Statistical behavior of joint least-square estimation in the phase diversity context

Idier, Jérôme; Mugnier, Laurent M.; Blanc, Amandine

doi:10.1109/tip.2005.859365

Cited by 8 publications

(5 citation statements)

References 26 publications

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“…Multi-frame joint deconvolution [9] can help since it increases the number of data for the same object but is only effective if the PSFs are different enough [10], such as in the case of phase diversity [11]. Therefore, another estimator with better statistical properties would be preferable, ideally capable of restoring the PSF on a single frame.…”

Section: Simulation Resultsmentioning

confidence: 99%

Marginal blind deconvolution of adaptive optics retinal images

Blanco¹,

Mugnier²

2011

Opt. Express

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Adaptive Optics corrected flood imaging of the retina has been in use for more than a decade and is now a well-developed technique. Nevertheless, raw AO flood images are usually of poor contrast because of the three-dimensional nature of the imaging, meaning that the image contains information coming from both the in-focus plane and the out-of-focus planes of the object, which also leads to a loss in resolution. Interpretation of such images is therefore difficult without an appropriate post-processing, which typically includes image deconvolution. The deconvolution of retina images is difficult because the point spread function (PSF) is not well known, a problem known as blind deconvolution. We present an image model for dealing with the problem of imaging a 3D object with a 2D conventional imager in which the recorded 2D image is a convolution of an invariant 2D object with a linear combination of 2D PSFs. The blind deconvolution problem boils down to estimating the coefficients of the PSF linear combination. We show that the conventional method of joint estimation fails even for a small number of coefficients. We derive a marginal estimation of the unknown parameters (PSF coefficients, object Power Spectral Density and noise level) followed by a MAP estimation of the object. We show that the marginal estimation has good statistical convergence properties and we present results on simulated and experimental data.

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Section: Simulation Resultsmentioning

confidence: 99%

Marginal blind deconvolution of adaptive optics retinal images

Blanco¹,

Mugnier²

2011

Opt. Express

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“…where * denotes complex conjugate. We set 2 / S o = close to 0, which means we under-regularize the inversion, because it has been shown [4] that doing so leads to a consistent estimator for the aberrations. Then, by introducing the estimated object of Eq.…”

mentioning

confidence: 99%

Analytical solution to the phase-diversity problem for real-time wavefront sensing

2009

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High-resolution optical systems require a very accurate control of the optical paths. For the measurement of aberrations on extended objects, several iterative phase-diversity algorithms have been developed, based on aberration estimation from focal-plane intensity measurements. Here we present an analytical estimator in the case of small aberrations. Under this assumption, a quadratic criterion is derived that allows us to express the solution (phase and object) under a simple analytical form. We also compare the performance of our algorithm with the iterative phase diversity, demonstrating that the analytic estimator is appropriate for closed-loop operation.

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“…This strategy is supported by the fact that it yields a phase estimation with satisfactory asymptotic properties, as shown in Ref. [12], and that these properties hold even if the noise is not Gaussian.…”

Section: Chosen Phase Estimation Methodsmentioning

confidence: 74%

Sensing Quasi-Static Aberrations of Adaptive Optics Systems On-Line with Long-Exposure Phase Diversity

Mugnier

Sauvage

Fusco

et al. 2010

1st AO4ELT Conference - Adaptive Optics for Extremely Large Telescopes

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Abstract.We validate by simulations an extension of the phase diversity technique that uses long exposure adaptive optics corrected images for sensing quasi-static aberrations during the scientific observation, in particular for high-contrast imaging. The principle of the method is that, for a sufficiently long exposure time, the residual turbulence is averaged into a convolutive component of the image and that phase diversity estimates the sole static aberrations of interest. The advantages of such a procedure, compared to the processing of short-exposure image pairs, are that the separation between static aberrations and turbulence-induced ones is performed by the long-exposure itself and not numerically, that only one image pair must be processed, that the estimation benefits from the high SNR of long-exposure images, and that only the static aberrations of interest are to be estimated. Long-exposure phase diversity can also be used as a phasing sensor for a segmented aperture telescope. Thus, it may be particularly useful for future planet finder projects such as EPICS on the European ELT.

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Statistical behavior of joint least-square estimation in the phase diversity context

Cited by 8 publications

References 26 publications

Marginal blind deconvolution of adaptive optics retinal images

Marginal blind deconvolution of adaptive optics retinal images

Analytical solution to the phase-diversity problem for real-time wavefront sensing

Sensing Quasi-Static Aberrations of Adaptive Optics Systems On-Line with Long-Exposure Phase Diversity

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