Widening the effective field of view of adaptive-optics telescopes by deconvolution from wave-front sensing: average and signal-to-noise ratio performance

A fundamental problem of adaptive-optics systems is the very narrow corrected field of view that can be obtained because turbulence is extended in altitude throughout the atmosphere. The correctable field of view is of the order of 5-10 μrad at visible wavelengths and increases as the wavelength increases. Previous concepts to broaden the corrected field of view have been hardware oriented, requiring multiple wave-front sensor (WFS) measurements to control multiple deformable mirrors. We analyze the average and the signal-to-noise-ratio performance of an image measurement and postprocessing technique that uses simultaneous measurements of a short-exposure compensated image measured in an off-axis direction; an additional WFS measurement is taken in the off-axis direction. Results are presented for infinite-altitude WFS beacons driving both the WFS for the adaptive optics and the WFS looking in the off-axis direction, a variety of seeing and WFS light-level conditions, and off-axis angles from two to six times the isoplanatic angle. This technique improves the average effective transfer function out to a field angle of at least six times the isoplanatic angle while providing a higher signal-to-noise ratio in the spatial frequency domain.     

Fundamental limits on isoplanatic correction with multiconjugate adaptive optics

We investigate the performance of a general multiconjugate adaptive optics (MCAO) system in which signals from multiple reference beacons are used to drive several deformable mirrors in the optical beam train. Taking an analytic approach that yields a detailed view of the effects of low-order aberration modes defined over the metapupil, we show that in the geometrical optics approximation, N deformable mirrors conjugated to different ranges can be driven to correct these modes through order N with unlimited isoplanatic angle, regardless of the distribution of turbulence along the line of sight. We find, however, that the optimal deformable mirror shapes are functions of target range, so the best compensation for starlight is in general not the correction that minimizes the wave-front aberration in a laser guide beacon. This introduces focal anisoplanatism in the wave-front measurements that can be overcome only through the use of beacons at several ranges. We derive expressions for the number of beacons required to sense the aberration to arbitrary order and establish necessary and sufficient conditions on their geometry for both natural and laser guide stars. Finally, we derive an expression for the residual uncompensated error by mode as a function of field angle, target range, and MCAO system geometry.     

Adaptive optics compensation for propagation through deep turbulence: initial investigation of gradient descent tomography

To implement adaptive optics compensation for propagation through deep turbulence, the concept of gradient descent tomography has been developed. Here two or more deformable mirrors are controlled by an efficient iterative algorithm that optimizes the integral I(2) image-sharpening metric. In this work a difficult case involving imaging over a 2 km path with a C(n)(2) of 2 x 10(-13)m(-2/3) is considered. For a wavelength of 1.06 microm and a 10-cm-diameter aperture, lambda/D is seven times the isoplanatic angle (theta(0)=1.54 microrad), and the Rytov number is 5.5. For three points placed along a line spanning approximately 70 isoplanatic patch sizes all three points are compensated somewhat, illustrating that anisoplanatism is addressed. The fact that the corresponding performance improvement ratios are 1.20, 1.34, and 3.26 in the presence of such strong scintillation and anisoplanatism is quite significant.     

Modal compensation and the atmospheric-turbulence outer scale: computer simulations

The influence of the turbulence outer scale on the Strehl ratio obtained with low-order adaptive optics systems is examined by numerical simulation. The Karhunen-Loeve approach is used to generate wave-front samples. A method that allows construction of the outer-scale-dependent Karhunen-Loeve functions is described. It is shown that the Strehl ratio produced by a second-order adaptive optics correction (tip-tilt, defocus, and astigmatism) is affected quite strongly by the finite outer scale. For the higher-order correction, the effect under study is weak and appears only when the outer-scale magnitude becomes less than the aperture diameter. It is also shown that the finite outer scale has a positive effect on the Strehl ratio of the uncorrected long-exposure image.     

Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.     

Adaptive-optics performance of Antarctic telescopes

The performance of natural guide star adaptive-optics systems for telescopes located on the Antarctic plateau is evaluated and compared with adaptive-optics systems operated with the characteristic mid-latitude atmosphere found at Mauna Kea. A 2-m telescope with tip-tilt correction and an 8-m telescope equipped with a high-order adaptive-optics system are considered. Because of the large isoplanatic angle of the South Pole atmosphere, the anisoplanatic error associated with an adaptive-optics correction is negligible, and the achievable resolution is determined only by the fitting error associated with the number of corrected wave-front modes, which depends on the number of actuators on the deformable mirror. The usable field of view of an adaptive-optics equipped Antarctic telescope is thus orders of magnitude larger than for a similar telescope located at a mid-latitude site; this large field of view obviates the necessity for multiconjugate adaptive-optics systems that use multiple laser guide stars. These results, combined with the low infrared sky backgrounds, indicate that the Antarctic plateau is the best site on Earth at which to perform high-resolution imaging with large telescopes, either over large fields of view or with appreciable sky coverage. Preliminary site-testing results obtained recently from the Dome Concordia station indicate that this site is far superior to even the South Pole.     

