The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier transform acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of fractional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.
© 2007 Chinese Optics Letters
(050.1220) Diffraction and gratings : Apertures
(070.2590) Fourier optics and signal processing : ABCD transforms
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(140.3300) Lasers and laser optics : Laser beam shaping
Jiannong Chen, Jinliang Yan, Defa Wang, and Yongjiang Yu, "Fractional Fourier transform of apertured paraboloid refracting system," Chin. Opt. Lett. 5, 18-20 (2007)