**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30848

##### Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method

**Authors:**
M. K. Balyan

**Abstract:**

The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

**Keywords:**
dynamical diffraction,
hologram,
object image,
X-ray holography

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1127004

**References:**

[1] R. G. Collier, Ch. B. Burckhardt, L. H. Lin, “Optical holography”, New York and London, Academic Press, 1971.

[2] P. Hariharan, “Basics of holography”, New York, Cambridge University Press, 2002.

[3] “Handbook of optical holography”, H. J. Caulfield, Ed., Bedford, Massachusets, Aerodyne research Inc., 1979.

[4] V. V. Aristov, G. V. Ivanova, “On the possibility of utilizing holographyc schemes in X-ray microscopy”, J. Appl. Cryst., v. 12, pp. 19-24, Febr. 1979.

[5] A. M. Egiazaryan and P. A. Bezirganyan, “The recording of X-ray short-wave hologram”, Proc. Nat. Acad. Sci. Armen. Phys., v. 15, pp.35-43, 1980 (in Russian).

[6] A. M. Egiazaryan, “The new perspectives of development of X-ray short-wave holography”, JTP, Pisma, v.24, pp.55-59, 1998 (in Russian).

[7] A. M. Egiazaryan, K. G. Trouni and A. R. Mkrtchyan, “X-ray interferometric short-wavelength holography with diffraction focusing”, JETP Letters, v.68, pp.711-715, 1998.

[8] K. T. Gabrielyan, “Using of crystal-diffraction image for obtaining visible image of an X-ray source”, JTP, Pisma, v.16, pp.5-9, 1990 (In Russian).

[9] A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov and I. Schelokov, “On the possibilities of X-ray phase-contrast microimaging by coherent high-energy synchrotron radiation”, Rev. Sci. Instrum., v.66, pp.5486-5492, 1995.

[10] K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin and Z. Barnea, “Quantitative phase imaging using hard X-rays”, Phys. Rev. Lett., v.77, pp.2961-2964, 1996.

[11] D. M. Paganin, “Coherent X-ray Optics”, Oxford, Oxford University Press, 2006.

[12] N. Watanabe, H. Yokosuka, T. Ohogashi, H. Takano, A. Takeuchi, Y. Suzuki and S. Aoki, “Optical holography in the hard X-ray domain”, J. Phys IV France, v.104, pp. 551-556, 2003.

[13] W. Leitenberger and A. Snigirev, “Microscopic imaging with high energy X-rays by Fourier transform holography”, J. Appl.Phys., v.90, pp. 538-544, 2001.

[14] H. Iwamoto and N. Yagi, “Hard X-ray Fourier transform holography from an array of oriented referenced objects”, J. Synchrotron Rad., v.18, pp. 564-568, 2011.

[15] M.K. Balyan, “Double slit dynamical diffraction of X-rays in ideal crystals (Laue case)”, Acta Cryst., v. A66, pp. 660-668, 2010.

[16] A. Momose, “Demonstration of phase contrast X-ray computed tomography using an X-ray interferometer”, Nucl. Instr. Meth., v.A352, pp. 622-628, 1995.

[17] M. K. Balyan, “X-ray dynamical diffraction Fraunhofer holography”, J. Synchrotron Rad., v.20, pp. 749-755, 2013.

[18] M. K. Balyan, “Numerical reconstruction of an object image using an X-ray dynamical diffraction Fraunhofer hologram”, J. Synchrotron Rad., v.21, pp. 127-130 (2014).

[19] M. K. Balyan, “Object image correction using an X-ray dynamical diffraction Fraunhofer hologram”, J. Synchrotron Rad., v.21, pp. 449-451, 2014.

[20] M. K. Balyan, “X-ray crystal-diffraction Fourier holography”, J. Contemp. Phys. Arm. Acad. Sci., v.50, pp.394-403, 2015.

[21] M. K. Balyan, “X-ray interferometric Fresnel holography”, J. Contemp. Phys. Arm. Acad. Sci., v.51, pp.79-88, 2016.

[22] M. K. Balyan, “X-ray interferometric Fourier holography”, Proceed. of Natl. Acad. Sci. Arm., v.51, pp.388-401, 2016 (In Russian).

[23] A. Authier, “Dynamical Theory of X-ray Diffraction”, Oxford, Oxford University Press, 2001.

[24] Z. G. Pinsker, “X-ray crystalloptics”, Moscow, Nauka, 1982 (In Russian).

[25] V. L. Indenbom, F. N. Chukhovskii, "The problem of image formation in X-RAY optics", Sov. Phys. Usp., v.15, pp.298–317, 1972.