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.     

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.     

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.     

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.     

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.     

Generalized aliasing and its implications in modal gain optimization for multi-conjugate adaptive optics

The error of generalized aliasing associated with the limited sampling of the atmospheric turbulence volume due to the finite number of wavefront sensing directions in wide-field-of-view adaptive optics is formally defined. Following a modal approach, we extend the direct problem formulation of star-oriented multi-conjugate adaptive optics (MCAO) to model and quantify this error analytically. We show that the turbulence estimation with the least-squares reconstructor is subject to strong generalized aliasing, in particular affecting the badly seen modes, whereas with the minimum-mean-square-error reconstructor the estimation is little affected. Finally, we show that the application of modal gain optimization techniques in closed-loop MCAO systems is jeopardized by the generalized aliasing error.     

Fast calibration of high-order adaptive optics systems

We present a new method of calibrating adaptive optics systems that greatly reduces the required calibration time or, equivalently, improves the signal-to-noise ratio. The method uses an optimized actuation scheme with Hadamard patterns and does not scale with the number of actuators for a given noise level in the wavefront sensor channels. It is therefore highly desirable for high-order systems and/or adaptive secondary systems on a telescope without a Gregorian focal plane. In the latter case, the measurement noise is increased by the effects of the turbulent atmosphere when one is calibrating on a natural guide star.     

Photometric observations of a polychromatic laser guide star

We report the photometric observation of a polychromatic laser guide star (PLGS) using the AVLIS laser at the Lawrence Livermore National Laboratory (LLNL). The process aims at providing a measurement of the tilt of the incoming wave front at a telescope induced by atmospheric turbulence. It relies on the two-photon coherent excitation of the 4D5/2 energy level of sodium atoms in the mesosphere. We used two laser beams at 589 and 569 nm, with a maximum total average output power of approximately 350 W. For the purpose of photometric calibration, a natural star was observed simultaneously through the same instrument as the PLGS at the focus of the LLNL 50-cm telescope. Photometric measurements of the 330-nm return flux confirm our previous theoretical studies that the PLGS process should allow us at a later stage to correct for the tilt at wavelengths as short as approximately 1 microm at good astronomical sites. They show also that, at saturation of two-photon coherent absorption in the mesosphere, the backscattered flux increases by a factor of approximately 2 when the pulse repetition rate decreases by a factor of 3 at constant average power. This unexpected behavior is briefly discussed.     

Discrete-time model of an adaptive optics systems

The standard adaptive optics system can be viewed as a sampled-data feedback system with a continuous-time disturbance (the incident wavefront from the observed object) and discrete-time measurement noise. A common measure of the performance of adaptive optics systems is the time average of the pupil variance of the residual wavefront. This performance can be related to that of a discrete-time system obtained by lifting the incident and residual wavefronts. The corresponding discrete-time model is derived, and the computation of the adaptive optics system residual variance is based on that model. The predicted variance of a single mode of an adaptive optics system is shown to be the same as that obtained via simulation (as expected). The discrete-time prediction is also shown to be superior to a continuous-time approximation of the adaptive optics system.     

Bit-error rate for free-space adaptive optics laser communications

An analysis of adaptive optics compensation for atmospheric-turbulence-induced scintillation is presented with the figure of merit being the laser communications bit-error rate. The formulation covers weak, moderate, and strong turbulence; on-off keying; and amplitude-shift keying, over horizontal propagation paths or on a ground-to-space uplink or downlink. The theory shows that under some circumstances the bit-error rate can be improved by a few orders of magnitude with the addition of adaptive optics to compensate for the scintillation. Low-order compensation (less than 40 Zernike modes) appears to be feasible as well as beneficial for reducing the bit-error rate and increasing the throughput of the communication link.     

Self-characterization of linear and nonlinear adaptive optics systems

We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.     

Wavefront correction with high-order curvature adaptive optics systems

We demonstrate the existence of higher-order curvature adaptive optics (AO) systems and compare their performance with the current 85-element system being built at the Institute for Astronomy at the University of Hawaii. Simulation results show that systems with in excess of 500 actuators are possible with actuator patterns that are simple extensions of the 85-element design. The attenuation of residual phase error within the Nyquist frequency of the deformable mirror (DM) satisfies the (-5/6) power law. A high-order system is also analyzed in which the pattern of wavefront sensor is synthesized from square pixels and the curvature actuators of the DM are also rectangular. The Strehl performance is approximately 2% worse than its annular analog.     

Minimum-variance control for woofer-tweeter systems in adaptive optics

The woofer-tweeter concept in adaptive optics consists in correcting for the turbulent wavefront disturbance with a combination of two deformable mirrors (DMs). The woofer corrects for temporally slow-evolving, spatially low-frequency, large-amplitude disturbances, whereas the tweeter is generally its complement, i.e., corrects for faster higher-order modes with lower amplitude. A special feature is that in general both are able to engender a common correction space. In this contribution a minimum-variance solution for the double stage woofer-tweeter concept in adaptive optics systems is addressed using a linear-quadratic-Gaussian approach. An analytical model is built upon previous developments on a single DM with temporal dynamics that accommodates a double-stage woofer-tweeter DM. Monte Carlo simulations are run for a system featuring an 8×8 actuator DM (considered infinitely fast), mounted on a steering tip/tilt platform (considered slow). Results show that it is essential to take into account temporal dynamics on the estimation step. Besides, unlike the other control strategies considered, the optimal solution is always stable.     

