Abstract

In the past 10 years astronomical image reconstruction based on a variety of speckle techniques has become a popular means of enhancing and improving the resolution of turbulence-degraded images. These techniques are based on the Fourier processing of a large number of turbulence-degraded snapshots or frames of the irradiance in the system’s image plane. The number of snapshots needed is largely a function of the signal-to-noise ratio (SNR) of the Fourier components of a single snapshot. Estimating these Fourier components is hampered by the inherent noise induced by the photon detection process and the random effect of the turbulent atmosphere. In most cases the SNR is much less than unity, and many frames are averaged to improve the overall SNR. It is well established that if the frames are uncorrelated then the SNR improves in comparison with the single-frame SNR by a factor of m, where m is the number of frames averaged. This fact implies that the smallest exposure time possible is desirable in order for m to be maximized for a given observation time. On the other hand, because of finite photon flux levels and read noise effects it can be shown that the exposure time should be increased at the cost of reducing m. Results from a detailed SNR analysis of estimating the modulus of an object’s Fourier spectrum from turbulence-distorted images are described. Unlike previous analyses, this work takes into account the proper temporal correlation properties of the atmosphere and the spatial frequency being estimated as well as the interframe correlations that degrade the SNR improvement factor from the ideal case of m.

© 1995 Optical Society of America

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