vely. 
ct to 
litter 
n the 
axis. 
ed in 
rded 
m in 
after 
laced 
n be 
lator 
onju- 
4 be 
(5) 
fereo 
(6) 
> eX- 
1ce a 
'ding 
not 
juare 
may 
(7) 
dant 
A 
nter- 
ssary 
per- 
Con- 
o ex- 
(8) 
re 4, 
EAD 
) 
| 
Multiplying equations (7) and (8) and collecting 
terms, 
T, (p. y) e 1*9? G (py) - 
[IKI2 IT, (5,0121 T, (p,y) eT P9? 
KT, (p.y) T, py) e rtp, 
K T, (p. y) Ti (p.y) e (Psp (9) 
The system output is the Fourier transform of 
equation (9). Letting the coordinates of the output 
plane be u,v, the first term of equation (9) gives rise 
to the image t, [x - (x, + p, ) y] located at 
u- (x, + Py) 
v=y (10) 
The second term gives the convolution signal located 
at 
utb-2x -Dp. 
v=y (11) 
The third term is the desired filter output or cor- 
relation signal located at 
us (btp.) 
ve (12) 
Since b is a constant offset from the system axis de- 
termined by the linear phase shift of the reference 
Collimated Beam Splitter 
Laser Light Beam 0 
a Nm 
     
  
  
Stereo Photo 2 
Reference Collimated 
Cylindrical Lens 
beam, inen the system output is p, versus y, that is, x 
parallax as a function of y photocoordinate, the de- 
sired result. 
The three output terms will not overlap or inter- 
fere as long as b is greater than the x dimension of the 
overlapping imagery. 
THE COHERENT OPTICAL 
PARALLEL-OUTPUT PROCESSOR 
The optical system for generating instantaneously 
the measure of x parallax as a function of y photo- 
coordinate is essentially a multi-channel correlator 
using a combination of spherical and cylindrical 
lenses. These lenses are so arranged as to take double 
Fourier transforms in y and single transforms in x so 
that imagery is retained in y and frequency plane 
filtering and correlation is carried out in x. 
The optical train of the parallel processor is shown 
schematically in Figure 5, and a view of the experi- 
mental equipment is shown in Figure 6. The reference 
beam arm of the interferometer is not shown in this 
figure. 
The optical processor was tested with stereo 
photographs of a mechanical model, Figure 7. The 
photographs were taken with the stereo base parallel 
to the meter stick. The two ramps presented 45- 
degree slopes in both x and y and the hemisphere 
presented a continuously variable slope from zero to 
90 degrees in both x and y. 
The operation of the correlator is as follows. Re- 
ferring to Figure 5, one of the stereo photographs is 
placed in the input plane with its x direction parallel 
to the axis of the cylindrical lens. A matched filter or 
Fourier transform hologram is made of the entire 
  
   
  
      
Light Beam Mirror 
Matched Filter 
Of Stereo Photo 1 
Diffracted 
Correlation Signal 
One Dimensional 
Correlation 
Output Plane 
Spherical Lens N 
Cylindrical Lens Y Stereo Photo 
X-Parallax Profile 
Figure 5 Instantaneous Stereo X-Parallax Profile Processor—One-Dimensional Coherent 
Optical Image/Matched-Filter Correlator 
PARALLEL PROCESSING 
63