Amandine Blanc

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.

Phase Diversity: A Technique for Wave-Front Sensing and for Diffraction-Limited Imaging

Abstract The theoretical angular resolution of an optical imaging instrument such as a telescope is given by the ratio of the imaging wavelength lambda over the aperture diameter D of the instrument. For real-world instrument, optical aberrations often prevent this so-called diffraction-limit resolution lambda/D from being achieved. These aberrations may arise both from the instrument itself and from the propagation medium of the light. The aberrations can be compensated either during the image acquisition by real-time techniques or a posteriori, i.e., by post-processing. Most of these techniques require the measurement of the aberrations, also called wave-front, by a wave-front sensor (WFS). The focal-plane family of sensors was born from the very natural idea that an image of a given object contains information not only about the object, but also about the wave-front. A focal-plane sensor thus requires little or no optics other than the imaging sensor; it is also the only way to be sensitive to all aberrations down to the focal plane. The first practical method for wave-front sensing from focal-plane data was proposed by Gerchberg and Saxton (1972). This so-called “phase-retrieval” method has two major limitations. Firstly, it only works with a point source. Secondly, there is generally a sign ambiguity in the recovered phase, i.e., the solution is not unique, as will be detailed below. Gonsalves (1982) showed that by using a second image with an additional known phase variation with respect to the first image (such as defocus), it is possible to estimate the unknown phase even when the object is extended and unknown. The presence of this second image additionally removes the above-mentioned sign ambiguity of the solution. This technique is referred to as “phase diversity”. This contribution attempts to provide a survey of the phase diversity technique, with an emphasis on its wave-front sensing capabilities. Section 1 gives an introduction to the image formation for the considered instruments (i.e. those working with spatially incoherent light, such as telescopes), reviews the sources of image degradation, and states the inverse (estimation) problem to be solved in phase diversity. Section 2 reviews the domains of application of phase diversity. Then, Sections 3 and 4 review the wave-front estimation methods associated with this technique and their properties, while Section 5 examines the possible object estimation (i.e., image restoration) methods. Section 6 gives some background on the various minimization algorithms that have been used for phase diversity. Section 7 illustrates the use of phase diversity on experimental data for wave-front sensing. Finally, Sections 8 and 9 highlight two fields of phase diversity wave-front sensing that have witnessed noteworthy advances: Section 8 reviews the methods used to estimate the large-amplitude aberrations that one faces when imaging through turbulence, and proposes a novel approach for this difficult problem. And Section 9 reviews the developments of phase diversity for a recent application: the phasing (also called cophasing) of multi-aperture telescopes.

Calibration of CONICA static aberrations by phase diversity

CONICA is the first AO equipped multimode near infrared camera which saw first light at the VLT in the end of 2001. A technique will be described to benefit of the AO system NAOS to correct not only for atmospheric turbulence but also for the internal optical aberrations of the high resolution camera. The aberrant optical components in the light path of CONICA are outside of the AO loop and therefore no self-acting correction is possible. Independently of the AO wave front sensor, a separate measurement of these minor aberrations using a method called phase diversity allows to predict for the variety of camera configurations the corresponding aberrations. They are quantified by sets of Zernike coefficients which are rendered to the adaptive optics. This technique turns out to be very flexible and results into a further improvement of the optical overall performance.

Novel estimator for the aberrations of a space telescope by phase diversity

In this communication, we propose a novel method for estimating the aberrations of a space telescope from phase diversity data. The images recorded by such a telescope can be degraded by optical aberrations due to design, fabrication or misalignments. Phase diversity is a technique that allows the estimation of aberrations. The only estimator found in the relevant literature is based on a joint estimation of the aberrated phase and the observed object. By means of simulations, we study the behavior of this estimator. We propose a novel marginal estimator of the sole phase by Maximum Likelihood. It is obtained by integrating the observed object out of the problem; indeed, this object is a nuisance parameter in our problem. This reduces drastically the number of unknown and provides better asymptotic properties. This estimator is implemented and its properties are validated by simulation. Its performance is equal or even better than that of the joint estimator for the same computing cost.

