COMMENTS ON VALUE FUNCTION ANALYSIS

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B05167A001800170027-9
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 10
• Document Creation Date: December 27, 2016
• Document Release Date: June 9, 2014
• Sequence Number: 27
• Publication Date: January 1, 1964
• Content Type: MEMO

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MEMORANDUM FOR THE RECORD
SUBJECT: Comments on Value Function Analysis
1. This memorandum discusses four aspects of the applica-
tion of the value function analysis approach to the OXCART/SR-71
comparison: i.e, the variation of "value" of stereo vs mono
coverage, the effect of the atmosphere, "theoretical" versus
"practical" approach, target contrast, and additive effects of
multiple sensors.
2. Variation in value with resolution: In the current
discussions, the "value" for resolutions below eight feet are
given in tabular form; values at resolutions larger than eight
feet are given by the formula K(r) - 2.5/R. However, the basic
resolution variation with viewing angle is estimated as being
proportional to the three halves power of the secant of the
viewing angle. Unfortunately, such a combination yields an
infinite area weighted value for 1800 scan angle, as the area
covered per unit angle is proportional to the secant squared.
A value function of 20/R2 would remove this divergence, and
yield a more realistic low value to large resolutions and match
the proposed value at resolutions of about eight feet.
3. The "value" of Stereoscopic vs. monoscopic coverage:
For some photo-interpretation and analysis tasks, stereoscopic
coverage has some value; the value function thus should contain
an explicit statement of the variation of values with stereo
angle. I am not sure what this functional relationship should
be for this mission (the value function chosen must, of course,
be determined by the mission reauirements).
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4. The effect of atmospheric d2gradations: Many studies
have shown that the resolution, for a given target contrast,
is a function of the total haze contribution. Such total
haze contribution (really the lowering of contrast of the target
as presented to the camera) is affected by haze density, path
length (hence obliquity), relative direction between sun-target
hue and camera-target line, etc. The currently accepted three
halves power of secant of the viewing angle primarily reflects
the increase of slant range and obliquity of horizontal targets.
On the basis of the haze considerations, it is suggested that
some higher power, say the square or five halves power, might
be more appropriate, although this functional relation should
be more carefully and explicitly considered.
5. Theoretical versus Practical Approach: Apparently
the current approach to the value function analysis is to
estimate ground resolution on the basis of a theoretical con-
volution of camera design parameters, vehicle motions, assumed
accuracies, et cetera. 1 suggest that a more logical and
pragmatic approach, in the case of operational cameras, is to
use flight test results of nadir resolution. If desired,
separate value functions could be derived for, say, the best,
the average, and the worst, flight data, giving an expected
spread in system value and concurrently, an estimate of the
significance of difference in "value" for different systems.
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6. Target Contrast: System resolution is directly
related to target contrast; the contribution of haze, etc., is
primarily in reduction of target contrast presented to the
camera. Extreme care must be taken that, in studies and results
applied, the contrast factors have been appropriately taken
into account. For example, Air Force studies on haze problems
assume a 9:1 contrast at the target; other aspects of perfor-
mance may be based on 2:1 target at the camera, etc.
7. Additions of Values of Individual Sensors for a
Multi-sensor System.
a. Case 1: Similar (e.g., two photo systems).
In this case we are considering the addition of
value of, say, an extremely high resolution, narrow
swath camera, and a moderate resolution, wide
swath camera.
b. Cast 2: Different sensors (e.g., a photo and an
infra-red camera)
(to be determined)
8. Lineal versus Area Weighted Mission Value. The
application of the value function analysis to satellite systems
of long life and repetitive overflight of the same area had to
consider film load limits and "non-duplicative" coverage. For
the presently contemplated missions, neither the SR-71 nor the
vS
OXCART vehicle are film limited, and the flight planner has a
high degree of control over the flight path and coverage ob-
tained. For these reasons, an adequate system value is
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obtained, for comparison purposes, if one considers the lineal
weighted value along a line perpendicular to the track of the
aircraft, or for a short distance, say twenty to fifty miles,
along the track. A further refinement, applicable to the
Vietnam mission, would establish such a value for straight and
level flight and another for banked flight; subsequently ob-
taining a weighted average based on an analysis of typical
missions and the fraction of coverage normally obtained in
banks.
cC:
ptipvisa- (2:3..-R
vR,S 1,JF'c',15
iocsi
STAT
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The; :;:c,bability Distribution of Camera Resolution
Milton D. Rosenau, Jr.
