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3 1293 017014

The is to certify that the

, thesis entitled

_ POLARIZATION EFFECTS IN OPTICAL
' DIFFRACTION

 

presented by

Robert Louis Gault

has been accepted towards fulfillment . r
of the requirements for

 

M. S. degree in Physics

algm

Major professor . --‘

Date W

0-1 69

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1198 cJClRC/DateDue.p65-p.14

3".

POLARIZATION EFFECTS

IN OPTICAL DIFFRACTION

by

Robert Louis Gault

.A Thesis
Submitted to the School of Graduate Studies of
Michigan State College of Agriculture and
Applied Science in partial fulfillment

of the requirements for the
degree of

MASTER OF SCIENCE

Department of Physics

1953

 

 

.{Ilf|.‘||l III"
[I I lllll'llllllll! ill I

.lLCKI‘Qr O’. JLEDGEl‘iEJ T

I wish to eXpress my sincere thanks to Professor
C. D. Hause for introducing me to this problem and for

his kind encouragement and assistance toward its com-

Pletion. 1 KM jM

 

.[lll'lul-IIIIIIIIIIIIII IIIIIIIII I

 

II.

III.

IV.

TABLE OF CONTENTS

INTRODUCTI O‘DI O O O O O O 0 O O O 0

THEORY OF DIFFRACTION OF LIGHT BY A HALF-PLENE

A. The Sommerfeld Theory. . . . . . .

B. Mathematical Expression for Polarization
Ratio 0 O O O O O O O O O O 0

C. Polarization by a Slit . . . . . .

APPARATUS AND METHODOLOGY . . . . . .

.A. Characteristics of the Photomultiplier Tube

. Light Source Requirements . . . . .
. The Comparator Detector . . . . . .
Photomultiplier Cooling System . . .

Optical Equipment . . . . . . . .

*dtIJUOUJ

. Operation of the System . . . . . .

DATA ANALYSIS AND CONCLUSIONS . . . . .

A. Sources of Error . . . . . . . .
B. Discussion of Results . . . . . .
C. Comparison with Previous Work . . . .
D. Suggestions for Improving the Equipment.
E. Summary of Conclusions . . . . . .

“'1‘?“ “’71- *1
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[ 'Il‘ln l. I [I'll l [I I‘ll] l I <l||llll| I! III Illllll

I. INTRODUCTION

When unpolarized light is scattered by a sharp straight
edge, it is possible to observe a polarization in the dif-
fracted light. This effect was first described by Gouy and
Wien in the 1880's.1 Arnold Sommerfeld's mathematically exact
solution for the problem of diffraction of electromagnetic

waves by a straight edge, which eXplained the polarization

P

‘ Later observations of the

effect, was published in 1696.
effect were made by Jentsch3 in 1927, using traditional opti-
cal methods. These observations were in close agreement with
the predictions made by Sommerfeld.

Interest in general diffraction theory has been stimulated
in the last few years by the development of the technology of
micro waves. Other contemporary technological developments
have made it possible to make measurements of optical phenomena
(particularly those of low intensity) by means other than the
traditional ones. In view of these two facts, it seems perti-
nent to re-investigate some particular aspects of the straight-
edge diffraction phenomena.

This paper deals with some observations of the polariza-
tion effect produced by the diffraction of light by a straight-
edge and by a narrow slit. The theoretical discussion begins

with the general results predicted by Sommerfeld, and is carried

{\3

out in detail to show the polarization intensity ratio to
be eXpected for light diffracted by a straight-edge. In
addition an approximate treatment for the polarization by a
slit is included.

Observations were made by means of the electron photo-
multiplier tube. The results agree with Sommerfeld's theory
as closely as may be expected, and for the best measurements
made, show a slight disagreement with the observations of
Jentsch.

The investigation has turned out to be a very interest-
ing one, and as experimental projects are wont to do, has led
the author into many unexpected problems as well as many sur-

prising and educational observations.

II. THEORY OF DIFFRACTION OF LIGHT BY A HALF-PLANE
A. The Sommerfeld Theory

Sommerfeld's exact solution of the problem of diffrac-
tion of electromagnetic waves by a semi-infinite, perfectly
conducting half-plane is one of the outstanding examples of
the application of mathematical ingenuity to the theoretical
treatment of a physical problem. Despite the ingenuity of
the method, the solution has so far been of restricted use-
fulness. It has not been found applicable to any but this
one very particular problem -- that of the diffraction of
light by a half-plane. (In this paper the word-"light" will
be used interchangeably with the phrase ”electromagnetic
radiation", but it must be realized that Sommerfeld's theory
is not restricted to visible radiation).

The problem at hand involves the solution of the wave
equation with the boundary conditions appropriate to a con-
ducting half-plane. If the screen (the half-plane) is a per-
fect conductor, then the necessary boundary condition is that
the tangential component of the electric field must vanish
everywhere on the screen. A three dimensional coordiante
system may be defined, in which the screen occupies all the
points included in the x-z plane for which x is positive. Thus
the edge of the screen lies along the z-axis, and the material

of the screen lies behind the edge, in the x-z plane.

