The design, manufacture, and testing of optical quality surface micromachined deformable mirrors (DMs) is described. With such mirrors, the shape of the reflective surface can be modified dynami-cally to compensate for optical aberrations and thereby improve image resolution in telescopes or microscopes. Over several years, we have developed microelectromechanical system (MEMS) processing technologies that allow production of optical quality of surface micromachined mirrors. These process steps have been integrated with a commercial foundry process to produce deformable mirrors of unprecedented quality. The devices employ 140 electrostatic actuators. Measurements of their performance detailed in this paper include 2µm of useful stroke, 3nm position repeatability, >90% reflectivity, and flatness better than 20nm RMS. A chemo-mechanical polishing process has been used to improve surface quality of the mirrors, and a gold coating process has been developed to improve the reflectivity without introducing a significant amount of stress in the mirror mem-brane. An ion bombardment technique has been developed to flatten mirrors. These silicon based deformable mirrors have the potential to modulate spatial and temporal features of an optical wave-front, and have applications in imaging, beam-forming, and optical communication systems. Design considerations and performance evaluation of recently fabricated DMs are presented.

As the spatial resolution, stroke and speed requirements for advanced adaptive optics applications increase, the addressing of large numbers of electrostatic actuators for wavefront correction becomes more demanding. In this paper, we review the requirements, limits and the challenges of electrically addressing a large array of electrostatic actuators using an integrated CMOS technology. We also review the issues of high-rate data sourcing, signal channelization and multiplexing, and electronics integration (VLSI) with an eye on system power and size requirements. In examining the various CMOS technologies, we find that a broadly applicable 40V technology is currently available. Higher voltages are also available, albeit with additional design restrictions. Finally, we report preliminary work on a specific addressing scheme for a vertically-integrated VLSI/electrostatic MEMS prototype spatial phase modulator with 288x256 pixels at framing rates of 2kHz.

Electrostatic Membrane Deformable Mirrors (DM) developed using silicon bulk micro-machining techniques offer the potential of providing low-cost, compact wavefront control systems for diverse optical system applications. The basic approach to electrostatic mirror construction, using bulk micro-machining, is relatively simple, allowing for custom designs to satisfy wavefront control requirements for most optical systems. An electrostatic DM consists of a thin membrane suspended over an actuator pad array that is connected to a high-voltage driver. Voltages applied to the array elements deflect the membrane to provide an optical surface capable of correcting for measured optical aberrations in a given system. The actuator voltages required to correct a given aberration are determined from wavefront sensor measurements and the mirror influence functions and/or through the minimization of measured error in the closed-loop control system. Electrostatic membrane DM designs are derived from well-known principles of membrane mechanics and electrostatics, the desired optical wavefront control requirements, and the current limitations of mirror fabrication and actuator drive electronics. In this paper, we discuss the electrostatic DM design process in some detail and present modeling results illustrating the performance of specific designs in terms of their ability to correct Zernike optical aberrations.

This paper describes design and fabrication of a microelectromechanical metal spatial light modulator (SLM) integrated with complementary metal-oxide semiconductor (CMOS) electronics, for high-dynamic-range wavefront control. The metal SLM consists of a large array of piston-motion MEMS mirror segments (pixels) which can deflect up to 0.78 µm each. Both 32x32 and 150x150 arrays of the actuators (1024 and 22500 elements respectively) were fabricated onto the CMOS driver electronics and individual pixels were addressed. A new process has been developed to reduce the topography during the metal MEMS processing to fabricate mirror pixels with improved optical quality.

There are three types of superresolving pupil filters in the optical systems, namely, amplitude type, phase-only type and amplitude-phase type. Among them, phase-only filter has received more attention because of its higher diffractive efficiency than others. The superresolving continuous phase filters were reported in Optics Letters in 2003 by Daniel M. de Juana et al. In this work, a new type of phase-only superresolving pupil filters, varying in discretely continuous way, is presented, whose phase distribution includes two parts: the first part is a sine function, that is, a continuous phase profile; the second part is a constant term, which can be different in the different range of the filter. The goal of the research is to find better results than the superresolving continuous phase filters. From the numerical results, we can see that this type filters can provide higher superresolving performance than the continuous phase filters. This filter with discrete continuous phase zones is also useful for analyzing the performance of a discrete phase filter illuminated with a continuous wavefront. Therefore, although this phase-only superresolving pupil filters are difficult to fabricate at present, the research on this type pupil has an important meaning both in theory and application.

