Any bolometer that is greater than a few wavelengths in size is receptive to the power in a number of fully coherent optical modes simultaneously. Knowing the amplitude, phase, and polarisation patterns of these modes, and their relative sensitivities, is central to being able to use a multimode detector effectively. We describe a procedure for measuring the spatial itate of coherence to which a detector is sensitive. Diagonalisation of the coherence function then gives the natural modes. The scheme is based on the result that the expectation value of the output of any detector, or indeed whole instrument or telescope, is given by the contraction of two tensor fields: one of which describes the state of coherence of the incoming radiation, and the other describes the state of coherence to which the detector is sensitive. It follows that if a detector is illuminated by two coherent point sources, in the near or far field, and the phase of one source rotated relative to the other, the output of the detector displays a fringe. By repeating the process with different source locations, the detector's coherence tensor can be reconstructed from the recorded complex visibilities. This new, powerful technique is essentially aperture synthesis interferometry in reverse, and therefore many of the data processing techniques developed in the context of astronomy can be used for characterising the optical behaviour of few-mode bolometers.
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