Directional edge enhancement in optical tomography of thin phase objects.

Abstract

In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projection data leaving the slice of a thin phase object. These modified projections are stacked in such a way that they form a modified sinogram called Hilbert-sinogram. We prove that the inverse Radon-transform of this sinogram is the directional Hilbert-transform of the slice function, and the reconstructed image is the directional edge enhancement of the distribution function on the slice. The Hilbert-transform is implemented by a 4f optical Fourier-transform correlator and a spatial filter consisting of a phase step of π radians. One important feature of this proposal is to perform a turn of 180° in the spatial filter at a certain value of the projection angle within the range [0°, 360°]. The desired direction of enhancement can be chosen by the proper selection of such turning angle. We present both the mathematical modeling and numerical results.

DOI: 10.1364/OE.19.002608

Cite this paper

@article{MenesesFabin2011DirectionalEE, title={Directional edge enhancement in optical tomography of thin phase objects.}, author={Cruz Meneses-Fabi{\'a}n and Areli Montes-Perez and Gustavo Rodr{\'i}guez-Zurita}, journal={Optics express}, year={2011}, volume={19 3}, pages={2608-18} }