The effect of fringing electric fields in a liquid crystal (LC) Optical Phased Array (OPA), also referred to as a spatial light modulator (SLM), is a governing factor that determines the diffraction efficiency (DE) of the LC OPA for high resolution spatial phase modulation. In this article, the fringing field effect in a high resolution LC OPA is studied by accurate modeling the DE of the LC blazed gratings by LC director simulation and Finite Difference Time Domain (FDTD) simulation. Influence factors that contribute significantly to the DE are discussed. Such results provide fundamental understanding for high resolution LC devices.

High-resolution, liquid-crystal spatial light modulators (SLMs) are being used as dynamic phase screens^1,2 for testing optical systems and as optical wavefront compensators^3,4 to dynamically correct distortions. An SLM provides hundreds of waves of adjustable phase modulation across the aperture of the device. Some of this phase adjustment can be used to compensate for distortions internal to the SLM such as backplane curvature. Because of modulo-2π operation, the dynamic range of the device is not significantly decreased by adding phase compensation, as long as the phase shift over the aperture is only a few waves. In this paper, we will discuss the techniques being used to determine the correct phase compensation for SLMs and how the compensation is being applied through the SLM control software.

A versatile, scalable wavefront control approach based upon proven liquid crystal (LC) spatial light modulator (SLM) technology was extended for potential use in high-energy near-infrared laser applications. The reflective LC SLM module demonstrated has a two-inch diameter active aperture with 812 pixels. Using an ultra-low absorption transparent conductor in the LC SLM, a high laser damage threshold was demonstrated. Novel dual frequency liquid crystal materials and addressing schemes were implemented to achieve fast switching speed (<1ms at 1.31 microns). Combining this LCSLM with a novel wavefront sensing method, a closed loop wavefront controller is being demonstrated. Compared to conventional deformable mirrors, this non-mechanical wavefront control approach offers substantial improvements in speed (bandwidth), resolution, power consumption and system weight/volume.

The self-referencing interferometer (SRI) is an innovative wavefront sensor (WFS) developed specifically for applications requiring laser propagation in strong scintillation. The performance of conventional gradient sensors, like Shack-Hartmann WFSs or lateral shearing interferometers, are severely limited in these environments due to the presence of branch points in the wavefront phase. In comparison, the SRI WFS directly measures the wavefront field so its performance is not affected by the presence of branch points. Over the last two years the Starfire Optical Range has been developing a prototype SRI WFS to demonstrate its advantages in strong scintillation environments. This paper discusses some practical lessons learned in building and operating an SRI WFS and presents initial results from laboratory tests.

Information theoretic bounds on the estimated Zernike coefficients for various diversity phase functions are analyzed in this paper. We will show that, in certain cases, defocus diversity may yield higher Cramer-Rao lower bound (CRLB) than some other diversity phase functions. Evaluating the performance of the phase diversity algorithm using simulated images, we find that for an extended scene and defocus diversity, the phase diversity algorithm achieves the CRLB for known objects and approaches the CRLB by about a factor of two for unknown objects.

The objective of Adaptive Optics is to achieve dynamic correction of severely abberated systems. This effort will develop a novel adaptive optics approach based on wavelets. Distortions are imprinted on the wavefront in the form of a spatially varying phase field. A wavelet-based method is being developed to subtract out distortions to yield a fully corrected image. This method will be initially developed for laser systems but aims eventually to be used for adaptive optical systems for ground-based telescopes.

We investigate the properties of a class of adaptive optics systems that do not employ a wave front sensor but rather optimise a photodetector signal by appropriate control of an adaptive element. Such wave front control methods have already been implemented in various applications. It is often convenient to represent a wave front aberration by the superposition of several aberration modes, for example, using the set of Zernike polynomials. In many practical situations the total aberration can be accurately represented by a small number of such modes. It is shown that the design of wave front sensor-less adaptive optics systems based upon Zernike modes is related to the mathematical problem of sphere packing. This involves the arrangement of spheres in multiple dimensions, where the coordinate for each dimension corresponds to a Zernike mode amplitude. This observation permits optimisation of the systems providing considerable increases in efficiency over schemes that take no account of the geometries involved. We combine this approach with modal wave front sensing to provide efficient, direct measurement of Zernike aberration modes.

