133
252

AN ‘M'ERFERENCE METHOD
OF MEASURWG LONG DISTANCES

THESIS FOR THE DEGREE OF M. 8.

Stuart Hay Chamberlain
1930 .

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we campus-p.14

 

AN INTERFERENCE‘METHOD
OF MEASURING LONG DISTANCES

 

Thesis for Degree of M.S.
Stuart Hay Chamberlain
1936:

M 5‘,

I desire to express my appreciation to my teacher,
Dr. C. W. Chamberlain, who suggested the solution of the
problem of employing waves of light for measuring long
distances, gave invaluable aid during the progress of the
research, and provided most of the instrumental equipment
required. I wish to thank Professor 0. W. Chapman, who
made possible the undertaking of this problem, for his
unfailing kindness, encouragement, and assistance. I also
wish to thank Professor W. E. Laycock for his valuable

assistance in the preparation of photographs.

94630.

The purpose of this thesis is to outline the
present status of the art of measuring distance and the
limitations of the instruments and methods employed.
These limitations, determined by the physical prOperties
of the materials from which the standards of length are
constructed and the finite length of the waves of light
employed in all Optical instruments, cannot be overcome
by the methods now employed.

Advance can be made along the lines described for
the first time in this thesis. The finite length of the
light wave, a handicap in all instruments employing
lenses, is turned to practical account by making it the
unit of measurement; thus securing an ideal standard of
length, possessing none of the limitations of present
standards.

The thesis describes an original type of instrument,
capable of measuring distances, small and great, with an

accuracy and convenience of Operation hitherto unattained.

Contents

Present Methods of Measuring Distance and their Limitations

Chaining Page 1.
Traversing Page 2.
Minor and Grand Triangulation Page 3.

The Telesc0pe as a Distance Measurer

Tacheometer Page 4.
Subtense Theodolite Page 5.
Cleps Page 5.
Omnimeter Page 6.

Range Finding

Telemeter Page 6.

Mekometer Page 7.

Range Finder Page 7.

Light Waves as Standards of Length Page 8.
Conditions Necessary for Production of

Interference of Light Page 9.

Methods of Producing Interference Page 9.

Interference of the First Class Page 10.

Interference of the Second Class Page 12.

Interference of the Third Class Page 13.

No Solution Possible with Any Known
Type of Interference.

A New Type of Interference: Fourth Class
The Diffractometer Page 16.

A New Type of Interference: Fifth Class
The Recording Interferometer Page 18.

Contents - concluded
Calibration of the Recording Interferometer
Measurement of Distance by Means of Light Waves
Advantages to be Gained.
Difficulties to be Surmounted.
Statement of the Problem

Problem Solved by a Combination of Fizeau
and Recording Interference Fringes

Description of Instruments

Method of Making Measurements
Adjustment of Interference System
Setting on a Distant Mirror
Calibration of the Instrument
Measuring a Long Distance
Data

Conclusion

Bibliography.

19.
25.

30.

30.
32.

37.
40.
41.
42.
44.

46.

PLATE I :

PLATE II :

Plate III :

PLATE IV :
PLATE V :

PLATE VI :

PLATE VII 3

PLATE VIII :

PLATE IX :

TABLE I
TABLE II
TABLE III

Illustrations

Michelson's Measurement
of the Meter

Wave Length Comparator

at National Physical
Laboratory

The Diffractometer

The Recording Interferometer

Photograph of
Recording Fringes

Interference Method of
Measuring Distance Along
a Beam of Light

Transmitting Apparatus:
lst Arrangement

Receiving Apparatus:
lst Arrangement

Final Transmitting and
Receiving Apparatus

Tables

Facing

Facing
Facing

Facing

Facing

Facing

Facing

Facing

Facing

page

page

page

page

Page
Page

8.
16.
18.

32.

35.

35.

36.

38.

44.

44.

Present Methods Of Measuring Distance
and their Limitations

Chaining

In making linear measurements with great accuracy
rods of glass or metalhave been employed; their lengths
being known at a given temperature and corrections applied
for variations from the standard temperature. Occasionally
compensated rods made of two metals have been used. The
most approved method (sepecially in the United States)
makes use of steel tapes, which are much more convenient
to use than rods. Tapes have been constructed Of invar
steel, with a temperature coefficient Of eXpansion one
tenth that Of steel or even zero, but such alloys have a
critical point at a temperature near that of the Operating
temperature and undergo a molecular rearrangement which
causes undue growth Of the metal with age. This fact, in
addition to temperature hysterisis, which makes the
temperature coefficient depend Upon the previous history
Of the tape, i.e., whether the temperature is rising or
falling, limits the use Of invar steel. ‘

An accurate measurement Of a "base line' necessitates
the sUpporting of the tape 60 to 100 meters long on stakes
10 to 20 meters apart. The measurements should be made at
night, so as to be subject to the smallest possible range
of temperature. The services of 12 men are required to make

a measurement. An Observer at each end Of the tape, 2

-1-

thermometer Observers, 3 stretchers, l recorder, and five
men to carry lamps and bring forward the tape after each
length is measured. As there is a tendency for the
temperature of the tape to lag behind that of the air,

the base line is measured first with a rising and then
with a falling thermometer. This procedure is repeated
several times in Opposite directions, and a mean taken. If
the ground is not level the measured length must be corrected
and reduced to the true horizontal length. The measurement
Of distance by means of a tape is a laborious and expensive
Operation. A base line thus Obtained is fixed and is of use

for the solution of but one problem.

Traversing

In surveying by traversing, the position of a point

 

is determined by one linear and one angular measurement,
requiring the use Of tape and theodolite. The accuracy of
the latter instrument depends upon the accuracy Of division
of the circle and the resolving power of the telescOpe,
which in turn depends on the diameter Of the Objective lens.
The limitations therefore of a theodolite, small enough to
be portable, are serious and these combined with the
difficulties and eXpense of chaining, already described,

make an improved method of measuring long distances most

desirable.

8
Minor and Grand Triamulation

In triangulation but one lineal measurement, that

 

Of the base line, is required. From such a base line the
relative distances Of numerous points and their coordinates
are calculated. When a survey Of a great country is made,
the position of a number of points at distances from 20 to
100 miles from each other. In such Grand Triangulation the
most powerful instruments are employed, the work is

executed with the highest degree Of accuracy possible, and
the curvature of the earth is taken into account. Upon the
completion of the grand triangulation the tOpOgraphy of

the country is determined by breaking up the great triangles
into a number of smaller triangles, having an average side
Of one mile or less. Less powerfil instruments are employed
and the curvature of the earth is neglected. The great cost
Of measuring the single base line in the grand triangulation
prevents the accurate measurement of any other line in either
grand or minor triangulation, although such measurements
would greatly increase the accuracy of the final result.
Engineering science awaits the develOpment Of an instrument
and method which will make possible the use of a.portable
‘base line , the length of which has been determined with

great accuracy.

The TelescOpe as a Distance Measurer
A telescOpe fitted with a special diaphragm, may
be used for measuring distances with the aid of a
graduated staff.

