Journal of the Society of Motion Picture Engineers (1930-1949)

manded by the director, whether this be intended to soothe or startle, and whether the continuity from shot to shot be a matching or a deliberate mismatching of planes. Recently, with the aid of metric units and other simplifications, it has proved possible to design a much more compact version of the Stereomeasure which contains the same information but lends itself to quantity production. So far we have been concerned with the space relationships obtaining between a scene existing in real space and the same scene as reconstructed in stereoscopic space by a binocular spectator sitting in the motion picture theater; and we have seen how these two quite different types of space can be related to one another by adopting new systems of measurement and comparison. Stereoscopic Magnification The next step is to examine how the size and shape of objects are affected by their stereoscopic transmission and reproduction. It is well known that a monocular image is essentially ambiguous, for the data it contains can (in the absence of other evidence) be construed by the spectator's mind as presenting a small object at a near distance or a much larger object farther away. By contrast, a binocular image — on the basis of the stereoscopic data it contains — is entirely unambiguous; it is determinate in size, shape and position. But these characteristics do not necessarily conform with those of the object represented; its image in space may be larger or smaller, widened or elongated, nearer or farther away. These distortions are certain to arise when presenting pictures on large screens; but whether they are objectionable or not depends on a great many factors, some stereoscopic, some extra-stereoscopic, and some psychological, which will vary greatly from one spectator to another. Nonetheless, it is important to be able to determine mathematically what distortions the image has undergone, and this .must form an inte gral partof the whole transmission theory, just as much as an analysis of waveform distortion forms part of the theory of electronic amplification. Considering the stereo image of an object in the real world, we may call the ratio of the stereoscopic image size to the real object size the stereoscopic magnification, which may of course be greater or less than unity. It can be shown that the depth of objects may undergo one type of magnification (called depth magnification, md), while the height and width of objects — dimensions between which a piano-stereoscopic transmission system does not discriminate — undergo another type of magnification, called width magnification, mw. Stereoscopic magnification varies, among other things, with the size and sign of the B factor. In the general case, in which B 7^ 0, we may write, for any given plane in the image having a nearness factor, N, Vt /B Mfct\Nt + 1 (11) When .5 = 0, the expression in brackets equals unity, and the equation reduces to Vt Mfctc It can also be shown that, in the same general case in which B ^ 0, the width magnification for an image plane having a nearness factor, N, is given by When 0, this reduces to (12) (12a) Finally, since it is often the shape of objects which is more important to their acceptability than their absolute magnification along any dimension, it is helpful to introduce the concept of the shape ratio, /*. Then 262 October 1952 Journal of the SMPTE Vol. 59