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arXiv · 1508.00701

Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization

Stephan W. Anzengruber·Steven Buerger·Bernd Hofmann·Guenter Steinmeyer
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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 $L^2$-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.

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Stephan W. Anzengruber, Steven Buerger, Bernd Hofmann, Guenter Steinmeyer. 2015-08-04. Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization. https://doi.org/10.1088/0266-5611%2F32%2F3%2F035002

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