Strategies to cope with sodium layer profile variations in laser guide star AO systems

The vertical profile of the mesospheric sodium layer varies significantly on a time scale of one minute. These variations can impact the random and systematic measurement errors of laser guide star Shack-Hartmann wave front sensors, particularly on extremely large telescopes. Sensor performance can be improved by selecting pixel processing weights matched to the sodium layer profile, assuming that the shape of the profile can be measured or estimated in real time. In this paper we describe the magnitude of these effects for the Thirty Meter Telescope AO system NFIRAOS. We review several existing approaches for measuring or estimating the sodium layer profile in real time. We then describe a new method for estimating the profile directly from the laser guide star wave front pixel intensities themselves, jointly with the subaperture tip/tilt measurements. The algorithm used for this purpose is based upon the multi-frame iterative blind deconvolution algorithm from image post processing: Subaperture tip/tilts and the sodium profile are estimated successively, bootstrapping the estimate of each quantity from the previous estimate of the other. We present promising initial simulation results on the potential performance of the algorithm, and suggest areas for future work

Spatial frequency domain model for adaptive optics compensation of segmented mirror misalignments and figure errors

In addition to their essential function of providing atmospheric turbulence compensation, astronomical Adaptive Optical (AO) systems also supplement the role of active optics (aO) by providing some additional correction of the wavefront aberrations introduced by mirror mounting, alignment, thermal distortion and/or fabrication errors. This feature is particularly desirable for segmented mirror telescopes such as the Thirty Meter Telescope (TMT), but wavefront discontinuities across segment boundaries are challenging to properly sense and correct. In this paper we describe a fast, analytical, frequency domain model which may be used to study and quantify the above effects, and discuss a range of sample results obtained to support the development of the top-level requirements for the TMT primary mirror. In general, AO compensation of mirror segment piston errors is not particulary useful unless the deformable mirror (DM) interactuator spacing is equivalent to no more than one-half of a mirror segment diameter (when both of these dimensions are expressed in the same pupil plane). Effective AO compensation of mirror segment tip/tilt errors, or low order segment figure errors such as astigmatism, typically requires 3-4 DM actuators per mirror segment. These results illustrate the importance of quantifying and minimizing uncorrectable telescope wavefront errors when developing performance predictions for adaptive optical systems

Wavefront reconstruction algorithms and simulation results for multiconjugate adaptive optics on giant telescopes

The very high-order multi-conjugate adaptive optics (MCAO) systems proposed for future giant telescopes will require new, computationally efficient, concepts for wavefront reconstruction. Advanced methods from computational linear algebra have recently been applied to this problem, and explicit simulations of MCAO wavefront reconstruction problems for 30-meter class telescopes are now possible using desktop personal computers. In this paper, we present sample simulation results obtained using these techniques to illustrate the trends in MCAO performance as the telescope aperture diameter increases from 8 to 32 meters. We consider systems based upon natural guidestars, sodium laser guidestars, and Rayleigh laser guidestars. The performance achieved by the first two classes of guidestars is similar, and the variation in their performance with respect to telescope size is very gradual over this range of aperture diameters. Next, we describe work in progress to adapt the minimum variance reconstruction algorithm, which is optimized for open-loop wavefront estimation, to the more realistic and meaningful case of closed-loop wavefront control. Finally, we summarize the current status of efforts to quantify the impact of sodium laser guide star (LGS) elongation on guidestar signal requirements for LGS AO systems on 30 meter class telescopes

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty

Adaptive Optics: introduction to the feature issue

This Applied Optics feature issue is a companion to the Journal of the Optical Society of America A feature issue on the same topic. The feature highlights the expansion of adaptive optics to different applications as well as its development to routine applications brought about because of significant advances in component technologies

Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes

The multi-conjugate adaptive optics (MCAO) systems proposed for future giant telescopes will require new, computationally efficient, concepts for wavefront reconstruction due to their very large number of deformable mirror (DM) actuators and wavefront sensor (WFS) measurements. Preliminary versions of such reconstruction algorithms have recently been developed, and simulations of MCAO systems with 9000 or more DM actuators and 33000 or more WFS measurements are now possible using a single desktop computer. However, the results obtained to date are limited to the case of open-loop wavefront reconstruction, and more work is needed to develop computationally efficient reconstructors for the more realistic case of a closed-loop MCAO system that iteratively measures and corrects time-varying wavefront distortions. In this paper, we describe and investigate two reconstruction concepts for this application. The first approach assumes that knowledge of the DM actuator command vector and the DM-to-WFS influence matrix may be used to convert a closed-loop WFS measurement into an accurate estimate of the corresponding open-loop measurement, so that a standard open-loop wavefront reconstructor may be applied. The second approach is a very coarse (but computationally efficient) approximation to computing the minimum variance wavefront reconstructor for the residual wavefront errors in a closed-loop AO system. Sample simulation results are presented for both concepts with natural guide star (NGS) AO and laser guide star (LGS) MCAO systems on 8- and 32-meter class telescopes. The first approach yields a stable control loop with closed-loop performance comparable to the open-loop estimation accuracy of the classical minimum variance reconstructor. The second approach is unstable when implemented in a type I servo system

