On the Stability of Reconstruction of Irregularly Sampled Diffraction Fields

Abstract

This paper addresses the problem of reconstruction of a monochromatic light field from data points, irregularly distributed within a volume of interest. Such setting is relevant for a wide range of three-dimensional display and beam shaping applications, which deal with physically inconsistent data. Two finite-dimensional models of monochromatic light fields are used to state the reconstruction problem as regularized matrix inversion. The Tikhonov method, implemented by the iterative algorithm of conjugate gradients, is used for regularization. Estimates of the model dimensionality are related to the number of degrees of freedom of the light field as to show how to control the data redundancy. Experiments demonstrate that various data point distributions lead to ill-poseness and that regularized inversion is able to compensate for the data point inconsistencies with good numerical performance.