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On the numerical solution of the inverse problem of \(X\)-ray diffraction optics. (English. Russian original) Zbl 0817.65133
Comput. Math. Math. Phys. 33, No. 9, 1215-1219 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 9, 1377-1382 (1993).
Summary: The two-dimensional inverse problem of synthesizing X-ray diffraction optical elements based on crystals with modulated crystal lattice deformation is investigated. The existence and uniqueness of a solution is proved in a kinematic approximation. An iterative procedure for solving the inverse problem in a dynamic approximation is proposed and its convergence is demonstrated.
MSC:
65Z05 Applications to the sciences
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
35R30 Inverse problems for PDEs
78A40 Waves and radiation in optics and electromagnetic theory
78A45 Diffraction, scattering
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