In a recent paper [ J. Opt. Soc. Am. A 9, 203 ( 1992)] the benefits of pupil apodization were examined for the near-infrared imaging of bright sources. In the current paper we extend these considerations to optical speckle imaging, in which photon noise rather than detector readout noise is important. We demonstrate that a one-dimensional pupil geometry (i.e., a thin slit) has several advantages over an unapodized aperture when faint sources are being observed through atmospheric turbulence. The use of a slit aperture does not decrease the signal-to-noise ratios of the power-spectrum and bispectrum measurements, and in many cases it increases them, despite the large reduction in signal level. The disadvantage of this apodization is a reduction in Fourier-plane coverage, which must be compensated for by observations with the slit aligned at several position angles. The performance of many of the current generation of photon-counting imaging detectors deteriorates at the high counting rates that can be experienced even when one is observing sources that are approaching the limiting magnitude of the speckle imaging technique. Under such conditions, we recommend the use of an apodized pupil, in contrast to the current preference for employing a neutral-density filter to reduce the detector count rate.
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