[INVOICE #7]

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B04770A002900010038-0
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 66
• Document Creation Date: December 28, 2016
• Document Release Date: June 8, 2005
• Sequence Number: 38
• Publication Date: January 31, 1966
• Content Type: LETTER

1TAT
Approved For Release 2005/06/23 : CIA-RDP78B04770A00290001003
Dear John:
Re: Invoice #7
January 31, 1966
Enclosed are two copies for Bill G., one copy
for Helen R. and one copy for your file.
Funding ran out on Thursday, January 27, 1966,
so the invoice covers time spent up to that date.
/al /2_64 67),-
We have continued on to finish theA report and
it is now ready for reproduction. It will 'Be ready to
mail in a couple of days.
Regards4-,
Approved For Release 2005/06/23 : CIA-REIMB047/0A00/213900W038-0
7-- C
STAT
STAT
STAT Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
27, 1966
1/3 1 3/4 day
1/4 1 3/4 day
1/5 I day
1/6 1 3/0 day
1 Dory
Monday, 1/10
Wednesday 1/12
1/12
Friday, 1/14
Thursday, 1/20
Triday, 1/21
Monday, 1/24
Tuesday? 1/25
Wednesdays 1/26
Thursday 1/27
3/4 day
1/2 4sY
2 days
1/4 day
1 day
1/4 day
1/2 day
Ida
1 day
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
STAT
voiced
6.46+
hours)
STAT
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Monthly
Task I
etter progress report, Contract
s on tus
Ifs
ecial In e
31 January 1966
Ther
period.
Task II em811.1etrololt
no specific requests for visitations this
Since there is an urgent requirement for the results of
the analytical investigations on Laser Metrology, effort was
concentrated during this period on the completion of the first
technical report. The report was completed and is being re-
viewed and prepared for submission. The recommendations and
a summary of the findings are included herewith.
tins - A laser interferometer can be applied to
ccuracy metrology to measure a meter or more by
rward engineering design and analysis with only two
areas of uncertainty. One area of uncertainty is in achieving
a high fringe counting rate and a suitable traversing rate.
Since a count reliability of one part in 400 million (6 standard
deviations) or better is desired, normal electronic component
reliability numbers (1 or 2 standard deviations) are not appli-
cable. It is recommended that a development program be initiated
to investigate this area prior to the incorporation of a laser
interferometer into proposed measuring engines.
The other area of uncertainty is in vibration control.
Since vibration control is intimately related to structural
design and melhine design, it is recommended that a parallel
program of ve.ration analysis and test be conducted concurrently
with new measuring engine designs.
Selma e tee analytical investigation was made of the problems
E..wucic ated with use of an interferometer for precision measure-
eent of length. The investigation was oriented toward the
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
omments an status (Continued)
usage of the helium-neon gas laser for the interferometer light
source. The precision criterion was the measurement of lengths
up to 1 meter to an accuracy of micron. Interferometers
have been used for many years for the precise measurement of
short lengths. Pre-laser light sources permitted precise
measurement of lengths up to about 10 cm. Laser light sources
permit precise measurement of lengths of at least several
meters and perhaps several hundred meters.
Quantitive estimates are presented in this report of
the effect on the precision of measurement of: wavelength
determination, mirror alignment, atmospheric variations, parti-
cles in the beam, traversing speed, polarization, spectral
purity and vibration. Spectral purity (i.e., spatial coherence)
and mirror alignment are of paramount importance. Only traversing
Speed presents unresolved problems and vibration of course
requires special analysis of detail structure.
The classic Michelson arrangement with minior madifications
has proved most practical for metrology. The Fabry-Perot
arrangement is well suited only to the measurement of a fixed
length.
STAT
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Task 11 item ?
Technical Report
"LASER METROLOGY"
,-;i1,2,01c4n.ltsIgiT4rT14-",,W4KW!-:
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78B04770A002900010038-0
. February 1, 1966
Task II Item 8 Technical Report
LASER METROLOGY
Work Statement: Investigate the use of the
helium neon gas laser for measuring engine
applications. The use of a laser interferometer
and fringe counting for measuring length has
problems with counting rate and with vibration
and thermal gradients interfering with counting.
There are certain precautions which must be
taken.
This report presents an analysis of the magnitude of
potential errors in applying a laser interferometer to a
high precision measuring engine.
Submitted by:
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Task II, Item 8, Technical Report "Laser Metrology"
CONTENTS
1. INTRODUCTION
J.1 Summary
1.2 Conclusions
1.3 Recommendations
2. BASIC INTERFEROMETRY
Page
1
1
1
4
5
2.1 Interference Phenomena
5
2.1.1 General Description
5
2.1.2 Coherence Conditions
6
2.1.3 Polarization Conditions
9
2.1.4 Spectrally and Spatially
Distributed Sources
12
2.2 Application of Interference to Length
Measurement
13
2.2.1 Classification of Interferometers
13
2.2.2 Favored Types for Metrology
14
2.2.3 Light Sources
15
2.2.4 'Fringe Counting
16
3. LENGTH MEASUREMENT LIMITATIONS AND ERROR SOURCES
18
3.1 General Discussion
18
3.2 Interferometer Geometry
18
3.2.1 Rigid Length
19
3.2.2 Variable Length
19
3.3 Fringe Contrast and Flutter
21
3.3.1 Vibration
21
3.3.2 Spectral Purity
25
3.3.3 Particles in Beam
27
3.4 Wavelength of Light
29
3.4.1 Wavelen&th Error
29
3.4.2 Wavelength Determination
31
4. RAPID MEASUREMENT - ADDITIONAL ERRORS
.11
4.1 Fringe Intensity Fluctuations
33
4.1.1 Quantum Noise from Light Source
33
4.1.2 Laser Noise
38
4.2 Fringe Sensing and Counting Errors
38
4.2.1 Photosensors
38
4.2.2 Digital and Counting Circuitry
40
Approved Foe Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
5. TABULATION OF PERFORMANCE OF EXISTING
MEASURING INTERFEROMETER SYSTEMS
6. COMMENTS ON MEASURING METHODS
7. BIBLIOGRAPHY
,Page
41
42
45
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Task II,
Following
Page
Item 8, Technical Report "Laser Metrology"
List of Figures
Fig.
?1
Michelson Interferometer Diagram
5
Fig.
2
asters Prism Michelson Modification
19
Fig.
3
Error in Measured Length due to
Deviation from Defined Axis
20
Fig.
4
Mirror Alignment
20
Fig.
5
Effect of Vibration on Fringe Counting
22
Fig.
6
Allowable Vibration Levels
24
Fig.
7
Spectral Line Width Distribution
25
Fig.
8
Wavelength Error due to Atmosphere
Effects
31
Fig.
