REMOVAL OF IMAGE MOTION ABERRATIONS

• Document Type: CREST
• Collection: NGA Records (Formerly NIMA)
• Document Number (FOIA) /ESDN (CREST): CIA-RDP79B00873A000100010063-4
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 17
• Document Creation Date: December 28, 2016
• Document Release Date: November 1, 2012
• Sequence Number: 63
• Publication Date: May 1, 1968
• Content Type: MISC

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REMOVAL OF IMAGE MOTION AB-ERRATIONS
a_toy
r-e_ 9 t' rt' I-cat
by
25X1
May 1968
PRELIMINARY DRAFT OF PAPER TO BE SUBMITTED TO APPLIED OPTICS.
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ABSTRACT
?. .The resolution of aberrated photographic images distorted by arbitrary
image motion have been substantially improved using holographic spatial
filtering techniques. Examples of imagery corrected for the effects of one
and two dimensional motion are presented. Also a novel technique is des-
cribed for constructing, on film, Fourier transform holograms of functions
with large amplitudes without exceeding the conventionally defined linear
dynamic range. Noise and distortion due to the photographic media and
filter alignment are minimized since the final filter, usually composed of two
or more discrete elements, is recorded on a single piece of film.
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REMbVAL. OF IMAGE MOTION ABERRATIONS
. Within the framework of linear systems analysis, O'Neill has shown
that a uniformly smeared image can be written as a superposition integral
over the object transparency. 1 Within this context a transfer function for
the aberration can be defined as the Fourier transform of the integrated
smear function that multiplies the transfer function of the non-aberrated
optical system. When the non-aberrated impulse response can be considered
rotationally symmetric and effectively a delta function, the transfer function
for the imaging process is the optical Fourier transform of the aberrated
impulse response. Since in this application this is the record of movement
of the/non-aberrated function, the incoherent transfer function can be ob-
taine,i by optical Fourier transformation, if the aberrated impulse response
can be recorded in a recoverable way on a film transparency. In the experi-
ment described, conditions were arranged to record and recover an impulse
response characteristic of an arbitrary image motion. Using a novel Fourier
trailIsforrn hologram filtering technique, it was possible to make significant
improvements in the deliberately aberrated imagery.
? In general a linear incoherent imaging process can be described by the
convolution equation.
3 Iob(x) S(x - x', y y') dx' dy'
-00
(1)
where Iim (ob)(xi'Y') refer to the intensity distribution in the object and
S(x - x', y - y') is the aberrated impulse response. In terms of the object
and image spatial frequency spectra, the Fourier transform of the convolution
equation is
T. (.0 , co ) = T (co , T (CO ,
1111 y.
(2)
where the tilda (-) refers to the Fourier transforM operation and T (CO , CO ) the
o x y
Fourier transform of the impulse response or the incoherent transfer function
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and w, co are the appropriate spatial frequency coordinates in the x,y plane
xy
(e.g., co =? in a coherent optical transformation system using lenses of
x
focal.lenth f).
When there is relative motion between the object and the image during
the exposure (assumed long compared to shutter opening and closing times)
the photographic record is a smeared image described by
Co
1. y) = A(t) Iob(x' - f(t), y' - g(t)) S(x - x', y - y') dx' dy' dt
00
wher, A(t) is an exposure function and f(t) and g(t) are linear functions des-
cribing the motion. When Fourier transformed Equation (3) becomes
-27ri(coxf(t) + cog(t) I.
wy) = Tob(wx' wy To (COx, CO? A(t) e dt
im x?-co
= lob (C.Ox COy) TM (COX,y ,
where Tm(cox. coy) (hereafter called (T(cox, coy) is the linear stationary effective
transfer function in the developed transparency that completely describes the
effects of the integrated image motion.
