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

different "O" points and a given image strip. The only difference is that a particular strip (in this case LI) is "seen" by (Oi)i, by (Oi)2, and by (Oi)3 through different barrier plane apertures. Barriers for More Than Two Image Elements per Aperture Instead of two viewing points (called "O" points) coupled to two mutually intermeshed image area sets, three or more intermeshed image area sets can be coupled to a corresponding number of viewing points. Such an arrangement is possible if the barrier has a ratio of aperture area to total barrier plane of 1/JV or less, where JV equals the number of points coupled to a similar number of sets of mutually exclusive area elements. For a three-element arrangement the width of the barrier member must be at least twice that of the aperture width; for a four-element arrangement the barrier width is at least three times the aperture width. A threeelement arrangement is shown in Fig. 4. One section of a six-element arrangement is shown in Fig. 5. While the "O" plane has been considered up to this point as a viewing plane, the various "O" points in the "O" plane may also be considered as origins of electrons or other radiation, for the purpose of creating a parallax system consisting of an image plane, a barrier plane and an origin (or object) plane. In order to generalize the theory of parallax barriers, consider the barrier plane to be covered with a regular repeating dot pattern (such as the rectangular dot pattern shown in Fig. 6). If there is a point source of rays in the O plane, the pattern in the barrier plane will be projected on the image plane I and will be enlarged in the ratio of I _ Y If any particular point in the above projected image plane I is considered as an origin, then it will project the barrier plane pattern onto the O plane and the pattern will be enlarged in the ratio of G/D. Any dot in the resulting O plane pattern can be shown to be in the correct position for projection of the barrier pattern onto the previously projected I plane pattern. The different dots in the O plane can be considered to correspond to the (OOi, (Oi)2, (Oi)3 points of Fig. 3. Thus we see that the patterns of image and origin planes bear reciprocal relationship to each other, and the functions of O and I may be interchanged. Mathematically: 1 = + B O T (3) where B, O and I are the pattern sizes in the B, O and I planes, respectively. The dots of these patterns serve as the centers for the area patterns actually used. Desirable area shapes and pattern arrangements are discussed below. To develop a two-element, a threeelement or an jV-element arrangement, it is necessary to intermesh two, three or JV patterns in both the image and origin planes between each other. Each image pattern is then coupled to a corresponding mutually exclusive origin pattern. Figure 7 illustrates a two and three-element arrangement. Arrangements of Image Elements Practical considerations call for the maximum utilization of available area in the image plane. Although many geometrical patterns exist which can cover an entire area, only a few meet the two following criteria: (1) The patterns must contain only the same shape and size elements. (2) All the elements must have the same orientation. Arrangements meeting these criteria are parallelograms (including rectangles and squares) and hexagons. Although an area may be covered by isosceles triangles, such an arrangement does not fulfill the second criterion since Sam H. Kaplan: Theory of Parallax Barriers 15