Adaptive Control of a Micromachined Continuous Membrane Deformable Mirror for Aberration Compensation

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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.     

Application of eigenmode in the adaptive optics system based on a micromachined membrane deformable mirror

The construction process and characteristics of a deformable mirror eigenmode are introduced. The eigenmode of a 37-element micromachined membrane deformable mirror (MMDM) from OKO, Ltd. is analyzed. The Gaussian-Seidel low-order aberrations are fitted with eigenmodes as basic functions. An experimental adaptive optics (AO) system is constructed with the MMDM as the wavefront corrector, a deformable mirror eigenmode as the wavefront control algorithm, and a Shack-Hartmann wavefront sensor as the wavefront detector. The experimental results demonstrate that the deformable mirror eigenmode can act as the wavefront control algorithm for the AO system based on the MMDM.     

Aberration-free dynamic focusing with a multichannel micromachined membrane deformable mirror

We demonstrate aberration-free dynamic focusing with a low-cost 19-channel continuous-surface micromachined membrane deformable mirror (MMDM). A lookup table of the optimum control voltages for various focal lengths is obtained with an adaptive optics algorithm. Diffraction-limited imaging resolution is achieved owing to the capablility of the MMDM for aberration compensation. The measured speed of the MMDM supports dynamic focusing operations at several hundred hertz. Our dynamic focusing approach is shown to function with either monochromatic or broadband optical sources.     

微机械薄膜变形镜的闭环校正模型

介绍了微机械薄膜变形镜(MMDM)面形影响函数的意义,并测量了Oko公司37通道MMDM的面形影响函数矩阵,实验验证了镜面形变和单个驱动电极电压平方之间的线性关系,分析了变形镜的校正能力,建立了自适应光学系统闭环校正的模型.搭建基于MMDM的自适应光学实验系统,采用人眼出射波前作为原始波前进行实验,结果表明,模型能快速有效的对动态畸变波前进行校正,为基于MMDM的自适应光学系统提供了算法支持.     

Calibration of a deformable mirror and Strehl ratio measurements by use of phase diversity

Calibration experiments with a bimorph mirror are presented. Phase-diversity wave-front sensing is used for measuring the control matrix, nulling wave-front errors in the optical setup, including the mirror, and measuring Strehl ratios and residual higher-order aberrations. The Strehl ratio of the calibrated system is measured to be 0.975, corresponding to 1/40 wave rms in the residual wave front. The conclusion is that a phase-diversity wave-front sensor is easier to install and use than interferometers and can replace them in optical setups for testing adaptive optics systems.     

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.     

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.     

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.     

Comparative analysis of Zernike aberrations generation with deformable mirrors for ocular adaptive optics

The micromachined membrane deformable mirror (MMDM) and piezoelectric deformable mirror (PDM) are two types of cost-effective deformable mirrors (DMs) that are widely used in ocular adaptive optics. In the current study, a 59ch MMDM and a 37ch PDM are tested and compared in generation of Zernike aberrations which are the most dominant of the human eye. The results reveal that although PDM performs better in larger scope, both DMs have almost similar performance if the individual generation coefficient is within the range of ±1 µm.     

Theory and laboratory demonstrations on the use of a nematic liquid-crystal phase modulator for controlled turbulence generation and adaptive optics

We discuss the use of liquid-crystal phase modulators (LCPM's) both as a repeatable disturbance test source and as an adaptive optics corrector. LCPM's have the potential to induce controlled, repeatable, dynamic aberrations into optical systems at low cost, low complexity, and high flexibility. Because they are programmable and can be operated as transmissive elements, they can easily be inserted into the optical path of an adaptive optics system and used to generate a disturbance test source. When used as wave-front correctors they act as a piston-only segmented mirror and have a number of advantages. These include low operating power requirements, relatively low cost, and compact size. Laboratory experiments with a Meadowlark LCPM are presented. We first describe use of the LCPM as a repeatable disturbance generator for testing adaptive optics systems. We then describe a closed-loop adaptive optics system using the LCPM as the wave-front corrector. The adaptive optics system includes a Shack-Hartmann wave-front sensor operated with a zonal control algorithm.     

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.     

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.     