9
Controlled Atmosphere Error Range
31
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23: CIA-RDP78604770A002900010038-0
1. INTRODUCTION
1.1 Summary
An analytical investigation was made of the problems
associated with use of an interferometer for precision measure-
ment of length. The investigation was oriented toward the
usage of the helium-neon gas laser for the interferometer light
source. The precision criterion was the measurement of lengths
up to 1 meter. to an accuracy of k micron. Interferometers
have been used for many years for the precise measurement of
short lengths. Pre-laser light sources permitted precise measure-
ment of lengths up to about 10 cm. Laser light sources permit
precise measurement of lengths of at least several meters and
perhaps several hundred meters.
Quantitive estimates are presented in this report
of the effect on the precision of measurement of: wavelength
determination, mirror alignment, atmospheric variations, parti-
cles in the beam, traversing speed, polarization, spectral
purity and vibration. Spectral purity (i.e? spatial coherence)
and mirror alignment are of paramount importance. Only traversing
speed presents unresolved problems and vibration of course re-
quires special analysis of detail structure.
The classic Michelson arrangement with minor
modifications has proved most practical for metrology. The
?Fabry-Perot arrangement is well suited only to the measurement
of a fixed length.
1.2 Conclusions
? There is no doubt as to the technical feasibility
of using a helium-neon gas laser interferometer to make
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78B04770A002900010038-0
'measurements of k micron accuracy over a. distance of a meter or
more. Whether or not satisfactory traversing speeds can be
obtained needs to be established by test. It is necessary to
recognize the critical elements involved in a laser interfero-
meter and the compensation.required.. The more important ones
are:
Wavelength: The wavelength of the interferometer light beam
must be accurately known since the wavelength error is multiplied
by the number of fringes counted. The spectra physics laser
Model 119 has a highly stable wavelength which can be determined .
to the required accuracy.
Mirror Alignment: Alignment of the mirror which moves over
the length being measured is extremely critical. The moving
mirror must be parallel to the virtual position of the fixed
mirror within a small fraction of a wavelength. This can be
accomplished by servo control of a plane mirror or by using
a corner cube reflector.
Atmosphere:, Changes in barometric pressure, air temperature
and humidity will cause errors in the measured length by causing
changes in the wavelength of the interferometer light beam.
The atmospheric changes must be measured and in part controlled
and corrections applied to the measured length.
Thermal Gradients: It appears that reasonable precautions
can prevent thermal gradients in .the interferometer light beam
from becoming a significant source of error.
Particles in the Beam: Under, ordinary laboratory conditions,
particles in the interferometer light beam will not affect
Approved For Release 2005/06/23 : CIA-RDP78B04770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
measuring and extraordinary clean room conditions are not
required.
Traversing Speed: To date, interferometer measuring engines
have used extremely slow traversing speeds and law counting
rates. With the recent advent of high speed reversible
counterst it appears to be possible to substantially increase
counting rates and traversing speeds. This implies broad-
band electronic components with attendant increase in noise
levels. Careful investigation is essential to achieving suit-
able traversing speeds and this aspect requires developmental
verification.
Polarization: The coincidence of the planes of polarization
of the interferometer light beams is not critical and the
requirement is easily met in the usual instrument design.
Spectral Purity: A high order of spectral purity is essential
to permit measurement of long lengths. Spectral side bands
must be eliminated to produce uniform fringe modulation along
Model 119 laser has STAT
the measured length. The
more, than adequate spectral purity.
Vibration: Machine vibration can be a serious detriment to
satisfactory operation. In a measuring engine particular at-
tention must be paid to the attenuation and the elimination of
vibration since the tolerable amplitudes are only a fraction
of a wavelength of light. Utilizing high fringe counting rates
helps and it appears that by careful design and analysis vibra-
tion can be controlled to tolerable levels.
Approved For Release 2005/06/23: CIA-RDP78B04770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
1.3 Recommendations
A laser interferometer can be applied to sub-micron
accuracy metrology to measure a meter or more by straight-
forward engineering design and analysis with only two areas
of uncertainty. One area of uncertainty is in achieving a
high fringe counting rate and a suitable traversing rate.
Since a count reliability of one part in 400 million (6 standard
deviations) or better is desired, normal electronic component
reliability numbers (1 or 2 standard deviations) are not ap-
plicable. It is recommended that a development program be
initiated to investigate this area prior to the incorporation
of a laser interferometer into proposed measuring engines.
The other area of uncertainty is in vibration
control. Since vibration control is intimately related to
structural design and machine design, it is recommended that
a parallel program of vibration analysis and test be conducted
concurrently with new measuring engine designs.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
2. BASIC INTERFEROMETRY ?
2.1 Interference Phenomena
2.1.1 General Description - Interferometry is
the utilization of optical interference phenomena for the
measurement of length. The interference phenomena are man-
ifested by variations in intensity in the regions in which
light beams are superimposed. The variations in intensity
are generated by the vector addition and subtraction of the?
electric vectors of the superimposed light beams. In the
measurement of length, one beam traverses a fixed length while
the other beam traverses a variable length. The variation in
the variable length is the distance to be measured. The ar-
rangement is illustrated in Figure 1. When the moveable
mirror is at point A, the electric vectors of the two beams
arrive at the photo detector in phase and add to give an in-
tensity maximum. When the moveable mirror is at point B
( wavelength from point A), the path length has been changed
by ? wavelength and the electric vectors of the two beams ar-
rive atthe photo detector out of phase and subtract to give an '
intensity minimum.
As the moveable mirror moves on to point C, which
may be many wavelengths from point A, the photo detector will
sense a maximum intensity and a minimum intensity for every k
wavelength of mirror travel. By counting the maxima and minima
and multiplying by the wavelength of.the light the distance
traversed by the mirror can be determined.
In order that the variations in intensity of the
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
Approved For Release 2005/06/ i1.klif 78604770A002900010038-0
PHOTODETECTORS
LIGHT SOURCE
(PINHOLE ILLUMINATED BY
MONOCHROMATIC LIGHT)
COLLIMATING LENS
/
2.7.7?..1?.._?
DECOLLIMATING LENS
BEAM
SPLITTER
r
?????
nm.1 1=sar amazus wow s
L_....
MOVEABLE MIRROR
COMPENSATING PLATE
FIXED MIRROR
FIG. 1t MICHELSON INTERFEROMETER DIAGRAM
collimating lens not required for laser light source.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
,6-
two superimposed beams be clearly and precisely defined and
measureable:
a. The electric vectors of the two beams must maintain
a fixed phase relationship, i.e., the beams must be
coherent.
b. The electric vectors must be rotationally coincident,
i.e., identically polarized. .
c. The beams must be parallel.
d. The beams must be spectrally pure.
The interference phenomenon of the two superimposed beams
will be degraded to the extent that the above requirements
are not met. The magnitude of the degradations and the factors
producing them will be considered in the following sections.
