(단색수차 보정에 대한 수학적 접근

학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2020. 2. 강명주.This thesis introduces efficient and effective methods for solving monochromatic aberration correction problems. The proposed methods are based on Forward-Backward proximal splitting method, which solves the optimization problem by iteratively solving two sub parts for each step: 1. gradient descent and 2. noise removal. Since the gradient descent part has high computational cost, we develop a low-cost implementation of computing aberration operator and its transpose. Then, we propose 6 different methods, which are based on 6 types of different regularization in the noise removal part. In this thesis, we perform experiments on the proposed image restoration methods. In the experiments, we use synthetic images generated by point spread functions (PSFs), which emulate the effects of monochromatic aberration in modern digital cameras.이 연구는 단색 수차 보정 문제를 풀기 위한 효율적이고 효과적인 방법들을 소개한다. 제안된 방법들은 Forward-Backward proximal splitting 방법에 기반한 것으로 이 방법은 최적화 문제를 경사하강법과 노이즈 제거의 두 문제로 나누어 반복 방법을 통해 푼다. 단색 수차 문제에 있어서 경사하강법은 큰 계산 비용을 요구하기 때문에 수차 연산자의 저비용 구현 방법을 개발한다. 이어서 6가지의 서로 다른 정칙 연산자에 기반한 노이즈 제거 방법을 적용한 영상 복원 방법을 제안한다. 이 연구에서는 제안된 영상 복원 방법들에 대한 실험을 수행한다. 실험에서는 점확산함수 (Point Spread Function)을 이용해 합성된 수차 영상을 이용하는데, 해당 점확산함수는 현대 디지털 카메라의 단색 수차 효과를 모방한 것이다.1 Introduction 1 2 Related Works 5 2.1 Approximation Methods 5 2.1.1 Methods 5 2.1.2 Methods Comparison and Conclusion 7 2.2 Basic Fourier Optics 8 2.2.1 Wavefront Optical Path Difference, W (x, y) 8 2.2.2 Pupil and Amplitude Transfer Functions 11 2.2.3 Point Spread Functions 12 2.3 Mathematical Preliminaries 14 2.3.1 Basic Properties of svcOperators 14 2.3.2 Regularizations in Inverse Problems 16 2.3.3 Convex Optimization Theory 21 3 Proposed Methods 30 3.1 Low Cost Implementation Using Small Support Assumption 31 3.1.1 Vectorization Techniques 33 3.2 Proposed Algorithm 34 3.2.1 Forward Backward Splitting Algorithm 35 3.2.2 Split Bregman Method 38 3.2.3 Algorithms 42 4 Experiments 47 4.1 Implementation Details 47 4.1.1 Generation of synthetic blurry images 47 4.2 Numerical Results 49 4.2.1 Synthetically Blurred Images 50 4.2.2 Image Restoration 52 5 Conclusion and Future Work 65 5.1 Conclusion 65 5.2 Future Work 66 Abstract (in Korean) 71Docto

Astigmatism and Pseudoaccommodation in Pseudophakic Eyes

noAdvanced IOLs with circumferential zones of different power provide pseudoaccommodation. We investigated the potential for power variation with meridian, namely astigmatism, to provide pseudo-accommodation. With appropriate power and axis orientations, acceptable pseudo-accommodation can be achieved