It would be a simple matter to satisfy the necessary
boundary conditions if the screen occupied the whole of the
x-z plane. The method would be similar to the method of
images used in solving electrostatic problems. That is, if
one considers a line source of electromagnetic radiation
parallel to the z axis and placed so that it intersects the
positive y-axis at an infinite distance from the origin, the
condition for vanishing of the tangential component of the
electric field on the x-z plane can be satisfied by merely
imagining another line source, equal to but out of phase with
the first, (and polarized in the same direction) placed paral-
lel to the z-axis, so that it intersects the negative y—axis
at an infinite distance from the origin. This make the
tangential component of the electric field vanish at every
point of the x-z plane, whereas for the problem at hand it is
desired to make it vanish Only on half of the plane. Sommer-
feld's solution involves such an ”image” type of solution, but
requires the use of a two-sheeted Riemannian surface to insure
that the electric field vanishes only on the half plane occup-
ied by the conducting screen. This argument is carried out
in a straight forward fashion in Born's thi§.4 The theoret-
ical material which follows is based upon the results of the
Sommerfeld theory.

It is found that the solution depends on the state of
polarization of the incident light. Since a line source

parallel to the half-plane is being cbnsidered, it is evident

that the situation is one which is not dependent on z, and
which can therefore be considered a two dimensional problem.
Figure 1 shows the x-y plane, in which the positive x-axis
represents the intersection of the screen with the x-y plane,
the point P represents the intersection of the line source
with the x-y plane, and the point Q represents the position
of the observer at a distance r‘ from the edge. The angle V%
is the angle of incidence of the plane waves from P, while
the angle 99 is the angle of diffraction. Both angles are
measured in a counter-clockwise direction from the positive
x axis.

Since the source is at an infinite distance from the edge,
the disturbance caused by it is a plane wave, polarized either
parallel to the line of the source (hereafter referred to as
the TT case) or perpendicular to the line of the source (here-
after referred to as the a— case). The strength of the source
is such that without the interference of the half-plane, the
amplitude of the disturbance is unity. The effect of inserting
the half-plane into this plane wave disturbance is to change
the form of the disturbance. The resultant disturbance takes
on three distinct forms, as may be seen in the three divisions

of the Space in Figure 1.

The first section (the reflection region) is one in

which the net disturbance consists of the incident plane wave,

 

 

 

P! Source at infinite distance

a. Observer at finite distance
I: Reflection region

11' Unehodowed region
III8 Shadow region

FIG. I- COORDINATE SYSTEM OF THE SWHERFELD THEORY.

a reflected plane wave, and a cylindrical wave radiating from
the edge of the half-plane. In the second region (unshadowed),
the net disturbance consists of the incident plane wave plus
the cylindrical wave from the edge; while in the third region
(the shadow region), the only disturbance is that due to the
cylindrical wave from the edge. For a unit amplitude incident
wave the amplitudes of these disturbances take the following
forms:
I Reflection region:
2%,; C05 [w cosiwaiizcosEKVCos I 50+ 9%)] + E
II {Unshadowed region:
urge“; COS [eroSIW-'%:‘:I +2 (1)
III Shadow region:

' Ll..- __ ”1.....—
up =- 2 = :1; If—éiiesywaIIicosgs Cog—e]

where the term Z represents the cylindrical wave, and k is
the propagation constant, equal ton1 . Where there is a
choice of signs, the upper sign corresponds to the W'case
while the lower sign corresponds to the 0’ case.

This problem.will be primarily concerned with that part
of the disturbance which is the cylindrical wave. It is con—
venient to use the terms ”inflection angle” and ”deflection
angle” when discussing this wave. The former refers to the
diffraction angle for light which is diffracted into the region

of the geometric shadow, while the latter refers to the dif-
-fraction angle for light which is diffracted into the non-shadow

region. The former is measured counter-clockwise from the
extension of the line of propagation of the incident wave,
and the latter is measured clock-wise from.the same line. In
other words, if the observer stands in the geometric shadow
he sees inflected light; while if he stands in the unshadowed
region, he sees deflected light from the edge (in addition to
the direct light from the source).

If one observes this phenomenon qualitatively, it may
be seen that it behaves as predicted by Sommerfeld. If one
standinn the shadow region and observes the edge which is
illuminated by a narrow source parallel to the edge and at
a reasonably large distance (50 cm. or so) from it, the edge
will appear to be the source of radiation. If the direction
of polarization of the incident light is changed, the apparent
intensity of this source changes. It appears most brightly
illuminated when the light is polarized perpendicular to the
edge. An important fact here is that the edge appears5 to be
the source of the diffracted light. Just the inverse polar-
ization effect“is observed in the light diffracted into the
unshadowed region. In order to see the effect in the latter
case, it is necessary to exclude light coming directly from

the original source to the observer.

B. Mathematical Expression for Polarization Ratio

If one takes the expression from equations (1) for the

amplitude in the shadow region and divides the amplitude for

parallel polarization by that for perpendicular polarization,
then squares the resultant ratio, there results an expression
for the ratio of intensities of the parallel to the perpen-

dicular polarization components:

25: (figggl'Cos(Z—ffi)
Z,- C:s(€-ig°) +c05(5f_’:%)

Upon expansion and simplification this expression leads to
the e uation
q Zl:—7&n.2gp7afi§eo
Ear (2)
Therefore the polarization intensity ratio is:

“(Tan 7317‘%91(5)

If

This expression holds for the cylindrical wave in both the
shadow and non shadow regions.
When (3) is written for an inflection angle equal to 5',

where 5‘54'56’77 ) 520)
177 -001“? Q5) (4)

——~-....

d‘

For deflection at an angle -n5,
I

in: .. —————-—-—-.
I, ‘ Cor‘{-§+-g—) (6)

These relationships may be derived as follows:

Let ,f’:u%: (the case of normal incidence),

0

z 2 23
then from (a), fin? raga”; =7Zm 2 .
f

Since :23? 177, 2. 77;)
V z ”(5) 3;““5’4/‘372. ,

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then in: - ”“*75”% ”7'0“”?—
Id’ /«-—7:a7n3_!£7&,, 5 /«/fh—-—-
=74» Zia/“'37

or, a: Cor-2(g,‘ .3.) a ' (4)
where the subscript "4:" refers to inflected light.

