This paper discuses the problem of reconstructing images in digital form with resolution that exceeds the limiting resolution of a diffraction-limited system from a set of images with spatially modulated illumination. The reconstruction method described here is based on a numerical–analytical solution of the problem of minimizing the mismatch functional of an array of recorded images with their mathematical model. Models of planar and three-dimensional objects are considered, and the effectiveness of the proposed method in computational experiments is demonstrated. By comparison with the classical reconstruction method, the proposed method is distinguished by good stability against deviations of the system parameters from the calculated values, allows the spatial-modulation parameters of the illumination to be automatically estimated, and makes it possible to use a priori knowledge concerning the signal to be reconstructed. Our results can be used when programs are being developed for reconstructing images in structured-illumination microscopy.
© 2020 Optical Society of America
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