Isotropic edge-enhancement by the Hilbert-transform in optical tomography of phase objects

In optical tomography, isotropic edge-enhancement of phase-object slices under the refractionless limit approximation can be reconstructed using spatial filtering techniques. The optical Hilbert-transform of the transmittance function leaving the object at projection angles ϕ∈(0°,360°), is one of these techniques with some advantages. The corresponding irradiance of the so modified transmittance is considered as projection data, and is proved that they share two properties with the Radon transform: its symmetry property and its zeroth-moment conservation. Accordingly, a modified sinogram able to reconstruct edge-enhanced phase slices is obtained. In this paper, the theoretical model is amply discussed and illustrated both with numerical and experimental results.