Adaptive optics: wave-front correction by use of adaptive filtering and control

A class of adaptive-optics problems is described in which phase distortions caused by atmospheric turbulence are corrected by adaptive wave-front reconstruction with a deformable mirror, i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, as opposed to the linear time-invariant control loops used in conventional adaptive optics. The basic problem is posed as an adaptive disturbance-rejection problem with many channels. The solution given is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. Simulation results are presented for a 1-m telescope with both one-layer and two-layer atmospheric turbulence profiles. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared with a classical linear time-invariant control loop.     

Sparse matrix approximation method for an active optical control system

We develop a sparse matrix approximation method to decompose a wave front into a basis set of actuator influence functions for an active optical system consisting of a deformable mirror and a segmented primary mirror. The wave front used is constructed by Zernike polynomials to simulate the output of a phase-retrieval algorithm. Results of a Monte Carlo simulation of the optical control loop are compared with the standard, nonsparse approach in terms of accuracy and precision, as well as computational speed and memory. The sparse matrix approximation method can yield more than a 50-fold increase in the speed and a 20-fold reduction in matrix size and a commensurate decrease in required memory, with less than 10% degradation in solution accuracy. Our method is also shown to be better than when elements are selected for the sparse matrix on a magnitude basis alone. We show that the method developed is a viable alternative to use of the full control matrix in a phase-retrieval-based active optical control system.     

High-aspect-ratio line focus for an x-ray laser by a deformable mirror

A high-aspect-ratio line focus is required on a plane target in x-ray laser experiments for obtaining a high gain-length product. Inherent wave-front aberrations in line-focusing optics, which consist of a cylindrical lens and a spherical lens, are discussed with respect to beam diameter. The nonuniformity of the linewidth that is due to the aberrations is also calculated by the ABCD matrix method. A deformable mirror of a continuous plate type with a diameter of 185 mm provides an adequate wave-front distribution for compensating for the wave-front aberration. The wave-front control by the deformable mirror realizes a fine linewidth of 25 mum and 18.2 mm long, corresponding to the aspect ratio of 728. The linewidth is three times the diffraction limit. The intensity distribution along the line focus is also improved.     

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.     

Evaluation of fitness parameters used in an iterative approach to aberration correction in optical sectioning microscopy

A major problem when imaging at depth within a biological sample in confocal or nonlinear microscopy is the introduction of sample induced aberrations. Adaptive optical systems can provide a technique to compensate for these sample aberrations and often iterative optimizations are used to improve on a particular parameter of the image (known as the fitness parameter). In this investigation, using a deformable membrane mirror as the adaptive optic element, we examine the effectiveness of a number of fitness parameters, when used with a genetic algorithm, at determining the optimal mirror shape required to compensate for sample induced aberrations. These fitness parameters are compared in terms of the number of mirror changes required to achieve optimization and the final axial resolution of the optical system. The effect that optimizing each fitness parameter has on the lateral and axial point-spread function is also examined.     

Shack Hartmann wave-front measurement with a large F-number plastic microlens array

A new plastic microlens array, consisting of 900 lenslets, has been developed for the Shack Hartmann wave-front sensor.The individual lens is 300 μm × 300μm and has a focal length of 10 mm, which provides the same focal size, 60 μm in diameter, with a constant peak intensity. One can improve thewave-front measurement accuracy by reducing the spot centroiding error by averaging a few frame memories of an image processor. A deformable mirror for testing the wave-front sensor gives anappropriate defocus and astigmatism, and the laser wave front is measured with a Shack Hartmann wave-front sensor. The measurement accuracy and reproducibility of our wave-front sensor are better than λ/20 and λ/50 (λ = 632.8 nm),respectively, in rms.     

Characterization and closed-loop performance of a liquid mirror adaptive optical system

A deformable mirror based on the principle of total internal reflection of light from an electrostatically deformed liquid-air interface was realized and used to perform closed-loop adaptive optical (AO) correction on a collimated laser beam aberrated by a rotating phase disk. Equations describing the resonant and oscillatory behavior of the liquid system were obtained and applied to the system under consideration. Characterization of the mirror included open- and closed-loop frequency responses, determination of rise times, the damping times of the liquid, and the influence of liquid surface motion in the absence of external optical aberrations. The performance of the AO system was determined for static and dynamic aberrations for various sets of system parameters. The predictions of the general expressions were compared to the results of the experimental realization and were found to be in good agreement.