## Fast algorithm for chirp transforms with zooming-in ability and its applications

JOSA A, Vol. 17, Issue 4, pp. 762-771 (2000)

http://dx.doi.org/10.1364/JOSAA.17.000762

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### Abstract

A general fast numerical algorithm for chirp transforms is developed by using two fast Fourier transforms and employing an analytical kernel. This new algorithm unifies the calculations of arbitrary real-order fractional Fourier transforms and Fresnel diffraction. Its computational complexity is better than a fast convolution method using Fourier transforms. Furthermore, one can freely choose the sampling resolutions in both *x* and *u* space and zoom in on any portion of the data of interest. Computational results are compared with analytical ones. The errors are essentially limited by the accuracy of the fast Fourier transforms and are higher than the order

© 2000 Optical Society of America

**OCIS Codes**

(050.1590) Diffraction and gratings : Chirping

(050.1940) Diffraction and gratings : Diffraction

(070.2590) Fourier optics and signal processing : ABCD transforms

(350.6980) Other areas of optics : Transforms

**History**

Original Manuscript: July 16, 1999

Revised Manuscript: December 7, 1999

Manuscript Accepted: December 22, 1999

Published: April 1, 2000

**Citation**

Xuegong Deng, Bipin Bihari, Jianhua Gan, Feng Zhao, and Ray T. Chen, "Fast algorithm for chirp transforms with zooming-in ability and its applications," J. Opt. Soc. Am. A **17**, 762-771 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-4-762

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