Most ground-based adaptive optics systems use one of a small number of wavefront sensor technologies, notably (for relatively high-order systems) the Shack-Hartmann sensor, which provides local measurements of the phase slope (first derivative) at a number of regularly-spaced points across the telescope pupil. The curvature sensor, with response proportional to the second derivative of the phase, is also sometimes used, but has undesirable noise propagation properties during wavefront reconstruction as the number of actuators becomes large. It is interesting to consider the use for astronomical adaptive optics of the "phase contrast" technique, originally developed for microscopy by Zernike to allow convenient viewing of phase objects. In this technique, the wavefront sensor provides a direct measurement of the local value of phase in each subaperture of the pupil. This approach has some obvious disadvantages compared to Shack-Hartmann wavefront sensing, but has some less obvious but substantial advantages as well. Here we evaluate the relative merits in a practical ground-based adaptive optics system.

MCAO is a very promising technique to increase the AO corrected field of view. By now, this method was mainly studied for astronomical purposes. In case of horizontal or slant path propagation, the effects of anisoplanatism and scintillation are quite stronger than for astronomy: MCAO seems specially well-suited in this context. Therefore, many authors propose to use MCAO for laser beam control. Imaging is another potential applications: we have studied the theoretical performance of MCAO for extended source observation. We will present the results of this study.

Programmable diffractive optics (PDO) based on liquid-crystal (LC) technology has been demonstrated as a wavelength-agile means of compensating large aberrations over limited instantaneous spectral bandwidths. Acousto-optic tunable filters (AOTF) based on acousto-optic Bragg diffraction have been demonstrated as wavelength-agile means for selecting narrow spectral bands from white light with high rejection ratios. These technologies are integrated into a telescope system that includes a conventional primary mirror utilized off axis with more than 40 waves of aberration to view a white-light illuminated object bar chart. A high-resolution LC PDO, situated in a pupil plane, compensates for the large primary mirror aberration. The AOTF, operating in an image plane, rejects light outside a 2 nm spectral band centered about the wavelength at which the modulo-lambda phase profile of the PDO is defined. Wavelength-agile operation is achieved by synchronously tuning the PDO and AOTF over a 100nm spectral range. Near-diffraction-limited image quality is demonstrated.

Adaptive system bandwidth estimation techniques that can be applied to the adaptive optical systems based on stochastic parallel gradient descent (SPGD) optimizations are described. A useful parameter characterizing temporal dynamics of phase fluctuations resulting from the pupil-plane phase distorting layer moving at a certain velocity (wind velocity) is the Greenwood frequency. The knowledge of the Greenwood frequency and clock frequency of the adaptive control system (first order controller) allows simple estimation of the performance metric Strehl ratio. The numerical analyses indicate that the system performance can be characterized through the ratio of the Greenwood frequency and the system iterative process clock-frequency. A formula that estimates how the degradation of the adaptation performance in SPGD based compensators are derived and analyzed numerically. The bandwidth estimation for SPGD control systems with different resolution and decoupled SPGD (D-SPGD) control system is detailed.

This article investigates the use of a multi-conjugate adaptive optics system to improve the field-of-view for the system. The emphasis of this research is to develop techniques to improve the performance of optical systems with applications to horizontal imaging. The design and wave optics simulations of the proposed system are given. Preliminary results from the multi-conjugate adaptive optics system are also presented. The experimental system utilizes a liquid-crystal spatial light modulator and an interferometric wave-front sensor for correction and sensing of the phase aberrations, respectively.

The Air Force Research Laboratory, Directed Energy Directorate, together with SRS Technologies Inc., Huntsville, AL, and Surface Optics Corporation, San Diego, CA, have developed meter-class optical quality membranes with dielectric coatings and custom spectral filtering. The windows range in thickness from 5 to 20 µm and can operate in the visible and the near-infrared. To date the largest membrane manufactured is slightly less than one meter in diameter and its optical thickness variation is on the order of 35 nanometers rms. Surface roughness, optical density, and other optical data will be presented. The intent of this article is to expose this technology to optical designers with the expectation that significant design opportunities for observatories, telescopes, and experiments will result.

Materials and processes have been developed for production of polymer membranes with optical quality surface characteristics. These materials have been successfully used to manufacture large, high quality, ultra lightweight, optical flats for beam splitters, lens covers and other applications. These materials can potentially be used to develop large aperture primary mirrors with areal densities less than 1kg/m2. However, for curved mirrors it is more difficult to establish and maintain desired optical figure from the initial packaged configuration. This paper describes design analysis being performed to support fabrication of a membrane mirror test article. Modeling was performed to evaluate the effectiveness of several different boundary control concepts for correcting different types of figure aberrations. Analyses of different combinations of boundary displacement actuators, electrostatic force actuators, and pressure are presented.

