image information can ve separated from the gross 
transmittance of the photograph. In addition, it is 
possible to handle photography with a spatially vari- 
ant power spectrum and achieve correlation signals 
with good signal-to-noise ratio. 
The potential capability of coherent optical 
methods to handle a wide range of photographic data 
processing problems has been demonstrated.?:6 The 
direct application of these optical techniques to 
photographic image processing has been facilitated 
greatly by the advent of the laser with its greater 
intensity, monochromaticity, and spatial coherence. 
The laser also makes possible an alternative experi- 
mental approach to image detection and image 
matching by the synthesis and realization of complex 
optical filters.” The use of the laser and coherent 
optical data processing techniques has been investi- 
gated with regard to their applicability to the cross 
correlation of aerial photography for point transfer. 
The results of this study indicated an rms image align- 
ment precision of the order of one micron. To 
achieve this level of performance it is necessary to 
compensate for perspective image distortion caused 
by terrain slope. The feasibility of incorporating 
optical correction for these effects in a coherent 
optical correlator was demonstrated. In general, 
coherent optical data processing techniques were 
shown to offer a great potential for automatic image 
matching and automatic stereocompilation. 
Within the present state of the art, whether the 
image matching is done by electronic scanning and 
correlation or by conventional two-dimensional opti- 
cal correlation, the automatic stereocompilation is 
still carried out point-by-point sequentially on the 
photograph. The electronic scanner and correlator 
must perforce operate sequentially point by point. 
However, it is possible to design optical correlators 
which have the capability to process simultaneously 
and independently a large number of image points 
and thereby offer a potential means for greatly in- 
creasing the speed of the automatic stereocompilation 
process. 
BASIC CORRELATOR IMPLEMENTATION 
The image correlation operation is defined mathe- 
matically by the equation 
rji? (Ax, Ay) 7 
LIM 1 
if t; GGy) tj (x Ax, y + Ay) dxdy (1) 
A 
60 
where 
ri? (Ax, Ay) ^ spatial two-dimensional cross- 
correlation function of the im- 
ages t, and t» 
A = image area 
X and y = photocoordinates 
t, (X,y) & t,(x,y) = imagery being compared 
t(xtAx,y t Ay) - image t (x,y) displaced in x 
and y an amount Ax and Ay 
In practice, the infinite area integration implied by 
the limiting process in equation (1) is always replaced 
by finite averaging. Although finite averaging intro- 
duces an uncertainty in the measurement, the uncer- 
tainty can be controlled by maintaining the product 
of the image area and image spatial frequency band- 
width (space-bandwidth product) large. The mini- 
mum image area being correlated is limited by this 
space-band width criterion. 
The fundamental electronic and optical imple- 
mentations of equation (1) are shown in Figures 1 
and 2. In the electronic correlator of Figure 1, the 
multiplication and integration of equation (1) are 
carried out using the temporal video signal representa- 
tion of the images t, and t,. In the optical correlator 
of Figure 2, the multiplication is carried out in the 
plane of the second stereo photograph as the product 
of the light amplitude distributions representing t, 
and t,, and the integration is performed by the final 
transform or integrating lens. For both implementa- 
tions, the output signal for a given Ax and Ay dis- 
placement is a single point on the surface representing 
the two-dimensional correlation function shown in 
Figure 3. Complete image match and alignment is 
achieved when the two-dimensional correlation signal 
is a maximum and the alignment error signal is nulled. 
Scan Generator 
    
  
Deflection Coil 
     
    
  
Distortion Error 
Control Signals 
X and Y Scan 
Signals 
Feedback Signals Image Error 
Signals 
Figure 1 Basic Electronic Correlation System 
KRULIKOSKI, KOWALSKI, AND WHITEHEAD 
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