Open-loop shape control for continuous microelectromechanical system deformable mirror

The Deformable Mirror Demonstration Mission (DeMi) is a 6U CubeSat that will characterize the on-orbit performance of a Microelectromechanical Systems (MEMS) deformable mirror (DM) with both an image plane wavefront sensor and a Shack-Hartmann wavefront sensor (SHWFS). Coronagraphs on future space telescopes will require precise wavefront control to detect and characterize Earth-like exoplanets. High-actuator count MEMS deformable mirrors can provide wavefront control with low size, weight, and power. The DeMi payload will characterize the on-orbit performance of a 140 actuator MEMS Deformable Mirror (DM) with 5.5 μm maximum stroke, with a goal of measuring individual actuator wavefront displacement contributions to a precision of 12 nm. The payload will be able to measure low order aberrations to λ/10 accuracy and λ/50 precision, and will correct static and dynamic wavefront phase errors to less than 100 nm RMS. We present an overview of the payload design, the assembly, integration, and test process, and report on the development and validation of an optical diffraction model of the payload. Launch is planned for late 2019.

A mechanically motivated strategy for determining actuator locations for minimum force modal control of continuous faceplate deformable mirrors in adaptive optics systems is proposed. It is shown that numerically or analytically derived eigenmodes of deformable mirrors can be used to determine optimal positions for a limited number of actuators. The actuators considered in this framework may either be of displacement type or of force type. Moreover, the presented methodology can be adapted to momentum actuators.

Biological studies, drug discovery, and medical diagnostics benefit greatly from automated microscope platforms that can outperform even the most skilled human operators in certain tasks. However, the small field-of-view of a traditional microscope operating at high resolution poses a significant challenge in practice. The common approach of using a moving stage suffers from relatively low dynamic bandwidth and agitation to the specimen. This paper describes an automated microscope station based on the novel adaptive scanning optical microscope (ASOM), which combines a high-speed post-objective scanning mirror, a custom design scanner lens, and a microelectromechanical systems (MEMS) deformable mirror to achieve a greatly expanded field-of-view. After describing the layout and operating principle of the ASOM imaging subsystem, we present a system architecture for an automated microscope system suitable for the ASOM's unique wide field and high-speed imaging capabilities. We then describe a low-cost experimental prototype of the ASOM that demonstrates all critical optical characteristics of the instrument, including the calibration of the MEMS deformable mirror. Finally, we present initial biological (living nematode worms) imaging results obtained with the experimental apparatus and discuss the impact of the ASOM on biomedical imaging activities.

A four-group stabilized zoom lens design of two focal-length-variable elements was discussed in our early work. The focal-length of the zoom system could be adjusted by tuning the surface shape of focal-length-variable element. In this paper, we propose to use the deformable mirror (DM) as the focal-length-variable device, and then we need to control the DM to forming the required surface shape and analyze the errors between actual surface and theoretic surface. This lays the foundation for analyzing the focusing zoom errors of the stabilized zoom lens in the zoom process. This paper firstly introduces a DM flatten method applied for using OKO Technologies’ Piezoelectric Deformable Mirror (PDM) and analyzes the high order errors of flattened surface with the help of ZYGO interferometer. Then we study the method of DM control to form sphere surfaces with different curvature. The analyses of the high order error of the actual surface and the measurement of the curvature range of the sphere surface are also included in this paper.