A Tacheometer is essentially a transit theodolite,

 

the diaphragm Of which is furnished with two or four stadia
webs, wires, lines, or points. The Object Of Tacheometry is
to enable horizontal and vertical distances to be computed.
from readings upon a stadia rod, thus rendering chaining
Operations unnecessary.

Let D = distance from axis Of instrument
to the stadia rod.

S = intercept on stadia rod.
f e.principal focal length of Object glass.
L a distance apart of the stadia webs.
d 2 distance of Object glass from axis
Of instrument.
Then f
D =SO_+ f +d o

L

The ordinary theodolite tacheometer is limited to
distances not exceeding 400 feet and in the hands of a
skilled Observer can determine such distances with an
accuracy of one part in two thousand; approximately the

accuracy Of good chaining.

The Subtense Theodolite
The principle of this instrument is the same as
that Of the tacheometer described above, except that for
each reading the cross-hairs are adjusted by means of
finely divided micrometer screws to intercept some constant
distance S on the stadia rod.

The same formula

L

holds, but 8 has a constant value, usually 10 feet, while
L or .5 is variable.

The Subtense Theodolite is capable of measuring
limited distances with an accuracy slightly greater than
that Obtained by a tacheometer. For distances between 800
and 1000 feet, however, the accuracy is about 1 part in 650.
The accuracy Of chaining over the same distance is
approximately 1 part in 1440.

The Cleps

The glgpg was invented by Professor Porro, Of Milan.
It differs considerably from the tacheometer. The latter
has its horizontal and vertical circles uncovered, while
the Cleps encloses them in a cubical box. In the tacheometer
the telescOpe and the angles are read by verniers; in the
Cleps the telescOpe is eccentric and angles are read by
micrometer wires applied to micrOsOOpes. The instrument was
used on the Mont Genie Tunnel Survey and is capable Of an

-5-

accuracy Of 1 part in 8000. It is extremely delicate and
its accuracy of adjustment cannot be tested.
The Omnimeter

The Omnimeter consists Of an ordinary theodolite

 

but with the graduated vertical scale replaced by a
horizontal scale read by a powerful microsc0pe mounted
vertically at right angles to the telescOpe. The latter
is focused first on one end of the distant stadia rod,
then on the other.
Let x = distance from omnimeter to stadia rod.
S a length Of stadia rod.

h a distance from axis Of telescOpe
to horizontal scale.

In and r: = readings on horizontal scale.

Then h s

2 Int 1‘!

«Iv

The instrument is somewhat more refined than the subtense
theodolite, but does not greatly exceed it in accuracy.
Range Finding
The Telemeter
The telemeter is a small and convenient instrument,
less than five inches long, Operating on the principle of
the sextant. The Observer determines the angle subtended
by the distant Object at Opposite ends of a base line which
he “steps Off". The scale is marked to read direct in feet.

The accuracy is small, about 1 part in 100.

-6-

The Mekometer

The Mekometer consists of two instruments, similar
tO the telemeter, connected by a silk covered hemp cord
about 150 feet long. It is very portable, rapid in use,
reads direct in feet, and has an accuracy for small
distances Of about 1 part in 1000.

The Range Finder

As this instrument is its own base line and is about
one meter long, it is somewhat awkward to use and transport.
The distant Object is viewed simultaneously from both ends
by means Of totally reflecting prisms. The varying angle
subtended by Objects at varying distances is compensated by
moving in the line Of sight of one of the two paths a prism
Of small angle. The movement Of the prism is calibrated to
read direct in feet. The accuracy Of the instrument for
distances up to 3000 feet is approximately 1 part in 250.
For distances up to 6000 feet the accuracy is only 1 part
in 125.

 

 

 

 

Michelson's Measurement of the Meter

PLATE I

 

 

Wave length Comparator at National Physical Laboratory
PLATE II

Light Waves as Standards Of Length

Prof. A. A. Michelson of Case School of Applied
Science and Prof. W. A. Morley Of Western Reserve University
first prOposed the use Of a wave Of light as a standard Of
length. In 1892 - 3 the former, working at the Bureau
International des Poids et Mesures, Sevres, determined the
value Of the meter in terms Of the wave length of certain
lines in the cadnium spectrum, thus affording the first
satisfactory approach to a natural standard Of length. He
found 1,553,163.5 red wave lengths in the meter. In 1906
MM. Benoit, Fabry, and Perot, employing a more refined
method reported 1,553,164.13 red wave lengths in the meter.
By international agreement the length Of the red cadnium
wave has been made the ultimate standard Of length.

Plate I illustrates the apparatus employed by Prof.
Michelson. While the wave Of light meets all requirements
for an ideal standard Of length, it will be noted that the
apparatus, well suited to the laboratory, would be useless
in the field or workshOp.

Plate II illustrates the wave length comparator
designed by Professor Tutton and used at the National
iPhysical Laboratory Of England. It is admirably adapted
.for comparing standards in terms of light waves, but is
Inassive and limited to a single use.

The length of a visible light wave is not much greater
‘than the smallest object which can be Observed in the best

-8--

compound miccrosCOpe. The limit of visibility of the
theoretically perfect microsc0pe is one half a wave Of
light. TO render light waves serviceable for purposes of
measurement they must be made to interfere, i.e., the
light intensity must be crowded out Of a portion of the
field of view, otherwise uniformly illuminated, and
crowded into other portions. In such a case the field,
when illuminated with monochromatic light, is crossed by
alternate light and dark bands. A movement Of the bands in
the field over a distance corresponding to the width Of one
band is produced by a change in the Optical path of one of
the two interfering beams an amount equal to the length of
a wave of light.

Conditions Necessary for the Production of
Interference of Light

1. Light must be taken from a single source.
2. The light must be divided into two equal parts.
3. The two beams must be reunited at a small angle.
Methods Of Producing Interference

Interference methods and interference apparatus are
always concerned with two wave fronts which are parallel or
nearly parallel and which are located one behind the other
a distance varying from zero tO a few centimeters. These
two wave fronts are equivalent to light reflected from the
front and back surfaces of an air wedge of corresponding

thickness and angle. This will be referred to as the 'air

-9-

plate”.

The character of the interference fringes obtainable
from such an air plate depends upon the method Of illumination
and the method of Observation. For convenience Of discussion
they will be divided into five classes. A

Class I. If the air plate is illuminated by a broad
source of monochromatic light and enters the eye, placed at
a convenient distance, the rays which reach the eye from
different points of the air plate are reflected from the
surfaces Of the latter at varying angles. The path difference
between the rays reflected from the two surfaces at any
point - 2 n t cos r, where r is the angle Of incidence on
the bag; surface of the air plate, n the index Of
refraction, and t the thickness of the plate. The fringes
will be the loci“ Of points for which 2 n t cos r is
constant. They indicate variations of n, t, and r,
jointly or separately..