In a uniformly illuminated coherent optical system the coherent transfer
function is effectively constant over the paraxial region. When a film trans-
parency: of a motion aberrated image is processed so that its specular ampli-
tude transmittance is proportional to the original object intensity distribution,
the optical Fourier transform of the coherently trans-illuminated transparency
will be given by Equation (4). Since in this discussion T(co , co ) characterizes
x y
the effect of image motion on an idealized perfect image, the undistorted image
can be recovered if the aberrated image spectra, Equation (4) is multiplied by
(T(co w)1. In this paper, a technique will be described for realizing a
Y
complex amplitude transmittance function that when multiplied by the aberrated
(3)'
(4)
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image spectra will yield a substantially improved image. Several examples
of restored images are presented to demonstrate the efficiency of the filtering
operations.
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REALIZATION OF T(cox, wy)1
Numerous techniques have been mentioned to realize good approximations
to complex optical filter functions since Tsujiuchi published his excellent
results on image restoration using complex transmission masks in 1963.2 Only
minor improvements have been reported in the usually complicated procedures
to construct phase filters by evaporation, thin films, polarization or other
elaborate techniques. After coherent illumination sources became readily
available, the capability of holograms to record continuous phase and amplitude
distributions photographically was seen as a relatively simple method to realize
a method of complex optical transmission filters. In 1964, Vander Lugt proposed
what is now nearly the standard modified Mach-Zehnder interferometer approach
to construct Fourier transform hologram filters for matched and detection
filtering.3 Cutrona extended the basic techniques to coding and image restoration
in 1965 when the removal of simulated one-directional linear image motion was
accomplished by inverse Fourier transform hologram filtering.4 At the time,
the principal limitation to an optimum realization of an image restoration filter
was film linearity. In more recent papers by Lohmann and Werlich and Stroke,
Indebetouw and Puech, 6 imagery aberrated by defocusing and circular image.
motion respectively, was partially restored by the same basic techniques with
approximate film linearity. In this paper a significant refinement in restored
image quality is demonstrated when the hologram filter is constructed through
an appupriate amplitude function and when both hologram and the amplitude
transmission masks are processed linearly in the conventional sense, which
? is made possible for some classes of large signals, by the exposure procedure.
. (The transmission through the amplitude filter is similar to the technique pro-
posed independently by Lohmann and 1,Verlich for code translation.)
-?
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The conventional technique to construct a filter proportional to the
aberrated transfer function, r(co , y)-1 is to approximate an amplitude
x
filter proportional to 1 2 and combine it with a Fourier transform
,
x y
. 2 -.)'/2
hologram of the same function F(co , co ) = (1k + T( ) e . For
x y
y = -2 (or for low contrast development) the aberrated object spectra
multiplied by the two element filter will be
1
I (CO ) T ?
0 x y wy) 1 T(co , co )12
x y
?
? [k2 + I T(c0 CO )12 , K + T (CO , ) e
x y, , ,
x y
+k T (0)x' 0)y) eix1
Ideally, the positive exponential term in the combined product will be
T (co , co )
y ?cox, coy)1 2
T (C0x COy)
iacoxx tacox
T (CO, w) ) e = , w ) e
X
x y o x y
which when Fourier transformed will be the unaberrated object distribution
separated from the zero order terms by an amount determined by a.
Unfortunately, the image quality resulting with the two element filter has
not been very encouraging. Extremely small misalignments between either
element and/or the object spectra will produce no correction, and the
inherent aberrations present when liquid gating any filter seem aggravated
with two films or plates, possibly because of the increased depth or combined
grain noise. More serious is the fact that in most cases only a small fraction
1
of can be recorded linearly. For example, if we consider a linear
1 T(co co , )12
x y
smear whose transfer function is proportional to sinc co x, the signal swing
between the central and first order maxima is about 4.5:1. To construct a
1
function on film with amplitude transmission TA(c) 2 , the intensity
sine co x
(5)
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??
1 4
transmission will be TI ? (al or D = log TI(a) log sinc wx, (Figure la).
sinc4coxx x
? 2
To record just the first two maxima of the sincxx function, 22 db film exposure
response is required. In the experiment described here, the function to be
recorded will be 1which for expressions no more extreme than sine or
I T(C0x, Cey) I
besinc function can be recorded linearly in the conventional sense except in the
ficinity of the zeros of the transfer function, (Figure lb). (Since there is no
scene information at these frequencies, and the optical filter is passive, this is
to be expected and is no practical consequence.)