At each spatial frequency within a camera's resolution limit, the modulation of the camera exposure
image will vary because of variation in object modulation, the atmosphere, the optical transfer function,
and image motion. Thus, for each spatial frequency there is a probability that the image modulation
will exceed that value required to resolve the image. This probability can be evaluated, even when the
modulation detectability limit itself is variable. The resulting probability of resolution for each spatial
frequency is directly observable in actual photographic results.
Introduction
The quality of a camera . may be specified in terms
of costs, cosmetic appearance, or other nontechnical
aspects, but, to the technical worker, quality is usually
synonymous with the ability of the camera to resolve
t detail, and to a lesser extent, with the field of view,
focal length, etc. In the sense that quality is related
solely to the actual resolution of detail, a considerable
problem exists because the fact is frequently over-
looked that quality varies from time to time and place
to place in the same camera. The problem is of
pr.ttitical importance primarily in special, purpose,
servomechanically controlled cameras of high acuity
such as ground-based telescopes and tracking cameras,
and space-borne planetary reconnaissance cameras.
in general, what follows concerns cameras with resolu-
tion of a few arc seconds or better, although much of
what?will be said has broader application.
Many descriptions, discussions, and specifications
still use a single resolution value to characterize a
camera despite evidence of the incompleteness of such
characterization. In 1951, MacDonald' pointed out.
that there is a probability of detecting certain symbols,
and, in 1953, in a discussion of how performance can
he assessed, he presented data showing the frequency
distribution of resolution for an aerial camera under
certain conditions.' In 1954, Colwell' discussed the
probability of detection as related to photographic
interpretation. But the fact that resolution should
be expected to vary for reasons inherent in high-acuity
!,.? photography has largely been ignored:
The quite satisfactory and generally widespread
application of modulation transfer functions to describe.
The author is with the Perkin-Elmer Corporation, Norwalk,
Connecticut. ?
Received 9 August 1963.
the photographic process now permits a rather simple
and direct explanation of this quality variance. Fur-
ther, as will be shown, the specific probability distribu-
tion to be expected of a particular camera can be
calculated under certain conditions. Most impor-
tantly, this calculated distribution can be compared to
directly observable resolution performance.
The most satisfactory basis for predicting and
explaining the resolution limit of a camera is by the
use of modulation transfer functions (MTF) to arrive
at the exposure (or aerial) image modulation and to
compare these values with modulation detectivity (as
a function of spatial frequency) to ascertain the
limiting resolution.4-6 The only, restriction on this
description of resolution limit is practical, in that a
modulation detectivity curve must be constructed for
the form of the resolution target and for the film-
processing combination being employed.
Variations of Transfer Functions
Optical
The modulation transfer function of an optical
system is the autocorrelation function of the pupil
function, G(x,y), where:
G(x,y) =
(1)
(x,y) is the coordinate of a point in the exit pupil, and
:6,(x,y) is the optical path difference of the image-forming
wavefront from an unaberrated spherical wavefront at
(s,Y).
The lens designer generally assumes A(x,y) to be
invariant in time, although recognizing that it may vary
from one lens to another if several copies of the design
are fabricated. Such variations are caused by homo-
geneity fluctuations in glass and by the fact that
opticians cannot make lens surfaces perfectly or even
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identically on two supposedly identical lenses. The lens
designer also recognizes that the modulation transfer
function will be different at different field positions
and focal planes because .6,(x,y) varies for these, and
further, the modulation transfer function varies for
different wavelengths. Thus, the basic lens cannot be
described by a single modulation transfer function.
In practice, a further complication arises. The
lens designer computes the required surface shapes on
the assumption that a spherical wavefront emanates
from the object and passes through the atmosphere
(and, in some photography, a window) to impinge on
the lens with a smooth shape, altered from spherical
only, uniformly due, for instance, to postulated index
gradients. However, atmospheric turbulence will dis-
tort the spherical (or, at least-, smooth) .wavefront and
time-variant temperature nonuniformities in the glass
(and window) will also distort the wavefront, so that
(x,y) can be expected to vary from time to time for
the same lens in any one field and focal position at one
wavelength.
