Laser guide star wavefront sensing for ground-layer adaptive optics on extremely large telescopes

We propose ground-layer adaptive optics (GLAO) to improve the seeing on the 42?m European Extremely Large Telescope. Shack-Hartmann wavefront sensors (WFSs) with laser guide stars (LGSs) will experience significant spot elongation due to off-axis observation. This spot elongation influences the design of the laser launch location, laser power, WFS detector, and centroiding algorithm for LGS GLAO on an extremely large telescope. We show, using end-to-end numerical simulations, that with a noise-weighted matrix-vector-multiply reconstructor, the performance in terms of 50% ensquared energy (EE) of the side and central launch of the lasers is equivalent, the matched filter and weighted center of gravity centroiding algorithms are the most promising, and approximately 10×10 undersampled pixels are optimal. Significant improvement in the 50% EE can be observed with a few tens of photons/subaperture/frame, and no significant gain is seen by adding more than 200 photons/subaperture/frame. The LGS GLAO is not particularly sensitive to the sodium profile present in the mesosphere nor to a short-timescale (less than 100?s) evolution of the sodium profile. The performance of LGS GLAO is, however, sensitive to the atmospheric turbulence profile.     

Impact of sodium laser guide star fratricide on multi-conjugate adaptive optics systems

Laser beams projected from the ground to form sodium layer laser guide stars (LGSs) for adaptive optics (AO) systems experience scattering and absorption that reduce their intensity as they propagate upward through the atmosphere. Some fraction of the scattered light will be collected by the other wavefront sensors and causes additional background in parts of the pupil. This cross-talk between different LGS wavefront sensors is referred to as the fratricide effect. In this paper we quantify the magnitude of four different sources of scattering/absorption and backscattering, and we evaluate their impact on performance with various zenith angles and turbulence profiles for one particular AO system. The resulting wavefront error for the Thirty Meter Telescope (TMT) multi-conjugate AO (MCAO) system, NFIRAOS, is on the order of 5 to 20 nm RMS, provided that the mean background from the fratricide effect can be calibrated and subtracted with an accuracy of 80%. We also present the impact on system performance of momentary variations in LGS signal levels due to variations in cirrus absorption or laser power, and we show that this affects the performance more than does an equal variation in the level of the fratricide.     

Adaptive optics sky coverage modeling for extremely large telescopes

A Monte Carlo sky coverage model for laser guide star adaptive optics systems was proposed by Clare and Ellerbroek [J. Opt. Soc. Am. A 23, 418 (2006)]. We refine the model to include (i) natural guide star (NGS) statistics using published star count models, (ii) noise on the NGS measurements, (iii) the effect of telescope wind shake, (iv) a model for how the Strehl and hence NGS wavefront sensor measurement noise varies across the field, (v) the focus error due to imperfectly tracking the range to the sodium layer, (vi) the mechanical bandwidths of the tip-tilt (TT) stage and deformable mirror actuators, and (vii) temporal filtering of the NGS measurements to balance errors due to noise and servo lag. From this model, we are able to generate a TT error budget for the Thirty Meter Telescope facility narrow-field infrared adaptive optics system (NFIRAOS) and perform several design trade studies. With the current NFIRAOS design, the median TT error at the galactic pole with median seeing is calculated to be 65 nm or 1.8 mas rms.     

Sky coverage modeling for the whole sky for laser guide star multiconjugate adaptive optics

The scientific productivity of laser guide star adaptive optics systems strongly depends on the sky coverage, which describes the probability of finding natural guide stars for the tip/tilt wavefront sensor(s) to achieve a certain performance. Knowledge of the sky coverage is also important for astronomers planning their observations. In this paper, we present an efficient method to compute the sky coverage for the laser guide star multiconjugate adaptive optics system, the Narrow Field Infrared Adaptive Optics System (NFIRAOS), being designed for the Thirty Meter Telescope project. We show that NFIRAOS can achieve more than 70% sky coverage over most of the accessible sky with the requirement of 191 nm total rms wavefront.     

Sampling error analysis of Shack–Hartmann wavefront sensor with variable subaperture pixels

Abstract

The sampling error of a Shack–Hartmann wavefront sensor with variable subaperture pixels is analysed under the consideration of various threshold values and detecting dynamic ranges. A generalized expression, which is used for fitting the sampling error of a Shack-Hartmann wavefront sensor with variable subaperture pixels, is presented. The computational results of the sampling error of a Shack–Hartmann wavefront sensor with different pixel numbers per subaperture, different detecting dynamic ranges, different atmospheric coherence length, different extended degree of the object and the different threshold values are also given. The results indicate that the sampling error of the Shack–Hartmann wavefront sensor is sensitive to the dynamic range of the subaperture, the pixel numbers per subaperture, the extended degree of the object and the coherent length of atmosphere, but not sensitive to the threshold value.     

