A VALUE FUNCTION BASIS FOR THE COMPARATIVE ANALYSIS OF HIGH-ALTITUDE PHOTOGRAPHIC RECONNAISSANCE SYSTEMS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP78B05167A001800170003-5
• Release Decision: RIFPUB
• Original Classification: S
• Document Page Count: 13
• Document Creation Date: December 27, 2016
• Document Release Date: June 4, 2014
• Sequence Number: 3
• Publication Date: November 7, 1967
• Content Type: MEMO

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IP
OSP-0892-67
7 November 1967
TECHNICAL MEMORANDUM NO. 17
SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
PREPARED BY: Leslie C. Dirks, Chief, Design and Analysis Division ?
I. Introduction
A problem of frequent occurrence is the comparative evaluation
of silver halide camera systems from the point of view of strategic
intelligence image utility. The primary difficulty which is inevitably
encountered in an attempt to undertake such an analysis is in relating
a measure of camera system performance which is meaningful in terms
of camera design parameters to a quantitative measure of the utility of
the resulting imagery as it is used for the broad range or strategic ?
intelligence applications. This paper outlines a technique for dealing
with this particular problem which has evolved over a long period of
time and has been successfully applied in a major camera system source-
selection. It should be emphasized that this technique has been developed
in the context of silver halide film imaging systems operated at high
altitudes against strategic reconnaissance objectives.
In addition to a description of this technique for comparative
analysis, this paper also includes summary discussions of the rationale
leading to the selection of the technique, along with comments on the
application of the technique to specific problems. It should be noted at
the outset that the problem of relating image utility to camera perfor-
mance in the real, operational world is an extremely difficult task. The
specific technique discussed below resulted from the review of large
quantities of data together with actual operational experience. The tech-
nique was subject to extensive review within the Government in the context
of a camera source selection proceedings and received a general con-
currence from several Government departments and agencies.
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I.
SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
II. Definition of the Area Value Function
The Area Value Function (VA) provides a means for estimating
the total worth of photographic coverage by a given camera system
under specified operational conditions over a specified ground area.
The Area Value Function is analytically defined as follows . ? .
VA = .A U(R) dA
?
. . . where the integration is to be carried out over the defined ground
area. The function U(R) is the Utility Function. The Utility Function
serves to associate a quantitative measure of worth with each incre- ?
mental element of ground area. The Utility Function depends only upon
the "minimum ground resolvable length" realized by the camera system
for each incremental ground area. The definition of "minimum ground
resolvable length" will be-treated in a subsequent section of this paper.
Of critical importance in applying the Area Value Function is
the selection of an appropriate utility function. In general, it is not
sufficient to construct the utility function based only on the level of
ground detail that can be extracted from a given image. It is essential
in constructing the utility function to take account of the relevance of
perceivable detail in the context of the intelligence problems to which
the photography is to be applied. In particular, assuming that the utility
function is proportional to the total number of resolvable elements in an
image is a very poor approximation in the case of strategic intelligence
problems. This assumption would lead to a utility function increasing
inversely as the square of the minimum resolvable ground length, and as
will be seen below, is a very much stronger function than is actually the
case.
There are three distinct steps involved in generating a meaningful
utility function. First, the specific photointerpretive tasks to be per-
formed with the imagery must be listed. Second, the ability of the
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
photointerpreter to perform these tasks must be related in a
quantitative fashion to image quality as described by minimum ground
resolvable length. It is, of course, critical that the definition of
minimum ground resolvable length used in characterizing image quality
be relateable to camera system performance. Third, the relative
importance of the various tasks must then be established so that the
collection of PI performance curves can be weighted and combined to
give a single overall relationship between image utility and minimum
ground resolvable length. ?Considerable community-wide effort has
been expended on these three tasks. Numerous controlled psycho-
physical experiments have been performed with the objective of measur-
ing photointerpreter performance as a function of image quality for.
various tasks. Based on these experiments and the photointerpreter
experience integrated over a long period of time, NPIC has cataloged
the level of ground resolved detail (essential elements of information)
required to perform the manifold of tasks assigned to the Center. In
addition to the various concerned USIB committees, I have attempted to
evaluate the .relative importance of the various photointerpreter tasks
in the context of the national strategic intelligence posture. The dis-
cussion which follows draws heavily on these activities.
