Sky coverage estimates for adaptive optics systems from computations in Zernike space

A sky coverage model for laser guide star adaptive optics systems is proposed. The atmosphere is considered to consist of a finite number of phase screens, which are defined by Zernike basis polynomials, located at different altitudes. These phase screens are transformed to the aperture plane, where they are converted to laser and natural guide star wavefront sensing measurements. These transformations incorporate the cone effect due to guide stars at finite heights, anisoplanatism due to guide stars off axis with respect to the science object, and adaptive optics systems with multiple guide stars. The wavefront error is calculated tomographically with minimum variance estimators derived from the transformation matrices and the known statistical properties of the atmosphere. This sky coverage model provides fast Monte Carlo simulations over random natural guide star configurations, irrespective of telescope diameter. The Monte Carlo simulations outlined show that inclusion of a finite outer scale for the atmosphere significantly reduces the median wavefront error, that increasing the number of laser guide stars in the asterism reduces the median wavefront error, and that a larger natural guide star patrol field provides a smaller median wavefront error when there is a low star density in the field.     

Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.     

Noise reduction in adaptive-optics imagery with the use of support constraints

The use of support constraints for noise reduction in images obtained with telescopes that use adaptive optics for atmospheric correction is discussed. Noise covariances are derived for these type of data, including the effects of photon noise and CCD read noise. The effectiveness of support constraints in achieving noise reduction is discussed in terms of these noise properties and in terms of the types of algorithms used to enforce the support constraint. Both a convex-projections and a cost-function minimization algorithm are used to enforce the support constraints, and it is shown with the use of computer simulations and field data that the cost-function algorithm results in artifacts in the reconstructions. The convex-projections algorithms produced mean-square-error decreases in the image domain of approximately 10% for high light levels but essentially no error decreases for low light levels. We emphasize images that are well resolved by the telescope and adaptive-optics system.     

Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics

Robustness of the recently proposed "pseudo open-loop control" algorithm against various system errors has been investigated for the representative example of the Gemini-South 8-m telescope multiconjugate adaptive-optics system. The existing model to represent the adaptive-optics system with pseudo open-loop control has been modified to account for misalignments, noise and calibration errors in deformable mirrors, and wave-front sensors. Comparison with the conventional least-squares control model has been done. We show with the aid of both transfer-function pole-placement analysis and Monte Carlo simulations that POLC remains remarkably stable and robust against very large levels of system errors and outperforms in this respect least-squares control. Approximate stability margins as well as performance metrics such as Strehl ratios and rms wave-front residuals averaged over a 1-arc min field of view have been computed for different types and levels of system errors to quantify the expected performance degradation.     

Development of an MKIDs-Based THz Superconducting Imaging Array (TeSIA) at 0.85 THz

Dome A, the highest point of the cold and dry Antarctic ice sheet, offers the best access to atmospheric windows at THz/FIR wavelengths on Earth. China is planning to build a 5-m THz telescope (DATE5) there. To achieve its scientific goals associated with large sky surveys, we are developing a THz superconducting imaging array (TeSIA) at 0.85 THz (350-μm window) with a pixel number of 32?×?32 and targeting background-limited sensitivity. In this paper, detailed system design and performance of the TeSIA based on aluminum MKIDs are presented.     

Performance of the Keck Observatory adaptive-optics system

The adaptive-optics (AO) system at the W. M. Keck Observatory is characterized. We calculate the error budget of the Keck AO system operating in natural guide star mode with a near-infrared imaging camera. The measurement noise and bandwidth errors are obtained by modeling the control loops and recording residual centroids. Results of sky performance tests are presented: The AO system is shown to deliver images with average Strehl ratios of as much as 0.37 at 1.58 microm when a bright guide star is used and of 0.19 for a magnitude 12 star. The images are consistent with the predicted wave-front error based on our error budget estimates.     

Increase in the compensated field of view with a double-conjugate adaptive-optics system

We analyze and quantify the capabilities and limitations of a double-conjugate adaptive-optics system. In the proposed system the contribution of two turbulent layers is treated separately, with Rayleigh guide stars for the bottom layer, sodium guide stars for the top layer, and two adaptive mirrors conjugate to the respective layers. The system substantially increases the compensated field of view. We give calculated results for the estimated number of guide stars needed, the wave-front sensor, and the adaptive-mirror resolution. Simulation results are also presented, and the residual error remaining after correction in our proposed system is compared with a conventional single-adaptive-mirror system.     