Equation (6) gives the polarization ratio for an inflec-
tion angle 5 , in the shadow region.

Consider the situation for deflection into the un-shadowed
region* at an angle -5, where fair—S; replacing 5 by (- 5 )

and changing the subscript to "d", for deflection,

IE. - 2 _.S ‘ (5)
Id d- 60" (TE 3-.) /
5 ,.————¢"'””'
raw/22* ‘2’) COPE?“ f); (6)
there results:
I”) 2:: if... ('7)
15* . 1S7 '

Thus the polarization ratio at a given inflection angle in
the shadow region is just the inverse of the polarization ratio

at; the same deflection angle in the non-shadow region.

C. Polarization by a Slit
This argument can be extended to yield an approximate

treatment for the polarization to be expected from a slit

—¥

* In all observations in the un-shadowed region, the
original light from the source is excluded.

ll

made up of two sharp edges. For simplicity we will consider
the case of normal incidence (Ifi:=§: ).

It has been proved that the intensity ratios for in-
flected and deflected light are reciprocal, and now it will
be shown that the intensity for parallel light inflected at
an angle CS is the same as the intensity for perpendicular
light deflected at an angle-zS, and therefore that no polar-
ization is to be expected for a slit composed of two sharp

half planes.

 

 

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  W m
2- 1 ,J ’
For inflection at an angle .5 j y—ggz :- 5
so that V: 542;...”
Thus #V+%_flé :22- Zzé 77
2: .l 2.4 1 «b4 2L¥ 2
FH’. __ s ._ .
and (’o 1 .. C05(—i-+7r), €05.52: 9
also, S’.$’,_ i433: i+Z
2. 2. 5r 2- 2.
and C05 W£V0:005(§£+§):—5flié.
Therefore '__/ / (9)
(277),; 3 C (C05 %_ ‘f 5’.” '3") )

which represents the amplitude of the light inflected at an
angle 5 for parallel polarization. To find the amplitude for
a deflection angle (”5: for perpendicular polarization, the
Sign of the first term in (9) is changed (necessary for the

6" case) and § is replaced by-5 .

12

II

/ /
Thus, (3r); CIEZ’JTE—‘W WI]

 

.. I /
C[C‘o$-§Zj 54;“ .25.] (10)
Therefore, from (9) and (10), (20.90) :: "('27,)4,‘ (ll)
and (1.4),; :2 (In); (13)

It is pertinent to refer to Figure 2, which shows schem-
atically a narrow slit formed of two sharp edges very close
to one another, and to consider the polarization intensity
ratio which will be observed at the point Q. For each state
of polarization, there is some light diffracted from each
edge. The d‘case is considered first. Depending upon the
phase difference between the light from the two edges, there
is observed some resultant intensity of light at Q. The phase
difference between the two rays from 1 and 2 depends upon
the differences in path length and upon a phase difference
of 180 degrees (at the slit) between the inflected and deflected
rays. (this 180 degree phase difference is indicated by the
negative sign in equation (ll) above). The amplitude of the
disturbance from edge 1 is larger than that from edge 2. Let
Z, =KZz’ where K is greater than unity. These disturbances
are out of phase by some angle.i when they arrive at Q, and
their net amplitude may be easily calculated.

Now for the 7T case E’s/(27 , where K is the same as

for the gr case, since from equation (9) the W” component

 

13

P (Source)

I

\]

9’2
\ EDGEI

 

2/

EDGE 2/
I3 ,.
l
|

Q (Observer)

FIG. 2- SLIT COORDINATE SYSTEM

14

from 1 is the same as thecf'component from 2, and vice versa.
Because the path difference is the same for both cases, the
phase difference here also is c%, so that the net amplitude
for the fl‘case is the same as that for the a‘case. The Tr
radiation cannot interfere with the J‘radiation, therefore

it follows that I” is equal to I(-.

Thus no polarization is predicted for a "sharp" slit so
long as the slit width is large compared with the wavelength
of the light and small compared with the distance of the
observer from the slit; that is, when the two edges do not
interact with one another. This simple treatment considers the
two edges to be independent sources.

The same conclusion is indicated, in the.more rigorous

treatment by Morse and Rubenstein6

of a slit made up of mathe-
matical half-planes, for slit widths large compared with the
wavelength. It is interesting to note in this connection

that for extremely narrow slits the Morse and Rubenstein
theory predicts a polarization effect with the ratio In-/IJ.
oscillating as the slit width decreases. In the limiting

case of slit width smaller than the wavelength, the theory
predicts a strong polarization perpendicular to the edge.
However, it will be mentioned later that a "physical" slit,

of the type ordinarily used in the laboratory, exhibits strong

parallel polarization for small widths.

