Effects of lens aperture on the average intensity in a fractional Fourier plane

Effects of the aperture of a lens which is used to conduct an optical fractional Fourier transform on the fractional average intensity are analysed numerically using a computer. The fractional average intensity means the average intensity of the optical field produced from a partially coherent source in a fractional Fourier plane. In the present study, the fractional average intensities of a monochromatic Gaussian Schell model (GSM) source are evaluated using the root-mean square (RMS) difference between those with and without the effects of the lens aperture. It is clearly shown from our analysis that the aperture size of the lens should be twice as large as the GSM source size or greater in order to satisfy the condition of the RMS difference .