Wavefront-based stochastic parallel gradient descent beam control

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.

The paper deals with with the on-sky performance of the pyramid wavefront sensor-based Adaptive Optics (AO) systems. These wavefront sensors are of great importance, being used in all first light AO systems of the ELTs (E-ELT, GMT, and TMT), currently in design phase. In particular, non-common path aberrations (NCPAs) are a critical issue encountered when using an AO system to produce corrected images in an associated astronomical instrument. The AO wavefront sensor (WFS) and the supported scientific instrument typically use a series of different optical elements, thus experiencing different aberrations. The usual way to correct for such NCPAs is to introduce a static offset in the WFS signals. In this way, when the AO loop is closed the sensor offsets are zeroed and the deformable mirror converges to the shape required to null the NCPA. The method assumes that the WFS operation is linear and completely described by some pre-calibrated interaction matrix. This is not the case for some frequently used wavefront sensors like the Pyramid sensor or a quad-cell Shack-Hartmann sensor. Here we present a method to work in closed-loop with a pyramid wavefront sensor, or more generally a non-linear WFS, introducing a wavefront offset that remains stable when AO correction quality changes due to variations in external conditions like star brightness, seeing, and wind speed. The paper details the methods with analytical and numerical considerations. Then we present results of tests executed at the LBT telescope, in daytime and on sky, using the FLAO system and LUCI2 facility instrument. The on-sky results clearly show the successful operation of the method that completely nulls NCPA, recovering diffraction-limited images with about 70% Strehl ratio in H band in variable seeing conditions. The proposed method is suitable for application to the above-mentioned ELT AO systems.

.Significance: A scene-based adaptive-optics (AO) system is developed and a method for investigating its imaging performance is proposed. The system enables derivation of Strehl ratios from observed images via collaboration with computer simulations. The resultant Strehl ratios are comparable with those of other current AO systems.Aim: For versatile and noninvasive AO microscopy, a scene-based wavefront-sensing technique working on a Shack–Hartmann wavefront sensor is developed in a modal control system. The purpose of the research is to clarify the imaging performance of the AO system via the derivation of Strehl ratios from observed images toward applications in microscopy of living cells and tissues.Approach: Two imaging metrics that can be directly measured from observed images (i.e., an energy concentration ratio and unbiased maximum ratio) are defined and related to the Strehl ratio via computer simulations. Experiments are conducted using artificial targets to measure the imaging metrics, which are then converted to Strehl ratios.Results: The resultant Strehl ratios are and 0.5 in the cases of defocus and higher aberrations, respectively. The half-widths at half-maximum of the AO-corrected bead images are favorably comparable to those of on-focus images under simple defocus aberration, and the AO system works both under bright-field illumination and on fluorescent bead images.Conclusions: The proposed scene-based AO system is expected to work with a Strehl ratio of more than 0.5 when applied to high-resolution live imaging of cells and tissues under bright-field and fluorescence microscopies.

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 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.

Improved Adaptive Optics (AO) systems continue to revolutionize ground-based astronomy. Key to understanding a new AO systems capability is a quantitative measurement of performance, such as the Strehl Ratio (SR). At the Large Binocular Telescope (LBT) we have undertaken a program to monitor the performance of our AO system in regular use for science operations. Input to our analysis includes data taken specifically for this purpose during twilight and on engineering nights. We report our findings thus far and in particular discuss the challenges of collecting consistent data sets in twilight, the methods we used to overcome those challenges, and preliminary results from data collected so far.

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.

In this paper we discuss the performance of low order adaptive optics (AO) systems. We present improved calculations of Strehl ratio achievable at various D/r<SUB>o</SUB> ratios for AO systems up to 7<SUP>th</SUP> order. Additionally we present calculations concerning the throughput of low order AO systems used in conjunction with spectrometers. We then show the results of a detailed simulation of the expected interaction of the University of Hawaii prototype AO system with spectrometers through the V,I,J,H,K optical bands. This simulation shows that AO spectroscopy performance should always be acceptable in the near IR (J,H,K), and often in the visible (V,I). We show the results of our initial efforts at deconvolving the AO PSF. These results indicate that deconvolution is likely to be quite widely applicable to AO images. Finally we discuss how it might be possible to extend the applicability and accuracy of deconvolution using the AO drive and wavefront error signals. The following results are for on-axis system, the effects of atmospheric anisoplanitism have not been addressed in this paper.

