对低层大气后向散射特性的测量与分析

激光导引星的亮度是决定自适应光学的系统工作状态的重要参数之一，它与大气散射和透过率等因素密切相关。为正确设计激光是引星系统提出用大气后向散射特性参数作为描述大气散射等对导引星影响的综合参数，并于１９９６年１２月首次在云南天文台对低层大气进行了后向散射特必参数测量，获得了５３２ｎｍ光的低层大气后向散射特性参数数据，并对测量结果进行了分析。     

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.     

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.     

高精度星敏感器星点光斑质心算法

高精度星敏感器星点光斑的质心精度是星敏感器整体精度的基础,它需要达到角秒级的量级。因此,提出了一种基于亚像元相关法的星像质心算法。这种算法是利用互相关匹配实现图像定位的原理,将星像质心定位到亚像素上来提高质心精度。它可以克服由于系统误差和图像采集所带来的误差。根据系统的光学参数设计以及星像的光谱、亮度及其在视场中的位置特征,仿真得到点列图模型,针对视场内与光轴的不同夹角仿真制作一系列亚像元理想模板,然后对星像加高斯随机噪声,把有随机噪声的星像与理想星像进行相关运算来求星像质心精度。通过仿真实验,得到相关法具有较高的星像质心精度,定位精度可以优于1/12个像素的量级。     

Sky coverage estimates for adaptive optics systems from computations in Zernike space

A sky coverage model for laser guide star adaptive optics systems is proposed. The atmosphere is considered to consist of a finite number of phase screens, which are defined by Zernike basis polynomials, located at different altitudes. These phase screens are transformed to the aperture plane, where they are converted to laser and natural guide star wavefront sensing measurements. These transformations incorporate the cone effect due to guide stars at finite heights, anisoplanatism due to guide stars off axis with respect to the science object, and adaptive optics systems with multiple guide stars. The wavefront error is calculated tomographically with minimum variance estimators derived from the transformation matrices and the known statistical properties of the atmosphere. This sky coverage model provides fast Monte Carlo simulations over random natural guide star configurations, irrespective of telescope diameter. The Monte Carlo simulations outlined show that inclusion of a finite outer scale for the atmosphere significantly reduces the median wavefront error, that increasing the number of laser guide stars in the asterism reduces the median wavefront error, and that a larger natural guide star patrol field provides a smaller median wavefront error when there is a low star density in the field.     

Basic principle of digital image correlation for in-plane displacement and strain measurement

The basic principle and the algorithm of a digital image correlation method, and the procedure for obtaining displacements and strains are described. In order to describe the basic principle precisely, only in-plane displacement and strain measurement of a planar object are explained. Gray levels between integer pixels of a digital image after deformation are interpolated to obtain displacements with subpixel resolution. Displacements are then determined by solving nonlinear simultaneous equations taking the deformation of a subset into consideration. Strains are obtainable by differentiating the measured displacements. In addition to the basic principle of digital image correlation, the example of the measurement and its results are shown.     

Including outer scale effects in zonal adaptive optics calculations

Mellin transform techniques are applied to evaluate the covariance of the integrated turbulence-induced phase distortions along a pair of ray paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. The derivation is for the case of a finite outer scale and a von Karman turbulence spectrum. The Taylor hypothesis is assumed if the two phase distortions are evaluated at two different times and amplitude scintillation effects are neglected. The resulting formula for the covariance is a power series in one variable for the case of a fixed atmospheric wind velocity profile and a power series in two variables for a fixed wind-speed profile with a random and uniformly distributed wind direction. These formulas are computationally efficient and can be easily integrated into computer codes for the numerical evaluation of adaptive optics system performance. Sample numerical results are presented to illustrate the effect of a finite outer scale on the performance of natural and laser guide star adaptive optics systems for an 8-m astronomical telescope. A hypothetical outer scale of 10 m significantly reduces the magnitude of tilt anisoplanatism, thereby improving the performance of a laser guide star adaptive optics system if the auxiliary natural star used for full-aperture tip/tilt sensing is offset from the science field. The reduction in higher-order anisoplanatism that is due to a 10-m outer scale is smaller, and the off-axis performance of a natural guide star adaptive optics system is not significantly improved.     