Subject to certain restrictions, Hufnagel7 has calcu-
lated the average modulation transfer function of an
unspherical optical wavefront with random wavefront
variations. Thus, if we do calculate this average
value and consider one field and focal position at one
wavelength, the MTF, (k), is a single curve as shown
in Fig. 1. For such a single-valued MTF, consider a
particular spatial frequency k'; the probability of T(V)
is unity, as shown in Fig. 2. (For simplicity, the MTF,
is treated as one-dimensional in this paper, but the
extension to two dimensions is straightforward.)
However, even at this one field and focal position at
one wavelength, the modulation transfer function is in
actuality time variant, since the atmosphere is time
variant.' As a consequence, the MTF has a probability
distribution, as shown in Fig. 3. The determination of
the exact shape of such a probability distribution is
difficult, but experiments maY permit a satisfactory
approximation.
The illustrated distribution is not Gaussian, since
there is nothing known to suggest it should be, and the -
particular shape shown is not presumed to be a better
estimate of what is correct. However, an upper limit
to the modulation transfer function is set by the diffrac-
tion limit.
Obviously, the distribution will vary with spatial
frequency and the other variables already discussed.
Therefore, the size and nature of the sample of. results
being studied will also affect the observed distribution.
Image Motion
The MTF of image motion is also not a single fixed
function. It varies with field angle, that is, from place
to place in he focal plane, and it varies from time to
SPATIAL FREQUENCY, k
kMA X
Fig. 1. Average modulation transfer function.
SPATIAL FREQUENCY. k
i.0
tf/
T14
0.5
0.
0.5 , 1.0
PROBABILITY OF Tlk)
Fig. 2. Probability distribution of invariant Yin'.
E 0.5
0 0o
SPATIAL FREOUENCY. k
PROBABILITY OF 1.0
Fig. 3. Probability distribution of variable MTF.
1.0-
Tm(1;)
0.1 '
2
3
P[Tm(q
T ,(k)
5
LIMITING SPATIAL FREQUENCY, k
Fig. 4. Graphical estimate of the probability distribution 01
image motion MTF.
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time at the same field position, but it is independent of
focal plane (for distant objects) and wavelength.
As an obvious example of the dependence of the
image motion MTF on field angle, consider the rotation
of a camera about its optical axis. The axial image is
iiiiblurred, while points off the axis are blurred propor-
tionally to the radius of the image from the axis in the
sagittal direction and are unblurred in the tangential
direction.
It is perhaps less obvious that the image motion
ITF may vary from time to time at a single field angle.
instance, a stabilized camera is usually allowed a
tolerable angular rate about each axis on the assumption
that these combine as the square root of the sum of the
squares. Thus, there are occasions of no angular
velocity, tolerable angular velocity, excessive angular
velocity, and, in fact, all rates up to that set by the
sum of the actually achieved perfection of the hard-
ware. Similarly, if sinusoidal vibration is present in
the camera, the phase of the sinusoid at the initiation
of exposure and the number of cycles occurring before
the end of exposure affect the MTF profoundly.9,1?
When several different kinds of image motion are
present, the MTF is. dependent on just how these
image motions interact.
Consider the problem as it confronts the camera
designer at the time mechanical tolerances must be
established. As a specific example, say four mecha-
nisms may produce image motion in one?direction. The
designer concludes that the magnitude of linear iniage
motion which produces an acceptable modulation re-
duction is a, and he then assigns the four mechanisms
0.7a, 0.5a, 0.4a, and 0.3a, or some other distribution,
such that the square root of the sum of the squares of
the individual mechanism effects is equal to the tolerable
total image motion. Now, even if these mechanisms
turned out to be always as bad as the entire tolerance
allowed and were random only in sign, then, for the
specific example, the hardware would perform, within
tolerance, about five-eighths of the time. An exact
prediction of the resultant image motion obviously re-
quires a detailed a priori knowledge of the way each
mechanism will perform within the assigned tolerance.
Thus, the camera designer will predict an image motion
which is determined by the square root of the sum of
the squares of the individual mechanism tolerances,
and, generally, the camera will have less image motion
than this value, but it may also occasionally have more.
The significant point is that the amount and type of
image motion in a camera are not always the values
predicted by the camera designer. As with the lens
ITF, the image motion MTF has a probability distri-
bution, the exact distribution depending on the sample
considered. ?
Probability of Resolution
Simplified Case
To simplify the notion of probability of resolution,
we temporarily restrict our attention to high-contrast
objects of a form for which the modulation detectability
curve is known, such as the USAF 1951 tri-bar pat-
tern4-6; and we further assume that there is no scatter-
ing in the atmosphere to alter the apparent modulation."
