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.
© 2006 Optical Society of America
Fourier Optics and Optical Signal Processing
Haldun M. Ozaktas, Aykut Koç, Ilkay Sari, and M. Alper Kutay, "Efficient computation of quadratic-phase integrals in optics," Opt. Lett. 31, 35-37 (2006)