In general, the functional relationship between photointerpreter
performance on a specific task and minimum ground resolvable length
is of the form depicted in Figure I. There will always be a region of
minimum ground resolvable length poor image quality (characterized by
large Minimum ground resolvable length) within which the PI's ability
to perform a particular task is unacceptably low or unreliable. In general,
there will also be a region where the image quality is sufficiently good
so that a particular task can almost always be performed with high
dependability. In both of these regions the rate of change in PI per-
formance with minimum ground resolvable length tends to be low. Between
these two regions of image quality lies a transition region. This region
is characterized by a more rapid rate of change of PI performance with
minimum ground resolvable length. It should be emphasized that almost
never does this curve of minimum ground resolvable length approximate
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
a step function. There are many reasons for this, but probably the
most important ones are variability in individual photointerpreter per-
formance and the fact that any simple engineering definition of minimum
ground resolvable length cannot be a complete measure of image quality
in the subjective sense of the term. If, for example, the task in question
is the identification of wheeled vehicles, the ability of a PI to perform
this task will be influenced by the ground scene in which the vehicles are
imbedded, the direction in which the vehicle shadow falls, the particular
mix of vehicles that must be sorted out, and numerous other parameters
which are entirely independent of camera system performance, atmospheric
viewing conditions, and scene illumination. Nevertheless, although the
slope of the transition region and where it falls on the absolute minimum
ground resolvable length scale may vary over broad ranges for the total
spectrum of strategic intelligence photointerpretive tasks, the general
shape of the PI performance vs. minimum ground resolvable length
curve is almost always found to be as depicted in Figure I.
As the image quality increases (the minimuin ground resolvable
length decreases), the number of photointerpretive tasks that can be
performed with the imagery increases. However, in examining the
relative importance of the various tasks, itis found that in general the
criticality of each individual task tends to decrease as the image quality
increases. The utility function is computed at a given image quality
by tabulating all the tasks that can be performed at this image quality
level as defined by NPIC, weighted by the relative importance of each
of these tasks. This computation can be performed for various image
qualities as measured by minimum ground resolvable length to generate
the curve of utility vs. ground resolvable length given in Figure II. It
should be emphasized again that this curve results from the summation
over a broad range of strategic intelligence problems.
The utility function computed as described above can be approximated
by two analytical functions. For resolvable length less than 10 feet, the
dependence of utility on resolvable length is nearly linear of the form
U(R) = 113.3
R < 10 ft.,
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
For resolvable length greater than 10 feet, a hyperbolic relationship
of the following form should be used . . .
U(R) - 2.5
R> 10 ft.
The data curve in, Figure II is a piece-wise approximation to the linear
portion of the utility function which has proven to be an adequate repre-
sentation of the utility function for some application.
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
III. Definition of the Target Value Function
Based on the same line of reasoning discussed above, it is
possible to define a quantity known as the Target Value Function as
follows:
V = U(R)
I = 1, N
A target is understood in this sense to designate a specific facility
which is sufficiently small in geographic extent so that image quality
can be considered as constant over the entire target. The Target
Value Function is then simply the summation of the utility function over
a defined set of discrete targets. The target value function idea is
particularly useful in comparing photographic systems where the primary
mission objective is not area coverage but rather the coverage of discrete,
small individual targets whose geographic position is known and can be
utilized in the execution of the photographic mission.' The discussion of
the utility function as applied to the area value function applies equally
well to the utility function fiQr the target value function.
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6LIAL I
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
IV. Definition of Minimum Ground Resolvable Length
The key to relating photointerpreter performance and camera
system performance is in the selection of an appropriate quantitative
performance parameter. The selected performance parameter must
be one that is meaningful in camera system engineering terms and also
meaningful in context of subjective photographic image quality. The
measure which best satisfies both of these conditions is Air Force tri-
bar target resolving power as defined in Mil. Spec. 150A. Therefore,
the definition of "minimum resolvable length" will be taken as the
length of one cycle (the width of a white bar plus the width of a black
bar) on the highest frequency Air Force tri-bar target for which the'
bars can be clearly distinguished.
The next question which must be addressed is how to relate
camera system resolution to minimum ground resolvable length (ground
resolution). Traditionally, this relationship has been established by
constructing an artificial model of the target scene consisting of
uniformly distributed tri-bar targets randomly oriented with respect to
the ground track of the camera. If such a ground scene were photographed
by a given camera system, the tri-bar target resolving power of the
system would depend upon the obliquity angle from which a given target
scene were viewed, and the orientation of the target bars with respect to.
the camera system. In general, when viewed at an oblique angle, the
bars in the target will tend to appear from the camera aspect to be more
closely spaced than they actually are. For the worst case of tri-bar
target orientation, a geometric argument leads to the conclusion that
camera system resolution and ground resolution are related by the secant,
squared of the viewing obliquity angle. However, if the bars are oriented
perpendicular to this worst case direction, similar arguments lead to a
secant to the first power dependence. It has been customary to take the
geometric mean of these two extreme cases which leads to the following
relationship between camera system resolving power and ground resolving
power in the tri-bar target sense.