15

III. APPARATUS AND METHODOLOGY

A. Characteristics of the Photomultiplier Tube

Since measurements of this phenomenon were made using
the electron photomultiplier tube, certain of its character-
istics had to be considered in the design of the equipment.
These difficulties are discussed in detail by Kessler and
Wolfe? and by Weekse, and will be only briefly mentioned here.

The electron photomultiplier tube is a very sensitive
light detecting device which responds more or less linearly
to the intensity of the incident light. Its two greatest
shortcomings are its high "dark current" and its large
"fatigue” effect. The term dark current refers to the elec-
tron current which flows in the output circuit of the tube
when no light falls on the photosensitive surface. The dark
current is probably mainly due to the random emission of
thermally excited electrons, and manifests itself as a more
or less steady D.C. component plus random alternating com-
ponents which produce a continuous spectrum of "noise" cover-
ing the audible range of frequencies. The term fatigue refers
to the decrease in sensitivity of the tube with continuing
exposure to light and the subsequent slow recovery of sensi-
tivity when the source of light is removed. Another difficulty

is the dependence of sensitivity upon accelerating voltage.

16

The dark current can be minimized in two ways. The first
method involves using a light source whose intensity varies
periodically, and an amplifier system whose response is high
at the frequency of the source intensity variation, but low
at all other frequencies. In this way, only those noise
frequencies which are nearly the same as the source frequency
will be amplified. A second method actually reduces the noise
at its source by cooling the tube. Since any reduction of
temperature produces some reduction of noise, the temperature
used will depend on the particular situation in which the
photomultiplier is to be used or the noise which can be toler-
ated.

The fatigue effect, however, cannot be minimized as effec-
tively. It has been noted.7 that the rate at which the sensi-
tivity changes is large for high intensities of incident light
and small for low incident intensities. Thus the treatment
of the fatigue problem requires admitting only the smallest
possible amount of light to the phototube. This of course
means a lower ratio of signal to noise, and so it is evident
that a compromise must be made between the allowable noise
level and the amount of fatigue which may be tolerated.

The effect of change in sensitivity with accelerating

voltage applied to the tube may be reduced simply by using a

well regulated power supply.

17

Photomultiplier tubes are in general sensitive to the
state of polarization of the incident light.9 The type which
displays this effect the least (RCA lPZB) was used for these

measurements.

B. Light Source Requirements

Since the conventional alternating current supply mains
have a frequency of 60 cycles per second, it is convenient to
make use of the resulting 120 cycle intensity variations in
the output of a light source supplied by these mains. One
complication involved in using this frequency for a tuned
amplifier is that any amplifier operated from a 60 cycle sup-
ply will have in its output a certain amount of energy at
both 60 and 120 cycles; this energy arises from various sources,
one of which is imperfect filtering in the power supply.
Thus, if the amplifier is tuned to 120 cycles for the sake of
minimizing the noise in a phototube, the amplifier "hum" at
120 cycles will also be amplified.

There are two possible ways to get around this difficulty,
both of which were tried and found to be fairly workable.
One method requires operation of the amplifier (or at least
its first stage) from a battery supply; the other requires
using a frequency other than 120 cycles for the intensity
variations of the source.. The latter can be achieved either
by using a D.C. operated light source in conjunction with a

chopper or by arranging for a primary supply at a frequency

18

other than 60 cycles. It happened that there was available
in the department a World War I surplus 400 cycle generator
having a capacity adequate to operate any available light
source. This allowed tuning the amplifier to 800 cycles and
practically eliminated the 120 cycle hum in the amplifier.

Any light source produces an output which is only approxi-
mately constant, even when operated from a very well regulated
power supply. In order to avoid errors occurring from these
random fluctuations, a comparator measurement system was used
such that light directly from the source was compared with
that observed in the diffraction pattern.

Since it is necessary in these measurements that the
light source be unpolarized, there is need to determine whether
or not this condition is satisfied.

In order to obtain the maximum possible light intensity
in the diffraction pattern, a high-powered (750 Watt) mercury
arc was used as a source. It was found later that a lower
powered arc (100 watts) of the high pressure type served just

as well as the larger arc.

C. The Comparator Detector
Since the random variation of intensity to be expected
from the light source had to be dealt with, a comparison detec-
tor was used. In this system, two photomultiplier tubes are
used. One "looks” directly at the source; the other looks at

the light diffracted from the straight edge. It is desired

19

to measure the change in intensity of the diffracted light

as the state of polarization of the incident light is changed
from parallel to perpendicular with respect to the edge. In
order to measure the ratio of the intensities observed by the
latter tube, a tuned two channel amplifier was used. Each
channel is tuned by a degenerative twin "T" filter. One of
the channels contains a calibrated attenuator. Figure 3 is

a block diagram of the circuit.

If the two phototubes are illuminated with light of the
proper intensity to produce equal voltages at the grids of
the phase balancing tubes, and the phasing adjustments are
made so that the two voltages are 180 degrees out of phase,
the output voltage at the commonly connected plates will be
essentially zero. If now the intensity of the light falling
on the upper tube is allowed to increase to, say, twice the
original intensity, the output voltage will be large. Then
if the signal in the upper channel is attenuated to half its
new value, the grid voltages at the phase balancer will be
equal again, and the output voltage on the plate will be
essentially zero.

