Phase retrieval from intensity measurements in one-parameter canonical-transform systems

M.J. Bastiaans, K.B. Wolf

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Samenvatting

Phase retrieval and local frequency estimation of a signal from intensity profiles are important problems in radio location, optical signal processing, quantum mechanics, and other fields. Several successful iterative algorithms for phase reconstruction from the squared modulus of the signal and its power spectrum, or its Fresnel spectrum, have been proposed recently, and related techniques are applied in various regions of the electromagnetic spectrum and in quantum mechanics. The development of non-iterative procedures for generic systems remains an attractive research topic. A non-iterative approach for phase retrieval, based on the so-called transport-of-intensity equation in optics, was proposed by Teague [1] and then further developed by others. It was shown that the longitudinal derivative of the Fresnel spectrum is proportional to the transversal derivative of the product of the instantaneous power and the instantaneous frequency of the signal. A similar procedure was proposed for the fractional Fourier transform [2]. In this paper we show that a non-iterative formulation applies for general one-parameter canonical transforms [3]. We show that the local frequency (the first derivative of the phase of the signal) is directly related to the derivative of the squared modulus of the one-parameter canonical transform with respect to the parameter, and given by the evolution Hamiltonian of the optical medium. From this relationship we conclude that the phase of the signal can be reconstructed by letting it propagate in such systems, and measuring the intensity profiles of the signal for two close values of the parameter. [1] M. R. Teague, "Deterministic phase retrieval: a Green function solution," J. Opt. Soc. Am., vol. 73, pp. 1434-1441, 1983. [2] T. Alieva, M. J. Bastiaans, and LJ. Stankovic, "Signal reconstruction from two close fractional Fourier power spectra," IEEE Trans. Signal Process., vol. 51, pp. 112-123, 2003. [3] K. B. Wolf, Integral Transforms in Science and Engineering, Chap. 9, Plenum Press, New York, 1979.
Originele taal-2Engels
TitelProceedings of the 14th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2003) 26 - 27 November 2003, Veldhoven, the Netherlands
Plaats van productieUtrecht, the Netherlands
UitgeverijSTW Technology Foundation
Pagina's319-322
ISBN van geprinte versie90-73461-39-1
StatusGepubliceerd - 2003
Evenement2003 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2003) - Veldhoven, Nederland
Duur: 26 nov 200327 nov 2003

Congres

Congres2003 Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2003)
Verkorte titelProRISC 2003
LandNederland
StadVeldhoven
Periode26/11/0327/11/03
AnderProRISC 2003, Veldhoven, the Netherlands

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  • Citeer dit

    Bastiaans, M. J., & Wolf, K. B. (2003). Phase retrieval from intensity measurements in one-parameter canonical-transform systems. In Proceedings of the 14th ProRISC, Annual Workshop on Circuits, Systems and Signal Processing (ProRISC 2003) 26 - 27 November 2003, Veldhoven, the Netherlands (blz. 319-322). Utrecht, the Netherlands: STW Technology Foundation.