Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra

Abstract

Adaptive optics systems provide a real-time compensation for atmospheric turbulence. However, the correction is often only partial, and a deconvolution is required for reaching the diffraction limit. The need for a regularized deconvolution is discussed, and such a deconvolution technique is presented. This technique incorporates a positivity constraint and some a priori knowledge of the object (an estimate of its local mean and a model for its power spectral density). This method is then extended to the case of an unknown point-spread function, still taking advantage of similar a priori information on the point-spread function. Deconvolution results are presented for both simulated and experimental data.

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics

“…The principle of the conventional procedure, as used in NAOS-CONICA, 11, 10 is recalled and commented in Section 2. The newly optimized algorithm for the NCPA measurements is described in Section 3 and is based on a Maximum A Posteriori approach (MAP) 12,13 for the phase estimation. The new approach for the NCPA pre-compensation is presented in Section 4.…”

AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data

“…Equation (12) intrinsically handles bandlimitedness of the OTF; frequencies beyond the optical system's resolution are essentially ignored, since they are not represented in the measured samples. Conan and co-workers 28,29 have shown that this harmonic OTF constraint performs noticeably better toward recovering the true OTF than a simple band-limited constraint typically used in blind deconvolution methods. 7,30 An harmonic constraint for each spatial frequency, |k|, which is functionally equivalent to using a radially averaged υ(k), may be used, although we have found that using the less stringent constraint, Eq.…”

“…(8) and (9), the following partition function-like integrals may be defined over the distribution of possible data-model variations, δ ≡ i − o ⊗ h, and the distribution of possible gradient norm values for each pixel element: (28) (29) A convenient relation linking θ r and λ o can be obtained by equating these integrals: (30) where the approximation holds for λ o ≲ 10. The element-by-element equivalence of these integrals essentially assumes that the behavior of each pixel/voxel element can be decoupled and that the Gibbs distribution (and thus partition function Z) of Eq.…”

“…Our scheme estimates the sum over all states using conglomerate variables instead [Eqs. (28) and (29)], leading to the approximate though analytical relation of Eq. (30).…”

Adaptive optics observations of asteroid (216) Kleopatra

“…In addition to the usual MLR technique, the MISTRAL (Myopic Iterative STep-preserving Restoration ALgorithm) deconvolution technique (Conan et al 1998(Conan et al , 1999, specially adapted to planetary objects, was applied. The main difference between this technique and other more "classical" methods is the avoidance of both noise amplification and creation of sharp-edges artifacts or "ringing effects", and better restoration of the initial photometry.…”