Optical images of astronomical objects viewed through ground-based telescopes are blurred by the atmosphere. The atmosphere is turbulent and as a consequence the density of air is not evenly distributed. This results in random, time-varying variations in refractive index. The wave-fronts passing through the atmosphere become aberrated, degrading the quality of the images. One solution is to include an adaptive optics system in the telescope. The system estimates the aberration of the wave-fronts and compensates the wave-front in real time using a corrector element, typically a deformable mirror. An important problem is how to estimate the aberrations optimally using only a small amount of light. This procedure is called wave-front sensing and is the subject of the research of this thesis. For turbulence with Kolmogorov statistics, the wave-front slope contains 87% of the energy of the aberrations. Hence, it is crucial to estimate the slope accurately. The displacement of an image is directly proportional to the wave-front slope and is used to estimate the slope. The conventional way of measuring the average slope of the wave-front in a Shack-Hartmann sensor is from the centroid of the image at the focal plane. It is demonstrated that using the centroid estimator produces an estimate with infinite variance. The Cramer-Rao lower bound (CRLB) is a theoretical lower bound for the variance of an unbiased estimator. The variance of the maximum-likelihood (ML) estimate for the displacement of a diffraction-limited image approaches the CRLB using a relatively small number of photons. The ML estimator is extended to the case where the image is randomly blurred by atmospheric turbulence. It is found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the ML estimator instead of the centroid. Curvature sensors use two defocused images to estimate the wave-front aberrations. It is shown using the CRLB that the focal plane is the optimal plane to measure the slope and the error using defocused images is quantified. The effect of using broadband light on the accuracy of the slope estimate is also investigated. When using laser guide stars, it is not possible to estimate the slope of the wave-front directly from the image because the beam is displaced on both the upward and downward journey. However, the displacement is a weak function of wavelength due to dispersion. In theory, the difference in wave-front slope as a function of wavelength is proportional to the absolute slope. Centering algorithms were implemented on experimental data taken at the Observatoire de Lyon to confirm this relationship. There is strong evidence pointing to a linear relationship between two pairs of differential tilt measurements, but not between the differential and the absolute tilt. However, the data appears to have been affected by a systematic experimental error and a new experiment is needed. Phase retrieval is a non-linear technique used to recover the phase in the Fourier domain using intensity measurements at the image plane and additional constraints. A method is described to solve the phase retrieval problem using linear iterations near the solution, which provides both analytical insight into phase retrieval and numerical results. The algorithm finds the maximum a posteriori estimate of the phase using prior information about the statistics of the noise and the phase and converges well in practice. When phase retrieval is performed on data from subdivided apertures, there is a loss of information regarding the relative piston terms of the subapertures and this error is quantified. It is found that there is a smaller wavefront error when estimating the phase from a full aperture than from a subdivided aperture. Using a combination of intensity measurements from a full and a subdivided aperture is shown to result in a small improvement at very high photon levels only. Curvature sensors measure the wave-front aberrations via a linear relationship between the curvature of the wave-front and the intensity difference between two defocused images. In practice, their performance is limited by their non-linear behaviour, which is characterised by solving simultaneously the irradiance transport equation and the accompanying wave-front transport equation. It is shown how the presence of non-linear geometric terms limits the accuracy of the sensor and how diffraction effects limit the spatial resolution. The effect of photon noise on the sensor is also quantified. A novel technique for deriving wave-front aberrations from two defocused intensity measurements is derived. The intensity defines a probability density function and the method is based on the evolution of the cumulative density function of the intensity. In one dimension, the problem is easily solved using histogram specification with a linear relationship between the wave-front slope and the difference in the abscissas of the histograms. This method is insensitive to scintillation. In two dimensions, the procedure requires the use of the Radon transform. Simulation results demonstrate that very good reconstructions can be attained down to 100 photons in each detector.