A domain coupling method for finite element digital image correlation with mechanical regularization: Application to multiscale measurements and parallel computing

A general method is proposed to couple two subregions analyzed with finite element digital image correlation even when using a mechanical regularization (regularized digital image correlation). A Lagrange multiplier is introduced to stitch both displacements fields in order to recover continuity over the full region of interest. Another interface unknown is introduced to ensure, additionally, the equilibrium of the mechanical models used for regularization. As a first application, the method is used to perform a single measurement from images at two different resolutions. Secondly, the method is also extended to parallel computing in regularized digital image correlation. The problem is formulated at the interface and solved with a Krylov‐type algorithm. A dedicated preconditioner is proposed to significantly accelerate convergence. The resulting method is a good candidate for the analysis of large data sets. Copyright © 2016 John Wiley & Sons, Ltd.     

Split atmospheric tomography using laser and natural guide stars

Laser guide star (LGS) atmospheric tomography is described in the literature as integrated minimum-variance tomographic wavefront reconstruction from a concatenated wavefront-sensor measurement vector consisting of many high-order, tip/tilt (TT)-removed LGS measurements, supplemented by a few low-order natural guide star (NGS) components essential to estimating the TT and tilt anisoplanatism (TA) modes undetectable by the TT-removed LGS wavefront sensors (WFSs). The practical integration of these NGS WFS measurements into the tomography problem is the main subject of this paper. A split control architecture implementing two separate control loops driven independently by closed-loop LGS and NGS measurements is proposed in this context. Its performance is evaluated in extensive wave optics Monte Carlo simulations for the Thirty Meter Telescope (TMT) LGS multiconjugate adaptive optics (MCAO) system, against the delivered performance of the integrated control architecture. Three iterative algorithms are analyzed for atmospheric tomography in both cases: a previously proposed Fourier domain preconditioned conjugate gradient (FDPCG) algorithm, a simple conjugate gradient (CG) algorithm without preconditioning, and a novel layer-oriented block Gauss-Seidel conjugate gradient algorithm (BGS-CG). Provided that enough iterations are performed, all three algorithms yield essentially identical closed-loop residual RMS wavefront errors for both control architectures, with the caveat that a somewhat smaller number of iterations are required by the CG and BGS-CG algorithms for the split approach. These results demonstrate that the split control approach benefits from (i) a simpler formulation of minimum-variance atmospheric tomography allowing for algorithms with reduced computational complexity and cost (processing requirements), (ii) a simpler, more flexible control of the NGS-controlled modes, and (iii) a reduced coupling between the LGS- and NGS-controlled modes. Computation and memory requirements for all three algorithms are also given for the split control approach for the TMT LGS AO system and appear feasible in relation to the performance specifications of current hardware technology.     

Incorporating higher-order modal measurements in tilt estimation: natural and laser guide star applications

Tilt compensation performance is generally suboptimal when phase measurements from natural or laser guide stars are used as the conjugate phase in an adaptive optics system. Optimal compensation is obtained when the conjugate-phase coefficients are estimated from beacon measurements, given knowledge of the correlation between the on-axis object phase and the beacon measurements. We apply optimal compensation theory to tilt correction for the case of an off-axis beacon. Because off-axis higher-order modes are correlated with the on-axis tilt components, a performance gain can be realized when the tilt estimator includes higher-order modal measurements. For natural guide star compensation, it is shown that equivalent tilt compensation can be achieved at beacon offsets that are three times larger when higher-order modes through Zernike 15 are used in the tilt estimator. For a laser guide star, although tilt information cannot be measured directly because of beam reciprocity, off-axis higher-order modal measurements can be used to estimate tilt components, leading to a maximum Strehl ratio of approximately 0.3 for the relative aperture diameter D/r(0) = 4 and the relative turbulence outer scale L(0)/D = 10.     