2.1.2 Coherence Conditions - Coherence conditions
for interferometry express the beam to beam periodicity rela-
tionships necessary for the occurrence of steady, clearly
observable fringes in regions of beam superposition. Two
beams are coherent when their electric vectors are each
periodic (in space and time) and their periods have a fixed
phase relationship. We will discuss Time and Space Coherence
separately.
Time Coherence requires a Timewise Constant Phase
Relation of the electric vectors of the superimposed beams
impinging on the interferometer photo sensor.
It is necessary to have time coherence over the
response time of the photo detector and its associated elec-
tronics. The photo detector does not detect the interference
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
Approved For Release 2005/06/23: CIA-RDP781304770A002900010038-0
phenomenon of individual wave fronts. It detects the time
integration of the interference phenomena of the multiplicity
of wave fronts arriving during the response time of the detector.
We must at this point distinguish between time
coherence of a beam relative to itself (which we shall call
time self-coherence) and time coherence of one beam relative
to another (which we shall call time relative coherence).
For most lamps, the emission of light at one instant of time
is an atomic event independent of the emission of light at
another instant of time. The electric vector phase relation-
ship of the two events is random and the light is time self-
incoherent. For a laser however, the resonance lasing action
produces light in which the electric vector is maintained in
constant phase relationship in time and the light is time
self-coherent.
It turns out, however, that time self-coherence
of a beam is not required for interferometry.
The usual interferometer used a single light source
and a beam splitter to produce two beams traversing separate
paths. The beams are recombined at the photo detector to pro?
-
duce the interference phenomenon. It is the relative phase
of the electric vectors of the two beams impinging on the photo
detectors which must be constant in time.
If the path length is constant and the interfero-
meter geometry rigid, time relative-incoherence cannot occur
-if the superimposed beams originate from one source.
We conclude therefore that the time self-coherence,.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
of the laser is not necessary and by using a single source,
time relative-coherence will always be obtained under the con-
ditions being considered. Note however that vibration of a
mirror which is not common to both beams (i.e., non-rigid
interferometer geometry) can cause time relative-incoherence.
The effects of vibration are considered in later sections.
Space Coherence requires a spacewise constant
phase relation of the electric vectors of the superimposed
beams. It is convenient for our purpose to consider separately
coherence across the beam and coherence along the beam in an
interferometer.
Coherence across the beam in an interferometer
denotes constant phase differences across the area of super-
posed beams viewed by the interferometer photo sensor. Were
there local variances in the phase differences the effective
integration over the total area by the photo sensor would pro-
duce an effective averaging of local intensities and resultant
loss of fringe contrast. Ideal cross beam coherence, which
would result from superposition of (at least instantaneously)
monochromatic beams with parallel, plane wavefronts, can be
closely approached in practical configurations. Coherence
along the beam in an interferometer implies superposition of
beams of identical periodic variation aside from fixed phase
differences in a common propagation direction. The degree to
which this coherence, and associated fringe contrast, can be
approached is fundamentally limited by the widths of the
narrowest utilizable quasi-monochromatic light sources and the4-'
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78B04770A002900010038-0
optical path length differences of the beams.
The coherence length, L, of a spectral line,
of spectral width AA.c,, is defined by
Xo
X0 AXo
2
Xo
and L
LA
o'
At the path length difference, L, the wave length width AX0
produces a spread, X,
L.X0
Xo
z
such that interference fringes are smeared beyond usable con-
trast. We shall see in a later section that a laser source can
increase L by orders of magnitude over the marginal values af-
forded by pre-laser sources.
2.1.3 Polarization Conditions - Since the interference
phenomenon of superimposed beams is produced by the vector ad-
dition of the electric vectors, it is optimum that light of
the two beams be identically polarized at impingement on the
photo detector. The intensity maxima and minima will be degraded
to the degree that the electric vectors are not rotationally co-
incident. The amplitude of the electric vectors El and E2 of
the two beams can be expressed as:
27r
El = EL sin (cot - x)
EL2 = E sin (tot - x (i) )
for equal maximum amplitudes,. E, of the two beams.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
. Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0 -10-
Where:
t = time dependent variation
27T
= k = propagation constant
? x = distance along the path of the beams
= phase angle of the two beams determined by the dif-
ference in path lengths
The resultant amplitude vector, A, is
A= E sin(co t - kx) + E sin(*) t - kx -
The intensity, I, detected by the photo detector is a scalar
quantity proportional to the square of the amplitude vector, A.
I = A ? A = A2
Substituting for A:
I E2 Ein2 (AI t kx) E2
sin2(o3 t - kx - )
+ 2E ? E sin(to t - kx) sin(a) t - kx -
Let 9 be the angle between the planes of polarization of the
two beams. The dot product is then:
E ? E = E2 cos
and
I = E sin2(o) t - kx) + sin2(co t -kx - 4:0 )
+ 2 cos 0 sin (to t - kx) sin (cii t - kx - 4:1) )
but sin0 t kx - ) = sin(co t - kx) cos - cos(*) t - kx)' sin
and
E2 Ein2 (a) t - kx) + sin2 (et) t - kx- )
+ 2 cos & sin2(c.) t - kx) cos 4,
- 2 cos sin(co t - kx) cos(eu t kx) sin
but sin(ea t kx) cos(ed t - kx) = k sin 2(ea t kx)
4)]
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
. ?Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
then
E Ein2(c43 t - kx) + sin200t - kx
+ 2 cos 0 cos 4, sin2(c4.t - kx)
- cos 0 sin cip sin 2(6)t - kx)]
Since the frequency response of the photo detector is very much
less than. the frequency of light, the intensity detected, 7f,
is the time average over many cycles. The average value of sin2
-11-
is 1/2 and is independent of phase angle. The average value of
sin 2(wt - kx) is zero.
T = E2Ei +? +
and
cos
Substituting
9 cos
I = E20. + cos 0 cos ch.)
The maximum value occurs for
6 = o, ci) = 0 or 8 7r ,
(.3]
=7r
2(l
max = E (1 + cos 0 cos 0) = 2E2
Also Tax E2(1,+ cos it cos 7r)= 2E2
m
The minimum value occurs when
9 = o,
mm
Also Tmin = E2(1 + cos 7T cos 0) = 0
='7t or6L =ir,4. .0
2
E (1 + cos .0 cos Tr) = o
average values, we get:
and is:
When the angle of polarization, 60 , between the two planes Of
polarization of the beams is 90? then
7900 = E2 2(1 + cos-7L cos p ) = E2
and no modulation occurs when 4, is varied by changing the
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
path..
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0 -12-
length. Cos 0 varies less than 11/2% for values ofe < 100
.
Therefore it is not necessary to maintain precise coincidence
of polarization of the two beams. In addition, since the polar-
ization of the two beams will normally maintain coincidence
unless deliberately changed, the problem can generally be
neglected,
2.1.4 Spectrally and Spatially Distributed Sources -
It is convenient to analyze and describe interference phenomena
on the basis of ideal light sources - geometric points emitting
light at single wavelengths.
