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

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, March 30, 2015 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Professor Andrei Martinez-Finkelshtein – University of Almería

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.