Andrei Lugovtsov , Georgy Kavenkov , Alexander Shtanko , Sergey Kalenkov , Sergey Nikitin , Alexey Semenov [1, 5], Alexander Priezzhev [1, 5]
 International Laser Center, M.V. Lomonosov Moscow State University, Leninskye Gory, 1-62, 119991, Moscow, Russian Federation
 Microholo Ltd, Raushskaya nab., 4/5, 115035, Moscow, Russian Federation
 Moscow State University of Technology “Stankin”, Vadkovskiy per., 1, 127994, Moscow, Russian Federation
 Moscow Polytechnic University, Bolshaya Semenovskaya ul., 38, 107023, Moscow, Russian Federation
 Department of Physics, M.V. Lomonosov Moscow State University, Leninskye Gory, 1-2, 119991, Moscow, Russian Federation
The laser beam diffraction by an ensemble of red blood cells is considered. An algorithm, which allows for determining the dispersion of the erythrocyte size parameter and the asymmetry of the distribution in sizes for the erythrocytes using the laser diffractometry and hyperspectral holography is presented.
Laser diffractometry is an advanced optical techniques used for in vitro determination of the sizes and ability of red blood cells (RBCs) to deform and change their shape when passing through capillaries with small diameters . In this method, the diffraction of laser beam on a suspension of RBCs is observed. The concentrations of the particles in suspension usually are chosen very small so that single light scattering condition in the gap is met. The laser beam diffraction pattern (DP) has an axial symmetry and represents a system of concentric dark and light rings. The rings radii and brightness depend on the particles sizes and shapes. The isointensity lines in the DP can be very well approximated by a system of dark and light rings on a screen. Since the resulting diffraction pattern is superposition of diffraction patterns from large number of red blood cells through which the laser beam passes this technique allows us to assess mean sizes of the erythrocytes.
Our studies  show that laser ektacytometry can be used not only to measure the mean cells sizes in suspension but also to measure the parameters of the distribution of erythrocytes in sizes. For correct interpretation of the measurement results one needs a theoretical model, which relates the experimentally measured parameters (size and shape of the DP isointensity curves) with the parameters of particles. In this paper, we present a straightforward theory of laser diffractometry. We have obtained the analytical expressions for laser diffraction by a set of transparent elliptical discs mimicking RBCs. However, practical implementation of these possibilities requires a specific information about diffraction pattern as well as information about particles shape which we use in our mathematical model which relate the DP parameters with erythrocyte size distribution.
In this work the method laser diffractometry was supplemented by hyperspectral holography technique [3, 4] to clarify the real cell shapes and obtain DPs with wide dynamic range. We derive the necessary diffractometric equations, as well as describe the procedure for the preparation of blood samples (smears). In addition, verification experiments of suggested data processing algorithm are presented.
Acknowledgements: This work was supported by the RFBR grants № 17-29-03507-ofi_m.
 M. Musielak, Red blood cell-deformability measurement: Review of techniques, Clinical Hemorheology and Microcirculation 42(1), 47–64 (2009)
 S.Yu. Nikitin, M.A. Kormacheva, A.V. Priezzhev, A.E. Lugovtsov, Laser beam scattering on an inhomogeneous ensemble of elliptical discs modeling red blood cells in an ektacytometer, Quantum Electronics, 43(1), p. 90 (2013)
 S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, "Spectrally-spatial fourier-holography," Opt. Express 21, 24985-24990 (2013)
 S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, "Hyperspectral holography: an alternative application of the Fourier transform spectrometer," J. Opt. Soc. Am. B 34, B49-B55 (2017)
Dr. Andrei Egorovich Lugovtsov
International Laser Center of M.V. Lomonosov Moscow State University, Ph.D., reseacher
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