Real light sources are not ideal in that they always
appear to have finite extensions in space and to have spreads
in wavelength during the response times ordinarily required for
observations of interference. It has been firmly established,
however, that light is emitted as a succession of very short
duration individually monochromatic wave trains (photons)
each of which originates from some extremely small region of
space (e.g., an atomic volume), and interacts with matter in-
dependently of other wave trains.
The intensity pattern of a real source can then be
treated as a summation of ideal, monochromatic, point source
intensity patterns, the point sources being distributed over
space and wavelength to be equivalent to the real source.
Since for given geometry the interference pattern
of an ideal source is in general a continuous function of its
wavelength and position a real source equivalent to a small,
smooth range of ideal sources over space and wavelength will
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-13-
produce an interference pattern that may be viewed as the some-
what smeared pattern of its mid-range ideal source.
2.2 Application ?of Interference to Length Measurement
2.2.1 Classification of Interferometers - Coherent
beams in an interferometer arise through division of light from
a single primary source either by division of wave front (as
in two slit experiments) or division of amplitude (as by a
partially reflector mirror). Interference fringes are formed
in an interferometer by superposition of two or more beams
originating from the same light source. On these bases inter-
ferometers are conventionally and conveniently divided into
three groups.
Types of Interferometers
Wave Front Divided, Dual Beam
Rayleigh (1896) - A simple two slit instrument
used to determine refractive indices of gases.
Stellar (Michelson, 1920) - A two slit device used
to measure angular diameters of stars by observing overlap
characteristics of fringe patterns.
Amplitude Divided, Dual Beam
Jamin (1856) - Used for refractive indices of
gases. The Mach-Zehnder modification is extensively used to
study air flow in wind tunnels.
Michelson (1881) and Modifications - Outstanding
for versatility, simplicity, and stability. Much used in
metrology. The Twyman-Green (lens testing) and asters (meter
comparator) are important modifications.
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
Approved For Release. 2005/06/23 : CIA-RDP781304770A002900010038-0 ?
-14-
Amplitude Divided, Multi Beam
Lummer-Gehrcke - Interference effects within a
plane parallel plate provide high wavelength resolution of
light incident at near grazing angle. Superceded by-
Fabry-Perot - Interference effects between partially
reflecting plane, parallel surfaces result from light at near
normal incidence. Most versatile of interferometers. Used
for metrology of absolute wavelength and meter determinations,
highest resolution spectroscopy.
?2.2.2 Favored TypesIbr MetroloAy - Amplitude
division (e.g., partially silvered mirror) of light from a
primary source is inherently more efficient than wave front
division (e.g., narrow slits). Only the most simple and stable
amplitude division interferometers of modified Michelson (dual
beam) or Fabry-Perot (multi beam) types have been employed in
metrology.
Fabry-Perot Etalons are interferometers of fixed
length notably employed in several multiples .of 'a unit length
to establish meter equivalents in standard wavelengths. Vari-
able length Fabry-Perot interferometers are impractical for
measurement of distances over a few millimeters by reason of
the difficulty of constructing ways to maintain the plates
sufficiently parallel for the multiple reflections of the beams.
Variants of the basic Michelson dual beam inter-
ferometer are the only types utilized for measurement of varying
lengths. Satisfactory ways for movement of a mirror (single
reflection) to distances over a meter have been produced.
Approved For Release. 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
With but a single reflection required, a corner reflector can
be substituted for the moving mirror with great relaxation in
parallelism requirements. If three or more interferometers
share the same movable mirror, parallelism of the mirror may
be servo controlled. All fringe counting interferometer length
mensuration systems commercially available or described in
the literature employ Michelson variants with collimated primary
beams.
2.2.3 Light Sources - The International Meter is
presently defined as 1,650,763.73 wavelengths of the extremely
sharp line of approximate wavelength 6056A emitted by krypton
isotope (KR86) lamps refrigerated to liquid nitrogen temper-
ature. While the KR86 lamps are suited to primary standard
measurements, their complexity makes them undesirable for light
sources in general interferometry. Mercury isotope (Hg198)
lamps emit a line somewhat less sharp at approximately 5461A
when operated at about 5 ?Centigrade.
Until the recent advent of lasers, the Hg198 lamp
was altogether the best light source for high accuracy inter-
ferometry. This was by reason of .
simplicity of operation
high intensity (particularly 5461A)
easy separation of lines (filtering)
spectral purity (.005A half width for 5461A)
The volume from which the light originates in the lamp, in
common with all its contemporary monochromatic sources, is
undesirably extended.
The Helium-Neon Laser, now readily available in
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-16--
practical configurations, excells every non-laser light source
in every respect with regard to interferometric application.
By reason of its coherent plane wave output (equivalent to a
collimated point source) it provides three to five orders of
magnitude greater useful light flux than the Hg198 lamp.
Its single wavelength (no filter required) is stable within the
half-width of any pre-laser spectral line. The half-width of
this line is several orders of magnitude less than that of
any pre-laser line.
2.2.4 Fringe Counting - Interferometric measure-
ment of length implies the counting of fringes. Three methods
are used.
For measurement to highest accuracy of a length
known to good accuracy (e.g., a standard meter) the number of '
fringes actually counted can be reduced to a small fraction
of the total number of fringes in the length. To illustrate:
count the number of fringes in a bar about 1/8 meter long.
Count the difference in fringes between this bar and a second
CDout.',qual length so that together they are
known number oaf fringe. Using a 1/4 meter
mete::: bar
YLel
1/4
in successn an approximate.
number :Lnally count the if
72eren.:.:e between the cont1::,- and standard meter
bars.
When suitable sources accurately known
wavelengths are utilized, lengths car. 1?termined in terms
of wavelengths without actual counting ..tLe. method of excess.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0 -17-
fractions. To illustrate: use two wavelengths A0 and Xizr--ri Ao
Starting at zero length, X0 and X1 have fringe coincidences
at every tenth fringe of -A0. At intermediate integral fringes
of X0' the excess fractional fringe of X1 is just one tenth
the least significant integer in the total integral number of
A fringes. Interpolation to non-integral values of A00
fringes can be made. If a second wavelength A2 be used where
100 10
2 = Tur A the second least significant integer in the total
integral number of Xo fringes can be determined.
In practical cases the ratios of wavelengths are
not as simple as above; but the principles nevertheless apply.
With sufficient wavelengths X0, Ai, An the exact distance
in terms of any of the wavelengths can be determined by excess
fractions alone. With fewer wavelengths distance can be
determined by an auxiliary measurement of less accuracy.
Finally, by measuring fringe intensities at points
effectively about k fringe apart to determine sense, fringes
can be directly counted as they increase or decrease in number
by triggering electronic counters that concurrently display the
number of fringes moved from a chosen zero or reference position.
Count reliability as affected by triggering levels and intensity
modulation is discussed in Section 4.2.
