Tesis sobre el tema "Shack- Hartmann Sensor"

Ocular wavefront sensing is vital to improving our understanding of the human eye and to developing advanced vision correction methods, such as adaptive optics, customized contact lenses, and customized laser refractive surgery. It is also a necessary technique for high-resolution imaging of the retina. The most commonly used wavefront sensing method is based on the Shack-Hartmann wavefront sensor. Since Junzhong Liang's first application of Shack-Hartmann wavefront sensing for the human eye in 1994, the method has quickly gained acceptance and popularity in the ophthalmic industry. Several commercial Shack-Hartmann eye aberrometers are currently available. While the existing aberrometers offer reasonable measurement accuracy and reproducibility, they do have a limited dynamic range. Although rare, highly aberrated eyes do exists (corneal transplant, keratoconus, post-lasik) that cannot be measured with the existing devices. Clinicians as well as optical engineers agree that there is room for improvement in the performance of these devices "Although the optical aberrations of normal eyes have been studied by the Shack-Hartmann technique, little is known about the optical imperfections of abnormal eyes. Furthermore, it is not obvious that current Shack-Hartmann aberrometers are robust enough to successfully measure clinically abnormal eyes of poor optical quality" Larry Thibos, School of Optometry, Indiana University. The ultimate goal for ophthalmic aberrometers and the main objective of this work is to increase the dynamic range of the wavefront sensor without sacrificing its sensitivity or accuracy. In this dissertation, we attempt to review and integrate knowledge and techniques from previous studies as well as to propose our own analytical approach to optimizing the optical design of the sensor in order to achieve the desired dynamic range. We present the underlying theory that governs the relationship between the performance metrics of the sensor: dynamic range, sensitivity, spatial resolution, and accuracy. We study the design constraints and trade-offs and present our system optimization method in detail. To validate the conceptual approach, a complex simulation model was developed. The comprehensive model was able to predict the performance of the sensor as a function of system design parameters, for a wide variety of ocular wavefronts. This simulation model did confirm the results obtained with our analytical approach. The simulator itself can now be used as a standalone tool for other Shack-Hartmann sensor designs. Finally, we were able to validate our theoretical work by designing and building an experimental prototype. We present some of the more practical design aspects, such as illumination choices and tolerance analysis methods. The prototype validated the conceptual approach used in the design and was able to demonstrate a vast increase in dynamic range while maintaining accurate and repeatable measurements.
Ph.D.
Optics and Photonics
Optics and Photonics
Optics PhD

Standard adaptive optics systems measure the aberrations in the wavefronts of a beacon guide star caused by atmospheric turbulence, which limits the corrected field of view to the isoplanatic patch, the solid angle over which the optical aberration is roughly constant. For imaging systems that require a corrected field of view larger than the isoplanatic angle, a three-dimensional estimate of the aberration is required. We are developing a wide-field imaging Shack-Hartmann wavefront sensor (WFS) that will characterize turbulence over a large field of view tens of times the size of the isoplanatic angle. The technique will find application in horizontal and downward looking remote sensing scenarios where high resolution imaging through extended atmospheric turbulence is required. The laboratory prototype system consists of a scene generator, turbulence simulator, a Shack Hartman WFS arm, and an imaging arm. The system has a high intrinsic Strehl ratio, is telecentric, and diffraction limited. We present preliminary data and analysis from the system.

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.

A Shack Hartmann wavefront sensor is used to detect the distortion of light in an optical wavefront. It does this by sampling the wavefront with an array of lenslets and measuring the displacement of focused spots from reference positions. These displacements are linearly related to the local wavefront tilts from which the entire wavefront can be reconstructed. In most Shack Hartmann wavefront sensors, a CCD is used to sample the entire wavefront, typically at a rate of 25 to 60 Hz, and a whole frame of light spots is read out before their positions are processed. This results in a data bottleneck. In this design, parallel processing is achieved by incorporating local centroid processing for each focused spot, thereby requiring only reduced bandwidth data to be transferred off-chip at a high rate. To incorporate centroid processing at the sensor level requires high levels of circuit integration not possible with a CCD technology. Instead a standard 0.7J..lmCMOS technology was used but photodetector structures for this technology are not well characterised. As such characterisation of several common photodiode structures was carried out which showed good responsitivity of the order of 0.3 AIW. Prior to fabrication on-chip, a hardware emulation system using a reprogrammable FPGA was built which implemented the centroiding algorithm successfully. Subsequently, the design was implemented as a single-chip CMOS solution. The fabricated optical centroid processor successfully computed and transmitted the centroids at a rate of more than 2.4 kHz, which when integrated as an array of tilt sensors will allow a data rate that is independent of the number of tilt sensors' employed. Besides removing the data bottleneck present in current systems, the design also offers advantages in terms of power consumption, system size and cost. The design was also shown to be extremely scalable to a complete low cost real time adaptive optics system.

