STEREOSCOPIC PHOTOGRAPHY 



577 



Limits of Stereoscopic Vision. — Binocular vision and consequently stereoscopic 

 vision occurs only within relatively near distances. The maximum distance depends 

 upon the minimum relative convergence that the eye is able to detect. This distance 

 differs considerably with different individuals. 



Helmholtz considered the minimum difference in convergence 

 angle that could be resolved to be 1 min. of arc. Later experi- 

 ments show the average value to be in the neighborhood of 20 

 sec. of arc, possibly less. 



Given two points at the same distance from the eyes, di. 

 They appear to be equidistant. If one point then recedes 

 from the eyes while the other remains stationary, the eyes are 

 not capable of detecting that a difference in distance exists until 

 the convergence angle for the receding point has diminished 20 

 sec. of arc. Calling the difference between the two distances 

 D and the distance to the far point ^2, there is, for any value of 

 di, a minimum value of D for which the difference in conver- 

 gence angle becomes 20 sec. of arc. 



This can be very closely determined from the formula : 



D = 



xdi^ 



e — ad\ 



(3) 



where e = interocular distance; i_Qff Ri'ghi- 



a = difference in convergence angle between di and d^ eye eye 



expressed in radians (1 rad. = 57.3°). Fig. 3. — Diagram 



Using 2.5 in. for e and 20 sec. of arc for <x, the following from which the data 



table gives the separation away from the eyes that two ° i + H ^^^ 



objects must have if a stereograph of them taken with a 



2.5-in. base is to show any depth. These are only approximate values that will give 

 the photographer some idea of the sort of depth effects he may expect with various 

 spacing of objects. The things to be noticed are the rapidity with which D must be 

 increased beyond 100 ft. and the fact that binocular vision disappears entirely near 

 2000 ft. 



Table I. — Conditions for Binocular Vision 



If di Equals 



10 inches 



2 ft 



5 ft 



10 ft 



25 ft 



100 ft 



200 ft 20 



500 ft 160 



1000 ft ; 925 



2000 ft oo 



D Must Equal or 



Exceed, Ft. 



0.005 



0.002 



0.01 



0.05 



0.3 



5.0 



The limit of stereoscopic vision on the near side is generally considered to be the 

 minimum distance for clear focusing by the eyes. A minimum value of 15 in. is 

 recommended. 



Stereography with a Single Camera or with Two Single Cameras. With Single 

 Camera. — Stereographs of motionless scenes may be made with any single camera. 

 It is important to remember, however, that in stereographs sharpness of detail over the 

 whole scene is more important than in ordinary photographs, as blurred details greatly 

 detract from the depth effect and the illusion of reality that a sharp stereograph gives. 



