n 
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ting 
pon- 
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the 
the 
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F2 
ion, 
Light diffraction by holograms makes 
possible corresponding elements detection. 
This is very easy made because each 
hologram point contents all the image of 
the photogram. 
Correlator working is based on the fonda- 
mental conception of the fact that the 
relief image is & spacial sign appearing 
in the same manner like temporary communi- 
cation signals. 
1.2. Photocrams holozram and the 2D 
correlation 
Resulting nologram from & photogram is 
realised by means of optical assemblage 
t 317.2 presented. 
   
Reference Beam— —7 
   
  
  
  
  
  
  
  
  
  
Fig.2. Optical assemblage for obtaining 
Fourier hologram 
Particularising general relationship of 
holograms for the case of plane holograms 
where the object becomes photogram, the 
Fourier hologram can be obtaining. 
The transmittance of the first photogram 
in this case is denoted by : 
hx-Xys y-y) (1) 
of which Fourier transformation is: 
FL (xx, y-y)1=Flfix.y)] expli(x,p+Y,q)]= 
= Tip) expli(xp+%g)] (2) 
where pete IT 3 Xpsÿp BTC plane 
coordinates of the £M er. 
Reference s or used in holographing can 
be wrote in the Pcr manner: 
R(x,y)e Reexp (ix,p) (3) 
The entire field in the hologram plane is: 
Hx,y)=f{x-X,, y-¥,) + R(x,y) (4) 
After exposing, the total intersity in 
the hologram plane is: 
E(x,y,)- [Hx]? (5) 
515 
This intensity distribution is in a 
photographic manner recorded and after 
developing, the transmittance in aplitu- 
de of the hologram becomes : 
Hxpy)= Re«[T pa) +ReT, (pq) exp{tl xp « y] « (6) 
* RS, Cp,g) exp(-iLx-x)p«y,01) 
The last term of the (5) relationship is 
the complex Fourier transformation 
needful in the subsequent correlation 
process. 
The Fourier transformation of the F2 
photogram containting the most actual 
information is needful to carry out the 
correlation aiming the corresponding 
images detection and selection. 
The F2 photogram transmittance can be 
wrote as follows : 
tz(x-x, y -y) 2 Dx 6- p). y - Ot p2)] (7) 
The bidimensional Fourier transformation 
has the form : 
F(&x-(x-p). y-(y-p,)]]- (8) 
= T(p,g) exp{i[04-p,)p+(y-p,)a } 
The correlation function gived multi- 
plying member by member the (6) and (E) 
relation ıship, is: 
r((f)+[Re*|T,(p.9) [*] T,(p.4) exp {iL{x=P,)P+(y-p,1a } + 
<Ro[T,(p,9) T,(p.)lexp {il(2x-x=P)p+(2y-p,)a}+ = (9) 
+ Ro[T,(p,9) T(p.9)1 exp{-i[{p-x)p+p,g } 
The second lens realises a second 
Fourier transformation on the entire 
distribution from the equation (9) and 
transfers this issue filter of the core- 
lation plan (x Ys 
This TelGttonshtp is reduced finally to 
the expresion : 
o(Xe, yols: ....t (Xo, yo) t (-Xe,yo) $[Xo-( Pe) 22 o-Py) e ] (10), 
1 1 
representing the two image-points 
transverse correlation sign,conjugated 
with the coordinates : 
j& 
Xo = (Xg- Px f i 
1 
yo= py (17),