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A First-Order Theory of Diffuse Reflecting and Transmitting Surfaces
By ARMIN J. HILL
Intensity of light emitted or reflected from a surface in accordance with Lambert's law varies in proportion to the cosine of the angle between the direction of the light beam and the normal to the surface. With many surfaces which do not follow this law, it is possible to approximate the variation of intensity with some power of the cosine. When such an approximation can be made, relatively simple relationships can be obtained for luminance (brightness), emittance and related factors. Use of this approach may take some of the mystery out of such problems as the determination of screen brightness and a study of transmission characteristics of process screens.
.LJAMBERT'S LAW, which states that the intensity of light emitted from a perfectly diffusing radiator is proportional to the cosine of the angle between the normal to the emitting surface and the direction in which the intensity is measured, provides a simple mathematical basis for treating luminous surfaces which radiate according to this law. Unfortunately, few surfaces are perfect diffusers and serious errors will result if the simple equations derived from Lambert's law are applied to them. Many of the reflecting and transmitting screens used in the motion-picture and television industries are, in fact, quite
Presented on October 9, 1952, at the Society's Convention at Washington, D.C., by Armin J. Hill, Motion Picture Research Council, 1421 North Western Ave., Hollywood 27, Calif.
(This paper was first received on November 3, 1952, and in revised form on May 12, 1953.)
highly directional, though not enough so that they can be treated according to the laws governing specular reflection or direct transmission.
Considerable literature is available on the theory of radiation transfer and on the processes by which light is diffused and scattered as it traverses various media. Most of this has approached the problem from too fundamental a viewpoint, however, to provide workable equations by means of which "partial diffusion" might be treated. This paper suggests an approach which is almost entirely empirical, based upon experimental tests on transmitting and reflecting screens, disregarding completely the processes by which this transmission or reflection takes place. These processes are therefore treated exactly as they are in applications of Lambert's law. The slight modification of the equations does not prevent, in most cases, an extension of the ideas
July 1953 Journal of the SMPTE Vol, 61
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