Real-time atmospheric compensation

Ghost imaging lidar system for remote imaging

Research towards practical applications of ghost imaging lidar system especially in longer sensing distance has been urgent in recent years. In this paper we develop a ghost imaging lidar system to boost an extension of remote imaging, where the transmission distance of the collimated pseudo-thermal beam can be improved hugely over long range and just shifting the adjustable lens assembly generates wide field of view suiting for short-range imaging. Based on the proposed lidar system, the changing tendency of illuminating field of view, energy density, and reconstructed images is analyzed and verified experimentally. Some considerations on the improvement of this lidar system are also discussed.

Average gradient of Zernike polynomials over polygons

Wavefront estimation from slope sensor data is often achieved by fitting measured slopes with Zernike polynomial derivatives averaged over the sampling subapertures. Here we discuss how the calculation of these average derivatives can be reduced to one-dimensional integrals of the Zernike polynomials, rather than their derivatives, along the perimeter of each subaperture. We then use this result to derive closed-form expressions for the average Zernike polynomial derivatives over polygonal areas, only requiring evaluation of polynomials at the polygon vertices. Finally, these expressions are applied to simulated Shack-Hartmann wavefront sensors with 7 and 23 fully illuminated lenslets across a circular pupil, with their accuracy and calculation time compared against commonly used integration methods.

Shack-Hartmann versus reverse Hartmann wavefront sensors: experimental results

With respect to the classical Shack-Hartmann (SH) wavefront sensor (WFS), the recently proposed reverse Hartmann (RH) sensor inverts the locations of the filtering and observation planes and forms a direct image of the pupil on a detector array. The slopes of the wavefront error (WFE) are then reconstructed by using a double Fourier transform algorithm. It turns out that the same algorithm can also be applied to the raw data acquired by SH sensors. This Letter presents the first, to the best of our knowledge, experimental results obtained with a simplified RH WFS and their comparison to those provided by a reference SH sensor, in both classical and double Fourier transform modes. They demonstrate that similar WFE measurement accuracy is achievable when using the three techniques, at least within the limit of our test bench that is estimated around $\lambda/10$λ/10 RMS.

Fresnel diffraction analysis of Ronchi and reverse Hartmann tests

This paper presents a Fresnel diffraction analysis of classical Ronchi and reverse Hartmann tests. Simplified analytical expressions of the intensity patterns observed by the camera are established, allowing quantitative measurements of the wavefront slopes of the tested optical system. The wavefronts are then reconstructed from their slopes using a double Fourier transform algorithm. The optimization of the operational parameters of the system is discussed in view of different quality criteria, including relative pupil shear and contrast factors in both monochromatic and polychromatic light. Practical examples of applications are studied with the help of numerical simulations, demonstrating that measurement accuracies better than λ/100 RMS are achievable on properly dimensioned systems. Finally, the technique is also applicable to wavefront sensing in adaptive optics systems.

Digital adaptive optics confocal microscopy based on iterative retrieval of optical aberration from a guidestar hologram

Guidestar hologram based digital adaptive optics (DAO) is one recently emerging active imaging modality. It records each complex distorted line field reflected or scattered from the sample by an off-axis digital hologram, measures the optical aberration from a separate off-axis digital guidestar hologram, and removes the optical aberration from the distorted line fields by numerical processing. In previously demonstrated DAO systems, the optical aberration was directly retrieved from the guidestar hologram by taking its Fourier transform and extracting the phase term. For the direct retrieval method (DRM), when the sample is not coincident with the guidestar focal plane, the accuracy of the optical aberration retrieved by DRM undergoes a fast decay, leading to quality deterioration of corrected images. To tackle this problem, we explore here an image metrics-based iterative method (MIM) to retrieve the optical aberration from the guidestar hologram. Using an aberrated objective lens and scattering samples, we demonstrate that MIM can improve the accuracy of the retrieved aberrations from both focused and defocused guidestar holograms, compared to DRM, to improve the robustness of the DAO.

Unimorph deformable mirror for space telescopes: design and manufacturing

Large space telescopes made of deployable and lightweight structures suffer from aberrations caused by thermal deformations, gravitational release, and alignment errors which occur during the deployment procedure. An active optics system would allow on-site correction of wave-front errors, and ease the requirements on thermal and mechanical stability of the optical train. In the course of a project funded by the European Space Agency we have developed and manufactured a unimorph deformable mirror based on piezoelectric actuation. The mirror is able to work in space environment and is designed to correct for large aberrations of low order with high surface fidelity. This paper discusses design, manufacturing and performance results of the deformable mirror.

