., Liley, P.E. , “Thermal Conductivity of Selected Materials”,
NSRDS-NBS 8, November 25, 1966

Puram C.K., “Measurement of steady and unsteady temperatures using infrared
thermography.”, Fundamental ExperimeLtal Measurements in Heat Transfer
ASME1991. HTD-Vol. 179.

Shelmire, Gary, “How to make accurate laser output measurements,” Laser Focus World,
April 1993

Siegrnan, A.E., Sasnett, M.W., Johnston, T.F., “Choice of Clip Levels for Beam Width
Measurements Using Knife Edge Techniques.” IEEE Journal of Quantum
Electronics, Vol. 27, No. 4, April 1991

Vorobei, V.V., “Thermoelastic Problems for Monodirectional Fiber Composites Exposed
to Pulse Thermal Action”, Soviet Applied Mechanics, Vol. 22, 1986.

Wilson, J. and J .F .B. Hawkes, Optoelectronics: An Introduction. 2"" Edition,
Prentice Hall, New York, NY (1989).

139

Wright, RE, Chirh K. Puram, and Kamran Darabeigi, "Desirable features of an infrared
imaging system for aerodynamic research." Thermosense SPIE Volume 1682. pp.
315-324, June 1992

Zhu, W., Stoner, R., Williams, BE, and Glass, J .T., “Growth and Characterization of
Diamond Films on Nondiamond Substrates for Electronic Applications”,
Proceedings of IEEE, Vol. 79, No. 5, May 1991.

140

APPENDIX A - LASER THEORY

The physical mechanisms of light emission are subtle and complex. Factors such as
the chemical makeup of the light-emitting material, its physical state (solid, gas, plasma),
the manner of excitation, temperature and even pressure can aﬂ‘ect the kind of light
created by incandescent lamps and gas discharges. These effects, however, only hint at
the forms of light emission.

Attempts to understand laser emission lead to Plank’s radiation law and the dawn
of quantum theory. Albert Einstein, who never hilly accepted the philosophical
implications of quantum theory, conceived two of its most fundamental concepts: the
photon (1905) and stimulated emission (1917). Both concepts were crucial to the
invention of the laser.

Niels Bohr, the “ardent champion” of quantum theory, constructed the ﬁrst
quantum model of an atom in 1913. Using this model he was able to accurately predict
the emission-line frequencies of atomic hydrogen. Soon afterward, Arnold Sommerfeld,
Wolfgang Pauli and others made important reﬁnement to the existing model which led to a
more complete explanation of line spectra and established a physical foundation for the
periodic table of elements.

Vlfrth ﬁirther investigation in the 1920’s, the Bohr model began to gain a ﬁrm
theoretical footing. “This help came in the form of Louis de Broglie’s particle waves,
Werner Heisenberg’s matrix mechanics, Schrodinger’s wave equation, and Born’s

probability of wave packets” It took just three decades for quantum theory to become a

141

new and successful explanation of matter and light. Today, quantum mechanics plays a
leading role in our present understanding of the universe.

The Bohr-Sommerfeld model, which consists of negatively charged electrons
orbiting around a positively charged nucleus along speciﬁc paths called orbitals. The
position of these discrete orbitals depend on a complex set of conditions, such as the
number of electrons surrounding the nucleus, the number of protons in the nucleus, the
electron spin, the presence of nearby atoms, and the existence of electronic and magnetic
ﬁelds.

Each orbital deﬁnes a unique, stationary energy state within the atom. When all of
the electrons occupy orbitals that have the lowest potential energies, the atom is said to be
in its ground state. At absolute zero all atoms are in their ground state. Electrons can be
excited into higher-energy orbitals by absorbing energy in many ways. Some of these
methods include the vibrations of elevated temperatures, by collisions with other atoms or
free electrons, via chemical reactions with other atoms, or through the absorption of
photons.

When electrons are excited into higher orbitals by the absorption of photons for
example, they will almost immediately decay back to the ground state. The process
usually takes only about 10 ns and happens spontaneously. Spontaneous decay often leads
to spontaneous emission of photons with exactly the same frequency as the photons that
excited the electrons in the ﬁrst place. Light created in this way radiates ﬁom the atoms in
random direction but at well - deﬁned wavelengths called emission lines. These emission

lines will intensify as more electrons are pumped into higher orbitals.

142

In atomic hydrogen, the set of absorption and emission lines that originate and
terminate in the ground state (n=1) deﬁne the Lyman series of energy transitions (see
Figure A1). In this ﬁgure arrowheads pointing in both directions indicate that these
energy transitions are “two way streets,” resulting in either resonance absorption or
resonance radiation. When electrons are excited to n=3 or higher orbitals, more than one
downward transition is possible. For example, ﬁ'om n=3 the electron could drop straight
back to the ground state or go ﬁrst to n=2 and then to the ground state. Depending on
which path is taken, three different photons could result. The more direct route to the
ground state generates a single photon with an energy of 12.1 eV, whereas the indirect
route might produce two photons in succession: one with 1.88 eV of energy and a second

with 10.2 eV.

“ .0403

Energy (eV)

 

Figure A]. An energy - level diagram of atomic hydrogen This ﬁgure illustrates the
energy transitions that terminate at levels designated by principal quantum numbers,
n= 1 (ground state), n=2, n=3. Upward arrows specrﬂ absorption, downward arrows
indicate emission. Atomic hydrogen is one of the simplest models, in more complex
models levels can split into many sublevels or even continuous bands of allowable
energies. Lasers: Theory aid Practice by J. Hawkes and I. Latimer - 1995]

143

The indirect emission process describes a kind of ﬂuorescence in which the energy
absorbed by an atom is quickly reradiated at longer wavelengths. The 1.88-eV photon
creates the red H. emission line at 656.3 nm. This line is one of a group of transitions
called the Balmer series. As the number of orbiting electrons grows through the ranks of
the periodic table, so does the intricacy of the orbital transitions.

In any atom, however, some transitions are more likely than others. There are
well-established selection rules in quantum mechanics that predict the probable occurrence
of a given transition in various circumstances. This is important to know because the
likelihood of a transition ultimately determines the strength of an absorption or emission
line. Moreover an excited atom sometimes can ﬁnd itself trapped in an energy state ﬁom
which a downward transition is unlikely. The atom can linger in this metastable state for
microseconds or even milliseconds before decaying to a lower energy level.

The existence of metastable states can upset the thermodynamic equilibrium that
normally prevails in atomic systems. Ifenough electrons get hung up in a metastable state,
the population of atoms in this state could exceed the population of atoms in a lower
energy state. If this happens, the atoms are said to be in a condition of population
inversion. Population inversion is a state which is thermodynamically unstable.

Population Inversion is illustrated in Figure A2.

Therm-l Equlllbrlum

 

Population lnvorslon

 

 

 

 

 

 

i I
i r
I I
| I
“ I") ’ It!) ‘\ '(1) ‘ ”m
r l
l \
\ \
\ \
\ E(1) \
5(2 ' \ . , , , .
> _r . m. . . .
\
Nm ‘ . "(2) \
\ \
\ \
s s
\ \
I rm) ‘~--__ NU) ‘~,~_‘“
Population NH). N(2) Populalion N(1).N(2)
(A) (3)

Figure A2. Populations of a two—energy system (A) in thermal equilibrium and (B) after

a population inversion has been produced [Laserss Principles and Applications by J.
Wilson and J Hawkes - 1987 ]

Population inversion is an avalanche waiting to happen. When more energy is
stored within the atoms at a higher state than at a lower one, the capacity of gain exists.
In fact, lasers depend on population inversion for their gain. All that is needed is some
kind of stimulus to set the downward transition in motion. It was Einstein who uncovered
the stimulus for lasers some 40 years before Schawlow and Townes described how it
could be put to use. Before Einstein offered a powerful thermodynamic argument for
stimulated emission, stimulated absorption and spontaneous emission were the only modes
known for energy transitions within an atom.

Unlike spontaneous emission, in which an electron randomly decays to a lower
energy level and gives oﬂ‘ a photon in the process, stimulated emission is neither

spontaneous nor random (See Figure A3). With stimulated emission an electron is

145

induced to decay by a photon that has the same energy as the transition energy of the
electron. When the electron encounters such a photon, it immediately decays and
generates another photon with exactly the same energy as the photon that triggered the
downward transition. As a result, not only do the two photons have the same energy,
frequency, and wavelength, they are headed in the same direction and have the same

polarization and phase.

 

 

 

 

 

 

 

 

 

carom: AFTER
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m. l
—..—.> i Abm
l
"V l
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SPONTANEOUS EMI$|CN
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STIMULATED EHISSOH
Figure A3. Stimulated absorption of a photon destroys the photon ( top) . Spontcmeous
emission creates a random photon (middle), and stimulated emission creates a photon
identical to the stimulating photon(bottom). [Optoelectronics' An Introduction by J.
Hawkes and J. Wilson - 1989].
With the concept of stimulated emission, a simple sketch of how a laser ﬁmctions
at the quantum level can be developed. The ﬁrst step is to attain a population inversion in

the atoms of the laser medium. This requires enough energy to pump more atoms into the

146

metastable state than there are in the lower energy state. Once this population inversion is
obtained the spontaneous decay of electrons from the metastable level will create photons
with just the right energy to cause an avalanche of stimulated emission.