The Hartmann-Shack (H-S) wavefront sensor is now deployed in many different fields, from astronomy to industrial inspection, where the quality of optical media or components can be measured by the distortions (wavefront aberrations) they impart on a wavefront transmitted or reflected by them. In ophthalmology, this sensor is a core component of major aberrometers, used in the assessment of the visual quality of the eye, academic research and clinical diagnosis. The H-S wavefront sensor is also found in adaptive optics (AO) systems, which are used to improve the quality and the capabilities of optical systems, by compensating for wavefront aberrations that affect light waves. These image distortions can represent a serious problem in many different applications where high-quality images are demanded. The microlens array is an important element in the H-S sensor, responsible for sampling the aberrated wavefront into light spots on the focal plane. The position of each light spot relates to the average tilt of the wavefront over the respective microlens. These spot­position coordinates are then used in the modal reconstruction to approximate the wavefront topology with a combination of orthogonal basis functions. The wavefront reconstruction error describes the deviation of the reconstructed wavefront from the reference one. The wavefront sampling is influenced by the microlens distribution pattern in the array, lens contour and size, number of microlenses and fill factor. Adopted grids typically consist in either rectangular or hexagonal configurations. The influence of the array geometry on the wavefront reconstruction error was already discussed in the literature, which demonstrated that random arrays might perform better than regular ones. This work proposes the optimization of the microlens-array geometry to be used in a specific context, such as ophthalmology. The workflow consisted of three major steps: numerical optimization, to find the optimal microlens arrays; fabrication of the arrays; and test on an optical bench, to comparatively assess the performance of the fabricated and commercial arrays. The optimization comprises the minimization of the wavefront reconstruction error and/or the number of necessary microlenses in the array, considering a known aberration statistics. Within the ophthalmological context, as a case study, it was demonstrated by the numerical simulations that 10 or 16 suitably located microlenses can be used to produce reconstruction errors as small as those of a 36-microlens rectangular array. The optimized arrays were then fabricated in a clean room, where KOH anisotropic etching was used to obtain the silicon molds from which the microlens arrays were replicated on polymer by casting. Four arrays were fabricated: 10- and 16-microlens optimized arrays and 16 and 36-microlens rectangular arrays. All four arrays were tested and compared to a standard 127-microlens hexagonal commercial array, using an arbitrary wavefront aberration, which is compatible with the used ophthalmological wavefront-aberration statistics. The final results corroborate with the predictions of the computational simulations.
O sensor de frente de ondas de Hartmann-Shack (H-S) é aplicado a diversas áreas do conhecimento, da astronomia à inspeção industrial, em que a qualidade de meios ou componentes ópticos pode ser medida através das distorções (aberrações de frentes de onda) que eles inserem em uma frente de onda, seja por reflexão ou refração. Em oftalmologia, este sensor é um componente central da maioria dos aberrômetros, que são usados na avaliação da qualidade óptica do olho, em pesquisas e em diagnóstico clínico. O sensor de frentes de onda de H-S é também encontrado em sistemas ópticos adaptativos, que são usados para aumentar a qualidade de sistemas ópticos, por meio da compensação de aberrações de frentes de onda. Essas distorções nas frentes de onda podem representar um sério problema em diversas aplicações que requerem imagens de alta qualidade. A matriz de microlentes é um importante elemento no sensor de H-S responsável pela amostragem da frente de onda aberrada em pontos de luz no flano focal. A posição de cada ponto de luz relaciona a inclinação média da parte da frente de onda amostrada pela respectiva microlente. As coordenadas das posições de todos os pontos de luz são usados no processo de reconstrução modal para aproximar a topologia real da frente de onda através de uma combinação de funções ortonormais. O desvio dessa aproximação é chamado de erro de reconstrução. A amostragem da frente de onda é influenciada pelo padrão de distribuição das microlentes na matriz, formato e tamanho das microlentes, número de microlentes e fator de preenchimento da matriz. As matrizes comumente encontradas no mercado possuem, em geral, configura·o retangular ou hexagonal. A influência da geometria da matriz sobre o erro de reconstrução já foi discutido na literatura, que demonstrou que geometrias aleatórias podem apresentar performance melhor do que as geometrias regulares. Este trabalho propôs a otimização da geometria da matriz de microlentes para ser usada em um contexto específico, como oftalmologia. O trabalho consistiu de três fases: optimização numéica, para encontrar as matrizes ótimas; fabricação e teste em bancada óptica, para avaliar comparativamente a performance das matrizes fabricadas e uma matriz comercial. A otimização consiste na minimização do erro de reconstrução e/ou do número de microlentes necessárias na matriz, considerando uma estatística de aberrações conhecida. No contexto oftalmológico, usado como estudo de caso, foi demonstrado pelas simula·es que matrizes otimizadas com 10 ou 16 microlentes podem ser usadas para produzir erros de reconstrução da mesma ordem que matrizes retangulares com 36 microlentes. As matrizes otimizadas foram então fabricadas em uma sala limpa, onde corrosão anisotróica por KOH foi utilizada para obter-se moldes dos quais as microlentes foram replicadas em polímero. Foram fabricadas as matrizes otimizadas com 10 e 16 microlentes e também as matrizes retangulares com 16 e 36 microlentes. Todas as matrizes foram testadas e comparadas com uma matriz hexagonal comercial, com 127 microlentes. Os testes foram feitos com uma aberração arbitrária, mas compatível com a estatística estudada. Os resultados finais corroboram com os previstos pelas simula·es computacionais.

Shack-Hartmann wavefront sensors are commonly used in optical alignment, ophthalmology, astronomy, adaptive optics and commercial optical testing. Wavefront error measurement yields Zernike polynomials which provide useful data for alignment correction calculations. In this thesis a practical alignment method of a helmet visor is proposed based on the wavefront error measurements. The optical system is modeled in Zemax software in order to collect the Zernike polynomial data necessary to relate the error measurements to the positioning of the visor. An artificial neural network based computer program is designed and trained with the data obtained from Zernike simulation in Zemax software and then the program is able to find how to invert the misalignments in the system. The performance of this alignment correction method is compared with the optical test setup measurements.

