Blind deconvolution of second harmonic microscopy images of the living human eye.

Second harmonic generation (SHG) imaging microscopy of thick biological tissues is affected by the presence of aberrations and scattering within the sample. Moreover, additional problems, such as uncontrolled movements, appear when imaging in-vivo. Deconvolution methods can be used to overcome these limitations under some conditions. In particular, we present here a technique based on a marginal blind deconvolution approach for improving SHG images obtained in vivo in the human eye (cornea and sclera). Different image quality metrics are used to quantify the attained improvement. Collagen fibers in both cornea and sclera are better visualized and their spatial distributions accurately assessed. This might be a useful tool to better discriminate between healthy and pathological tissues, especially those where changes in collagen distribution occur.

Jointly super-resolved and optically sectioned Bayesian reconstruction method for structured illumination microscopy.

Structured Illumination Microscopy (SIM) is an imaging technique for achieving both super-resolution (SR) and optical sectioning (OS) in wide-field microscopy. It consists in illuminating the sample with periodic patterns at different orientations and positions. The resulting images are then processed to reconstruct the observed object with SR and/or OS. In this work, we present BOSSA-SIM, a general-purpose SIM reconstruction method, applicable to moving objects such as encountered in in vivo retinal imaging, that enables SR and OS jointly in a fully unsupervised Bayesian framework. By modeling a 2-layer object composed of an in-focus layer and a defocused layer, we show that BOSSA-SIM is able to jointly reconstruct them so as to get a super-resolved and optically sectioned in-focus layer. The achieved performance, assessed quantitatively by simulations for several noise levels, compares favorably with a state-of-the-art method. Finally, we validate our method on open-access experimental microscopy data.

High loop rate adaptive optics flood illumination ophthalmoscope with structured illumination capability.

The design and performance of an adaptive optics flood illumination ophthalmoscope (AO-FIO) platform, based on eye motion and dynamic aberrations experimental analysis, are described. The system incorporates a custom-built real-time controller, enabling up to 70 Hz loop rate without jitter, and an AO-corrected illumination capable of projecting high-resolution features in the retina. Wide-field (2.7°×5.4°) and distortionless images from vessel walls, capillaries, and the lamina cribrosa are obtained with an enhanced contrast and signal-to-noise ratio, thanks to careful control of AO parameters. The high spatial and temporal resolution (image acquisition up to 200 Hz) performance achieved by this platform enables the visualization of vessel deformation and blood flow. This system opens up the prospect of a return to favor of flood illumination adaptive optics systems provided that its high pixel rate and structured illumination capabilities are exploited.

First on-sky results of the CO-SLIDAR C(2)(n) profiler.

COupled SLope and scIntillation Detection And Ranging (CO-SLIDAR) is a recent profiling method of the vertical distribution of atmospheric turbulence strength (C(2)(n) profile). It takes advantage of correlations of slopes and of scintillation, both measured with a Shack-Hartmann wavefront sensor on a binary star. In this paper, we present the improved CO-SLIDAR reconstruction method of the C(2)(n) profile and the first on-sky results of the CO-SLIDAR profiler. We examine CO-SLIDAR latest performance in simulation, taking into account the detection noise bias and estimating error bars along with the turbulence profile. The estimated C(2)(n) profiles demonstrate the accuracy of the CO-SLIDAR method, showing sensitivity to both low and high altitude turbulent layers. CO-SLIDAR is tested on-sky for the first time, on the 1.5 m MeO (Métrologie Optique) telescope at Observatoire de la Côte d'Azur (France). The reconstructed profiles are compared to turbulence profiles estimated from meteorological data and a good agreement is found. We discuss CO-SLIDAR's contribution in the C(2)(n) profilers' landscape and we propose some improvements of the instrument.

Laser beam complex amplitude measurement by phase diversity.

The control of the optical quality of a laser beam requires a complex amplitude measurement able to deal with strong modulus variations and potentially highly perturbed wavefronts. The method proposed here consists in an extension of phase diversity to complex amplitude measurements that is effective for highly perturbed beams. Named camelot for Complex Amplitude MEasurement by a Likelihood Optimization Tool, it relies on the acquisition and processing of few images of the beam section taken along the optical path. The complex amplitude of the beam is retrieved from the images by the minimization of a Maximum a Posteriori error metric between the images and a model of the beam propagation. The analytical formalism of the method and its experimental validation are presented. The modulus of the beam is compared to a measurement of the beam profile, the phase of the beam is compared to a conventional phase diversity estimate. The precision of the experimental measurements is investigated by numerical simulations.

LIFT: a focal-plane wavefront sensor for real-time low-order sensing on faint sources.

We propose the linearized focal-plane technique (LIFT) and compare it to classical sensors, such as the quad-cell wavefront sensor (WFS), pyramid WFS, and Shack-Hartmann WFS. The number of modes sensed by LIFT can be tuned without any hardware modification nor degradation of low-order sensing performance. We derive an analytic model of the noise propagation law, which we validate on end-to-end simulations.

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

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.

Optimal method for exoplanet detection by angular differential imaging.

We propose a novel method for the efficient direct detection of exoplanets from the ground using angular differential imaging. The method combines images appropriately, then uses the combined images jointly in a maximum-likelihood framework to estimate the position and intensity of potential planets orbiting the observed star. It takes into account the mixture of photon and detector noises and a positivity constraint on the planet's intensity. A reasonable detection criterion is also proposed based on the computation of the noise propagation from the images to the estimated intensity of the potential planet. The implementation of this method is tested on simulated data that take into account static aberrations before and after the coronagraph, residual turbulence after adaptive optics correction, and noise.