Then we choose some spatial frequency, k', at which
the probability distributions of optical and image
motion MTF's have been calculated. The probability
distribution of the optical MTF, P[To(k')], could be
determined as follows: first, from optical design data
or laboratory measurement, the MTF is determined at
several field and focal positions; second, these are
weighted by the expected frequency of occurrence;
third, an estimated or experimentally determined
adjustment is made for atmospheric turbulences; and
fourth, these are combined to provide the probability
distribution at each spatial frequency for which the
optical transfer function has a particular value.
In the case of the probability distribution of the
image motion MTF, P[T?,(k')], this can be estimated
in the camera design stage by estimating the probability
of a certain magnitude of linear image motion. This
estimate would result from a study of the tolerances of
the camera's mechanisms and the interactions of these
mechanisms. The easiest way to convert this to
P[T?,(k')] is graphically: first, the probability distribu-
tion of limiting spatial frequency is determined by
taking the reciprocal of the image motion magnitude
and weighting it appropriately; second, image motion
MTF's are drawn for several cumulative percentages of
occurrence, as in Fig. 4: and third, P [T,n(k')] can be
derived for each spatial frequency k'.
These two distributions, P [To(k')] and P [T?,(k')],
respectively, are suitably combined* to arrive at the
probability distribution of the system MTF (without
film), P [718(e)]. In this simplified case, this is numeri-
cally equal to the probability distribution of modulation
in the exposure image P PIERO]. Since the film
MTF can be placed in the modulation detectability
function, this latter distribution determines the
probability that the image at frequency k' will have
sufficient modulation to be detected, as shown in Fig.
5. In this simplified case, the modulation detectability,
111",(1c'), is assumed invariant. The probability distri-
butions are presumed to be suitably normalized.
Similar determinations are made at other spatial
frequencies, and the result, the probability of resolving
* A method similar to that discussed in the Appendix, in which
equal probability "bands" are suitably multiplied, is probably
adequate. For a rigorous mathematical method see, for in-
stance, J. S. Bendat, Principles and Applications, of Random
Noise Theory (Wiley, New York, 1958), pp. 105-124.
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each frequency, can be related to the frequency, as
shown in Fig. 6.
General Case
in the general case, the modulation reduction due to
scattering, 49, has a probability distribution," P[}.
Since g5 is independent-of spatial frequency, so is P [05].
Again, the exact nature of this distribution depends on
the sample of photography considered, since depends
on the length and orientation of the air column through
which the photograph is taken, the condition of the
atmosphere, and brightness. Except for very short air
columns, is considerably less than 1.0, and (I) = 0.8
seems to be a maximum value for practical conditions
when photographing through the complete atmosphere
under the clearest observed conditions.
Since < 1 simply lowers the modulation in the
exposure (or aerial) image, P[] can be combined with
P [IVO] to obtain a probability distribution of the
exposure image modulation, P [M E(k')] which is a
function of spatial frequency, k' , because P[Ts(k')] is a
function of spatial frequency.
Similarly, object modulation, M0, may be less than
1.0, and this too will have a probability distribution.
In some cases, this distribution will be dependent on
the spatial frequency of the object,12 and for complete
generality, we characterize, this object modulation
probability distribution as P[Mo(V)].
Now, it is clear that the general statement of the
probability distribution for exposure, (or aerial) image
modulation is
P[111E(k')] = {PIM 0(k')]){.13[0]}{.13[7' o(k')]) {P[T.m(e)]) (2)
where the right-hand side of the equation is understood
to be an appropriate combination in which modulations
and transfer functions are multiplied. This complete
probability distribution must be evaluated at each
frequency k' of interest to determine the probability
of the exposure modulation exceeding that required
for resolution, as given by the modulation detectability
curve. The final result is graphed as in Fig. 6. Alter-
natively, P [111 o(k')] can be omitted from P[M E(k')]
and separate curves, like those in Fig. 6, can be drawn
for several values of M 0.
The evaluation of the probability that the exposure
image modulation exceeds that required by the modula-
tion detectability limit is more complicated when the
modulation detectability limit is also variable as
when granularity fluctuations are integrated over only
small target images or when processing variations are
significant. In such a case, the probability distribu-
tion of the modulation detectability, P[111 a(k')], will
be a function of spatial frequency.