Real-time turbulence profiling with a pair of laser guide star Shack-Hartmann wavefront sensors for wide-field adaptive optics systems on large to extremely large telescopes

Real-time turbulence profiling is necessary to tune tomographic wavefront reconstruction algorithms for wide-field adaptive optics (AO) systems on large to extremely large telescopes, and to perform a variety of image post-processing tasks involving point-spread function reconstruction. This paper describes a computationally efficient and accurate numerical technique inspired by the slope detection and ranging (SLODAR) method to perform this task in real time from properly selected Shack-Hartmann wavefront sensor measurements accumulated over a few hundred frames from a pair of laser guide stars, thus eliminating the need for an additional instrument. The algorithm is introduced, followed by a theoretical influence function analysis illustrating its impulse response to high-resolution turbulence profiles. Finally, its performance is assessed in the context of the Thirty Meter Telescope multi-conjugate adaptive optics system via end-to-end wave optics Monte Carlo simulations.     

Analysis of the improvement in sky coverage for multiconjugate adaptive optics systems obtained using minimum variance split tomography

The scientific utility of laser-guide-star-based multiconjugate adaptive optics systems depends upon high sky coverage. Previously we reported a high-fidelity sky coverage analysis of an ad hoc split tomography control algorithm and a postprocessing simulation technique. In this paper, we present the performance of a newer minimum variance split tomography algorithm, and we show that it brings a median improvement at zenith of 21 nm rms optical path difference error over the ad hoc split tomography control algorithm for our system, the Narrow Field Infrared Adaptive Optics System for the Thirty Meter Telescope. In order to make the comparison, we also validated our previously developed sky coverage postprocessing software using an integrated simulation of both high- (laser guide star) and low-order (natural guide star) loops. A new term in the noise model is also identified that improves the performance of both algorithms by more properly regularizing the reconstructor.     

Centroid gain compensation in Shack-Hartmann adaptive optics systems with natural or laser guide star

In an adaptive optics system with an undersampled Shack-Hartmann wave-front sensor (WFS), variations in seeing, laser guide star quality, and sodium layer thickness and range distance all combine to vary WFS centroid gain across the pupil during an exposure. While using the minimum of 4 pixels per WFS subaperture improves frame rate and read noise, the WFS centroid gain uncertainty may introduce static aberrations and degrade servo loop phase margin. We present a novel method to estimate and compensate WFS gains of each subaperture individually in real time for both natural and laser guide stars.     

Projection approach to complexity reduction in tomographic alignment of extremely large telescopes

We describe a complexity reduction approach intended to solve the tomographic alignment problem for the Thirty Meter Telescope by means of its alignment and phasing system (APS) with little loss of information. This approach is computationally efficient enough to perform detailed Monte-Carlo simulations of the APS on a standard PC. We present sample simulations to model error propagation through the system and to build a preliminary APS alignment error budget.     

Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions

Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack-Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack-Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods.     

Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.     

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.     

激光散斑引起的象强度中心漂移的理论计算

在传感技术的许多应用中，经常需要用探测器在象面上接收一个成象斑点，以便从中提取空间深度和位置信息，由于激光的高亮度和极好的方向性，使之成为非常理想的投影光源，但是由于激光散斑噪声的存在，使得象斑强度中心与象斑几何中心不再重合，导致对物体空间深度和位置的估计错误。     

Wavefront error caused by centroid position random error

The wavefront error caused by centroid position random error is derived in detail, and an exact formula, which evaluates the wavefront error associated with the centroid position random error, is obtained when the Zernike modes are used as the basis for wavefront reconstruction. The formula is proved by two Shack–Hartmann wavefront sensors with different wavefront reconstruction matrices, and it can precisely describe the wavefront measuring error caused by centroid position random error.     

Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility

The wavefront aberrations in a large-scale, flash-lamp-pumped, high-energy, high-power glass laser system can degrade considerably the quality of the final focal spot, and limit severely the repetition rate. The various aberrations induced on the Laboratoire pour l'Utilisation des Lasers Intenses (LULI), laser facility (LULI2000) throughout the amplification are identified and analyzed in detail. Based on these analyses, an optimized procedure for dynamic wavefront control is then designed and implemented. The lower-order Zernike aberrations can be effectively reduced by combining an adaptive-optics setup, comprising a bimorph deformable mirror and a four-wave lateral shearing interferometer, with a precise alignment system. This enables the laser chain to produce a reproducible focal spot close to the diffraction limit (Strehl ratio approximately 0.7). This allows also to increase the repetition rate, initially limited by the recovery time of the laser amplifiers, by a factor of 2 (one shot per hour). The proposed procedure provides an attractive alternative for dynamic correction of the wavefront aberrations of a laser facility as complex as the LULI2000.     

