SPECKLE IMAGING SIGNAL-TO-NOISE RATIO PERFORMANCE AS A FUNCTION OF FRAME INTEGRATION TIME

In the past 10 years astronomical image reconstruction based on a vari ety of speckle techniques has become a popular means of enhancing and improving the resolution of turbulence-degraded images. These techniqu es 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 sig nal-to-noise ratio (SNR) of the Fourier components of a single snapsho t. Estimating these Fourier components is hampered by the inherent noi se induced by the photon detection process and the random effect of th e 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 e stablished that if the frames are uncorrelated then the SNR improves i n comparison with the single-frame SNR by a factor of root 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 det ailed SNR analysis of estimating the modulus of an object's Fourier sp ectrum from turbulence-distorted images are described. Unlike previous analyses, this work takes into account the proper temporal correlatio n properties of the atmosphere and the spatial frequency being estimat ed as well as the interframe correlations that degrade the SNR improve ment factor from the ideal case of root m.