Cramer–Rao bound and phase-diversity blind deconvolution performance versus diversity polynomials

Abstract

Information theoretic bounds on the estimated Zernike coefficients for various diversity phase functions are presented. We show that, in certain cases, defocus diversity may yield a higher Cramer-Rao lower bound (CRLB) than some other diversity phase functions. Using simulated images to evaluate the performance of the phase-diversity algorithm, we find that, for an extended scene and defocus diversity, the phase-diversity algorithm achieves the CRLB for known objects. Furthermore, the phase-diversity algorithm achieves the CRLB by a factor of approximately 2 for unknown objects.

Wave-front sensing for space active optics: Rascasse project

“…It was the object of many experimental demonstrations in the case of monolithic telescopes [11]; or with segmented telescopes [12]. Different limitations linked with noise in acquired data were analysed [13] [14]. Some algorithmic developments were leaded in parallel to optimize the noise reduction [15] or to reduce computation time for cophasing applications [16].…”

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

“…The first is the development of algorithm-independent image-quality performance bounds such as Cramér-Rao lower bounds (CRBs) [25]. A number of papers have been published in this area, including the use of CRBs to compare two algorithms assuming white Gaussian noise and single-input single-output systems [26], asymptotic CRB expressions for a multiple-input multiple-output system with white non-Gaussian noise [27,28] and analyses of phase-diversity-based blind deconvolution [29,30].…”

Evaluation of the phase diversity algorithm for noise statistics error and diversity function combination

“…The Phase Diversity (PD) method [1][2][3][4][5][6][7] has been used extensively over the last decade to measure the wavefront of optical systems. The utility of the PD algorithm came about because it is not limited to point sources but applies also to extended scenes.…”

“…Various papers have analyzed the PD algorithm and determined the optimum phase diversity strength mainly for defocus diversity [8][9][10] . These papers have been augmented recently with results 5 showing that astigmatism may yield better performance than defocus diversity in certain cases. These authors have also shown that, for scenes exceeding a certain extent, Poisson noise statistics may yield better residual wavefront aberration than Gaussian noise statistics.…”

“…From the recent work of [5], one may ask, "Could one combine phase diversities, defocus and astigmatism, to obtain performance better than either defocus or astigmatism considered separately?". This question will be answered in this paper.…”