Laurent M. Mugnier

NOISE PROPAGATION IN WAVE-FRONT SENSING WITH PHASE DIVERSITY

The phase diversity technique is studied as a wave-front sensor to be implemented with widely extended sources. The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images (in focus and out of focus) by use of a maximum-likelihood approach. The propagation of the photon noise in the images on the estimated phase is derived from a theoretical analysis. The covariance matrix of the phase estimator is calculated, and the optimal distance between the observation planes that minimizes the noise propagation is determined. The phase error is inversely proportional to the number of photons in the images. The noise variance on the Zernike polynomials increases with the order of the polynomial. These results are confirmed with both numerical and experimental validations. The influence of the spectral bandwidth on the phase estimator is also studied with simulations.

Joint maximum a posteriori estimation of object and PSF for turbulence-degraded images

The performance of high resolution imaging with large optical instruments is severely limited by the atmospheric turbulence. Adaptive optics offers a real time compensation of the turbulence. The correction is however only partial and the long exposure images must be deconvolved to restore the fine details of the object. The aim of this communication js to further study and validate on AO images a recently proposed myopic deconvolution scheme. This approach takes into account the noise in the image, the imprecise knowledge of the PSF, and the available a priori information on the object to be restored as well as on the PSF. The PSF is characterized by its ensemble mean and power spectral density which can be derived from the turbulence statistics. Various object priors are tested (quadratic and L norm regularization). The myopic deconvolution is first compared, on a simulated astronomical extended source, to classical deconvolution. It is shown to improve the object restoration particularly in the case poor PSF estimations due to rapidly evolving turbulence conditions. The myopic deconvolution is then applied on the experimental image of a triple star. A good astrometric and photometric precision is obtained, especially when using a multiple star model for the object. Keywords: adaptive optics, atmospheric turbulence, deconvolution, image restoration, inverse problems, telescope

Pupil configuration optimality criterion in synthetic aperture optics

This paper addresses the optimization of the relative arrangement (pupil configuration) of a phased array of optical telescopes, coherently combined to form images of extended objects in a common focal plane. A new optimality criterion, which is directly linked to the restoration error of the original object from the recorded image, is derived. The optimal configuration is a function of the maximum frequency of interest (or sought resolution), and takes into account the diameter of the elementary telescopes. Simulations illustrate the usefulness of this criterion for designing a synthetic aperture optical instrument.

Reconstruction of a three-dimensional object from its conoscopic hologram

Conoscopic holography is a method for recording holograms with incoherent light, first presented in 1985. Its applications range from 3D microscopy to 3D satellite imaging and include robotics. The Point Spread Function (PSF) is a Gabor Zone Pattern, which is known to have zeros in Fourier space. We present an experimental technique to obtain an invertible PSF with an experimental image reconstruction, and an original algorithm to find the object shape, validated with both simulations and first experimental results.

Wave-front sensing for space active optics: Rascasse project

The payloads for Earth Observation and Universe Science are currently based on very stiff opto-mechanical structures with very tight tolerances. The introduction of active optics in such an instrument would relax the constraints on the thermo-mechanical architecture and on the mirrors polishing. A reduction of the global mass/cost of the telescope is therefore expected. Active optics is based on two key-components: the wave-front sensor and the wave-front corrector.

Deconvolution of adaptive optics images using object autocorrelation and positivity

Adaptive Optics systems provide a real time compensation for atmospheric turbulence, which severely limits the resolution of large telescopes. However, the correction is often only partial and a deconvolution is required to reach the telescope diffraction limit. The need for a regularized deconvolution is discussed, and a Maximum A Posteriori based deconvolution technique is presented. This technique incorporates a positivity constraint and the knowledge of the object Power Spectral Density. This method is then extended to the case of an unknown PSF. Deconvolution results are presented for both simulated and experimental data.

Eléments-clés de la conception d'un instrument spatial à synthése d'ouverture optique

This paper, “Eléments-clés de la conception dun instrument spatial à synthése douverture optique, was presented as part of International Conference on Space Optics—ICSO 1997, held in Toulouse, France.

Registration and restoration of Adaptive-Optics corrected retinal images

Raw individual Adaptive-Optics-corrected flood-illuminated retinal images are usually quite noisy because of safety flux limitations. These flood-illuminated images are also of poor contrast. Interpretation of such images is therefore difficult without an appropriate post-processing, which typically includes the registration of the recorded image stack into a mosaic image and the restoration of the latter.We have developed an image registration method in a MAP framework, based on previous work in astronomical imaging, and tailored for the specifics of retinal imaging, more precisely to the fact that the illumination of the retina and the transmission of the instrument is non-homogeneous, which makes conventional registration methods likely to fail. The mosaic image must then be deconvolved in order to visually restore the high-resolution brought by adaptive optics. To this aim, we perform an unsupervised myopic deconvolution that takes into account the 3D nature of the object being imaged. We successfully apply this whole processing chain to experimental in vivo images of retinal vessels.

Optimal phase reconstruction in large field of view: application to multiconjugate adaptive optics systems

We propose an optimal approach for the phase reconstruction in a large Field Of View (FOV) for Multiconjugate Adaptive Optics (MCAO). This optimal approach is based on a Minimal Mean Square Error (MMSE) estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the Cn2 profile in order to optimally estimate the correction wavefront to be applied to each DM. This optimal approach also accounts for the fact that the number of DM will always be smaller than the number of turbulent layers since the Cn2 profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consist in a full tomographic reconstruction of the turbulence volume followed by a projection on the deformable mirrors accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions (model- approximation approach), which might be a crude approximation, is also considered for comparison. This model-approximation approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and model-approximation approach is proposed. It is shown that the optimal approach provides very good performance even with small number of DMs (typically one of two). Accurate results are obtained, on simulation for a 4- m telescope on a 150 x 150 arcseconds FOV only using 3 guide stars and 2 DM.

Post-processing for anisoplanatic AO corrected images

The point spread function (PSF) of an adaptive optics system evolves in the Field Of View (FOV). This variation strongly limits the conventional deconvolution methods for the processing of wide FOV images. A theoretical expression of this PSF variation is derived. This expression is both validated on simulations and experimental data. It is then applied to the a posteriori processing of stellar fields. Using the available prior information about the object (point-like sources), this technique allows the restoration of the star parameters (positions and intensities) with a precision much better than the conventional methods, in a FOV much larger than the isoplanatic field.