In contrast to the conventional adaptive optics (AO) system, the wavefront sensorless (WFSless) AO system doesn’t need a WFS to measure the wavefront aberrations. It is simpler than the conventional AO in system architecture and can be applied to the complex conditions. The model-based WFSless system has a great potential in real-time correction applications because of its fast convergence. The control algorithm of the model-based WFSless system is based on an important theory result that is the linear relation between the Mean-Square Gradient (MSG) magnitude of the wavefront aberration and the second moment of the masked intensity distribution in the focal plane (also called as Masked Detector Signal-MDS). The linear dependence between MSG and MDS for the point source imaging with a CCD sensor will be discussed from theory and simulation in this paper. The theory relationship between MSG and MDS is given based on our previous work. To verify the linear relation for the point source, we set up an imaging model under atmospheric turbulence. Additionally, the value of MDS will be deviate from that of theory because of the noise of detector and further the deviation will affect the correction effect. The theory results under noise will be obtained through theoretical derivation and then the linear relation between MDS and MDS under noise will be discussed through the imaging model. Results show the linear relation between MDS and MDS under noise is also maintained well, which provides a theoretical support to applications of the model-based WFSless system.

In conventional Adaptive optics (AO) system, wavefront aberration is measured by wavefront sensor. However, a point source is usually not available in most imaging systems. Therefore development of deformable mirror control scheme in adaptive optics system based on vision information will extend the application area of AO technique. A focus measure (FM) is a measure of image quality and can be calculated from image data obtained from the image sensor. It can be used to find the optimal shape of the deformable mirror that compensates the wavefront aberration. In this paper, we analyze the performance of focus measures under different types of wavefront aberrations. The relation of FM vs. the aberration strength is analyzed systematically for different aberration modes and different FM functions. The FM performance under combination of aberrations is also investigated. This research supplies a guide for selection of the suitable FM function and strategy for control of deformable mirror in the AO system.

Most large telescopes are now implementing sodium laser guide star (LGS) adaptive optics (AO) systems. Most of these systems plan to use the Shack-Hartmann approach for wavefront sensing. In these systems, the laser spots that are imaged in the Shack-Hartmann subapertures suffer spot elongation due to the 10 km extent of the sodium layer. The spot elongation extends radially from the projection point, and increases linearly with the distance the subaperture is separated from the laser. For 8-meter class telescopes with laser projection behind the secondary mirror, the spot elongation is ~1 arc sec at the edge of the pupil, and does not significantly affect the performance of the AO system. However, for the coming generation of extremely large telescopes, sodium LGS spot elongation will significantly degrade the quality of wavefront measurement. Attention should now be given to the development of technologies that can reduce or eliminate the spot elongation problem. The laser spot elongation can be greatly reduced by projecting the sodium laser in a series of short (1-3 μsec) pulses. The Lawrence Livermore National Laboratory (LLNL) has been funded to develop a pulsed fiber laser. In parallel, a new kind of wavefront sensor detector must be developed to properly sense the pulsed laser return. In this paper, we present our project that will develop a novel CCD which is optimized for sensing the return from a pulsed sodium LGS. Our CCD design uses custom pixel morphology that aligns the pixels of each subaperture with the radial extension of the LGS spot. This pixel geometry will allow each subaperture to follow the yellow-orange rabbit (i.e. the 589 nm laser pulse) as it traverses the sodium layer, providing optimal sampling of a limited number of detected photons. This CCD will attain photon-noise limited performance at high frame rates, using MOSFET amplifiers that exist today (2-3 electrons noise). However, we seek even lower noise amplifiers, and as part of our project, we are testing a new generation of JFET amplifiers that may attain sub-electron noise performance. The test CCD will be a standard geometry, 160x160 pixel image area with split frame transfer and a total of 20 readout ports. This test CCD will easily surpass the performance of the CCDs presently in use in astronomical AO systems, and should provide a significant performance improvement in the AO systems of the 8-10 meter telescopes. This project is a collaboration between the Keck Observatory, MIT Lincoln Laboratory, SciMeasure Analytical Systems, Gemini Observatory, Lick Observatory, the University of California, and the Rockwell Scientific Company. Our efforts are being coordinated with the developments at LLNL so that the pulsed laser and novel geometry CCD can be mated together in 3 years when both are fully developed.