Evaluation of the impact of finite-resolution effects on scintillation compensation using two deformable mirrors.

The impact of finite-resolution deformable mirrors and wave-front sensors is evaluated as it applies to fullwave conjugation using two deformable mirrors. The first deformable mirror is fixed conjugate to the pupil, while the second deformable mirror is at a finite range. The control algorithm to determine the mirror commands for the two deformable mirrors is based on a modification of the sequential generalized projection algorithm. The modification of the algorithm allows the incorporation of Gaussian spatial filters into the optimization process to limit the spatial-frequency content applied to the two deformable mirrors. Simulation results are presented for imaging and energy projection scenarios that establish that the optimal spatial filter waist to be applied is equal to the subaperture side length in strong turbulence. The effect of varying the subaperture side length is examined, and it is found that to effect a significant degree of scintillation compensation, the subapertures, and corresponding spacing between actuators, must be much smaller than the coherence length of the input field.     

Layer-oriented adaptive optics for solar telescopes

First multiconjugate adaptive-optical (MCAO) systems are currently being installed on solar telescopes. The aim of these systems is to increase the corrected field of view with respect to conventional adaptive optics. However, this first generation is based on a star-oriented approach, and it is then difficult to increase the size of the field of view beyond 60-80?arc sec in diameter. We propose to implement the layer-oriented approach in solar MCAO systems by use of wide-field Shack-Hartmann wavefront sensors conjugated to the strongest turbulent layers. The wavefront distortions are averaged over a wide field: the signal from distant turbulence is attenuated and the tomographic reconstruction is thus done optically. The system consists of independent correction loops, which only need to account for local turbulence: the subapertures can be enlarged and the correction frequency reduced. Most importantly, a star-oriented MCAO system becomes more complex with increasing field size, while the layer-oriented approach benefits from larger fields and will therefore be an attractive solution for the future generation of solar MCAO systems.     

Analysis of modes and behavior of a multiconjugate adaptive optics system

We study the so-called three-dimensional mapping of turbulence, a method solving the cone effect (or focus anisoplanatism) by using multiple laser guide stars (LGSs). This method also permits a widening of the corrected field of view much beyond the isoplanatic field. Multiple deformable mirrors, conjugated to planes at chosen altitudes among the turbulent layers, are used to correct in real time the wave fronts measured from the LGSs. We construct an interaction matrix describing the multiconjugate adaptive optics system and analyze the eigenmodes of the system. We show that the global tilt mode is singular because it cannot be localized in altitude, so that it must be corrected only once at any altitude. Furthermore, when the tilt from the LGS cannot be measured, the singularity of the global tilt yields the delocalization of particular forms of defocus and astigmatism. This imposes the use of a single natural guide star located anywhere in the corrected field to measure these modes. We show as an example that the cone effect can be corrected with a Strehl of 0.8 with four LGSs (tilt ignored) on an 8-m telescope in the visible when a single laser star provides a Strehl of 0.1. The maximum field of view of 100 arc sec in diameter can be reconstructed with an on-axis Strehl ratio of 30%. We also show that the measurement of the height of the layers can be done with current techniques and that additional layers, not accounted for, do not significantly degrade the performance in the configuration that we model.     

Approach for reconstructing anisoplanatic adaptive optics images

Atmospheric turbulence corrupts astronomical images formed by ground-based telescopes. Adaptive optics systems allow the effects of turbulence-induced aberrations to be reduced for a narrow field of view corresponding approximately to the isoplanatic angle theta(0). For field angles larger than theta(0), the point spread function (PSF) gradually degrades as the field angle increases. We present a technique to estimate the PSF of an adaptive optics telescope as function of the field angle, and use this information in a space-varying image reconstruction technique. Simulated anisoplanatic intensity images of a star field are reconstructed by means of a block-processing method using the predicted local PSF. Two methods for image recovery are used: matrix inversion with Tikhonov regularization, and the Lucy-Richardson algorithm. Image reconstruction results obtained using the space-varying predicted PSF are compared to space invariant deconvolution results obtained using the on-axis PSF. The anisoplanatic reconstruction technique using the predicted PSF provides a significant improvement of the mean squared error between the reconstructed image and the object compared to the deconvolution performed using the on-axis PSF.     