Self-calibration approach for optical long-baseline interferometry imaging.

Current optical interferometers are affected by unknown turbulent phases on each telescope. In the field of radio interferometry, the self-calibration technique is a powerful tool to process interferometric data with missing phase information. This paper intends to revisit the application of self-calibration to optical long-baseline interferometry (OLBI). We cast rigorously the OLBI data processing problem into the self-calibration framework and demonstrate the efficiency of the method on a real astronomical OLBI data set.

Unambiguous phase retrieval as a cophasing sensor for phased array telescopes.

Cophasing a multiple-aperture optical telescope (MAOT) or optical interferometer requires the knowledge of the tips/tilts and of the differential pistons on its subapertures. In this paper we demonstrate in the case of a point source object that a single focal-plane image is sufficient for MAOT cophasing. Adopting a least-square approach allows us to derive an analytic estimator of the subaperture aberrations, provided that these are small enough (typically for closed-loop operation) and that the pupil is diluted noncentrosymmetric. We then provide the validation of this estimator by simulations as well as a performance comparison with a more conventional iterative algorithm of phase retrieval. Finally, we present the experimental validation of both estimators on a laboratory test bench; our results, especially subnanometric repeatability, demonstrate that focal-plane sensors are appropriate for the cophasing of phased array telescopes.

3D phase diversity: a myopic deconvolution method for short-exposure images: application to retinal imaging.

3D deconvolution is an established technique in microscopy that may be useful for low-cost high-resolution imaging of the retina. We report on a myopic 3D deconvolution method developed in a Bayesian framework. This method uses a 3D imaging model, a noise model that accounts for both photon and detector noises, a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas, a positivity constraint, and a smart parameterization of the point-spread function (PSF) by the pupil phase. It estimates the object and the PSF jointly. The PSF parameterization through the pupil phase constrains the inversion by dramatically reducing the number of unknowns. The joint deconvolution is further constrained by an additional longitudinal support constraint derived from a 3D interpretation of the phase-diversity technique. This method is validated by simulated retinal images.

Convex approximation to the likelihood criterion for aperture synthesis imaging.

Aperture synthesis allows one to measure visibilities at very high resolutions by coupling telescopes of reasonable diameters. We consider the case where visibility amplitudes and phase are measured separately. It leads to an estimation problem where the noise model yields a nonconvex data-likelihood criterion. We show how to optimally approximate the noise model while keeping the criterion convex. This approximation has been validated both on simulations and on experimental data.

Reconstruction method for weak-phase optical interferometry.

Current optical interferometers are affected by unknown turbulent phases on each telescope. We account for this lack of phase information by introducing system aberration parameters, and we solve the image reconstruction problem by minimizing an original joint criterion in the aberrations and in the object. We validate this method by means of simulations. Tests on experimental data are under way.

MISTRAL: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images.

Deconvolution is a necessary tool for the exploitation of a number of imaging instruments. We describe a deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics. This method uses a noise model that accounts for both photonic and detector noises. It additionally contains a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas. Finally, it reckons with an imperfect knowledge of the point-spread function (PSF) by estimating the PSF jointly with the object under soft constraints rather than blindly (i.e., without constraints). These constraints are designed to embody our knowledge of the PSF. The implementation of this method is called MISTRAL. It is validated by simulations, and its effectiveness is illustrated by deconvolution results on experimental data taken on various adaptive optics systems and telescopes. Some of these deconvolutions have already been used to derive published astrophysical interpretations.

Optimal control law for classical and multiconjugate adaptive optics.

Classical adaptive optics (AO) is now a widespread technique for high-resolution imaging with astronomical ground-based telescopes. It generally uses simple and efficient control algorithms. Multiconjugate adaptive optics (MCAO) is a more recent and very promising technique that should extend the corrected field of view. This technique has not yet been experimentally validated, but simulations already show its high potential. The importance for MCAO of an optimal reconstruction using turbulence spatial statistics has already been demonstrated through open-loop simulations. We propose an optimal closed-loop control law that accounts for both spatial and temporal statistics. The prior information on the turbulence, as well as on the wave-front sensing noise, is expressed in a state-space model. The optimal phase estimation is then given by a Kalman filter. The equations describing the system are given and the underlying assumptions explained. The control law is then derived. The gain brought by this approach is demonstrated through MCAO numerical simulations representative of astronomical observation on a 8-m-class telescope in the near infrared. We also discuss the application of this control approach to classical AO. Even in classical AO, the technique could be relevant especially for future extreme AO systems.

Marginal estimation of aberrations and image restoration by use of phase diversity.

We propose a novel method called marginal estimator for estimating the aberrations and the object from phase-diversity data. The conventional estimator found in the literature concerning the technique first proposed by Gonsalves has its basis in a joint estimation of the aberrated phase and the observed object. By means of simulations, we study the behavior of the conventional estimator, which is interpretable as a joint maximum a posteriori approach, and we show in particular that it has undesirable asymptotic properties and does not permit an optimal joint estimation of the object and the aberrated phase. We propose a novel marginal estimator of the sole phase by maximum a posteriori. It is obtained by integrating the observed object out of the problem. This reduces drastically the number of unknowns, allows the unsupervised estimation of the regularization parameters, and provides better asymptotic properties. We show that the marginal method is also appropriate for the restoration of the object. This estimator is implemented and its properties are validated by simulations. The performance of the joint method and the marginal one is compared on both simulated and experimental data in the case of Earth observation. For the studied object, the comparison of the quality of the phase restoration shows that the performance of the marginal approach is better under high-noise-level conditions.