Journal ArticleDOI
Optical implementation of the fractional Hilbert transform for two-dimensional objects.
TLDR
This work shows how to implement the fractional Hilbert transform for two-dimensional inputs, which is now suitable for image processing.Abstract:
The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is π-phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.read more
Citations
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Journal ArticleDOI
Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform.
TL;DR: A novel two-dimensional transform is developed in terms of two multiplicative operators: a spiral phase spectral (Fourier) operator and an orientational phase spatial operator that results in a meaningfulTwo-dimensional quadrature (or Hilbert) transform.
Journal ArticleDOI
Image processing with the radial Hilbert transform: theory and experiments
TL;DR: A radially symmetric Hilbert transform is introduced that permits two-dimensional edge enhancement and is implemented with a programmable phase-only liquid-crystal spatial light modulator.
Journal ArticleDOI
Spiral phase filtering and orientation-selective edge detection/enhancement
TL;DR: It is found that one can achieve anisotropic edge enhancement by breaking down the symmetry of the filtering process and interpreting this process as a vortex formation due to the diffraction of the Fourier spectrum of the input pattern by a SPF with an integer and fractional topological charge.
Book ChapterDOI
IV: Fractional Transformations in Optics
TL;DR: The chapter explores the fractionalization procedure of Zernike's phase contrast microscope, a spatial filtering process similar to the optical Hilbert transformation that provides the applications of several fractional transformations.
Journal ArticleDOI
Analysis of the fractional Hilbert transform
TL;DR: A one- dimensional fractional Hilbert transform acting on a one-dimensional rectangle function is analyzed and it is shown how it produces an output image that is selectively edge enhanced.
References
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Journal ArticleDOI
Fractional Hilbert transform.
TL;DR: The Hilbert transform is generalized by defining the fractional Hilbert transform (FHT) operation, which is characterized by two parameters.
Journal ArticleDOI
Observation of phase objects by optically processed hilbert transform
Serge Lowenthal,Yves Belvaux +1 more
TL;DR: In this article, a method for observing phase objects based on the Hilbert transform is defined, which is achieved by spatial filtering, and the amplitude images obtained are characterized by their high luminosity.
Journal ArticleDOI
Isotropic Hilbert spatial filtering
J.K.T. Eu,Adolf W. Lohmann +1 more
TL;DR: In this article, a modified Hilbert transform spatial filtering method is presented that does not suffer from angular anisotropy, where the image will also change its appearance drastically when rotating the object.
Journal ArticleDOI
Controle de l'etat de surface ou d'homogeneïte de materiaux optiques “par contraste de phase” a dephasage quelconque
Y. Belvaux,J.C. Vareille +1 more
TL;DR: In this article, the authors describe a method of observation of very small phase defects by spatial filtering, where the filter is an absorbing screen, and the phase-shift introduced is quite unimportant, and therefore need not be known.