Mthin the laser medium there is a mixture of spontaneous and stimulated
emission, but it is not a laser in the customary sense of the word because light radiates in
all directions. Nevertheless, the medium will have a small gain while the population
inversion persists, and the radiation will have laser like qualities. But if the radiation can
be partly contained with optics (usually two mirrors in various conﬁgurations), then the
stimulated emission will be extracted from the medium much more efﬁciently. One of the
most common ways to contain this radiation is to place the laser medium inside a Fabry-

Perot interferometer (see Figure A4).

TOTALLY REFLECTIVE EXCHED Arous PARTIALLY REFLECTIVE

 

 

 

. . .J../‘.\... 223.17..
'.‘._2.:';é.’ “‘r
.o.o.o.o.0/.

 

 

 

 

 

GAIN M EDIUM

Figure A4. Placing a laser medium in an optical cavity formed by two parallel mirrors
eﬂectively stretches the medium to many to times its actual length and creates a feecﬁack
environment for eﬂicient ampliﬁcation of the simulated emission.

147

The F abry-Perot consists of two parallel mirrors placed some distance apart.
Some of the light trapped inside this optical cavity will experience multiple reﬂections as it
bounces back and forth between the mirrors. In this condition the light is said to be
resonant with the cavity.

This resonant condition transforms the interferometer into a highly selective ﬁlter.
At resonant wavelengths, the reﬂectivity inside the cavity can be very high, creating an
excellent feedback environment for the laser gain medium. Because a portion of the
spontaneous and stimulated light inside the cavity passes back and forth through the
medium, the medium is effectively stretched many times its actual length. And with each
pass, more photons are stimulated into existence.

If the population inversion is high enough to overcome all the energy loss inside
the cavity, the so-called threshold condition will be met and lasing will begin. To allow
light out of the laser cavity, one mirror is usually made partially reﬂective. Because laser
light consists mostly of the stimulated emission generated with each pass through the gain
medium, it is coherent and highly directional.

Unlike the light ﬁom a conventional source, such as incandescent lamps or gas
discharges, laser light is exceptionally monochromatic (possessing only one color, or more
speciﬁcally, a speciﬁc wavelength in the electromagnetic spectrum). A Nd:YAG laser, for
example, is about 10 million times more monochromatic than a common lamp. And
because lasers are ampliﬁed light sources, their intensities can reach levels many orders of

magnitude greater than the sun.

148

The light from most lasers also diverges very slowly as it propagates through
space, a result of its monochromaticity and the multipass cavity design. The real
difference between laser light and other forms of radiation is the high degree of phase
correlation across the wavefront and in time (This is deﬁned as spatial and temporal
coherence, respectively). This means the crests and troughs of the individual wave trains
stay in step with each other across the beam and for an extended interval of time.

These unique properties make the laser an indispensable tool for a variety of
applications. Some of the most successful laser designs are the result of some of the
research conducted by Maiman and Schawalow in the 1960’s. v Some of the most
successful lasers include gas lasers such as HeNe, C02, argon-ion, and HeCd; solid-state
lasers such as rudy, Nd:YAG, and Nd:YLF, tunable solid-state lasers such as Tizsapphire
and alexandrite: semiconductor lasers as AlGaAs, InAlGaAs, DFBs, VCSELs, and
quantumwells; and liquid dye lasers.

For an example of simulated emission the HeNe laser can be examined. The laser
medium consists of a narrow discharge tube ﬁlled with a helium-neon gas mixture (A
typical ratio for the mixture is 10 helium atoms for every neon atom.) As with standard
neon tubes commonly seen in store windows, an electrical discharge excites the gases.
Basically, however, the similarity between this advertising mechanism and the laser ends
there. In the laser much of the energy of the ﬁ'ee electrons created by the electronic

discharge is absorbed by the more numerous helium atoms. This is illustrated in Figure

149

 

 

 

 

 

 

 

 

 

LEVEL
T COLLISIONS \
_ 2° LASER
EMISSION g 632 8 nm
5 TRANSITIONAL
L— 19 Z) 3)
LEVEL
ELECTRON
_18 COLLISIONS FAST DECAY
ENERGY (eV)
17 .
T 20 3s
16
FAST DECAY
.\ Q, \‘i
\‘f T\\ \ \\
1s2 6 2o6
__ O GROUND STATE
HELIUM NEON

Figure A5. Simpliﬁed energy-level diagram of a HeHe laser operating at 632.8 nm.

These collisions increase the energy of the helium atoms and pump them into the
metastable energy state (1525). The energy of this state happens to be identical to a
metastable state of neon (2p’55). Through collisions between the excited helium atoms
and the ground state neon atoms, the helium gives up its energy to the neon, raising it to a
metastable state. From this long-lived(z100 as) energy state, stimulated transitions to a
short-lived(alens) lower energy state (2p5 3p) will generate laser light at 632.8 nm once
suﬂicient population inversion is achieved between the two states. Neon atoms, the lower

energy state, called terminal laser level, quickly decay to an even lower energy state

150

(2p5 3 s), from which they quickly decay back to ground state. At this point the process
can start all over.

The HeNe laser illustrates one way to create laser light. There are dozens of other
methods. Whatever the approach, however, the basic prerequisites for laser light are the
presence of metastable states, some mechanism for pumping atoms into the metastable
state, a population inversion of atoms in the metastable state, stimulated emission, and
some kind of optical feedback to enhance the stimulated emission and control its output.
“Without all ﬁve of these conditions, a laser would be just another ﬂashlight and electro-

optics would be just another branch of optics.”

151

APPENDIX B

Calibration of IPPLUS for Infrared Temperature Measurements

This appendix discusses the steps involved in obtaining a calibration between the IPPLUS
image processing system and the Inﬁ'ametrics thermal imaging system.

EXPERIMENTAL E MENT

A thin (1/8”) Aluminum disc 2 inches in diameter
Minco disc heater 2” inches in diameter
Omega-High Thermal Conductivity Paste
Radiometer and Control Unit

Video Recorder

DC Power Supply

IPPLUS image processing system

NQ’SPPSA’N.‘

EXPERIMENTAL PREPARATION
1. Aluminum disc is painted with black paint to improve emissive properties.
2. Minco heater is attached to disc using paste.

EXPERIMENTAL SETUP

C 1 IR Agrrri'ineumnd
8111i?) Scanner 8180 e er

_ —- j /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ca sette DC
ecorcier 532m;

152

Figure BI. Experimental Setup

EXPERIMENTAL PROCEDURE

1. In calibrating the system the radiometer was operated in the point mode. As shown in
Figure B2, the crosshairs were placed near the center of the disk and the cursor
temperature in the text line was used in the calibration.

7 Cursor
Temperature

 

Figure B2. Camera operated in the point mode. The temperature at the location of the
“cross hairs” is indicated in the text line along the bottom of the image.

2. In the ﬁrst calibration test the temperature span was set to ﬁve degrees and the range
was adjusted so the entire ﬁeld of view was dark. Therefore, initially the temperature
of the disk was below the range of the radiometer.

3. Then as the voltage supplied to the heater was slowly increased the output of the
radiometer was stored on video cassette. The test continued until the disk
temperature exceeded the radiometer’s temperature range.

4. The recorded data was then analyzed using the IPPLUS image processing system. As
the temperature of the disk slowly increased, thermal ﬁelds as shown in Figure B2
were randomly captured.

5. Using the line proﬁle or bit map analysis ﬁmction of IPPLUS the gray scale intensities
of four regions, indicated in Figure BZ with red rectangles, were average and
compared with the cursor temperature. If this is done several times throughout the
temperature range, a plot of temperature versus gray scale can be developed. Since
the output of the radiometer is a standard 8 bit video format, the gray scale intensities

153

will range between 0 and 255. Therefore, regardless of the temperature setting the
output of the radiometer is divided into 256 discrete levels. This being the case, the
slope of a gray scale to temperature calibration curve with radiometer in the 20
temperature range is different than the slope of the of a gray scale to temperature
calibration curve with the radiometer temperature range at 5 degrees. These
differences in slope can be eliminated if the gray scale is plotted as a ﬁmction of non-
dirnensional temperature.
6. A non-dimensional temperature was determined based on the minimum and maximum

temperature for the particular temperature span setting. For example, in Figure B2

the minimum temperature TL=27.O°C
the maximum temperature TH=127°C
and the temperature at the location of the cursor is T = 98°C.

T H — TL
7. This non-dimensional temperature is then plotted as a function of the gray scale
intensity and a linear regression can be performed on the data to ﬁnd a relationship
between gray scale and temperature. This plot is illustrated in Figure B3.
8. Steps 1 through 7 are repeated with the temperature span set at 10°C, 20°C, 50°C, and
100°C.

154

Calibration of IPPLUS (DOS Version)

Non-Dimensional Temperature as a
Function of Gray Scale Intensity

 

   

 

   

O Ten'perature Range = 5°C
— Linear Regression 5°C

0 Tenperature Range = 10°C
— Linear Regression 10°C

0 Termerature Range = 50°C
— Linear Regression 50°C

0 Temperature Range = 1m°C
— Linear Regression 100°C
0 ‘i T T V T

0 50 100 150 2CD 250

Gray Scale Intensity (0-255)

9=T-TL/TH-TL

 

 

 

 

Figure B3. Non-dimensional temperature as function of gray scale intensity.

