Diffraction Considerations for Planar Detectors in the Few-Mode Limit

Filled arrays of bolometers are currently being employed for use in astronomy from the far-infrared through millimeter parts of the electromagnetic spectrum. Because of the large range of wavelengths for which such detectors are applicable, the number of modes supported by a pixel will vary according to the specific application of a given available technology. We study the dependence of image fidelity and induced polarization on the size of the pixel by employing a formalism in which diffraction due to the pixel boundary is treated by propagating the second-order statistical correlations of the radiation field through a model optical system. We construct polarized beam pattern images of square pixels for various ratios of p/\lambda where p is the pixel size and \lambda is the wavelength of the radiation under consideration. For the limit in which few modes are supported by the pixel (p/\lambda<1), we find that the diffraction due to the pixel edges is non-negligible and hence must be considered along with the telescope diffraction pattern in modeling the ultimate spatial resolution of an imaging system. For the case in which the pixel is over-moded (p/\lambda>1), the geometric limit is approached as expected. This technique gives a quantitative approach to optimize the imaging properties of arrays of planar detectors in the few-mode limit.