The ratio of the two voltages (from the upper tube) is
determined by the two settings of the attenuator for exact
balance. Since the signal level in the lower amplifier is
constant, and the signal level in the upper amplifier is
constant when the attenuator is set for balance, the only

Part of the circuit except for the attenuator which could

20

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affect the accuracy of the ratio is the pre-amplifier. As
long as the pre—amplifier is operated linearly, it will not
affect the results. In order to insure that this condition
is satisfied, the output voltage of the comparator is observed
on an oscilloscope. Whenever the signal is large enough to
produce distortion in the pre-amplifier, there appears on
the oscilloscope the harmonic content of the pre-amplifier
output, which cannot be balanced out. The light intensity
must then be reduced to eliminate the distortion. In practice,
this is accomplished by inserting a neutral density filter
into the optical path ahead of the polarizer.

Figure 4 is the circuit diagram of the pre—amplifier.
All voltages are battery supplied in order to reduce hum. The
type 5879 tube was chosen for its low microphonic response.

Figure 5 is the circuit diagram of the two channel ampli-
fier. It should be noted that in order to obtain cancella-
tion it is necessary to have the voltages at the two output
tube grids equal and out of phase. This is accomplished by
having one more stage of amplification in one arm of the
system than in the other. The extra stage is the pre-ampli-
fier. Precise phase cancellation is obtained by adjusting
one or both of the phase control rheostats.

Figure 6 contains diagrams of the high voltage and low
voltage power supplies. The high voltage supply incorporates
a 6Y6 series regulator controlled by a 65J7 amplifier, which

is in turn biased by three VR-lSO gaseous regulator tubes.

22

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D. Photomultiplier Cooling System

It has been mentioned previously that the noise output
of the photomultiplier may be reduced by lowering its tempera-
ture. Attempts were made to cool the tube using solid carbon
dioxide. In the photograph (Figure 7) of the optical system
it is possible to see the polystyrene foam ("styro-foam")
box surrounding the main pickup. Solid carbon dioxide was
placed inside the box, and the box was covered with a styro-
foam lid. The thermal insulation properties of the box were
excellent. However, it was not found possible to sufficiently
reduce the frost formation at the aperture. .After a period of
half an hour the frost would begin building up on the aperture
thereby increasing the pickup of stray light.

For this reason the system was abandoned, despite the

increase in signal to noise ratio effected by the cooling.

E. Optical Equipment

There will be two optical systems discussed here. The
first, which incorporated two lenses, was used for all obser-
vations except the last set shown in Figure 13b. This last
set of observations was made on a lens-free system.

The early optical set up is shown diagramatically in
Figure 8. Light from the 750 Watt Hanovia Mercury vapor lamp
‘was passed through the slit, the filter for the mercury green
line, the variable neutral density filter, the Polaroid polar-

izer, and thence through the 12.5 cm. lens to the diffracting

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edge. The slit was imaged on the diffracting edge. Light
diffracted from the edge was focused on the photomultiplier
tube by means of the 6.5 inch lens.

Early attempts were made to use a Nicol prism as a
polarizer, but it was discarded due to its small aperture
and the internal reflections which caused the intensity of
the light striking the edge to vary as the Nicol was rotated.
An attempt was made to use a Wollaston prism as a polarizer,
but this had to be abandoned when it was found that the prism
available was nOt exactly symmetrical, with the result that
the two beams were deviated at different angles from the axis
of the optical system and caused a variation (at the razor
edge) of intensity with polarization direction. The Polaroid
was used because of its large aperture and freedom from inten-
sity variations with changing polarization. It was found
necessary to use monochromatic light, since the particular
type of polaroid used was a rather poor polarizer in the violet
region but polarized very well in the green region of the
spectrum. It should be noted that the polarization ratio is
independent of wavelength according to Sommerfeld's theory,
and that monochromatic light was used here only to insure com~
plate polarization. P

The neutral density filter was used to reduce the inten-
sity of the light observed at small diffraction angles in order

to avoid overloading the amplifiers.

The 12.5 cm. lens was used to increase the intensity
of light incident on the edge and thus minimize the effect
of stray scattered light, which tended to mask the polariza-
tion effect. The 6.5 inch lens was used to eliminate as
much as possible of the stray light scattered into the photo-
multiplier from unwanted sources. In practice, the edge was
imaged on the phototube, and the phototube aperture was
restricted to the dimensions of this image.

The diffracting edge finally used was simply an ordinary
safety razor blade. Microscopic examination of several brands
indicated that Gillette Blue blades were most consistently
sharp. Under the microscope it was possible to see the grooves
made by the operation of grinding the edge. On a well sharpened
edge the final honing operation removes all these grinding
grooves in the vicinity of the edge. The completeness of this
final honing operation was used as a criterion in selecting
blades to be used.

After examination under a 400 power microscope, the
blades were silver coated by evaporation under a high vacuum.
The thickness of the coating was approximately 400 Angstroms,
as judged by the opacity of the coat on a glass microscope
slide. To illustrate the importance of the shape of the edge,
a few blades were modified by blunting their edges. This was
accomplished by drawing the blades once very lightly over an

extremely fine whetstone, previous to the silvering operation.

50

In order to minimize the amount of stray light reaching
the phototube, light shields were employed. These paper

baffles are not shown in the photograph of the optical system.

