SIGNAL-TO-NOISE RATIO FOR ASTRONOMICAL IMAGING BY DECONVOLUTION FROM WAVE-FRONT SENSING

One method for improving the quality of astronomical images measured t hrough a atmospheric turbulence uses simultaneous short-exposure measu rements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurement s are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function, which is then used in a deconvolution procedure. This imaging method has been called both d econvolution from wave-front sensor (DWFS) measurements and self-refer enced speckle holography. We analyze the signal-to-noise ratio (SNR) b ehavior of this imaging method in the spatial frequency domain. The an alysis includes effects arising from differences in the correlation pr operties of the incident and the estimated pupil phases and the fact t hat the object-spectrum estimator is a randomly filtered doubly stocha stic Poisson random process. SNR results obtained for the DWFS method are compared with the speckle-imaging power-spectrum SNR for equivalen t seeing conditions and light levels, It is shown that for unresolved stars the power-spectrum SNR is superior to the DWFS SNR. However, for extended objects the power-spectrum SNR and the DWFS SNR are similar. Since speckle imaging uses a separate Fourier phase-reconstruction pr ocess not required by the DWFS method, the DWFS method provides an alt ernative to speckle imaging that uses simple postprocessing at the cos t of a wave-front sensor measurement but with no loss of SNR performan ce for extended objects.