Approved For Release '2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23: CIA-RDP78604770A002900010038-0 -18-
3. LENGTH MEASUREMENT LIMITATIONS AND ERROR SOURCES
3.1 General Discussion
The limitation of maximum length continuously
measurable by an interferometer is primarily a result of wave-
length spread in the light source used. We shall see that use
of laser .sources extends this limitation by several orders of
magnitude.
Serious errors in interferometry can result from
a) defects and shifts in the geometry of the interferometer
configuration, b) limitations on 'fringe resolution, and c) light
source wavelength magnitude determination.
3.2 Interferometer Geometry
? Variations of dimension and alignment that effect
the metrological accuracy of an interferometer may be considered
in three groups.
Long term shifts can result from wear, creep, or
stress relief of materials. Considerable caution in design
and attention to selection of materials are necessary to reduce
such shifts to negligible levels. In addition a regular schedule
of system calibrations is necessary to verify the long term
maintenance of geometry.
Short term shifts which may be considered rapid
variations of geometry are treated in a later section on
vibration (see 3.3.1).
? Thermal variations of dimension and alignment and
variations of alignment with length to which the interferometer
is extended constitute an intermediate group that will be
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0 -19-
considered in this section. They are discussed with reference
to a basic Michelson interferometer configuration, this being
as noted previously, the only type employed in measurement of
variable length.
3.2.1 Rigid Length - The fixed length reference
arm of a Michelson type interferometer can be immunized to
significant thermal variations by means of a Koster's prism
Michelson modification (see Figure 2).
Here the variable optical path length to the movable
mirror from the reference plane is greater than the fixed
reference path length by 2L, no matter how prism A B C expands
or contracts as long as the prism experiences no significant
thermal gradients. ?
3.2.2 Variable Length - The defined axis of measure-
ment of an interferometer must coincide with the actual axis
of translation of the reference point onthe movable mirror.
If the direction of the actual axis shifts from ihat established
for the axis defined by calibration, error will occur as a
unity less cosine of error angle function. This is a weak
dependence for small angles.
Let:
Lm = measured distance between two positions of the
reference point on the movable mirror
LD = distance between positions in the direction of ?
defined axis
angle between axes in radians, assumed small
AL = error in measured distances, assumed as distance
in direction of defined axis
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
MONOCHROMATIC LIG HT SOURCE
PHOTODETECTORS
COLLIMATING LENS
DECOLLIMAT1NG LENS
KOSTER' S PRISM
A
FIXED MIRROR
BEAM DIVIDING
SURFACE
MOVING MIRROR
FIG. 2: KOSTER' S PRISM -- MICHELSON MODIFICATION
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
. Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Then
and
2
AL = Lm -LD = Lm(1 - cos ) , for small 4,
-20-
Figure 3 illustrates the error magnitude.
The movable mirror must be held rigidly parallel
throughout its range of motions in order that the fringe pattern
be maintained.
? In Figure 4 note that:
a= angle between the fixed mirror and the virtual
position of movable mirror, an extremely small
? angle
d = diameter of the beam on the fixed and movable
? mirror
n = number of fringes occurring across the mirrored
beam
A= wavelength = 0.6329 micron for He-Ne Laser
Then:
d sin cx 2 dcx
n= X/2
For mirrors 2 cm. in diameter to be parallel within 1/5 fringe
(about .06 micron) requires
< nX 1 X.
= 3.2 x 10-6 radian = 0.64 second of arc
The automatic fringe counting interferometer at
the National Bureau of Standards applies servo control to the
tip and tilt of the movable mirror to maintain parallelism.
Approved For.Release 2005/06/23 : CIA-RDP78604770A002900010038-0.
10
9
8
7
5
4
3
10
5
4
?3
[1:1P 3
2
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
--I
H H-
=IMO
i
11-
lid:
El
1"
MU=
- -181
CIONEMBIE111111111/1111111111011169111111111ilEMIIIIICERIMEill
NEM
I
-
aq
I ,;1111111E1111111211121112
soul ,41
ME
-
EN
511su
1-,H11,1L!
'
-I
1 I
moo'
-1 I
--a
- , Ammuffir
11
'
"
m

L
-H HH L.,
---ri,
--ii ,
L,,,
,,,
1 :
-1-1-1/1
i
ii
?
__.._!_
_t,i-
_,_,
_
--1_'-----1:
-:_
I 1,1',_
'i
-iti:41- :-
ii-,
f ; -
' -1-q---ii
-=t-i-.
-/-ig-
fig
. ,
I-
-Ili
14 II,
HI

It
74
Pi'
?
-
-
IN
.1-- -'--
-
--I
k -1-91-
To
I:-
t
I-
Til:=--
1 A
n
I i
i i-, t
J
,
i_
--
j
r-Ir Fir.
.....
---i-t
h-ti' ?
?.
-
--i-
-
-
1: it.-i
1-
?-7-1-
-1--I
174
-1 ti
-TITT
-rI-I'
1-i-
7-7
ii-
1--
1
r--1-
1
4,
1
1 1
1
I" 1
;U.
i'l ii
1 i d
-t
I:t1
Bill
lyll
1-
"?'?
- ---k-1-1--'-
?1-1-11
=
=-LdiT
1 '
-1
11
'TT .
ti-
i
--,-
i---,
---
_
.1_ 1
T-L1 1
--a
-i-
=-1--
-r
? -
IT_ 7
,
. i---
--.--,--.--I
1
i .
Egli
ummuitirl
in
rTh-
r_.,__
11
II
?
?
.111'
t,
'
!
,
L
ili
1
miti
, _r_i_
r
EH
I,
- ;
-
if
T '
I
i
ist.,
,
1
i?
ii!
-t
i
ma
I
;
4
1,1
1
, i
0----
1
II
1
LLL_2-t
---1-'''.
I
1
1
i
-
-r
s
H
i
1 1
Mt
-L
;
'_,,
-4
r

I-,
IMBIENIMMIENNMENUMMENIMMINEN
sus
=EEO
111111111
NAINERIIIIIMI
TN
H
-1
4-'
-4-,
rill
-1-
-i-H;
H
' }1
i i il
+in
'
--
E
El
-I-
?
i-
MUM=
IHNIMMERIONI
La
'---
;
EMI
r=MEE
=MU
_ ---4.--
1
_1_4_
r-I--?
.
---
0
-, .._,.
,_,,
,
,
1--
FH-
;
;
;
-
LH"
11,-
J--
---
1,-- -11-4
_44r,
-1-H;
IT
-
I
,
,
,
,,
Tr-
TI I
mum
,
, ,
1
,
, 1 I
MOROI
IHII T
-1111,12EMI
,
,
I
,
Bffigal
EM10-11
4-----c-LT-I--r-I--I1124-
1
,
1
--t-i-
-d-
?--ii
.
-
ti
---` '
,_
f
-,
1
:le
, .
LP
-'1
, i
-'11INP4-i-i
.11E11
Cm
.
