High Resolution Imaging Testbed Utilizing Sodium Laser Guide Star Adaptive Optics: The Real Time Wavefront Reconstructor Computer

The Subaru laser guide star adaptive optics (AO) system was installed at the Nasmyth focus of the Subaru Telescope, and had the first light with natural guide star on October 2006. The AO system has a 188-element curvature based wavefront sensor with photon-counting avalanche photodiode (APD) modules. It measures high-order terms of wavefront using either of a single laser (LGS) or natural guide star (NGS) within a 2' diameter field. The AO system has also a source simulator. It simulates LGS and NGS beams, simultaneously, with and without atmospheric turbulence by two turbulent layer at about 0 and 6 km altitudes, and reproduces the cone effect for the LGS beam. We describe the design, construction, and integration of the curvature wavefront sensor and calibration source unit.

Mellin transform techniques are applied to evaluate the covariance of the integrated turbulence-induced phase distortions along a pair of ray paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. The derivation is for the case of a finite outer scale and a von Karman turbulence spectrum. The Taylor hypothesis is assumed if the two phase distortions are evaluated at two different times and amplitude scintillation effects are neglected. The resulting formula for the covariance is a power series in one variable for the case of a fixed atmospheric wind velocity profile and a power series in two variables for a fixed wind-speed profile with a random and uniformly distributed wind direction. These formulas are computationally efficient and can be easily integrated into computer codes for the numerical evaluation of adaptive optics system performance. Sample numerical results are presented to illustrate the effect of a finite outer scale on the performance of natural and laser guide star adaptive optics systems for an 8-m astronomical telescope. A hypothetical outer scale of 10 m significantly reduces the magnitude of tilt anisoplanatism, thereby improving the performance of a laser guide star adaptive optics system if the auxiliary natural star used for full-aperture tip/tilt sensing is offset from the science field. The reduction in higher-order anisoplanatism that is due to a 10-m outer scale is smaller, and the off-axis performance of a natural guide star adaptive optics system is not significantly improved.

An Adaptive Optic (AO) system is a fundamental requirement of 8m-class telescopes. We know that in order to obtain the maximum possible resolution allowed by these telescopes we need to correct the atmospheric turbulence. Thanks to adaptive optic systems we are able to use all the effective potential of these instruments, drawing all the information from the universe sources as best as possible. In an AO system there are two main components: the wavefront sensor (WFS) that is able to measure the aberrations on the incoming wavefront in the telescope, and the deformable mirror (DM) that is able to assume a shape opposite to the one measured by the sensor. The two subsystem are connected by the reconstructor (REC). In order to do this, the REC requires a “common language" between these two main AO components. It means that it needs a mapping between the sensor-space and the mirror-space, called an interaction matrix (IM). Therefore, in order to operate correctly, an AO system has a main requirement: the measure of an IM in order to obtain a calibration of the whole AO system. The IM measurement is a 'mile stone' for an AO system and must be done regardless of the telescope size or class. Usually, this calibration step is done adding to the telescope system an auxiliary artificial source of light (i.e a fiber) that illuminates both the deformable mirror and the sensor, permitting the calibration of the AO system. For large telescope (more than 8m, like Extremely Large Telescopes, ELTs) the fiber based IM measurement requires challenging optical setups that in some cases are also impractical to build. In these cases, new techniques to measure the IM are needed. In this PhD work we want to check the possibility of a different method of calibration that can be applied directly on sky, at the telescope, without any auxiliary source. Such a technique can be used to calibrate AO system on a telescope of any size. We want to test the new calibration technique, called “sinusoidal modulation technique”, on the Large Binocular Telescope (LBT) AO system, which is already a complete AO system with the two main components: a secondary deformable mirror with by 672 actuators, and a pyramid wavefront sensor. My first phase of PhD work was helping to implement the WFS board (containing the pyramid sensor and all the auxiliary optical components) working both optical alignments and tests of some optical components. Thanks to the “solar tower” facility of the Astrophysical Observatory of Arcetri (Firenze), we have been able to reproduce an environment very similar to the telescope one, testing the main LBT AO components: the pyramid sensor and the secondary deformable mirror. Thanks to this the second phase of my PhD thesis: the measure of IM applying the sinusoidal modulation technique. At first we have measured the IM using a fiber auxiliary source to calibrate the system, without any kind of disturbance injected. After that, we have tried to use this calibration technique in order to measure the IM directly “on sky”, so adding an atmospheric disturbance to the AO system. The results obtained in this PhD work measuring the IM directly in the Arcetri solar tower system are crucial for the future development: the possibility of the acquisition of IM directly on sky means that we are able to calibrate an AO system also for extremely large telescope class where classic IM measurements technique are problematic and, sometimes, impossible. Finally we have not to forget the reason why we need this: the main aim is to observe the universe. Thanks to these new big class of telescopes and only using their full capabilities, we will be able to increase our knowledge of the universe objects observed, because we will be able to resolve more detailed characteristics, discovering, analyzing and understanding the behavior of the universe components.