When the air plate is extremely thin, and t is
very small, the difference Of phase due to the variation
of r at different points of this air “film“ may be
negligible, sO that if the Optical thickness n t is
uniform the fringes will be very broad and the air film
will appear uniformly dark or bright all over, as the air
film is made to increase or decrease in thickness. If

either n or t vary, fringes will appear which are the

loci of equal Optical thickness.
-10-

When the thickness Of the air plate is appreciable
the change Of phase due to the varying angle of incidence
becomes effective and for all air plates except very thin
films the fringes are loci Of points from which the light
reaching the eye meets the plate at equal angles of
incidence. With an air plate Of uniform thickness the
fringes are circles concentric with the normal from the
eye to the air plate and are in focus at infinity. If the
air plate or film is wedge shaped the fringes are arcs Of
circles whose centers are displaced from the normal. If
the surfaces Of the air film are not regular, or if the
air is not homogenous, causing local variations Of n t,
the circular fringes will be locally distorted at these
points. Such irregularities are most noticeable near the
center of the system where the fringes are broadest.

With any but the thinnest air films the fringes are closely
packed as the angle of incidence increases and are visible
only in neighborhood of normal incidence.

It is important to note that fringes Of Class I are
formed when light corresponding to each point in the fringe
system reaches the eye from separate points (or very small
regions) of the film, and is reflected from the film at
varying angles. Except for extremely thin films, the fringes
are mainly loci Of equal incidence angles, and are very
slightly affected in shape and position by variations in
film thickness.

-11-

Class II. Instead Of viewing the fringe system
at infinity with the naked eye, one may use a telescOpe
Of large aperture focused for infinity, so that for all
points of the field of view light from the whole surface
or the air film is received by the telescope. The fringes
are now purely loci of equal illumination and are not
affected in shape or position by variations in the Optical
thickness of the film. When the telescOpe is directed
normally to the film circular fringes concentric with the
axis are seen in the focal plane of the eyepiece. Since
at any point in this plane, light from the whole Of the
film is focused, the phase at any such point depends on
the mgag film thickness and the angle of incidence Of the
ray. Any variations in film thickness contribute their
effect equally to all points in the fringe system, which
therefore indicates the inclination of the rays only, and
tells us nothing about the flatness, homOgeneity, or
parallelism of the air film.

If, however n t varies much, the distinctness of
the fringes will be impaired; for we can regard the
resultant illumination at the focal plane Of the telescOpe
as due to the superposition of a number of exactly similar-
fringe systems, Of which some differ in phase from others.
This results in diminishing the contrast between the bright
and dark parts of the field.

It is important to note that fringes of Class II are

- 13-

 

formed when light corresponding to each point of the fringe
system comes from the whole Of the film (or from some part
Of it), but meets it at varying angles of incidence. The
fringes are bands of equal illumination. If sharp and
distinct we infer that the film is Of fairly uniform Optical
thickness over the region utilized; but no information of
_the character or position of any variations which may
actually be present can be gained.

Class III. If the source is a point located at
infinity, such as'a small illuminated pinhole at the
principal focus Of a collimating lens, all rays strike the
air film at the same angle of incidence. There are no
variations in phase from one part of the film to another
except such as may be due to variations of n t. TO Observe
a fringe system Of Class III it is necessary to employ a
telescOpe with the eyepiece removed. The Object glass
collects the parallel rays after they leave the air film
and produce an image Of the source in the focal plans. If
the eye is placed at this image, the whole surface Of the
air film is seen illuminated and traversed by fringes
which are true contours Of the Optical thickness n t.

It is important to note that fringes of Class III
are not located at a definite distance from the eye, like
those of Classes I and II. They are visible at ggl distances,
and appear to coincide with any surface on which the eye is
focused. If the film is thick the fringes will be most

-13...

distinct at normal incidence. A theoretical point source
is not available. To secure secure brightness the hole
must have an appreciable area, and its image in the focal
plane of the telescOpe lens may be considered a small
portion of the Class II fringe system produced by a broad
source. If this portion is in the center, where the phase
varies slowly with the angle Of incidence, there will be
no phase difference between the light from one part Of the
pinhole and another; but if it is at an outer part of the
system where the Class II fringes are closely packed, the
small cone Of rays which reach the eye from any point of
the air film comprises an appreciable range Of phase
retardation, and the contour fringes are rendered indistinct.
The interferometers designed by Young, Fizeau,
Rayleigh, Michelson, Barus, and Tutton, all employ
interference fringes of the three classes described above,
which are generally known as Fizeau fringes. In 1910
Dr. C. W. Chamberlain designed the Compound Interferometer
with which he accurately measured magnitudes 200 times
beyond the limit of the compound microsOOpe. The fringes
employed are compound Fizeau fringes.

A thorough study Of all known types of interference

led to the conclusion that none were capable Of solving

the problem of measuring a distance along a beam of light.
The Director Of the United States Coast and Geodetic Survey,
as late as 1920, seemed to have reached the conclusion

-14-

that no such solution was possible and sought to improve
the method Of Grand Trianulation by measuring longer base
lines over rough terrain and undertook, at great eXpense,
the measurement of a base line from a point on Mt. Wilson
to Mt. San Antonio peak as a distance over which Prof.
Michelson should make an accurate determination of the
velocity of light, “realizing that it might lead to the
determination of distance in terms of the velocity of -
light and thus might furnish a means of measuring base
lines in mountainous regions or on archipelagoes". As the
velocity Of light isI86,420 miles per second the above
suggestion would involve the accurate measurement of
exceedingly small intervals Of time, and does not seem to
Offer much.promise, but indicates the pressing need for

better methods of measuring large distances.

_15-

 

 

 

 

 

 

 

 

 

The Diffractometer

PLATE III

A New Type of Interference : Fourth Class
The Diffractometer

Any type of interferometer employing Fizeau fringes
is most useful when illuminated with monochromatic light.
Only five or six fringes can be Observed in white light,
when the air film is wedge-shaped and the Optical paths are
equal. In 1911 Dr. C. W. Chamberlain invented an instrument
called the Diffractometer, which combines an interference
with a diffracting or refracting system. Plate III is a
line drawing illustrating the principle of the instrument.
M and N are the rear and front faces Of the reflecting
air film Of a Fizeau interference system, inclined at an
angle t. The difference in Optical path is 10 waves of
light, or 10L. Let M and N produced meet at P', at a
distance B' from P, the foot of the perpendicular from
the point of Observation to the mirror M. Place a grating
at a distance A from N, and parallel to N, so that 10
grating spaces lie between the point where the ray from M
meets the grating and where the ray from N meets it. To
an Observer, looking through the grating at an angle t,
the retardation Of 10L produced by the grating in the light
from N brings the two beams into phase and interference
in white light destroyed at P is restored at P'. As the
difference in Optical path Of the two interfering beams is
increased, the fringes may be restored at P' by increasing

the distance A. The Diffractometer pgoduces white light

5

-lb"

fringes at the intersection g: the surfaces M and N.

 

Draw a line from the intersection Of the ray from M
with the grating, making an angle with the grating equal
to the diffracting angle 9.