The wave front corrector is one of the three key elements in adaptive optics, along with the wave front sensor and the control computer. Low cost, compact deformable mirrors are increasingly available. We have tested the AOptix bimorph deformable mirror, originally developed for ultra-high bandwidth laser communication systems, to determine its suitability for vision science applications, where cornea and lens introduce optical aberrations. Measurements of the dynamic response of the mirror to a step input were obtained using a commercial Laser Doppler Vibrometer (LDV). A computer-controlled Twyman-Green interferometer was constructed to allow the surface height of the deformable mirror to be measured using Phase-Shifting Interferometry as a function of various control voltages. A simple open-loop control method was used to compute the control voltages required to generate aberration mode shapes described by the Zernike polynomials. Using this method, the ability of the deformable mirror to generate each mode shape was characterized by measuring the maximum amplitude and RMS error of each Zernike mode shape up to the fifth radial order. The maximum deformation amplitude was found to diminish with the square of the radial order of the Zernike mode, with a measured deformation of 8 microns and 1.5 microns achieved at the second-order and fifth-order Zernike modes, respectively. This deformation amplitude appears to be sufficient to allow the mirror to correct for aberrations up to the fifth order in the human eye.

In conventional Adaptive optics (AO) system, wavefront aberration is measured by wavefront sensor. However, a point source is usually not available in most imaging systems. Therefore development of deformable mirror control scheme in adaptive optics system based on vision information will extend the application area of AO technique. A focus measure (FM) is a measure of image quality and can be calculated from image data obtained from the image sensor. It can be used to find the optimal shape of the deformable mirror that compensates the wavefront aberration. In this paper, we analyze the performance of focus measures under different types of wavefront aberrations. The relation of FM vs. the aberration strength is analyzed systematically for different aberration modes and different FM functions. The FM performance under combination of aberrations is also investigated. This research supplies a guide for selection of the suitable FM function and strategy for control of deformable mirror in the AO system.

A novel deformable mirror using 52 independent magnetic actuators (MIRAO 52, Imagine Eyes) is presented and characterized for ophthalmic applications. The capabilities of the device to reproduce different surfaces, in particular Zernike polynomials up to the fifth order, are investigated in detail. The study of the influence functions of the deformable mirror reveals a significant linear response with the applied voltage. The correcting device also presents a high fidelity in the generation of surfaces. The ranges of production of Zernike polynomials fully cover those typically found in the human eye, even for the cases of highly aberrated eyes. Data from keratoconic eyes are confronted with the obtained ranges, showing that the deformable mirror is able to compensate for these strong aberrations. Ocular aberration correction with polychromatic light, using a near Gaussian spectrum of 130 nm full width at half maximum centered at 800 nm, in five subjects is accomplished by simultaneously using the deformable mirror and an achromatizing lens, in order to compensate for the monochromatic and chromatic aberrations, respectively. Results from living eyes, including one exhibiting 4.66 D of myopia and a near pathologic cornea with notable high order aberrations, show a practically perfect aberration correction. Benefits and applications of simultaneous monochromatic and chromatic aberration correction are finally discussed in the context of retinal imaging and vision.

We propose a novel deformable mirror (DM) for adaptive optics in high power laser applications. The mirror is made of a Silicon carbide (SiC) faceplate, and cooling channels are embedded monolithically inside the faceplate with the chemical vapor desposition (CVD) method. The faceplate is 200 mm in diameter and 3 mm in thickness, and is actuated by 137 stack-type piezoelectric transducers arranged in a square grid. We also propose a new actuator influence function optimized for modelling our DM, which has a relatively stiffer faceplate and a higher coupling ratio compared with other DMs having thin faceplates. The cooling capability and optical performance of the DM are verified by simulations and actual experiments with a heat source. The DM is proved to operate at 1 kHz without the coolant flow and 100 Hz with the coolant flow, and the residual errors after compensation are less than 30 nm rms (root-mean-square). This paper presents the design, fabrication, and optical performance of the CVD SiC DM.

