Efficient computation of quadratic-phase integrals in optics.
We present a fast NlogN 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.
Ozaktas
Haldun M
HM
Department of Electrical Engineering, Bilkent University, TR-06800, Bilkent, Ankara, Turkey. haldun@ee.bilkent.edu.tr
Koç
Aykut
A
Sari
Ilkay
I
Kutay
M Alper
MA