Geodesic
Some inverse problems of Fourier optics
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 332-341

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We consider a general formulation of the problem of signal reconstruction from incomplete a priori information about it and measurements of the intensity of its Fourier transform. Some special cases are studied when a priori information is the even or odd part of the signal, as well as the real or imaginary part of the signal. Exact solutions in quadratures are constructed. An algorithm for solving the problem is proposed when only the signal and image intensities are known.
Keywords: Fourier transforms, inverse problems of optics, Gerchberg–Saxton algorithm. 
@article{CMFD_2023_69_2_a9,
     author = {V. \`E. Petrov},
     title = {Some inverse problems of {Fourier} optics},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {332--341},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a9/}
}
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V. È. Petrov. Some inverse problems of Fourier optics. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 332-341. http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a9/