Then

tan t

tan 6 = -—7r— °
Neglecting quantities-of the third and higher orders

tant .-. .9431013.

Therefore

d
.A‘BI‘.

As d and L are known, A can be found if B can be

.943 .

determined. This is accomplished by counting the fringes

in monochromatic light as the intersection is moved back
from P' to P, and measuring the width Of a fringe. The
product of the fringe width by the number of fringes equals
the distance B.

The Diffractometer fringes are exceedingly useful in
locating the white light fringes in the process of adjusting
interferometers. As an instrument for measuring distance it
will be noted that the angular width Of the fringes is small
when the distance A is large, and large and expensive
plates are required for the measurement Of great distances.
The Diffractometer is not the best solution of the problem

but is of great interest as the first successful attempt 32

 

-17-

 

olt.
------
.......
.....

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I [In

INVENTOR.

By (“fl/{mefld’m

 

ATTORNEY.

 

 

The Recording Interferometer

PLATE IV

am f light.

\D

I

measure distance glen [a b

I“ .I

 

A New Type of Interference : Fifth Class
The Recording Interferometer

This instrument was develOped at Michigan State
College by Dr. C. W. Chamberlain and represents a very
great advanve in the science Of precision measurement.
It ras described before the American Physical Society
in February, 1950, and is at the writing of this thesis
in the process of manufacture by the Bausch and Lomb
Optical 00., Rochester, N. Y.

Plate IV shows the arrangement of Optical parts.
Light from a broad slit, illuminated by an incandescent
filament, is collimated and divided into two parts which
travel separate paths, one variable in length. The beams
are reunited, with their wave fronts parallel, passed
through a Wadsworth or constant deviation prism, and
viewed through a telescOpe focused for infinity. With
eyepiece removed circular Fizeau fringes are seen in
monochromatic light, when the interfering paths are
unequal. With the eyepiece in position, a new type Of
interference system in white light is brought into view.
The continuous spectrum is crossed by sharp dark bands
whose positions in the spectrum correspond with the wave
lengths for which the interference system is Opaque, or
the path difference is an Odd number of half wave lengths.

The number Of bands appearing in an octave is identical

-18-

with the path difference Of the interfering beams, measured
in terms of the longest wave. Lines appearing in that
portion of the spectrum between 5016 and 6676 A. U. of
helium correspond to a linear movement of one ten-thousandth
of a centimeter. In a similar manner, a range Of spectrum
may be arranged such that a change Of one line in the range
corresponds to a movement Of one twenty-thousandth of an
inch, or any desired decimal part Of a centimeter or inch.

Calibration of the
Recording Interferometer

The Recording Interferometer is calibrated to read
exact decimal parts Of an inch or centimeter without the use
Of standard gauges or other auxillary means, This feature
makes the instrument reliable and convenient. The sensitiveness
of the instrument is variable from one millionth to one
thousandth Of an inch: a single instrument taking the place
of an entire set of instruments of any design now used. The
movement of the plunger, the anvil, or the interferometer
head changes the relative lengths of the interfering paths
of light.

Let e = movement Of plunger.
then Be a change of Optical path.

If Be is an Odd number of half wave lengths
2s = L(N - g)
the two beams will interfere destructively, and a black band

‘will appear in the continuous spectrum at the position of

_19_

the wave length L. The Optical system is Opaque for this
particular wave length, which does not enter the prism but
is reflected back toward the source. There will be other
wave lengths for which Be is exactly some Odd number of
half wave lengths which will also be absent in the spectrum.
Vertical dark bands will cross the spectrum wherever the
wave length is such that 2e = L(N - 5), where N is
any integer. If the wave lengths corresponding to any two
of these bands are known, the wave lengths Of Q1; the rest
Of them can be calculated as follows:

Let L' and L" represent the two known wave lengths;
L 'is the wave length to be calculated; also let n', n',
and n be their corresponding integers in the above formula.
Then 26 = L'(n' - i), or Ze/L' = n' - g (1)
and 2s = L"(n" - g), or Be/L' hr - g . (2)

Subtracting (2) from (1)

2e(l/L' - l/L') = n' - n'l . (3)
Similarly we may derive an equation

2e(l/L - 1/L') = n - n" . (4)
Dividing (4) by (3)

11L - I/L' _..n ‘3 ha
l/LI - l/L" - nl — nu

and simplifying
l/LIn' - n~> - 1/Lw<n' - n ) + l/L"(n - n")

_l_= n' - n l_ n - n" _l_
L n1 - n'l L'I 'n' 4 n" Lt ' (5)

In applying this formula (n' - n ) is Obtained by counting
-20-

the bands between L and L"; similarly (n' - n") is
the number Of bands between L' and L". The number Of bands,
and therefore the accuracy of calibration, can be increased
by increasing the difference Of path between the interfering
bands.

TO calibrate the instrument to read .00005 of an inch,
(the appearance or disappearance of one band in the field
should indicate a movement of the moveable jaw of the
interferometer Of .00005 inch. The helium tube may be
conveniently employed.

Helium red .0000667815 cm. or .00002629 in.

Helium yellow = .0000587562 cm. or .000023132 in.

Helium blue = .000050477 cm. or .000019873 in.

Helium blue = .0000501567 cm. or .00001975 in.

Placing the left jaw of the shutter eyepiece on the red
helium line, the problem is to find the exact location for
the right jaw Of the shutter such that a change of one band

in the field indicates a movement Of .00005 inch.

Red: Unknown: Blue:
L" = .00002629 L = ? L' = .00001975
When the plunger moves .00005

the Optical path changes 2(.00005) = .00010

Number of waves passing at L" = '0001 .
H u u u u L 3' + " 000002629

(no. Of waves)x(length of wave) = distance moved by plunger

LII + 'OQ°l ) = .0001 .
.00002529

 

 

-21...

Computing the above

L = .000020819 inch.

Having found the length of the light wave which locates the

correct position Of the right hand shutter, this wave length

is accurately located in the spectrum in the following manner:
SUppOse the Optical paths are such that 50 bands lie

between L" and L. (100 bands, or any ether number, may

be used.) Employing equation (5)

n - n” = 50

n' - n" = 50 - X

n' - n = X

1 X l 50

L 50 - x L" 50 - x' L‘
Solving for X

 

x = 50 L" (L ‘ L1) = 13 bands.
L'(L“ - L)

 

We next set 50 + X = 63 bands between the red and blue
helium lines, then set the left shutter on the red line

and the right shutter on the 50th band. The field 2: view

 

Further calibration is carried out in a similar
manner, leaving the left shutter set on the red line and

in succession setting the right shutter
Number of Number
light waves Of bands
pass by pass by

on band 62 1/2 instrument reads .00004 in. 2 waves 4 bands
on.band 50 instrument reads .00005 in. 2.5 waves 5 bands

-22....

continued:

on band 41 2/3 instrument reads .00006 in. 3 waves 6 bands
on band 31 1/4 instrument reads .00008 in. 4 waves 8 bands
on band 25 instrument reads .0001 in. 5 waves 10 bands
on band 12 1/2 instrument reads .0002 in. 10 waves 20 bands
on band 8 1/3 instrument reads .0003 in. 15 waves 30 bands
on band 6 1/4 instrument reads .0004 in. 20 waves 40 bands
on band 5 instrument reads .0005 in. 25 waves 50 bands
on band 4 1/6 instrument reads .0006 in. 30 waves 60 bands
on band 3 1/8 instrument reads .0008 in. 40 waves 80 bands
on band 2 1/2 instrument reads .001 in. 50 waves 100 bands

The accuracy of setting the smaller

ranges may be

increased by increasing the number of bands employed. For

example, having determined that the range 12: bands equals

.0002 of an inch, the number of bands in this range may then

be increased to 50. If so, the number of bands fixing all the

ranges following will then be multiplied by 4.

