Stilwell 



Thus q is identical to the scale factor in equation (12) relating 



a sinusoidal spatial wave of spacing 5 in the scene plane to 

 its focal point position in the transform plane as derivable from 

 Huygens Principle. 



The power density of equation (lO) exposes the film placed 

 in the transform plane for which the equation (using an alternate 

 form of equation (l) is 



10^2 ^ K3 [ '^'^a) ] ^3 (14) 



e2 



where A is the ratio of D to 7 and the subscript 2 refers to the 

 transform photograph (the second photo involved in the analysis). 

 Thus equations (7), (8)^ (9), and (ik) yield 



where the dc term has been suppressed. (The cross product terms in 

 the squaring operation is weighed so heavily to the delta function 

 that they can be ignored. ) This equation can be simplified by 

 noting the term K^UqI^ is equivalent to a term like 



10 in which A3 is the optical density arising by exposing film 

 in the scene plane to the laser intensity Uq. This film must be 

 developed along with the transform in order that the constants 

 K be the same. It is not always convenient to expose the third 

 film for the same time used for the transform photo but the 

 identity 



UsTs 



allows a different exposure time and laser intensity to be used. 

 Thus the expression for the square of the Fourier transform is 

 just 



1^(L\)- 



^3 ^ ^HiAj_ U3T3 10^1 -^+A2 (1^) 



SPECTRUM 



The photographic spectrum is obtained from equation (17) 

 by an integration over an elemental area in the transform space as 

 is indicated by 



176 