_.,7
,
irj.....,..4..11.
i
1 rESIEN111
'
I
,-
i
-IJE -?-
IIIIIMINIMINI
-7-i-
-
LT,:
-1-'
4
;ILI
1
,
11-H
d.8111
EMS=
I
r_
1111?11M
. , ,
i41-I
_LI
La,
7-Hi
r
1
,
IT
La
1 . r
,
4 I-
_
i-
Liam
-4
1-1-14---1-
-It
I
.
1-1111C1-
---i-r
I
'
4,7
1-.--i
?
1--.-
.
--I-
,
,
,.i.
J-,
_,T
+
+1:
..
."
-,-.
-.
,
.
-t-_1
1--,
tt
_,_
___
T _,____--,--17,-:
Turt-1-,/
-11,111---,-
,
....
i. t,

....,
._
di
I
1
..
-1=
,
t
-1
'
T-1
. ,
,..
..?
-,
..
IA
i
4_1
--i
I
1, =,

..
:
i-
,?,
. i
1
HI
-LT
I
-I
ME
?
BlInn=
MIIMIErAmin
MINBNIE
111111111131
al
INIUM=111
1 :II
MEM
H
1
rt,
,
--1-1
-?
1
I
,
-77
i
7 i
/ . ,
',7'
-11-71+
..iflTT
I
I,
H
....
"
i
....
.
,
,
(
H
-111111
1.161+11T
j....
MI
BEI

7
r
Hi
1 1
111
-,
t
IMMESIIIIIIIIMIBEICIMIIINIMIIIM
-
,--
- ?i'
44
---I -
4 H
;
MINI=1"manustOMBIZEMEM====0
ai
r i
,./f-
-1
MIIIMMEN
.
!
H
H 4
-'-
alliiIMEMIE
?
, -m-
-
-,----o ,
ME
I
__,
_I
4 .--
'
--H
,:+i,
MIENNRE
me
14-1
? ,
.
1
inowimuum
--'--I
IMMEMIIMENfilli
ii,
1
'4
EN
NPR
EME
? _I
14,'
-
T
d
q : '
4
--t- '
? -
_
._
-1-
. /
r ' ''''
1
'17
---, -----r-
i 1-
1
T-!T!
-
IMMIMINI=M11
=MINIUM
_
t
U ft'
--,
12- 4
I-
-IT
"I
i-
4 i
-H 1-
-1
i
-I-;-t
H
Tht+i
f-d-;"
IIIIIMMINI
-L4
i
RI-,
nu
11
, -t-ri
-i-ti
,
1 INN
?
1-
+11
-Ens=
IIIIIIIIIIIIIII
I_1_
1
-1,--
-1-1
--I,
-1-ii
_;
11
'
i---
1+11
1-1-ri
'

---t--
- I-.
,--t-
_t -t
=1-
-I
-I-
I
i--
M
m ....d
11
-

,
-1,-
t__
il
i
H
H
L
_ -r-7
;
j_
1 ...di
'
!-C-
H
INN
MIN
1-,_,
Ma
II
MINIM
IIM
1
,
t '
'MR
1
t
I
-
Mminin
RH
I
-1-
LI
4
wilmul
IIIII
I
F
11
1
111111111
is
1
1
11
MOMMI
i
I
I
II
MI
I
MI
il?
IIIIIIIIIIIIIII
IIIIIIIII
I
III
I
a
I iI
I
EMU
II
ft III
I'II
EM
MMU
I
LIM
IIIIIIIIII
Il II
III
II
I
min
no
amino
1 I
.1
I
2 3. 4 5 6 7 8910 2
3 4 5 6 7 8 10
2 3 4
0.004 0.01 0.04 0.1 0.4
ANGULAR DEVIATION FROM DEFINED AXIS --- DEGREES
1 . 0
FIG. 3 ERROR IN MEASURED LENGTH DUE TO DEVIATION FROM DEFINED AXIS.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
MOVEABLE MIRROR
(VIRTUAL POSITION)
A
FIXED MIRROR
FIG. 4:MIRROR ALIGNMENT.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-21-
If a corner reflector is substituted for a plane
mirror, beam reflection sufficiently parallel to maintain the
fringe pattern is readily obtained despite relatively gross
translational or angular deviations of the reflector carriage.
However, since the position of the reference point on the
carriage can change significantly before the fringe pattern is
significantly affected, there must be either independent means
of taking account of reference point shift with reflector shift
and orientation, or the ways guiding the carriage must
shown to be of such quality as to prohibit
from this source.
3.3 Fringe Contrast and Flutter
3.3.1 Vibration - The effect of vibration
significant
be
error
on a
fringe counting interferometer measurement system differs with
vibration frequency relative to the cutoff frequency of the
counting equipment. If the vibration frequency is well below
the counter cut off frequency, the counter will change count
with the vibration and the count will not be lost. If the
vibration frequency is well above the counter cut off frequency,
the counter will not respond and will in effect record the
average position. If the vibration frequency is in a region
near the counter cut off frequency, the count may or may not
be recorded and count errors can be generated. What contitutes
Tia region near the counter cut off frequency" depends upon the
characteristics of the particular electronic components involved
in the counter. It is particularly difficult to assess because
of the extremely high count reliability desired.
The effect of vibration is intimately related to
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
-22-
amplitude as well as frequency. For a vibration amplitude of
where A. is the wavelength of the light from the inter-
ferometer light source, the fringe will shift from one intensity
maxima to an adjacent maxima and will obviously constitute a
change in count. If the vibration amplitude is only a fraction
of 4- , the triggering level of the electronic equipment will
determine whether or not a change in count will occur. We
have selected my as being a reasonably good lower limit. We
have assumed that if the vibration amplitude is less than
, the fringe count will not change. If the vibration ampli-
tude is between -2? and 7 , the count may or may not change and
an unsteady fringe count will occur. The relation between fre-
quency and amplitude as expressed in acceleration units of g
is shown in Figure 5. In Figure 5, the region above and to the
left of the amplitude line is one of excessive vibration
and fringe count flutter. At low frequencies the eye or the
recording equipment can follow the flutter but at high fre-
quencies, the least count will be unresolvable.
The region below and to the right of the 7,-,-, line is
. "
the region of acceptable vibration and steady fringe counts will
be obtained.
X
The region between the two lines y and .2-5. constitutes
unacceptable vibration causing unsteady fringe counting and
generating counting error. Note that at very low frequencies,
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
icr2
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
AMPLITUDE =
REGION OF EXCESSIVE
VIBRATION CAUSING
FRINGE COUNT FLUTTER.
lo-6
icr7
3.0"
AMPLITUDE= -20
REGION OF ACCOPTABLE
VIBRATION FOR STEADY
FRINGE COUNT
z..
10-1 1 ? 10 102 103 104 105
FREQUENCY, CPS
FIG. 5: EFFECT OF VIBRATION ON FRINGE COUNTING.
