Stilweli 



a sinusoidal modulation of the normal angle to the wave surface, 

 this Figure indicates that the resultant reflectivity variation 

 would be a minimum for an observer angle of 90°^ ox vertical 

 incidence. Grazing incidence would give the greatest sensitivity 

 but the scene would be highly distorted and much of the wave surface 

 would be obscured by the peaks of the waves. The inteirmediate re- 

 gion, that near Brewster's angle, can be used. For this region a 

 polarizing filter is required since the vertical component would 

 not yield a unique reflectivity with wave angle and would therefore 

 introduce extraneous spectral components. 



Reflectivity does not completely define the light directed 

 toward the camera since the sky itself may have variations of 

 brightness. With sky luminance entering the analysis the problem 

 loses definiteness but certain requirements can be deduced. That 

 part of the sky from which light is reflected into the camera must 

 have monotonic variation of luminance if there is to be a one-to- 

 one mapping of the surface normal angle onto the film. Thus, the 

 sky must be either clear or uniformly overcast for the technique 

 to work. 



Denoting the product of luminance and reflectivity by g 

 one can expand this function in terms of normal angle variations 

 in the form 



g(x,y) = g^ [1 + g'/gQ 9 (x,y) + . . .] (3) 



Noting that the power density in equation (l) is proportional to 

 g, one can obtain 



^ = 0=7^^ (h) 



d9 CD gQ 



The g term in equation (3) will relate to the average density of 



the scene negative and can be estimated by a direct measurement 

 of this density. 



The scene photograph under these' conditions would consist 

 of an increasing density in the direction away from the observer 

 which by knowing the camera field of view would allow a measurement 

 of density variation to yield an average of the angular gradient of 

 density from 



D = ^ (5) 



This quantity expresses the sensitivity of the photograph density 

 variations to the angular disturbances of the surface. It should 

 be pointed out that waves traveling in a direction other than 

 toward or away from the observer will not be transferred onto the 



173 



