Diffuser assessment using surface spherical harmonics

The problem of deriving a diffusion figure of merit may be alleviated by forming a continuous, functional representation of its polar pattern, expressing the polar patterns mathematically, as a continuous function of direction. This paper develops a form of continuous, orthogonal representation by expressing a diffusers polar pattern as a weighted sum of surface spherical harmonics (a hierarchical set of basis functions which are orthogonal upon the surface of a sphere). The surface spherical harmonic weights can be calculated from a limited set of experimental measurements by means of a discrete Fourier analysis. The resulting spherical harmonic representation is continuous, yielding a modeled polar pattern for any arbitrary direction. It is also hierarchical, in that the more harmonics that are included the greater the accuracy of the model, and has a meaningful spatial structure, with particular surface spherical harmonic weights expressing particular patterns of directional variation in the polar pattern. The paper first explains surface spherical harmonics and a means of efficiently deriving them from measured or calculated data. The implication and applications to diffuser assessment are then discussed and finally some results of the analysis applied to diffuser assessment are presented.