The eyepiece of the Recording Interferometer will be

constructed with a fixed left hand shutter. The right hand

shutter will move by a screw with divided head to give the

above or any other desired readings.

For laboratory measurements of the highest precision

the Recording Interferometer surpasses any other previous

design of interferometer, as a movement of f wave of light
may cause one band to move across the entire visible spectrum,

and measurements accurate to l/lOO of a light wave can be

made.

llllllll Ill.

" '.'.'.'.'.'.? ' ' ' ' ' ' ' 'H |

"In”.

 

Photograph of Recording Fringes
PLATE V

The chief value of the instrument lies in its
ability to leave a record of the measurement, and for
shop purposes to skip a selected number of bands in the
record, thus recording every fourth, tenth, fiftieth, or
hundredth band. In shOp use, having determined the amount
of "tolerance" allowed, the Recording Interferometer may
be set to read in terms of that tolerance. The Operator
would then set a small number of bands in the field of
view. The allowed tolerance would then admit of an increase
or decrease of one band.

As the Recording Interferometer renders unnnecessary
the counting of bands during actual movement, the record
may be photOgrapnic, frOm which observations may be made
at any time under the most favoraole conditions. This
allows the use of the comparator for determining exact
whole and fractional number of bands within a given range.

Plate V is a photograph taken of recording fringes
which shows the permanent record of a small movement of
the mirror M. The upper portion-shows the spectrum record
of recording fringes before movement and the central spectrum
the fringes after a small movement of the mirror M. The
lower spectrum duplicates the position of m in the upper
spectrum, and constitutes a check on the former. The
helium spectrum is superimposed on the three and records
a check and makes possible the calculation of the distance

moved by the distane mirror M.
-34-

recording photographically with any degree of sensitivity
at any predetermined intervals of small diaplacements,
Opens up whole new avenues of research in many fields of
science.

Measurement of Distance
by Means of Light Waves

Due to the difficulty encountered in the direct
measurement of very small angles, the present practice is
to measure off a base line as long as existing conditions
will permit. This has led to the practice of constructing
high platforms to carry tape line over such common natural
obstructions as irregularities in the terrain, highways,
orchards, etc. If a short, portable base line is to be
used for the accurate determination of great distances, the
length of this base line must be known with a high degree
of accuracy requiring direct measurement of this length in
wave lengths of light. Moreover,equally accurate Optical
methods must be devised for determining the very small angle
subtended by this short base line at great distances.

An ideal tape line may be considered to possess the
following advantages: It should be of unlimited length,
though at the same time remaining readily portable. Its
graduations should be closely and accurately spaced, and
capable of being read to greater or lesser degrees of precision.
Its weight should be hero for there should be no sag,
eliminating the necessity of supports and stretching to
secure tauntness. Its temperature coefficient of expansion

-25....

should be zero and it should have no critical point near
Operating temperatures. Irregularities of temperature
along its path should have no effect upon its accuracy
in use. The effect of windage, stretching, and the
.curvature of the earth, should be eliminated. Best of
all, fixed at one end, it should be capable of extending
itself rapidly over inaccessible places and of returning
the free end to the Observer for reading.

Such an ideal tape line fulfilling all these
conditions is formed when two beams of light are sent
out from a source. With the velocity of light they are
projected in an absolutely straight line to the distant
point from whence they may return by reflection to their
starting point; accurately calibrated in terms of the
absolute and unvarying standard, there is no drOp of the
catenary, stretch, windage, or temperature coefficient.
This ideal tape requires no supports and extends itself.
The limiting distance it may be sent out becomes, in the
end,the limit of visibility. The paths the two beams travel
are not affected by curvature of the earth's surface, beyond
that due to the changing index of refraction of the air
through which the two beams must travel.

Before two beams of light may be utilized for
measuring large distances, a number of very serious
difficulties must be overcome. Were the two beams to travel
parallel to each other, a change in distance will change the

-26..

the two paths exactly the same amount, leaving no Optical

difference which could be measured. If the two beams are
caused to diverge,at great distances their Optical paths
will be subject to individual disturbances which will
affect one beam and not the other. This difficulty may be
obviated by causing the two beams to be only slightly
separated and converging slightly. In this case, most of
the way they travel nearly identical paths, and any slight
differences due to localized inequalities of temperature
tend to integrate out over long paths. It is well to
remember that a beam of monochromatic light, though
accurately subdivided, carries no numbers on its divisions
and hence no division can be identified unless laboriously
determined from the central white light fringe. Practicality
demands that at great distances intense white light be used,
but only a few white light fringes, eight or ten at the
most, are known. In this case the use of the diffractometer
fringe suggests itself. But when fringes in monochromatic
light , a definite distance apart, let us say, of three
fringes to the width of an interferometer end mirror, are
set on an interferometer and mirror and viewed through a
teleSCOpe and grating from a great distance, the angle
subtended by an ordinary interferometer plate is so small
that the individual fringes in focus on its surface are

not resolved. This necessitates the use of large and costly
plates and teleSCOpes of high resolving power. When the

_ g7-

image of the central white light fringe is located in some
diffracted order of the grating spectrum, it is necessary
to employ monochromatic light and laboriously count back
fringes, occasionally substituting white light to relocate
the central fringe, until the central white light fringe
stands in the center of the field Of view. It is difficult
to accurately determine the width of fringe, so the
distance traveled by the white light fringe in this process
is only approximately known. In this method the base line
and the observer are located at Opposite ends of the distance
to be measured, the difficulties of accurate counting of
fringes increasing with the distance. The Diffractometer
represents the first, and up to 1929 the only known, method
of measuringOdistance along a beam of light by means of
interference, but the eXpense and difficulty of Operation
limit its field of applicatiOn.