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-23-
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
such as 1/10 cps to 10 cps, very small vibration levels, such
as 10-8 g to 10-5 g, can seriously affect the count. At the
higher frequencies, 1,000 cps requires vibration levels over
1/10 g and 100,000 ?cps requires vibration levels over 100 g to
affect the fringe count. It is unlikely that these high vibration
levels will be encountered. If we assume for example that in
normal operation no vibration levels over 1 g will be encountered,
then any counting rate above 2700 cps will be adequate. The
counter will count all vibrations below 2700 cps with amplitude
above -2? . All vibrations above 2700 cps will have an amplitude
less than -27 and will not affect the count.
The Bureau of Standards laser interferometer counts
at 1,200 cps which is shown at A in Figure 5. Their vibration
levels must therefore be less than 1/5 g. The Cutler Hammer
laser interferometer counts at about 80,000 cps which is shown
at B in Figure 5 and no normal vibration levels can exceed its
count rate.
Low frequency vibration of amplitude between -2 ?\
- and
X
Ty is the region of concern. The exact boundaries of the
region are not 7 and -2-5. but are determined by count triggering
levels. Whether or not a count is lost is determined by 'the
hysteresis of the counter. Since the hysteresis can be made
small but cannot be zero, there is some small but finite probability
that a vibration amplitude will occur which will cause loss of
a count. As the counting rate is increased to accommodate
faster traversing rates, the probability of a critical vibration
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0 ?
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-24-
occurring and a count being lost is increased. Further
analysis of count reliability should be coupled with experimental
measurements of appropriate counters and is beyond the scope
of the present investigation. Therefore, further work must
be reserved for later consideration.
. In Figure 6 some vibration levels are superimposed
on the regions of Figure 5. It is easy to see from consideration
of Figure 6 why it is desirable to bbtain the greatest possible
attenuation of vibration and why the natural frequency and
damping of structural members must be carefully considered.
Vibration A in Figure 6 illustrates the maximum
allowable mirror motion due to a structure with 5% damping
excited at 10-5 g. Note that 35 cps is the minimum allowable
natural frequency of the structure. Lower frequencies will
cause the peak amplitude to penetrate the TT line.
Since 5%
damping is the maximum to be expected in bolted and riveted
structures, it is essential that structural members and com-
ponents have natural frequencies above 35 cps. This can be
readily achieved in good structural design. Note that excitation
-3
at 10 g would require natural frequencies of 350 cps which
are very difficult to obtain.
Vibration B in Figure 6 illustrates the maximum
allowable mirror motion due to a structure with 1/27o damping
-5
excited at 10 g. Note that 100 cps is the minimum allowable
natural frequency of the structure. 1/2% damping is probably
the minimum to be encountered in general and is associated with
pure elastic materials such as quartz or glass. Even steel
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
10-
10
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
VOW
A
AMPLITUDE =
EXPECTED RANGE OF
VIBRATION INPUT LEVELS
'a-
10?
-2 AMPLITUDE =
20
DESIGN GOAL FOR
VIBRATION ATTENUATION
VIBRATION B.
1/2% DAMPING
10-5g EXCITATION
100 cps
VIBRATION A.
? 50/. DAMPING
cps 10-5g EXCITATION
35
10- ?
10-1 1 10 102 103
FREQUENCY, CPS
? FIG. 6: ALLOWABLE VIBRATION LEVELS
104
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
105 .
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-25-
has a somewhat higher internal damping factor. The monolithic
structures in a measuring engine such as the base and the platen
should therefore have natural frequencies over 100 cps. If
there is attenuation between the vibrating structure and the
mirror, or if considerable damping is deliberately added, the
natural ?fvequency limits can be relaxed.
3.3.2 Spectral Purity - Spectral line sources
are never ideally monochromatic. With line splitting effects
(Stark, Zeeman) absent and line broadening effects (Doppler,
pressure, resonance) negligible a spectrum line has yet a
finite natural width with a typical gaussian distribution of
intensity.
In Figure 7, AX0 is the half (intensity) breadth
of the line centered on wavelength A.0. The Heisenberg Uncer-
tainty Principle, basic in quantum mechanics, relates the
uncertainties in energy and life-time of an excited state of
an atom or molecule by:
tAEo
Also we know that:
where:
ITT
Eo = hy and X0 1/ = c
o
(1)
t = half-life for spontaneous decay from the
excited state to the ground state, seconds.
E = energy of the photon, ergs
AID= wavelength of the photon, cm
?
7/0 = frequency of the photon, cps
?
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
FIG. 7: SPECTRAL LINE WIDTH DISTRIBUTION.
am.
Approved For Release 2005/06/23.: CIA-RDP78B04770A002900010036-0
Approved For Release 2005/06/23: CIA-RDP78604770A002900010038-0 -26-
AE = half-breadth around Eo, of the distribution
of photon energies radiated in spontaneous
decays to ground state, ergs
h = Planck's constant = 6.624 x 10-27 erg sec
c = velocity of light = 2.998 x 108 m/sec
Differentiating, we get
? AE0 = hANyo and A-yo
by substitution
t4E0 = th110 - 21T
and t Ayo rrl _ -tcA2L0
Xo2
Thus:
x - A02
? 27v Ct
(2)
For given wavelength, then, the half-breadth of
a spontaneously emitted (i.e, non-laser) spectral line is inversely
proportional to the half-life of an excited state that decays
to ground to produce it.
For the neighborhood of .5 micron wavelengths
Ao
- 4 x 1015 t seconds
1"0
The half-life times of excited states are ordinarily no longer
than about 10-8 seconds which corresponds to
XO
40x io6AXo
and indicates that interference fringes in an interferometer
will be smeared over, substantially a whole wavelength when the
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0 -27-
length being measured reaches about t 40 million wavelengths.
Thus normal spectral source half-widths limit usable contrast
fringes to the order of meter measured length.
Metastable excited states have longer than normal
lifetimes for spontaneous decay, in some cases seconds, minutes,
and even hours. Such longer lifetimes correspond to lines of
higher spectral purity (shorter half breadth) but lower inten-
sity. Spontaneous metastable line intensities are generally
too low for practical use in interferometry.
Metastable states are, however, the sources of
extremely pure, high intensity spectral lines produced by
lasers. A metastable state serves as a laser reservoir when
atoms are excited or "pumped" into the state and then stimulated
to emit photons within subsequent times short compared to the
spontaneous half-life of the state. Since stimulated emission
is a-cresonant process involving repeated interactions that
occur most strongly at the center of the wavelength band that
the metastable state emits spontaneously, the.purity.of laser
lines is greater thanspontaneous emission half-widths alone
indicate. Gas laser sources provide lines of such purity that
fringe contrast is not significantly degraded at tens to,
hundreds of meters measurement distance. (?Lc/ AA > 1014 has
been measured for the He-Ne CW Laser).
