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

Table II Table III Magnifi Screen cation Width (Af)* (WO Total projected film parallax, zp (mils) for M Minimum values of zp (mils) for SN = 0.1 200 13ft9in. 12.5 25.0 37.5 250 17 2 10.0 20.0 30.0 300 20 8 8.3 16.7 25.0 350 24 1 7.1 14.3 21.4 400 27 6 6.25 12.5 18.75 * Based on the standard 35-mm projector aperture width, 0.825 in. employing depth contents of AJVi, AjV2 and AA^3. The *N\ column is of interest merely because there remain some conservative spirits in the 3-D film field who think that no action should take place in front of the screen plane. In realizing a given depth content in the cinema, there is however another factor to consider. The representation of a given depth space may be imagined as built up of an infinite number of infinitely thin planes. Were this achievable, we might say that the stereoscopic resolving power was infinite, for the system would have an infinite capacity to discriminate depth. In actual practice, however, these planes will be replaced by more or less shallow zones, within each of which a position in depth will not be accurately reproducible. The depth of the zones will therefore be a measure of the stereoscopic resolving power of the system. These zonal depths may conveniently be denoted by the change in nearness factor, bN, which they represent, and we accordingly employ the concept of dN to clarify discussions of resolving power, without suggesting that this will necessarily be the unit finally accepted.* Assume, then, that any volume of space denoted by A7Vi is to be representable in 10 zones of depth; in other words, dN * Experiments are being undertaken with trained observers to determine whether 8N, dP or perhaps some other concept corresponds best with the subjective impression of depth resolution. 200 1.25 (250 <300 (350 1.00) 0.83> 0.71 J 400 0.63 Note: The bracketed range comprises approximately 67% of existing motion picture theaters, as revealed in the recent SMPTE survey.7 = 0.1. We can then tabulate the minimum film parallaxes which it will be necessary to have recorded reproducibly on the projected film — that is, after taking into account all possible random parallactic errors in previous stages of the transmission system. Table III shows that, for screens found in the majority of commercial theaters, the minimum reproducible film parallaxes needed to achieve a depth resolving power of 0.1 do not much exceed the dimensional tolerances of the film itself, let alone allowing for shrinkages which may occur at intermediate stages in commercial laboratory practice, or for mechanical errors in the stereoscopic adjustments of the camera. The need for extreme precision is still further emphasized by the fact that 8N = 0.1 is equivalent to only 20 separable zones in space for a normal 3-D film having a depth content The General Equation Reverting to our main theme, it will be evident that the greater the magnification, M, the greater the screen parallax to be derived from a given film parallax. Turning to the camera, it can be seen from Fig. 2 that an object point at a given distance produces a greater film parallax, (a) the longer is the focal length, fc, of the camera lens(es), and (b) the greater is the lateral separation, tc, of the lenses or optical systems. Thus an increase in these three factors, Af, fe Spottiswoode, Spottiswoode and Smith: 3-D Photography 257