This thesis consists of two parts: a report on the use of a binocular Shack-Hartmann (SH) sensor to study the dynamic correlation of ocular aberrations; and the application of an adaptive optics (AO) system to investigate the effect of the manipulation of aberrations on the accommodation control. The binocular SH sensor consists of one laser source and one camera to reduce system cost and complexity. Six participants took part in this study. Coherence function analysis showed that coherence values were dependent on the subject, aberration and frequency component. Inter-ocular correlations of the aberration dynamics were fairly weak for all participants. Binocular and monocular viewing conditions produced similar wavefront error dynamics. The AO system has a dual wavefront sensing channel. The extra sensing channel permits direct measurement of the eye's aberrations independent of the deformable mirror. Dynamic correction of aberrations during steady-state fixation did not affect the accommodation microfluctuations, possibly due to the prior correction of the static aberration level and/or the limited correction bandwidth. The inversion of certain aberrations during dynamic accommodation affected the gain and latency of accommodation response (AR), suggesting that the eye used the aberrations to guide its initial path of accommodative step response. Corrections of aberrations at various temporal locations of AR cycle produced subject- and aberration-dependent results. The gain and phase lag of the AR to a sinusoidally moving target were unaffected by aberration correction. The predictable nature of the target had been suggested as the reason for its failure to produce any significant effect on the AR gain and phase lag.

Este trabalho descreve os passos envolvidos no desenvolvimento de um protótipo de aberroscópio para uso oftalmológico. Este instrumento faz incidir no fundo do olho humano um feixe luminoso de baixa potência e amostra, por meio do método de Hartmann, as frentes de onda da luz espalhada. A partir dos dados coletados, a forma das frentes de onda são reconstituídas e as aberrações eventualmente existentes no olho são calculadas e representadas por intermédio dos polinômios de Zernike. Aqui são expostos os fundamentos deste método, algumas das suas propriedades e limitações. Também é mostrada a caracterização funcional do protótipo desenvolvido, testando-o com elementos ópticos de propriedades conhecidas
This work describes the steps involved in the aberroscope prototype development for ophthalmological use. This instrument injects inside the human eye a low power light beam and sample, by Hartmann method, the wavefronts produced by ocular fundus light scattering. From collected data, the wavefront shape is reconstructed and the eye aberrations that eventually existent are calculated and adjusted by Zernike polynomials. Are discussed the method foundations, some of properties and limitations. Also the functional characterization of the developed prototype is shown, by testing it with optical elements of known properties

Con el cambio del siglo XX al XXI, la importancia de las tecnologías ópticas, como herramientas esenciales para otras ciencias, está llamando la atención en diferentes ámbitos científicos y económicos. El desarrollo de técnicas relacionadas con la imagen óptica aparece en diferentes puntos de vista como por ejemplo, la tecnología de la información y de las comunicaciones, la salud humana y las ciencias de la vida, los sensores ópticos y nuevas lámparas para una mejora en el consumo de energía, el desarrollo de equipos destinados a procesos de fabricación en la industria, etc. Las aplicaciones en la industria han tenido un gran impacto económico: por ejemplo, todos los circuitos integrados de semiconductores que se producen en el mundo se fabrican mediante litografía óptica. El desarrollo de la industria de semiconductores ha dado un impulso a la investigación básica y al desarrollo de técnicas ópticas: la disminución de los tamaños en la fabricación implica la exigencia de nuevos materiales, nuevos componentes ópticos, nuevas fuentes de iluminación. En la actualidad, la mayoría de la población europea es usuaria de la Tecnología de la Información y de la Comunicación (del inglés, "Information Communication Technology"), por ejemplo a través de ordenadores personales, telefonía móvil, electrónica empleada en medicina, internet, control de robots inteligentes, detección de obstáculos para la guía de un vehículo,. y la calidad de este tipo de productos aumenta considerablemente cada pocos años para un mismo precio (un factor ~2 cada 3 años). La base de tal progreso se debe, en gran parte, al rápido progreso en la calidad de los componentes que se emplean en esta ICT, como por ejemplo, los circuitos integrados y su conexión con otros dispositivos. La industria semiconductora se está preparando para promover una reducción del detalle más pequeño en los circuitos integrados, por debajo de los 130 nanómetros. Tal reducción requiere una evaluación de la ausencia de gradientes ondulatorios y abruptos con una precisión de 10 nanómetros para el caso particular de obleas de 300 milímetros de diámetro. El diámetro actual standard de las obleas es de 200 milímetros aunque actualmente ya se están produciendo obleas de 300 milímetros y el objetivo es fabricar obleas todavía más grandes. Además, la velocidad de procesado aumentará hasta 100 obleas por hora. Así, el control en la producción y pulido de obleas requiere una instrumentación para la medición rápida de la topografía tridimensional que en la actualidad, no está disponible técnicamente. Otro de los problemas que aparece en la industria semiconductora concierne a los substratos que forman las obleas. La tecnología actual permite producir detalles muy pequeños mediante procesos litográficos. Esto exige mayores requerimientos en la planitud de las obleas sobre las que se depositan repetidamente circuitos integrados. El problema consiste en que la inspección de la planitud requiere mucho tiempo, varias horas para una única oblea. Otro de los problemas con los que se encuentra la industria semiconductora es el procesado de las obleas. Después de la deposición de cada substrato, se neutraliza depositando una capa muy delgada de SiO2. Antes de la siguiente deposición, la oblea se somete a procesos de pulido químicos y mecánicos para conseguir de nuevo la planitud deseada. Se trata de un proceso lento que aumenta el coste de producción. Sin embargo, en un futuro inmediato se fabricarán obleas de 450 mm de diámetro mientras que las actuales son de 200 mm; de forma que se podrán depositar más circuitos integrados ganando tiempo y reduciendo el coste de producción. La situación es similar en otros campos, como por ejemplo, los dispositivos de cristal líquido: en la línea de producción se requiere un rápido control de la topografía tridimensional de dichos cristales, que tampoco está disponible en la actualidad. En este caso las dimensiones pueden llegar a ser de 1m por 1m.

