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

and tc, increases the final parallax on the screen, whose absolute magnitude determines the N value of the image point corresponding to the original object point, 0. In fact the product Mfctc is combined into what is called the C factor in our general equation. This equation, which will be stated but not derived here, expresses the distance, P, of a fused image point from the spectator in terms of the distance, p, from the camera of the original object point, together with the other variables of the transmission system. (4) Thus, besides M , fc, tc and p, which we have already mentioned, there is an A factor and a B factor. * The A factor, Vt, is a function of the spectator and his viewing distance from the screen, as may be seen from Fig. 1 . The B factor denotes an important transmission concept, which is governed by the convergence of the camera optical axes (or its preferable equivalent, inward lateral displacement of the lenses relative to the films). The B factor can be related to a camera convergence half-angle, <p, and a projector convergence half-angle, 6, as follows, taking account of the fact that an optical printing displacement, zd, may have been introduced between the camera film and the projected film: B = tp t + 2M(fc tan <p fp tan 0 + zd} (5) If lens displacement is employed instead of toe-in in the camera, h, and projector, H, we may write instead, B = tp t + 2M(h H + Zd) (5a) As a transmission factor, B may be very much more simply defined. Let mzt denote the screen parallax of a point which was at infinity in the scene, i.e. at DQ. Then B = °>z. t (6) Expressed in words, B is the excess of screen parallax of a point originally at infinity over the separation of the human eyes. B+, B = 0 and B— Transmission Three important cases now arise : that in which B is positive, that in which it is zero, and that in which it is negative. The discussion of the three types of stereoscopic transmission system will help to clear up the vexed question of camera convergence, a subject on which much ink has been spilt in the effort to establish as fundamental relationships what have been only rough-and-ready rules. Several of these are now being purveyed by inventors in France, Germany and Holland, but on investigation they are found to be merely crude approximations, the errors in which may be masked by the fact that they have been applied only to films projected on very small screens. Figure 3 shows in graphical form the principal characteristics of B-+-, B = 0 and B— transmission systems. It is to be noticed that both axes are scaled in a reciprocal type of unit, the x-axis in terms of D, and the ^-axis in terms of N. Hence the origin represents infinity on both axes. From Eq. (6) it will be seen that when B = 0, mzs = /. When, as here, the screen parallax of a point equals the eye separation, /, rays reaching the eyes will be parallel, as they are when reflected from points at infinity. In other words, infinity in the scene (see definition of °°2-g) appears at infinity in the cinema. Thus a B = 0 shot must be represented in Fig. 3 by a line passing through the origin, and no other type of shot can be so represented. Referring again to Eq. (6), if °°zs exceeds t, it must be that some point short of infinity in the scene produces on the screen a parallax equal to / (because a point at infinity produces a parallax greater than t). Thus, when B is positive, a point nearer than infinity in the scene will correspond on the screen with a point which tends to appear at infinity. On the other hand, if "z, falls short of /, so that B is negative, it must 258 October 1952 Journal of the SMPTE Vol. 59