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HANDBOOK OF PHOTOGRAPHY 



relative positions of points in the image. They also give an accurate method of deter- 

 mining the actual location of points in space from stereographs of them. 



Figure 1* represents a plan view of a pyramid ABC photographed by the double- 

 lens camera focused on the plane AB, with sufficient depth of field to include the 

 entire object. The images of ^4, for instance, are at ^l and Ar, respectively, for the 

 left and right lenses. This figure is used because of its simplicity. Any other figure 

 would lead to the same formulas. 



,L^ff eye 



RigMeye \^ ^, _; |^ _ _^ 



K- d' ->l 



Fig. 2. — Conditious existing when viewing object by means of a stereoscope. 



Figure 2 represents the conditions which exist when the resultant plates are trans- 

 posed and enlarged m times and viewed as a stereograph. A'B'C is the resultant 

 stereographic image in space as fused from the two halves of the stereograph — A'j^B'j^C'n 

 and A'j^B'i^C'j^ 



The following formulas can be derived from Figs. 1 and 2: 



d' ~ /' f 

 AB ^h^ng 

 A'B' ~ h' f 



(1) 



(2) 



An orthostereoscopic view is one in which the resultant image is of exactly the 

 same size and shape and has the same location with respect to the observer's eyes as 

 the original space scene. 



Formulas (1) and (2) indicate that the following conditions are necessary to obtain 

 an orthostereoscopic view: 



1. Without enlargement, / must equal /'. With enlargement, mf must equal /'; 

 i.e., the distance from the eyes to the plate, in viewing, must equal the distance from 

 the lens to the plate, in taking, multiplied by the enlargement of the plates. 



It is illuminating to state this thus: the angle subtended by the object at the camera 

 nmst equal the angle subtended by the print at the eye. 



2. B must equal e; i.e., the photographic base — the distance between camera lenses 

 for the two views — must equal the interocular distance. 



The abo^^e mathematical treatment covers the basic features of the theorj' of con- 

 vergence. A complete mathematical analysis with especial reference to the conditions 

 necessary for obtaining orthostereoscopic views may be found in an article entitled 

 Orthostereoscopy, by Henry Kurtz, in the October, 1937, issue of the Journal of the 

 Optical Society of A merica. 



Effect of Other Depth Factors. — The absolute location and size of a stereoscopic 

 image depend upon the degree to which the various depth factors listed above are 

 present, upon the particular method of viewing, and, being partly subjective, upon 

 the individual observer. No rigid rules for locating such images can be laid down. 

 Consequently the subject must be discussed in general terms. It is assumed in the 



* After Hard\" and Perrin. 



