The ABCD-Hankel Transformation
in Two-Dimensional Frequency-Domain
with Polar Coordinates
M. Ibnchaikh, A. Belafhal*
Laboratoire de Physique Moléculaire, Département de Physique, B.P 20,
Faculté des Sciences, Université Chouaïb Doukkali, 24000 El Jadida, Morocco
*Corresponding author. E-mail : Belafhal@ucd.ac.ma
Received 01 November 2000; revised version accepted 06 April 2001
This work is devoted to a theoretical study of the ABCD-Hankel transformation. As the frequency-domain is very important in optics, we investigate a novel general Collins formula in two dimensions with polar coordinates. We also investigate the direct relationship between input and output spatial frequency spectra of a light field in this frame system in the case of a Fourier, Fresnel and fractional Fourier (FRT) transformations for two families of beams: Bessel-Gaussian and Bessel-modulated Gaussian beams.
Keywords: ABCD-Hankel; Transformation; Collins Formula; Fourier; Fresnel; Fractional Fourier.