This paper continues the work of a previous paper by investigating the concept of an initially parabolic membrane that is "flattened" due to intrinsic stresses and then re-inflated. The pressure to obtain zero apex displacement is determined, and root mean square (RMS) error is calculated. The RMS error is then minimized by varying the pressure. We also investigate the frequency response of a support ring connected to such a membrane. It is shown that the compressive loads applied by the membrane do not change the natural frequencies of the support ring appreciably.

A compact, low-cost wavefront sensor has been demonstrated to measure dynamic disturbances in 1-3 m diameter optical systems. With 448 subapertures and 4 KHz frame rate, it can measure disturbances up to 2 KHz at a level of 1/3800 waves rms at 0.65 μm. It also has a linear dynamic range of 3 X 10⁶:1 for ease of alignment. The principles of operation and test data are presented for the subaperture sensors (called NanoTrackers), which are lateral shearing interferometers capable of measuring tilt to 1.7 nanoradians rms at 8 µW of input power as well as phasing for segmented optical systems to 75 picometers rms (at 4 KHz).

Optical reducing systems for the extreme ultraviolet projection lithography are actively developed in the last few years. Optical elements of these systems are required to be of super-high optical quality. For the systems operatingin the 13-nm wavelength range, their optical distortions should not exceed 1 nm in magnitude. Manufacturing of such elements requires large financial injections. In this report, we consider how to use thermal deformation of an optical element exposed to light for improvement of optical quality of the element. It is shown, in particular, that residual quasi-static large-scale (20% of diameter of the element) optical distortions, about 15nm in magnitude, can be compensated with the proposed technique down to 0.5 nm (i.e.≈λ₀/20 - λ₀/30 in the EUV).

Test and evaluation of laser warning devices is important due to the increased use of laser devices in aerial applications. This research consists of an atmospheric aberrating system to enable in-lab testing of various detectors and sensors. This system employs laser light at 632.8nm from a Helium-Neon source and a spatial light modulator (SLM) to cause phase changes using a birefringent liquid crystal material. Measuring outgoing radiation from the SLM using a CCD targetboard and Shack-Hartmann wavefront sensor reveals an acceptable resemblance of system output to expected atmospheric theory. Over three turbulence scenarios, an error analysis reveals that turbulence data matches theory. A wave optics computer simulation is created analogous to the lab-bench design. Phase data, intensity data, and a computer simulation affirm lab-bench results so that the aberrating SLM system can be operated confidently.

Horizontal path correction of optical beam propagation presents a severe challenge to adaptive optics systems due to the short transverse coherence length and the high degree of scintillation incurred by propagation along these paths. The system presented operates with nearly monochromatic light. It does not require a global reconstruction of the phase, thereby eliminating issues with branch points and making its performance relatively unaffected by scintillation. The systems pixel count, 1024, and relatively high correction speed, in excess of 800 Hz, enable its use for correction of horizontal path beam propagation. We present results from laboratory and field tests of the system in which we have achieved Strehl ratios greater than 0.5.

Speckles in a highly corrected adaptive optic imaging system have been studied through numerical simulations and through analytic and algebraic investigations of the Fourier-optical expressions connecting pupil plane and focal plane, which simplify at high Strehl ratio. Significant insights into the behavior of speckles, and the speckle noise caused when they vary over time, have thus been gained. Such speckle noise is expected to set key limits on the sensitivity of searches for companions around other stars, including extrasolar planets1. In most cases, it is advantageous to use a coronagraph of some kind to suppress the bright primary star and so enhance the dynamic range of companion searches. In the current paper, I investigate speckle behavior and its impact on speckle noise in some common coronagraphic architectures, including the classical Lyot coronagraph and the new four quadrant phase mask (FQPM) concept.

We describe a simple optical system for generating atmospheric-like turbulence in the laboratory which allows for well-controlled testing of advanced adaptive-optical components and concepts. The system models a two-layer atmosphere using static phase plates and is capable of simulating a wide range of atmospheric conditions. The design of the hardware is presented along with results from the initial system modelling describing the theory of operation.

