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

tangles are used and the elements are under one another, only an open-barrier band-type arrangement is possible (shown in Fig. 9). In the three-element arrangement one origin point is usually selected from each of the three intermeshed O plane patterns. For most purposes it is desirable to choose the O points as close together as possible. The three points may be selected from three adjacent O points in a single line, leading to a "collinear" arrangement shown in Fig. lOa, or the O points may be selected to constitute the apices of a triangle — a "delta" arrangement — leading to an even closer pattern, as shown in Fig. lOb. Higher Order Barriers. The barriers already described have a reciprocal arrangement between image, source and barrier pattern centers. By looking again at Fig. 4, one may see that there are other possible barrier locations (formed by ray intersections) which fulfill the basic condition of having each image area "seen" by only one of the O points. These locations are shown on the drawing as B2, B3, etc. and correspond to the selection of nonadjacent O points from a smaller submultiple O plane pattern. The first barrier plane shown has the O points taken from adjacent points of a pattern having a separation of distance O. The second barrier plane corresponds to the selection of alternate points of a pattern having points separated by distance £O. The third plane corresponds to the selection of every third point of a pattern with point separation of %O. This third barrier plane cannot be used in a threeelement arrangement since it means all three O points have been taken from the same point set in the O plane, instead of having one O point taken from each of the three intermeshed sets. Each O point would "see" the same image set, and the other two image area sets would be seen by none of the O points. The formula for these other image-to-barrier-plane spacings is given as: D /TIC 0 + Kl (4) where K is the ratio of O distance to the smallest O pattern spacing. When using these higher order barriers, the elements of a given image cluster are "seen" by the O points through different apertures, instead of through a single aperture as is the case for the first barrier plane. Nonplanar Barriers and Images. The parallax barrier principle is not limited to three parallel planes. Consider a spherical surface I and two O points, as shown in Fig. 11 a. The locus of the intersections of pairs of rays which are a fixed distance apart on the image surface and pass through the two given 0 points will sweep out a curve which meets the parallax criteria. This surface will not be a sphere. In this case the size of the elements on the image surface is uniform. By sacrificing this condition, any given barrier B and image 1 surfaces can be arbitrarily chosen to meet the parallax condition for any given O points. For example, in Fig. lib, curve I can be a circle (in three dimensions spherical) and curve B may be a plane or a sphere with any given radius. The patterns on I and B must be constructed by a point-by-point method. An example of a two-element construction is illustrated in Fig. lla. Starting with line 1 connecting O2 and Ii, draw line 2 connecting d and B3 (the point of intersection of line 1 and curve B), continuing on to curve I. Line 3 then connects O2 and I2 (the point of intersection of line 2 and I). Line 4 connects Oi and B2 (the point of intersection of line 3 with B), etc. In other words, O2 lines connect with previous intersection points on I and Oi lines connect with previous intersection points on B. The examples are shown in two dimensions. The three Sam H. Kaplan: of Parallax Barriers 17