Open AccessDirectional edge enhancement in optical tomography of thin phase objects
Author(s) -
Cruz Meneses-Fabián,
Areli Montes-Pérez,
Gustavo Rodríguez-Zurita
Publication year - 2011
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.19.002608
Subject(s) - hilbert transform , radon transform , fourier transform , optics , projection (relational algebra) , edge enhancement , transformation (genetics) , filter (signal processing) , spatial filter , hilbert spectral analysis , computer science , phase (matter) , point spread function , iterative reconstruction , algorithm , image processing , computer vision , mathematics , physics , mathematical analysis , image (mathematics) , biochemistry , chemistry , quantum mechanics , gene
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.