3/2
R = ? R (Sec 0 )
g F
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
In this experssion, H is the altitude of the camera system above the
target scene, F is the focal length of the camera system, and ( 0 )
is the obliquity angle at which a given element of the target scene is
viewed (this angle is defined as the angle between the vertical at the
target element and the line of sight from the target to the camera).
The above relationship between camera resolving power and
minimum ground resolvable length is based on an idealized model of
the target scene. For a target scene with three-dimensional develop-
ment, such as is always the case with cultural scenes, the image
quality never falls off as rapidly as secant squared and most often is
closer to secant to the first power. However, the impact on image
quality of atmospheric haze is generally higher at high obliquity angles
than at lower obliquity angles which tends to argue in favor of a stronger
dependency than secant to the first power. In the final analysis, it
has been concluded that the secant to the three-halves power law represents
an acceptable approximation to the physical world in the case of this
application.
When the value function approach is to be employed in the com-
parative evaluation of camera systems, it is necessary to define the
manner in which camera resolving power (RC) is to be computed. It is
important that the camera resolving power be a sufficiently detailed
measure of camera performance to reveal the differences between?different
camera system designs. The definition of camera system resolving power
to be used in computing either the area value function or the target value
function takes into account the following factors:
a. Optical system performance
b. Image motion compensation
c. Camera focus
d. Target scene illumination and contrast as a function of
solar elevation angle
e. Film sensitivity and resolution characteristics.
As the first step in computing camera system resolving power, the
modulation transfer function (MTF) for the optical system design as
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11, ?
? _ _
SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
degraded by manufacturing and alignment tolerances is computed.
This MTF is then combined with the MTF's for the predicted image
smear and the focus error. It is important to treat all of the above
degrading factors in a statistically correct manner in that some of
the degrading errors vary rapidly in time (throughout a given mission)
and others will vary only from one production item to another, while
still other errors are inherent in a given camera system design. It is
usually best to take a worst set of conditions for comparative evaluation
purposes. The image smear will be a function of the scene brightness
(which must be specified) and the film sensitivity (which also must be
specified). All of the above system MTF's will be a function of the
location in the total image format of a particular point being evaluated.
The system MTF resulting from the above computations must then be
lowered to be representative of the scene contrast of the real world as
viewed from high-altitude platforms. The above scene contrast will
depend not only on meteorlogical conditions but also on the sun eleva-
tion angle. Based on a large sample of scene characteristics, an
average scene model has been compiled, as presented in Table I.
This table gives both scene contrast and scene illumination as a
function of solar elevation angle.
The next step in the process is to intersect the total system MTF
as degraded to the appropriate scene contrast with the curve giving the.
Aerial Image Modulation required for a human observer to resolve a
given Air Force tri-bar target. The intersection between the AIM
curve and the system MTF will yield the limiting resolving power for
the camera system. The AIM curve must be empirically determined
for a given film type and film processing conditions.
The computation outlined above can be repeated for all points in
the photograph format and converted to minimum ground resolvable length
using the expression defined above. On this basis, an area value function
can be evaluated over any defined ground area. Similarly, a target value
function can be evaluated for any defined target description. Both of
these quantities will, of course, depend upon selection of a particular sun
angle or variation in sun angle over the defined target or area model.
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SUBJECT: A Value Function Basis for the Comparative Analysis
of High-Altitude Photographic Reconnaissance Systems
The above scheme for defining camera system resolving power has
proven to be adequate when utilized in comparative evaluations of
camera systems which have generally similar optical system MTF,1s.
However, it should be noted that serious anomalies can occur in
cases where the similarity constraint is not adequately satisfied.
These anomalies are not usually of concern, however, in comparing
practical, high-performance photograph reconnaissance camera
systems.
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Sun Angle
TABLE I
SCENE BRIGHTNESS AND TARGET CONTRAST
Min Scene Brightness Target Contrast
in Foot Lanberts ? at Entraftce Pupil
0 ZOO 1.1
50
240 1.3
100 300 1.5
200 450 1.8
30?f 600 / 2.0
400 650 2.1
50o
700 2.2
600 720 2.1
700 750 2.0
80? 750 1.9
900 750 1.8
z
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