The experimental procedure is to optically Fourier transform the impulse
response characteristic of the aberration and record it through the film backing
on appropriately prefogged film at y = +1, so that the processed amplitude
tran m 1ission is . After processing, this transparency is replaced
I T2(cox' coy)!
intd a congruous position and the hologram filter is constructed by exposure
through the transparency of the Fourier transform of the impulse response and
a reference wave producing a filter function with amplitude transmission
T2(cox, coy)!
? ?
la ?-- y/2
(k + T1(COx' w)
If processed to y = -2 (by direct reversal process), the appropriate filter
function term becomes
* *
kco k' T (CO CO)
T1 ( 70 wy) iax x' y
, e eiax
I T (CO , CO )1,
-
2 x' y x y
(6)
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since T1 and T2 differ only by a constant which can be adjusted to optimize the
filter characteristics. ?
If we examine the construction of the filter for linear unidirectional function
on the basis of the amplitude transmission of the elements as in Figure 2, it
can be shown that the desired function (Figure 2d) can be recorded linearly in
the conventional sense as in Figure 3. The net effect of this technique is to
reduce the size of the signal as seen by the film so that a closer approximation
to the calculated filter function can be realized with conventional techniques.
DESCRIPTION OF THE EXPERIMENT
To generate a transmission function whose optical Fourier transform is
the appropriate incoherent transfer function, a small pinhole, whose dimension
establishes the upper limit on recoverable resolution, was placed in the format
of an object scene transparency. While being moved in an arbitrary fashion in
the object plane, the integrated motion of the modified transparency is recorded
on film. The photographic record of the path of the point object is the appropriate
impulse response for the motion aberration if the resulting transparency is
processed linear in amplitude or to a gamma of -2. If this impulse response is
isolated and optically Fourier transformed, the complex amplitude distribution
existing in the transform plane is the transfer function characteristic of the
aberration. Admittedly this simulation by-passes the difficulty of extracting an
.impulse response from an arbitrary scene but it is useful to optimize this filtering
operation in preliminary stages of the experiment.
In the first experiment the simulation experiment described by Cutrona was
duplicated. The impulse response characteristic of a unidirectional linear
smear was simulated by a slit 1 mm long and 0.080 mm wide. An inverse
- Fourier transform filter was constructed as described above using the optical
Fourier transform of the small rect function as T(co , y). Figure 4a is a slightly
x
tapered slit about 2 mm wide which in Figure 4b has been shrunk to a mean width
? o 0.016 mm or about twice the impulse response width. Figure 4d is a micro-
densitometer trace of the filtered output indicating a signal to noise ratio of 7.5:1.
An additional reason for performing this experiment is that the physical parameters
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of the aberration could be very closely controlled permitting independent
optimization of the filter function exposure and processing.
In the more general application to non-symmetric, two-dimensional smears
the general procedure is the same but exposure control and filter adjustment
becomes very critical. In Figure 6 and 7 a - d, the experimental procedure is
illustrated for two different aberrations of a printed page containing a small
point to generate the aberrated impulse response (Figure 5). Figures 6 and 7b
have been smeared to generate the aberrated imagery with the impulse
responses seen magnified in c. After filtering,most of the aberrations have
been removed as exemplified in d and e. One characteristic of the data presented
here that should be noted is that the entire format could not be restored by a
single adjustment of the filter. Optimum filtering in different regions of the
format could be obtained by only a small readjustment of the filter. This
tend icy, due primarily to astigmatism and spherical aberration, can be mini-
miz d if all elements, especially the liquid gates in both the construction and
filtering operations, are as nearly identical as possible.
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REFERENCES
1. E. L. O'Neill, "Introduction to Statistical Optics," (Addison-Wesley,
? Reading, Mass., 1963) p. 27.
. J. Tsujiuchi, Progress in Optics, Wol. II (North Holland Publishing
Company, Amsterdam, 1963) pp. 133-180.