F. Operation of the System

The attenuator in the upper channel of the amplifier is
set for minimum attenuation, the polarizer set for parallel
polarization, and the variable slit on the auxiliary pickup
tube adjusted to attain a balance at the phase balancer. If
the main pickup tube is in the geometrical shadow region.
the intensity of the light falling on it will increase when
the polarizer is rotated to produce polarization perpendicular
to the edge. In order to again obtain a balance, it is neces-
sary to attenuate the signal from the main pickup tube.
When the signal is attenuated by the exact amount necessary
to obtain a balance, the attenuator setting is observed.
Reference to the attenuator calibration chart gives the out—
put to input voltage ratio. This ratio is interpreted as the
intensity ratio of the weaker component to the stronger. In
the geometrical shadow region this is the ratio Ifl/Id. When
this process is carried out for various deviation angles, it
is then possible to plot the polarization ratio as a function

of the inflectien angle.

As mentioned before, it is necessary to keep the light
level low enough to avoid distortion in the amplifiers. When
distortion appears, the intensity may be reduced by inserting

the appropriate neutral filter into the main optical path.

31

IV. EXPERIMENTAL OBSERVATIONS

In addition to the quantitative data there are included
hereunder several items which represent observations of a
qualitative nature but which are nevertheless pertinent to

the investigation.

These are the phenomena which were measured:

1. The ratio In—/Id- for sharp, silvered razor edges,
for inflection angles up to 60 degrees, for incidence angles
of 90, 75, and 60 degrees, respectively. See Figures 9a, 10a.
lla, below.

2. The same as above for blunted, silvered edges. See
Figures 9b, lOb, llb.

3. The ratio IJ-/IW" for a sharp, silvered edge, for
deflection angles up to 60 degrees in the unshadowed region.
See Figure 12a.

4. The ratio Irr/Ic- for a slit formed of two sharp,
silvered edges, with a slit separation of 0.16 mm. with light
normally incident. See Figure 13a.

5. The ratio Ifl-/Id— for a sharp, silvered edge in the
shadow region, using an optical system with no lenses, and
using a 100 Watt, concentrated, high-pressure mercury arc

for a source. See Figure 15b.

32

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57

In addition to these measured phenomena, the following
information was obtained:

6. While attempting to control the light flux into the
main pickup tube by means of an adjustable slit, it was ob-
served that when the slit was closed down it acted as a polar-
izing element. .As the slit width was decreased, the degree
of polarization was increased, and the polarization was always I
parallel to the slit. ‘

7. In the process of attempting to track down the varia-
tion caused by the slit polarization, the state of polarization
of the light from the mercury arc was investigated. Within
the limits of the accuracy of the instrument, there was found
to be no polarization of the source.

8. The degree of polarization produced in the incident
light by the Polaroid was measured and found to be sufficiently
perfect for the purposes of this investigation when the light
was filtered to pass only the Mercury green line. The ratio
of the uncrossed to crossed transmission of a pair of such
Polaroids was found to be greater than 100 to l.

9. A small amount of dust or smoke in the air near the
diffracting edge will produce erroneous results, as was ob-
served when an ash tray containing a smouldering cigarette
was inadvertently placed near the diffracting edge. When such
a high concentration of particles exists in the air near the
diffracting edge, the amount of light scattered by these

particles is much greater than the light diffracted from the

38

razor edge, thus masking the polarization effect or even ob-
literating it.

10. One set of blades was unintentionally silvered in
a poor vacuum, with the result that the silvered surface
took on a bluish color. The discoloration may have been due
to some chemical reaction between the evaporated silver and
the gases in the evaporator, or to a reaction involving
Molybdenum unintentionally evaporated from the heating element.
When measurements were made of the polarization ratio in the
shadow region, it was found to be Just the inverse ratio
(qualitatively speaking) of that which is normally observed.
That is, the parallel component was stronger than the perpen-
dicular component. Examination of the edges under a 400 power
microscope showed an aggregation of crystalline lumps on the
surface.

11. In general it was found that after exposure to the
air for a day or so the edges underwent changes which tended
to reduce the intensity of the overall diffraction pattern.
This was true for silvered as well as unsilvered steel edges.
As a result, all observations included in this report were
made on freshly silvered blades. The effect, however, might
be considered as a method for the determination of relative
sharpness of razor blades.

12. Some measurements were.made of the change of inten-
sity with distance for constant incidence and diffraction

angles, and constant state of polarization. The intensity

was measured at distances of 40 and 80 cm. from the edge. For
the system containing lenses, the intensity ratio observed
varied between l/S and 1/4, while for the lens-free system

the value observed was between 1/2 and 3/8. In order to make
this observation on the system containing lenses, it was
necessary to remove the 6.5 inch lens, since at the shorter
distance it was not possible to focus the edge on the pickup
tube. For both measurements the length of the pickup tube
aperture was one inch, while the length of the blade was 1 1/4

inches and that of the source 2 inches.

40

V. DATA ANALYSIS AND CONCLUSIONS

A. Sources of Error

It is expected that all the observations on the system
containing lenses yielded intensity ratios which were too
high. There are three reasons for this. They are: l. Ef-
fective source broadening due to the source lens; 2. Effec-
tive pickup aperture broadening due to the pickup lens; and
3. Masking of the diffracted light by stray scattered light.

