Abel transform inversion using Kalman filter

E. González-Ramírez; E. de la Rosa Miranda; J. G. Arceo-Olague; J. J. Villa-Hernández; Ismael de la Rosa Vargas; Tonatiuh Saucedo Anaya; L. R. Berriel-Valdos; Ma Auxiliadora Araiza-Esquivel

doi:10.1117/12.2025494

18 November 2013 Abel transform inversion using Kalman filter

E. González-Ramírez, E. de la Rosa Miranda, J. G. Arceo-Olague, J. J. Villa-Hernández, Ismael de la Rosa Vargas, Tonatiuh Saucedo Anaya, L. R. Berriel-Valdos, Ma Auxiliadora Araiza-Esquivel

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Proceedings Volume 8785, 8th Iberoamerican Optics Meeting and 11th Latin American Meeting on Optics, Lasers, and Applications; 8785B6 (2013) https://doi.org/10.1117/12.2025494
Event: 8th Ibero American Optics Meeting/11th Latin American Meeting on Optics, Lasers, and Applications, 2013, Porto, Portugal

Abstract

Refractive index, temperature, pressure, velocity and many other physical magnitudes of phase objects in the refraction less limit are of great interest in engineering and science. Optical tomography is a technique used to estimate these magnitudes. For axially symmetrical phase objects the tomographic reconstruction can be carried out from just one projection when using Abel transform. However, for noisy projections the reconstruction shows low quality. This quality can be improved when using the Kalman filter to compute the inverse Abel Transform. In this paper a tomographic reconstruction method for syntectic axially symmetrical phase objects using Kalman filter is presented.

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E. González-Ramírez, E. de la Rosa Miranda, J. G. Arceo-Olague, J. J. Villa-Hernández, Ismael de la Rosa Vargas, Tonatiuh Saucedo Anaya, L. R. Berriel-Valdos, and Ma Auxiliadora Araiza-Esquivel "Abel transform inversion using Kalman filter", Proc. SPIE 8785, 8th Iberoamerican Optics Meeting and 11th Latin American Meeting on Optics, Lasers, and Applications, 8785B6 (18 November 2013); https://doi.org/10.1117/12.2025494

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