System performance evaluation of refractive surgical lasers: a mathematical approach

A study was conducted for the purpose of improving the designs of the next generation of refractive surgical laser systems. Two common refractive laser systems, variable-spot scanning (type A) and small-spot scanning (type B), are discussed by identifying sources of error that could adversely affect the capability of these lasers to accurately produce complex, customized wavefront guided ablations. A mathematical model was used to construct a laser simulator that models the two common laser systems in terms of the root-mean-square error. Error sources from ablation profile fitting, ablation registration, eye tracking, and the laser delivery system are compared, and the relative contribution of each to the overall system error is analyzed. This system-level analysis can be helpful to the improvement of both laser systems.     

Optical control of the Advanced Technology Solar Telescope

The Advanced Technology Solar Telescope (ATST) is an off-axis Gregorian astronomical telescope design. The ATST is expected to be subject to thermal and gravitational effects that result in misalignments of its mirrors and warping of its primary mirror. These effects require active, closed-loop correction to maintain its as-designed diffraction-limited optical performance. The simulation and modeling of the ATST with a closed-loop correction strategy are presented. The correction strategy is derived from the linear mathematical properties of two Jacobian, or influence, matrices that map the ATST rigid-body (RB) misalignments and primary mirror figure errors to wavefront sensor (WFS) measurements. The two Jacobian matrices also quantify the sensitivities of the ATST to RB and primary mirror figure perturbations. The modeled active correction strategy results in a decrease of the rms wavefront error averaged over the field of view (FOV) from 500 to 19 nm, subject to 10 nm rms WFS noise. This result is obtained utilizing nine WFSs distributed in the FOV with a 300 nm rms astigmatism figure error on the primary mirror. Correction of the ATST RB perturbations is demonstrated for an optimum subset of three WFSs with corrections improving the ATST rms wavefront error from 340 to 17.8 nm. In addition to the active correction of the ATST, an analytically robust sensitivity analysis that can be generally extended to a wider class of optical systems is presented.     

Accuracy analysis in laser keratopography

We analyze the accuracy of a laser keratopographer in the evaluation of corneal topography for non-smooth corneal surfaces and when some noise is introduced into measured data. Through some numerical simulations, cosinesoidal deformations with different amplitudes and spatial periods are introduced on theoretical surfaces. Gaussian noise is introduced on the simulated x and y position coordinates for the measured position of the reflected beam in order to simulate detection errors that are due to vibrations or electric and other noise on the position-sensing detector. We found that the topography of the surface could be obtained with reliable accuracy if the height-to-width ratio of the deformations of the surface is smaller than 0.02 and the error in the detection of position at the position-sensing detector is under 0.5 mm.     

Characteristics of lateral-shearing nulling interferometry by use of double Fresnel rhombs

Abstract

Nulling interferometer for directly imaging exoplanets with a segmented-mirror telescope is investigated. Lateral shearing interferometry is applied to a segmented-mirror telescope such as the Thirty Meter Telescope. Use of a pair of double Fresnel rhombs in Mach–Zehnder interferometer achieves achromatic nulling and lateral shearing simultaneously. In this paper, computer simulations of the lateral interferometry with the Fresnel rhombs in the near infrared region are carried out to analyze the effects of segmentation errors, tip-tilt errors, amplitude and optical-path difference errors on its nulling performance.     

High-resolution lidar observations of mesospheric sodium and implications for adaptive optics

Observations of sodium density variability in the upper mesosphere/lower thermosphere, obtained using a high-resolution lidar system, show rapid fluctuations in the sodium centroid altitude. The temporal power spectrum extends above 1 Hz and is well-fit by a power law having a slope that is -1.95±0.12. These fluctuations produce focus errors in adaptive optics systems employing continuous-wave sodium laser guide stars, which can be significant for large-aperture telescopes. For a 30 m aperture diameter, the associated rms wavefront error is approximately 4 nm per meter of altitude change and increases as the square of the aperture diameter. The vertical velocity of the sodium centroid altitude is found to be ~23 ms(-1) on a 1 s time scale. If these high-frequency fluctuations arise primarily from advection of horizontal structure by the mesospheric wind, our data imply that variations in the sodium centroid altitude on the order of tens of meters occur over the horizontal scales spanned by proposed laser guide star asterisms. This leads to substantial differential focus errors (~107 nm over a 1 arc min separation with a 30 m aperture diameter) that may impact the performance of wide-field adaptive optics systems. Short-lasting and narrow sodium density enhancements, more than 1 order of magnitude above the local sodium density, occur due to advection of meteor trails. These have the ability to change the sodium centroid altitude by as much as 1 km in less than 1 s, which could result in temporary disruption of adaptive optics systems.