DISCUSSION OF RESULTS

Calibrations such as those in Figure B3 illustrate that the gray scale output of the
radiometer is linearly related to temperature. It is interesting that the calibration curve
does not cross through the origin and causes an oﬁ‘set in the relationship between gray
scale and temperature. This offset is a characteristic of the radiometer’s output.

Normally, a black image will have a gray scale intensity of 0, while a white image
will have a gray scale value of 255. Although the output of the radiometer varies
between “black or cold” and “white or hot”, these images do not produce typical gray

scale values. For example, pixels which are below the temperature range of the

155

radiometer appear “black”. Normally, the gray intensity of these pixels would be zero.
However, the “black” pixels produced by the radiometer are digitized to values higher
than zero. Therefore, since the “black” values produced by the radiometer are not truly

black an oﬁ‘set exist.

156

APPENDIX C

SPATIAL CALIBRATION OF IPPLUS FOR
INFRARED TEMPERATURE MEASUREMENT

Often it will be important to illustrate the temperature variations along a surface as a function of
position. This appendix presents an example of how a spatial calibration using IPPLUS can be used to
provide this information.

In this test, a small piece of braided composite material was heated along one edge with a
Nd:YAG laser as shown in Figure Cl. As the sample was being engerized, temperature measurements

were made with the infrared camera. Due to the small sample

Composite Sample Cylindrical 11'“:
Used to tom beam Into
8 [bill line

Sample \Mdth

 

 

    

Beamexpanding optic
w/W ~ 1/5
il
li-
[nﬁ'aled Camera:
Outpntstoredonv'rleo tape 2

 

 

 

 

 

_ ‘ L is ,-
for my“ Beam Wdth
W

(a.) (b.)

Figure C1. (a) The test setup used to heat a small braided composite sample. (b. ) A schematic
representation of the heated region.

157

size the 3X telescopic and the 6” close-up lenses were used to incrcase the spatial resolution. A typical

thermal image developed under these hcating conditions is shown in Figure C2.

 

Figure C2. The output of the Inﬁametrics Radiometer illustrating the surface variations across the test
sample.

Speciﬁc arcas of interest within this themral image can be analyzed using IPPLUS. For example,
abitmapanalysiscanbeconductedonthearcawithintheredrectangleinFigureCZ. Thisproducesa
two dimensional array of gray scale values as a function of X and Y pixel orientation.

The above information becomes more valuable if temperature variations can be represented as a
function of geometric position. This can be accomplished be positioning an object of known length in the
radiometer’s ﬁeld of view. In this case, an aluminum ruler was used to provide a reference length. As
shown in Figure C3, the emissivity variations between the ruler’s aluminum surface and the black scale
indications cause apparent temperature differences.

These apparent temperature differences are used to spatially calibrate the system. For example,
the line proﬁle function of IPPLUS (represented by the red line in Figure C3) can be uwd to determine
how many pixels correspond to a certain length. This infomration yields the pixel width in horizontal

direction and similar steps can be repeated to ﬁnd the pixel width in the vertical direction.

158

 

Figure C3. A ruler imaged with the Inframetrics radiometer used for a horizontal calibration. In this
case, the line profile function (represented by the red line) is used to determine to the number of pixels in
a given length.

A LabVIEW program, shown in Figure C4, has been created to use this information and spatially
calibrate the output of the radiometer. This program allows the user to enter parameters pertaining to a
temperature to gray scale calibration and the information necessary for the determination of the horizontal
and vertical pixel widths. This program also transforms the data from the two-dimensional gray scale
array, generated with IPPLUS, into a X-Y-Z listing as shown in Figure C5. Data in this format is easily
analyzed and plotted using software packages such as SigmaPLOT, TableCurveSD, and Tecplot.

As an example of this utility, a bitmap analysis was performed on the rectangular region in
Figure C2. The data was calibrated with the LabVIEW program and plotted using Tecplot. This pseudo-

colored plot is illustrated in Figure C6.

 

Figure C5. The front panel of the Lab VIEW program used to spatially and thermally calibrate the gray
scale information form IPPLUS. This program also transforms the data into a format that can be easily
plotted using commercially available software.

29555

X5

Y1
G1

Gll
Gl6
G21

(21.)

 

160

Y3 Y4 Y5

G3 G4 Gs

G8 G9 610

013 GM G15

018 619 620

623 624 625
Transformed
Data

 

X1 Y1 G1
X1 Y2 G2
X1 Y3 G3
X1 Y4 G4
X1 Y5 G5

X2 Y1 G6

X2 Y2 G7

X2 Y3 G8

X2 Y4 G9

X2 Y5 G10
03-)

Figure C5. (a.) The output of bitmap analysis of IPPLUS, formatted as a 2 dimensional array of gray
scale intensity as a ﬁinction of X and Y pixel orientation. (b.) An XYZ format which is eaa‘ly plotted
using commercially developed software. In this case the data is spatially and thermally calibrated.

Y Axis (cm)

0.1

0.2

 

0.3

Tupi-n

was

up

“I!

an

”N

77.”

m

751-

':"m Figure C6. A Pseudo-colored plot

rm illustrating the temperature variations

m across a selected region in the thermal

an: image in Figure C2. This data was

m spatially and thermally calibrated using the
LabVIEW program in Figure C4 and
plotted using Tecplot..

0.4 0.5 0.8

x Axis (cm)

161

APPENDIX D - BEAM DIA GNOS T I CS

Laser beam diagnostics includes measurement of energy/power, intensity/beam
proﬁle, temporal/time dependence and measurements of beam diameter. These
measurements provide a thorough understanding of the characteristics of the laser beam
and become important when attempting to optimize the laser for a particular application.
In this appendix, two of the initial steps towards developing beam proﬁle measurement

techniques are discussed.

CCD CAMERA:

Charged - coupled - device (CCD) cameras have many useful characteristics for
doing laser-beam diagnostics. The cameras, when coupled with image processing
software, have two primary features. First they provide a picture of the beam proﬁle so
the user can eﬂ‘ectively see what the beam looks like. The ability to see the proﬁle when
adjusting the laser or aligning the optical train provides improvement in laser performance
and experimental accuracy. Second, the quantitative and visual feedback complement
each other by allowing for precise laser operation and provide a permanent record of the
setup and results.

In this study a Javelin JE206ZIR CCD camera was used in conjunction with Image
Pro Plus (IPPLUS) image processing software to provide information about the spatial
distribution of energy throughout the diameter of the laser beam. This CCD camera has a

high response at the wavelength of the laser (1064 nm) and is ideally suited for low light

162

applications. In a typical setup, as shown in Figure DI, the laser beam is positioned to
strike the center of the camera’s lens. When the output of the laser is attenuated either by
the use of beamsplitters or by a reduction in lamp current, beam analysis is possible.
Power Meter Beam Stop
CCD Camera:
Output displayed, stored

on video tape or immediately
analyzed using IPPLUS

     

Beamsplitters

Nuetral Density Filters
Figure D]. A typical setup using the CCD camera to obtain a beam proﬁle.
The output of the CCD camera, shown in Figure D2, is a two dimensional
monochrome image with varying gray scale intensity, and can be displayed on a standard
black and white monitor. This simple setup provides useﬁil “real time analysis” since the

results of course adjustments can be visualized on the monitor with the naked eye.

 

Figure DZ. The output of the laser when visualized with a black and white monitor.

163

In order to examine the results of ﬁne adjustments or to obtain a surface ﬁt of the
radiation distribution the CCD camera’s output must be analyzed using IPPLUS.
IPPLUS is a general purpose image processing system which provides the user with an
intensity analysis toolbox. Using this type of analysis the user can collect data from the
CCD’s output based on the intensity values it contains. The bitmap analysis tool is
extremely useful in this situation since it provides the intensity values of individual pixels
within a user deﬁned area of interest. For example, if the image in Figure D2 was
analyzed using a bitmap analysis, information could be represented in a three dimensional
plot. As shown in Figure D3, plots such as this give the user information pertaining to the

beam’s proﬁle.

Intensity (0’255)

 

Y Axis

Figure D3. A three dimensional representation of a laser beam proﬁle. This information
was plotted using Jandel Scientiﬁc ’s SigmaPlot.

The output of the IPPLUS bitmap analysis is in the form of a 2 dimensional array

as shown in Figure D4(a.). In order to use the automated surface ﬁtting software,

TableCurve3D, this output must be transformed into three columns representing (1.) the
pixel numbers along the X axis, (2.) the pixel numbers along the Y axis and (3.) the gray
scale intensity of each pixel. The transformed output is illustrated in Figure D4(b.). This
transformation can be done fairly quickly using a LabVIEW VI called the

“CONVERTOR”, shown in Figure D5. In running this program the user is prompted by a

165

dialog box to enter the ﬁle to be converted. Once the conversion is complete, the user is
asked to create a new ﬁle name.