An adjustable surface shape with a high accuracy attracts a significant interest in the development of X-ray optical elements. However, the optical parameters of the conventional polished mirror are fixed, lacking adaptability and leading to significantly limited application targets. Based on adaptive optics technology, the X-ray deformable mirror can be achieved using the bending principle of a piezoelectric bimorph. In this study, we developed an X-ray lead-zirconate-titanate-(PZT) deformable mirror with an adjustable surface shape. The X-ray deformable mirror was simulated and optimized using the ANSYS software to ensure the feasibility of the design scheme. An X-ray deformable mirror prototype was manufactured based on the simulation results. It had a simple structure consisting of a 400-μmthick D263 glass substrate and 500-μm-thick PZT thin sheet. The PZT thin sheet consisted of 11 element electrode actuators. We used a ZYGO interferometer for an on-line surface shape feedback of the X-ray deformable mirror. By changing the voltage loads of the actuators, the glass substrate surface shape could be adjusted, and a target cylinder with a radius of curvature of 30 m was obtained. The curvature radius of the target cylinder could be changed, from 5 m to infinity.

For satisfying the boarder application requirement of adaptive optics (AO) and solving the problem of large volume and high cost of conventional deformable mirrors (DM), micro DM based on micro-electro-mechanical system (MEMS) technology is developed and measured. The developed DM has 140 hexagonal parallel plate capacitor electrostatic actuators. The actuators are arranged as a square array and the pitch is 400 μm. A DM prototype is fabricated by MEMS surface micromachining process and packaged by a ceramic pin grid array (CPGA). A miniaturization multi-channel high voltage driver for the DM is developed too. The measurement results show that the prototype has a surface PV value of 411 nm, RMS value of 78 nm, reflectivity of about 80% in 600 nm to 900 nm wavelength, stroke of 1.8 μm, actuator coupling of 15%, working bandwidth of 13 kHz and step response time of 23 μs. Thus the DM has the advantages of small volume, low cost and fast response. Besides the measurement of single element, the whole DM is controlled open loop to fit Zernike aberration and its fitting capability is demonstrated. Above results indicate that the DM prototype can satisfy initially the requirement of AO system.

The technology of membrane deformable mirror (DMs) that has the potential to achieve comprehensive wavefront compensation and control in high power laser has been developed rapidly in recent years. Experimental results reveal that strong nonlinearity is induced to the deformation of DMs with respect to the square of input voltage when operating voltage is more than 120V. The nonlinear response and strong coupling effect of control channel in DMs make it difficult to obtain the desired mirror surface shapes. A test bed is built up to measure the deformation of DMs driven by specified voltages. An efficient nonlinear model of deformation with respect to input voltages is presented using a back propagation neural network (BPNN). Deformation due to arbitrary actuator voltages applied to actuators to correct wavefront aberration can be calculated directly with a higher precision using the BPNN model proposed. The residual relative error of the proposed model shows the improvement of accuracy of an order about 5 as compared to that of linear model, and with no significant increase of time consumption. A preliminary open-loop control experiment of laser wavefront compensation is performed to exam the validity of applying the proposed BPNN model in laser wavefront compensation application.

In astronomy and microscopy, distortions in the wavefront affect the dynamic range of a high-contrast imaging system. These aberrations are either imposed by a turbulent medium such as the atmosphere, by static or thermal aberrations in the optical path, or by imperfectly phased subapertures in a segmented mirror. Active and adaptive optics (AO), consisting of a wavefront sensor and a deformable mirror, are employed to address this problem. Nevertheless, the non-common-path between the wavefront sensor and the science camera leads to persistent quasi-static speckles that are difficult to calibrate and which impose a floor on the image contrast. In this paper, we present the first experimental demonstration of a novel wavefront sensor requiring only a minor asymmetric obscuration of the pupil, using the science camera itself to detect high-order wavefront errors from the speckle pattern produced. We apply this to correct errors imposed on a deformable microelectromechanical segmented mirror in a closed loop, restoring a high-quality point spread function and residual wavefront errors of the order of ∼10 nm using 1600 nm light, from a starting point of ∼300 nm in piston and ∼0.3 mrad in tip–tilt. We recommend this as a method for measuring the non-common-path error in AO-equipped ground based telescopes, as well as an approach to phasing difficult segmented mirrors such as on the James Webb Space Telescope primary and as a future direction for extreme AO.

