Luc Gilles

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.

Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes.

We present sample Monte Carlo simulation results to illustrate the trends in multiconjugate adaptive optics (MCAO) performance as the telescope aperture diameter increases from 8 to 32 m with all other first-order system parameters held constant. The MCAO system considered includes three deformable mirrors, a 1-arc min square field of view, and five wave-front-sensing references consisting of either natural guide stars or laser guide stars at a range of either 30 or 90 km. The rms residual wave-front error decreases slowly with increasing aperture diameter with natural guide stars, whereas performance degrades significantly with increasing aperture diameter for laser guide stars at 30 km if the number of guide stars is held fixed. Performance with laser guide stars at 90 km is a weak function of telescope aperture diameter in the range from 8 to 32 m, with rms wave-front errors no more than 20% greater than the corresponding natural guide-star case for the same level of wave-front sensors measurement noise.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

NFIRAOS: first facility AO system for the Thirty Meter Telescope

NFIRAOS, the Thirty Meter Telescope’s first adaptive optics system is an order 60x60 Multi-Conjugate AO system with two deformable mirrors. Although most observing will use 6 laser guide stars, it also has an NGS-only mode. Uniquely, NFIRAOS is cooled to -30 °C to reduce thermal background. NFIRAOS delivers a 2-arcminute beam to three client instruments, and relies on up to three IR WFSs in each instrument. We present recent work including: robust automated acquisition on these IR WFSs; trade-off studies for a common-size of deformable mirror; real-time computing architectures; simplified designs for high-order NGS-mode wavefront sensing; modest upgrade concepts for high-contrast imaging.

Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes

This paper discusses the performance and cost of two computationally efficient Fourier-based tomographic wavefront reconstruction algorithms for wide-field laser guide star (LGS) adaptive optics (AO). The first algorithm is the iterative Fourier domain preconditioned conjugate gradient (FDPCG) algorithm developed by Yang et al. [Appl. Opt.45, 5281 (2006)], combined with pseudo-open-loop control (POLC). FDPCGs computational cost is proportional to N log(N), where N denotes the dimensionality of the tomography problem. The second algorithm is the distributed Kalman filter (DKF) developed by Massioni et al. [J. Opt. Soc. Am. A28, 2298 (2011)], which is a noniterative spatially invariant controller. When implemented in the Fourier domain, DKFs cost is also proportional to N log(N). Both algorithms are capable of estimating spatial frequency components of the residual phase beyond the wavefront sensor (WFS) cutoff frequency thanks to regularization, thereby reducing WFS spatial aliasing at the expense of more computations. We present performance and cost analyses for the LGS multiconjugate AO system under design for the Thirty Meter Telescope, as well as DKFs sensitivity to uncertainties in wind profile prior information. We found that, provided the wind profile is known to better than 10% wind speed accuracy and 20 deg wind direction accuracy, DKF, despite its spatial invariance assumptions, delivers a significantly reduced wavefront error compared to the static FDPCG minimum variance estimator combined with POLC. Due to its nonsequential nature and high degree of parallelism, DKF is particularly well suited for real-time implementation on inexpensive off-the-shelf graphics processing units.

Progress toward developing the TMT adaptive optical systems and their components

Atmospheric turbulence compensation via adaptive optics (AO) will be essential for achieving most objectives of the TMT science case. The performance requirements for the initial implementation of the observatorys facility AO system include diffraction-limited performance in the near IR with 50 per cent sky coverage at the galactic pole. This capability will be achieved via an order 60x60 multi-conjugate AO system (NFIRAOS) with two deformable mirrors optically conjugate to ranges of 0 and 12 km, six high-order wavefront sensors observing laser guide stars in the mesospheric sodium layer, and up to three low-order, IR, natural guide star wavefront sensors located within each client instrument. The associated laser guide star facility (LGSF) will consist of 3 50W class, solid state, sum frequency lasers, conventional beam transport optics, and a launch telescope located behind the TMT secondary mirror. In this paper, we report on the progress made in designing, modeling, and validating these systems and their components over the last two years. This includes work on the overall layout and detailed opto-mechanical designs of NFIRAOS and the LGSF; reliable wavefront sensing methods for use with elongated and time-varying sodium laser guide stars; developing and validating a robust tip/tilt control architecture and its components; computationally efficient algorithms for very high order wavefront control; detailed AO system modeling and performance optimization incorporating all of these effects; and a range of supporting lab/field tests and component prototyping activities at TMT partners. Further details may be found in the additional papers on each of the above topics.

First light adaptive optics systems and components for the Thirty Meter Telescope

Adaptive optics (AO) is essential for many elements of the science case for the Thirty Meter Telescope (TMT). The initial requirements for the observatorys facility AO system include diffraction-limited performance in the near IR, with 50 per cent sky coverage at the galactic pole. Point spread function uniformity and stability over a 30 arc sec field-ofview are also required for precision photometry and astrometry. These capabilities will be achieved via an order 60×60 multi-conjugate AO system (NFIRAOS) with two deformable mirrors, six laser guide star wavefront sensors, and three low-order, IR, natural guide star wavefront sensors within each client instrument. The associated laser guide star facility (LGSF) will employ 150W of laser power at a wavelength of 589 nm to generate the six laser guide stars. We provide an update on the progress in designing, modeling, and validating these systems and their components over the last two years. This includes work on the layouts and detailed designs of NFIRAOS and the LGSF; fabrication and test of a full-scale prototype tip/tilt stage (TTS); Conceptual Designs Studies for the real time controller (RTC) hardware and algorithms; fabrication and test of the detectors for the laser- and natural-guide star wavefront sensors; AO system modeling and performance optimization; lab tests of wavefront sensing algorithms for use with elongated laser guide stars; and high resolution LIDAR measurements of the mesospheric sodium layer. Further details may be found in specific papers on each of these topics.

Wavefront error budget development for the Thirty Meter Telescope laser guide star adaptive optics system

This paper describes the modeling effort undertaken to derive the wavefront error (WFE) budget for the Narrow Field Infrared Adaptive Optics System (NFIRAOS), which is the facility, laser guide star (LGS), dual-conjugate adaptive optics (AO) system for the Thirty Meter Telescope (TMT). The budget describes the expected performance of NFIRAOS at zenith, and has been decomposed into (i) first-order turbulence compensation terms (120 nm on-axis), (ii) opto-mechanical implementation errors (84 nm), (iii) AO component errors and higher-order effects (74 nm) and (iv) tip/tilt (TT) wavefront errors at 50% sky coverage at the galactic pole (61 nm) with natural guide star (NGS) tip/tilt/focus/astigmatism (TTFA) sensing in J band. A contingency of about 66 nm now exists to meet the observatory requirement document (ORD) total on-axis wavefront error of 187 nm, mainly on account of reduced TT errors due to updated windshake modeling and a low read-noise NGS wavefront sensor (WFS) detector. A detailed breakdown of each of these top-level terms is presented, together with a discussion on its evaluation using a mix of high-order zonal and low-order modal Monte Carlo simulations.

Computational methods for a large-scale inverse problem arising in atmospheric optics

The inverse problem of interest is the reconstruction of an astronomical object and wavefront aberrations due to atmospheric turbulence from a sequence of short time exposure (speckle) phase diversity images obtained from a ground-based telescope. A regularized least squares approach is taken, and two numerical techniques are applied to the resulting unconstrained optimization problem. The first technique is the limited memory BFGS method with line search globalization. The second is a Newton/trust region iteration in which the trust region subproblem is solved using a truncated conjugate gradient method. A numerical comparison based on real data is presented, and the roles of preconditioning and cost functional reduction (elimination of the object) are examined.