The fact that the new fifth type of white light
fringe, employed in the Recording Interferometer, cannot
be used alone to solve the problem may be explained in the
following way: The two converging beams after crossing may
be thought of as forming the base and hypotenuse of a right-
angled triangle. As the crossing point of the two beams
moves farther away, due to a movement of the distant source,
the leg of this triangle grows longer. If an interference
system at the receiving end is to reunite these two diverging
beams, then as the base increases the leg increases

_28_

prOportionally, or stated in another way, the beam
representing the hypotenuse of this triangle will fall a
little farther back and off to one side of that point on

its mirror where it was originally incident, as the distance
to be measured increases. This will result in a shift, or
shearing, of the interfering wave fronts laterally, Egg

laterally only, which, due to their very nature, produces

 

absolutely no change in the appearance of a recording fringe

system. But it Lg the chance 19 length 33 the 198.2; this

#

triangle which g3 wish 39 measure, since it is the change

 

in length of the base line subtended by a fixed angle at
this increased distance and is to be used in measuring this
change in distance due to the movement of the source. The
distance required of this mirror to be moved back is just

that amount necessary to keep its beam always pg some fixed

 

.EElEE of its mirror, or in other words, to again reduce the
shear to zero. Thus it becomes evident that, since recording
fringes are not sensitive to a shearing of the interfering
wave fronts laterally, they cannot be used alone to solve

the problem. However, it is also evident that if some other

 

entirely independent method were devised for detecting when,

 

“by a movement 2: this mirror backwards, the beam again fell

 

 

22 the same point, the retardation in this beam could be

 

 

measured by the recording fringes in white light.

 

 

 

-29..

Statement of the Problem
1. To find a method, preferably an interference one, for
determining when a returning beam falls always on some
fixed point of its mirror in the receiving apparatus. This
,amounts to the problem knowing when the two interfering
wave fronts are sheared on each other laterally by 5332
amount.
2. To find an interference method, using white light, for
measuring the change in base line subtended between two
beams of light, with fixed angle between, at varying
distances.
3. To find two such interference methods wholly independent
.3: each other, for an adjustment of the apparatus must not
introduce in the recording fringe system a change not due
to a movement of the distant source, nor must the measurement
produce a change in the adjustment.
4. To use an interference method in calibration of the
instrument.

Problem Solved by a Combination
of Fizeau and Recording Fringes

The circular, or straight line, interference bands
in monochromatic light, first described by Fizeau and used
in most interference systems, form a most excellent method
for determining when a beam of light falls on some fixed
point of its mirror. In monochromatic light when zero shear
exists, the eye sees the center of the Fizeau Circular Fringe

system, hereafter described as the F. C. F. system. A shearing

.— 30—

of the interfering wave fronts laterally exposes a new

 

portion of the F. C. F. system. The radii of the circles
is determined as follows:
Let

2t

distance between interfering wave fronts

r = radius of successive rings

P 2 distance from front surface of air plate
to point of observation

n = number of ring; any integer

L = wave length of light

- nL
r ‘ PVaFIHE

If a perpendicular passed through two congruent points on

then

the air plate is not the pole P, we are not looking at
the center Of the system of circles, but off to one side.
Due to the small size of the ordinary interferometer plate
only sections of the larger rings are seen at any one time,
and appear curved toward the center of the system. The
effect is exactly the same if congruent points are sheared
on each other. The location of the center of the F. C. F.
system is extremely sensitive, and watching for the center
of this system of circles in monochromatic light, the
setting of a mirror so that a beam falls always on some
fixed point may be reproduced with great precision. When a
setting has been made for zero shear before and after the

-31...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interference Method of Measuring Distance
Along a Beam of Light

PLATE VI

 

change lg distance, the difference in path Of one beam over
the other resulting from the change lg the change in base
line subtended by thisznhange in distance, and is readily
measured by the recording fringes in white light.
Description of Instruments

Plate VI is a line drawing illustrating the arrangement
of Optical parts and shows the paths of the interfering beams
of light. Light from a broad slit illuminated with white
light is first collimated,then by means of a 50% silver
film on a plane parallel plate of glass is divided into two
parts; a transmitted and a reflected portion. The latter
beam falls upon a full-silvered surface from which it is
reflected in such a manner as to cause the two beams to be
slightly separated and converging at a slight angle toward
a distant Optical surface M full-silvered On the front
face; the two beams crossing at or just before they strike
the mirror. The returning beams, now slightly diverging at
the same small angle, are received by an interference
system which reunites them, renders them parallel, and
permits both linear and lateral displacements of the two
interfering wave fronts. The two beams thua reunited pass
through a Wadsworth (or other constant deviation prism) and
are viewed through a telescOpe, which during the entire
process of adjustment and measurement remains focused for
parallel rays. When in adjustment, and when the paths

traveled by the two interfering beams are nearly equal,

-33-

an eye placed at the telescOpe sees a white light spectrum
crossed by a number of dark interference bands of the
Recording Interferometer type. SUperimposed on these distinct
bands may be caused to appear the red, yellow, and blue,
bright lines of helium from a discharge tube placed
immediately before the slit for the dual purpose of acting
as a cylindrical lens to focus white light in the slit and

to furnish monochromatic light both for adjusting the
instrument and for conveniently locating the range between
which the recording fringes are to be counted. The S .mirror
moves on ways which are at right anglesto the ways along
which moves the carriage on which the two C mirrors are
mounted. Consider for a moment that the S beam falls always
on some fixed point of the S mirror. As the distance of

the receiving station from the distant mirror increases,

due to a movement of the distant mirror M,parallel to itself,
from A to B, the S mirror must be moved back parallel

to itself in order that the light may fall on the same fixed
point of this S mirror. After a displacement of the distant
mirror M no such movement is ever required of the mirror C
as its beam always strikes the same point on it. The distance
moved by the S mirror represents the increase in length

of a base line subtended by the two diverging beams resulting
from a movement of the distant mirror. This increase in

length of the S path over the C path is compensated for

by a movement of the C carriage along its ways a distance

-33-

one-half the distance moved by the S mirror. The motion
of the carriage on which the C mirrors are mounted,
resulting from turning the divided head which turns the

the calibrated screw which drives the carriage, is measured
directly in wave lengths of light. In order that the change
in position of the C mirrors may not affect the accuracy
with which the setting of the S mirror is made, it is
essential that the method for making the adjustment of the
latter be entirely independent Of the movement of the C
carriage and mirrors. This is accomplished by using the
Fizeau Circular Fringe system for setting the S mirror.
With a fairly broad slit the intense yellow line of helium,
appearing in the spectrum viewed through the telescOpe,
forms an excellent monochromatic source for locating the
center of this fringe system which is in focus at infinity.
When the center Of the system is located, white light is
substituted and the C carriage is moved backwards or
forwards until some definite number of recording fringes
appear between the red and blue lines of helium flashed

at intervals. A movement of the S mirror made necessary
by a movement of the distant mirror by an unknown amount,
shears the interfering wave fronts on each other laterally
only, eXposing a new portion of the F. C. F. system. When
the S mirror, hereafter called the "shear" mirror, is
moved back to the point where the center of the F. C. F.
system reappears, the increase in the S path over the C

-34-

3‘ . a
, / f
i
Transmitting Apparatus : lst Arrangement

PLATE VII

A
--

Receiving Apparatus : lst Arrangement

PLATE VIII

 

