We outline a procedure for modelling the behaviour of partially-coherent long-wavelength optical systems. The procedure is of considerable importance to microwave background astronomy, where sequences of high-throughput optical components are often used. In the paper, we give a symbolic description of the basic method, and illustrate its use by calculating the radiation pattern of an overmoded waveguide bolometer. To confront a number of fundamental issues, we consider the case where the absorbing disc does not completely fill the waveguide. We also demonstrate the technique by showing how the optical behaviour of an imaging array can be determined by propagating all of the beams in the array simultaneously.
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