Y1 Y2 Y3 Y4 Y5
Xl Gl G2 G3 G4 G5
X2 G6 G7 G8 G9 G10
X3 G1] 612 G13 G14 GlS
X4 G16 G17 G18 G19 G20
X5 G21 G22 G23 G24 625

(to)

X1 Y1 G1
X1 Y2 G2

 

 

 

 

x1 Y3 G3
Transformed x 1 Y4 G4
Data x1 Y5 65
x2 Y1 G6
J x2 Y2 G7
x2 Y3 68
x2 Y4 G9
x2 Y5 (310
(b.)

Figure 04. (a.) The output of bitmap analysis of IPPL US, formatted as a 2 dimensional
array. (b. ) The necessary format for the automated surface ﬁtting program,
T ableCurve3D.

 

Figure D5. A INVITE VI used to quickly tramfonn the output of the bitmap catalysis
into the format necessary for the automated surface ﬁtting program, T ableCurve3D.

Once the data has been converted to the proper format it can be imported into
TableCurve3D as an ASCH ﬁle. This powerful program allows the user to deﬁne the type
of equations used to ﬁt the data. Then, based on these choices the program automatically
generates several equations to ﬁt the data.

The F-statistic is used to measure the extent to which each of the generated
equations represent the data. If an additional parameter makes a signiﬁcant contribution
to a model, the F-statistic increases. Otherwise, a decrease occurs. Therefore, the higher

the F-statistic, the more effectively a given equation models the data.

167

For example if it rs of interest to determine how accurately the beam proﬁle in

Figure D6 represents a Gaussian distribution, the user can customize the surface-ﬁt

equations” to ﬁnd the best Gaussian ﬁt

In this case, 12 non-linear gaussian equations
were automatically ﬁt to the data.

 

300

250
"to?
0., 200
8
g; 150 gig!”
:5 100

50

0

 

Figure D6. A three dimensional representation of a laser beam proﬁle This information
was plotted using Jandel Scientiﬁc ’s SigmaPlot.

Based on the value of the F-statistic the generated equations are ranked In this

case a Gaussian equation of the form

 

 

z=a+bexp —05[(x;0)

2
f
produced the highest F-statistic and best represented the experimental data. Along with
yielding the best equation to ﬁt the data, TableCurve3D plots the generated surface and

the residuals. These plots are shown in Figure D7 and D8.

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Figure D7. A plot of the curve generated to ﬁt the experimental data

169

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Figure D8. A plot of the differences between the generated curve and the experimental
data.

Although a great deal of information can be obtained from this type of analysis,
saturation problems with the CCD camera limit the application. Whenever the power
density of the measured beam exceeds approximately 1.43 W/cm2 saturation exists.
Therefore, even when beamsplitters and neutral density ﬁlters are used to attenuate the
laser’s power and external optics are used to expand the beam, high laser lamp currents

cause saturation in the output of the CCD camera as shown in Figure D9.

170

 

Figure D9. An example of the saturation problems that occur when attempting to obtain
the beam proﬁle.

Apart ﬁ‘om the speciﬁc saturation problems with the currently used CCD camera,
Roundy and Slobodzian state in their October 1994 Laser Focus World article that CCD
cameras generally have some other deﬁciencies that affect their ability to make accurate
laser beam measurements. First, CCD cameras have a low signal-to-noise (S/N) ratio,
even when the signal is close to the saturation of the camera. This is important when the
signal cannot be adjusted when close to camera saturation, or when information in the
low-signal-level wings of the beam is important to the measurement of the laser
characteristics.

A second drawback of CCD cameras is the variation in the camera baseline offset

or zero signal level. Because all signal levels are measured depending on the baseline

171

offset, errors in the adjustment can directly affect the measurement of beam proﬁle
proprieties. The offset level driﬁs with time, environmental temperature, and aging. Also
this drift is present as the camera heats up as a result of long operating times.

These errors combine to cause problems in obtaining precise laser-beam

dimensional measurements.

KNIFE - EDGE METHOD:
One way to obtain accurate dimensional measurements of the laser and eliminate
some of the problems associated with CCD cameras is to scan a knife edge across the

width of the beam. As shown in Figure D9, a razor blade is traversed across the beam

PHOTODETECTOR:

MEASURE BEAM INTENSITY (ENERGY)

AS KNIFE PASSES THROUGH THE DOUBLE EDGED RAZOR BLADE
LASER BEAM. OUTPUT IS MEASURED

WITH DATA ACQUISITION BOARD.

 

 

 

 

 

 

 

TRAVERSE SYSTEM: LASER BEAM

USED TO MOVE THE
KNIFE ACROSS THE
LASER BEAM

Figure D9. Experimental setup for knife edge method In this method a razor blade is
passed through the beam. As the razor blade traverses across the beam proﬁle, the
unblocked portion of the beam is measured with a photodetector or energy meter. From
this output the diameter of the beam is determined

172

proﬁle using a micro-positioner. The beam diameter is considered to be the distance
between the points where the knife-edge blocks 10% and 90% of the total beam energy.
As illustrated in Figure D10, the choice of this “clip level” is based on the assumption that

the measured beam has a Gaussian proﬁle [Siegman, Sasnett, and Johnston 1991].

Distance

10°/o 90%

r.

/ Power Measured
—_>

_> “_—

Effective Beam Diameter

 

 

 

Figure D10. A knife edge scanned across the beam proﬁle produces an S-shaped curve
as the detected power goes from 0%-100%. According to an ISO standard, the beam
width is distance between the points where the detector output is between 10% and 90%
of the maximum. [Siegman Sasnett, and Johnston 1991]

In order to automate this experimental procedure a LabVIEW program was
developed. This program, pictured in Figure D11, allows the user to chose between
measuring devices and to select the traversing step size. At each location, 30
measurements from one of the devices are averaged and the result is plotted as a function
of position. When the measurements at each speciﬁc location are complete, the user is
prompted to traverse the knife edge to the next location. This procedure is repeated until

the knife edge is traversed to a point where it no longer blocks the beam. Based on the

acquired information, a regression algorithm calculates the beam diameter and the user

173

has the option to save the data to a ﬁle. Depending on the traverse step size and the beam

diameter this test typically takes less than 5 minutes to complete.

 

 

 

 

 

 

 

Figure D11. The front panel of the knife edge traverse Lab VIEW V]. This program is
used to record the laser intensity as a function of knife edge scan position.

174

The knife edge technique has been used to determine the diameter of the laser and
to quantify the spatial distribution of radiation generated by a optical train. Based on
manufacture speciﬁcations, the diameter of the laser is known to be approximately 0. 7
mm.. In the ﬁrst set of experiments, the knife edge traversed across the beam and the
LabVIEW program was used to record the laser intensity as a ﬁinction of scan position.

Based on this information, shown in Figure D12, the beam diameter was determined to be

 

0.7128 mm.
Intensity as a Function of Scan Location
Knife Edge Measurement Technique
2 " o o O O O 0
a .
E‘ 1 ‘ .
m
E .
s .
0.100000000000000...

 

 

 

0.00 0.05 0.10 0.15 0.20 0.25
Scan Location (mm)

Figure D12. A plot of the beam intensity as a ﬁinction of scan location. This
information is used to determine the eﬂective beam diameter. In this case, the beam
diameter was determined to be 0. 7128 mm.

175

In a second set of experiments the laser beam was passed through a beam expander
and a plano-concave cylindrical lens. The output of this optical system is a line at the
focal length of the cylindrical lens. If this optical system is ever to be used to provide a
uniform heat ﬂux along a surface, the distribution of radiation along the line must be
quantiﬁed. This quantiﬁcation was completed using an experimental setup similar to that
in Figure D13. In this setup the beam is passed through a 6.35 mm slot prior to being
blocked by the knife edge. If the distribution of radiation is truly uniform along this line,
the output of the detector beyond the knife edge would increase linearly as it was exposed
to larger amounts of laser radiation. As shown in Figure D14, the output of the detector

did linearly increase as a ﬁinction knife position.

635 mm ALUMINUM SLIT: USED TO MASK THE
BE SO CERTAIN PORTIONS OF IT COULD BE

SAMPLED. \
POWER METER \

IQ

 

 

 

[DI

   

 

3* CYLINDRICAL LENS
AND OPTIC HOLDER

 

 

Figure D13. A schematic representation of the experimental setup used to measure the
distribution of radiation generated by an cylindrical lens.

176

Intensity as a Funciton of Sean Location
Knife Edge Measurement Technique

 

0.8

0.6 ~

0.4 ~

Intensity

0.2 —

 

 

 

0.0
0.0

T T I T I

0.1 0.2 0.3 0.4 0.5 0.6
Scan Location Along 0.635mm Slit

Figure D14. Laser intensity as a function of scan location. In this case the laser

was passed through a 0. 635mm slit and the detector output was recorded as the knife

edge was traversed across the slit. The linear increase with scan location is a good

indication that the distribution of energy across the line of laser radiation is uniform.

177

APPENDIX E

 

Infrared Thermography used to Measure the Temperature
Distribution of Boron Doped Diamond Films Heated with Joule
Heating

Due to the extended operational environments of modern sensors, it becomes
necessary to investigate new materials for optimal sensing performance, especially under
harsh environments. In most heating applications, temperature control is essential. Heat
generation and temperature sensing are also required for liquid level sensing, mass ﬂow
meters, vacuum and pressure gauges, which are based on measurements of heat
dissipation. Since the materials commonly used as heating elements lack high sensitivity to
temperature change, diﬂ‘erent materials are utilized for heating and temperature sensing.
In such a conﬁguration, the thermal and chemical properties of the materials involved, if
not careﬁilly considered, may cause problems. It is also important to minimize the
response time and uncertainties in the measurements associated with heat dissipation and
the placement of sensing and heating elements.