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.

Laser guide stars (LGSs) have been deployed for the last 20-30 years in ground-based astronomical telescopes to overcome the limited sky coverage of classical adaptive optics (AO) systems. Unfortunately, slow altitude drifts of the sodium layer compromise focus measurements, generating the so-called slow focus error, and, consequently, a natural guide star (NGS) is needed to compensate that error. The Keck I telescope AO system uses a 20x20 Shack-Hartmann (SH) wavefront sensor (WFS) for slow focus tracking (with a 5x5 mode used on fainter stars). This approach is far from optimal due to limited sky coverage, since the available NGSs are usually very faint. Our goal is to develop a different technique for slow focus tracking and make it fully operational using focal plane wavefront sensing (FPWFS), which can significantly increase sky coverage and allow slow focus tracking at higher frequencies, reducing the lag error. The Keck I near-infrared (NIR) tip-tilt sensor, known as TRICK, is used to obtain the focal plane images without any hardware modifications being necessary. We develop, characterize, and compare three different FPWFS algorithms, namely Gerchberg-Saxton (GS), linearized focal plane technique (LiFT), and Gaussian fit (Gf). These algorithms are studied for the specific purpose of slow focus sensing in the NIR (H and K bands) using numerical simulations and data collected at Keck in 2025 (bench and on-sky). The three algorithms were studied and characterized against different criteria such as linearity, computational costs, and resistance to low signal-to-noise ratio and/or residuals. From the results obtained, the main candidate for an on-sky deployment was GS, for which the main deciding factor was its higher stability and robustness under the presence of residuals. For that reason, on-sky tests in closed loop were made with GS. On-sky tests showed promising results, with GS successfully compensating for purposely introduced focus errors, even under the presence of high turbulence conditions. These tests represent an important step toward the full operationalization of this tool, expected in the coming months. This work can also be extrapolated to other existing 8-10 m class telescopes, or even future 30-40 m class telescopes, where the use of FPWFS can significantly improve sky coverage and reduce the lag error.

It is well known that using two or more deformable mirrors (DMs) can improve the compensation ability of an adaptive optics (AO) system. However, to keep the stability of an AO system, the correlation between the multiple DMs must be suppressed during the correction. In this paper, we proposed a slope-based decoupling algorithm to simultaneous control the multiple DMs. In order to examine the validity and practicality of this algorithm, a typical woofer-tweeter (W-T) AO system was set up. For the W-T system, a theory model was simulated and the results indicated in theory that the algorithm we presented can selectively make woofer and tweeter correct different spatial frequency aberration and suppress the cross coupling between the dual DMs. At the same time, the experimental results for the W-T AO system were consistent with the results of the simulation, which demonstrated in practice that this algorithm is practical for the AO system with dual DMs.

The Integrated Optical System (IOS) is an extreme adaptive optics system designed for NASA’s Laser Com- munication Relay Demonstration mission. There is a great deal of overlap between the requirements for laser communication AO and high-contrast exoplanet imaging AO systems. Both require very high Strehl ratios with narrow fields of view. This overlap allows the IOS to serve as a testbed and technology demonstrator for astronomical extreme adaptive optics systems. There are several example technologies from the IOS that are already making the transition to astronomical AO systems. The first is that the real time controller based on Direct Memory Access transfer between the WFS camera link frame-grabber and a DSP board is being reused on the upgrade to PALM-3000 AO system at Palomar Observatory. This enables the system to minimize latency by bypassing the CPU and its inherent timing jitter. Technologies like this will be crucial to enabling high contrast imaging on the next generation of extremely large telescopes. In addition, the IOS measures Fried’s parameter from wavefraont measures in near real time. This technology has already been deployed to PALM-3000. The main function of Laser Communication AO systems is to couple the incoming light into single mode fiber. This is the same configuration that will be used by AO coupled radial velocity spectrographs. The adaptive optics system is a woofer/tweeter design, with one deformable mirror correcting for low spatial frequencies with large amplitude and a second deformable mirror correcting for high spatial frequencies with small amplitude. The system uses a Shack-Hartmann wavefront sensor. The system has achieved first light and is undergoing commissioning. We will present an overview of the system design and initial performance.