3. A. Vander Lugt, IEEE Trans. IT-10, 139 (1968).
4. D. Ansley, L. Cutrona, C. Thomas, Coherent Light Investigations;
Final Report AF 33(615)-2738 (AD-476825) (Conductron Corporation,
Ann Arbor, Michigan, 1965) pp. 60-69.
5, A. W. Lohmann, H. W. Werlich, "Holographic Production of Spatial
Filters for Code TranslatiOn and Image Restoration," Physics Letters
25A, 8 (1967) p. 570.
6. G. Stroke, G. Indebetouw, C. Puech, "A Posteriori HolographieSharp-
gocus Image Restoration from Ordinary Blurred Photographs of Three-
imensional Objects Photographed in Ordinary White Light," Physics
L et ter s 26A, 9 (1968) p. 443.
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. . - .
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W ? . ? ? .
Figure la Density Distribution Necessary to Record T
: 2.0
? co
-. ? z
w
010
0
-3.1r -2r
? Ir
Density Distributiorl Necessary to Record TA(L.t. ) =.1
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"
A ?
OBJECT: SLIGHTLY TAPERED SLIT
WITH 1mm MEAN WIDTH
IMPULSE RESPONSE 0.08mm
DIAMETER:
CORRECTED SLIT WIDTH 0.16 mm
(CENTER):
SIGNAL / NOISE. 7.5.
A-A _Awn
(d)
Figure 4 Simulated Smear of Typical Line Source (a), Enlargement of Simula-
ted Imptuse Response (b), Corrected Image (c), and Microdensitometer Trace
Across Corrected Image (d)
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7
? the premises it is reasonable to place-mori.
.11 A. At SCYMI later date, however, we may
?
Infonration which? without changing our .rel
Ds. may change e Xi about AI we r-y
Iola, or we wayeve.. ..:eed in proving A fa
it constitute en oblaxtion against the patte
(a) Nonaberrated Image
(b) Aberrated
Impulse Re- (c) Resultant Aberrated
? sponse Image
?
Ay 1141 {I-mil-A 11 E r,?%?i-,n,hria 14;vsa
rh ,k? wit Xra h?rerre-ti??
IF-ey
? 'Ph OA-741111;h -Slt Ph , twol ::?"KS-r3irpc., /441 .
Pc'el%, 1Fri 7S.,71 2es ei/Pei; 41.1. Ka 'PI
1. ?
. 'Fatal v's 17,1. .tre. rh I%
? ? *Ai 4-0.1Th-t?ga tz:v
if II
At.se?ka 1;tair
witnreit :
es.
. ?
e.pr ".? k--At ..i.trt in
2n Pt
itiAird ,C,h'Y'renc.au-a?cii:.:
(d) Filtered Image
(e) Enlargement of Smear
'4737Z-T-.?;:>
if, ? ?
????,- 7;4
? 0
?
V
4.:W tt
r!..
c-41
WA,
(f) Enlargement of Filtered Image
Figure 6 Printed Page with "L" Smear
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the premises Ir Is reasonable to place mos%
A. At se later Gate, however. we may
Information which. without chang.inq our tel
...Sas? may change e *n about A; we may
. ?
*We, or we may eve. ..:eed In proving A fa
tonstitute:an objextlen a2aInst the iatte
(a) Nonaberrated Image
? e.. V. -I
Ibtjta.
Irs-FC2 inqa fi gr- T1
?
(b) Aberrated
Impulse Re-
sponse
?clTa
A. .
a4.14
0) Resultant Aberrated
Image
- ? i?itif.;47.:. Y.' a
.1re, -I.!
?i Nirtirrgt
. ? ?
; ? i? .1 ? z;r.e.rait L;
? ;if. :..;;;7?..1?fri:eirozjit
Aurts--Prafr; ? t
(d) Filtered Image
,- ?
rirt?-?41-1.
? w,
.R
;
. .
?
? .(e) Enlargement of Smear
(f) Enlargement of Filtered Image
Figure 7 _Printed Page with "Z" Smear
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?
r?
? 2 0 _
LOG EXPOSURE
-Figure 8 Coherent H and D Curve for Recordak Microfilm, 7
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