Traditionally, adaptive optics (AO) systems for microscopy have focused on AO at the pupil plane, however this produces poor performance in samples with both spatially-variant aberrations, such as non-flat sample interfaces, and spatially-invariant aberrations, such as spherical aberration due to a difference between the sample index of refraction and the sample for which the objective was designed. Here, we demonstrate well-corrected, wide field-of-view (FOV) microscopy by simultaneously correcting the two types of aberrations using two AO loops. Such an approach is necessary in wide-field applications where both types of aberration may be present, as each AO loop can only fully correct one type of aberration. Wide FOV corrections are demonstrated in a trans-illumination microscope equipped with two deformable mirrors (DMs), using a partitioned aperture wavefront (PAW) sensor to directly control the DM conjugated to the sample interface and a sensor-less genetic algorithm to control the DM conjugated to the objective’s pupil.

The impact of uncoordinated growth of the optical components of the eye may stimulate different levels of monochromatic aberrations in the growing eyes of the children. This thesis aimed to examine the impact of age, visual acuity and refractive error on higher order aberrations as well as to determine the relationship between them. Hartman Shack images taken with the Welch Allyn® SureSight Autorefractor were calibrated in order to determine the Zernike coefficients up to the 8th order for a pupil diameter of 5mm. The MATLAB code proposed by Thibos et al that follows the standard for reporting the optical aberrations of the eye was the basis of code written for this study. Modification was required to suit the specific needs of the Welch Allyn® SureSight Autorefractor. After calibration the lower order aberrations could then be compared with the results from cyclopledged retinoscopy. RMS values of aberrations and Strehl ratios were computed to examine the optical performance of the eye. A total of 834 Hartmann-Shack images of 436 children (mean age 3.94± 0.94 years, range 3 to 6 years) were examined in this study (right eyes 436; left eyes 398).The sample had a mean (± STD) spherical equivalent of 1.19 ± 0.59D, a mean with-the-rule astigmatism (J0) of 0.055 ± 0.22D, and a mean oblique astigmatism (J45) of 0.01±0.14D. Visual acuity varied from 6/6 to 6/18. Moderate mirror symmetry was found between the eyes. Like refractive error, higher order aberrations declined with age in this sample. There was an impact of higher order aberrations on refractive error. Significantly higher ocular aberrations were found in the higher hyperopic group (SE>+2.0D) compared to emmetropic (-0.5<SE<+0.5D) and low hyperopic groups (+0.5<SE<+2.0D). The Strehl ratio was significantly lower in the high hyperopic group. Higher Strehl ratios were observed for better acuity groups but the average Strehl ratios among the different visual acuity groups were not statistically significant. In conclusion, there was an impact of age on the ocular aberrations. A wider range of age from birth to adolescence is required for further investigation. This could be indirectly influenced by the age related changes in refractive error as the correlation between refractive error and the higher order aberrations were significant. This finding also concludes that Strehl Ratio alone is not capable of perfectly describing the visual acuity of the eye; other metrics such as the neural transfer function and neural noise are necessary to describe the resultant visual performance of the eye.