Atmospheric turbulence limits the resolving power of astronomical telescopes by distorting the paths of light between distant objects of interest and the imaging camera at the telescope. After many light-years of travel, passing through the turbulence in that last 100km of a photon’s journey results in a blurred image in the telescope, no less than 1” (arc-second) in width. To achieve higher resolutions, corresponding to smaller image widths, various methods have been proposed with varying degrees of effectiveness and practicality. Space telescopes avoid atmospheric turbulence completely and are limited in resolution solely by the size of their mirror apertures. However, the design and maintenance cost of space telescopes, which increases prohibitively with size, has limited the number of space telescopes deployed for astronomical imaging purposes. Ground based telescopes can be built larger and more cheaply, so atmospheric compensation schemes using adaptive optical cancellation mirrors can be a cheaper substitute for space telescopes. Adaptive optics is referred to here as the use of electronic control of optical component to modify the phase of an incident ray within an optical system like an imaging telescope. Fast adaptive optics systems operating in real-time can be used to correct the optical aberrations introduced by atmospheric turbulence. To compensate those aberrations, they must first be measured using a wavefront sensor. The wavefront estimate from the wavefront sensor can then be applied, in a closed-loop system, to a deformable mirror to compensate the incoming wavefront. Many wavefront sensors have been proposed and are in used today in adaptive optics and atmospheric turbulence measurement systems. Experimental results comparing the performance of wavefront sensors have also been published. However, little detailed analyses of the fundamental similarities and differences between the wavefront sensors have been performed. This study concentrates on fourmain types of wavefront sensors, namely the Shack-Hartmann, pyramid, geometric, and the curvature wavefront sensors, and attempts to unify their description within a common framework. The quad-cell is a wavefront slope detector and is first examined as it lays the groundwork for analysing the Shack-Hartmann and pyramid wavefront sensors. The quad-cell slope detector is examined, and a new measure of performance based on the Strehl ratio of the focal plane image is adopted. The quad-cell performance based on the Strehl ratio is compared using simulations against the Cramer-Rao bound, an information theoretic or statistical limit, and a polynomial approximation. The effects of quad-cell modulation, its relationship to extended objects, and the effect on performance are also examined briefly. In the Shack-Hartmann and pyramid wavefront sensor, a strong duality in the imaging and aperture planes exists, allowing for comparison of the performance of the two wavefront sensors. Both sensors subdivide the input wavefront into smaller regions, and measure the local slope. They are equivalent in every way except for the order in which the subdivision and slope measurements were carried out. We show that this crucial difference leads to a theoretically higher performance from the pyramid wavefront sensor. We also presented simulations showing the trade-off between sensor precision and resolution. The geometric wavefront sensor can be considered to be an improved curvature wavefront sensor as it uses a more accurate algorithm based on geometric optics to estimate the wavefront. The algorithm is relatively new and has not found application in operating adaptive optics systems. Further analysis of the noise propagation in the algorithm, sensor resolution, and precision is presented. We also made some observations on the implementation of the geometric wavefront sensor based on image recovery through projections.

Over the last four decades there has been considerable research in the improvement of imaging exo-atmospheric objects through air turbulence from ground-based instruments. Whilst such research was initially motivated for military purposes, the benefits to the astronomical community have been significant. A key topic in this research is isoplanatism. The isoplanatic angle is an angular limit that separates two point-source objects, where if independent measurements of wavefront perturbations were obtained from each source, the wavefront distortion would be considered equivalent. In classical adaptive optics, perturbations from a point-source reference, such as a bright, natural guide star, are used to partially negate perturbations distorting an image of a fainter, nearby science object. Various techniques, such as atmospheric tomography, maximum a posteriori (MAP), and parameterised modelling, have been used to estimate wavefront perturbations when the distortion function is spatially variant, i.e., angular separations exceed the isoplanatic angle, θ₀, where θ₀ ≈ 10 μrad for mild distortion at visual wavelengths. However, the effectiveness of such techniques is also dependent on knowledge a priori of turbulence profiles and configuration data. This dissertation describes a new method used to estimate the eigenvalues that comprise wavefront perturbations over a wide, spatial field. To help reduce dependency on prior knowledge for specific configurations, machine learning is used with a recurrent neural network trained using a posteriori wavefront ensembles from multiple point-source objects. Using a spatiotemporal framework for prediction, the eigenvalues, in terms of Zernike polynomials, are used to reconstruct the spatially-variant, point spread function (SVPSF) for image restoration. The overall requirement is to counter the adverse effects of atmospheric turbulence on the images of extended astronomical objects. The method outlined in this thesis combines optical wavefront sensing using multiple natural guide stars, with a reservoir-based, artificial neural network. The network is used to predict aberrations caused by atmospheric turbulence that degrade the images of faint science objects. A modified geometric wavefront sensor was used to simultaneously measure phase perturbations from multiple, point-source reference objects in the pupil. A specialised recurrent neural network (RNN) was used to learn the spatiotemporal effects of phase perturbations measured from several source references. Modal expansions, in terms of Zernike coefficients, were used to build time-series ensembles that defined wavefront maps of point-source reference objects. The ensembles were used to firstly train an RNN by applying a spatiotemporal training algorithm, and secondly, new data ensembles presented to the trained RNN were used to estimate the wavefront map of science objects over a wide field. Both simulations and experiments were used to evaluate this method. The results of this study showed that by employing three or more source references over an angular separation of 24 μrad from a target, and given mild turbulence with Fried coherence length of 20 cm, the normalised mean squared error of low-order Zernike modes could be estimated to within 0.086. A key benefit in estimating phase perturbations using a time-series of short exposure point-spread functions (PSFs) is that it is then possible to determine the long exposure PSF. Based on the summation of successive, corrected, short-exposure frames, high resolution images of the science object can be obtained. The method was shown to predict a contiguous series of short exposure aberrations, as a phase screen was moved over a simulated aperture. By qualifying temporal decorrelation of atmospheric turbulence, in terms of Taylor's hypothesis, long exposure estimates of the PSF were obtained.