Abordando las importantes características dinámicas del ojo, se han planteado una serie de experimentos que permiten el estudio de algunas de estas propiedades dinámicas, para proporcionar nueva información sobre el sistema visual. Para dichos experimentos, se han diseñado y construido tres instrumentos de medida basados todos en el concepto del sensor de Hartmann-Shack (HS), cada uno con características particulares: sensor HS de alta resolución temporal, sensor HS de campo amplio y sensor HS con iluminación invisible. Con estos instrumentos se abordan condiciones específicas que pueden afectar la dinámica del ojo, como los posibles efectos que tiene el cambio en la línea de mirada (o la torsión del ojo) sobre las aberraciones, así como las potenciales diferencias que se puede generar sobre las aberraciones cuando los sujetos observan con visión monocular o binocular, o evaluar si en el ojo existe una longitud de onda "preferida" para enfocar estímulos policromáticos.
Addressing the important dynamic characteristics of the eye, a number of experiments were performed to study some of these dynamic properties, in order to provide new information about the visual system. To carry out these experiments, three instruments were designed and implemented, all of them based on the Hartmann-Shack sensor (HS) principle, but each one with particular characteristics: high time resolution HS sensor, wide field HS sensor and HS sensor with invisible illumination. Specific conditions that can affect the dynamics of the eye were addressed with these instruments, for example the possible effects arising from changes in the line of sight (gaze) on the aberrations, or the potential differences that can be generated on aberrations when subjects are under monocular or binocular vision, or evaluate if is there a "preferential" wavelength the eye uses to focus polychromatic stimuli.

Las lentes progresivas (LP) para gafas es una solución muy extendida para la presbicia, ya que proporcionan una visión continua a todas las distancias debido a un cambio progresivo de potencia. En este trabajo se han medido las aberraciones de frente de onda espacialmente resueltas y la calidad visual en estas lentes. Además del astigmatismo que aumenta periféricamente, también se han encontrado pequeños valores de aberraciones de tercer orden, coma y trefoil, que producen un bajo deterioro de la calidad óptica y visual. El logaritmo de métricas sobre la PSF del sistema lente con ojo son las que mejor predicen la agudeza visual. Durante la primera semana de adaptación, no se aprecia una mejora significativa de la agudeza visual a través de distintas zonas de las LPs. Al comparar diferentes LPs, las aberraciones, principalmente el astigmatismo, se comporta como un colchón de agua, que se puede mover pero no eliminar.
Progressive lenses (PL) are designed to provide continuous vision at all distances by means a progressive change in spherical power from upper to lower zones. In this thesis, we measure the spatially resolved aberrations and the visual quality of PLs. In addition to astigmatism, third order aberrations, coma and trefoil, are also found in the PLs, but the impact of these aberrations on visual performance is limited. The logarithm of metrics on the PSF of the entire system eye plus PL are the parameters that best predict the visual acuity. There is not a significant improvement of visual acuity through the different zones of the PLs during the first week of adaptation. The current designs of PLs are somehow similar to a waterbed, with the aberrations, mainly astigmatism, being the water: they can be moved but they cannot be eliminated.

