Efficient computation of quadratic-phase integrals in optics
Özaktaş, H. M.
Kutay, M. A.
Optical Society of America
35 - 37
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Please cite this item using this persistent URLhttp://hdl.handle.net/11693/11423
Received June 29, 2005; revised manuscript received August 22, 2005; accepted September 12, 2005 We present a fast N log N time algorithm for computing quadratic-phase integrals. This three-parameter class of integrals models propagation in free space in the Fresnel approximation, passage through thin lenses, and propagation in quadratic graded-index media as well as any combination of any number of these and is therefore of importance in optics. By carefully managing the sampling rate, one need not choose N much larger than the space–bandwidth product of the signals, despite the highly oscillatory integral kernel. The only deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus the algorithm computes quadratic-phase integrals with a performance similar to that of the fast-Fourier-transform algorithm in computing the Fourier transform, in terms of both speed and accuracy. © 2006 Optical Society of America