The impact of uncoordinated growth of the optical components of the eye may stimulate different levels of monochromatic aberrations in the growing eyes of the children. This thesis aimed to examine the impact of age, visual acuity and refractive error on higher order aberrations as well as to determine the relationship between them. Hartman Shack images taken with the Welch Allyn® SureSight Autorefractor were calibrated in order to determine the Zernike coefficients up to the 8th order for a pupil diameter of 5mm. The MATLAB code proposed by Thibos et al that follows the standard for reporting the optical aberrations of the eye was the basis of code written for this study. Modification was required to suit the specific needs of the Welch Allyn® SureSight Autorefractor. After calibration the lower order aberrations could then be compared with the results from cyclopledged retinoscopy. RMS values of aberrations and Strehl ratios were computed to examine the optical performance of the eye. A total of 834 Hartmann-Shack images of 436 children (mean age 3.94± 0.94 years, range 3 to 6 years) were examined in this study (right eyes 436; left eyes 398).The sample had a mean (± STD) spherical equivalent of 1.19 ± 0.59D, a mean with-the-rule astigmatism (J0) of 0.055 ± 0.22D, and a mean oblique astigmatism (J45) of 0.01±0.14D. Visual acuity varied from 6/6 to 6/18. Moderate mirror symmetry was found between the eyes. Like refractive error, higher order aberrations declined with age in this sample. There was an impact of higher order aberrations on refractive error. Significantly higher ocular aberrations were found in the higher hyperopic group (SE>+2.0D) compared to emmetropic (-0.5<SE<+0.5D) and low hyperopic groups (+0.5<SE<+2.0D). The Strehl ratio was significantly lower in the high hyperopic group. Higher Strehl ratios were observed for better acuity groups but the average Strehl ratios among the different visual acuity groups were not statistically significant. In conclusion, there was an impact of age on the ocular aberrations. A wider range of age from birth to adolescence is required for further investigation. This could be indirectly influenced by the age related changes in refractive error as the correlation between refractive error and the higher order aberrations were significant. This finding also concludes that Strehl Ratio alone is not capable of perfectly describing the visual acuity of the eye; other metrics such as the neural transfer function and neural noise are necessary to describe the resultant visual performance of the eye.

Since its invention in the early seventies, the Shack-Hartmann wavefront sensor has seen a wide variety of applications and has had great success in the fields of Adaptive Optics and Ophthalmology, where interferometry is usually impractical. Its application to optical shop testing has been less visible perhaps because shop environments can be manipulated to sufficiently remove vibration and turbulence to a degree that can support interferometry. However, with the growing need to accurately test aspheric optics, the Shack-Hartmann has an advantage; its dynamic range can be manipulated through the design of the lenslet array, rather than being directly tied to the wavelength of light and therefore lessen the need for expensive null optics.When the Shack-Hartmann is pushed to the limits of dynamic range, several issues must be dealt with. First, to reach the limits of dynamic range, those limits must be well understood. This dissertation presents a graphical approach to designing the Shack-Hartmann sensor that makes the trade-off between sensitivity and dynamic range, and accuracy and resolution intuitively clear. Next, the spots that once landed neatly in the region behind each lenslet, may now wander several lenslets away and the data reduction must be able handle this. This dissertation presents a novel and robust method for sorting these widely wondering spots and is shown to work in measurements of highly aspheric elements. Finally, in the high dynamic range regime, induced aberrations can severely limit the accuracy of the instrument. In this dissertation, these non-linear and measurement-dependent errors are studied in detail and a method of compensation is presented along with experimental results that illustrate the efficacy of the approach.

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.

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.

In preparation for the Astro 2020 Decadal Survey NASA has commissioned the study four flagship missions spanning to a wide range of observable wavelengths: the Origins Space Telescope (OST, formerly the Far-Infrared Surveyor), Lynx (formerly the X-ray Surveyor), the Large UV/Optical/Infrared Surveyor (LUVOIR) and the Habitable Exoplanet Imager (HabEx). One of the key scientific objectives of the latter two is the detection and characterization of the earth-like planets around nearby stars using the direct imaging technique (along with a broad range of investigations regarding the architecture of and atmospheric composition exoplanetary systems using this technique). As a consequence dedicated exoplanet instruments are being studied for these mission concepts. This paper discusses the design of the coronagraph instrument for the architecture "A" (15 meters aperture) of LUVOIR. The material presented in this paper is aimed at providing an overview of the LUVOIR coronagraph instrument. It is the result of four months of discussions with various community stakeholders (scientists and technologists) regarding the instrument's basic parameters followed by meticulous design work by the the GSFC Instrument Design Laboratory team. In the first section we review the main science drivers, presents the overall parameters of the instrument (general architecture and backend instrument) and delve into the details of the currently envisioned coronagraph masks along with a description of the wavefront control architecture. Throughout the manuscript we describe the trades we made during the design process. Because the vocation of this study is to provide a baseline design for the most ambitious earth-like finding instrument that could be possibly launched into the 2030's, we have designed an complex system privileged that meets the ambitious science goals out team was chartered by the LUVOIR STDT exoplanet Working Group. However in an effort to minimize technological risk we tried to maximize the number of technologies that will be matured by the WFIRST coronagraph instruments.

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.