Geometrical modes as a general method to treat diffuse interreflections in radiometry

The problem of interreflections for Lambertian surfaces of arbitrary shape and with varying reflectance is of interest for many practical applications. We present a general method to approach this problem. We define photometric modes that are uncoupled in the sense that each mode may be assigned a (pseudo) reflectance and that interreflections among modes vanish. Then the problem is formally identical with that of a convex body, in which interreflections are of no importance. The photometric modes depend on the shape of the body. In many practical cases one or a few modes dominate, and the reflected radiance depends more on the shape of the body (the dominant mode) than on the precise irradiance distribution. A few examples are treated explicitly. The redistribution of radiation described by the modes is treated by means of the net vector flux and the space density of radiation. Knowledge of these fields for the dominant mode yields considerable intuitive insight in the physical situation and provides the means to estimate the effects of painting part of the surface or of the introduction of screens.