Digital adaptive optics line-scanning confocal imaging system

A digital adaptive optics line-scanning confocal imaging (DAOLCI) system is proposed by applying digital holographic adaptive optics to a digital form of line-scanning confocal imaging system. In DAOLCI, each line scan is recorded by a digital hologram, which allows access to the complex optical field from one slice of the sample through digital holography. This complex optical field contains both the information of one slice of the sample and the optical aberration of the system, thus allowing us to compensate for the effect of the optical aberration, which can be sensed by a complex guide star hologram. After numerical aberration compensation, the corrected optical fields of a sequence of line scans are stitched into the final corrected confocal image. In DAOLCI, a numerical slit is applied to realize the confocality at the sensor end. The width of this slit can be adjusted to control the image contrast and speckle noise for scattering samples. DAOLCI dispenses with the hardware pieces, such as Shack–Hartmann wavefront sensor and deformable mirror, and the closed-loop feedbacks adopted in the conventional adaptive optics confocal imaging system, thus reducing the optomechanical complexity and cost. Numerical simulations and proof-of-principle experiments are presented that demonstrate the feasibility of this idea.

Non-common path aberration correction in an adaptive optics scanning ophthalmoscope

The correction of non-common path aberrations (NCPAs) between the imaging and wavefront sensing channel in a confocal scanning adaptive optics ophthalmoscope is demonstrated. NCPA correction is achieved by maximizing an image sharpness metric while the confocal detection aperture is temporarily removed, effectively minimizing the monochromatic aberrations in the illumination path of the imaging channel. Comparison of NCPA estimated using zonal and modal orthogonal wavefront corrector bases provided wavefronts that differ by ~λ/20 in root-mean-squared (~λ/30 standard deviation). Sequential insertion of a cylindrical lens in the illumination and light collection paths of the imaging channel was used to compare image resolution after changing the wavefront correction to maximize image sharpness and intensity metrics. Finally, the NCPA correction was incorporated into the closed-loop adaptive optics control by biasing the wavefront sensor signals without reducing its bandwidth.

Scalable stacked array piezoelectric deformable mirror for astronomy and laser processing applications

A prototype of a scalable and potentially low-cost stacked array piezoelectric deformable mirror (SA-PDM) with 35 active elements is presented in this paper. This prototype is characterized by a 2 μm maximum actuator stroke, a 1.4 μm mirror sag (measured for a 14 mm × 14 mm area of the unpowered SA-PDM), and a ±200 nm hysteresis error. The initial proof of concept experiments described here show that this mirror can be successfully used for shaping a high power laser beam in order to improve laser machining performance. Various beam shapes have been obtained with the SA-PDM and examples of laser machining with the shaped beams are presented.

Fourier transform digital holographic adaptive optics imaging system

A Fourier transform digital holographic adaptive optics imaging system and its basic principles are proposed. The CCD is put at the exact Fourier transform plane of the pupil of the eye lens. The spherical curvature introduced by the optics except the eye lens itself is eliminated. The CCD is also at image plane of the target. The point-spread function of the system is directly recorded, making it easier to determine the correct guide-star hologram. Also, the light signal will be stronger at the CCD, especially for phase-aberration sensing. Numerical propagation is avoided. The sensor aperture has nothing to do with the resolution and the possibility of using low coherence or incoherent illumination is opened. The system becomes more efficient and flexible. Although it is intended for ophthalmic use, it also shows potential application in microscopy. The robustness and feasibility of this compact system are demonstrated by simulations and experiments using scattering objects.

Imaging single cells in the living retina

A quarter century ago, we were limited to a macroscopic view of the retina inside the living eye. Since then, new imaging technologies, including confocal scanning laser ophthalmoscopy, optical coherence tomography, and adaptive optics fundus imaging, transformed the eye into a microscope in which individual cells can now be resolved noninvasively. These technologies have enabled a wide range of studies of the retina that were previously impossible.

Recent advances in astronomical adaptive optics

The imaging performance of large ground-based astronomical telescopes is compromised by dynamic wavefront aberration caused by atmospheric turbulence. Techniques to measure and correct the aberration in real time, collectively called adaptive optics (AO), have been developed over the past half century, but it is only within the past decade that the delivery of diffraction-limited image quality at near- and mid-infrared wavelengths at many of the world's biggest telescopes has become routine. Exploitation of this new capability has led to a number of ground-breaking astronomical results, which has in turn spurred the continued development of AO to address ever more technical challenges that limit its scientific applicability. I review the present state of the art, highlight a number of noteworthy scientific results, and outline several ongoing experiments designed to broaden the scope of observations that can be undertaken with AO. In particular, I explore the significant advances required in AO technology to satisfy the needs for a new generation of extremely large telescopes of diameter 25 m and larger that are now being designed.

