Abel Transform Inversion using Kalman Filter

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.