Use of a single element as both a heater and temperature sensor may help to
eliminate such problems. The desired material properties for such an element include high
thermal conductivity, ability to be used as an electrical conductor and insulator, high
sensitivity to temperature, micro-machining capability, resistance to chemical attack and
mechanical stability. The unique intrinsic properties of diamond make it an excellent
material for this sensor/heater application . Recent progress in the technology of chemical

vapor deposited (CVD) diamond has lead to inexpensive device quality p-type

178

polycrystalline ﬁlms . Since the motivation is present it seems logical to determine the
heating characteristic of CVD diamond ﬁlm. In this appendix, two diamond samples are
heated with an AC voltage of 100 V and temperature measurements are made using
infrared thermography.
EXPERIMENTAL SETUP

The experimental setup comprised of ﬁve primary components: 1.) Inframetrics
Model 600L Infrared Imaging Radiometer, 2.) thermal image processing system, 3 .)
FOR.A VTG33 Video Timer, 4.) a video cassette recorder, and 5.) a variac power supply
The ﬁrst two components, the inﬂated radiometer and the image processing system,
comprised the temperature measurement system. The video timer was used to
superimpose digital indications of time and date onto the transient output ﬁom radiometer.
This output was collected in standard RS-170 on a video cassette recorder. The power
supply was used to energize each of the samples with an AC voltage of 100 V. A diagram

Of experimental setup is displayed in Figure E1.

VIDEO CASSETTE RECORDER INFRARED CAMERA
VINO TIMER DIAMOND SAMPLE

YD CAMERA CONTROL WIT

Figure E1. Diagram of the data acquisition system

     

DATA AOUISITION
AND IMAGE PROCESSING
SYSTEM

IQ-

VARIAC POWER SU’PLY

 

 

 

5km

 

 

 

 

 

 

 

 

 

 

 

 

179

Experimental Procedure

While applying an AC voltage of 100V to each of the samples, the dynamic
temperature proﬁles of diamond/ sensor substrates were measured with the infrared
camera. The samples were suspended vertically using two lateral copper clamps which
also served as electrical contacts. With this arrangement, heat was dissipated by
conduction through the clamps and by natural convection. The emissivity of the samples
were determined by comparing the measured radiosity from two heated bodies transmitted
through and reﬂected by the surface. Using this method, the emissivities of the samples
were determined to be. 0.64 and 0.72.

Under these conditions the temperature distributions across each of the samples
were captured at various heating times. These results are shown in Figures E2 through

E12

180

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Figure E2. Temperature distribution (‘C) of sample #1 after 10 seconds of heating.

 

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182

 

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mm; 301 57 315.27 3M4 342.00 358.41 1 870.15 seem 897.52

 

Figure E7. Temperature distribution (‘C) of sample # 1 after 80 seconds of heating.

183

mm: 17m 21m 5156 2&8” W1 38.1752 saws 45214

2W

 

0 so 100 150
Figure E8. Temperature distribution (‘1?) of sample #2 after 5 seconds of heating.

mm: _ ensue 87.9824 7m 1 08.518 M14 99.911 1

 

Figure E9. Temperature distribution (°C) of sample #2 after 15 seconds of heating.

184
mus-15:11:11.3“ 1Q547 112)! 116.013 119.247 15.713 18.948

200

 

0 50 100 150

Figure E10. Temperature distribution (‘C) of sample #2 after 35 seconds of heating.

1mm: I—Gﬂﬂ 114.731 121.Q1 13.111 141449 1&18 1m

 

Figure E11. Temperature distribution (°C) of sample #2 qﬁer 50 seconds of heating.

185

TEH'EHATLIE: 1“ 110.404 124.” 19.015 19.510 147m 15.07 1M2

200

 

Figure E I 2. Temperature distribution (‘C) of sample #2 after 65 seconds of heating.
These results illustrate that the high thermal conductivity of the diamond substrates
produce relatively isothermal surfaces even at high temperatures. As an application, these
results verify that a diamond sensor/heater structure is capable of delivering high power

densities along a uniforrnally heated surface.

This appendix represents a portion of a paper written by G.S. Yang, D.M. Aslam, M.
White, and J.J. McGrath. This paper, “The Characterization of a Single Structure
Diamond Heater and Temperature Sensor, “ will be published in September 1996

APPENDIX F

This appendix describes the speciﬁc operating conditions for the LabVIEW program developed to

monimrthemupmofthephotodetectorandextemallytriggerthevideoﬁmer.Thefrontpanelofthis

programisshowninFigureFl.

 

Step I. Accept the program default settings.

Ifthedefault setﬁngsamacceptedbymeuser,meprogramissamesmuishmmmummonwimﬂmdam
acquisiﬁonboardmslm(device)6.1hephmodeteaorresponseismommredwith A/Dchanne10,and
thedigitaltoanalog signal isgeneratedusingD/Achannelo.

Step 2. Run the program

Theprogiamisstartedbydepreasingthe arrowontheleﬁhandsideofthe menubar. A‘Virtual”LED
ontheﬁontpanelisilluminatedunderthe“POSl’I‘lON PHOI‘ODETECTOR” label. Ifthephotodetector
isproperlypositioned,thetogglebuttoncanswithedto“CORRECT’. Oncethisbuttonisdepressedthe
IEDunderthe“LASERSI-IUTI‘ERCIDSED”labe1islitup.Ifthelasershutterisclosed,thetoggle
buttoneanswitchedto“CORRECI‘.” Atﬂuspoimtheresponseofthephotodetectorissampledéotim
andmmgevﬂwisohﬂmdwmesemmersponxofthedaeaorwhenmeshuuerisclom

187

When the average value is obtained the LED under the “LASER SHUTTER OPEN” label is illuminated
Once the shutter is opened, the toggle button is pressed and output of the photodetector is once again
sampled 60 times. The average of these samples represent the response of the detector when the shutter is
opened These average responses are used to develop the trigger criteria and once established do not have
to be repeated from test to test unless the laser’s power is signiﬁcantly reduced At this point the LED
under the “BEGIN TEST” label is illuminated and as soon as the experimental components are prepared
for data acquisition the toggle button can be switched to correct. Once the button is depressed, the
photodector response is sampled at 200 kHz until the laser shutter is opened When the shutter opens the
trigger conditions are meet and a 'I'I'L low signal is sent to the video timer. Once the signal is sent, the
program loopsback andprepares itselfforthe next test.

188

APPENDH G - NLIN HVPU T FILE

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196

APPENDR I - NLIN OUTPUT FILE

 

BEGIN LISTING INPUT QUANTITIES

BLOCK 1

N = NO. DATA POINTS, NP = NO. PARAMETERS

NT = NO. OF INDEPENDENT VARIABLES

ITMAX = MAXIMUM NO. OF ITERATIONS

MODEL = MODEL NUMBER, IF SEVERAL MODELS IN SUBROUTINES: MODEL AND SENS
[PRINT = 1 FOR USUAL PRINT OUTS, 0 FOR LESS

N NP NT ITMAX MODEL [PRINT
417 3 2 25 0 0

BLOCK 2
B(l),B(2),..,B(NP) ARE INITIAL PARAMETER ESTIMATES

13(1) = .2005013+01
13(2) = 400001303
13(3) = .250001~:+02

BLOCK 3

J = DATA POINT INDEX, Y(J) = MEASURED VALUE
SIGMAU) = STANDARD DEVIATION OF Y(.1)

T(J,1) = FIRST INDEPENDENT VARIABLE

J Y0) SIGMAu) T(J,l) T(J,2)
126.82518 1.00000 1.00000 .00249
2 26.79217 1.00000 1.00000 .00264
3 26.72616 1.00000 1.00000 00279
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1126.36311 1.00000 1.00000 .00399
12 26.34661 1.00000 1.00000 .00415
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15 26.21459 1.00000 1.00000 .00460
16 26.18158 1.00000 1.00000 .00475
17 26.14858 1.00000 1.00000 .00490
18 26.16508 1.00000 1.00000 .00505
19 26.13208 1.00000 1.00000 .00520
20 26.13208 1.00000 1.00000 .00535
2126.13208 1.00000 1.00000 .00550
22 26.11557 1.00000 1.00000 .00565
23 26.04956 1.00000 1.00000 .00580
24 26.00006 1.00000 1.00000 .00595
25 26.01656 1.00000 1.00000 .00611
26 26.00006 1.00000 1.00000 .00626
27 25.95055 1.00000 1.00000 00641
28 25.91754 1.00000 1.00000 .00656
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30 25.86804 1.00000 1.00000 .00686
3125.86804 1.00000 1.00000 .00701
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33 25.90104 1.00000 1.00000 .00731
34 25.86804 1.00000 1.00000 00746
35 25.83503 1.00000 1.00000 00761
36 25.81853 1.00000 1.00000 00776

