On the Stability of Reconstruction of Irregularly Sampled Diffraction Fields

This paper addresses the problem of reconstruction of amonochromatic light field from data points, irregularlydistributed within a volume of interest. Such setting is relevantfor a wide range of three-dimensional display andbeam shaping applications, which deal with physically inconsistentdata. Two finite-dimensional models of monochromaticlight fields are used to state the reconstructionproblem as regularized matrix inversion. The Tikhonovmethod, implemented by the iterative algorithm of conjugategradients, is used for regularization. Estimates of themodel dimensionality are related to the number of degreesof freedom of the light field as to show how to control thedata redundancy. Experiments demonstrate that variousdata point distributions lead to ill-poseness and that regularizedinversion is able to compensate for the data pointinconsistencies with good numerical performance