Compressive Imaging and Characterization of Sparse Light Deflection Maps

Abstract

Light rays incident on a transparent object of uniform refractive index undergo deflections, which uniquely characterize the surface geometry of the object. Associated with each point on the surface is a deflection map (or spectrum) which describes the pattern of deflections in various directions. This article presents a novel method to efficiently acquire and reconstruct sparse deflection spectra induced by smooth object surfaces. To this end, we leverage the framework of compressed sensing (CS) in a particular implementation of a schlieren deflectometer, i.e., an optical system providing linear measurements of deflection spectra with programmable spatial light modulation patterns. In particular, we design those modulation patterns on the principle of spread spectrum CS for reducing the number of observations. Interestingly, the ability of our device to simultaneously observe the deflection spectra on a dense discretization of the object surface is related to a particular multiple measurement vector mode...