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197

108 25.35646
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110 25.40597
11] 25.45548
112 25.35646
113 25.29045
114 25.35646
115 25.43897
116 25.38947
117 25.38947
118 25.40597
119 2542247
120 25.37296
121 25.32346
122 25.30695
123 25.33996
124 25.35646
125 25.29045
126 25.27395
127 25.33996
128 25.37296
129 25.32346
130 2532346
13] 25.32346
132 25.29045
133 25.27395
134 25.24094
135 25.19144
136 2519144
137 25.19144
138 25.17493
139 25.15843
140 28.22788
141 28.16188
142 28.04636
143 27.93084
144 27.83183
145 27.76582
146 27.76582
147 27.76582
148 27.6998]
149 27.63380
150 27.58429
15] 27.55128
152 27.55129
153 27.55129
154 27.51828
155 27.45227
156 27.38626
157 27.35325
158 27.32025
159 27.27074
160 27.25424
161 27.20473
162 27.12222
163 27.0562]
164 27.0232]
165 27.0562]
166 27.0397]
167 27.02321
168 27.00670
169 27.00670
170 27.00670
171 26.99020
172 26.94069
173 26.94069
174 26.94069
175 26.99020
176 26.95720
177 26.94069
178 26.87468

.0070]
.00716
.0073 1
.00746
.0076]
.00776
.00791
.00806
.00822

198

179 26fﬂ2217
180 26(79217
18] 26.84168
1821H584168
183 2687468
184 2687468
185 26.89119
186 26.84168
187 26329217
188 26.77567
189 26377567
190 26.75917
19] 26.72616
192 2667666
193 26.69316
194 26H70966
195 26.75917
196 26U12616
197 2667666
198 26.66015
199 261R2315
200 261RH315
201 26.57764
202 26.59414
203 26.57764
204 2660065
205 26.61065
206 2664365
207 26.59414
208 2652813
209 26.59414
210 26.62715
21] 26.62715
212 26.62715
213 26.66015
214 26.59414
215 26.49513
216 26.49513
217 2654464
218 26.56114
219 26.51163
220 26454464
22] 26.56114
222 2657764
223 26.56114
224 26.56114
22512656114
226 26.59414
227 26.56114
228 26.52813
229 26.49513
230 26.52813
23] 2657764
232 2652813
233 26.49513
234 26.44562
235 26Jt4562
236 26.49513
237 26Jf7863
238 26042912
239 2639611
240 26347863
24] 26.56114
242 26057764
243 26.56114
244 26.51163
245 26.49513
246 26147863
247 2647863
248 26309513
249 26.49513

.00837
.00852
.00867
.00882
.00897
.00912

.00942
.00957

.00987
.01002
.01018
.01033
.01048
.01063
.01078
.01093
.01108
.01123
.01138
.01153
.01168
.01183
.01198
.01213
.01229
.01244
.01259
.01274
.01289
.01304
.01319
.01334
.01349
.01364
.01379
.01394
.01409
.01425
.01440
.01455
.01470
.01485
.01500
.01515
.01530
.01545
.01560
.01575
.01590
.01605
.01620
.01636
.01651
.01666
.0168]
.01696
.0171]
.01726
.01741
.01756
.0177]
.01786
.0180]
.01816
.01832
.01847
.01862
.01877
.01892

199

250 26.54464
25] 26.49513
252 26.3961]
253 2637961
254 26.3796]
255 26.33010
256 26.28060
257 26.31360
258 26.3631]
259 2634661
260 26.31360
26] 26.28060
262 26.26410
263 26.29710
264 26.3631]
265 26.3631]
266 26.31360
267 26.24759
268 26.21459
269 26.28060
270 26.39611
27] 26.3796]
272 26.31360
273 26.28060
274 26.29710
275 26.24759
276 26.21459
277 26.26410
278 26.23109
279 29.01296
280 28.93045
28] 28.91395
282 28.93045
283 28.86444
284 28.83144
285 28.71592
286 28.6334]
287 2861690
288 28.53439
289 28.46838
290 28.45188
29] 28.45188
292 28.38587
293 28.30336
294 28.23735
295 28.25385
296 28.22085
297 28.22085
298 28.22085
299 28.27035
300 28.23735
30] 28.18784
302 28.13833
303 28.10533
304 28.12183
305 28.05582
306 28.02282
307 28.02282
308 27.9898]
309 28.00632
310 27.9733]
31] 27.9568]
312 27.92380
313 27.9733]
314 27.97331
315 27.9403]
316 27.92380
317 27.92380
318 27.90730
319 27.87430
320 27.80829

200

32] 27.79178
322 27.87430
323 27.92380
324 27.92380
325 27.90730
326 27.87430
327 27.85779
328 27.84129
329 27.85779
330 27.82479
331 27.80829
332 27.79178
333 27.77528
334 27.72578
335 27.72578
336 27.74228
337 27.70927
338 27.69277
339 27.65976
340 27.67627
341 27.64326
342 27.62676
343 27.67627
344 2764326
345 27.59375
346 2756075
347 27.57725
348 27.57725
349 2754424
350 27.56075
35] 2756075
352 27.57725
353 27.56075
354 2754425
355 27.56075
356 27.52774
357 2751124
358 2752774
359 27.56075
360 2757725
36] 27.61026
362 27.62676
363 2754424
364‘2747824
365 27.47824
366 27.51124
367 2754424
368 2756075
369 27.59375
37012761026
371 27.54424
372‘2747824
373 27.49474
374 2752774
375 2749474
376 27.41223
377 2742873
378 27.39572
379 2737922
380 27.39572
38] 27.44523
382 2746173
383 27.42873
384 27.39572
385 27.44523
386 2746173
387 2744523
38812742873
389 27.44523
390 2746173
391 27.42873

.00882
.00897
.00912

.00942
.00957

.01002
.01018
.01033
.01048
.01063
.01078
.01093
.01108
.01123
.01138
.01153
.01168
.01183
.01198
.01213
.01229
.01244
.01259
.01274
.01289
.01304
.01319
.01334
.01349
.01364
.01379
.01394
.01409
.01425
.01440
.01455
.01470
.01485
.01500
.01515
.01530
.01545
.01560
.01575
.01590
.01605
.01620
.01636
.0165]
.01666
.0168]
.01696
.0171]
.01726
.01741
.01756
.01771
.01786
.0180]
.01816
.01832
.01847
.01862
.01877
.01892
.01907
.01922
.01937

201

202

392 27.37922 1.00000 3.00000 .01952
393 27.42873 1.00000 3.00000 .01967
394 27.49474 1.00000 3.00000 .01982
395 27.44523 1.00000 3.00000 .01997
396 27.34622 1.00000 3.00000 .02012
397 27.37922 1.00000 3.00000 .02027
398 27.42873 1.00000 3.00000 .02043
399 27.41223 1.00000 3.00000 .02058
400 27.37922 1.00000 3.00000 .02073
40] 27.41223 1.00000 3.00000 .02088
402 2744523 1.00000 3.00000 .02103
403 27.41223 1.00000 3.00000 .02118
404 27.37922 1.00000 3.00000 .02133
405 27.42873 1.00000 3.00000 .02148
406 27.42873 1.00000 3.00000 .02163
407 27.37922 1.00000 3.00000 .02178
408 27.39572 1.00000 3.00000 .02193
409 27.46173 1.00000 3.00000 .02208
410 27.46173 1.00000 3.00000 .02223
41] 27.41223 1.00000 3.00000 .02239
412 27.39572 1.00000 3.00000 .02254
413 27.39572 1.00000 3.00000 .02269
414 27.37922 1.00000 3.00000 .02284
415 27.34622 1.00000 3.00000 .02299
416 27.31321 1.00000 3.00000 .02314
417 27.3132] 1.00000 3.00000 .02329

BLOCK 4
[EXTRA = NO. OF EXTRAH) PARAMETERS. 0 IF NONE
IEXTRA = 2
BLOCK 5
EXTRA“)... ARE EXTRA CONSTANT S USED AS DESIRED
EXTRA( 1) = .00050
EXTRA( 2) = .02540

END INPUT QUANTITIES - - BEGIN OUTPUT CALCULATIONS

SY = SUM OF SQUARES FOR PRESENT PARAMETER VALUES

SYP = SUM OF SQUARES FOR GAUSS PARAMETER VALUES, SHOULD BE SMALLER THAN SY
SYP DECREASES TOWARD A POSITIVE CONSTANT

G = MEASURE OF THE SLOPE, SHOULD BECOME SMALLER AS ITERATIONS PROCEED
G SHOULD APPROACH ZERO AT CONVERGENCE

H = FRACTION OF THE GAUSS STEP, AS GIVEN BY THE BOX-KANEMASU METHOD

MAX 11 G sv SW

1 1000041 .424764E+03 .4270741~:+03 .229201£+01
13(1)= .17312513+01
B(2)= 3977391303
13(3) = .243881E+02

P(LKP) Pam H310) P(4.KP) P(5,10’)
.41716360—01 -.8303156D-05 -.4902552D-02
-.83031 56D—05 .2024217D-08 -. 1333698D-05
-.4902552D-02 -. l333698D—05 .1732886D-01
CORRELATION MATRIX
. 1000000E+01
-.9035692E+00 .1000000E+01
-.1823409E+00 -.2251873E+00 .1000000E+01
XTX(1,K),K=1,NP
.895 56 16E+03 .404672 1E+07 .5648878E+03
.404672 1E+07 . 1879476E+1 l .2591869E+07
.5648878E+03 .2591 869E+07 .4170000E+03
XTY(I),1=1,NP, WHERE Y IS RESID
-.6000 1 47E+03 -.27361 83E+07 -.41 56496E+03
XTY(1),I=1,NP, Y IS Y, NOT RESID
-.2038851EH)1 -.1093333E+05 -.1 172693E+01
MAX NP INDEX 11’
1 3 0 4

