Comparison of Multi-Frame Blind Deconvolution and Speckle Imaging Energy Spectrum Signal-to-Noise Ratios (Preprint); Conference paper

摘要

An analytical signal-to-noise ratio (SNR) expression is derived for unbiased estimates of energy spectra obtained using multi-frame blind deconvolution (MFBD) algorithms. Because an analytical variance expression cannot, in general, be derived, Cramer-Rao lower bounds are used in place of the variances. As a result, the SNR expression provides upper bounds to the achievable SNRs that are independent of the MFBD algorithm implementation. The SNR expression is evaluated for the scenario of ground-based imaging of astronomical objects. It is shown that MFBD energy-spectrum SNRs are usually greater, and often much greater, than their corresponding speckle imaging (SI) energy-spectrum SNRs at all spatial frequencies. One reason for this SNR disparity is that SI energy spectrum SNRs are proportional to the object energy spectrum and the ensemble-averaged atmosphere energy spectrum, while MFBD SNRs are approximately proportional to the square root of these quantities. Another reason for this SNR disparity is that single-frame SI energy spectrum SNRs are limited above by one, while the MFBD energy-spectrum SNRs are not.