The Adaptive Optics Laboratory at the University of Victoria (Canada) and the Subaru Telescope NAOJ (Hawaii) are collaborating to develop a simple method allowing open-loop control of MEMS deformable mirrors. This method consists of an iterative algorithm based on 3 simple equations and 4 constants. The 4 constants are different for each mirror, therefore a characterization step is necessary to evaluate their values for a given mirror. In this paper we describe the model and the 3 equations it relies on. We also propose a characterization methodology and finally present the preliminary results respectively obtained on Victoria and Subaru test beds.

The next generation of extremely large telescopes (ELTs) that will be built on a scale of 30–50 meters in diameter necessarily require an increased ability to correct wavefront errors. Currently, wavefront correction is achieved through the use of a deformable mirror (DM). The degree and amount of correction depends on amechanical displacement of segments of themirror (stroke), and the number of actuators in the mirror surface (order). An effective ELTwill require a high-stroke (10microns) and high-order (100X100 actuators) mirror, a costly prospect using current technology.1 Lowering the cost while improving the performance of DMs is possible using microelectromechanical systems (MEMS) technology. However, current surface machining processes used to fabricate MEMS deformable mirrors, such as the Sandia ultra-planar multilevel MEMS technology (SUMMiT) and MEMSCAP’s PolyMUMPS process, limit a DM’s stroke due to the use of thin-film sacrificial layers (which are dissolved away after the etching process to free up micromechanical components in the actuators).2, 3 Commercially available surface micromachined MEMS mirrors are limited in stroke to approximately 5.5 microns, about half of the stroke required by ELTs. A high aspect ratio fabrication process capable of depositing thick layers will allow the DM’s to provide both high-stroke and highorder corrections, thus bypassing the need for a complex dual woofer (high stroke, low order)/tweeter (high order, low stroke) DM configuration.4 In our work, we tested different actuator designs with a bonded faceplate constructed using the LIGA (German acronym for lithography, electroplating, and molding) process, enabling multilayer fabrication of MEMS devices.5 Various types of high-stroke gold actuators consisting of folded springs with Figure 1. Diagram showing the final release of the monolithic fabricated structure created using our technique. The gap for the Xbeam electrostatic actuators is 20 microns, enabling a mirror stroke of 10 microns. WMS-15: specific glass-ceramic substrate. Not to scale.

Shack-Hartmann wavefront sensor (SHWFS) is considered as an efficient and complementary tool in the field of optics metrology. It is widely used for evaluating and characterizing rigid glass and soft eye contact lenses. However, the presence of any type of aberrations will cause measurement errors decreasing the precision of the sensor. Therefore, in the current study an experimental configuration based on an active adaptive SHWFS was presented for optical testing of circular optical elements such as thin and soft eye contact lenses. As an adaptive element, deformable mirror (DM), was integrated to the SHWFS setup to dynamically compensate for the wavefront aberrations of the illumination laser beam to provide an ideal plane. The concept was firstly verified by measuring standard thin lenses then applied to measure soft eye contact lenses. For the quantitative evaluation, Zernike polynomials was used to accurately define the dominant modes of wavefront aberrations and thus to calculate the wavefront to be written on the DM. Based on the standard deviation (1σ) between the given and the measured focal lengths of the tested thin glass lenses, the measurements show an improvement of the measurement error from 15.18% difference of the uncompensated wavefront and 3.90% of the referencebased method to only 2.11% after aberration compensation of the illumination beam. While for the contact lenses, the measurement error was 22.93% for uncompensated aberrations, 51% for the reference-based method, and 1.75% after aberrations compensation. The results reveal that the aberrations of the illumination laser beam and the wet cell induced aberrations affect the accuracy of the measurements which can be drastically improved by compensating the existing aberrations utilizing the active adaptive SHWFS setup. In conclusion, adaptive-SHWFS can be considered as an in-production, accurate and complementary tool for testing of optical components.