Brent L. Ellerbroek

First-order performance evaluation of adaptive-optics systems for atmospheric-turbulence compensation in extended-field-of-view astronomical telescopes

An approach is presented for evaluating the performance achieved by a closed-loop adaptive-optics system that is employed with an astronomical telescope. This method applies to systems incorporating one or several guide stars, a wave-front reconstruction algorithm that is equivalent to a matrix multiply, and one or several deformable mirrors that are optically conjugate to different ranges. System performance is evaluated in terms of residual mean-square phase distortion and the associated optical transfer function. This evaluation accounts for the effects of the atmospheric turbulence Cn2(h) and wind profiles, the wave-front sensor and deformable-mirror fitting error, the sensor noise, the control-system bandwidth, and the net anisoplanatism for a given constellation of natural and/or laser guide stars. Optimal wave-front reconstruction algorithms are derived that minimize the telescope’s field-of-view-averaged residual mean-square phase distortion. Numerical results are presented for adaptive-optics configurations incorporating a single guide star and a single deformable mirror, multiple guide stars and a single deformable mirror, or multiple guide stars and two deformable mirrors.

Two generations of laser-guide-star adaptive-optics experiments at the Starfire Optical Range

We report results that were obtained with two generations (Generation I and Generation II) of a laser-guide-star adaptive-optics system that is capable of continuous compensation at 65-Hz (Generation I) and 130-Hz (Generation II) closed-loop bandwidths on a 1.5-m telescope. We used a copper-vapor laser that was focused at a 10-km range as the laser guide star and a range-gated Shack–Hartmann sensor to operate a continuous-facesheet deformable mirror that controlled either 149 or 241 actuators. We used a separate full-aperture sensor and a steering mirror to remove overall tilt. System performance was measured by imaging stars with a high-resolution CCD camera in a narrow spectral band that was centered at 0.88 μm, from which we computed point-spread functions, optical transfer functions, and Strehl ratios. Using the laser guide star, we achieved a FWHM image resolution of 0.13 arcsec and a Strehl ratio of 0.48. Using a natural guide star, we achieved a Strehl ratio of 0.64 at 0.13 arcsec FWHM resolution. We also obtained compensated images of the Trapezium region in Orion in H-α light, using only the laser guide star.

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.

Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths

The performance of a closed-loop adaptive-optics system may in principle be improved by selection of distinct and independently optimized control bandwidths for separate components, or modes, of the wave-front-distortion profile. We describe a method for synthesizing and optimizing a multiple-bandwidth adaptive-optics control system from performance estimates previously derived for single-bandwidth control systems operating over a range of bandwidths. The approach is applicable to adaptive-optics systems that use either one or several wave-front sensing beacons and also to systems that include multiple deformable mirrors for atmospheric-turbulence compensation across an extended field of view. Numerical results are presented for the case of an atmospheric-turbulence profile consisting of a single translating phase screen with Kolmogorov statistics, a Shack–Hartmann wave-front sensor with from 8 to 16 subapertures across the aperture of the telescope, and a continuous-face-sheet deformable mirror with actuators conjugate to the corners of the wave-front-sensor subapertures. The use of multiple control bandwidths significantly relaxes the wave-front-sensor noise level that is permitted for the adaptive-optics system to operate near the performance limit imposed by fitting error. Nearly all of this reduction is already achieved through the use of a control system that uses only two distinct bandwidths, one of which is the zero bandwidth.

Fundamental performance comparison of a Hartmann and a shearing interferometer wave-front sensor

The performance of ground-based optical imaging systems is severely degraded from the diffraction limit by the random effects of the atmosphere. Adaptive-optics techniques have been used to compensate for atmospheric-turbulence effects. A critical component in the adaptive-optics system is the wave-front sensor. At present, two types of sensors are common: the Hartmann-Shack wave-front sensor and the shearing interferometer wave-front sensor. In this paper we make a direct performance comparison of these two sensors. The performance calculations are restricted to common configurations of these two sensors and the fundamental limits imposed by shot noise and atmospheric effects. These two effects encompass the effects of extended reference beacons and sensor subaperture spacings larger than the Fried parameter r(0). Our results indicate comparable performance for good seeing conditions and small beacons. However, for poor seeing conditions and extended beacons, the Hartmann sensor has lower error levels than the shearing interferometer.

Profiles of nighttime turbulence above Mauna Kea and isoplanatism extension in adaptive optics

We use 414 turbulence profiles obtained by scidar over 20 nights to characterize the structure of the nighttime free atmosphere above Mauna Kea, Hawaii and to examine the isoplanatic patch enlargement that can be achieved in adaptive optics by conjugating the deformable mirror (DM) to the seeing layers. It is found that the typical night-time profile is composed of an underlying background of turbulence upon which are often superposed only one or two thin dominant layers. Low level turbulence is weak at the site. The turbulence structure is such that conjugation of a DM to turbulence rather than to the telescope entrance pupil increases the size of the isoplanatic patch by a factor of two (median); much larger gains are occasionally possible. When a single dominant layer is present, which occurs some 60 percent of the time, conjugation of the DM to that thin layer would typically reduce the seeing spread angle by a factor of two over a field of view of many arcmins. These results should be useful in the design and evaluation of AO systems for the site.

