Abstract
We consider the 3D coefficient inverse problem for parabolic wave equation. It involves determining the spatial distribution of refractive and absorption indices by processing phase diffraction patterns obtained by irradiating an object with a set of Gaussian beams. Unlike tomography and ptychography, rotation or scanning of the sample is not required. The problem is solved by expanding the wave field and the complex dielectric constant \(\varepsilon \left(\overrightarrow{r}\right)\) over the full set of Gaussian beam functions. To determine \(\varepsilon \left(\overrightarrow{r}\right),\) we obtain a nonlinear matrix equation. The condition of its solvability allows the selection of sampling frequencies by coordinates in accordance with the practical task.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Levy, Parabolic Equation Methods for Electromagnetic Wave Propagation, IET (2000).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Elsevier, Amsterdam (2013), Vol. 3, §40.
N. F. Mott and H. S. W. Massey, Theory of Atomic Collisions, 3rd ed., Oxford Univ. Press (1965).
M. Born and V. Fock, Zeitschrift für Physik, 51, 165 (1928).
E. Kieri, G. Kreiss, and O. Runborg, Adv. Appl. Math. Mech., 7, 687 (2015).
E. Abramochkin and V. Volostnikov, J. Opt. A: Pure Appl. Opt., 6, S157 (2004).
H. M. Moya-Cessa, I. Ramos-Prieto, D. Sánchez-de-la-Llave, et al., “Cauchy–Riemann beams,” arXiv: 2311.07825 (2023).
F.Wu, Y. Luo, and Z. Cui, Photonics, 10, 1041 (2023).
A. V. Goncharskii and S. Yu. Romanov, Comput. Math. Math. Phys., 52, 245 (2012).
T. I. Kuznetsova, Sov. Phys. Usp., 31, 364 (1988).
T. S. Argunova and V. G. Kohn, Physics-Uspekhi, 62, 602 (2019).
J. Rodenburg and A. Maiden, Ptychography, Springer Handbook of Microscopy, Springer Nature Switzerland AG (2019), p. 819.
T. Latychevskaia, Phys. Rev. Lett., 127, 063601 (2021).
C. Jacobsen, X-Ray Microscopy, Cambridge University Press (2019).
Z. Hu, Y. Zhang, P. Li, et al., Opt. Express, 31, 15791 (2023).
R. Bellman, Introduction to Matrix Analysis, Mcgraw-Hill, New York (1960), Ch. 10, §5.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Artyukov, I.A., Busarov, A.S., Popov, N.L. et al. An Approach to Direct 3D Imaging with Coherent Light. J Russ Laser Res 45, 278–285 (2024). https://doi.org/10.1007/s10946-024-10212-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-024-10212-7