Imaging characteristics of square law media

An object illuminated with partially coherent light is imaged through a square law medium characterized by the dielectric variation (r, z) = 0(1 - α2 r2). We have studied the performance of this medium as an imaging element. An expression for the intensity distribution at the observation plane is derived and is found to be formally identical to the homogenous case. This formal identity is used to obtain an expression for the optical transfer function in the incoherent case. The variation of the degree of coherence at the observation plane is also considered in a special case when the object is incoherently illuminated.