Fractional Hankel transform and the diffraction of misaligned optical systems

Under the condition of rotational symmetry fractional Fourier transforms become fractional Hankel transforms. The relationships between the fractional Hankel transform and the diffraction of a misaligned optical system are established in this paper. By settling and discussing the diffraction integral formulae of a misaligned ABCD optical system, the fractional Hankel transform of an input function can be obtained by selecting a suitable reference plane under given conditions.