Optimal control of laser beams for propagation through a turbulent medium

Concerning the problem of transmitting a laser beam from one telescope to another telescope through a turbulent medium, it is established that using an adaptive optical system on both telescopes to precompensate an outgoing laser beam based on the aberrations measured on the received laser beam leads to an iteration that maximizes the transmission (neglecting attenuation losses) of laser power between the telescopes. Simulation results are presented demonstrating the effectiveness of this technique when the telescopes are equipped with either phase-only or full-wave compensation systems. Simulation results are shown that indicate that for a uniform distribution of the strength of turbulence, 95% transmission of laser power is attained when both telescopes can achieve full-wave compensation provided that the aperture diameter D of the two telescopes is greater than twice the Fresnel length square root of lambdaL, where A is the wavelength of propagation and L is the distance between the two telescopes.     

Field-of-view limitations of phased telescope arrays

The optical performance of imaging phased telescope arrays is degraded by various design, manufacturing, and operational errors. Perhaps the most basic and fundamental of these error sources are the residual aberrations of the optical design chosen for the individual telescopes. We show that third-order field curvature and distortion, which are rather benign aberrations in a conventional telescope, result in relative phase and tilt errors between the individual telescopes making up the array. The field-dependent image degradation caused by these relative phase and tilt errors is then predicted for different subaperture configurations and telescope design parameters. For phased arrays made up of simple two-mirror telescopes, distortion limits the field of view to less than 5 arcmin for small subapertures (D < 0.5 m), and field curvature limits the field of view to less than 1 arcmin for subaperture diameters greater than 2 m. Quantitative parametric results yielding tolerances for residual field curvature as the phased array is scaled up in size are presented graphically. If a 0.5-deg field of view is desired for telescope diameters greater than 2 m, complex telescope configurations are necessary to satisfy the rather tight tolerances on both field curvature and distortion.     

Eyeglass. 1. Very large aperture diffractive telescopes

The Eyeglass is a very large aperture (25 100-m) space telescope consisting of two distinct spacecraft, separated in space by several kilometers. A diffractive lens provides the telescope s large aperture, and a separate, much smaller, space telescope serves as its mobile eyepiece. Use of a transmissive diffractive lens solves two basic problems associated with very large aperture space telescopes; it is inherently launchable (lightweight, packagable, and deployable) it and virtually eliminates the traditional, very tight surface shape tolerances faced by reflecting apertures. The potential drawback to use of a diffractive primary (very narrow spectral bandwidth) is eliminated by corrective optics in the telescope s eyepiece; the Eyeglass can provide diffraction-limited imaging with either single-band ( 0.1), multiband, or continuous spectral coverage.     

Navy Prototype Optical Interferometer observations of geosynchronous satellites

Using a 15.9 m baseline at the Navy Prototype Optical Interferometer (NPOI), we have successfully detected interferometric fringes in observations of the geosynchronous satellite (geosat) DirecTV-9S while it glinted on two nights in March 2009. The fringe visibilities can be fitted by a model consisting of two components, one resolved (?3.7 m) and one unresolved (～1.1 m). Both the length of the glint and the specular albedos are consistent with the notion that the glinting surfaces are not completely flat and scatter reflected sunlight into an opening angle of roughly 15°. Enhancements to the NPOI that would improve geosat observations include adding an infrared capability, which could extend the glint season, and adding larger, adaptive-optics equipped telescopes. Future work may test the feasibility of observing geosats with aperture-masked large telescopes and of developing an array of six to nine elements.     

Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) is a technique for correcting turbulence-induced phase distortions in three dimensions instead of two, thereby greatly expanding the corrected field of view of an adaptive optics system. This is accomplished with use of multiple deformable mirrors conjugate to distinct ranges in the atmosphere, with actuator commands computed from wave-front sensor (WFS) measurements from multiple guide stars. Laser guide stars (LGSs) must be used (at least for the forseeable future) to achieve a useful degree of sky coverage in an astronomical MCAO system. Much as a single LGS cannot be used to measure overall wave-front tilt, a constellation of multiple LGSs at a common range cannot detect tilt anisoplanatism. This error alone will significantly degrade the performance of a MCAO system based on a single tilt-only natural guide star (NGS) and multiple tilt-removed LGSs at a common altitude. We present a heuristic, low-order model for the principal source of tilt anisoplanatism that suggests four possible approaches to eliminating this defect in LGS MCAO: (i) tip/tilt measurements from multiple NGS, (ii) a solution to the LGS tilt uncertainty problem, (iii) additional higher-order WFS measurements from a single NGS, or (iv) higher-order WFS measurements from both sodium and Rayleigh LGSs at different ranges. Sample numerical results for one particular MCAO system configuration indicate that approach (ii), if feasible, would provide the highest degree of tilt anisoplanatism compensation. Approaches (i) and (iv) also provide very useful levels of performance and do not require unrealistically low levels of WFS measurement noise. For a representative set of parameters for an 8-m telescope, the additional laser power required for approach (iv) is on the order of 2 W per Rayleigh LGS.     

Active optics and modified-Rumsey wide-field telescopes: MINITRUST demonstrators with vase- and tulip-form mirrors

Wide-field astronomy requires the development of larger aperture telescopes. The optical properties of a three-mirror modified-Rumsey design provide significant advantages when compared to other telescope designs: (i) at any wavelength, the design has a flat field and is anastigmatic; (ii) the system is extremely compact, i.e., it is almost four times shorter than a Schmidt. Compared to the equally compact flat-field Ritchey-Chrétien with a doublet-lens corrector, as developed for the Sloan digital sky survey-and which requires the polishing of six optical surfaces-the proposed modified-Rumsey design requires only a two-surface polishing and provides a better imaging quality. All the mirrors are spheroids of the hyperboloid type. Starting from the classical Rumsey design, it is shown that the use of all eight available free parameters allows the simultaneous aspherization of the primary and tertiary mirrors by active optics methods from a single deformable substrate. The continuity conditions between the primary and the tertiary hyperbolizations are achieved by an intermediate narrow ring of constant thickness that is not optically used. After the polishing of a double vase form in a spherical shape, the primary-tertiary hyperbolizations are achieved by in situ stressing. The tulip-form secondary is hyperbolized by stress polishing. Other active optics alternatives are possible for a space telescope. The modified-Rumsey design is of interest for developing large space- and ground-based survey telescopes in UV, visible, or IR ranges, such as currently demonstrated with the construction of identical telescopes MINITRUST-1 and -2, f/5-2 degrees field of view. Double-pass optical tests show diffraction-limited images.     

Wide-field Fizeau imaging telescope: experimental results

A nine-aperture, wide-field Fizeau imaging telescope has been built at the Lockheed-Martin Advanced Technology Center. The telescope consists of nine, 125 mm diameter collector telescopes coherently phased and combined to form a diffraction-limited image with a resolution that is consistent with the 610 mm diameter of the telescope. The phased field of view of the array is 1 murad. The measured rms wavefront error is 0.08 waves rms at 635 nm. The telescope is actively controlled to correct for tilt and phasing errors. The control sensing technique is the method known as phase diversity, which extracts wavefront information from a pair of focused and defocused images. The optical design of the telescope and typical performance results are described.     

Tip-tilt reconstruction with a single dim natural guide star in multiconjugate adaptive optics with laser guide stars

A solution to the problem of detecting the tip-tilt modes in multiconjugate adaptive optics (MCAO) with laser guide stars (LGS) is presented. This solution requires the presence of only a single relatively dim natural guide star (NGS) within the reconstructed field of view (FoV). The dim NGS is used for the reconstruction of the tip-tilt modes on the entire FoV, while the tomographic reconstruction of second-order and higher-order modes is made possible by having an LGS constellation with LGSs at different heights. Due to the relatively low brightness required for the tip-tilt NGS and the large corrected FoV (as compared with the case of conventional adaptive optics) the presented solution provides a means to achieve near-diffraction-limited performance of a 10-m-class telescope in the near infrared over a large portion of the sky. Sky coverage calculations assuming median seeing conditions indicate that this technique could be applied to 75% (95%) of the sky, achieving corrections with an average Strehl ratio approximately 0.42(approximately 0.33) in the 2.2 microm K band across the 1.5' reconstructed FoV.     

