Compressive Imaging and Characterization of Sparse Light Deflection Maps

TL;DR

This paper introduces a compressed sensing-based method for efficiently acquiring and reconstructing sparse deflection spectra of transparent objects, enabling detailed surface characterization with fewer measurements and extracting main deflection directions directly.

Contribution

The paper presents a novel compressed sensing framework for deflectometric imaging that reduces measurement requirements and allows direct extraction of main deflection directions without full spectrum reconstruction.

Findings

Successful reconstruction of deflection spectra from simulated and experimental data.

Efficient extraction of main deflection directions with minimal measurements.

Demonstrated applicability on simple lenses and intra-ocular lenses.

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. We design those modulation patterns on the principle of spread spectrum CS for reducing the number of observations. The ability of our device to simultaneously observe the deflection spectra on a dense discretization of the object surface is related to a Multiple Measurement Vector (MMV) model. This scheme allows us to estimate both the noise power and the instrumental point spread function. We formulate the spectrum reconstruction task as the solving of a linear inverse problem regularized by an analysis sparsity prior using a translation invariant wavelet frame. Our results demonstrate the capability and advantages of using a CS based approach for deflectometric imaging both on simulated data and experimental deflectometric data. Finally, the paper presents an extension of our method showing how we can extract the main deflection direction in each point of the object surface from a few compressive measurements, without needing any costly reconstruction procedures. This compressive characterization is then confirmed with experimental results on simple plano-convex and multifocal intra-ocular lenses studying the evolution of the main deflection as a function of the object point location.