This thesis deals with the design and experimental validation of Deformable Mirror Electronics (DME) for Extremely Large Telescope (ELT) Adaptive Optics (AO) applications. Modern ground based telescopes achieve their best possible imaging resolution through the application of AO. However, due to the fundamental diffraction of optical elements, the next generation of ELTs will employ primary mirrors of an increasingly large diameter as the final means of improving imaging resolution further. The corresponding increase in diameter and actuator count of the Deformable Mirrors (DMs) in these systems has led to the rapid development of high order DM technology. A significant challenge to operating these multi-thousand channel DMs is related to the DM Electronics (DME), which are required to be highly efficient so-as to operate within practical budgetary constraints. This thesis develops a DME reference design based on the requirements for the Thirty Meter Telescope’s next generation AO system, the Narrow Field Infrared Adaptive Optics System (NFIRAOS), which operates two DMs with a total of 7673 piezoelectric actuators. The basis of the DME is the DM actuator driver, which has been developed to be suitable for very high order reproduction by optimization of its size, power, cost and reliability. A complication is that the piezoelectric actuators in NFIRAOS DMs require high voltage drive signals of ±400 V to obtain the rated stroke and must be current limited to avoid damage. Candidate amplifiers are evaluated in simulation and hardware based on a combination of performance, physical and functional criteria; with the most suitable circuit chosen for a multi-channel prototype implementation and testing with a DM breadboard prototype. The development and optimization of an amplifier capable of meeting NFIRAOS performance criteria and budgetary constraints is demonstrated. / Graduate / 0544 / 0606

The quality of microscopy imaging is often degraded by sample-induced aberrations. Adaptive optics (AO) is a standard approach to counter such aberrations. In common practice of AO, an active optical correction element, usually a deformable mirror (DM), is usually inserted in the pupil plane of the objective lens, namely pupil AO. However, as first proposed in the astronomy community and now gradually recognized by the optical microscopy community, the placement of the DM in a plane conjugate to a primary sample-induced aberration plane can be more advantageous, especially in situations where the aberration is spatially varying and arises mainly from a dominant layer. We refer to this technique as conjugate AO. In this thesis, we describe two novel implementations of sensor-based conjugate AO in wide-field microscopy, as well as the wavefront sensing techniques we developed for these implementations. Our first implementation is in trans-illumination configuration. The wavefront sensor is based on a technique called partitioned aperture wavefront (PAW) sensing, previously developed in our lab for quantitative phase contrast imaging. Our second conjugate AO is implemented with fluorescence microscopy. The wavefront sensing strategy is based on oblique back-illumination. In both implementations, we addressed the key challenges of developing wavefront sensors that are capable of operating with uncollimated light, which exhibits large diverging angles and may arbitrarily distribute as well. We show that both conjugate AO systems and their wavefront sensors are not only robust, well-suited for video-rate imaging, but also provide large corrected field of view, which is only limited by the microscope itself.

