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 portion of the electromagnetic spectrum. Because of the large range of wavelengths for which such detectors are applicable, the size of a pixel (p) relative to the wavelength (?) will vary according to the specific application of a given available technology. As the pixel size becomes comparable to a wavelength of the absorbed radiation, correlations in the radiation field at the pixel can affect the imaging properties of the system independent of the correlations introduced by the front-end optics. 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 an optical system. We construct simulated polarized images of square pixels for various ratios of p/?. For the limit in which few modes are supported by the pixel (p/? ? 1), we find that the diffraction due to the pixel edges is nonnegligible 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/??1), the geometric limit is approached as expected. This technique provides a quantitative approach to understand and optimize the imaging properties of planar detectors in the few-mode limit.