Measurements of scattered sunlight often employ simple radiometers that are incapable of scanning azimuth ø and zenith angle θ. Instead, they measure integral moments of the radiance. Consider a set of N + 1 meters designed to measure moments Λ_l through Λ_N+1. If each meter is judiciously designed, the Λ_j may be processed quite simply to deduce inherent properties of the scattering medium, namely, N moments of the volume scattering function. In the optimum design, each meter has an angular response that approximates a polynomial of degree N in cosθ. The theory of these meters is based on Boltzmann’s equation of radiative transfer expressed in terms of spherical harmonics, a form in which this equation is particularly simple.

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