## Phase retrieval of images using Gaussian radial bases |

Applied Optics, Vol. 52, Issue 36, pp. 8627-8633 (2013)

http://dx.doi.org/10.1364/AO.52.008627

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### Abstract

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction pattern’s frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transform’s modulus, without background constraints. A practical example is shown.

© 2013 Optical Society of America

**OCIS Codes**

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

(100.3190) Image processing : Inverse problems

(100.5070) Image processing : Phase retrieval

(110.2990) Imaging systems : Image formation theory

(100.3175) Image processing : Interferometric imaging

(110.3175) Imaging systems : Interferometric imaging

**ToC Category:**

Image Processing

**History**

Original Manuscript: October 4, 2013

Revised Manuscript: November 13, 2013

Manuscript Accepted: November 13, 2013

Published: December 11, 2013

**Citation**

Russell Trahan and David Hyland, "Phase retrieval of images using Gaussian radial bases," Appl. Opt. **52**, 8627-8633 (2013)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-36-8627

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