Turbulence-induced edge image waviness: theory and experiment

A theoretical model for the edge image waviness effect is developed for the ground-to-ground imaging scheme and validated by use of IR imagery data collected at the White Sands Missile Range. It is shown that angle-of-arrival (AA) angular anisoplanatism causes the phenomenon of edge image waviness and that the AA correlation scale, not the isoplanatic angle, characterizes the edge image waviness scale. The latter scale is determined by the angular size of the imager and a normalized atmospheric outer scale, and it does not depend on the strength of turbulence along the path. Spherical divergence of the light waves increases the edge waviness scale. A procedure for estimating the atmospheric and camera-noise components of the edge image motion is developed and implemented. A technique for mitigation of the edge image waviness that relies on averaging the effects of AA anisoplanatism on the image is presented and validated. The edge waviness variance is reduced by a factor of 2-3. The time history and temporal power spectrum of the edge image motion are obtained. These data confirm that the observed edge image motion is caused by turbulence.     

Tomography approach for multi-object adaptive optics

Multi-object adaptive optics (MOAO) is a solution developed to perform a correction by adaptive optics (AO) in a science large field of view. As in many wide-field AO schemes, a tomographic reconstruction of the turbulence volume is required in order to compute the MOAO corrections to be applied in the dedicated directions of the observed very faint targets. The specificity of MOAO is the open-loop control of the deformable mirrors by a number of wavefront sensors (WFSs) that are coupled to bright guide stars in different directions. MOAO calls for new procedures both for the cross registration of all the channels and for the computation of the tomographic reconstructor. We propose a new approach, called "Learn and Apply (L&A)", that allows us to retrieve the tomographic reconstructor using the on-sky wavefront measurements from an MOAO instrument. This method is also used to calibrate the registrations between the off-axis wavefront sensors and the deformable mirrors placed in the science optical paths. We propose a procedure linking the WFSs in the different directions and measuring directly on-sky the required covariance matrices needed for the reconstructor. We present the theoretical expressions of the turbulence spatial covariance of wavefront slopes allowing one to derive any turbulent covariance matrix between two wavefront sensors. Finally, we discuss the convergence issue on the measured covariance matrices, we propose the fitting of the data based on the theoretical slope covariance using a reduced number of turbulence parameters, and we present the computation of a fully modeled reconstructor.     

From the grating scale monitor to the generalized seeing monitor

An instrument named the grating scale monitor for measuring the outer scale L0 from the angle-of-arrival (AA) fluctuations of a perturbed wave front was developed a few years ago at Nice University. The AA is detected with a 5-ms time resolution by modulation of the stellar image in a small telescope with a grating. One uses the normalized covariance of AA fluctuations to estimate L0. A new version of this instrument, the generalized seeing monitor (GSM) is described. It consists of four identical modules for measuring the AA at four locations on the wave front. A spatiotemporal analysis of these data leads to the determination of seeing epsilon0, outer scale L0, and the wave-front speed. In addition, isoplanatic angle theta0 is determined from scintillation, making the characterization of turbulence with the GSM almost complete. We describe the instrument and make a detailed analysis of its performance and accuracy. Several site-testing campaigns have been conducted with the GSM: at La Silla (Chile), Ouka?meden (Morocco), Maidanak (Uzbekistan), and Cerro Pachon and Cerro Paranal (Chile). The main results of these campaigns are presented and discussed.     

A method for single image restoration based on the principal ergodic

We present a method to extract from a single image both object and point spread function using low contrast features of an extended field of view. Invoking the principal ergodic on stochastic turbulent phenomena, we show that the aberration parameters, characteristics of the earth's turbulence, can be recovered from multiple features within an isoplanatic patch. The ensemble statistics is replacing the spatial statistics of a single realization to derive an equivalent modulation transfer function and to apply usual deconvolution techniques such as Richardson-Lucy algorithms. The reliability of this postprocessing treatment has been tested on synthetic data, on solar granulation observations performed at La Lunette Jean Rosch du Pic du Midi, and during the event of the Venus transit at La Tour Solaire de Meudon.     

Effect of wavefront corrugations on fringe motion in an astronomical interferometer with spatial filters

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is < or = 30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is < or = 30%.     