Ground layer adaptive optics: analysis of the wavefront sensing issue

Here are presented the basis of an analytical development whose purpose is to give arguments for the evaluation of wavefront sensing concepts for Ground Layer Adaptive Optics. Simple hypothesis make possible the derivation of analytical expressions for the phase measurement error and reveal consequent differences between Star Oriented and Layer Oriented concepts. Influence of key parameters such as guide star statistics or strength of the turbulence in altitude are then studied. In the Layer Oriented case, necessity of reducing the guide stars flux dispersion to achieve a uniform correction in the field of interest is demonstrated.

Modeling and analysis of XAO systems: application to VLT-Planet Finder

A end-to-end model of an Extreme Adaptive Optics system developed is the framework of the project VLT-PF is presented. The different components are exposed with their specificities. Several AO and XAO issues are discussed like scintillation, vibration and calibration effects among others. A full simulation of an XAO system coupled to a coronagraph and designed to detect faint companion in the vicinity of a bright star is shown.

Cophasing a wide field multi-aperture array by phase-diversity: influence of aperture redundancy and dilution

Future high-resolution space telescoeps will use discontinuous apertures, either primary segments or sub-telescopes. One of the most critical points in the operation of such instruments will be the cophasing of the sub-apertures. Cophasing sensors are available on ground interferometers, allowing sub-aperture piston/tip/tilt measurement on unresolved or slightly resolved starts. But when observing a very extended object, such as the Earth as seen from space, no reference star can be found in the field. In this case, the cophasing measurement must be derived from the observed object itself, which is a major issue for extended objects. Phase diversity is one of the very few solutions to this problem. Phase diversity consists in the joint estimation of the object and the instrument aberrations from the analysis of several images obtained with different but perfectly known aberrations, for example the focal image and a slightly defocused image. Theoretical analysis and numerical simulations were carried out to investigate how our phase diversity algorihtm behaves when estimating sub-aperture piston and tip/tilt in various conditions. Our study shows that the aperture configuration has a major impact on performance. For diluted apertures, when the optical transfer function has zeros within the frequency domain of interest, it can be shown that at least two possible solutions can be derived by phase diversity. For redundant apertures, when several pairs of sub-aperture contribute to the same spatial frequency, the piston or tip/tilt estimation is degraded for sub-apertures contributing to redundant frequencies.

Optimization of the Pre-Compensation of Non-Common Path Aberrations for Adaptive Optics Systems

We present experiental results of a new procedure of measurement and pre-compensation of the AO non-common path aberrations. A significant Strehl ratio increase (from 70 to 90 % in R band) is demonstrated.

Fine calibration and pre-compensation of non-common path aberrations for high performance AO system

Non common path aberrations (NCPA) are one of the main limitations to achieve ultimate performance of an adaptive optic system. These static optical aberrations are unseen by the wave front sensor and therefore not corrected by closed AO loop. We present experimental results of a new procedure of measurement and pre-compensation of the AO non-common path aberrations. This new procedure has been studied with simulations, and tested on the AO bench (BOA) at ONERA. Strehl Ratio (SR) obtained on the imaging path reaches 93 % @ 632.8 nm even for low SNR.

Marginal estimator for the aberrations of a space telescope by phase diversity

In this communication, we propose a novel method for estimating the aberrations of a space telescope from phase diversity data. The images recorded by such a telescope can be degraded by optical aberrations due to design, fabrication or misalignments. Phase diversity is a technique that allows the estimation of aberrations. The only estimator found in the relevant literature is based on a joint estimation of the aberrated phase and the observed object. We recall this approach and study the behavior of this joint estimator by means of simulations. We propose a novel marginal estimator of the sole phase. it is obtained by integrating the observed object out of the problem; indeed, this object is a nuisance parameter in our problem. This reduces drastically the number of unknown and provides better asymptotic properties. This estimator is implemented and its properties are validated by simulation. its performance is equal or even better than that of the joint estimator for the same computing cost.