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Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain

Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain,10.1364/OL.21.000842,Optics Letters,Zeev Zalevsky,David Mendlovic,R

Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain   (Citations: 31)
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Journal: Optics Letters , vol. 21, no. 12, pp. 842-844, 1996
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    • ...Unlike the traditional Gerchberg-Saxton (GS) algorithm [3], we use the non-paraxial version of the angular spectrum of plane waves (ASPW) to propagate the fields from one plane to another [4, 5] (rather than the Fourier transform) allowing for the intensities from any plane to be used (not just the focal plane, and the plane just before the lens)...

    Pamela Bowlanet al. Phase retrieval and the measurement of the complete spatiotemporal ele...

    • ...In spite of the existence of several successful iterative algorithms for phase reconstruction from the squared modulus of the signal and its power spectrum, or its Fresnel spectrum, that were proposed recently [1]-[4], the development of noniterative procedures remains an attractive research topic...
    • ...Note that the Gerchberg-Saxton algorithm applied in the fractional Fourier domain for phase retrieval from two fractional FT power spectra for angles and + becomes unstable, and does not converge if < 15 [1], while our method works especially for small ...
    • ...Note that the noise robustness was not considered in [1]- [4], which papers were devoted to the recursive algorithms for phase retrieval from the fractional FT power spectra...

    Tatiana Alievaet al. Signal reconstruction from two close fractional Fourier power spectra

    • ...We consider Eq. (14) to be our main result, because it relates the phase derivative of the signal, p(x) in (1), with a convolution integral of the derivative of the signal intensity | (x)|2 with respect...
    • ...The integration of (1) recovers the signal phase (up to an overall constant) through ’(x) = R x p(x0) dx0...

    Martin J. Bastiaanset al. Phase reconstruction from intensity measurements in linear systems

    • ...The phase retrieval from intensity distributions is a very old problem, which can be solved in different ways, see for example [1, 2, 3, 4, 5]. In order to create a more optimal algorithm, all possible additional knowledge about an optical signal has to be taken into account...
    • ...Recently several methods of phase retrieval based on the properties of the fractional FT were proposed: iterative and recursive algorithms for phase recovering from the intensity distributions in two fractional FT domains were discussed in [4] and [5], respectively...
    • ...Therefore, our method of phase retrieval is based on other initial information than the Gerchberg-Saxton algorithm [4] or the recursive algorithm for phase retrieval in the fractional FT domain [5], which both use two fractional Fourier power spectra for phase reconstruction...

    Tatiana Alievaet al. Finite-mode analysis by means of intensity information in fractional o...

    • ...We can also use the fractional convolution for the application of beam shaping [28]...

    Soo-Chang Peiet al. Relations between fractional operations and time-frequency distributio...

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