Comparison of curvature-based and Shack–Hartmann-based adaptive optics for the Gemini telescope

We present the results of independent numerical simulations of adaptive optics systems for 8-m astronomical telescopes that use both Shack-Hartmann and wave-front curvature sensors. Four differents codes provided consistency checks and redundancy. All four simulate a complete system and model noise and servo-lag effects. A common atmospheric turbulence generator was used for consistency. We present the main characteristics of the codes, and we report the system performance in term of Strehl ratio and full width at half-maximum versus the magnitude of the (on-axis) guide star. We show that a Shack-Hartmann plus stacked actuator mirror system with 10 x 10 subapertures or a curvature plus bimorph mirror system with 56 subapertures yields a 50% Strehl ratio at 1.6 mum for a m(R) = 14.7 magnitude star, with almost equivalent performance at both brighter and dimmer light levels.

Real-time adaptive optimization of wavefront reconstruction algorithms for closed-loop adaptive optical systems

In recent years several methods have been presented for optimizing closed-loop adaptive-optical (AO) wave-front re- construction algorithms. These algorithms, which can significantly improve the performance of AO systems, compute the reconstruction matrix using measured atmospheric statistics. Since atmospheric conditions vary on time scales of minutes, it becomes necessary to constantly update the reconstruction so that it adjusts to the changing atmospheric statistics. This paper presents a method for adaptively optimizing the reconstructor of a closed-loop AO system in real time. The method relies on recursive least square techniques to track the temporal and spatial correlations of the turbulent wave-front. The performance of this method is examined for a sample scenario in which the AO control algorithm attempts to compensate for signal processing latency by reconstructing the future value of the wave-front from a combination of past and current wave-front sensor measurements. For this case, the adaptive reconstruction algorithm yields Strehl ratios within a few percent of those obtained by an optimal reconstructor derived from a priori knowledge of the strength of the turbulence and the velocity of the wind. This level of performance can be a dramatic improvement over the Strehls achievable with a conventional least squares reconstructor.

Gemini north and south laser guide star systems requirements and preliminary designs

In the near future, the Gemini Observatory will offer Laser Guide Star Adaptive Optics (LGS AO) observations on both Gemini North and South telescopes. The Gemini North AO system will use a 10W-class sodium laser to produce one laser guide star at Mauna Kea, Hawaii, whereas the Gemini South AO System will use up to five such lasers or a single 50W-class laser to produce one to five sodium beacons at Cerro Pachon, Chile. In this paper we discuss the similarities and differences between the Gemini North and South Laser Guide Star Systems. We give a brief overview of the Gemini facility Adaptive Optics systems and the on-going laser research and development program to procure efficient, affordable and reliable lasers. The main part of the paper presents the top-level requirements and preliminary designs for four of the Gemini North and South Laser Guide Star subsystems: the Laser Systems (LS), Beam Transfer Optics (BTO), Laser Launch Telescopes (LLT), and their associated Periscopes.

Comparison of Shack-Hartmann wavefront sensing and phase-diverse phase retrieval

The effect of focus anisoplanatism upon the performance of an astronomical laser guide star (LGS) adaptive optics (AO) system can in principle be reduced if the lowest order wavefront aberrations are sensed and corrected using a natural guide star (NGS). For this approach to be useful, the noise performance of the wavefront sensor (WFS) used for the NGS measurements must be optimized to enable operation with the dimmest possible source. Two candidate sensors for this application are the Shack-Hartmann sensor and “phase-diverse phase retrieval,” a comparatively novel approach in which the phase distortion is estimated from two or more well-sampled, full-aperture images of the NGS measured with known adjustments applied to the phase profile. We present analysis and simulation results on the noise-limited performance of these two methods for a sample LGS AO observing scenario. The common parameters for this comparison are the NGS signal level, the sensing wavelength, the second-order statistics of the phase distortion, and the RMS detector read noise. Free parameters for the two approaches are the Shack-Hartmann subaperture geometry, the focus biases used for the phase-diversity measurements, and the algorithms used to estimate the wavefront. We find that phase-diverse phase retrieval provides consistently superior wavefront estimation accuracy when the NGS signal level is high. For lower NGS signal levels on the order of 103 photodetection events, the Shack-Hartmann (phase diversity) approach is preferred at a RMS detector read noise level of 5 (0) electrons/pixel.