Extending the method illustrated in Fig. 5, the
probability of resolving an image at frequency k' is:
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fo
PLilf0(e)l 3 Lip PfilfE(k')] dME1 dMo. (3)
THE MODULATION
REQUIRED ED FOR RESOLUTION
1.0
05
PROBABILITY OF
NOT RESOLVING k
0 1.0
SPATIAL FREQUENCY, k P[mE(1:1] THE PROBABILITY DISTRIBUTION
OF ATTAINING A GIVEN MODULATION IN THE
EXPOSURE IMAGE AT FREQUENCY I
Fig. 5. Probability of resolving frequency k'.
SPATIAL FREQUENCY, k
Fig. 6. Probability distribution of resolution.
\
I"\
IMAGE MOTION \
ASSUMED LINEAR \
IMAGE MOTION A\
ASSUMED RANDOM ?,\
? ACTUAL RESULTS
----PREDICTIONS
100
RESOLUTION (LINES /MM)
Fig. 7. Actual and predicted results.
MODULATION
Fig. 8. Graphical evaluation of Eq. (3).
As a practical matter, this can be approximately evalu-
ated graphically or in the form
i=n
E pi[mp(k,)] IfmD PIM E(k')] (]ME, (4)
=
where n is a small number (e.g., 3, 4, or 5) and M
is the average value of modulation detectability in a
region of the distribution. (See Appendix.)
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32 APPLIED OPTICS / Vol. 3, No. 1 / January 1964
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Other Variables
In the discussion so far, it has been presumed that the
ny other variables affecting photographic quality are
under good control. This is not unreasonable for a wide
variety of practical situations. However, it, must be
recognized that many variables (e.g., exposure, specular
reflections, atmospheric absorption, spectral sensitivity,
degree of polarization, processing, etc.) affect the quality
of the final image. If any of these other variables have
influence which is substantial compared with those
previously considered, then suitable probability distri-
butions for these must ?also be included in the analysis.
Experimental Example
irown" provided data from laboratory tests of a
camera which showed the kind of probability distribu-
tion illustrated in Fig. 6. This is shown in Fig. 7.
Also shown in Fig. 7 are two a posteriori predictions of
the actual results. The actual result is in reasonable
:agreement with both predictions; whether the dif-
ference in prediction and actual result is significant
would depend on the application.
The actual result was obtained with a USAF 1951
high-contrast tri-bar target projected into the camera'
idea test from a laboratory collimator; 140 images
were obtained from a total of twelve different test con-
i tio ns. Only axial images were obtained. Kodak
SO-130 film developed in D-19 for 8 min was used.
The 140 images provided 280 radial and tangential
resolution readings, which were made through a binocu-
lar microscope. Table I contains the raw data.
The two predictions were made from theoretical lens
;Ind film data, and the image motion was estimated
from other laboratory tests of the camera performed.
with Kodak SO-102 film. These other laboratory tests
NV(`11! performed under the same twelve conditions, but
the number of images obtained in each condition dif-
fered, and only 113 images were obtained, so these
results were weighted by the ratio of images with SO-130
to images with- SO-102. Table II contains the raw
data from SO-102.
To obtain an "effective" modulation detectability
curve, the MTF of the film and lens were added into
the modulation detectability function, iliD(k), as given
for SO-102.4 An ogive of linear image motion limiting
frequency and also of random image motion limiting
frequency was derived so as to satisfy the weighted
results obtained on SO-102 film. The intersection of
linear and random image motion MTF's with an "ef-
fective" modulation detectability function for SO-130
produced the two predicted results shown in Fig. 7,
where the percentages are those from the ogives ob-
tained from SO-102. (The constant, 0.04, used in the
modulation detectability function with SO-102 film was
replaced by 0.03 for SO-103 film.") Since the prob-
ability distribution of modulation detectability was
.felt to be very small compared to the image motion
variability, a single value of detectability was used at
each frequency.
No plausible explanation has so far been found to
improve the agreement of prediction and results shown
in Fig. 7. Differences in image motion between the
test with SO-102 and SO-130 are most likely, but incor-
rect assumptions regarding the optical transfer func-
tion, the modulation detectability for the films, and the
variability of exposure and processing are also quite
possible.
