Image processing with the radial Hilbert transform: theory and experiments

Abstract

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement one-dimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented.

Broader view on extreme ultraviolet masks: adding complementary imaging modes to the SHARP microscope

“…15 The technique has been implemented, adding a vortex-like phase plate H p of the form H p ðr; φÞ ¼ expðiPφÞ to the back focal plane of an imaging system. 16 The phase plate retards the phase by P-times 2π along its circumference. Combination of phase modification and focusing power in a single optical element is demonstrated in Ref.…”

Orbital angular momentum light in microscopy

“…SPC is an optical implementation of the edge-enhancing transformation, replacing the numerical post-processing. Early attempts to implement a spiral phase filter in an optical set-up had already been made in the 1990s [21,22], and in [18] a proof-of-principle experiment with an SLM was carried out, taking an aperture as the object, before the effect was independently found and interpreted in the context of digital microscopy in [12].…”

Edge Enhancement Computed Tomography

“…Some have proposed to obtain the transform under a rectangular system [Davis et. al., 2000] with a sign filter and others say that it is possible to find the radial Hilbert transform with a spiral step filter [Davis et. al., 2000].…”