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

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