203

MAX NP INDEX 1P
2 3 1 3
MAX 3 G SY SYP
2 .999196 .1912403-02 .229194E+01 .229003E+01
3(1) = .172848E+Ol
3(2) = .398018E-03
3(3)= .2438843+02
FOX?) FOX?) FOX?) POLK?) P(5,KP)
.4259919D-01 -.9786584D-05 -.4885013D-02
-.9786584D—05 .2747824D-08 ~.1558354D-05
-.4885013D—02 -.1558354D-05 .1734423D-01
CORRELATION MATRD<
.1000000E+01
-.9045571E+00 .10000003+01
-.l797l63E+00 -.2257326E+00 .1000000E+01
XTX(1,K),K=1,NP
.8864573E+O3 .3475908E+O7 .5619645E+03
.3475908E+O7 .14012923+11 .2237994E+07
.5619645E+03 .2237994E+07 .41700003+03
XTY(I),l=l,NP, WHERE Y 18 RESID
-.1286398E+Ol -.49255853+04 -.7841158E+00
XTY(I),1=1,NP, Y IS Y, Norr RESID
-.1151528E+00 -.5364410E+03 -.6663583E-01
MAX NP INDEX 1P
2 3 1 4
MAX NP INDEX 1P
3 3 1 1
MAX NP INDEX 1P
3 3 2 2
MAX NP INDEX 1P
3 3 3 3
MAX H G SY SYP
3 1.000000 .412786E-07 .229003E+01 .229003E+Ol
3(1) = .172850E+01
3(2)= .398007E-03
3(3) = .243885E+02
PUJU’) P(2,KP) P(3,KP) POLK?) P(5.KP)

.4260317D-0] -.9810796D-05 -.4880215D-02
-.9810796D-05 .2760675D-08 -.1563382D-05
-.4880215D—02 -. 1 563382D-05 .1735952D—01

CORRELATION MATRIX

.1000000E+01

-.9046397E+00 .1000000E+01
-. 1794523E+00 -.2258336E+00
WLK),K=LNP

.8875802E+03 .3472610E+07

.3472610E+07 .1396815E+11 .2234416E+07

.5623259E+03 .2234416EHJ7 .4170000E+03
XTY(I),I=1,NP, WIERE Y 18 RESID

.1574945E-02 .5687588E+01 .1635058E-02
XTY(I),I=1,NP, Y IS Y. NOT RESID
-.1]14548E+00 -.5179943E+03 -.6444745E-01

MAX NP INDEX IP
3 3 3 4

.1000000E+01

.5623259E+03

SEQUENTIAL ESTIMATES OF TIE PARAMETERS GIVEN BEIDW

ETA RES. 3(1) 3(2) 3(3) 3(4)

26.82
26.7]
26.72
26.68
26.63
26.59
26.55
26.52

I
1
2
3
4
5
6
7
8
9 26.48
10

.006
.024
.005
.000
-.056
-.049
-.059
-.056
-.070

.1732E+01
.1 144E+01
. 1743E+01
.1854E+01
.2264E+01
.2284E+01
.2286E+01
.2236E+01
.2222E+01 . .
26.45 -.085 .2227E+01 .2632E-03 .2407E+02

.3984E-03
.5628E-03
.3962E-03
.3657E—03
.2532E—03
.2477F203
.2473E-03
.2606E-03

2645E-03

.2439E+02
.2478E+02
.2438E+02
.2431E+02
.2405E+02
.2404E+02
.2403E+02
.2407E+02

2408E+02

26.42
26.38
26.35
26.33
26.30
26.27
26.25
26.22
26.20
26.17
26.15
26.13
26.1 1
26.08
26.06
26.04
26.02
26.01
25.99
25.97
25.95
25.94
25.92
25.90
25.89
25.87
25.86
25.84
25.83
25.81
25.80
25.79
25.77
25.76
25.75
25.74
25.72
25.71
25.70
25.69
25.68
25.67
25.66
25.65
25.64
25.63
25.62
25.61
25.60
25.59
25.58
25.57
25.56
25.55
25.54
25.54
25.53
25.52
25.51
25.50
25.50
25.49
25.48
25.48
25.47
25.46
25.46
25.45
25.44
25.44
25.43

-.018

-.039

-.059
-.036
-.080

.2154E+01
.2074E+01
.2041E+01
.2038E+01
.2036E+01
.2035E+01
.2037E+01
.2003E+01
.1980E+01
.1945E+01
.1903E+01
.1865E+01
.1856E+01
.1863E+01
.1851E+01
.1839E+01
.1840E+01
.1846E+01
.1862E+01
.1868E+01
.1868E+01
.1853E+0]
.1835E+01
.1823E+01
.1818E+01
.1813E+01
.1808E+01
.1794E+01
.1774E+01
.1761E+01
.1762E+01
.1773E+01
.1772E+01
.1762E+01
.1752E+0]
.1732E+01
.1711E+01
.1699E+01
.1693E+01
.1687E+01
.1681E+0]
.1673E+01
.1668E+01
.1669E+01
.1678E+01
.1684E+01
.1678E+01
.1674E+01
.1674E+01
.1677E+01
.1674E+01
.1667E+01
.1669E+01
.1678E+01
.1686E+01
.1692E+01
.1696E+01
.1700E+01
.1704E+01
.1707E+01
.1704E+01
.1703E+01
.1708E+01
.1712E+01
.1715E+01
.1716E+01
.1718E+01
.1719E+01
.17]9E+01
.1722E+01
.1726E+01

.2825E4I3
.303 5E-03
.3 12 1E-03
.3 130E-03
.3136Ek03
.3136Ek03
.3132EL03
.3220E-03
.3278Ek03
.3366E}03
.3473E>03
.3 568E-03
.3589Ek03
.3 573E-03
.3603E413
.3633E-03
.3629E}03
.3614Ek03
.3577EF03
.3560Ek03
.3560E4I3
.3597EL03
.3641E4I1
.3668E4I3
.3682E—03
.3694E}03
.3704EPO3
.3738Ek03
.3784Ek03
.38 1 613-03
.3813E-03
.3786E}03
.3790E4I!
.38 1 2E-03
.3836Ek03
.3882ELO3
.3928Ek03
.3957E413
.3969E903
.3985E-03
.3997Ek03
.4016Ek03
.4027EP03
.4026E413
34x30303
.3991E}03
JﬂXﬂﬂ§03
.4014ELO3
.4012E4I3
.4006Ek03
.4013EEO3
.4029EPO3
.4025EL03
.4004E4I3
.3986E4I3
.3975EF03
.3966EF03
.3956E-03
.3948Ek03
.3942EE03
.3949E203
.3951Ek03
.3941EF03
.3932EF03
.3924ELO3
.3924Ek03
.3919Ek03
.3916EEO3
.3916E>03
.3910Ek03
.3902EE03

.2412E+02
.2417E+02
.2419E+02
.2419E+02
.2419E+02
.2419E+02
.2419E+02
.2421E+02
.2422E+02
.2424E+02
.2427E+02
.2429E+02
.2430E+02
.2429E+02
.2430E+02
.2431E+02
.2431E+02
.2430E+02
.2429E+02
.2429E+02
.2429E+02
.2430E+02
.2431E+02
.2432E+02
.2432E+02
.2432E+02
.2432E+02
.2433E+02

.2434E+02
.2435E+02

.2435E+02
.2434E+02
.2434E+02
.2435E+02

.2435E+02
.2437E+02
.2438E+O2
.2438E+02
.2439E+02
.2439E+02
.2439E+02
.2440E+02
.2440E+02

.2440E+02
.2439E+02
.2439E+02

.2439E+02
.2440E+02

.2440E+02
.2439E+02

.2440E+02
.2440E+02

.2440E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2438E+02
.2438E+02
.2438E+02

.2438E+02

.2438E+02
.2438E+02
.2438E+02
.2438E+02
.2438E+02
.2437E+02
.2437E+02
.2437E+02
.2437E+02
.2437E+02

204

3288838938893

2542
2542
2541
2541
2540
2540
2539
2539
2538
2538
2537
2537
2536
2536
2535
2535
2534
2534
2534
2533
2533
2532
2532
2532
2531
2531
2531
2530
2530
2530
2530
2529
2529
2529
2528
2528
2528
2528
2527
2527
2527
2527
2527
2526
2526
2526
2526
2526
2526
2525
2525
2525
2525
2525
2525
2525
2525
2524
2789
2784

2774
2770

2762
2758
2755
2751

27:45
27.42

4068
a029
4023
4084
m062

.015
4029

4151
4147
a076
4055
a067
4079
4108
4136
a083
.020

4021
4034
n03]

.1728E+01
.1727E+01
.1726E+01
.1728E+01
.1730E+01
.1725E+0]
.1722E+01
.1721E+01
.1724E+01
.1731E+01
.1737E+01
.1739E+01
.1739E+01
.1740E+01
.1742E+01
.1745E+01
.1750E+01
.1751E+01
.1747E+01
.1743E+01
.1741E+01

.1741E+01
.1740E+01

.1735E+01
.1728E+01
.1723E+01
.1719E+01
.1715E+01
.1709E+01
.1701E+01
.1697E+0]
.1696E+01
.1692E+01
.1685E+01
.1680E+01
.1675E+01
.1669E+01
.1663E+01
.1659E+01
.1656E+01
.1655E+01
.1652E+01
.1648E+01
.1647E+01
.1647E+01
.1644E+01
.1640E+01
.1638E+01
.1636E+01
.1633E+Ol
.1632E+01
.1632E+01
.1632E+01
.1634E+01
.1636E+01
.1638E+01
.1640E+01
.1643E+01
.1643E+01
.1643E+01
.1643E+01
.1644E+01
.1645E+01
.1646E+0]
.1647E+01
.1647E+01
.1648E+01
.1649E+01
.1651E+01
.1652E+01
.1653E+01

.3899EHO3
.3900EF03
.3903E413
.3897E403
.3894EP03

.3903Ek03
.3910Ek03

.3911E}03
.3905E}03
.3892Ek03

.3880ELO3

.3876E4I!

