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 :

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.

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