Abstract

The recovery of the true intensity dependence of some nonlinear-optical process from discrete, noisy, spatially and/ or temporally averaged data by a collocation scheme employing polynomial splines is discussed. Regularization of this Volterra-type inversion problem is achieved by constraining the discontinuities in the highest derivatives of the splines at the knots. A general theoretical formulation is given, and the method is applied to specific, simulated experimental conditions. Thus guidelines are established for choosing optimum values for the spline and regularization parameters. Surprisingly, linear splines yield the best fidelities. This scheme is compared with that of Tikhonov regularization.

© 1990 Optical Society of America

Inversion of ellipsometry data using constrained spline analysis

Mickaël Gilliot
Appl. Opt. 56(4) 1173-1182 (2017)

Hybrid regularization method for the ill-posed inversion of multiwavelength lidar data in the retrieval of aerosol size distributions

Christine Böckmann
Appl. Opt. 40(9) 1329-1342 (2001)

Invariant recovery of curves in m-dimensional space from sparse data

Robert L. Stevenson and Edward J. Delp
J. Opt. Soc. Am. A 7(3) 480-490 (1990)

Information-content analysis of aureole inversion methods: differential kernel versus normal

Michael A. Box and Gabriel Viera
J. Opt. Soc. Am. A 7(6) 1015-1018 (1990)

Probabilistic regularization in inverse optical imaging

Enrico De Micheli and Giovanni Alberto Viano
J. Opt. Soc. Am. A 17(11) 1942-1951 (2000)