Abstract
A new method for image reconstruction from holograms with a high spatial resolution based on hologram shifts by values smaller than the size of aperture is considered. The method uses the discretization equation obtained with the help of generalized functions. Mathematical modeling of the process of reconstruction of a high-resolution image from low-resolution holograms is performed. The proposed method can be used to obtain digital holograms with the help of the photodetector array with a low resolution. This method does not require solving directly a large-dimensional system of algebraic equations.
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REFERENCES
E. N. Leith and J. Upatnieks, ‘‘Reconstructed wavefronts and communication theory,’’ J. Opt. Soc. Am. 52, 1123–1130 (1962). https://doi.org/10.1364/JOSA.52.001123
R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic Press, New York, 1971).
Handbook of Optical Holography, Ed. by H. J. Caulfield (Academic Press, New York, 1979).
M. Miller, Holografue: Teoretické a Expreimentální Základy a Její Použití (SNTL—Nakladatelství Technické Literatury, Praha, 1974).
V. I. Guzhov, S. P. Il’inykh, and S. V. Khaibullin, ‘‘Phase information recovery based on the methods of phase shifting interferometry with small angles between interfering beams,’’ Optoelectron., Instrum. Data Process. 53, 288–293 (2017). https://doi.org/10.3103/S875669901703013X
M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, ‘‘Super-resolution in digital holography by a two-dimensional dynamic phase grating,’’ Opt. Express 16, 17107–17118 (2008). https://doi.org/10.1364/OE.16.017107
D. Claus, ‘‘High resolution digital holographic synthetic aperture applied to deformation measurement and extended depth of field method,’’ Appl. Opt. 49, 3187–3198 (2010). https://doi.org/10.1364/AO.49.003187
A. E. Tippie, A. Kumar, and J. R. Fienup, ‘‘High-resolution synthetic-aperture digital holography with digital phase and pupil correction,’’ Opt. Express 19, 12027–12038 (2011). https://doi.org/10.1364/OE.19.012027
S. V. Blazhevich and E. S. Selyutina, ‘‘Improvement of resolution of digital image using subpixel scanning,’’ Nauchn. Ved. Belgorod. Gos. Univ. Ser.: Mat. Fiz., No. 5, 186–190.
V. I. Guzhov, S. P. Il’inykh, and I. O. Marchenko, ‘‘Method of increasing the spatial resolution in digital holographic microscopy,’’ Optoelectron., Instrum. Data Process. 54, 301–306 (2018). https://doi.org/10.3103/S8756699018030135
V. S. Vladimirov, Generalized Functions in Mathematical Physics (Nauka, Moscow, 1979).
I. M. Gel’fant and G. E. Shilov, Generalized Functions and Actions upon Them (Gos. Izd-vo Fiz.-Mat. Literatury, Moscow, 1959).
I. M. Gel’fant and G. E. Shilov, Space of Basic and Generalized Functions (Gos. Izd-vo Fiz.-Mat. Literatury, Moscow, 1958).
S. T. Vaskov, V. M. Efimov, and A. L. Reznik, ‘‘Fast digital image and signal reconstruction by the minimum energy criterion,’’ Optoelectron., Instrum. Data Process. 39 (4), 11–17.
V. I. Guzhov, I. O. Marchenko, E. E. Trubilina, and A. A. Trubilin, ‘‘Sampling signals with finite set of apertures,’’ Omskii Nauchn. Vestn., No. 1, 55-58 (2021). https://doi.org/10.25206/1813-8225-2021-175-55-58
V. I. Guzhov, I. O. Marchenko, and E. E. Trubilina, ‘‘Increasing the spatial resolution of signals in optical systems,’’ Komp’yut. Opt. 46 (1), 65–70 (2022). https://doi.org/10.18287/2412-6179-CO-924
V. I. Guzhov, Computer Holography (Izd-vo Novosibirskogo Gos. Tekh. Univ., Novosibisrk, 2018).
Stereoscopic Microsope MBS-10. User’s Guideline ATsZ.850.005 RE. http://www.mbs10.ru/pdf/MBS-10_manual.pdf. Cited March 11, 2022.
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Translated by E. Smirnova
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Guzhov, V.I., Il’inykh, S.P., Zakharov, K.V. et al. Reconstruction of Images from a Series of Holograms Registered with a Low Resolution with the Help of a New Discretization Equation. Optoelectron.Instrument.Proc. 58, 425–429 (2022). https://doi.org/10.3103/S8756699022040082
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DOI: https://doi.org/10.3103/S8756699022040082