Processing wave-front-sensor slope measurements using artificial neural networks

For adaptive-optics systems to compensate for atmospheric turbulence effects, the wave-front perturbation must be measured with a wave front sensor (WPS), and key parameters of the atmosphere and the adaptive-optics system must be known. Two parameters of particular interest include the Fried coherence length r(0) and the WPS slope measurement error. Statistics-based optimal techniques, such as the minimum variance phase reconstructor, have been developed to improve the imaging performance of adaptive-optics systems. However, these statistics-based models rely on knowledge of the current state of the key parameters. Neural networks provide nonlinear solutions to adaptive-optics problems while offering the possibility of adapting to changing seeing conditions. We address the use of neural networks for three tasks: (l) to reduce the WPS slope measurement error, (2) to estimate the Fried coherence length r(0), and (3) to estimate the variance of the WPS slope measurement error. All of these tasks are accomplished by using only the noisy WPS measurements as input. Where appropriate, we compare our method with classical statistics-based methods to determine if neural networks offer true benefits in performance. Although a statistics-based method is found to perform better than a neural network in reducing WPS slope measurement error, neural networks perform better in estimating the variance of the WPS slope measurement error, and both methods perform well in estimating r(0).     

Including outer scale effects in zonal adaptive optics calculations

Mellin transform techniques are applied to evaluate the covariance of the integrated turbulence-induced phase distortions along a pair of ray paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. The derivation is for the case of a finite outer scale and a von Karman turbulence spectrum. The Taylor hypothesis is assumed if the two phase distortions are evaluated at two different times and amplitude scintillation effects are neglected. The resulting formula for the covariance is a power series in one variable for the case of a fixed atmospheric wind velocity profile and a power series in two variables for a fixed wind-speed profile with a random and uniformly distributed wind direction. These formulas are computationally efficient and can be easily integrated into computer codes for the numerical evaluation of adaptive optics system performance. Sample numerical results are presented to illustrate the effect of a finite outer scale on the performance of natural and laser guide star adaptive optics systems for an 8-m astronomical telescope. A hypothetical outer scale of 10 m significantly reduces the magnitude of tilt anisoplanatism, thereby improving the performance of a laser guide star adaptive optics system if the auxiliary natural star used for full-aperture tip/tilt sensing is offset from the science field. The reduction in higher-order anisoplanatism that is due to a 10-m outer scale is smaller, and the off-axis performance of a natural guide star adaptive optics system is not significantly improved.     

Comparison of measurements of the outer scale of turbulence by three different techniques

We have made simultaneous and nearly simultaneous measurements of L0, the outer scale of turbulence, at the Palomar Observatory by using three techniques: angle-of-arrival covariance measurements with the Generalized Seeing Monitor (GSM), differential-image-motion measurements with the adaptive-optics system on the Hale 5-m telescope, and fringe speed measurements with the Palomar Testbed Interferometer (PTI). The three techniques give consistent results, an outer scale of approximately 10-20 m, despite the fact that the spatial scales of the three instruments vary from 1 m for the GSM to 100 m for the PTI.     

Segment aberration effects on contrast

High-contrast imaging, particularly the direct detection of extrasolar planets, is a major science driver for the next generation of telescopes. This science requires the suppression of scattered starlight at extremely high levels and that telescopes be correctly designed today to meet these stringent requirements in the future. The challenge increases in systems with complicated aperture geometries such as obscured, segmented telescopes. Such systems can also require intensive modeling and simulation efforts in order to understand the trade-offs between different optical parameters. The feasibility and development of a contrast prediction tool for use in the design and systems engineering of these telescopes is described. The performance of a particular starlight suppression system on a large segmented telescope is described analytically. These analytical results and the results of a contrast predictor are then compared with the results of a full wave-optics simulation.     

Influence of Seidel distortion on combining beams from a phased telescope array

When beams from an array of afocal telescopes are presented to a beam-combining telescope, tilt errors of the beam wave fronts with respect to the combined wave front place limits on the achievable field of view (FOV); these limits, to the best of our knowledge, have not previously been correctly described in the literature. We show that if the front-end telescopes have just the right Seidel distortion coefficient, then tilt error does not limit the FOV. If this is not the case, at least small FOV's can still be obtained, even if the FOV is not centered on the on-axis direction.