Dual wavefront sensing channel monocular adaptive optics system for accommodation studies

Manipulation of the eye's aberrations using adaptive optics (AO) has shown that optical imperfections can affect the dynamic accommodation response. A limitation of current system designs used for such studies is an inability to make direct measurements of the eye's aberrations during the experiment. We present an AO system which has a dual wavefront sensing channel. The corrective device is a 37-actuator piezoelectric deformable mirror. The measurements used to control the mirror, and direct measurements of the eye's aberrations, are captured on a single Shack-Hartmann sensor. Other features of the system include stroke amplification of the deformable mirror and a rotating diffuser to reduce speckle.We demonstrate the utility of the system by investigating the impact of aberration dynamics on the control of steady-state accommodation on four subjects.

Wavefront expansion basis functions and their relationships

Wavefront expansion basis functions are important in representing ocular aberrations and phase perturbations due to atmospheric turbulence. A general discussion is presented for the conversions of the coefficients between any two sets of basis functions. Several popular sets of basis functions, namely, Zernike polynomials, Fourier series, and Taylor monomials, are discussed and the conversion matrices between any two of these basis functions are derived. Some analytical and numerical examples are given to demonstrate conversion of coefficients of different basis function sets.

Analysis of stellar interferometers as wave-front sensors

The basic principle and theoretical relationships of an original method are presented that allow the wave-front errors of a ground or spaceborne telescope to be retrieved when its main pupil is combined with a second, decentered reference optical arm. The measurement accuracy of such a telescope-interferometer is then estimated by means of various numerical simulations, and good performance is demonstrated, except in limited areas near the telescope pupil's rim. In particular, it permits direct phase evaluation (thus avoiding the use of first- or second-order derivatives), which will be of special interest for the cophasing of segmented mirrors in future giant-telescope projects. Finally, the useful practical domain of the method is defined, which seems to be better suited for periodic diagnostics of space- or ground-based telescopes or to real-time scientific observations in some specific cases (e.g., the central star in instruments that search for extrasolar planets).

Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils

An iterative zonal wave-front estimation algorithm for slope or gradient-type data in optical testing acquired with regular or irregular pupil shapes is presented. In the mathematical model proposed, the optical surface, or wave-front shape estimation, which may have any pupil shape or size, shares a predefined wave-front estimation matrix that we establish. Owing to the finite pupil of the instrument, the challenge of wave front shape estimation in optical testing lies in large part in how to properly handle boundary conditions. The solution we propose is an efficient iterative process based on Gerchberg-type iterations. The proposed method is validated with data collected from a 15 x 15-grid Shack-Hartmann sensor built at the Nanjing Astronomical Instruments Research Center in China. Results show that the rms deviation error of the estimated wave front from the original wave front is less than lambda/130-lambda/150 after approximately 12 iterations and less than lambda/100 (both for lambda = 632.8 nm) after as few as four iterations. Also, a theoretical analysis of algorithm complexity and error propagation is presented.

MISTRAL: a myopic edge-preserving image restoration method, with application to astronomical adaptive-optics-corrected long-exposure images

Deconvolution is a necessary tool for the exploitation of a number of imaging instruments. We describe a deconvolution method developed in a Bayesian framework in the context of imaging through turbulence with adaptive optics. This method uses a noise model that accounts for both photonic and detector noises. It additionally contains a regularization term that is appropriate for objects that are a mix of sharp edges and smooth areas. Finally, it reckons with an imperfect knowledge of the point-spread function (PSF) by estimating the PSF jointly with the object under soft constraints rather than blindly (i.e., without constraints). These constraints are designed to embody our knowledge of the PSF. The implementation of this method is called MISTRAL. It is validated by simulations, and its effectiveness is illustrated by deconvolution results on experimental data taken on various adaptive optics systems and telescopes. Some of these deconvolutions have already been used to derive published astrophysical interpretations.