Experimental study of laser-generated shear waves using interferometry

The shear displacements generated by short laser pulses have been measured in aluminum semicylindrical samples, both in the thermoelastic and ablation regimes. We measured the waveforms at different angles and obtained the angular distribution pattern of the amplitudes. For the thermoelastic regime good agreement has been found between the measured and the theoretically predicted shear waveforms. In the ablation regime, the absolute values of the amplitudes are comparable to the ones of compressional waves. The shear waveforms are difficult to interpret, particularly in the case where both thermoelastic and ablative effects play a role, because the phases of the shear pulses are opposite to one another in these two regimes. To measure the in-plane displacements, and hence the shear displacement field generated by the pulsed laser, a speckle heterodyne interferometer was used.This article is dedicated to Professor Dr. Paul Höller on the occasion of his 65th birthday.     

Modal Pursuit to Detect Large Displacements and Strain Fields by Digital Image Correlation

Digital image correlation offers a useful approach to resolve displacements and strains by picture comparisons. However, many of the several methods proposed in the past suffer the occurrence of large displacements between the two compared pictures. The modal pursuit approach here introduced intends giving a possible strategy to prevent this limitation. The main advantage is that the method uses a global approach for the solution strategy. The procedure uses a displacement basis that derives from a modal analysis on a membrane structure whose shape is the same as the image region under investigation. The modes are introduced a little at a time so that the procedure is facilitated to converge, even when only two pictures (undeformed and final state) are used for the matching.     

Analysis of the improvement in sky coverage for multiconjugate adaptive optics systems obtained using minimum variance split tomography

The scientific utility of laser-guide-star-based multiconjugate adaptive optics systems depends upon high sky coverage. Previously we reported a high-fidelity sky coverage analysis of an ad hoc split tomography control algorithm and a postprocessing simulation technique. In this paper, we present the performance of a newer minimum variance split tomography algorithm, and we show that it brings a median improvement at zenith of 21 nm rms optical path difference error over the ad hoc split tomography control algorithm for our system, the Narrow Field Infrared Adaptive Optics System for the Thirty Meter Telescope. In order to make the comparison, we also validated our previously developed sky coverage postprocessing software using an integrated simulation of both high- (laser guide star) and low-order (natural guide star) loops. A new term in the noise model is also identified that improves the performance of both algorithms by more properly regularizing the reconstructor.     

Experimental Study of Laser-Generated Shear Waves Using Interferometry

Abstract

The shear displacements generated by short laser pulses have been measured in aluminum semicylindrical samples, both in the thermoelastic and ablation regimes. We measured the waveforms at different angles and obtained the angular distribution pattern of the amplitudes. For the thermoelastic regime good agreement has been found between the measured and the theoretically predicted shear waveforms. In the ablation regime, the absolute values of the amplitudes are comparable to the ones of compressional waves. The shear waveforms are difficult to interpret, particularly in the case where both thermoelastic and ablative effects play a role, because the phases of the shear pulses are opposite to one another in these two regimes. To measure the in-plane displacements, and hence the shear displacement field generated by the pulsed laser, a speckle heterodyne interferometer was used.     

星敏感器中快速星匹配跟踪算法研究

阐述了基于星体中心位置信息匹配的跟踪原理,提出了一种基于匹配的星跟踪方法.采用FPGA实现实时的星点位置信息的获取,解决了传统星跟踪过程中图像数据获取的瓶颈,增加了跟踪星体的个数,加快了匹配跟踪的速度;并且采用先排序后匹配的匹配方法,减少无谓的星体间的比较.仿真测试结果表明,此方法使得匹配跟踪的时间大约降低为原来的10%,提高了整个跟踪算法的计算速度,对星敏感器整体效能的提高也非常明显.     