Polarization Aberrations in Astronomical Telescopes: The Point Spread Function

Detailed knowledge of the image of the point spread function (PSF) is necessary to optimize astronomical coronagraph masks and to understand potential sources of errors in astrometric measurements. The PSF for astronomical telescopes and instruments depends not only on geometric aberrations and scalar wave diffraction but also on those wavefront errors introduced by the physical optics and the polarization properties of reflecting and transmitting surfaces within the optical system. These vector wave aberrations, called polarization aberrations, result from two sources: (1) the mirror coatings necessary to make the highly reflecting mirror surfaces, and (2) the optical prescription with its inevitable non-normal incidence of rays on reflecting surfaces. The purpose of this article is to characterize the importance of polarization aberrations, to describe the analytical tools to calculate the PSF image, and to provide the background to understand how astronomical image data may be affected. To show the order of magnitude of the effects of polarization aberrations on astronomical images, a generic astronomical telescope configuration is analyzed here by modeling a fast Cassegrain telescope followed by a single 90° deviation fold mirror. All mirrors in this example use bare aluminum reflective coatings and the illumination wavelength is 800 nm. Our findings for this example telescope are: (1) The image plane irradiance distribution is the linear superposition of four PSF images: one for each of the two orthogonal polarizations and one for each of two cross-coupled polarization terms. (2) The PSF image is brighter by 9% for one polarization component compared to its orthogonal state. (3) The PSF images for two orthogonal linearly polarization components are shifted with respect to each other, causing the PSF image for unpolarized point sources to become slightly elongated (elliptical) with a centroid separation of about 0.6 mas. This is important for both astrometry and coronagraph applications. (4) Part of the aberration is a polarization-dependent astigmatism, with a magnitude of 22 milliwaves, which enlarges the PSF image. (5) The orthogonally polarized components of unpolarized sources contain different wavefront aberrations, which differ by approximately 32 milliwaves. This implies that a wavefront correction system cannot optimally correct the aberrations for all polarizations simultaneously. (6) The polarization aberrations couple small parts of each polarization component of the light (∼10^(-4)) into the orthogonal polarization where these components cause highly distorted secondary, or “ghost” PSF images. (7) The radius of the spatial extent of the 90% encircled energy of these two ghost PSF image is twice as large as the radius of the Airy diffraction pattern. Coronagraphs for terrestrial exoplanet science are expected to image objects 10^(-10), or 6 orders of magnitude less than the intensity of the instrument-induced “ghost” PSF image, which will interfere with exoplanet measurements. A polarization aberration expansion which approximates the Jones pupil of the example telescope in six polarization terms is presented in the appendix. Individual terms can be associated with particular polarization defects. The dependence of these terms on angles of incidence, numerical aperture, and the Taylor series representation of the Fresnel equations lead to algebraic relations between these parameters and the scaling of the polarization aberrations. These “design rules” applicable to the example telescope are collected in § 5. Currently, exoplanet coronagraph masks are designed and optimized for scalar diffraction in optical systems. Radiation from the “ghost” PSF image leaks around currently designed image plane masks. Here, we show a vector-wave or polarization optimization is recommended. These effects follow from a natural description of the optical system in terms of the Jones matrices associated with each ray path of interest. The importance of these effects varies by orders of magnitude between different optical systems, depending on the optical design and coatings selected. Some of these effects can be calibrated while others are more problematic. Polarization aberration mitigation methods and technologies to minimize these effects are discussed. These effects have important implications for high-contrast imaging, coronagraphy, and astrometry with their stringent PSF image symmetry and scattered light requirements

Characterization of a Hyperspectral Chromotomographic Imaging Ground System

A field-deployable hyperspectral chromotomographic imager has been developed and tested as a risk-reduction prototype to assist design of a space-based system. The instrument uses a high-speed video camera looking through a rotating direct-vision prism to simultaneously observe the full field of view in all visible wavelength channels. The chromotomographic process multiplexes the spectral and spatial so an advanced reconstruction algorithm is required to separate the spectral channels. A physics-based model of the instrument was developed to assist in future trade-space choices for design of the spaced-based system. Additionally, the model is used for the development and assessment of the filtered backprojection reconstruction algorithm. Laboratory experiments from the field-deployable instrument were collected, and the results are compared to physics-based model predictions. Results from the simulated and experimental data show that the instrument and algorithm are capable of detecting spectral and spatial information of complex scene

Adaptive Optics for Stellar Interferometry

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

An Evaluation of multispectral earth-observing multi-aperture telescope designs for target detection and characterization

Earth-observing satellites have fundamental size and weight design limits since they must be launched into space. These limits serve to constrain the spatial resolutions that such imaging systems can achieve with traditional telescope design strategies. Segmented and sparse-aperture imaging system designs may offer solutions to this problem. Segmented and sparse-aperture designs can be viewed as competing technologies; both approaches offer solutions for achieving finer resolution imaging from space. Segmented-aperture systems offer greater fill factor, and therefore greater signal-to-noise ratio (SNR), for a given encircled diameter than their sparse aperture counterparts, though their larger segments often suffer from greater optical aberration than those of smaller, sparse designs. Regardless, the use of any multi-aperture imaging system comes at a price; their increased effective aperture size and improvement in spatial resolution are offset by a reduction in image quality due to signal loss (less photon-collecting area) and aberrations introduced by misalignments between individual sub-apertures as compared with monolithic collectors. Introducing multispectral considerations to a multi-aperture imaging system further starves the system of photons and reduces SNR in each spectral band. This work explores multispectral design considerations inherent in 9-element tri-arm sparse aperture, hexagonal-element segmented aperture, and monolithic aperture imaging systems. The primary thrust of this work is to develop an objective target detection-based metric that can be used to compare the achieved image utility of these competing multi-aperture telescope designs over a designated design parameter trade space. Characterizing complex multi-aperture system designs in this way may lead to improved assessment of programmatic risk and reward in the development of higher-resolution imaging capabilities. This method assumes that the stringent requirements for limiting the wavefront error (WFE) associated with multi-aperture imaging systems when producing imagery for visual assessment, can be relaxed when employing target detection-based metrics for evaluating system utility. Simple target detection algorithms were used to determine Receiver Operating Characteristic (ROC) curves for the various simulated multi-aperture system designs that could be used in an objective assessment of each system\u27s ability to support target detection activities. Also, a set of regressed equations was developed that allow one to predict multi-aperture system target detection performance within the bounds of the designated trade space. Suitable metrics for comparing the shapes of two individual ROC curves, such as the total area under the curve (AUC) and the sample Pearson correlation coefficient, were found to be useful tools in validating the predicted results of the trade space regression models. And lastly, some simple rules of thumb relating to multi-aperture system design were identified from the inspection of various points of equivalency between competing system designs, as determined from the comparison metrics employed. The goal of this work, the development of a process for simulating multi-aperture imaging systems and comparing them in terms of target detection tasks, was successfully accomplished. The process presented here could be tailored to the needs of any specific multi-aperture development effort and used as a tool for system design engineers

