Development of Computational Algorithm for Reconstruction of Volumetric Images in X-Ray Computed Tomography Using Holographic Methods
DOI:
https://doi.org/10.14529/ctcr180401Keywords:
x-ray computed tomography, holography, two-dimensional and three-dimensional radon transformationAbstract
A computational algorithm for solving the inverse problem of x-ray tomography for reconstruction of the internal structure of micro objects in the near Fresnel zone using holographic methods of visualization of three-dimensional images is considered. Holographic methods do not provide a direct solution to the problem of reconstruction of the internal structure of the object. They can only solve the problem of volumetric display of some object surface. However, using data on the absorption of x-ray radiation of the object and phase-contrast holographic signals in the near Fresnel zone, the possibility of obtaining a three-dimensional holographic image of the inner layers of the object is shown. The solution of this complex problem required the use of three-dimensional (3D) Radon transformation of the internal function of the object and two-dimensional (2D) Radon transformation of phase-contrast holographic projection. An algorithm for reconstruction of phase-contrast tomographic images of the internal structure of the object was obtained and based on it a computational algorithm for the practical reconstruction of three-dimensional tomographic images of the internal structure of micro objects was developed. The results of the research were confirmed by mathematical modeling of the algorithm for reconstruction of three-dimensional images. For this purpose, a mathematical model of the test phantom was developed and phase-contrast projections were simulated for it with subsequent reconstruction of phase-contrast tomographic images by tomographic methods using the program reenactor developed by the authors. A compact algorithm for reconstruction of phase-contrast tomographic images for experimental facilities for the study of small biological objects, when two arrays of measurements are carried out to obtain phase-contrast projections: measurements of brightness from the object on the detector in the near Fresnel zone and measurements from the object on the detector in the absorption zone. The practical application of the developed approach in obtaining phase-contrast tomographic images by tomographic methods can be found for the study of micro objects where high resolution is required in the image than in the application of classical CT methods.
References
Snigirev A., Snigireva I., Kohn V., Kuznetsov S., Schelokov I. On the Possibilities of X-Ray Phase Contrast Microimaging by Coherent High-Energy Synchrotron Radiation. Rev. Sci. Instrum., 1995, 66, pp. 5486–5492. DOI: 10.1063/1.1146073
Davis T., Gao D., Gureyev T., Stevenson A., Wilkins S. Phase Contrast Imaging of Weakly Absorbing Materials Using Hard X-Rays. Nature, 1995, 373, pp. 595–598. DOI: 10.1038/373595a0
Wilkins S.W., Gureyev T.E., Gao D., Pogany A., Stevenson A.W. Phase-Contrast Imaging Using Polychromatic Hard X-Rays. Nature, 1996, 384, pp. 335–338. DOI: 10.1038/384335a0
Cloetens P., Ludwig W., Baruchel J., Van Dyke D., Van Landuyt J., Guigay J.P., Schlenker M. Holotomography: Quantitative Phase Tomography with Micrometer Resolution Using Hard Synchrotron Radiation X-Rays. Appl. Phys. Let., 1999, 75, pp. 2912–2914. DOI: 10.1063/1.125225
Anastasio M.A., Shi D., De Carlo F., Pan X. Analytic Image Reconstruction in Local PhaseContrast Tomography. Phys. Med. Biol., 2004, 49, pp. 121–144. DOI: 10.1088/0031-9155/49/1/009
Groso A., Stampanoni M., Abela R., Schneider P., Linga S., Muller R. Phase Contrast Tomography: an Alternative Approach. Appl. Phys. Let., 2006, 88, p. 214104. DOI: 10.1063/1.2207221
Groso A., Abela R., Stampanoni M. Implementation of a Fast Method for High Resolution Phase Contrast Tomography. Optics Express, 2006, vol. 14, iss. 18, pp. 8103–8110. DOI: 10.1364/OE.14.008103
Gureyev T.E., Paganin D.M., Myers G.R., Nesterets Ya.I., Wilkins S. Phase-and-Amplitude Computer Tomography. Appl. Phys. Let., 2006, 89, p. 034102. DOI: 10.1063/1.2226794
Bronnikov A.V. Theory of Quantitative Phase-Contrast Computed Tomography. J. Opt. Soc. Am. A., 2002, vol. 19, no. 3, March, pp. 472–480. DOI: 10.1364/JOSAA.19.000472
Bronnikov A.V. Reconstruction Formulas in Phase-Contrast Tomography. Optics Communications, 1999, 171, pp. 239–244. DOI: 10.1016/S0030-4018(99)00575-1
Bronnikov A.V. Theory of Quantitative Phase-Contrast Computed Tomography. J. Opt. Soc. Am. A., 2002, 19, pp. 472–480. DOI: 10.1364/JOSAA.19.000472
Ярославский Л.П., Мерзляков Н.С. Цифровая голография. М.: Наука, 1982. 219 с. [Yaroslavskiy L.P., Merzlyakov N.S. Tsifrovaya golografiya [Digital Holography]. Moscow, Nauka Publ., 1982. 219 p.]
Gabor D. A New Microscopic Principle. Nature, 1948, 161, pp. 777–778. DOI: 10.1038/161777a0
Симонов Е.Н. Рентгеновская компьютерная томография: моногр. Снежинск: Изд-во РФЯЦ-ВНИИТФ, 2002. 364 с. [Simonov E.N. Rentgenovskaya komp'yuternaya tomografiya: monografiya [X-Ray Computer Tomography: Monograph]. Snezhinsk, RFNC VNIITF Publ., 2002. 364 p.]
Симонов Е.Н. Физика визуализации изображений в рентгеновской компьютерной томографии. Челябинск: Издат. центр ЮУрГУ, 2014. 505 с. Simonov E.N. Fizika vizualizatsii izobrazheniy v rentgenovskoy komp'yuternoy tomografii [Physics of Visualization of Images in a X-Ray Computer Tomography]. Chelyabinsk, South Ural St. Univ. Publ., 2014. 505 p.