 

 

 

path represents the increase in base line subtended between
the two beams at the increased distance. In white light the
number of recording fringes will be seen to have increased
with the displacement of the S mirror. The C mirrors,
hereafter called the "compensator" mirrors, are moved back
an amount necessary to reduce the number of recording
fringes within the range to their original number. The C
mirror moves a distance necessary to compensate for the
increase in the S mirror path. The amount of movement of
the carriage of the compensator mirrors along its ways in
wave lengths is one-half the increase in shear mirror path,
which is one-half the increase in base line subtended at
the increased distance resulting from the movementrlB - A.
The distance moved by the carriage of the compensator
mirrors is determined either directly from the recording
fringes, or indirectly from the screw and divided head,
which drive the compensator mirrors' carriage, which are
calibrated in wave lengths of light.
Description of Apparatus

Plates VII and VIII show the first arrangement of
the experimental apparatus. Plate VII shows the transmitting
apparatus and Plate VIII shows the receiving apparatus,
located at Opposite ends of the distance to be measured.
The compensator system of mirrors must be two in number in.
order that there may be as many reflections for the C

5-

-33..

 

 

 

 

 

Final Transmitting and Receiving Apparatus
PLATE IX

beam as for the S beam. Otherwise, as the reflection takes
place from a silver surface, they could not be caused to
finally interfere. It is inconvenient to have the adjustments
of the transmitting apparatus out Of reach of the observer
stationed at the receiving apparatus, especially since it
is found necessary that the two plates which carry the
dividing and reuniting films be adjusted to exact parallelism.
Plate IX shows the final experimental arrangement in
which a single large plane parallel plate serves for both

dividing and reuniting the two beams, thus eliminating the

 

most difficult and objectionable adjustment of the first
arrangement. At the Opposite end of the distance to be
measured, instead of placing the receiving apparatus, a
plane mirror is substituted, which returns the two beams

to another point on the same plate from whence they started;
here they are reunited and pass through the remainder of
the Optical system exactly as before. In this arrangement
all adjustments, save that of the distant mirror are within
close reach of the observer. It is the intention that the
"rodman" carry the mirror to which is mounted a telescOpe,
adjusted so as to sight along a normal to the mirror. In
this case, after the mirror is firmly mounted the rodman
sights the telesCOpe on the distant source, which brings
the returning beams into correct position. The apparatus is
mounted on a rotating table which enables the Operator to

take a measurement in any direction without readjusting.

-36-

Method of making Measurements
Adjustment of Interference System

Plate VI shows the slit of the collimator illuminated
by a small incandescent lamp and a helium discharge tube.
The latter does not interfere with the former but serves
rather as a cylindrical lens to focus the light of the
incandescent filament on the slit. This arrangement makes
it possible to view a line spectrum or to superimpose it
on a continuous spectrum or view the latter alone.

For long distances a small tungsten arc lamp is
recommended. The intensity is high and the lamp is easy to
Operate. Two small spherical tungsten electrodes are sealed
in a bulb filled with gas of low ioniaing potential. When
an e. m. f. is applied the gas is sufficiently ionized to
start the discharge, soon bringing the spheres to
incandescence and maintaining a tungsten are. A slit
illuminated by such a source produces in the field of view
a line spectrum between two continuous spectra; an ideal
arrangement for making measurements.

Referring to Plate VI, the mirrors C, M, m, and
S, Optically flat to 1/10 wave of light, are heavily silvered
on their front faces and polished. The plate P, with plans
and parallel surfaces figured to an accuracy of 1/20 of a
light wave, is silvered on the face toward m and“ C with
a 50% film. The beam of light which is to be made to

interfere is divided into equal parts; 50% is transmitted

-37-

to the mirror M and 50% is reflected to the mirror m.
As already explained, the plate P serves both as a
dividing and reuniting plate, making it possible to secure

gptically equal paths, i.e., the two beams travel equal

paths in air and glass. The beam which is first transmitted

is finally reflected, and the reflected beam is transmitted.

A failure to secure a film which will exactly divide the
incident beam produces no serious results as is shown by
the following table:

TABLE I

%reflected 4 5 63 80 50 4o 10 50 50
by thin film 10 O O

% reflected
transmitted .009 .024 .025 .024 .009 .05 .048 .018 .10 .15
ray

%trw8mitted .08 .24 .25 .24 .08 [.25 .24 .08 .25 .25
reflected ray

‘% reflected
rayreflected ...10 .10 .10 .10 .10 .20 .20 .20 .40 .60
byendmirror

‘%transmitted

rayreflected 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

by and mirror

% of total .018 .048 .05 .048 .018 .1 .088 .036 .2 .3
interference

%°1f088§1ne .081 .218 .225 .218 .081 .2 .182 .072 .15 .10
light

Ratio of

interfering 450 450 450 450 450 200 200 200 75 33
to fogging

light

-38-

.051

From the table on the preceding page it will be noted that:
l. The percent of fogging, which should be a minimum, depends
upon the relative intensity of the light reflected by the
pair of mirrors m and S and the pair 0 C, and not upon
the thin film.
2. Paired reflecting films of 10 and 90%, 20-and 80%, 40
and 60%, etc., produce the same results.
3. The maximum interference and minimum fogging are secured
with a 50% thin film and and mirrors of equal reflecting
power.

The plane parallel plate P and the mirrors 0, C,
m, and S, are adjusted.perpendicular to the same plane and
parallel to the vertical axis of the instrument. The angle
between m and P, always small, depends Upon whether the
instrument is to be used for measuring small or great
distances. The mirror M is mounted on an Optical bench in
the same plane and at a distance of one meter from the
vertical axis. A rough adjustment will bring the transmitted
reflected and reflected transmitted beams into the field of
view.

By adjusting the mirrors C or S the two images
of a single line in the spectrum may be made to coincide and
Fizeau fringes will appear in monochromatic light. The field

of view may now be enlarged if necessary by widening the slit.

~39-

Setting on a Distant Mirror

Fizeau fringes are segments of concentric circles
whose center should be brought into the field of view. This
is easily done by moving the S mirror so as to move the
Fizeau fringes in the direction of their concavity. They
will widen as the center of the Fizeau system approaches
the field of view. Next by moving back the C mirrors, as
the Optical paths approach equality the recording fringes
begin to appear in the continuous spectrum, at first very
fine and in great numbers, their number indicating the
distance yet to be moved.

