Fractional Fourier transform of hard-edge apertured and misaligned Lohmann’s optical system

To study the influence of hard-edge apertured and misaligned Lohmann's optical system on fractional Fourier transforms,the flat-topped multi-Gaussian beam model was adopted to simulate hard-edge apertures.The analytical expressions for transformation of plane wave in a hard-edge apertured and off-axis Lohmann's fractional Fourier transform optical system were derived.The numerical simulation for outputs when the system was apertured with aperture radius of 7.696cm and the lenses were off-axis was also given.It is shown that the two Lohmann's setups are not equivalent when they are apertured and misaligned.