As advanced wavefront control components and systems are developed, they must be tested. This paper describes the methodology and hardware used in the laboratory at FGAN-FOM, The Research Institute for Optronics and Pattern Recognition in Germany, to evaluate components and systems to be used for wavefront control. The test bed described is unique in two ways: (1) it uses a Hamamatsu parallel aligned liquid crystal phase modulator as a pupil plane phase screen to generate degraded input wavefronts for testing the wavefront control systems, and (2) it may be used to evaluate a variety of wavefront sensor, corrector, and control elements without changing the layout or realigning the optical components that comprise the basic test bed. For example, once the test bed is assembled and aligned, a desired wavefront sensor, with its matching telecentric pupil-imaging lens pair, is simply inserted at the end of the beam train, aligned with the test bed output beam, calibrated, and tested. Similarly, a desired wavefront corrector is inserted at the appropriate pupil plane, aligned, and tested. The paper also presents typical test results.

A large aperture dynamic wavefront sensor (WFS) was tested and qualified for use against its design requirements. The WFS was designed to measure the relative slope of dynamic wavefronts; therefore, the test system created dynamic wavefronts, moving at 35 Hz to 315 Hz, with slopes on the order of 50 nanoradians (nR). The essential test system was an f/2.3 parabolic mirror with a laser source at the focal point, offset laterally by a fold mirror. The reflected light was nominally collimated and incident on the WFS at zero degrees. The source hardware was mounted on two crossed-translation stages that could drive a 540 μm, 1/2 Hz trapezoidal motion, inducing tilt in the collimated beam. This 100 microradians (μR) wavefront modulation calibrated the WFS. The fold mirror was mounted on a PZT, which oscillated the fold mirror from 35 Hz to 315 Hz, at tilt angles near 10 μR. This tilt moved the virtual source point, inducing wavefront tilts in the collimated output beam on the order of 100 nR. These fast, very small wavefront tilts were used to test the WFS performance. The test system, procedure, and calibration procedures are described.

Micro Mirror Arrays (MMAs) offer the potential of a high spatial and temporal resolution technology for wavefront control applications. In this paper a new Micro-Electro-Mechanical-System (MEMS) based MMA type is investigated. As opposed to most other MMA technologies which involve flip mirrors with only two possible orientations, this system can support two different mirror designs, piston-type mirrors for a continuous phase adjustment and tilt mirrors for light discarding purposes. The MMA's wavefront correction capabilities are being investigated in a breadboard which simulates continuous distortions and step errors, such as those that could be expected from lightweight primary mirrors of space telescopes or segmented mirrors, respectively. The wavefront is corrected by the MMA, then coupled into a monomode fiber. Four different correction methods have been tested, two stochastic approaches, a closed-loop Shack-Hartmann approach and an interferometric approach. Comparison of coupling efficiency is made between these approaches and against theoretical calculations.

A convenient method for exact recognitions of the curved shape and amplitudes of vibrated micro cantilevers is presented. The method includes the analysis based on preliminary introduction of the formulas for the shapes of deviated cantilevers to get the intensity distribution R(ξ) of the optical pattern of image. The feature of this method is the possibility to get high accuracy for MEMS orientation.

Agile beam steering of optical radiation using phased arrays offers significant advantages, such as weight, stability, speed and power requirements, over conventional beam steering systems based on large optics, telescopes, and gimbals. Phased arrays incorporating programmable diffractive optics systems based on MEMS or liquid crystal spatial light modulators are being investigated for a number of applications including large aberration compensation, near-diffraction-limited imaging and agile beam steering. A prototype system uses discrete phase steps to approximate modulo-2π phase profiles and operates with 307,200 independently addressable elements, 100% fill factor and total optical efficiencies of up to 93%. This paper presents analysis of an agile beam steering phased array system incorporating physical parameters such as fill factor, 2π reset fidelity and influence function. Diffractive wavefront control with non-2π resets is shown to produce continual beam steering. Expressions and modeling of the far-field beam pattern and off-axis beam steering efficiency are presented. Measured diffraction efficiencies show close comparison with calculated values.

The Wollaston prism with large deflection angle usually has small cross section size, which constrains its application in beam steering. This paper investigates the possibility of assembling the prisms together to increase the cross section size. Single-layer- and double-layer- assembled Wollaston prisms are investigated. The compression ratio and transmission ratio associated with the diffraction efficiency of assembled prisms are calculated and formulated.