INVERSE PROBLEMS IN PHASE-SPACE OPTICS
Keywords:
Inverse problems in optics, interferometry, phase media, Abel transformation, Gladstone–Dale formula, axisymmetric inhomogeneity.Abstract
This article addresses the theoretical and practical aspects of solving inverse problems in the optics of phase media, specifically the reconstruction of the wavefront phase based on the results of interferometric studies. The authors consider two main types of inhomogeneities: two-dimensional and axisymmetric. The paper describes in detail the geometric and photometric methods for decoding interferograms. Particular attention is paid to the mathematical relationship between the refractive index and the density of the medium via the Gladstone–Dale formula. For axisymmetric objects, a solution is presented using the Abel transformation, and various approximation methods (Chardin, Likhushin, Emelyanov) are analyzed, which allow for improved accuracy in reconstructing density fields in supersonic gas flows and other physical objects.
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