Optical testing in adverse environments, ophthalmology and applications where characterization by curvature is leveraged all have a common goal: accurately estimate wavefront shape. This dissertation investigates wavefront sensing techniques as applied to optical testing based on gradient and curvature measurements. Wavefront sensing involves the ability to accurately estimate shape over any aperture geometry, which requires establishing a sampling grid and estimation scheme, quantifying estimation errors caused by measurement noise propagation, and designing an instrument with sufficient accuracy and sensitivity for the application. Starting with gradient-based wavefront sensing, a zonal least-squares wavefront estimation algorithm for any irregular pupil shape and size is presented, for which the normal matrix equation sets share a pre-defined matrix. A Gerchberg–Saxton iterative method is employed to reduce the deviation errors in the estimated wavefront caused by the pre-defined matrix across discontinuous boundary. The results show that the RMS deviation error of the estimated wavefront from the original wavefront can be less than λ/130~ λ/150 (for λ equals 632.8nm) after about twelve iterations and less than λ/100 after as few as four iterations. The presented approach to handling irregular pupil shapes applies equally well to wavefront estimation from curvature data. A defining characteristic for a wavefront estimation algorithm is its error propagation behavior. The error propagation coefficient can be formulated as a function of the eigenvalues of the wavefront estimation-related matrices, and such functions are established for each of the basic estimation geometries (i.e. Fried, Hudgin and Southwell) with a serial numbering scheme, where a square sampling grid array is sequentially indexed row by row. The results show that with the wavefront piston-value fixed, the odd-number grid sizes yield lower error propagation than the even-number grid sizes for all geometries. The Fried geometry either allows sub-sized wavefront estimations within the testing domain or yields a two-rank deficient estimation matrix over the full aperture; but the latter usually suffers from high error propagation and the waffle mode problem. Hudgin geometry offers an error propagator between those of the Southwell and the Fried geometries. For both wavefront gradient-based and wavefront difference-based estimations, the Southwell geometry is shown to offer the lowest error propagation with the minimum-norm least-squares solution. Noll's theoretical result, which was extensively used as a reference in the previous literature for error propagation estimate, corresponds to the Southwell geometry with an odd-number grid size. For curvature-based wavefront sensing, a concept for a differential Shack-Hartmann (DSH) curvature sensor is proposed. This curvature sensor is derived from the basic Shack-Hartmann sensor with the collimated beam split into three output channels, along each of which a lenslet array is located. Three Hartmann grid arrays are generated by three lenslet arrays. Two of the lenslets shear in two perpendicular directions relative to the third one. By quantitatively comparing the Shack-Hartmann grid coordinates of the three channels, the differentials of the wavefront slope at each Shack-Hartmann grid point can be obtained, so the Laplacian curvatures and twist terms will be available. The acquisition of the twist terms using a Hartmann-based sensor allows us to uniquely determine the principal curvatures and directions more accurately than prior methods. Measurement of local curvatures as opposed to slopes is unique because curvature is intrinsic to the wavefront under test, and it is an absolute as opposed to a relative measurement. A zonal least-squares-based wavefront estimation algorithm was developed to estimate the wavefront shape from the Laplacian curvature data, and validated. An implementation of the DSH curvature sensor is proposed and an experimental system for this implementation was initiated. The DSH curvature sensor shares the important features of both the Shack-Hartmann slope sensor and Roddier's curvature sensor. It is a two-dimensional parallel curvature sensor. Because it is a curvature sensor, it provides absolute measurements which are thus insensitive to vibrations, tip/tilts, and whole body movements. Because it is a two-dimensional sensor, it does not suffer from other sources of errors, such as scanning noise. Combined with sufficient sampling and a zonal wavefront estimation algorithm, both low and mid frequencies of the wavefront may be recovered. Notice that the DSH curvature sensor operates at the pupil of the system under test, therefore the difficulty associated with operation close to the caustic zone is avoided. Finally, the DSH-curvature-sensor-based wavefront estimation does not suffer from the 2-ambiguity problem, so potentially both small and large aberrations may be measured.
Ph.D.
Optics and Photonics
Optics and Photonics
Optics PhD

Plenoptic cameras and Shack-Hartmann wavefront sensors are lenslet-based optical systems that do not form a conventional image. The addition of a lens array into these systems allows for the aberrations generated by the combination of the object and the optical components located prior to the lens array to be measured or corrected with post-processing. This dissertation provides a ray selection method to determine the rays that pass through each lenslet in a lenslet-based system. This first-order, ray trace method is developed for any lenslet-based system with a well-defined fore optic, where in this dissertation the fore optic is all of the optical components located prior to the lens array. For example, in a plenoptic camera the fore optic is a standard camera lens. Because a lens array at any location after the exit pupil of the fore optic is considered in this analysis, it is applicable to both plenoptic cameras and Shack-Hartmann wavefront sensors. Only a generic, unaberrated fore optic is considered, but this dissertation establishes a framework for considering the effect of an aberrated fore optic in lenslet-based systems. The rays from the fore optic that pass through a lenslet placed at any location after the fore optic are determined. This collection of rays is reduced to three rays that describe the entire lenslet ray set. The lenslet ray set is determined at the object, image, and pupil planes of the fore optic. The consideration of the apertures that define the lenslet ray set for an on-axis lenslet leads to three classes of lenslet-based systems. Vignetting of the lenslet rays is considered for off-axis lenslets. Finally, the lenslet ray set is normalized into terms similar to the field and aperture vector used to describe the aberrated wavefront of the fore optic. The analysis in this dissertation is complementary to other first-order models that have been developed for a specific plenoptic camera layout or Shack-Hartmann wavefront sensor application. This general analysis determines the location where the rays of each lenslet pass through the fore optic establishing a framework to consider the effect of an aberrated fore optic in a future analysis.

