Brent Ellerbroek

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.

Gemini multiconjugate adaptive optics system review - I. Design, trade-offs and integration

The Gemini multiconjugate adaptive optics system (GeMS) at the Gemini South telescope in Cerro Pachon is the first sodium-based multilaser guide star (LGS) adaptive optics system. It uses five LGSs and two deformable mirrors to measure and compensate for atmospheric distortions. The GeMS project started in 1999, and saw first light in 2011. It is now in regular operation, producing images close to the diffraction limit in the near-infrared, with uniform quality over a field of view of two square arcminutes. This paper is the first one in a two-paper review of GeMS. It describes the system, explains why and how it was built, discusses the design choices and trade-offs, and presents the main issues encountered during the course of the project. Finally, we briefly present the results of the system first light.

Principles, limitations, and performance of multiconjugate adaptive optics

Multi-Conjugate Adaptive Optics (MCAO) holds the promise of moderate to large adaptively compensated field of view with uniform image quality. This paper is a first effort to analyze the fundamental limitations of such systems, and that are mainly related to the finite number of deformable mirrors and guide stars. We demonstrate that the ultimate limitation is due to the vertical discretization of the correction. This effect becomes more severe quite rapidly with increasing compensated field of view or decreasing wavelength, but does not depend at first order on the telescope aperture. We also discuss limitations associated with the use of laser guide stars and ELT related issues.

Shack-Hartmann wavefront sensing with elongated sodium laser beacons: centroiding versus matched filtering

We describe modeling and simulation results for the Thirty Meter Telescope on the degradation of sodium laser guide star Shack-Hartmann wavefront sensor measurement accuracy that will occur due to the spatial structure and temporal variations of the mesospheric sodium layer. By using a contiguous set of lidar measurements of the sodium profile, the performance of a standard centroid and of a more refined noise-optimal matched filter spot position estimation algorithm is analyzed and compared for a nominal mean signal level equal to 1000 photodetected electrons per subaperture per integration time, as a function of subaperture to laser launch telescope distance and CCD pixel readout noise. Both algorithms are compared in terms of their rms spot position estimation error due to noise, their associated wavefront error when implemented on the Thirty Meter Telescope facility adaptive optics system, their linear dynamic range, and their bias when detuned from the current sodium profile.

Split atmospheric tomography using laser and natural guide stars.

Laser guide star (LGS) atmospheric tomography is described in the literature as integrated minimum-variance tomographic wavefront reconstruction from a concatenated wavefront-sensor measurement vector consisting of many high-order, tip/tilt (TT)-removed LGS measurements, supplemented by a few low-order natural guide star (NGS) components essential to estimating the TT and tilt anisoplanatism (TA) modes undetectable by the TT-removed LGS wavefront sensors (WFSs). The practical integration of these NGS WFS measurements into the tomography problem is the main subject of this paper. A split control architecture implementing two separate control loops driven independently by closed-loop LGS and NGS measurements is proposed in this context. Its performance is evaluated in extensive wave optics Monte Carlo simulations for the Thirty Meter Telescope (TMT) LGS multiconjugate adaptive optics (MCAO) system, against the delivered performance of the integrated control architecture. Three iterative algorithms are analyzed for atmospheric tomography in both cases: a previously proposed Fourier domain preconditioned conjugate gradient (FDPCG) algorithm, a simple conjugate gradient (CG) algorithm without preconditioning, and a novel layer-oriented block Gauss-Seidel conjugate gradient algorithm (BGS-CG). Provided that enough iterations are performed, all three algorithms yield essentially identical closed-loop residual RMS wavefront errors for both control architectures, with the caveat that a somewhat smaller number of iterations are required by the CG and BGS-CG algorithms for the split approach. These results demonstrate that the split control approach benefits from (i) a simpler formulation of minimum-variance atmospheric tomography allowing for algorithms with reduced computational complexity and cost (processing requirements), (ii) a simpler, more flexible control of the NGS-controlled modes, and (iii) a reduced coupling between the LGS- and NGS-controlled modes. Computation and memory requirements for all three algorithms are also given for the split control approach for the TMT LGS AO system and appear feasible in relation to the performance specifications of current hardware technology.

Adaptive optics: wave-front correction by use of adaptive filtering and control

A class of adaptive-optics problems is described in which phase distortions caused by atmospheric turbulence are corrected by adaptive wave-front reconstruction with a deformable mirror, i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, as opposed to the linear time-invariant control loops used in conventional adaptive optics. The basic problem is posed as an adaptive disturbance-rejection problem with many channels. The solution given is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. Simulation results are presented for a 1-m telescope with both one-layer and two-layer atmospheric turbulence profiles. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared with a classical linear time-invariant control loop.

Constrained matched filtering for extended dynamic range and improved noise rejection for Shack-Hartmann wavefront sensing.

