Stilwell 



film with a density variation as large as the angular excursion 

 ■would indicate using the value of D obtained above. This results 



9 

 because only the projection of the- normal angle excursions in the 

 vertical plane directly away from the observer is effective in 

 causing reflectivity variation of light into the camera. The 

 sensitivity must be reduced by some function of the azimuth angle 

 of the waves \|r to be called pCj). 



The p(i|;) function can be calculated by considering the 

 projection of arc length for a skewed wave onto a plane parallel 

 to camera direction. The approximate equation is 



p2(^) = Sin2 6 + Cos2 6 Cos^ \|; 

 where 6 is the camera depression angle which for 6 = ^5° is 



P^dlf) = J- (3 + Cos 2 ij;). 

 OPTICAL ANALYSIS 



The scene transparency with the properties previously 

 described is inserted into the input plane of the optical computer 

 and illuminated with a collimated beam of laser light. Modifying 

 equation (2) to a form involving light amplitude gives 



a = a^lO"^/^ (6) 



Substituting in equation (l) with the power density being the g 

 function of equation (k) , one obtains 



a = a 

 o 



[{Kag^T}"^^^] (1 + j:-p(|)cp+ . . .)-2^^ (7) 



The quantity a (the incident laser light amplitude) can be written 



as proportional to the square root of the laser power density 

 (= s /i^q). 



The term in brackets can be written as 



10" 2^ (8) 



where the bar denotes an average over the area of the photo illu- 

 minated by the laser beam. The subscript 1 refers to the scene 

 photograph to distinguish similar terms referring to different 

 photographs occurring later in the analysis. If a small angle or 

 density gradient assumption is made the term in parenthesis can be 

 approximated by 



174 



