AERIAL PHOTOGRAPHY 



723 



other than in the exact center (Pole 2, T2B2), it will appear as a radial image with the 

 top displaced radially outward from the base of the pole (^2^2). Thus it will be seen 

 that a vertical photograph of rough terrain is a completely distorted image, with each 

 point being out of position along the radial line passing through that point by an 

 amount which is the result of the height of the object and its distance away from the 

 center of the picture. The radial-displacement 

 formula is fundamental in aerial photography 

 and follows: 



R2 



El 



Ei 



(6) 



This means that the true radial distance R] is 

 to the displaced radial distance Ri as the 

 theoretical altitude of the airplane above 

 datum E\ is to the actual elevation of the 

 airplane above the particular picture point Ei. 

 Another way of expressing this situation is 

 as follows: 



A5 = 



^E 



(7) 



Fig. 10. — Rectification of photo- 

 graphs made when a tilt can be accom- 

 plished in printing by, using a recti- 

 fying camera. /, source of illumina- 

 tion; N, negative; L, lens; E, easel; 

 P, point at which plans of negative and 

 lens must intersect to effect perfect 

 rectification. 



which means the difference in scale A*SI, equals the difference in elevation divided by 

 the focal length /. Thus, if there is a difference in elevation of 1000 ft. between the 



\>t- Rac/i'al //he 



^^ Image ofpo/e 2 

 \b2 



\ / Imaqe of 

 y pole! 

 t| b) 



t, b, t.b 



Fig. 11 a. — Image of two poles 

 (exaggerated) as seen by the camera 

 lens. The pole 1 at t\h\ is on the 

 optical axis, whereas pole 2 is not. 



Focal plane 



Fig. lis. — Elevation view of 



camera photographing an object on 



optical axis, and another object re- 

 moved from the axis. 



top of a hill and the datum scale of the flight and if the camera used for photography 

 has a focal length of 10 in., we have: 



^„ 1000 ,„„,, 



A5 = yr— = 100 ft. per in. 



(8) 



The scale of the picture at the top of this hill will be 100 ft. per in. larger than the 

 datum scale of the picture. Carrying this a step further, if the desired scale of the 

 flight is 1 in. = 1000 ft., the airplane will be flying at 1000 X 10 = 10,000 ft. above 

 the datum plane. If, while flying at this elevation, a mountain is photographed 