We recently introduced matched filtering in the context of astronomical Shack-Hartmann wavefront sensing with elongated sodium laser beacons [Appl. Opt. 45, 6568 (2006)]. Detailed wave optics Monte Carlo simulations implementing this technique for the Thirty Meter Telescope dual conjugate adaptive optics system have, however, revealed frequent bursts of degraded closed loop residual wavefront error [Proc. SPIE 6272, 627236 (2006)]. The origin of this problem is shown to be related to laser guide star jitter on the sky that kicks the filter out of its linear dynamic range, which leads to bursts of nonlinearities that are reconstructed into higher-order wavefront aberrations, particularly coma and trifoil for radially elongated subaperture spots. An elegant reformulation of the algorithm is proposed to extend its dynamic range using a set of linear constraints while preserving its improved noise rejection and Monte Carlo performance results are reported that confirm the benefits of the method.

Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope

This paper focuses on two main categories of the multiconjugate adaptive optics (MCAO) parameter space for performance optimization: the geometrical configuration of guide stars and deformable mirrors (DMs), and the wavefront reconstructors. From the first category it is shown how, for a fixed reconstructor and imaging wavelength, the performance metrics with a few important exceptions improve with an increasing number of (1) DMs, (2) actuators per DM and (3) guide stars. The metrics are seen to degrade with (1) an increasing field of compensation and (2) DM conjugation altitude mismatch with the significant turbulent atmospheric layers. In the second category, this study also compares the performance with a fixed MCAO configuration using the least- square estimator (LSE) and the maximum a posteriori estimator (MAP) for wavefront reconstruction. The MAP is shown to perform significantly better than the LSE at low or intermediate signal-to-noise ratios (SNRs), and somewhat better even in the absence of noise due to its a priori knowledge of the phase statistics.

Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope

Laser guide star (LGS) adaptive optics systems for extremely large telescopes must handle an important effect that is negligible for current generation telescopes. Wavefront errors, due to improperly focusing laser wavefront sensors (WFS) on the mesospheric sodium layer, are proportional to the square of the telescope diameter. The sodium layer, whose mean altitude is approximately 90 km, can move vertically at rates of up to a few metres per second; a few seconds lag in refocusing can substantially degrade delivered image quality (15 m of defocus can cause 120 nm residual wavefront error on a 30-m telescope.) As well, the range of temporal frequencies of sodium altitude focus, overlaps the temporal frequencies of focus caused by atmospheric turbulence. Only natural star wavefront sensors can disentangle this degeneracy. However, applying corrections with representative focus mechanisms having modest control bandwidths causes appreciable tracking errors. In principle, electronic offsets measured by natural guide star detectors could be rapidly applied to laser WFS measurements, but to provide useable sky coverage, integrating sufficient photons causes an unavoidable time delay, again resulting in potentially serious focus tracking errors. However, our analysis depends on extrapolating to temporal frequencies greater than 1 Hz from power spectra of sodium profile time series taken at 1-2 minute intervals. In principle, with a pulsed laser, (e.g. 3-μs pulses) and dynamic refocusing on a polar-coordinate CCD, this focus tracking error may be eliminated. This result is an additional benefit of dynamic refocusing beyond the commonly recognized amelioration of LGS WFS spot elongation.

Prospects for measuring supermassive black hole masses with future extremely large telescopes

The next generation of giant-segmented mirror telescopes (>20 m) will enable us to observe galactic nuclei at much higher angular resolution and sensitivity than ever before. These capabilities will introduce a revolutionary shift in our understanding of the origin and evolution of supermassive black holes by enabling more precise black hole mass measurements in a mass range that is unreachable today. We present simulations and predictions of the observations of nuclei that will be made with the Thirty Meter Telescope (TMT) and the adaptive optics assisted integral-field spectrograph IRIS, which is capable of diffraction-limited spectroscopy from Z band (0.9 μm) to K band (2.2 μm). These simulations, for the first time, use realistic values for the sky, telescope, adaptive optics system, and instrument to determine the expected signal-to-noise ratio of a range of possible targets spanning intermediate mass black holes of ~10^4 M_☉ to the most massive black holes known today of >10^(10) M_☉. We find that IRIS will be able to observe Milky Way mass black holes out the distance of the Virgo Cluster, and will allow us to observe many more of the brightest cluster galaxies where the most massive black holes are thought to reside. We also evaluate how well the kinematic moments of the velocity distributions can be constrained at the different spectral resolutions and plate scales designed for IRIS. We find that a spectral resolution of ~8000 will be necessary to measure the masses of intermediate mass black holes. By simulating the observations of galaxies found in Sloan Digital Sky Survey DR7, we find that over 10^5 massive black holes will be observable at distances between 0.005 < z < 0.18 with the estimated sensitivity and angular resolution provided by access to Z-band (0.9 μm) spectroscopy from IRIS and the TMT adaptive optics system. These observations will provide the most accurate dynamical measurements of black hole masses to enable the study of the demography of massive black holes, address the origin of the M_(BH) – σ and M_(BH) – L relationships, and evolution of black holes through cosmic time.