Geodesic
Numerical methods and algorithms for reconstruction of holographic images with an flexibility choice of physical size of the object and observation area
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 1, pp. 99-110
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Within the framework of this work, the numerical results of simulation and reconstruction of holographic images with different physical sizes of the object and observation areas are presented. Simple and practical approaches to relatively flexibility choice of physical areas (e. g., units of $m^2$) in both planes are proposed. Algorithms are presented in the case when the dimensions of the plane of the object and observation coincide. Two-step scattering algorithms are presented for the simulation and reconstruction of holographic images with a relatively flexibility choice of the physical areas of the object plane and observation.
Keywords: electron holography, digital image processing, Fresnel method, angular spectrum method.
Mots-clés : Fourier transform 
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A. G. Fedorov; V. V. Trofimov; A. G. Karpov. Numerical methods and algorithms for reconstruction of holographic images with an flexibility choice of physical size of the object and observation area. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 1, pp. 99-110. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_1_a7/

[1] Gabor V., “A new microscope principle”, Nature, 161 (1948), 777–778 | DOI

[2] Fink H.-W., Stocker W., Schmid H., “Holography with low-energy electrons”, Phys. Rev. Lett., 65:10 (1990), 1204–1206 | DOI

[3] Egorov N. V., Karpov A. G., Antonova L. I., Fedorov A. G., Trofimov V. V., “Technique for investigating the spatial structure of thin films at a nanolevel”, Journal of Surface Investigation: $X$-Ray, Synchrotron and Neutron Techniques, 5:5 (2011), 992–995 | DOI

[4] Karpov A. G., Trofimov V. V., Fedorov A. G., “Information and program support of the analysis and processing of holographic information”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Process, 17:4 (2021), 409–418 (In Russian) | DOI

[5] Goodman J. W., Introduction to Fourier optics, Second ed., The McGraw-Hill Companies, New York, 1988, 457 pp.

[6] Schmidt J. W., Numerical simulation of optical wave propagation with examples in MATLAB, SPIE, Bellingham, 2010, 133–146

[7] Schnars U., Juptner W. P. O., “Digital recording and numerical reconstruction of holograms”, Meas. Sci. Technol., 13 (2002), 85–101 | DOI

[8] Latychevskaia T., “Practical algorithms for simulation and reconstruction of digital in-line holograms”, Applied Optics, 54 (2015), 2424–2434 | DOI

[9] Molony K. M., Hennelly B. M., Kelly D. P., Naughton T. J., “Reconstruction algorithms applied to in-line Gabor digital holographic microscopy”, Optics Communications, 283 (2010), 903–909 | DOI

[10] Kreis T. M., Juptner W. P. O., “Suppression of the dc term in digital holography”, Optical Engineering, 36 (1997), 2357–2360 | DOI

[11] Latychevskaia T., Fink H.-W., “Solution to the Twin Image Problem in holography”, Phys. Rev. Lett., 98:233901 (2007)

[12] Ersoy O. K., Diffraction, Fourier optics, and imaging, John Wiley and Sons Inc., New Jersey, 2007, 429 pp. | MR | Zbl

[13] Voelz D. G., Computational Fourier optics: a MATLAB tutorial, SPIE, Bellingham, 2010, 199–205

[14] Schmidt J. D., Numerical simulation of optical wave propagation with examples in MATLAB, SPIE, Bellingham, 2010, 115–130 | MR

[15] Kim M. K., “Principles and techniques of digital holographic microscopy”, SPIE, 1 (2010), 018005, 50 pp.