Die vorliegende Arbeit beschäftigt sich mit dem Konzept der radial nicht-oszillierenden, zeitlich stabilen ultrakurzen Bessel ähnlichen Strahlen oder "Nadelstrahlen" ("needle beams"), die zu einer Klasse von optischen hochlokalisierten Wellenpaketen generalisiert werden. Hierbei wird die Theorie über das räumlich-zeitlichen Ausbreitungsverhaltens von nicht auseinanderdriftenden Nadelstrahlen mit Pulsdauern von kleiner als 10 fs näher diskutiert. Dies wird durch eine systematische Darstellung der Methoden zur Generierung und Detektierung von lokalisierten Wellen komplettiert, die ein optischen Drehmoment tragen. Für die Erzeugung von HLWs kommen räumliche Lichtmodulatoren zum Einsatz, die ein flexibles Zuschneiden von Wellenpaketen mit der Dauer weniger Zyklen des EM-Feldes erlauben. Es wird gezeigt, dass solche optischen Pulse sich über beträchtliche Entfernungen ausbreiten, ohne dass sich dabei signifikant der Strahldurchmesser vergrößert oder der Puls zeitlich verbreitert. In variabler Weise werden verschiedene geometrische (z.B. ringförmige) Lichtverteilungen erzeugt. Anwendungspotential findet sich insbesondere in den Techniken der räumlichen Pulsformung und Diagnostik. Als besonders wichtiger Ansatz ist der Zeit-Wellenfront-Sensor zu erwähnen, welcher die nichtlineare, mehrkanalige Autokorrelation, die Wellenfrontdetektion mittels nichtdiffraktiver Teilstrahlen nach dem Shack-Hartmann-Prinzip und eine adaptive Funktionalität miteinander vorteilhaft verbindet. Das enorme Potential solcher Ansätze wird durch die hohe Genauigkeit orts-, winkel- und zeitabhängiger Rekonstruktionen der Wellenpakete nachgewiesen. Darüber hinaus ermöglicht das räumliche Kodieren und anschließende Verfolgen der Teilstrahlen eine wesentliche Verbesserung der Identifikation relevanter Parameter von Verteilungsfunktionen. Schließlich werden erste Schritte zur experimentellen Generation von optischen "light bullets" mit ganzzahligen und fraktalen orbitalen Drehmomenten präsentiert.
This thesis deals with the concept of radially non-oscillating, temporally stable ultrashort-pulsed Bessel-like beams or "needle pulses", which are an example of a highly localized wave packet (HLW). HLWs are the closest approximation of linear-optical light bullets and provide specific benefits compared to conventional Gaussian-like light bullets. The spatio-temporally nonspreading propagation behavior of few-cycle needle beams of less than 10 fs duration will be theoretically discussed in detail. An overview of the generation and detection of localized waves carrying an orbital angular momentum is also given. High fidelity spatial light modulators are used for the generation of HLWs. The flexible tailoring of few-cycle wave packets at near-infrared wavelengths is reported. It is shown that such pulses propagate over a huge depth of focus, neither significantly changing their spot size or nor the pulse duration. Variable geometrical distributions like circular disks, rings, or bars of light are shaped and exploited as building blocks for structures of higher complexity. Another section of the thesis emphasizes the numerous potential applications of related techniques for an optimized two-dimensional spatial pulse shaping and diagnostics (reduce ambiguities) based on localized waves. As a particularly important example, time-wavefront sensing is used to combine nonlinear multichannel autocorrelation with Shack-Hartmann wavefront sensing by means of localized sub-beams and adaptive functionality. The capabilities of such devices are illustrated by the results of angular and temporal mapping of few-cycle wave packets. Moreover, spatial encoding and subsequent tracking of individual sub-beams, even at incident angles of up to 50°, enables to significantly improve the spot recognition. Finally, first steps towards the generation of optical light bullets carrying integer or non-integer orbital angular momenta are presented.

Within the visual system, the optics of the eye is responsible for forming images of external objects on the ocular fundus for its photo-reception and neural interpretation. However, the eye is not perfect and its capabilities may be limited by aberrations and scattering. Therefore, the quantification of optical factors affecting the eye is important for diagnosis and monitoring purposes. In this context, this document summarizes the work done during the implementation of the Multimodal Eye's Optical Quality (MEOQ) system, a measurement device that integrates a double-pass (DP) instrument and a Hartmann-Shack (HS) sensor to provide not only information on aberrations, but also on scattering that occurs in the human eye. A binocular open-view design permits evaluation in natural viewing conditions. Furthermore, the system is able to compensate for both spherical and astigmatic refractive errors by using devices of configurable optical power. The MEOQ system has been used to quantify scattering in the human eye based on differences between DP and HS estimations. Moreover, DP information has been employed to measure intraocular scattering using a novel method of quantification. Finally, the configurable properties of the spherical refractive error corrector have been used to explore a method for reducing speckle in systems that rely on reflections of light in the ocular fundus.
Dentro del sistema visual, la óptica del ojo es responsable de la formación de imágenes de objetos externos en el fondo de ojo para su fotorrecepción e interpretación neuronal. Sin embargo, el ojo no es perfecto y sus capacidades pueden verse limitadas por la presencia de aberraciones o de luz dispersa. De esta manera, la cuantificación de los factores ópticos que afectan al ojo resulta importante para fines de diagnóstico y de monitoreo. En este contexto, el presente documento resume el trabajo realizado durante la implementación del sistema Multimodal Eye’s Optical Quality (MEOQ), un dispositivo de medición que integra un instrumento de doble paso (DP) y un sensor de Hartmann-Shack (HS) para proporcionar no sólo información sobre aberraciones, sino también en la dispersión que se produce en el ojo humano. Un diseño binocular de campo abierto permite evaluaciones en condiciones visuales naturales. Además, el sistema es capaz de compensar tanto errores refractivos esféricos como astigmáticos mediante el uso de dispositivos de potencia óptica configurable. El sistema MEOQ se ha utilizado para cuantificar la dispersión en el ojo humano basándose en las diferencias entre estimaciones de DP y HS. Además, la información de DP se ha empleado para medir la dispersión intraocular utilizando un nuevo método de cuantificación. Por último, las propiedades configurables del corrector de refracción esférica se han utilizado para explorar un método para la reducción de ruido speckle en sistemas basados en reflexiones de luz en el fondo ocular.
Innerhalb des visuellen Systems ist die Optik des Auges verantwortlich für die Abbildung externer Objekte auf dem Fundus des Auges, damit Licht umgewandelt und neural interpretiert wird. Dennoch ist das Auge nicht perfekt und seine Möglichkeiten sind durch Abbildungsfehler und Streuung begrenzt. Daraus ergibt sich, dass die Quantifizierung der optischen Faktoren, welche das Auge betreffen, wichtig für die Diagnose und Überwachung sind. Innerhalb dieses Rahmens fasst dieses Dokument die Arbeit zusammen, welche die Implementierung eines System zur multimodalen Bestimmung der optischen Qualität des Auges (MEOQ), bestehend aus einem Doppelpass-Instument (DP) und einem Hartmann-Shack-Sensor (HS), beschreibt, um nicht nur Informationen über Abbildungsfehler, sondern auch über Streuung im menschlichen Auge zu erhalten. Ein biokulares Freisicht-Design ermöglicht natürliche Sehverhältnisse. Darüberhinaus ist das System in der Lage sphärische und astigmatische Brechungsfehler mit einem Gerät einstellbarer optischer Leistung zu korrigieren. Das MEOQ System wurde genutzt um Streuung im menschlichen Auge mit Hilfe der Unterschiede der bschätzungen des DP und des HS zu quantifizieren. Darüberhinaus wurden die DP Informationen angewandt um intraokulare Streuung durch eine neue Methode der Quantifizierung zu messen. Schließlich wurden die konfigurierbaren Einstellungen des sphärischen Brechungsfehlerskorrektor genutzt um eine Methode zur Reduzierung von Speckle in Systemen, welche auf Reflektionen von Licht vom Fundus des Auges basieren, zu untersuchen.

