Convergence rates for iterative vector space projection methods for control of two deformable mirrors for compensation of both amplitude and phase fluctuations

The control of two deformable mirrors for compensation of time-varying fluctuations in the complex field that results from wave propagation through a turbulent medium is considered. Iterative vector space projection methods are utilized to determine the control commands to be applied to the two deformable mirrors. Convergence of the iterative algorithm is accelerated when the algorithm is initialized, at each measurement period, with the values for the phase commands obtained from the previous measurement period. Furthermore, it is found that, if the sample frequency is sufficiently greater than the Greenwood frequency, then only a single iterative step at each measurement period is required to obtain good compensation of both amplitude and phase fluctuations.     

Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation.

A modification of the parallel generalized projection algorithm is presented that allows for the use of projections in a weighted norm. Convergence properties of the modified algorithm, denoted the weighted parallel generalized projection algorithm, are developed. The weighted parallel generalized projection algorithm is applied to the control of two finite-resolution deformable mirrors to compensate for both the amplitude and the phase fluctuations that result from propagation through a turbulent medium. Numerical results are shown that indicate that a two-deformable-mirror system can provide improved performance over that of a single-deformable-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.     

Stroke amplifier for deformable mirrors

We demonstrate a simple optical configuration that amplifies the usable stroke of a deformable mirror. By arranging for the wavefront to traverse the deformable mirror more than once, we correct it more than once. The experimental implementation of the idea demonstrates a doubling of 2.0 and 2.04 by two different means.     

Optical zoom module based on two deformable mirrors for mobile device applications

In recent years, optical zoom functionality in mobile devices has been studied. Traditional zoom systems use motors to change separation of lenses to achieve the zoom function, but these systems result in long total length and high power consumption, which are not suitable for mobile devices. Adopting micromachined polymer deformable mirrors in zoom systems has the potential to reduce thickness and chromatic aberration. In this paper, we propose a 2× continuous optical zoom system with five-megapixel image sensors by using two deformable mirrors. In our design, the thickness of the zoom system is about 11 mm. The effective focal length ranges from 4.7 mm at a field angle of 52° to 9.4 mm. The f-number is 4.4 and 6.4 at the wide-angle and telephoto end, respectively.     

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.     

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.     

Modeling and parameter estimation for point-actuated continuous-facesheet deformable mirrors

We present a variant of the model introduced by Vogel and Yang [J. Opt. Soc. Am. A23, 1074 (2006)] for point-actuated deformable mirrors (DMs) with continuous facesheets, and we describe a robust efficient regularized- output least-squares computational scheme to estimate the parameters in the model, given noisy discrete observations of the DM response to known actuation. We demonstrate the effectiveness of this approach with experimental data obtained from a pair of DMs--a piezo-actuated prototype DM built by CILAS for the Thirty Meter Telescope Project and an electrostatically actuated commercial micro-electro-mechanical systems (MEMS) DM produced by Boston Micromachines Corporation.     

Broadband phase and intensity compensation with a deformable mirror for an interferometric nuller

Nulling interferometry has been proposed for the direct detection of Earth-like planets. Deep stable nulls require careful control of the relative intensity and phase of the beams that are being combined. We present a novel compensator, the Adaptive Nuller, that corrects the intensity and phase as a function of wavelength from 8 to 12 microm using a deformable mirror. This compensator has been used to produce rejection ratios of 82,000:1 over a bandwidth of 3.2 microm centered around 10 microm.     

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.     

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.     

Classification of stable configurations of plane mirrors

We have studied the stability of systems of plane mirrors by using a new way to describe ray transformations caused by such systems. All stable systems comprising as many as three mirrors are described and classified. Besides the well-known corner cube, infinitely many stable retroreflecting and direction-preserving three-mirror systems have been found.     

The fabrication of stable platinum-silicon oxide multilayers for X-ray mirrors

An investigation has been carried out to determine the conditions required for the fabrication of stable SiO₂-Pt multilayers using DC-magnetron sputtering for the Pt and RF-magnetron sputtering for the SiO₂. As a preliminary investigation, single layers of Pt on SiO₂ were analysed by X-ray reflectivity (XRR) and X-ray photoelectron spectroscopy (XPS) to develop a model of the Pt-SiO₂ interface layer. The results indicated that a distinct interface layer develops as a Pt silicate approximately 6 Å thick. SiO₂-Pt multilayers fabricated with a period d>65 Å using pure argon as the sputtering gas, display X-ray reflectivity patterns which can be accurately characterised by a repeating bilayer model. When d<65 Å the multilayer becomes unstable upon exposure to air. Additional peaks develop in the XRR pattern which increase in magnitude with time. These peaks arise from the expansion of the SiO₂ layers in the multilayer starting from the top bilayer and gradually working through the multilayer. In the as-prepared specimens the SiO₂ layers are incompletely oxidised and have a composition SiO_x (x<2) and, on exposure to air, oxygen diffuses through the multilayer surface converting the SiO_x to SiO₂. By introducing a small partial pressure of oxygen into the sputtering gas during deposition, multilayers with d<65 Å remained stable on exposure to air. Under these conditions the density of the platinum layers determined from XRR measurements was reduced by approximately 25%. XPS showed that the platinum layer contained bonded oxygen in the form of platinum oxide PtO_x (x<1). SiO₂/PtO_x multilayers have been fabricated with periods down to 13 Å, but the intensity of the first order peak drops off dramatically once the thickness of the PtO_x layer is less that 10-12 Å.     

Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch-Zernike polynomials

Recording methods for making aberration-corrected holographic gratings are greatly simplified by use of a plane multimode deformable mirror (MDM) upon one of the two recording beams. It is shown that MDM compensators easily provide the superposition of many interesting active optics modes, which we have named Clebsch-Zernike modes. When we apply only a uniform loading or no loading at all onto the rear side of the MDM clear aperture, the available Clebsch-Zernike modes are made to belong to a subclass of the Zernike modes that includes the three modes of the third-order aberration theory as well as a well-defined part of the Zernike higher-order modes. Such a recording method is considered to be universal, since it does not require the use of a sophisticated optical system such as a compensator. Active optics 12-arm MDM's in the vase form have been designed from the elasticity theory. The design of six-arm MDM's is currently carried out with theoretical results. As an example of the method, the recording of three holographic gratings of the Hubble Space Telescope Cosmic Origins Spectrograph has been investigated. Substantial improvements in image quality have been found by use of a six-arm MDM as recording compensator. The result is that aberrations of much higher order can simultaneously be corrected so that the residual blur images of the spectra occupy areas approximately 10 (direction of dispersion) x 3 (cross dispersion) = 30 times smaller-also in terms of pixel number-than those obtained by our American colleagues. Therefore the active optics recording method appears to provide substantial gains in resolving power and in sensitivity: (i) For all three gratings the spectral resolution would be increased by a factor of 10, and (ii), in addition, for the two higher dispersion gratings, the limiting magnitude on the sky appears to be increased by a magnitude of approximately 1-1.2.     

Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors

We propose a new way of recording in which a spherical blank and a deformable mirror are used to obtain high-resolution holographic gratings. The reflection of one of the two laser recording waves upon this mirror provides the deformations necessary to image correction to as much as seventh-order aberrations inclusively.     

双压电片变形镜的人眼像差拟合能力分析

针对三种不同空间分辨率的双压电片变形镜(Bimorph DM),采用仿真实验分析其对3~35项Zernike静态像差和实际人眼(包括疾病人眼)像差的拟合能力。实验表明,Bimorph变形镜特别适用于校正低阶像差,拟合误差小于0.15,随着空间分辨率的增加,Bimorph变形镜对Zernike像差和人眼像差的拟合能力总体表现为增强的趋势,其中,35单元的Bimorph变形镜的像差拟合能力最优,对前20项Zernike像差的拟合误差稍优于传统分立式压电变形镜。通过对Bimorph变形镜像差拟合能力的实验分析,为人眼视网膜高分辨率系统的Bimorph变形镜选型提供了分析方法,也为进一步提升Bimorph变形镜的像差校正能力奠定了研究基础。     

Closed-loop control of a woofer-tweeter adaptive optics system using wavelet-based phase reconstruction

A novel closed-loop control technique for adaptive optics (AO) systems based on a wavelet-based phase reconstruction technique and a woofer-tweeter controller is presented. The wavelet-based reconstruction technique is based on obtaining a Haar decomposition of the phase screen directly from gradient measurements and has been extended here with the use of a Poisson solver to improve performance. This method is O(N) (i.e., a linear computation cost as number of actuators increases) and is the fastest of the known O(N) reconstruction techniques. The controller configuration is based on the woofer-tweeter controller to control low- and high-spatial-frequency aberrations, respectively. The separation of the woofer and tweeter signals is done using a computationally efficient method that is based on the availability of a low-spatial-resolution reconstruction during the wavelet synthesis process. The performance of the proposed technique is evaluated using a simulated AO system and phase screens generated to reflect atmospheric turbulence with various dynamic characteristics. Results indicate that the combination of the wavelet-based phase reconstruction and woofer-tweeter controller leads to very good results with respect to speed and accuracy.     

Sensing wave-front amplitude and phase with phase diversity

We show in benchtop experiments that wave-front phase estimation by phase diversity can be significantly improved by simultaneous amplitude estimation. Processing speed, which will be important for real-time wave-front control applications, can be enhanced by use of small-format detectors with pixels that do not fully sample the diffraction limit. Using an object-independent phase-diversity algorithm, we show that, for both pointlike and extended objects, the fidelity of the phase and amplitude estimates degrades gracefully, rather than catastrophically, as the sampling becomes coarser. We show in simulation that the same algorithm also improves the fidelity of image reconstruction of complex targets.