Advanced vibration suppression algorithms in adaptive optics systems

Vibration suppression in astronomical adaptive optics (AO) systems has gathered great attention in the context of next-generation instrumentation for current telescopes and future Extremely Large Telescopes. Laser tomographic AO systems require natural guide stars to measure the low-order modes such as tip-tilt (TT) and TT-anisoplanatism. To increase the sky coverage, the guide stars are often faint, thus requiring lower temporal sampling frequencies to work on a more favorable signal-to-noise regime. Such sampling frequencies can be of the order of, or even lower than, the range of frequencies where vibrations are likely to appear. Ideally, vibrations affecting the low-order modes could be corrected at the higher laser loop frame rate using an upsampling procedure. This paper compares the most relevant solutions proposed hitherto to a novel multirate algorithm using the linear-quadratic-Gaussian (LQG) approach capable of upsampling the correction to further reduce the impact of vibrations. Results from numerical Monte Carlo simulations span a large range of parameters from pure sinusoids to relatively broad peak vibrations, covering the likely-to-be signals in a realistic AO system. The improvement is shown at sampling frequencies from 20 to 800 Hz, including below the vibration itself, in the example of 29.5 Hz on a Thirty Meter Telescope-like scenario. The multirate LQG ensures the least residual for both faint and bright stars for all the peak widths considered based on telemetry from the Keck Observatory.     

Minimum variance control structure for adaptive optics systems

The adaptive optics minimum variance control problem is formulated as a linear-quadratic-Gaussian optimization. The formulation incorporates the wavefront sensor frame integration in discrete-time models of the deformable mirror and incident wavefront. It shows that, under nearly ideal conditions, the resulting minimum variance controller approaches the integral controller commonly used in adaptive optics systems. The inputs to the controller dynamics are obtained from a reconstructor with the maximum a posteriori structure that uses the estimation error covariance of the wavefront error. The ideal conditions assumed to obtain the integral controller are as follows; isotropic first-order (but nonstationary) temporal atmospheric aberrations, no computational loop delay, and no deformable mirror dynamics. The effects of variations in these conditions are examined.     

Comparison of vibration mitigation controllers for adaptive optics systems

Vibrations are detrimental to the performance of modern adaptive optics (AO) systems. In this paper, we describe new methods tested to mitigate the vibrations encountered in some of the instruments of the Gemini South telescope. By implementing a spectral analysis of the slope measurements from several wavefront sensors and an imager, we can determine the frequencies and magnitude of these vibrations. We found a persistent vibration at 55 Hz with others occurring occasionally at 14 and 100 Hz. Two types of AO controllers were designed and implemented, Kalman and H∞, in the multiconjugate AO tip-tilt loop. The first results show a similar performance for these advanced controllers and a clear improvement in vibration rejection and overall performance over the classical integrator scheme. It is shown that the reduction in the standard deviation of the residual slopes (as measured by wavefront sensors) is highly dependent on turbulence, wind speed, and vibration conditions, ranging--in terms of slopes RMS value--from an almost negligible reduction for high speed wind to a factor of 5 for a combination of low wind and strong vibrations.     

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.     

Spectrometer slit-power-coupling calculations for natural and laser guide-star adaptive optics

We use numerical calculations to examine the relation between adaptive optics (AO) turbulence compensation and power coupled through a spectrometer slit for both laser and natural guide-star AO systems. The AO system and observing parameters used are relevant to the Gemini-North 8-m telescope. For this study, we separate residual tilt from residual higher-order aberrations to isolate their relative effects under a variety of operating conditions. Our results demonstrate that slit-coupled intensity is not uniquely determined by system Strehl alone; we show that this is due to the differing effects of higher-order and tilt aberrations on the shape of the compensated point-spread function. For the Gemini spectrometer and AO system, the wider point-spread function halo associated with an added residual higher-order aberration reduces slit-coupled intensity more rapidly than a broad point-spread function core induced by residual tilt.     

High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors

Adaptive optics scanning laser ophthalmoscopes have been used to produce noninvasive views of the human retina. However, the range of aberration compensation has been limited by the choice of deformable mirror technology. We demonstrate that the use of dual deformable mirrors can effectively compensate large aberrations in the human eye while maintaining the quality of the retinal imagery. We verified experimentally that the use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the micro-electro-mechanical-system mirror alone and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. We also demonstrated that the large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.     

Robust control of a bimorph mirror for adaptive optics systems

We apply robust control techniques to an adaptive optics system including a dynamic model of the deformable mirror. The dynamic model of the mirror is a modification of the usual plate equation. We propose also a state-space approach to model the turbulent phase. A continuous time control of our model is suggested, taking into account the frequential behavior of the turbulent phase. An H(infinity) controller is designed in an infinite-dimensional setting. Because of the multivariable nature of the control problem involved in adaptive optics systems, a significant improvement is obtained with respect to traditional single input-single output methods.