A novel two-dimensional high-bandwidth Shack-Hartmann wavefront sensor was designed, addressing the high temporal bandwidth of optical aberrations caused by compressible flows. The principle of operation and modifications from an earlier version of the wavefront sensor are presented and compared to a commercially available wavefront sensor. A wavefront reconstruction algorithm is derived. The high-temporal resolution and spatial resolution of the sensor is demonstrated. A two-dimensional, acoustically forced heated jet was used to test the sensor.

Adaptive optics (AO) systems on airborne platforms must be able to sense fields degraded by strong turbulence often over long horizontal propagation paths. This paper presents results of simulated hybrid-wavefront-sensor performance when measuring optical fields due to propagation of a distant point source through Kolmogorov turbulence. The hybrid-wavefront-sensor simulation combines Shack-Hartmann and self-referencing-interferometer (SRI) measurements degraded by photon noise and produces higher-resolution wavefront estimates that are less susceptible to noise than either sensor acting alone and that inherit the SRI's insensitivity to scintillation.

The use of a laser guidestar (LGS) for the purpose of a beacon in an adaptive-optics (AO) system is prone to perspective elongation effects on the spots of a Shack-Hartmann wavefront sensor. The elongated spots can vary in size over the subapertures and affect the gradient sensitivity of the sensor. The Air Force Research Laboratory (AFRL) has developed a LGS model that outputs gradient gains which represent the effects of an extended beacon on the spots for a Shack-Hartmann wavefront sensor. This paper investigates the application of these gains in an experimental setup in order to both analyze the effects of the variation in those gains due to spot size elongation and to measure the impact on the performance of an AO system.

It has long been known that branch points cause degradation in adaptive optic performance. Here, we begin a study on the aggregate nature of branch points, specifically beginning the process to relate branch points measured in the pupil to the upstream turbulence that created them. As such, we study not only the wave as measured in the telescope's pupil, but also the wave in the intervening region between the turbulence layer and the pupil with this paper's focus on the intervening region. We show that for optical waves propagating in atmospheric turbulence upstream of the pupil, branch points are created infinitesimally close together in pairs of opposite polarity. Branch points are shown to be enduring features of the propagating wave and their branch cuts are shown to evolve smoothly in time. It is postulated that atmospherically created branch point pairs separate as they propagate, and that they carry both the velocity of, and distance to, the turbulence layer that created them. Subsequent papers will demonstrate this to be true.

The Atmospheric Turbulence Simulator used in testing in the Atmospheric Simulation and Adaptive-optic Laboratory Test-bed at Air Force Research Laboratory, Directed Energy Directorate's Starfire Optical Range is configured based on three characteristics; Fried's parameter, r₀, the Rytov number, σ²_χ , and the Greenwood Frequency, f_G. All three may be estimated from open loop data as a means of verifying the simulated turbulence conditions for a given test configuration. However, unlike r₀ and f_G, the Rytov number isn't directly calculated. Instead the scintillation index is estimated from intensity measurements. At low Rytov values, (< 0.3 - 0.4), this measurement can approximate the Rytov number, however beyond a Rytov of 0.4 this parameter becomes saturated. Branch Points begin to appear after the Rytov value exceeds 0.1. In this work the behavior of the branch point density is examined to determine its viability as another parameter for calibration our turbulence simulator.

Recent research has shown that branch points, as they appear in astronomical applications, have a rich collective behavior, showing, in particular, that branch point pairs have a well-defined, non-stoichastic velocity, and that once a branch point pairs location is measured, it can be tracked in open-loop adaptive optics operation. The research presented here uses this new information as a priori knowledge in closed-loop AO. Specifically, an algorithm was developed that measures branch point location and velocity at time t_k and then uses this to estimate the phase contribution at time t_k+n, giving it an effective memory of where branch points appear and allowing it to determine more accurately between real branch points and noise. The output of the new algorithm is used as a second input to the DM control law. Results of initial closed-loop AO tests will be presented.

This paper presents results from an adaptive optics experiment in which an adaptive control loop augments a classical adaptive optics feedback loop. A membrane deformable mirror is used for wavefront correction, and a set of frequency-weighted modes based on the actuator geometry are used to define the control channels for the adaptive controller. In the adaptive optics experiment, the wavefront sensor in the control loop is a three step phase shifting self-referencing interferometer. The corrected laser beam is imaged by a diagnostic CCD camera. The effect of atmospheric turbulence is simulated in the experiment by a sequence of wavefronts that is generated by a WaveTrain adaptive optics model and added to the laser beam by a spatial light modulator. The experimental results show the improved closed-loop wavefront errors and diagnostic images produced by the adaptive control loop as compared to the classical adaptive optics loop.

