Variational regularization of complex deautoconvolution and phase retrieval in ultrashort laser pulse characterization. (8th February 2016)

• Record Type: Journal Article
• Authors: Anzengruber, Stephan W; Bürger, Steven; Bernd Hofmann, ; Steinmeyer, Günter
• Is Part Of: Inverse problems. Volume 32:Number 3(2016:Mar.)
• Publication Date: 2016-02-08
• Subjects: deautoconvolution -- phase retrieval -- regularization -- Ill-posed problem -- SD-SPIDER -- NURBS -- TIGRA; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/3/035002
• Languages: English
• ISSNs: 0266-5611

Abstract

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 the 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 limitations due to measurement deficits.