Scaled Fractional Fourier Transform for Partially Coherent Beams

The definition of scaled fractional Fourier transform (SFRT) is extended to partially coherent beams based directly on the cross-spectral density. Based on this formula, an equivalent tensor ABCD law for the SFRT of partially coherent twisted anisotropic Gaussian-Schell model beams is derived. The derived formulae provide a powerful tool for analysing and calculating the SFRT of partially coherent beams. An application example is provided.