Fractional Fourier transform for incoherent one-dimensional off-axis Gaussian beams

Based on the Collins formula, the transformation properties of incoherent one-dimensional off-axis Gaussian beams passing through the fractional Fourier transform(FRFT) system were studied. The analytical expressions for the intensity distribution of this beam were derived. By using the derived expressions, some numerical calculation examples were presented to illustrate the intensity properties on the FRFT plane. It is shown that the intensity distribution on the FRFT plane depend on FRFT order and sub-beams number. The variation of intensity distribution with FRFT order is periodic, and the period is 2. When the FRFT order is even, the number of sub-beam has a great effect on the normalized intensity distribution and the effect decreases with the order in crease; when the FRFT order incr