Image-adaptive deconvolution for three-dimensional deep biological imaging

Deconvolution algorithms are widely used in conventional fluorescence microscopy, but they remain difficult to apply to deep imaging systems such as confocal and two-photon microscopy, due to the practical difficulty of measuring the system's point spread function (PSF), especially in biological experiments. Since a separate PSF measurement performed under the design optical conditions of the microscope cannot reproduce the true experimental conditions prevailing in situ, the most natural approach to solve the problem is to extract the PSF from the images themselves. We investigate here the approach of cropping an approximate PSF directly from the images, by exploiting the presence of small structures within the samples under study. This approach turns out to be practical in many cases, allowing significantly better restorations than with a design PSF obtained by imaging fluorescent beads in gel. We demonstrate the advantages of this approach with a number of deconvolution experiments performed both on artificially blurred and noisy test images, and on real confocal images taken within an in vitro preparation of the mouse hearing organ.

Broadband, static wave-front generation: Na-Ag ion-exchange phase screens and telescope emulation

We test the statistical properties of static, atmospherelike wave fronts in glass that allow repeatable testing of astronomical adaptive optics instrumentation. The technology is mask-structured ion exchange (MSI) in glass and has significant advantages over other transmissive technologies. The screens are easy to clean, are insensitive to ambient temperature changes, and have high optical-to-near-infrared transmission. However, the effective coherence length (r0) on each of the fabricated screens is systematically too large or, equivalently, the fabricated aberrations are too weak. Despite this strong caveat, the screens appear to be quite useful: Long-exposure point-spread functions have realistic shapes, and power spectrum indices closely match those of the computer-generated wave fronts. Most significant, stacking screens with similar r0 values reduced r0 by the amount predicted by turbulence theory. The refractivity of MSI screens remains unmeasured. Finally, we present our design of an optical system that emulates the key characteristics of the Very Large Telescope, made to contain glass phase screens and to mimic an array of stars for multiconjugate adaptive optics system testing.

Rapidly convergent phase-retrieval strategy for use with reflected laser light

An approach for wave-front sensing using reflected laserlight from a rough object is proposed. Light from a single laser beam is split into two beams, and the beams are launched from spatially separated apertures to illuminate an object. The reflected laser light is measured in the pupil plane of a receive telescope and in a plane conjugate to the object. By modulation of one of the two illuminator beams, the intensity pattern associated with each beam, as well as the field cross product of the two beams, is measured in each plane. A phase-retrieval algorithm is formulated by using projections onto constraint sets to recover the complex field associated with each illuminator. The algorithm is found to converge rapidly to the correct solution, particularly when compared with the convergence rates of more conventional phase-retrieval approaches. The new algorithm exhibits excellent performance in strong scintillation and is very tolerant to noise, exhibiting only a very small noise gain.

Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques

The complexity of computing conventional matrix multiply wave-front reconstructors scales as O(n3) for most adaptive optical (AO) systems, where n is the number of deformable mirror (DM) actuators. This is impractical for proposed systems with extremely large n. It is known that sparse matrix methods improve this scaling for least-squares reconstructors, but sparse techniques are not immediately applicable to the minimum-variance reconstructors now favored for multiconjugate adaptive optical (MCAO) systems with multiple wave-front sensors (WFSs) and DMs. Complications arise from the nonsparse statistics of atmospheric turbulence, and the global tip/tilt WFS measurement errors associated with laser guide star (LGS) position uncertainty. A description is given of how sparse matrix methods can still be applied by use of a sparse approximation for turbulence statistics and by recognizing that the nonsparse matrix terms arising from LGS position uncertainty are low-rank adjustments that can be evaluated by using the matrix inversion lemma. Sample numerical results for AO and MCAO systems illustrate that the approximation made to turbulence statistics has negligible effect on estimation accuracy, the time to compute the sparse minimum-variance reconstructor for a conventional natural guide star AO system scales as O(n3/2) and is only a few seconds for n = 3500, and sparse techniques reduce the reconstructor computations by a factor of 8 for sample MCAO systems with 2417 DM actuators and 4280 WFS subapertures. With extrapolation to 9700 actuators and 17,120 subapertures, a reduction by a factor of approximately 30 or 40 to 1 is predicted.

Description and simulation of an active imaging technique utilizing two speckle fields: root reconstructors

Quasi-monochromatic light will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of the illuminated object. Further information can be obtained if two colors of coherent light are used, provided that the colors are sufficiently close in wavelength that the interference is also measurable. It is shown that no more than two intensities of two speckle patterns and their interference are required to produce an unambiguous band-limited image of an object, to within an overall spatial translation of the image, in the absence of measurement errors and in the case where all roots of both fields and their complex conjugates are distinct. This result is proven with a root-matching technique, which treats the electric fields as polynomials in the pupil plane, the coefficients of which form the desired complex object. Several root-matching algorithms are developed and tested. These algorithms are generally slow and sensitive to noise. So motivated, several other techniques are applied to the problem, including phase retrieval, expectation maximization, and probability maximization in a sequel paper [J. Opt. Soc. Am. A 19, 458 (2002)]. The phase-retrieval and expectation-maximization techniques proved to be most effective for reconstructions of complex objects larger than 10 pixels across.