This paper presents the design of an Adaptive Optics (AO) system for retinal imaging applications. The development of retinal imaging systems allows for early diagnosis of eye diseases. Such systems can increase the quality of life of patients as well as curtail increasing health care costs through early eye disease detection and treatment. Until recently, AO systems have been prohibitively expensive and cumbersome. This has been mainly due to the size and cost of flexible membrane mirrors normally used as the aberration correction device. Recent developments in the technology of Microelectromechanical System (MEMS) based actuators allow the implementation of AO systems which would have been difficult to implement a few years ago due to exorbitant costs. The aim of this paper is to present the design of a compact and flexible low cost AO system using off the shelf components to measure and compensate for the aberrations of the eye. The design is based around the system’s main components which include a 52 channel magnetically actuated deformable membrane mirror, a Shack Hartmann wavefront sensor and a control system which runs on a single processor personal computer. All the components are commercially available. The use of the MEMS-based magnetically actuated mirror allows for increased resolution and force compared to conventional membrane mirrors designed mainly for use in astronomical applications. The performance of the closed-loop system is evaluated through experiments. Although designed as a diagnostic tool for eye diseases, such a system will find a number of applications in basic research in the visual sciences, including the study of microscopic structures in the living retina that could not be seen before. Optometrists, retinal surgeons, and ophthalmologists will also benefit from using such a system, through potential improvements on commonly used instruments such as phoropters and fundus cameras.

Aims. The utilisation of artificial laser guide star (LGS) obviates the necessity for a prominent natural guide star (NGS) within adaptive optics (AO) systems. High-power lasers are fundamental components of most AO systems today. The generation of an LGS relies on the excitation of sodium (denoted by its symbol Na) atoms situated in the upper atmosphere. Therefore, the sodium vertical column density (denoted as CNa) is a crucial parameter. Beyond ensuring the optimal and stable performance of an AO system, knowledge of the return flux from an LGS is imperative during the design phase, aiding in the accurate specification of both the LGS and the AO system. The availability of sodium in the upper atmosphere has been the focal point of diverse studies, exhibiting a pronounced dependence on the specific observatory site. Furthermore, it is well established that CNa varies across multiple timescales, including hours, nights, months, seasons, and even several years. As many of the world’s largest telescopes are located in the Atacama Desert in northern Chile, our objective is to provide CNa statistics pertinent to this specific region. Methods. We used telemetry data from the AO systems operational at the Paranal Observatory (24.6°S, 70.4°W): Ground Atmospheric Layer Adaptive Corrector for Spectroscopic Imaging (GALACSI) and Ground layer Adaptive Optics system Assisted by Lasers (GRAAL). We combined these data with measurements from two space instruments: SCanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY) and Optical Spectrograph and Infrared Imaging System (OSIRIS), as well as with simulated data from the Whole Atmosphere Community Climate Model (WACCM). We carefully analysed and compared these datasets to develop a statistical model for the temporal variations of CNa. Results. We validated the use of the AO telemetry data from Paranal systems to retrieve the CNa. The near-continuous measurements encompassing the period from mid-2017 to the end of 2023 facilitated the determination of monthly and yearly abundance and variability of Na in the mesopause region. Throughout the complete years of measurement, the annual and semi-annual variations exhibit consistent characteristics that align with previously documented findings in atmospheric studies. Through meticulous comparison and the fitting of various long-term datasets, we formulated a model depicting the evolution of CNa over time. The validity of our data processing and model is scrutinised, and the results obtained for the Paranal latitude exhibit noteworthy concordance with the findings of other studies.

In this paper, we study a method of simulating optical wave propagation from a sodium laser beacon, specifically applied to Shack-Hartmann wavefront sensing. A Gaussian laser is propagated from the ground to the three-dimensional scattering volume in the mesosphere (80-100km). The resonant backscatter acts as the laser beacon for the adaptive optics (AO) system. This volumetric aspect is modeled by using multiple slices at different altitudes in the sodium layer. Weak turbulence is used in the experiment and the AO system is operated in the open-loop regime only. This paper investigates the number of slices required to adequately reproduce perspective elongation in the Shack-Hartmann spots. The study showed that the most stringent case in the simulations required nine evenly-spaced slices. Other ways of distributing the slices may lead to different results.

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.