The conventional adaptive-optics (AO) system configuration consisting of a Shack-Hartmann wavefront sensor using the Fried geometry is prone to an unsensed waffle mode because of an inability to have discrete point reconstruction of the phase at the actuator positions. Techniques that involve filtering and/or projecting out the waffle mode in the reconstructor have been shown to be effective at not allowing the unwanted mode to occur, but come at the cost of also omitting relevant high frequency content from the measured phase. This paper analyzes a technique of sensing the waffle mode in the deformable mirror commands and applying a spatial filter to those commands in order to mitigate for the waffle mode. Directly spatially filtering the deformable mirror commands gives the benefit of maintaining the reconstruction of high frequency phase of interest while having the ability to alleviate for the waffle pattern when it arises.

An adaptive optics (AO) system is most effective when there is a known alignment between the wave front sensor (WFS) and the deformable mirror (DM). Misregistration is the term for the unknown alignment between the WFS and DM. Misregistration degrades system performance and can make the system unstable. An AO system uses a reconstruction matrix to transform WFS measurements into DM commands. A standard AO system uses a model reconstruction matrix that assumes perfect registration between the WFS and DM. The object of this research is to mitigate the negative effects of misregistration by using offline WFS measurements to create the reconstruction matrix. To build the reconstruction matrix, each actuator on the DM is poked to a fixed amount, and then the resulting measurement on the WFS is recorded. Analytic studies of the model and measured matrices show that the measured matrix yields a more stable AO system. Additional simulations indicate that applying the measured matrix improves the overall system performance compared to that of the model reconstruction matrix.

Adaptive optics applies advanced sensing and control to improve the ability of optical systems to collect images through a turbulent atmosphere. The results of this research effort demonstrate that the combination of two recent approaches improves the performance of adaptive optics in directed energy and laser communication scenarios. The first approach is adaptive control, which offers improved performance over fixed-gain controllers in the presence of rapidly changing turbulence. The second approach incorporated into the study is a dual-mirror system. The two mirrors are a high-bandwidth, low-actuator-stroke (tweeter) mirror and a low-bandwidth, large-actuator-stroke (woofer) mirror. The woofer-tweeter combination allows for better compensation of the large-variance, high-spatial-frequency phase distortion generated by strong turbulence. Two different adaptive controllers are presented, one using a relatively simple model reference adaptive system controller and one using a lattice filter controller. The lattice filter is implemented in two ways. In one implementation the filter operates on the individual actuators, while in the other it operates on frequency-weighted modes. The modal implementation reduces the computational burden of the filter. The performance of the different adaptive controllers is compared to both each other and to a traditional fixed-gain controller. Simulations show that adaptive control of woofertweeter adaptive optics can increase the mean Strehl ratio by up to 20%. In general, the lattice filter controllers outperform the model reference adaptive system controller. However, in cases where the lattice filter cannot use a sufficient number of modes, the model reference adaptive system can outperform the lattice filter.

In moderate-to-strong scintillation, multi-conjugate adaptive optics (MCAO) appears promising to compensate for amplitude and phase fluctuations. In this research, a MCAO system is simulated with a segmented deformable mirror (DM) reshaping the amplitude and the second DM (continuous) flattening the phase after propagation from the segmented mirror. A Gerchberg-Saxton (GS) type algorithm is used with Fresnel propagation between DM planes. The effects of varying the phase's apparent resolution on a segmented DM in the pupil plane is investigated. Results show the mean square error in the reshaped beam decreases as D/r_o and Rytov number increase over the range of conditions tested (r_o: 0.11 m - 0.36 m). The field-estimated Strehl ratio drops precipitously when the number of subapertures is increased beyond about 36 across, using a branch-pointtolerant unwrapper, due to the presence of branch points. On the second DM, by using the mean of the phase within each subaperture before back propagating to the first DM plane (inside the GS loop), the Strehl ratio was improved 6 - 11 percent using 4 - 19 actuators across. Further a novel method of cascading segmented DMs, of increasingly higher resolution, doing amplitude reshaping followed by a continuous DM to flatten the phase is explored.

Effective application of membrane deformable mirrors requires understanding of the operating characteristics of these devices. Using custom developed hardware and software tools, we were able to quantify the temporal and spatial response characteristics of a membrane deformable mirror. Temporal characteristics were analyzed using a frequency sweep stimulus while measuring the DM response on a feedback photodiode. Spatial characteristics of the DM were analyzed in terms of its ability to reproduce Zernike polynomials of increasing order using a variety of actuator patterns. We present here both the techniques for performing these measurements and the results from simulation and the laboratory.

Iris AO has been developing microelectromechanical systems (MEMS) based deformable mirrors (DM) for a number of years. This paper presents a review of the basic segmented DM design and shows test results of a 111-actuator, 37- piston/tip/tilt (PTT) segment DM. A 489-actuator 163-PTT-segment design is described as well as progress towards the fabrication of the device. A view to the future is shown by describing path-finding research towards 3000-actuator, 1000- PTT-segment DMs.