Optimal wave-front reconstruction strategies for multiconjugate adaptive optics

We propose an optimal approach for the phase reconstruction in a large field of view (FOV) for multiconjugate adaptive optics. This optimal approach is based on a minimum-mean-square-error estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the C2n profile in order to optimally estimate the correction wave front to be applied to each deformable mirror (DM). This optimal approach also accounts for the fact that the number of DMs will always be smaller than the number of turbulent layers, since the C2n profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consists of a full tomographic reconstruction of the turbulence volume followed by a projection onto the DMs accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions [model-approximation (MA) approach], which might be a crude approximation, is also considered for comparison. This MA approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and MA approaches is proposed. It is shown that the optimal approach provides very good performance even with a small number of DMs (typically, one or two). For instance, good Strehl ratios (greater than 20%) are obtained for a 4-m telescope on a 150-arc sec x 150-arc sec FOV by using only three guide stars and two DMs.

Adaptive optics with advanced phase-contrast techniques. I. High-resolution wave-front sensing

High-resolution phase-contrast wave-front sensors based on phase spatial light modulators and micromirror/ liquid-crystal arrays are introduced. Wave-front sensor performance is analyzed for atmospheric-turbulence-induced phase distortions described by the Kolmogorov and the Andrews models. A high-resolution phase-contrast wave-front sensor (nonlinear Zernike filter) based on an optically controlled liquid-crystal phase spatial light modulator is experimentally demonstrated. The results demonstrate high-resolution visualization of dynamically changing phase distortions within the sensor time response of approximately 10 ms.

Generalized wave-front reconstruction algorithm applied in a Shack-Hartmann Test

A generalized numerical wave-front reconstruction method is proposed that is suitable for diversified irregular pupil shapes of optical systems to be measured. That is, to make a generalized and regular normal equation set, the test domain is extended to a regular square shape. The compatibility of this method is discussed in detail, and efficient algorithms (such as the Cholesky method) for solving this normal equation set are given. In addition, the authors give strict analyses of not only the error propagation in the wave-front estimate but also of the discretization errors of this domain extension algorithm. Finally, some application examples are given to demonstrate this algorithm.

Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra

Adaptive optics systems provide a real-time compensation for atmospheric turbulence. However, the correction is often only partial, and a deconvolution is required for reaching the diffraction limit. The need for a regularized deconvolution is discussed, and such a deconvolution technique is presented. This technique incorporates a positivity constraint and some a priori knowledge of the object (an estimate of its local mean and a model for its power spectral density). This method is then extended to the case of an unknown point-spread function, still taking advantage of similar a priori information on the point-spread function. Deconvolution results are presented for both simulated and experimental data.

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 microm 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.

Synthetic-aperture imaging through an aberrating medium: experimental demonstration

A simple technique for high-resolution imaging of distant objects is described and experimentally demonstrated. The technique, referred to as Fourier telescopy, is a variant of Fourier microscopy, which additionally uses phase closure for correction of intervening aberrations. It is an active-illumination technique that is scalable to angular resolutions of 1 nrad and to illuminators of extremely low power. A laboratory experiment demonstrates reconstruction of images of two simple objects with an angular resolution of 83 µrad.

Active Optics, Adaptive Optics, and Laser Guide Stars

Optical astronomy is crucial to our understanding of the universe, but the capabilities of ground-based telescopes are severely limited by the effects of telescope errors and of the atmosphere on the passage of light. Recently, it has become possible to construct inbuilt corrective devices that can compensate for both types of degradations as observations are conducted. For full use of the newly emerged class of 8-meter telescopes, such active corrective capabilities, known as active and adaptive optics, are essential. Some physical limitations in the adaptive optics field can be overcome by artificially created reference stars, called laser guide stars. These new technologies have lately been applied with success to some medium and very large telescopes.

Linear quadratic Gaussian control of a deformable mirror adaptive optics system with time-delayed measurements

We present a technique for controlling a ground-based deformable mirror adaptive optics telescope to compensate for optical wave-front phase distortion induced by a turbulent atmosphere. Specifically, a predictive linear quadratic Gaussian (LQG) controller is designed that generates commanded control voltages to the mirror actuators based on a set of time-delayed wave-front slope measurements from a Hartmann-type wave-front sensor.