The source lens has the effect of broadening the source,

as may be seen in Figure 14. The angles recorded for incidence

\ Ml

/ '\
\ \
-' w

/ .
‘:<1_:> SCURCE LENS

 

 

 

Fig. 14 - Source broadening effect of source lens.

and inflection are)§ and¢§ respectively. These angles are

appropriate only for axial rays from S. For oblique rays,

41

as for example R', the inflection angle should be measured
from the extension of R'. For the same observer's position,
the inflection angle would be a smaller angle,éy. Since the
light from R' has been inflected through a smaller angle ( él)
than the light from R, the intensity of both its polarization
components will be larger and more nearly equal than the in-
tensities of the two polarization components from R. In
other words the light from R' is more intense and less highly
polarized than the light from R; therefore the observed polar-
ization ratio will be higher than would be appropriate for
light incident only along R.

The pickup lens adds to this effect by collecting light

from a large number of inflection angles. Here again, the

{3
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Fig. 15 - Pickup broadening effect by pickup lens.

highest intensity light is light which is less highly polarized
than would be appropriate for the measured inflection angle 5 .
On the scales used to plot the intensity ratios, a large value
of the intensity ratio corresponds to a low degree of polari-
zation. Conversely, a low ratio corresponds to a high degree
of polarization. Thus, on these scales, the observed
values are probably too high, for the reasons just mentioned.

Both of these effects are partially nullified by the
light from the other side of the lens, and therefore the ef-
fects should be most noticeable for small inflection angles.

When the ratio is observed at large inflection angles,
the effect of the stray scattered light becomes important.

For example, let us say the intensity ratio I,r/Ia~ of the
light actually coming from the edge to the pickup is l to 4,
or ITT/IJ-:= 0.25. Suppose the stray light is twice as strong
as thevT component. What the pickup would see would be a
ratio of 2 to 4, or I,r/IJ»= 0.5. Thus for increasing values
of the inflection angles the observed ratios are increasingly
too large.

Another source of error was the frequency instability of
the 800 cycle source. Since the phase responses of the two
amplifiers cannot be made identical, when the frequency of
the source changes it is no longer possible to reach an exact

cancellation. That is, the signals at the grids of the phase
balancer tubes are no longer exactly 180° out of phase and

therefore complete cancellation cannot be effected, without

readjusting the phase controls.

43

In all the measurements, the photomultiplier noise was
present and made it difficult to determine the exact position
of balance. In addition to the noise, the fatigue effect was
always present.

The latter two effects are mainly responsible for the
variation of the observed values from one trial to the next.
This variation is of the order of 0.05 on the scales used to

plot the ratios.

B. Discussion of results

1. Sharp edge (Figures 9a, 10a, 11a): The results for
inflected light for incidence angles of 900 and 75° appear
to agree with the Sommerfeld theoretical curves, but must be
interpreted as being too high for the reasons mentioned above.
For 603 incidence the intensity of both components was low.

The large scatter of the points is attributed to the large
noise level, and the fact that they are higher than the theor-
etical curve is attributed to the masking effect of the scat-
tered light.

2. Blunt edge (Figures 9b, 10b, 11b): Since the exact
shape of the edge is not known, these curves are mainly
valuable for showing that a variation in the shape does drasti-
cally change the polarization effect. The fact that the points
start to swing up at large inflection angles is probably due

to the masking effect of scattered light.

44

3. Sharp edge in deflected light (Figure llc): The
ratios observed in the non-shadow region (i.e. for deflected
light) show good agreement with those for the shadow region
(Figure 9a), as is shown in Figure 12b, on which the two sets
of points are plotted together. It should be noted here that
the ratios plotted in the non-shadow region are Id-/Irr, so
that in Figure 12b, the circles are ratios of Ifl./Ia-, while
the dots are Ia-/Ifl . The observations essentially confirm
the predictions that the ratios for inflected and deflected
light would be the reciprocals of one another.

4. Sharp sl_i_t (Figure 13a): Within the limits of the '
accuracy of the system, the light diffracted by a sharp
edged slit is shown to be unpolarized. The data agree with
the predictions of the approximate theory for the slit, and
are complementary to the data obtained for single edges in
the shadowed and unshadowed regions. The fact that the ratio
Ifl/I, drops off at large angles is attributed to the fact
that the near edge (which contributes mainly perpendicularly
polarized light) begins to shield the far edge (which contri-
butes mainly parallel polarized light), and that therefore
the parallel component suddenly begins to decrease more rapidly
than the perpendicular component.

5. Physical slit: The qualitative observation of polari-
zation by a slit having flat jaws may perhaps be explained by
the fact that the light traveling through the slit is multiply

45

reflected from its faces. As the slit becomes narrower, the
number of reflections increases, and therefore the degree of
polarization increases. From this argument, the direction of
polarization would be along the long dimension of the slit,
which is the same direction as the observed polarization.

6. Sharp_edge polarization ratio, lens-free system
(Figure 13b): The observed ratio was always less than the
theoretical value. There was somewhat less variation in the
observed values than in all the earlier measurements, which
may be due to the fact that with practice it becomes possible
to perform the necessary manipulations more quickly, and there-
fore to reduce the variation caused by photomultiplier tube
fatigue. In addition, the amount of scattered light entering
the pickup was reduced by placing the equipment so that the
nearest wall was some thirty feet distant. In the earlier
measurements, the nearest wall (painted flat black) was only
two feet from the equipment.

7. Changg of intensity_with distance: These observations
were difficult to reproduce, and so the results are interpreted
in a more or less qualitative manner. Apparently in the lens-
free system, light is radiated from the edge somewhat in the
form of cylindrical waves, since the intensity varies approxi-
mately as l/R.

