Photon statistics of quantum light on scattering from rotating ground glass

When a laser beam passes through a rotating ground glass (RGG), the scattered light exhibits thermal statistics. This is extensively used in speckle imaging. This scattering process has not been addressed in photon picture and is especially relevant if non-classical light is scattered by the RGG. We develop the photon picture for the scattering process using the Bose statistics for distributing $N$ photons in $M$ pixels. We obtain analytical form for the P-distribution of the output field in terms of the P-distribution of the input field. In particular we obtain a general relation for the $n$-th order correlation function of the scattered light, i.e., $g_{\text{out}}^{(n)}\simeq n!\,g_{\text{in}}^{(n)}$, which holds for any order-$n$ and for arbitrary input states. This result immediately recovers the classical transformation of coherent light to pseudo-thermal light by RGG.