## Direct method for phase retrieval from the intensity of cylindrical wave fronts

JOSA A, Vol. 16, Issue 7, pp. 1838-1844 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001838

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### Abstract

The phase-retrieval problem for a physical system with strong support constraints is investigated. Propagation of an optical field in a system with no variation along one transverse axis results in cylindrical wave fronts. Scalar propagation in such systems is a purely two-dimensional process. We show that, given the optical intensity in a plane, the phase of the wave field can be calculated directly if the system has this special symmetry. The procedure relies on a simple geometric relation between the system pupil function (or angular spectrum) and the system optical transfer function in the Debye theory of scalar wave focusing. The inherent autocorrelation operation can be undone, and the phase directly retrieved, with a simple coordinate transformation.

© 1999 Optical Society of America

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(050.1960) Diffraction and gratings : Diffraction theory

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(070.2590) Fourier optics and signal processing : ABCD transforms

(100.0100) Image processing : Image processing

(100.1830) Image processing : Deconvolution

(100.3190) Image processing : Inverse problems

(100.5070) Image processing : Phase retrieval

(120.5060) Instrumentation, measurement, and metrology : Phase modulation

**Citation**

Kieran G. Larkin and C. J. R. Sheppard, "Direct method for phase retrieval from the intensity of cylindrical wave fronts," J. Opt. Soc. Am. A **16**, 1838-1844 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1838

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