It would be appropriate to make these measurements with

a pickup aperture whose length is much smaller than the

length of the edge. However, it is believed that the only
requirements for observing the change of intensity with dis—
tance are that the length of the pickup be less than the
length of the edge, which in turn must be less than the length

of the source.

0. Comparison with Previous Work

Observations of the amplitude polarization ratios were
made in 1927 by Jentsch? Earlier observations were made by
Gouy and Wien, but it is believed that the later measurements
of Jentsch are probably more of interest for our purposes.

Jentsch's observations were made on a modified prism
spectrometer. A polychromatic 0sram.tungsten point light
was used as a light source. Light from the source was co-
limated, after which it passed through a Nicol prism oriented
at an angle of 45° to the vertical. From the polarizer, the
light went to the diffracting edge (a steel razor blade)
which was mounted upon the prism table with its edge vertical.
The diffracted light from the edge passed through another
Nicol prism, thence through the telescope, which was focused
upon the diffracting edge.

The plane of polarization of the diffracted light was
observed to be rotated, due to the inequality of the paral-
lel and perpendicular diffraction components, and the rota-

tion was recorded as a function of the diffraction angle.

47

From the amount by which the plane of polarization was
rotated, Jentsch calculated the amplitude ratios of the two
polarization components.

The results of this investigation were originally com-

pared with a plot of Jentsch's results in the Handbuch der

 

EEXELEll. This Plot showed one of Jentsch's experimental
values to be larger than Sommerfeld's theoretical predictions,
and seemed to indicate a major discrepancy between our results
and Jentsch's. However, after reviewing Jentsch's own paper3
it was found that his values were all less than Sommerfeld's
prediction.

For comparison purposes, a plot of the intensity ratios
calculated from Jentsch's amplitude ratios is included in
Figure 13b. The fact that his ratios are smaller is possibly
due to the lower conductivity of the steel blades which he

used.

D. Suggestions for Improving the Equipment

The attenuator used has two controls--a ten position
switch for coarse adjustment and a potentiometer for fine
adjustment. It would be easier to determine the exact situa-
tion of balance if a completely continuous type attenuator
were used. A possible substitute is the ”Helipot” l megohm
type AZ ten turn helical potentiometer.

A possible method for cooling the photomultiplier tube

would be to immerse it in liquid nitrogen in a Dewar flask.

48

It would be necessary to make a small transparent window in
the flask by removing the evaporated metal. There probably
would be little frost formation if the "window" were small
enough. However, it is not known whether the glass to metal
seals on the photomultiplier tube would withstand such
treatment.

The fatigue effect can be eliminated by using a method
of measurementlo in which the comparison light signal is fed
to the same pickup as the one which ”looks" at the diffrac-
tion pattern by means of a chopper system. In this system,.
the pickup sees the light from the two sources during alter-
nate time intervals. Since the fatigue affects both signals
in the same way, it will not contribute to the error of the

measurement.

E. Summary of Conclusions

The eXperimental results which have been obtained agree
in general with the predictions of Sommerfeld's theory and
the approximate slit theory. Sommerfeld's theoretical work
is based on the assumptions of perfect conductivity and
infinitesmal thickness of the diffracting edge. At present
there is no way to alter the theory to take these factors
into account. In view of this fact, the observed discrepan-
cies seem reasonable, since the diffracting edges, being real

edges, suffer from some of the imperfections of reality.

49

REFERENCES

lGouy, G., "Sur la polarisation de la lumiere diffractée,"

Comptes Rendus 96, 697 (1885).

280mmerfeld, Arnold, "Mathematische Theorie der Diffraction,"
Math. Ann. 31, 517 (1896).

3Jentsch, Felix, "fiber die Beugung des Lichtes an Stahl-
schneiden," Annallen der Physik gg, 292 (1927).

4Born, Max, Optik: Ein Lehrbuch der Elektromagnetischen
Liqhttheorie, Berlin, Julius Springer,‘l955, pp. 209-218.

 

5Meyer, 0. F., The Diffraction of Light, X—rays, and
Material Particles, Ann Arbor, Michigan, J. W. Edwards,
1949. p. 276.

 

 

°Morse, Philip I., and Rubenstein, Pearl J., "Diffraction
of Waves by Ribbons and Slits," Phys. Rev. gg, 895 (1958).

7Kessler, K. G., and Wolfe, R. A., "The Measurement of
Intensity Ratios of Spectral Lines with Electron Photo-
multiplier tubes," Journ. Opt. Soc. Am. 51, 155 (1947).

8Weeks, Walter L., Development of Instruments for the Direct
Measurement of Spectral Intensity. Unpublished M. S. Thesis.
Michigan State College, 1949, 25 numb. leaves, 9 Figures.

9Clancy, Edward P., "Polarization Effects in Photomultiplier
Tubes," Journ. Opt. Soc. Am. 32, 557 (1952).

lolMilatz, J. M. W., Boeschoten, F., and Smit, J. A.

"A spectrometer for measuring relative intensities’with

the alternating light method," Physics. XVIII, 646 (1952).

llWolfsohn, G., "Strenge Theorie der Interferenz und Beugung,"

Handbuch der Physik, Vol. XX, Berlin, Julius Springer, 1955,

p. 275.

 

 

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