amplitude transmitted by the transparency of amplitude transmit- 
tance t4 04 ,y4) may be written as: 
  
   
   
  
   
   
     
    
   
   
     
     
  
  
  
  
   
  
   
   
   
  
1 ; n. “iE (xy) 
V. y) z 22 P(x d y, dle Ad: 
qp id Lx, y) (8) 
uhere Bx, d fd > y,d'/d) is the affective pupil function P(x,y) 
projected on the object plane and characterizes the filtered 
laser beam amplitude distribution and the lens aperture. 
Assumirg Fresnel diffraction from the P 
plane to the P 
plane, it results: 
1 2 
ELE xy) H y EG +) 
Vy.) ue Ad oy) P xd dé Ad : dx, dy, 
where (x,,y,) and (x yY,) are the coordinates at tne scene and 
transform plane respSctively. An intuitive approach to this 
result may be achieved by considzring the lens L, as composed 
of tuo lenses; the first uould collimste the beaf and the second 
(of focal distance d') would focus it on Po. 
Thus, up to a quadratic phase factor -yhich has no importan 
ce in this study, since it does not affect the intensity dis- 
tribution in P,- the focal plane amplitude distribution is 
preoortional t8 the product of convolution of the Fourier trens- 
form (# ) of the amplitude transmittance t4 0 y4) end the 
effective pupil function 
V. sy) «€ f [66.) e F Ps. y£)} (10) 
The second convolution factor aives the central spot in the 
transfom plane when the transparency is taken away and gives in 
consequence a measure of the resolution of the overall optical 
transform system. 
The result presented by equations (9,10) are essentially the 
same results obtained by other authors (103,(15), (16), (49), (20) 
in uhose uork the object uas placed either against or in front 
of the lens itself, follouing the classical configuration. - How- 
ever it has to be stressed out that with the present configurat- 
ion three main advantages have been obtained: 
1. The system is very simple and rather easy to align. 
2. The system uses one lens less, uhich results in an 
increase of resolution; in particular, the central dot 
in the plane of the Fourier transform may be reduced, 
allowing so the detection of lower wave numbers and 
increasing the resolution. 
3. The scale of the Fourier transformate is under the con- 
trol of the experimenter, depending only on the position