Wavefront reconstruction algorithms and simulation results for multiconjugate adaptive optics on giant telescopes

The very high-order multi-conjugate adaptive optics (MCAO) systems proposed for future giant telescopes will require new, computationally efficient, concepts for wavefront reconstruction. Advanced methods from computational linear algebra have recently been applied to this problem, and explicit simulations of MCAO wavefront reconstruction problems for 30-meter class telescopes are now possible using desktop personal computers. In this paper, we present sample simulation results obtained using these techniques to illustrate the trends in MCAO performance as the telescope aperture diameter increases from 8 to 32 meters. We consider systems based upon natural guidestars, sodium laser guidestars, and Rayleigh laser guidestars. The performance achieved by the first two classes of guidestars is similar, and the variation in their performance with respect to telescope size is very gradual over this range of aperture diameters. Next, we describe work in progress to adapt the minimum variance reconstruction algorithm, which is optimized for open-loop wavefront estimation, to the more realistic and meaningful case of closed-loop wavefront control. Finally, we summarize the current status of efforts to quantify the impact of sodium laser guide star (LGS) elongation on guidestar signal requirements for LGS AO systems on 30 meter class telescopes

Adaptive optics without borders: performance evaluation in the infinite aperture limit

The limit case of an infinite aperture adaptive optics (AO) system eliminates the modeling complications associated with aperture edge effects, and thereby enables the application of simplified methods for system performance evaluation in the spatial frequency domain. We review prior work in this field and describe a new approach that enables a wider range of error sources and AO options to be evaluated with a reduced number of approximations. These errors and AO options include: Fitting error and spatial aliasing for a Shack-Hartmann wavefront sensor (WFS) and one particular deformable mirror influence function; WFS noise; servo lag for a continuous temporal filter function; anisoplanatism in either a single evaluation direction or averaged over an extended field of view; piston removal within a finite aperture; minimum variance and modal wavefront reconstruction algorithms; and multi-conjugate AO. Laser guidestars, however, are excluded. A wide range of classical results for the independent effects of individual error sources can be immediately derived from this integrated model. Performance estimates for more complex problems involving the full range of first-order AO error sources are in good agreement with the results produced by more detailed Monte Carlo simulations

Strategies to cope with sodium layer profile variations in laser guide star AO systems

The vertical profile of the mesospheric sodium layer varies significantly on a time scale of one minute. These variations can impact the random and systematic measurement errors of laser guide star Shack-Hartmann wave front sensors, particularly on extremely large telescopes. Sensor performance can be improved by selecting pixel processing weights matched to the sodium layer profile, assuming that the shape of the profile can be measured or estimated in real time. In this paper we describe the magnitude of these effects for the Thirty Meter Telescope AO system NFIRAOS. We review several existing approaches for measuring or estimating the sodium layer profile in real time. We then describe a new method for estimating the profile directly from the laser guide star wave front pixel intensities themselves, jointly with the subaperture tip/tilt measurements. The algorithm used for this purpose is based upon the multi-frame iterative blind deconvolution algorithm from image post processing: Subaperture tip/tilts and the sodium profile are estimated successively, bootstrapping the estimate of each quantity from the previous estimate of the other. We present promising initial simulation results on the potential performance of the algorithm, and suggest areas for future work

Spatial frequency domain model for adaptive optics compensation of segmented mirror misalignments and figure errors

In addition to their essential function of providing atmospheric turbulence compensation, astronomical Adaptive Optical (AO) systems also supplement the role of active optics (aO) by providing some additional correction of the wavefront aberrations introduced by mirror mounting, alignment, thermal distortion and/or fabrication errors. This feature is particularly desirable for segmented mirror telescopes such as the Thirty Meter Telescope (TMT), but wavefront discontinuities across segment boundaries are challenging to properly sense and correct. In this paper we describe a fast, analytical, frequency domain model which may be used to study and quantify the above effects, and discuss a range of sample results obtained to support the development of the top-level requirements for the TMT primary mirror. In general, AO compensation of mirror segment piston errors is not particulary useful unless the deformable mirror (DM) interactuator spacing is equivalent to no more than one-half of a mirror segment diameter (when both of these dimensions are expressed in the same pupil plane). Effective AO compensation of mirror segment tip/tilt errors, or low order segment figure errors such as astigmatism, typically requires 3-4 DM actuators per mirror segment. These results illustrate the importance of quantifying and minimizing uncorrectable telescope wavefront errors when developing performance predictions for adaptive optical systems