Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization
Abstract
The SD-SPIDER method for the characterization of ultrashort laser pulses requires the solution of a nonlinear integral equation of autoconvolution type with a device-based kernel function. Taking into account the analytical background of a variational regularization approach for solving the corresponding ill-posed operator equation formulated in complex-valued -spaces over finite real intervals, we suggest and evaluate numerical procedures using NURBS and the TIGRA method for calculating the regularized solutions in a stable manner. In this context, besides the complex deautoconvolution problem with noisy but full data, a phase retrieval problem is introduced which adapts to the experimental state of the art in laser optics. For the treatment of this problem facet, which is formulated as a tensor product operator equation, we derive well-posedness of variational regularization methods. Case studies with synthetic and real optical data show the capability of the implemented approach as well as its limitation due to measurement deficits.
Cite
@article{arxiv.1508.00701,
title = {Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization},
author = {Stephan W. Anzengruber and Steven Buerger and Bernd Hofmann and Guenter Steinmeyer},
journal= {arXiv preprint arXiv:1508.00701},
year = {2016}
}