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.

We discuss the chosen concepts, detailed design, implementation and calibration of the 85-electrode adaptive optics (AO) system of the Swedish 1-meter Solar Telescope (SST), which was installed in 2013. The AO system is unusual in that it uses a combination of a monomorph mirror with a Shack-Hartmann (SH) wavefront sensor (WFS) and a second high-resolution SH microlens array to aid the characterization, calibration, and modal control of the deformable mirror. An Intel PC workstation performs the heavy image processing associated with cross-correlations and real-time control at a 2 kHz update rate with very low latency. The computer and software continue the successful implementation since 1995 of earlier generations of correlation tracker and AO systems at SST and its predecessor, the 50-cm Swedish Vacuum Solar Telescope, by relying entirely on work-station technology and an extremely efficient algorithm for implementing cross-correlations with the large field of view of the WFS. We describe critical aspects of the design, calibrations, software, and functioning of the AO system. The exceptionally high performance is testified through the highest Strehl ratio (inferred from the measured granulation contrast) of existing meter-class solar telescopes, as demonstrated here at wavelengths shorter than 400 nm and discussed in more detail in a previous separate publication We expect that some aspects of this AO system may also be of interest outside the solar community.

The Gemini 8 meter telescopes performance with active and adaptive optics as a system is given. The telescopes are being designed to deliver near diffraction limited images at infrared wavelengths to the focal plane. This is achieved with a combination of innovative telescope design, a fully active control system and a natural guide star adaptive optics (AO) system for the Mauna Kea Telescope. The predicted delivered performance while under full active control is given at 2.2 microns. The top level AO system error budget is presented including the effects of instrumentation. The Gemini telescopes have been designed from the outset to be fully active; from control of the primary mirror surfaces and positioning of the secondary to ventilation of the enclosure by control over the ventilation gates. Descriptions of the concepts used in the various subsystems have been published previously. Here, we emphasize the system level interactions between the Gemini adaptive optics system and the telescope and instruments. This includes a performance summary of how the telescope operates with and without AO. First, the current system concept is outlined, which includes wavefront sensors/guiders in the following areas: (1) acquisition and guiding system, peripheral wavefront sensors; (2) scientific instruments, on instrument wavefront sensors; (3) adaptive optics system, facility wavefront sensor. The system performance depends upon the interactions of these three key sensor areas. For non-AO use, both peripheral and on instrument wavefront sensor may be used to support fast and slow guiding and active control of the telescope alignment and wavefront. For AO use, combinations of all three types of wavefront sensors may be used for adaptive atmospheric compensation in addition to the functions listed above. The system is designed to quickly change between modes of operation (AO to non-AO and back) under remote control.

We present our plans for a second-generation laser guide star adaptive optics system for the 3-meter Shane Telescope at Lick Observatory. The Shane hosted the first groundbreaking experiments in sodium laser guidestar adaptive optics, with observations starting in 1996, and provides for regular astronomical science observing to this day. The replacement new generation system will incorporate many of the recent advancements in AO technology and lessons learned from laboratory and on-sky experiments in order to provide higher Strehl, higher sensitivity, and greater wavelength coverage for astronomers. The proposed system uses a 32x32 actuator MEMS deformable mirror, along with higher sensitivity wavefront sensor, and a new fiber laser developed at Lawrence Livermore National Laboratory. Our experiences from the Villages project, reported at earlier Photonics West meetings, provide much of the basis for the new system design.

