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.     

Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes

We present sample Monte Carlo simulation results to illustrate the trends in multiconjugate adaptive optics (MCAO) performance as the telescope aperture diameter increases from 8 to 32 m with all other first-order system parameters held constant. The MCAO system considered includes three deformable mirrors, a 1-arc min square field of view, and five wave-front-sensing references consisting of either natural guide stars or laser guide stars at a range of either 30 or 90 km. The rms residual wave-front error decreases slowly with increasing aperture diameter with natural guide stars, whereas performance degrades significantly with increasing aperture diameter for laser guide stars at 30 km if the number of guide stars is held fixed. Performance with laser guide stars at 90 km is a weak function of telescope aperture diameter in the range from 8 to 32 m, with rms wave-front errors no more than 20% greater than the corresponding natural guide-star case for the same level of wave-front sensor's measurement noise.     

Methods for the characterization of deformable membrane mirrors

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.     

Increase in the compensated field of view with a double-conjugate adaptive-optics system

We analyze and quantify the capabilities and limitations of a double-conjugate adaptive-optics system. In the proposed system the contribution of two turbulent layers is treated separately, with Rayleigh guide stars for the bottom layer, sodium guide stars for the top layer, and two adaptive mirrors conjugate to the respective layers. The system substantially increases the compensated field of view. We give calculated results for the estimated number of guide stars needed, the wave-front sensor, and the adaptive-mirror resolution. Simulation results are also presented, and the residual error remaining after correction in our proposed system is compared with a conventional single-adaptive-mirror system.     

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.     

Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation

The nonlinear response and strong coupling of control channels in micromachined membrane deformable mirror (MMDM) devices make it difficult for one to control the MMDM to obtain the desired mirror surface shapes. A closed-loop adaptive control algorithm is developed for a continuous-surface MMDM used for aberration compensation. The algorithm iteratively adjusts the control voltages of all electrodes to reduce the variance of the optical wave front measured with a Hartmann-Shack wave-front sensor. Zernike polynomials are used to represent the mirror surface shape as well as the optical wave front. An adaptive experimental system to compensate for the wave-front aberrations of a model eye has been built in which the developed adaptive mirror-control algorithm is used to control a deformable mirror with 19 active channels. The experimental results show that the algorithm can adaptively update control voltages to generate an optimum continuous mirror surface profile, compensating for the aberrations within the operating range of the deformable mirror.     

Spatial spectrum analysis of wave-front correction with a segmented mirror

An expression is derived for the spatial power spectrum of wave-front errors after correction with a segmented mirror. This includes estimates of the spectral contributions of segment piston and tilt corrections and spatial aliasing by a regular array of segments. The approach allows rapid computation of wave-front error spectra in systems with highly segmented mirrors.     

Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration

Wave-front distortion compensation using direct system performance metric optimization is studied both theoretically and experimentally. It is shown how different requirements for wave-front control can be incorporated, and how information from different wave-front sensor types can be fused, within a generalized gradient descent optimization paradigm. In our experiments a very-large-scale integration (VLSI) system implementing a simultaneous perturbation stochastic approximation optimization algorithm was applied for real-time adaptive control of multielement wave-front correctors. The custom-chip controller is used in two adaptive laser beam focusing systems, one with a 127-element liquid-crystal phase modulator and the other with beam steering and 37-control channel micromachined deformable mirrors. The submillisecond response time of the micromachined deformable mirror and the parallel nature of the analog VLSI control architecture provide for high-speed adaptive compensation of dynamical phase aberrations of a laser beam under conditions of strong intensity scintillations. Experimental results demonstrate improvement of laser beam quality at the receiver plane in the spectral band up to 60 Hz.     

Prediction of wave-front sensor slope measurements with artificial neural networks

For adaptive optical systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave-front sensor (WFS) and corrected with a deformable mirror. One limitation in this process is the time delay between the measurement of the aberrated wave front and implementation of the proper correction. Statistical techniques exist for predicting the atmospheric aberrations at the time of correction based on the present and past measured wave fronts. However, for the statistical techniques to be effective, key parameters of the atmosphere and the adaptive optical system must be known. These parameters include the Fried coherence length r(0), the atmospheric wind-speed profile, and the WFS slope measurement error. Neural networks provide nonlinear solutions to adaptive optical problems while offering the possibility to function under changing seeing conditions without actual knowledge of the current state of the key parameters. We address the use of neural networks for WFS slope measurement prediction with only the noisy WFS measurements as inputs. Where appropriate, we compare with classical statistical-based methods to determine if neural networks offer true benefits in performance.     

Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror

We investigate the characteristics of a 37-channel micromachined membrane deformable mirror for wave-front generation. We demonstrate wave-front generation of the first 20 Zernike polynomial modes, using an iterative algorithm to adjust driving voltages. The results show that lower-order-mode wave fronts can be generated with good accuracy and large dynamic range, whereas the generation of higher-order modes is limited by the number of the actuator channels and the working range of the deformable mirror. The speed of wave-front generation can be as fast as several hundred hertz. Our results indicate that, in addition to generation of wave fronts with known aberrations, the characteristics of the micromachined membrane deformable mirror device can be useful in adaptive optics systems for compensating the first five orders of aberration.     

Membrane mirror and bias electronics

We have designed and built an electrostatically deformable membrane mirror with simple bias and driver electronics to evaluate its suitability for a curvature-sensing adaptive optics system. It has a 100-mm-diameter aluminized nitrocellulose membrane, with 31 actuators arranged concentrically. The unit operates at atmospheric pressure with a high bias voltage applied to the membrane. The high-voltage electronics are contained within the mirror housing for safety reasons. An entrance window reduces the effects of air-coupled vibration. Details of the device and design rationale are presented. With a proper bias, the unit can provide low-order (including tip-tilt) wave-front correction.     

变形镜参数变化对湍流像差校正效果的影响

利用61单元自适应光学系统湍流校正过程仿真模型,分析计算了变形镜的交连值、高斯 指数与自适应光学系统校正能力的关系。发现当交连值的稳定性变差时,引起校正效果的波动程度与高斯指数有关。高斯指数取1.9~2.1时,波前位相差的校正效果受交连值变化的影响最大,原因是校正算法的前提为各个驱动器的影响函数是线性叠加的。     

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.     

Branch-point reconstruction in laser beam projection through turbulence with finite-degree-of-freedom phase-only wave-front correction

Wave-front sensing and deformable mirror control algorithms in adaptive optics systems are designed on the premise that a continuous phase function exists in the telescope pupil that can be conjugated with a deformable mirror for the purpose of projecting a laser beam. However, recent studies of coherent wave propagation through turbulence have shown that under conditions where scintillation is not negligible, a truly continuous phase function does not in general exist as a result of the presence of branch points in the complex optical field. Because of branch points and the associated branch cuts, least-squares wave-front reconstruction paradigms can have large errors. We study the improvement that can be obtained by implementing wave-front reconstructors that can sense the presence of branch points and reconstruct a discontinuous phase function in the context of a laser beam projection system. This study was conducted by fitting a finite-degree-of-freedom deformable mirror to branch-point and least-squares reconstructions of the phase of the beacon field, propagating the corrected field to the beacon plane, and evaluating performance in the beacon plane. We find that the value of implementing branch-point reconstructors with a finite-degree-of-freedom deformable mirror is significant for optical paths that cause saturated log-amplitude fluctuations.     

High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors

Adaptive optics scanning laser ophthalmoscopes have been used to produce noninvasive views of the human retina. However, the range of aberration compensation has been limited by the choice of deformable mirror technology. We demonstrate that the use of dual deformable mirrors can effectively compensate large aberrations in the human eye while maintaining the quality of the retinal imagery. We verified experimentally that the use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the micro-electro-mechanical-system mirror alone and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. We also demonstrated that the large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.     

Geometric view of adaptive optics control

The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A 73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures.     