Conclusions
A logical approach and physical basis to account for
and predict the probability distribution of camera reso-
lution has been proposed. The distribution curve ob-
tainable from a priori prediction (Fig. 6) is an observ-
able function, and, therefore, an experimental verifica-
tion is possible. Specifically, the percentage of images
resolving a higher frequency than each spatial frequency
k' can be determined by inspecting actual photographic
results. If the sample of actual photography was ob-
tained under the conditions on which the analytic pre-
Table I.
Number of Images Having Given Resolution.
SO-130 Test Data
Test
Resolution (L/ MM)
alanatit on
128
114
102
91
81
72
64
57
51
46
41
37
33
29
4
7
4
1
2
2
12
11
5
3
1
1
3
3
1
2
1
3
2
2
4
3
1
2
1
6
13
16
6
1
1
2
1
1
2
7
2
1
1
15
3
3
8
3
13
6
4
1
1
1
1
1
1
9
1
2
1
3
2
3
2
2
1
1
to
7
4
5
11
3
12
7
5
8
1
12
2
4
3
3
3
2
1
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Table II.
umber of Images Having Given Resolution.
SO-102 Test Data
Test
Resolution (L/MM)
91
81
72
64
57
51
40
41
37
33
29
condition
3
4
3
2,
2
3
10
9
13
3
1
1
0
4
1
3
4
2
4
5
1
12
6
7
5
0
1
6
2
1
3
1
2
7
1
4
4
2
1
11
11
'0
2
3
9
1
1
3
1
2
10
4
4
2
1
11
1
5
5
7
9
7
1
12
2
1
2
3
1
dictions were made, the percentage of images resolv-
ing more than each frequency k' should be identical
with a prediction curve like Fig. 6. An experimental
example shows a reasonable agreement of prediction
and result.
Finally, it should be evident that discussions of a
resolution limit of a camera must be qualified by the
frequency of attainment which is intended.
The data used in the example resulted from work
being carried out by E. B. Brown and were called to
our attention by him. It is also a pleasure to acknowl-
edge helpful discussion with R. C. Babish, R. E. Huf-
nagel, H. D. Polster, F. Scott, R. M. Scott, and R. V.
Shack.
Appendix
Graphical Evaluation of Eq. (3)
Equation (3) evaluates the probability that the
exposure image modulation exceeds the modulation
detectability limit, where both modulations are variable
and described by probability distributions. In Fig. 8
a hypothetical case is illustrated for a single spatial
frequency. The probability distribution for the expo-
sure image modulation is divided into five bands, each
?
representing 20% total probability. The midpoint
modulation of each band is located and the cumulative
percentage of the modulation detectability which fall;
below this value is noted. This is repeated for each
of the five 20% bands. In the illustrated case, where
Gaussian probability distributions are used; ' the
probability of resolution would be estimated as:
0.2 X 0.94 + 0.2 X 0.98 0.2 X 0.996 + 2 X 0.2 X 1.0 = 0.98.
References
1. D. E. MacDonald, "Optical Image Evaluation", NBS
Circular 526, 5Iff (1951).
2. D. E. MacDonald, J. Opt. Soc. Am. 43, 290 (1953).
3. R. N. Colwell, Photogram. Eng. 20, 433 (1954).
4. The Practical Application of Modulation Transfer Functions,
(Perkin-Elmer Corporation, Norwalk, Connecticut, 1963),
chap. 4.
5. G. C. Brock, W. L. Attaya, and E. P. Myskowski, "Study of
Image-Evaluation Techniques", Itek Report 9048-1
(1962), Astia Doc. No. AD286488.
6. C. E. Campbell, Photogram. Eng. 28, 446 (1962).
. 7. Reference 4, chap. 3.
8. E. Djurle and A. Back, J. Opt. Soc. Am. 51, 1029 (1961).
9. "A Scientific Investigation into Photographic Reconnais-
sance from Space Vehicles", Cornell Aero. Lab. Report No.
VF-1260-P-2 (1959), Astia Doc. No. 289667.
10. R. V. Shack, "The Influence of Image Motion and Shutter
Operation on the Photographic Transfer Function" (to be
published).
11. M. D. Rosenau, Phot. Sci. Eng. 6, 265 (1962).
12. Reference 4, chap. 1.
13. E. B. Brown, private communication (April 1963).
14. R. E. Hufnagel, private communication (June 1963).
George C. Higgins Eastman Kodak, (left) Editor for this issue's
feature on Optics of the Photographic System, and W. Lewis
Hyde Institute of Optics.
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