This paper is the 3rd in a series of papers discussing characterization of a Micro-Electrical-Mechanical-System (MEMS) deformable mirror in adaptive optics. Here we present a comparison between a conventional adaptive optics system using a Xinetics continuous face sheet deformable mirror with that of segmented MEMS deformable mirror. We intentionally designed the optical layout to mimic that of a conventional adaptive optics system. We present this initial optical layout for the MEMS adaptive optics system and discuss problems incurred with implementing such a layout; also presented is an enhanced optical layout that partially addresses these problems. Closed loop Strehl highlighting the two systems will be shown for each case as well. Finally the performances of both conventional adaptive optics and the MEMS adaptive optics system is presented for a range of adaptive optics parameters pertinent to astronomical adaptive optics leading to a discussion of the possible implication of introducing a MEMS adaptive optics system into the science community.

Adaptive Optics is established as essential technology in current and future ground based (extremely) large telescopes to compensate for atmospheric turbulence. Deformable mirrors for astronomic purposes have a high number of actuators (> 10k), a relatively large stroke (> 10μm) on a small spacing (< 10mm) and a high control bandwidth (> 100Hz). The availability of piezoelectric ceramics as an actuator principle has driven the development of many adaptive deformable mirrors towards inappropriately stiff displacement actuation. This, while the use of force actuation supersedes piezos in performance and longevity while being less costly per channel by a factor of 10-20. This paper presents a model which is independent of the actuator type used for actuation of continuous facesheet deformable mirrors, to study the design parameters such as: actuator spacing & coupling, influence function, peak-valley stroke, dynamical behavior: global & local, etc. The model is validated using finite element simulations and its parameters are used to derive design fundamentals for optimization.

The wavefront control community relies on fast and accurate subsystems for optical tilt correction. New technology enables large diameter (172 mm), optically-flat (<32 nm rms surface error), highly accurate, fast (500 Hz) steering mirrors (FSMs) with very low stabilization errors (50 nrad jitter). Applied Technology Associates (ATA) builds and tests FSMs using Silicon Carbide lightweight optics on very rigid aluminum mounts. Optical encoders provide position feedback and the mirror control algorithms are embedded in an FPGA processing architecture with fabric-based doubleprecision arithmetic capability. To characterize mirror performance, ATA integrated a performance verification system using an xPC MATLAB-based Track Loop Controller to close a 200 Hz optical loop around the FSM. This paper describes the mirror and FPGA control that enables a new level of FSM stabilization performance and presents both modeled and measured performance for the system.

We introduce a new beam steering concept of the "Risley grating" that consists of independently rotating inline polarization gratings (PGs). The Risley grating concept replaces the bulky prismatic elements of the Risley prisms with thin plates containing polarization gratings, and employs their highly polarization-sensitive diffraction. As rotating two PGs, the output beam tracks within a field-of-regard (FOR), which is determined by the grating period and their relative orientations. Since PGs are typically patterned in thin liquid crystal layers (a few μm thick), the system can be implemented with far less thickness and weight. In addition, these thin gratings can be placed with virtually zero proximity and the beam walk-off becomes negligible. We demonstrate the Risley grating that performs continuous steering with 62° FOR and 89-92% transmittance at 1550 nm wavelength. The governing equations for the steering angles of the Risley grating in the direction cosine space are also presented.

Most non-conventional approaches to image restoration of objects observed over long atmospheric paths require multiple frames of short exposure images taken with low noise focal plane arrays. Multi-frame blind deconvolution is such an approach. In most cases the object is assumed to extend only over a single isoplanatic patch. However, when one is observing scenes over a near horizontal slant path the isoplantic patch size is small due to extended atmospheric turbulence over the entire slant path, and the scene usually extends over many isoplanatic patches. In addition base motion jitter in the observing platform introduces a frame-to-frame linear shift that must be compensated for in order for the multi-frame restoration to be successful. In this paper we describe a maximum a-posteriori parameter estimation approach to the simultaneous estimation of the frame-to-frame shifts and non-isoplanatic point spread functions. This approach can be incorporated into an iterative algorithm. We present a brief derivation of the algorithm as well as its application to actual image data collected from airborne and ground based platforms.

In this paper we examine the effect of the addition of uncompensated jitter on adaptive optics performance by modeling the effects of diffraction, atmospheric turbulence, and jitter as Gaussian beam spread terms. The anisoplanatic effect of jitter is shown to be a necessary addition to this Gaussian beam spread model. We develop a simplified method for including the effect of the jitter induced angular anisoplanatism in the Gaussian beam spread model.

The Laser Interferometer Space Antenna mission is a planned gravitational wave detector consisting of three spacecraft in heliocentric orbit. Laser interferometry is used to measure distance fluctuations between test masses aboard each spacecraft to the picometer level over a 5 million kilometer separation. Laser frequency fluctuations must be suppressed in order to meet the measurement requirements. Arm-locking, a technique that uses the constellation of spacecraft as a frequency reference, is a proposed method for stabilizing the laser frequency. We consider the problem of arm-locking using classical optimal control theory and find that our designs satisfy the LISA requirements.