地面层自适应光学系统多颗激光导引星位置优化研究

对地面层自适应光学系统而言,多采用呈正多边形排列的多颗激光导引星星座作为参考来测量大气湍流对系统的影响。针对多颗激光导引星应当如何排布的问题,本文采用简化的地面层自适应光学几何模型作为系统性能评价函数,通过遗传算法优化获得不同湍流廓线下导引星的最优分布。同时,采用多进程、Numba库和多线程提高海量大气湍流廓线下对整个系统性能的估计速度。利用上述方法,以一个视场为14'的地面层自适应光学系统为例,用实测的大气湍流廓线数据分析了不同天文观测台址下湍流廓线与最优位置分布的关系。研究结果表明,同一台址下不同数目导引星的最优位置分布差异不大,其统计最优位置均呈中心一颗或角半径接近视场边缘的正多边形分布;不同台址下的导引星最优位置分布差异明显;大气湍流廓线测量的空间分辨率直接影响系统性能评价结果：其测量结果中的等效层数越多,导引星位置分布越接近规则的多边形。

     

Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments

An approach for compensation of turbulence-induced amplitude and phase distortions is described. Two deformable mirrors are placed optically conjugate to the collecting aperture and to a finite range from this aperture. Two control algorithms are presented. The first is a sequential generalized projection algorithm (SGPA) that is similar to the Gerchberg-Saxton phase retrieval algorithm. The second is a parallel generalized projection algorithm (PGPA) that introduces constraints that minimize the number of branch points in the control commands for the deformable mirrors. These approaches are compared with the approach of placing the second deformable mirror conjugate to the far field of the collecting aperture and using the Gerchberg-Saxton algorithm to determine the optimal mirror commands. Simulation results show that placing the second deformable mirror at a finite range can achieve near-unity Strehl ratio regardless of the strength of the scintillation induced by propagation through extended paths, while the maximum Strehl ratio of the far-field approach drops off with increasing scintillation. The feasibility of the solutions is evaluated by counting the branch points contained in the deformable mirror commands. There are large numbers of branch points contained in the control commands that are generated by the Gerchberg-Saxton SGPA-based algorithms, irrespective of where the second deformable mirror is located. However, the control commands generated by the PGPA with branch point constraints achieves excellent Strehl ratio and minimizes the number of branch points.     

Wave-front design algorithm for shaping a quasi-far-field pattern

To design a fully continuous wave-front distribution suitable for focused beam shaping by a deformable mirror, we modify the phase-retrieval algorithm by employing a uniformly distributed phase as a starting phase screen and spatial filtering for the near-field phase retrieved during the iteration process. A special phase unwrapping algorithm is not required to obtain a continuous phase distribution from the retrieved phase since the boundary of the 2pi-phase-jumped region in the designed phase distribution is perfectly closed. From the computational result producing a uniform square beam transformation from a circular defocused beam, this algorithm has provided a fully continuous wave-front distribution with a lower spatial frequency for a deformable mirror. The transformed square beam has a normalized intensity nonuniformity of varsigma(rms) = 0.14 with respect to a desired flat-topped square beam pattern. This beam-shaping method also provides a high energy-concentration rate of more than 98%.     

Isoplanatism in a multiconjugate adaptive optics system

Turbulence correction in a large field of view by use of an adaptive optics imaging system with several deformable mirrors (DM's) conjugated to various heights is considered. The residual phase variance is computed for an optimized linear algorithm in which a correction of each turbulent layer is achieved by applying a combination of suitably smoothed and scaled input phase screens to all DM's. Finite turbulence outer scale and finite spatial resolution of the DM's are taken into account. A general expression for the isoplanatic angle thetaM of a system with M mirrors is derived in the limiting case of infinitely large apertures and Kolmogorov turbulence. Like Fried's isoplanatic angle theta0,thetaM is a function only of the turbulence vertical profile, is scalable with wavelength, and is independent of the telescope diameter. Use of angle thetaM permits the gain in the field of view due to the increased number of DM's to be quantified and their optimal conjugate heights to be found. Calculations with real turbulence profiles show that with three DM's a gain of 7-10x is possible, giving the typical and best isoplanatic field-of-view radii of 16 and 30 arcseconds, respectively, at lambda = 0.5 microm. It is shown that in the actual systems the isoplanatic field will be somewhat larger than thetaM owing to the combined effects of finite aperture diameter, finite outer scale, and optimized wave-front spatial filtering. However, this additional gain is not dramatic; it is less than 1.5x for large-aperture telescopes.