An exact solution for the crosscorrelation between two different apertures of circular symmetry under defocused conditions in a two-pupil system is developed. Application to some nonstandard pupil topologies is described. Previous experimental and theoretical work demonstrates that two optical fields with different temporal frequencies when mixed through an optical heterodyne action at a photodetector can if properly preconditioned produce an electronic signal related directly to the crosscorrelation of the two corresponding pupil functions . Applying this concept several aperture topologies are proposed which lead to OTFs with bandpass and bandreject properties. The approach presented herein is to calculate without approximation the crosscorrelation of two different circular apertures in a two-pupil system. This result will serve as the essential function through which OTFs for various more complicated apertures are expressible. This approach is based on an extension of a previous analysis carried out for the autocorrelation of a circular aperture with defocus .