High-resolution ground-based coronagraphy using image-motion compensation

The first results of a new approach to ground-based stellar coronagraphy are reported. A coronagraph has been equipped with an image-motion compensation system for the stabilization of the telescope field, permitting both improved image resolution and contrast at optical wavelengths. By stopping the telescope aperture D to ~ 4 r(0), where r(0) is Fried's parameter, the maximum attainable resolution gain factor of 2.2 was achieved. Gains measured for D/r(0) > 14 were below the theoretical value of 1.3 theory and were indicative of centroid anisoplanatism, a small spatial coherence outer scale, or both. These effects are also evidenced by diminished power at low frequencies in the power spectrum of image motion over the full telescope aperture. A comparison of stabilized and unstabilized images shows that this coronagraph may detect circumstellar objects 2 magnitudes fainter than those detectable with a conventional coronagraph.

Temporal response of atmospheric turbulence compensation

The temporal kernel for the phase error variance due to atmospheric turbulence is calculated. This kernel, convolved with the servo transfer function, determines the temporal error of any turbulence compensation scheme.

First astronomical application of postdetection turbulence compensation: images of alpha Aurigae, nu Ursae Majoris, and alpha Geminorum using self-referenced speckle holography

We describe a postdetection turbulence compensation technique for obtaining high resolution imagery through the atmosphere. We present preliminary results fromfield experiments.

Optimal wavefront control for adaptive segmented mirrors

A ground-based astronomical telescope with a segmented primary mirror will suffer image-degrading wavefront aberrations from at least two sources: (1) atmospheric turbulence and (2) segment misalignment or figure errors of the mirror itself. This paper describes the derivation of a mirror control feedback matrix that assumes the presence of both types of aberration and is optimum in the sense that it minimizes the meansquared residual wavefront error. Assumptions of the statistical nature of the wavefront measurement errors, atmospheric phase aberrations, and segment misalignment errors are made in the process of derivation. Examples of the degree of correction are presented for three different types of wavefront measurement data and compared to results of simple corrections.

Direct phase estimation from phase differences using fast elliptic partial differential equation solvers

Obtaining robust phase estimates from phase differences is a problem common to several areas of importance to the optics and signal-processing communities. Specific areas of application include speckle imaging and interferometry, adaptive optics, compensated imaging, and coherent imaging such as synthetic-aperture radar. We derive in a concise form the equations describing the phase-estimation problem, relate these equations to the general form of elliptic partial differential equations, and illustrate results of reconstructions on large M by N grids, using existing, published, and readily available FORTRAN subroutines.

Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

A ground-based adaptive optics imaging telescope system attempts to improve image quality by measuring and correcting for atmospherically induced wavefront aberrations. The necessary control computations during each cycle will take a finite amount of time, which adds to the residual error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper investigates this possibility by studying the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for adaptive optics use.

Multichannel phase-shifted interferometer

A new real-time interferometer based on diffraction phenomena is discussed. It consists of a point-diffraction interferometer fabricated on a transmission grating. The real-time data-analysis capability is achieved by simultaneously introducing a phase shift (piston) on the three separate channels of diffracted interferograms. Mathematical analysis and preliminary observational results are included.

Multiple-order radial-grating shearing interferometer

A shearing interferometer suitable for coherent phasing of multiple-aperture optical systems is described. The interferometer uses the properties of a rotating radial square wave grating to simplify interaperture phase measurements. A theoretical development and the results of experiments conducted at a wavelength of 10.6 microm are presented.

Deformable mirrors for all seasons and reasons

The use of adaptive optics has been increasingly proposed as a solution to a variety of optical phase distortion problems. Deformable (rubber) mirror concepts have utilized numerous design techniques for phase distortion correction. Deformable mirror requirements are reviewed for several applications along with projected requirements to meet the demands of future optical systems. Actuator and mirror design requirements are addressed along with their interrelationship with electronic driver design.

Radial grating lateral shear heterodyne interferometer

A variable lateral shear heterodyne interferometer has been developed that is capable, for example, of measuring the high-bandwidth wave fronts in adaptive optical systems. The interferometer is used with a radial Ronchi grating and operates with a variety of spatially and temporally coherent light sources such as whitelight extended sources. The interferometer has been operated successfully in a real-time atmospheric compensation adaptive optical system.