Measurement of material anisotropy by dual-probe laser interferometer

A novel dual-probe laser interferometer, which has the advantage that it measures the surface displacements of the same surface wave at two locations, has been used to measure the speeds of surface waves and pseudo-surface waves on a silicon single crystal. Two configurations have been investigated. When the distance between the two points of detection is large relative to the length of the acoustic wave, the two signals detected by the probes are separated in the time domain. Hence the signal travel time can be found by the autocorrelation method. When the distance between the two points of detection is short relative to the acoustic wave, a composite signal is obtained consisting of two overlapping signals. Then the power cepstrum method is employed to extract the signal travel time between the probe points. The speeds for both types of surface waves are shown as functions of direction relative to the [001] crystal axis. The results have been compared with theoretical calculations and line-focus acoustic microscopy measurements.     

Open-loop control of liquid-crystal spatial light modulators for vertical atmospheric turbulence wavefront correction

We present an open-loop adaptive optics (AO) system based on two liquid-crystal spatial light modulators (LCSLMs) that profit from high precision wavefront generation and good repeatability. A wide optical bandwidth of 300 nm is designed for the system, and a new open-loop optical layout is invented to conveniently switch between the open and closed loop. The corresponding control algorithm is introduced with a loop frequency (the reciprocal of the total time delay of a correction loop) of 103 Hz. The system was mounted onto a 2.16 m telescope for vertical atmospheric turbulence correction. The full width at half-maximum of the image of the star α Boo reached 0.636 arc sec after the open-loop correction, while it was 2.12 arc sec before the correction. The result indicates that the open-loop AO system based on LCSLMs potentially has the ability to be used for general astronomical applications.     

Measurement of Material Anisotropy by Dual-Probe Laser Interferometer

Abstract

A novel dual-probe laser interferometer, which has the advantage that it measures the surface displacements of the same surface wave at two locations, has been used to measure the speeds of surface waves and pseudo-surface waves on a silicon single crystal. Two configurations have been investigated. When the distance between the two points of detection is large relative to the length of the acoustic wave, the two signals detected by the probes are separated in the time domain. Hence the signal travel time can be found by the autocorrelation method. When the distance between the two points of detection is short relative to the acoustic wave, a composite signal is obtained consisting of two overlapping signals. Then the power cepstrum method is employed to extract the signal travel time between the probe points. The speeds for both types of surface waves are shown as functions of direction relative to the [001] crystal axis. The results have been compared with theoretical calculations and line-focus acoustic microscopy measurements.     

Ground-to-Satellite Narrow-Laser-Beam Pointing by Use of a Backscattered Image

A technique for transmitting a narrow laser beam from a ground station to a satellite has been developed. The principle of pointing a laser beam to a distant target in a scattering medium by use of a backscattered laser beam image is described. We calculated the intensity distribution of the image by using a typical model of atmospheric coefficients. The method was applied to transmit a laser beam from a ground station to Engineering Test Satellite-VI. The accuracy of pointing the laser beam to the satellite was approximately 10 murad in this experiment.     

Photometric observations of a polychromatic laser guide star

We report the photometric observation of a polychromatic laser guide star (PLGS) using the AVLIS laser at the Lawrence Livermore National Laboratory (LLNL). The process aims at providing a measurement of the tilt of the incoming wave front at a telescope induced by atmospheric turbulence. It relies on the two-photon coherent excitation of the 4D5/2 energy level of sodium atoms in the mesosphere. We used two laser beams at 589 and 569 nm, with a maximum total average output power of approximately 350 W. For the purpose of photometric calibration, a natural star was observed simultaneously through the same instrument as the PLGS at the focus of the LLNL 50-cm telescope. Photometric measurements of the 330-nm return flux confirm our previous theoretical studies that the PLGS process should allow us at a later stage to correct for the tilt at wavelengths as short as approximately 1 microm at good astronomical sites. They show also that, at saturation of two-photon coherent absorption in the mesosphere, the backscattered flux increases by a factor of approximately 2 when the pulse repetition rate decreases by a factor of 3 at constant average power. This unexpected behavior is briefly discussed.