Wavefront sensing is an old yet fundamental problem in adaptive optics. Traditional wavefront sensors are limited to time-consuming measurements, complicated and expensive setup, or low theoretically achievable resolution. In this thesis, we introduce an optically encoded and computationally decodable novel approach to the wavefront sensing problem: the Coded Shack-Hartmann. Our proposed Coded Shack-Hartmann wavefront sensor is inexpensive, easy to fabricate and calibrate, highly sensitive, accurate, and with high resolution. Most importantly, using simple optical flow tracking combined with phase smoothness prior, with the help of modern optimization technique, the computational part is split, efficient, and parallelized, hence real time performance has been achieved on Graphics Processing Unit (GPU), with high accuracy as well. This is validated by experimental results. We also show how optical flow intensity consistency term can be derived, using rigor scalar diffraction theory with proper approximation. This is the true physical law behind our model. Based on this insight, Coded Shack-Hartmann can be interpreted as an illumination post-modulated wavefront sensor. This offers a new theoretical approach for wavefront sensor design.

碩士
國立中央大學
光電科學與工程學系
102
Shack-Hartmann（SH）wavefront sensor is a powerful and robust tool in wavefront sensing and has a good performance even compare with phase- shifting interferometer or shearing interferometer. It also can do absolute measurement in very high accuracy and has applied to many other fields like position sensing and ocular optics. However, in a common configuration of a SH wavefront sensor, there is always a relay optics placed before the sensor to relay the test beam. The relay optics is not perfect, thus additional aberrations and measurement uncertainties will be introduced into the system. 　　To reduce the system uncertainties and additional aberrations, a system without relay optics is constructed. A convergent beam, instead of a collimated beam, is incident into the wavefront sensor. Without using the relay optics, the system aberrations and uncertainties could be reduced. 　　However, since the lens arrays are not perfect, off-axis aberrations occurs when a convergent beam is incident on it. These aberrations incur shifts in the focal spot positions. Therefore, calibration on the lens array at different angle of incidence is needed. Besides, the shifts will larger than lens array’s lens pitch, which means that the shift spot will out of its relative lens region and this cannot be satisfied with the conventional algorithm. Thus, a proper spot assignment algorithm should be adopted. Furthermore, since the system becomes simpler and clearer, it is possible to remove the alignment error through analytical methods. Through remove the alignment error, the requirement for alignment could be looser. 　　In this thesis, we demonstrate a SH wavefront sensor that is free of relay optics and investigate the feasibility of remove the alignment error. Measured the lenses with different f-number then compare the results with Fizeau interferometer and analyze the system’s performance.

碩士
國立臺灣大學
機械工程學研究所
104
After STM was invented, phenomenon in nanometer dimension could be observed. In this thesis, we present a multiaxial actuation measurement system by using Shack-Hartmann wavefront sensor (SHWS). According to our preliminary analysis and experiment, it is found that the tilting and actuating motions of actuator have influences on Zernike tilting and defocusing modals. For developing the system, the optical engineering software is applied to prove its operational feasibility and to optimize its performance. Appropriate wavefront type is chosen to optimize the measurement ability. Wavefront without any optical path difference couldn’t be applied on linear displacement measurement. On the other hand, wavefront without defocus optical path difference with different diameter should trade off to apply on angular measurement. The system performance is also experimentally verified by using autocollimator and laser rangerfinger. Our multiaxial measurement system will be devoted to studying the cross coupling behavior of multiaxial actuation.

碩士
國立成功大學
工程科學系碩博士班
100
An adaptive optics system (AOS) consists of three main components: wavefront sensor, wavefront corrector, and reconstruction controller. This thesis has developed a Shack-Hartmann wavefront sensor (SHWS) that can achieve 30 Hz frame rate via a video decoder circuit. Moreover, a 32-channel deformable mirror (DM) is used to compensate the phase distortion from external disturbances. A field programmable gate array (FPGA)-based Shack-Hartmann wavefront sensor has been setup for AOS, and it can compensate the optical aberration from surrounding environment in real time. The overall system of the wavefront sensor is composed of a lab-made SHWS, a video decoder circuit, and a FPGA-based control model. A FPGA-based control model not a CPU base, the AOS can achieve a real-time compensation. Due to the multitasking operation system of a CPU-based PC Window system, the timer of the control loop will be unstable at a speed higher than 10 Hz. The lab-made wavefront sensing system depends on the hardware clock of the FPGA, so it can maintain a fixed speed easily. The frontend of the wavefront sensing system is based the Shack-Hartmann configuration. The wavefront information is obtained by positioning the focal spots on a charge coupled device camera, and then uses a Zernike model to remodel the wavefront information. The system between the DM and the SHWS is identified by a multichannel-input-multichannel-output (MIMO) state-space system identification algorithm, and then the controller is designed by a linear-quadratic-integral (LQI) controller via the identified system model. Currently, the lab-made AOS can reduce the aberrations caused by external disturbances at control loop of 30 Hz and the Strehl ratio of focusing spot is increased up to 1.75 times.