Heterodyne detection through rain, snow, and turbid media: effective receiver size at optical through millimeter wavelengths

Both scattering and turbulence can effect the spatial coherence of short wavelength signals propagating through the open atmosphere. In this paper, the influence of forward scattering on heterodyne receiver performance is investigated, taking into account turbulence. It is shown that the effect of forward scattering is to reduce the effective heterodyne receiver area through spatial coherence degradation. A common approach to scattering as an attenuation phenomenon is not always valid. Generally, this approach underestimates the SNR. The accuracy of the attenuation approach depends on the ratio R of the actual receiver diameter to the scattering particle diameter. If R >100, scattering is essentially large angle and the typical treatment of scattering as an attenuation effect is indeed justified. However, for small R, forward scattering is primarily small angle, field coherence is noticeably affected by forward scattering, and the attenuation approach is not valid. Further, it is shown that the SNR is improved when the ratio of the scattering particulate size to turbulence coherence diameter decreases. From the practical point of view, the most important result of this study is that small receivers use their area more effectively than large receivers. Thus, an array of several small receivers may perform better than one large receiver with the same total area. The treatment here is particularly relevant for coherent detection through clouds, fog, precipitation, and turbid media in general, including liquid media.     

ICF驱动器靶场角漂的实时修正

通过光线追迹 ICF(惯性约束聚变)驱动器的靶场光路,建立靶场角漂的修正模型。在每次打靶实验中,实时测量靶场光路的角漂;将此角漂输入角漂修正模型,计算最后两块伺服反射镜的调整量,并调整这些反射镜,修正下次打靶时的角漂。其结果为角漂和修正偏差的比值大于 1。在八组实验中,角漂平均减小了 7.3 倍,最小修正偏差 0.009°,平均修正偏差 0.02°。     

Effects of finite inner and outer scales on the scintillation index of turbulent slant path

In this paper, the effects of nonzero inner scales and finite outer scales are investigated, in the context of Gaussian beam propagation along a slant path under general turbulence conditions. Theoretical expressions for the cut-off spatial frequencies are derived with an approach method, and thereby a modified scintillation model is developed to incorporate inner scale and outer scale parameters in the analysis. Then, inner and outer scale effects on the downlink are analysed with respect to the zenith angle, the altitude of the transmitter, the initial beam radius, as well as the turbulence strength. Numerical results indicate that the effects of a finite outer scale mainly influence transmission that occurs at large zenith angles or high altitudes, while the inner scale effects are more prevalent. This study may be helpful to improve the accuracy of calculation of slant-path scintillation index, and thus benefit the characterization and optimization of space/air-ground laser communication systems.     

Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes

We present an analytical algorithm for deriving the shapes of the deformable mirrors to be used for multiconjugate adaptive correction on a large telescope. The algorithm is optimal in the limit where the overlap of the wave-front contributions from relevant atmospheric layers probed by the guide stars is close to the size of the pupil. The fundamental principle for correction is based on a minimization of the sum of the residual power spectra of the phase fluctuations seen by the guide stars after correction. On the basis of the expressions for the mirror shapes, so-called layer transfer functions describing the distribution of the correction of a single atmospheric layer among the deformable mirrors and the resulting correction of that layer have been derived. It is shown that for five guide stars distributed in a regular cross, two- and three-mirror correction will be possible only up to a maximum frequency defined by the largest separation of the conjugate altitudes of the mirrors and by the angular separation of the guide stars. The performance of the algorithm is investigated in the K band by using a standard seven-layer atmosphere. We present results obtained for two guide-star configurations: a continuous distribution within a given angular radius and a five-star cross pattern with a given angular arm length. The wave-front fluctuations are subjected to correction using one, two, and three deformable mirrors. The needed mirror dynamic range is derived as required root-mean-square stroke and actuator pitch. Finally the performance is estimated in terms of the Strehl ratio obtained by the correction as a function of field angle. No noise has been included in the present analysis, and the guide stars are assumed to be at infinity.     

Optimized algorithm for the spatial nonuniformity correction of an imaging system based on a charge-coupled device color camera

We present an optimized linear algorithm for the spatial nonuniformity correction of a CCD color camera's imaging system and the experimental methodology developed for its implementation. We assess the influence of the algorithm's variables on the quality of the correction, that is, the dark image, the base correction image, and the reference level, and the range of application of the correction using a uniform radiance field provided by an integrator cube. The best spatial nonuniformity correction is achieved by having a nonzero dark image, by using an image with a mean digital level placed in the linear response range of the camera as the base correction image and taking the mean digital level of the image as the reference digital level. The response of the CCD color camera's imaging system to the uniform radiance field shows a high level of spatial uniformity after the optimized algorithm has been applied, which also allows us to achieve a high-quality spatial nonuniformity correction of captured images under different exposure conditions.