Journal of the Society of Motion Picture and Television Engineers (1950-1954)

based on this useful law to include directional screens and to treat these screens in the simple manner otherwise only safely applicable to perfect diffusers. In analyzing the characteristics of translucent screens used for background process projection, it was noticed that the fall-off of intensity with increasing angle from the normal would be closely approximated, not by a cosine curve as for a perfect diffuser, but by using some power of the cosine of the angle. To show how closely this approximation holds, Figs, la-d show experimental curves obtained by means of a goniophotometer on experimental screens analyzed by Dr. Herbert Meyer of the Motion Picture Research Council. (Data were taken according to requirements of A.S.T.M. Designation D63643.) The dashed curves in each set represent suitably selected cosine power curves, with the selected power used as a "shape factor" and symbolized by the letter s. It is immediately apparent that except for very low intensities, the cosine curve matches the experimental curve within a few percent — in fact in most cases within the instrumental error of the goniophotometer. Since most of the errors at very low intensities tend to make the readings too high, actual fit may be even better than that shown by the diagrams. This comparison was then tried on data for typical reflecting types of surfaces with results as shown in Figs. 2a-d.1 It will be seen that within angles of interest for most photographic work, the approximations again are good within a few percent. Care must be used, of course, in applying these 1 Sources for these data were: (a) for sandblasted mirror, James R. Cameron, Motion Picture Projection, Cameron Publishing Co., Coral Gables, Fla., 4th ed., p. 199; (b) for others, Ellis W. D'Arcy and Gerhart Lessman (De Vry Corp.), "Objective evaluation of projection screens," presented on April 22, 1952, at the Society's Convention at Chicago. in such cases as the beaded screen where a considerable portion of the total flux is emitted at large angles, for in such cases relations involving this total flux will be seriously in error. However, the particularly important relations between intensity, luminance and illuminance will hold when only small angles are involved. In the following formulae, notation follows that employed by Sears.2 Definitions: F, luminous flux; I, luminous intensity or flux per unit solid angle; B, luminance (brightness); E, illuminance or flux per unit area received at a surface; and L, luminous emittance or total flux emitted per unit area. Defining equations: jpi I = , where co is solid angle with dco vertex at source; dF 10 cos 6 = — — , where 6 is angle B = dA r" with normal to surface; AI0 • and AAcos0 AF L = — -, F is total emitted flux. AA The following equations compare intensity and brightness for a surface which follows Lambert's law, with one which is directional but for which the intensity falls off in proportion to some power s of the cosine of the angle with the normal to the surface. Lambert Surface Directional Diffuser 10 = I0 cos 0 10 = I0 cos8 0 B0 = BL B0 Here BL represents the brightness of the Lambert surface, and BD the normal brightness of the directional surface. 2 E. W. Sears, Principles of Physics, Vol. 3 — Optics, AddisonWesley, Cambridge, Mass., 1948, 3d ed., chap. 13. 20 Jqly 1953 Journal of the SMPTE Vol. 61