INVERSE ANALYSIS APPLIED TO AN ILLUMINATION DESIGN

Abstract

This work investigates the application of the  inverse analysis to an illumination design of a three-dimensional rectangular enclosure. The problem consists of finding the luminous fluxes on the light source elements, located on the top of the enclosure, that satisfies a prescribed uniform luminous flux on the design surface, located on the bottom surface. The solution assumes that all the surfaces emit and reflect diffusely, and that the hemispheric spectral emissivities are wavelength independent in the visible region of the spectrum. The inverse analysis is described by a system of linear equations that is expected to be ill-conditioned since it involves the solution of a Fredholm integral equation of the first kind. To tackle the ill-conditioned system of equations, the TSVD (Truncated Singular Value Decomposition) regularization method is applied. In addition to presenting a methodology to solve for the luminous exchanges in a enclosure, starting from a thermal radiation energy balance, this work considers two design cases: one in which the light source elements cover the entire top surface; and one in which a reduced number of light sources are considered, a more practical solution. In both cases, the proposed inverse design is capable of providing a solution that satisfies the prescribed luminous flux on the design surface within average and maximum errors less than 1.0 % and 5.0 %, respectively.