3.3.3 Particles in Beam - Particles as large as
25 micron may be passed by air conditioner filters and float
in the interferometer beams. To facilitate assessing the pos-
sible effects of such particles, we assume independent, single.:
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-28-
scattering without wavelength shifts.
Independent scattering occurs when the scattering
particles are sufficiently far from one another with random
orientations that intensities scattered by various particles
are additive. A mutual distance of 3 radii or greater between
particles is usually a sufficient condition. In a dense fog
mutual distances are some 20 particle radii. The assumption
of independent scattering for normal conditions in the inter-
ferometer beam is obviously well justified.
Single scattering holds when the intensity scat-
tered is proportional to the number of scattering particles.
Single scattering holds from beam entrance into a particle
cloud to such.a distance that beam intensity is significantly
reduced below the entrant value, conventionally by about 10%
of the entrant value. Since even 1% loss of intensity in a
beam length of about a meter would imply abnormally smoky or
dirty atmosphere, single scattering is assured.
The scattering of intensity out of an interferometer
beam has little significance for 1% total intensity loss or
less. But forward scattering along the beam Might conceivably
produce a phase shift equivalent to a significant variation
in the index of refraction along the beam path.
However, if we except such unusual anomalies as
oriented, lens-like particles, the fraction of total scattered
amplitude that is singly scattered effectively parallel to a
sharply aperatured beam is very small indeed (Ref., Van de Hulst,
Light Scattering by Small Particles). Thus if 1% of the total"
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-29-
amplitude were singly scattered only a small fraction of this
scattered amplitude could effectively rejoin the beam and ?there
could therefore be no significant reduction in fringe contrast.
We conclude therefore that under reasonably .clean
laboratory conditions, particles in an interferometer beam
will not affect mensuration and no .extraordinary precautions
need to be taken to assure an adequate clean room.
3.4 Wavelength of Light,
3.4.1 Wavelength Error - The velocity of light
in air is affected by the temperature, pressure and humidity of
the air and also by the presence of contaminants such as CO2 or
ozone. We will now examine the magnitude of the effects of air
temperature, barometric pressure, and water vapor (humidity).
To measure length, L, we count the number, N, of
wavelengths, X, occuring.
L = N X.
Differentiating with respect to X gives the error in length
dL due to the error in wavelength., dX.
dL = NdX
The error ratio is:
but
dL _ NdX
L NA.
where A.= wavelength in air.
= wavelength in vacuum
n = refractive index ir air
and--X dn
Approved For Releaile 2005/06/23 : CIA-R1DP781304770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0 -30-
0dn
2
? n dn
The partial derivatives of n may be taken for temperature, T,
pressure, P, and Humidity, H.
an an 3 n
dn = dT + dP H dH
where
dT =air temperature change in C.
dP = barometric pressure change in mm of Hg.
dH = water vapor pressure change in mm of Hc0,-
Thus the measurement error is:
n 122)V P a H J
The partial derivatives as obtained from the U.S. Bureau of
Standards in Washington, D.C. are.:
Air Temperature: an/ DT = -9:28 x 10-7/oC
? Barometric Pressure: 3n/ 6P = +3.57 x 10-7/mm Hg
Humidity: ain/ H= -0.57 x 10-7/mm Hg.
The index of refraction of air, n, may be found for a given
set of conditions.
?
For ? X= 6329.9 A.
? T = 20 ?C
P = 760 mm Hg
H = 0 mm Hg (dry air)
n = 1 + 2713.30 x 10-7
To find the relative error, the partial derivatives must be
divided by n. .Since
1/n = 1/1.00027133 = 0.99999+
Approved For Release 2005/06/23 : CIA-RDP781304770A002900010038-0
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
-31-
we consider the l/n factor negligible as a correction of the
partial derivatives. We can thus, express the measurement error
introduced by atmospheric effects in microns per meter (or
parts per million, ppm) directly as:
Air Temperature: -0.928 ppm/?C
Barometric Pressure: +0.357 ppm/mm Hg
Humidity: -0.057 ppm/mm Hg.
The coefficients are illustrated in the graph, Figure 8.
The significance of the algebraic signs may be illus-
trated by considering air temperature. As air temperature
increases, the index of refraction of the air decreases and the
wavelength of the light increases. Thus the wavelength count
for a given distance will be too small and the error will be
negative as shown on Figure 8.
The relative importance of the atmospheric effects
is illustrated in Figure 9. For the purposes of the illustration,
it was assumed that humidity 'can be controlled to -I-10%, that
air temperature can be controlled to - + o1 C and that barometric
pressure is uncontrolled and can vary ? 1" Hg. From the
figure it can be seen that the humidity correction can be neg-
lected, the air, temperature correction is marginally significant
and the barometric correction is essential. If the measurement
of a given length is accomplished in a few minutes, then the
barometric changes occurring in the course of a measurement are
probably non-significant.
+
3.4.2 Wavelength Determination - In order to
calibrate the measuring device the basic wavelength must be
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
?
Li
A ?
_
11111!
MEI
? 1161
.1'
A
.111.11=1111 11 II III I H
0 - 0, 0
IMMO
Ms
- -
- II I.
?
ME
Ms
4
;:
I I
,
1-1
r-
-
1 I I i__
pH_ _
I ? _
I f?
?
1AI ?III I
?r?
lIft
rduuuauuss
LAM ME 11111MMINIM
MINIMMEMEMPONAMMEM IMMM MEM1117
air si mum
m ? m mammas ammummumak a I, 011411111.0.
MOM= MEM AMMO= MMEMMOMMO
MMEMMEMM MIIMM AMMOIMMEMENUMMIIMMN OmINN

' MUMMEMMOMMMIIMMEMMUMMWOMM MUM
MEE INIMMIIIMMUMMOMMEMM =NM
MI" NEMINIIMMEI
MMI IIMIMMUMEMEM ? MEM
AIM
plopirleitSW
1111111 I 11111
11
...M=Eammis Wilrai Aftrmarla
????????? . .
Noratrar -- -- IN.Frommm
, HINriill A 1.11, eIP
figIrtw,
? .. ...6.4111... ?
II
.1 I
II I IBM WNW 11811
AdOe
inc
a
IIIMMEMM111111111.111111111110
U.
f
1111111111MME MMEMEMMEMEMMIIIIIIMEMM11111111 III
'III"' ' 1111 11 11111 11
?
1-I
IT
_uIUIIi
I 1 U
a
? 11?11?1???r???????? ENE 11 ?
EMMIMMINIS MEM MEMINIMMMEMMIIM
11.1 MMEMMENM H ? II Ms 1 M
.., I mill IM
III OMB=
MUM
?
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
+10
Approved For Release 2005/06/23 : CIA-RDP78604770A002900010038-0
+8
+6
10
HUMIDITY CHANGE (at 20?C, 2 mm Hg =11 1/27. R.H. )
c