A method of computation of 2D Fourier transforms and diffraction integrals with applications in vision science

Applied and Computational Mathematics Seminar
Monday, March 30, 2015 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Professor Andrei Martinez-Finkelshtein – University of Almería
Martin Short
The importance of the 2D Fourier transform in mathematical imaging and vision is difficult to overestimate. For instance, the impulse response of an optical system can be defined in terms of diffraction integrals, that are in turn Fourier transforms of a function on a disk. There are several popular competing approaches used to calculate diffraction integrals, such as the extended Nijboer-Zernike (ENZ) theory. In this talk, an alternative efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions is discussed. Its outcome is a rapidly converging series expansion for the integrals, allowing for their accurate calculation. The proposed method yields a reliable and fast scheme for simultaneous evaluation of such kind of integrals for several values of the defocus parameter, as required in the characterization of the through-focus optics.