Solar Adaptive Optics (AO) shares many issues with night-time AO, but it also has its own particularities. The wavefront sensing is performed using correlations to efficiently work on the solar granulation as a reference. The field of view for that measurement usually is around 10". A sensor collecting such a wide field of view averages wavefront information from different sky directions, and the anisoplanatism thus has a peculiar impact on the performance of solar AO and MCAO systems. Since we are entering the era of large solar telescopes (European Solar Telescope, Advanced Technology Solar Telescope) understanding this issue is crucial to evaluate its impact on the performance of future AO systems. In this paper we model the correlating wide field sensor and the way it senses the high altitude turbulence. Thanks to this improved modelling, we present an analysis of the influence of this sensing on the performance of each AO configuration, conventional AO and MCAO. In addition to the analytical study, simulations similar to the case of the EST AO systems with FRiM-3D (the Fractal Iterative Method for Atmospheric tomography) are used in order to highlight the relative influence of design parameters. In particular, results show the performance evolution when increasing the telescope diameter. We analyse the effect of high altitude turbulence correlation showing that increasing the diameter of the telescope does not degrade the performance when correcting on the same spatial and temporal scales.

An optical design for a compact near-infrared (0.8--2.5 μm) spectrometer is presented, optimized for use with an adaptive optics system on a 4-m class telescope. The various observing modes of the design accommodate a large fraction of the spectroscopic observations desired for this region of the spectrum. The design does not contain any radical optical concepts, but demonstrates that a small instrument without exotic components is well suited to the application. While designed specifically for the NAOMI adaptive optics system on the William Herschel 4.2-m telescope, the basic concepts used -- a slow/small-diameter beam allowing a small cryostat volume, single-element off-axis focusing mirrors, and a small collection of cross-dispersed spectroscopic modes selected to provide complete wavelength coverage without exchanging gratings in and out of the cryostat -- are valid for other telescope/adaptive optics systems. Most of these advantages are not available for dual-purpose spectrometers designed to accommodate both uncorrected and corrected images. Two issues critical to infrared spectroscopy with adaptive optics are investigated in some detail. The first is the relation between spectral resolving power and system sensitivity. We arrive at a range of optimum resolutions to be used even with astronomical targets that require low resolution. We also show that adaptive optics do not provide substantial gains in point-source sensitivity where the sky emission is dominated by OH− lines, the contributing factors including the adaptive optics system throughput, less than ideal Strehl ratios, and losses associated with real optical systems operating at the diffraction limit. The second issue critical to spectroscopy with adaptive optics is the light losses resulting from slit diffraction. We present plots showing the relation between slit size, the size of the optical elements downstream of the slit, and the vignetting associated with both. Performance estimates are presented for the design. The combined system sensitivity compares favourably with a similar spectrometer mounted on the Hubble Space Telescope.

For performance evaluation of an adaptive optics (AO) system, the probability of the system residual wavefront variance can provide more information than the wavefront variance average. By studying the Zernike coefficients of an AO system residual wavefront, we derived the exact expressions for the probability density functions of the wavefront variance and the Strehl ratio, for instantaneous and long-term exposures owing to the insufficient control loop bandwidth of the AO system. Our calculations agree with the residual wavefront data of a closed loop AO system. Using these functions, we investigated the relationship between the AO system bandwidth and the distribution of the residual wavefront variance. Additionally, we analyzed the availability of an AO system for evaluating the AO performance. These results will assist in designing and probabilistic analysis of AO systems.

It is well-known that cone effect or focus anisoplanatism is produced by the limited distance of a laser guide star (LGS) which is created within the Earth atmosphere and consequently located at a finite distance from the observer. In this paper, the cone effect of the LGS for different vertical profiles of the refractive index structure constant is numerically investigated by using a revised computer program of atmospheric propagation of optical wave and an adaptive optics (AO) system including dynamic control process. According to the practice, the overall tilt for the tilt-correction mirror is obtained from a natural star and the aberrated wavefront for phase correction of the deformable mirror is obtained from a LGS in our numerical simulation. It is surprisingly found that the effect of altitude of the LGS on the AO phase compensation effectiveness by using the commonly-available vertical profiles of C²_n and the lateral wind speed in the atmosphere is relatively weak, and the cone effect for some C²_n profiles is even negligible. It is found that the cone effect does not have obvious relationship with the turbulence strength, however, it depends on the vertical distribution profile of apparently. On the other hand, the cone effect depends on the vertical distribution of the lateral wind speed as well. In comparison to a longer wavelength, the cone effect becomes more obvious in the case of a shorter wavelength. In all cases concerned in this paper, an AO system by using a sodium guide star has almost same phase compensation effectiveness as that by using the astronomical target itself as a beacon. Effect of dynamic control process in an AO system on the cone effect is studied in this paper for the first time within our knowledge.