The limitations of current stellar interferometers is their low sensitivity, and the next generation will account for this by using larger apertures. The phase aberrations from seeing will need the consideration of adaptive optics (AO). Accordingly, this dissertation will first examine the problem that seeing causes in stellar interferometers. The application of Adaptive Optics in Stellar Interferometry will then consider these results to achieve the final goal: reduced losses in fringe visibility and increased sensitivity. The thesis is organised with the second chapter discussing the theory of seeing phase aberrations; their origin and effect on image resolution and fringe visibility. These are used to quantify and compare performance metrics in AO and interferometry, and the specific benefits of AO for interferometry and its method of implementation are used to highlight areas of research that are discussed in other chapters. The third chapter discusses a solution to the problem of making high sensitivity wavefront measurements is presented in this chapter. Starting with existing WFSs used in interferometer AO systems, the methods of measuring high order aberrations are considered. A new WFS method, Diffractive Phase Sensing, is presented and an implementation is described in the context of a specific WFS design: the Nine Element Sensor (NES). The fourth chapter concerns numerical simulations of the NES to evaluate its performance in an AO system. Comparisons are made with two existing WFS designs, one commonly used in astronomical AO and the other in use within current interferometer AO. The conclusions drawn specify the observation regimes for which each of the three WFS designs is most appropriate. The design and construction of a NES prototype is discussed in the fifth chapter. The prototype WFS is first tested in the laboratory, and its novel optic and CCD detector operation were analysed prior to use. The prototype was then used to make measurements of defocus phase aberrations at COAST, and results from these observations are presented and discussed to understand their implication. The final chapter considers the existing AO system at COAST—the autoguider—and its measurements of tip/tilt aberrations. The aim and method used to parameterise the atmospheric turbulence is detailed, and the results are verified with measurements from a DIMM and with fringe visibilities. Using the autoguider, the statistics of the seeing at the COAST site is presented from a year long dataset.

Residual speckles in adaptive optics (AO) images represent a well-known limitation on the achievement of the contrast needed for faint source detection. Speckles in AO imagery can be the result of either residual atmospheric aberrations, not corrected by the AO, or slowly evolving aberrations induced by the optical system. We take advantage of the high temporal cadence (1 ms) of the data acquired by the System for Coronagraphy with High-order Adaptive Optics from R to K bands-VIS forerunner experiment at the Large Binocular Telescope to characterize the AO residual speckles at visible wavelengths. An accurate knowledge of the speckle pattern and its dynamics is of paramount importance for the application of methods aimed at their mitigation. By means of both an automatic identification software and information theory, we study the main statistical properties of AO residuals and their dynamics. We therefore provide a speckle characterization that can be incorporated into numerical simulations to increase their realism and to optimize the performances of both real-time and postprocessing techniques aimed at the reduction of the speckle noise. (C) 2017 Society of PhotoOptical Instrumentation Engineers (SPIE).

The Magellan Telescope Adaptive Optics System (MagAO) is subject to resonance effects induced by elements within the system instrumentation, such as fans and cooling pumps. Normalized PSDs are obtained through frequency-based analysis of closed-loop on-sky data, detecting and measuring vibration effects. Subsequently, a space-state model for the AO loop is obtained, using a standard AO loop scheme with an integrator-based controller and including the vibration effects as disturbances. Finally, a new control alternative is proposed, focusing on residual phase variance minimization through the design and simulation of an optimal LQG control approach.

Deformable mirror is a widely used wavefront corrector in adaptive optics system, especially in astronomical, image and laser optics. A new structure of DM-3D DM is proposed, which has removable actuators and can correct different aberrations with different actuator arrangements. A 3D DM consists of several reflection mirrors. Every mirror has a single actuator and is independent of each other. Two kinds of actuator arrangement algorithm are compared: random disturbance algorithm (RDA) and global arrangement algorithm (GAA). Correction effects of these two algorithms and comparison are analyzed through numerical simulation. The simulation results show that 3D DM with removable actuators can obviously improve the correction effects.

The Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) instrument, under development for the Subaru Telescope, has currently the fastest on-sky wavefront control loop, with a pyramid wavefront sensor running at 3.5 kHz. But even at that speed, we are still limited by low-frequency vibrations. The current main limitation was found to be vibrations attributed mainly to the rotation of the telescope. Using the fast wavefront sensors, cameras and accelerometers, we managed to identify the origin of most of the vibrations degrading our performance. Low-frequency vibrations are coming from the telescope drive in azimuth and elevation, as well as the elevation encoders when the target is at transit. Other vibrations were found at higher frequency coming from the image rotator inside Subaru's adaptive optics facility AO188. Different approaches are being implemented to take care of these issues. The PID control of the image rotator has been tuned to reduce their high-frequency contribution. We are working with the telescope team to tune the motor drives and reduce the impact of the elevation encoder. A Linear Quadratic Gaussian controller (LQG, or Kalman filter) is also being implemented inside SCExAO to control these vibrations. These solutions will not only improve significantly SCExAOs performance, but will also help all the other instruments on the Subaru Telescope, especially the ones behind A0188. Ultimately, this study will also help the development of the TMT, as these two telescopes share very similar drives.