Small movements of the shear mirror 8 and
compensator mirrors 0 will reduce to zero the number of
Fizeau bands in the monochromatic field and the recording
fringes in the continuous spectrum. When the number of both
types of fringes is reduced to zero the setting on the
distant mirror M is complete, and the reflected transmitted
beam falls on the shear mirror 8 at a.point which can be
duplicated with great accuracy. In actual practice it has
been found.preferable not to reduce the number of recording
fringes to zero, but to work with a fixed number, three or
four, in the field. Whether the fixed number is positive
or negative is instantly determined by applying a slight
pressure to the carriage of the C mirrors; a.plus reading
being indicated by a fringe movement toward the red and of
the spectrum, and a minus reading by a movement toward the

blue 0 -40-

Calibration of the Instrument
The instrument is first set on the mirror M at a
known distance from its vertical axis - say 1 meter. The
mirror M is then moved a meter farther along the Optical
bench and adjusted to return the transmitted reflected beam
to the field bf view. This will cause the reflected~
transmitted, or shear, beam to fall on another point of the
shear mirror 8, which must be moved farther back. The mirror
S is correctly set in its new position when the Fizeau
bands in the monochromatic field are reduced to zero, or
their original number. The correct setting on the mirror M
in its second position lengthens the shear path. gggg lg
‘Ehg change Ag base line 39 pg determinedt l£.$§.£gggg
recorded by Egg recording fringes ;g the continuous gpectrum.
With a fixed angle between P and m, hereafter
called collectively the 'wedge', the recording fringes
measure the movement of the mirror M. Then
tan a = .25;
where a 2 angle of the wedge
n: number of recording fringes added
L = length of longest wave in the range.
D a distance moved by mirror M.
A permanent wedge is secured by grinding a hollow
quartz cylinder, approximately one inch long, and with a
diameter equal to the aperture of the mirror M. It is not

necessary to grind the quartz cylinder to any exact angle.

-41-

It is ground at random and the angle determined in the
£0110W1ng way: With the plate P and mirror m clamped
against the ends of the quartz cylinder, the diverging
beams are directed toward the mirror M at a distance of
one meter from the axis of the instrument (in this case
the axis of the table). Suppose that 100 fringes are
recorded when the mirror M is moved one meter farther

away. If L is .00005;cm.,

_ 100 x .00005 _ 1
tan a ‘ 100 ‘ '2005

Measuring a Long Distance

The wedge having been calibrated, it is reversed
in the instrument, which is now ready to measure long
distances. It will be noted from the photograph of the
instrument that the linear separation of P and m is
approximatelt 2.5 cm. With the wedge reversed the beams
will converge and then diverge. As the angular separation
between S and C is 2.5 cm., the mirror M cannot be
placed closer than the crossing point of the rays, which
in this case is 500 meters. Shorter distances can be
measured with a wedge of larger angle.

When the mirror M is placed at a greater distance,
the shear mirror S must be moved farther back, each recording
fringe between the red and blue of helium indicating a
movement of the distant mirror M by one centimeter. If

the short base line of the instrument is limited to 20 cm.,

-42-

one wedgp measures distances from 500 22 jg 2999 meters

flit; isnaccuragy .959 the 4000 meter limit if Jig. E 400,000.
A second wedge of l/8th the angle will record 12%

fringes for a movement of one meter. The interfering beams

converging from such a wedge will meet 4000 meters away,

 

and Egg gggg.§hg£3 base line will measure distances from
.g.£g‘§§ kilometers with 3g accuracy g§.§ 2g. One instrument
furnished Eggh.g wedges gig; measure Ell distances from g
.ggg-meters.gg.;gg kilometerg with pa accuracy hitherto
thought igpossible.

A greater degree of calibration of the wedges can
be attained by moving the mirror M along the testing
Optical bench a distance greater than one meter. Such
Optical benches, constructed from standard steel railroad
rails are part of the regular equipment of many engineering

laboratories.

-43-

Data
Two test wedges were constructed in the laboratory

and measured, with the following results:

TABLE II

Wedge NO. l : Divefgang ________________
Number of
observation 1 2 3 4 5
Number of 3 3 0 4 4
Fizeau fringes
1318138110e t0 800 800 800 600 600
mirror M
Distance moved 5 5 10 15 15
by mirror M
Number 0! 18.4 18.8 82.7 48. 48.1
recording fringes
Movement of . .008073 .003054 .008128 .009183 .008201

shear mirror 8

Angle of wedge .000615 .000811 .000812 .000812 .000613
Mean EEEEE-2£-!E§EE-:-:999§l§§-£§§£§2°

---_-----------------2§§EE_£££ ............................
Wedge No. 2 : Converging

Number Of

Observation 1 2 3 4 5

Number of 5 5 5 5 5

Fizeau fringes

Distance to

mirror M 600 VSOO 600 600 600

Number °f 21.4 42.8 42.7 84.1 84.2

recording fringes

Egggfiegfrggr s .004010 .008021 .008002 .012012 .012081

Angle of wedge .000802 .000802 .000802 .000801 .000802
Mean angle of wedge - .000802 radian.

 

-44-

In the above measurements the recording fringes
were noted between the red and green lines of helium.
These lines are 4861 and 6563 Angstrom Units respectively.
Using the formula develOped on page 20 the movement of
the shear mirror corresponding to a change of one recording
fringe in this range of spectrum equals

L' L' - .00006563 x .00004881 _
L' - L' ‘ .00008883 - .00004881 ‘ '0001874 cm°

Employing wedge no. 1 the addition of one recording fringe

in the field of view corresponds to a movement of the mirror

M of 0.305 cm., and in the case of wedge no. 2 of 0.236 cm.

With an interferometer base line limited to 20 cm., wedge

no. 1 can measure distances Up to 323 meters, and wedge no. 2
to 250 meters.

NO added difficulties present themselves in the
construction of wedges of smaller angle and greater range.
No attempt was made in this direction as it would appear
that the practicability of the method had been established.
All measurements made in connection with this thesis were

small enough to admit of checking by direct measurement.

-45-

Conclusion

The present methods of measuring long distances
have been carried to their limit, and leave much to be
desired.

A new method of measurement has been devised,
tested, and found to be acceptable. It combines the use
of Fizeau interference fringes and a new type devised
by Dr. C. W. Chamberlain, and called by him recording
interference fringes. The instrument can be calibrated
in the laboratory in light waves with great precision,

and is thus independent of subsidiary standards of length.

-46-

Bibliography
Surveying - R. E. Middleton and Osbert Chadwick.
Surveying - W. Norman Thomas.
Trav. et Mem. de B. I. P. M - XI : 1; XV : 1.
Dictionary of Applied Physics - Glazebrook; Vol's. II, III, IV.
Phil. Mag. - 1887, 1888, and 1888.
Phys. Soc. Proc. - 1820, XXXIII : 32.
AstrOphys. Journ. - 1804, 1808, 1811, 1817, 1818, and 1827.
Optics - C. R. Mann.
Photographic Journal - Nov. 1818.
Roy. Soc. Phil. Trans. - 1802.
Gilbert's Ann. - 1817.
Wied. Ann. - 1884, 1881, 1884, and 1887.
Physical Review - 1803, and 1810.
Trav. et Mem. - 1883.
Ann. de Chemie et de Physique - 1902.
Bureau of Standards Bulletin - 1815, and 1818.
Thesis for M. S. Degree - S. H. Dwight.
Ann. d. Physik. - 1811.
Am. Sc. - 1881.
Proc. Roy. Soc. - 1811, and 1817.

-47-

 

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