Light-field reconstruction from scattered light using plenoptic data

A full description of light propagation in the ray regime is provided by the plenoptic function, where both the location and angle of each ray is known. In this paper, we investigate the utility of plenoptic data for extracting information from a scene where the light from objects in the scene is viewable only after scattering from a diffuse surface. The detected light is mathematically described as a light field that varies as a function of both space and propagation angle. The relationship between the object light field and the scattered light field is cast in terms of a system of Fredholm integral equations of the first kind, where the bidirectional reflectance distribution function (BRDF) of the scattering surface is incorporated into the kernel of the integral equations. The object information from the original scene is retrieved by solving the resulting system of integral equations. We apply our mathematics to BRDFs containing the superposition of a quasi shift-invariant specular component and a diffuse component. This permits the use of efficient Fourier methods to solve the integral equations. These analytical solutions are verified via numerical simulation. In addition, we show experimental results from a light-field measurement studio equipped with a high-dynamic range scientific camera connected to a high-precision motorized stage. This studio is capable of measuring light fields with high accuracy. Experimental results of reconstructed light-fields will be reported.