Automatic Estimation of Modulation Transfer Functions

The modulation transfer function (MTF) is widely used to characterise the performance of optical systems. Measuring it is costly and it is thus rarely available for a given lens specimen. Instead, MTFs based on simulations or, at best, MTFs measured on other specimens of the same lens are used. Fortunately, images recorded through an optical system contain ample information about its MTF, only that it is confounded with the statistics of the images. This work presents a method to estimate the MTF of camera lens systems directly from photographs, without the need for expensive equipment. We use a custom grid display to accurately measure the point response of lenses to acquire ground truth training data. We then use the same lenses to record natural images and employ a data-driven supervised learning approach using a convolutional neural network to estimate the MTF on small image patches, aggregating the information into MTF charts over the entire field of view. It generalises to unseen lenses and can be applied for single photographs, with the performance improving if multiple photographs are available

Interferometric Metrology Using Reprogrammable Binary Holograms

Interferometric methods for surface metrology have been widely used for many years due to their speed, accuracy and versatility. It is frequently necessary however to produce a known comparison reference surface to minimise the optical path difference and hence enhance the dynamic range. An alternative to this is to use a computer generated hologram to act as the reference wave, or to correct a spherical reference wave to match a highly aspheric optic in order to achieve a null test. This thesis shall present a novel method of producing such holograms through the use of a binary ferroelectric liquid crystal on silicon spatial light modulator (FLCOS SLM) rather than using the more common lithographically produced plates. One of the primary advantages this could introduce is the ability for arbitrarily reprogrammable holograms to be created upon demand rather than needing to produce a series of holographic plates, saving both time and money in the testing of surfaces. We present results characterising the ability of a FLCOS SLM to produce increasingly large Zernike aberrations as well as quantifying the resulting errors, before using the device to reduce interferometric fringe density allowing us to measure aberrated optics and reveal low amplitude surface variations on the scale of 0.045 waves RMS

Design And Assessment Of Compact Optical Systems Towards Special Effects Imaging

A main challenge in the field of special effects is to create special effects in real time in a way that the user can preview the effect before taking the actual picture or movie sequence. There are many techniques currently used to create computer-simulated special effects, however current techniques in computer graphics do not provide the option for the creation of real-time texture synthesis. Thus, while computer graphics is a powerful tool in the field of special effects, it is neither portable nor does it provide work in real-time capabilities. Real-time special effects may, however, be created optically. Such approach will provide not only real-time image processing at the speed of light but also a preview option allowing the user or the artist to preview the effect on various parts of the object in order to optimize the outcome. The work presented in this dissertation was inspired by the idea of optically created special effects, such as painterly effects, encoded in images captured by photographic or motion picture cameras. As part of the presented work, compact relay optics was assessed, developed, and a working prototype was built. It was concluded that even though compact relay optics can be achieved, further push for compactness and cost-effectiveness was impossible in the paradigm of bulk macro-optics systems. Thus, a paradigm for imaging with multi-aperture micro-optics was proposed and demonstrated for the first time, which constitutes one of the key contributions of this work. This new paradigm was further extended to the most general case of magnifying multi-aperture micro-optical systems. Such paradigm allows an extreme reduction in size of the imaging optics by a factor of about 10 and a reduction in weight by a factor of about 500. Furthermore, an experimental quantification of the feasibility of optically created special effects was completed, and consequently raytracing software was developed, which was later commercialized by SmARTLens(TM). While the art forms created via raytracing were powerful, they did not predict all effects acquired experimentally. Thus, finally, as key contribution of this work, the principles of scalar diffraction theory were applied to optical imaging of extended objects under quasi-monochromatic incoherent illumination in order to provide a path to more accurately model the proposed optical imaging process for special effects obtained in the hardware. The existing theoretical framework was generalized to non-paraxial in- and out-of-focus imaging and results were obtained to verify the generalized framework. In the generalized non-paraxial framework, even the most complex linear systems, without any assumptions for shift invariance, can be modeled and analyzed