.3875E}03
.3873Ek03
.3870E4I3

.3863E}03

.3854Ek03
.3851Ek03

.3858E—03
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.2437E+02
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.2440E+02

.2440E+02
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.2440E+02
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.2410E+02
.2410E+02
.2411E+02
.2412E+02
.2413E+02
.2414E+02
.2414E+02

205

27.39
27.36
27.34
27.3 1

.159

-.0 l 9
-.088
-.074
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.014

.1653EH11
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.5024E-03
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.2414E+02
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.2420E+02
.242 1E+02

.2423E+02
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.2425E+02
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.2428E+02
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.243 1E+02
.243 1E+02
.243 1E+02
.243 1E+02

2431E+02

.243 1E+02
.243 1E+02
.243 1E+02
.243 1E+02
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.243 1E+02
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.243 1E+02
.243 1E+02
.243 1E+02
.243 1E+02
.243 1E+02
.243 1E+02
.243 1E+02

206

26.33
26.33
26.33
26.33
26.33
26.32
26.32
26.32
26.32
26.32
26.32
26.32
26.31
26.31

26.31
28.95
28.90
28.85
28.81
28.77

28.69
28.65
28.62
28.58
28.55
28.52
28.49
28.46
28.43
28.40

.1746E401
.1745E+01
.1743E+01
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.1723E+01
.1721E+01

.41 5613-03
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.2431E+02
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207

2838
2835
2833
2830
2828
2826
2824
2822
2820
2818
28J6
2814
28J2
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2809
2807
2805
2804
2802
2800
2799
2797
2796
2795
2793
2792
2791
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2782
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2770
2769
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2758
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2755
2755
2753
2753

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208

410
411
412
413
414
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2750
2750
2749
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2748
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2741
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.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02
.2439E+02

SYP
L000000 .408732ELO7 .229003E+01

P(4J(P)

.229003E+01

l’(iKP)

209

-.1795586E+00 -.2256428E+00 .1000000E+01
XTX(1,K),K=1,NP
.8875370E+03 .3472562E+07 .5623120E+03
.3472562E+07 .1396846E+11 .2234441E+07
.5623120E+03 .2234441E+07 .4170000E+03
XTY(1).1=],NP, WHERE Y IS RESID
-.2978191E-02 -.9529109E+01 -.3557077E-02
XTY(I),I=1,NP, Y IS Y, NOT RESID
-.1114359E+00 -.5179274E+03 -.6443841E-01
MAX NP INDEX IP
4 3 3 4

210

APPENDIX J - A Listing of the Estimated Thermal Diﬁ'usivities

211

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Copper Sample:
Test Estimated Test Estimated Test Estimated
Number 01 x 106 Number 01 X106 Number 01 X106
[mzlsl [m2/s] [mzls]
1 100.24 16 101.23 31 105.56
2 97.23 17 104.35 32 100.52
3 100.98 18 102.91 33 102.94
4 99.54 19 106.86 34 105.57
5 94.02 20 102.095 35 100.34
6 97.59 21 103.56 36 101.268
7 97.8 22 98.86 37 103.45
8 98.82 23 98.669 38 99.47
9 97.6 24 106.16 39 97.17
10 99.44 25 100.3 40 95.24
11 100.31 26 103.18 41 99.57
12 96.68 27 97.88 42 97.26
13 99.29 28 98.54
14 98.16 29 100.61
15 100.68 30 100.53
Iron Sample:
Test Estimated
Number a x 10‘5
[m2/sl
1 14.27
2 11.02
3 13.34
4 12.95
5 12.25
6 13.65
7 13.49
8 10.86
9 11.28
10 10.95
11 13.06
12 13.49
13 13.98
14 11
15 1409

 

 

 

 

212

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Diamond Sample AT#4:
Test Estimated

Number 01 x 10‘5
[mzls]

1 425

2 401

3 456

4 400

5 410

6 420

7 392

8 428

9 446

10 425

11 377

12 401

13 451

14 396

15 433

Diamond Sample ST#192:
Test Estimated

Number 01 x 10‘
[m2/SJ

1 492

2 457

3 442

4 474

5 479

6 480

7 499

8 476

9 497

10 492

11 436

12 490

13 481

14 459

 

 

 

 

213

APPENDIX K - Fast Line Scan Mode

Introduction:
The Inframetrics Model 600L radiometer is equipped with a high speed measurement mode

 

known as the fast line scan mode. This feature is designed to capture thermal events along a litre
with a sampling rate of 8 KHz.

The horizontal scan mechanism in the radiometer is a resonant galvanometer. The
frequency of this galvanometer is 3933 Hz. The “galvo” operates in a sinusoidal scan mode and
produces 3933 left to right scans and 3933 right to leﬁ scans in one second. Therefore during this
second 7866 lines are scanned. This results in a diﬁ‘erence of 127.1 microseconds between
consecutive scan lines.

In order to scan at this rate the vertical scan galvanometer is stopped somewhere near the
center of the ﬁeld of view. In many application it is important to know which line is being
measured. In this study a simple experiment, shown in Figure l and Figure 2, was conducted to
determine if the vertical scan galvanometer is positioned in the same location each time the fast line

scan mode is used.

214

LASER STRIKE PAD

 

 

 

 

 

 

 

 

TH I N F INS
Figure 1. Copper test specimen used for fast line scan mode experiment.

MODEL 600L RADIOMETER CONFIGURED 1N TEST SPECIMEN SHOWN |N
FAST LINE SCAN MODE. THE OUTPUT 13 FIGURE |
RECORDED ON A STANDARD VWCR

\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\A

\ .35

Figure 2. Experimental Setup

Eagleriment @d Result;
In this experiment the beam of the Nd:YAG laser is positioned in the center of the laser

strikepadshowninFigure l. Thetwothinﬁnsareusedtocarryhemawayﬁ’omme strikepad.

215

The radiometer is conﬁgured in the fast line mode and the temperatures are recorded along some
line at ~8000 Hz.

The measured temperatures will depmd on the location of the vertical scan galvanometer.
In this experiment several measurements were taker and the test specimen was adjusted to
vertically move the position of the thin ﬁns. In the ﬁrst series of tests, the specimen was
positioned in a way that the line scan mode would not read the temperatures along the two thin ﬁns.

The results are shown in Figures 3 and 4.

position

 

L‘ Di] DDIDD’OD'DD

 

 

Figure 3. (A) Radiometer placed in image mode. The red line indicates approximate
location of the fast line scan. (B) The radiometer is placed the fast line scan mode and
the specimen heated with a Nd: YAG laser.

216

Temperature distribution along test specimen
with radiometer in fast line scan mode. In this case
radiometer is not scanning along the thin ﬁns.

 

TemmMC)
3

244

 

22

 

 

0 11X) 200 300

:_ 1.....-

X D‘nction (Plxeb)

Figure 4. The temperature proﬁle along a line not corresponding to the location of the
two thin ﬁns.
In the next series of tests, the specimen was positioned so the line scan mode would read

theternperature distribution alongthethin ﬁns. Theresultsofthesetestsareshown in Figures

and Figure 6.

:‘Zr‘ E113 001011.50 ED

   

Figure 5. (A) Radiometer placed in image mode. The red line indicates approximate location of

the fast line scan. (B) The radiometer is placed the fast line scan mode and the specimen heated
with a Nd: YAG laser.

217

Temperature distribution along test specimen
with radiometer in fast line scan mode. In this case
radiometer is scanning along the thin ﬁns.

 

34

 

 

 

32W
A304
9..
g 0
§ZB~ ,
o
I— 234
O -
24~
22 T Y 1 l' T T
0 100 200 300 400 500 600
XD'I'ection

Figure 6. The temperature proﬁle along a line corresponding to the location of the two
thin ﬁns.

Tests similar to this were repeated several times. It was found that the vertical scan “ vo”
positions itself in the same location of the radiometer ﬁeld of view each time the fast line scan
mode in used. When data is analyzed with the ThermoGRAM processing software this position

corresponds to line ntnnber 95.