碩士
國立中央大學
光電科學與工程學系
102
This thesis provide a new method improving the classical Shak-Hartmann wavefront sensor system(SHWS). Compare with the classical SHWS system, there are two advantages in this new measurement system : 1. Avoiding the wavefront aberration error by removing the collimator lens and the optical elements of the image system in the SHWS. 2. Increasing the measurement efficiency during we replace tested lens with different numerical aperture .

碩士
元智大學
電機工程學系
95
The error simulation and experiment analysis of Hartmann Shack wavefront sensor Student：Ting Ju Chen Advisor：Dr. Chung Ping Liu Institute of Electrical Engineering Yuan Ze University ABSTRACT Hartmann Shack wavefront sensor is used in astronomy to measure the aberrations and correct them to get the clear image. Recently, it is widely used in ophthalmology field, like the LASIK surgery. The precision must be kept to eliminate the surgery error. In this article, there are two parts to estimate the reconstructed error of Hartmann Shack wavefront sensor. In the first part, the optical simulation is used to produce the spot distribution, then reconstruct the incident wavefront by suitable algorithm. The tolerance analysis is also done to analyze the tolerance of optical component in experiment setup. In the second part, the test lens and reflective mirror are used to simulate the human eye in the experiment setup. Light is reflected from the mirror, passed through the test lens and micro-lens array, and finally focused on CCD. The comparison of ZYGO interferometer measurement result and HS reconstruction result is shown in the article. The RMS error is 0.02λ.

碩士
國立臺灣大學
光電工程學研究所
99
In adaptive optics, microlens array (MLA) is used to detect and divide the incidence wavefront into small parts which will be focused on the image sensor (CMOS) of Shack-Hartmann wavefront sensor (SHWS). In this paper, we present the fabrication method of long focal length (millimeter range) MLA with various structure and arrangement based on thermal reflow process. In order to extend the focal length, we used Polydimethysiloxane (PDMS) cover on our glass substrate of MLA. Because of the small refractive index difference between PDMS and MLA interface (UV-resin), the incidence light is less bended and focused in further distance. Besides, other specific focal lengths could be realized by modifying the refractive index difference. After the long-focal-length MLA film was fabricated, it could be integrated with an image sensor to build a SHWS. A longer focal length MLA will provide high sensitivity in determining the average slope across each lenslet under a given wavefront, and the spatial resolution of the wavefront sensor is increased by the number of lenslets across the detector. Thus, the accuracy improves with greater sensitivity and spatial resolution. The experimental result of the system is discussed and compared between the long focal length, the shorter focal length and the commercial SHWS.

碩士
國立成功大學
工程科學系
106
In this thesis, a field programmable gate array (FPGA)-based Shack-Hartmann wavefront sensor (SHWS) programmed on LabVIEW can be highly integrated into customized applications such as adaptive optics system (AOS) for performing real-time wavefront measurement. A Camera Link frame grabber embedded with FPGA is adopted to enhance the sensor speed reacting to variation considering its advantage of the highest data transmission bandwidth. Instead of waiting for a frame image to be captured by the FPGA, the Shack-Hartmann algorithm are implemented in parallel algorithm and let the image data transmission synchronize with the wavefront reconstruction. On the other hand, we design a mechanism to control the deformable mirror in the same FPGA and verify the Shack-Hartmann sensor speed by controlling the frequency of the deformable mirror dynamic surface deformation. This FPGA-bead SHWS design can achieve a 266 Hz cyclic speed limited by the camera frame rate. For the further use of AOS, the system identification with the control loop of 100 Hz can be implemented. The fitting result in 1-input/2-output is 84 % and in 32-input/8-output is around 70 ~ 80 %.

碩士
國立交通大學
影像與生醫光電研究所
107
In many Laser applications, the Laser processing is not uniform due to the non-uniform distribution of intensity. Therefore, beam shaping technology is needed to convert the original non-uniform distribution of intensity to a uniform flat-top distribution beam. In this thesis, the spatial light modulator is used and designing the hologram by applying Iterative Fourier Transform Algorithm and displaying the hologram on spatial light modulator. The laser intensity distribution is converted from Gaussian distribution to flat-top distribution by diffraction. However, in actual experiments, the flat top intensity distribution is non-uniform owing to the errors in optical set up or extra disturbances. Respectively, intensity based feedback and phase based feedback are used to correct the aberration in optical set up here. Intensity based feedback is done by using Iterative Fourier Transform Algorithm for aberration correction; however, the effect of this method is limited. Compared with Intensity based feedback method, phase based feedback method can be a better way to correct the aberration. By using lab-made Shack-Hartmann wavefront sensor to detect the wavefront information, it can compare the phase change with the wavefront on the spatial light modulator and correct the aberration by phase conjugation method. In the experiment of intensity based feedback, the root mean square error improves from 40.8% to 33%. Besides, in the experiment of phase based feedback, the aberration correction improves from 2.63π to 0.61π. Owing to the limit of Shack-Hartmann wavefront sensor’s spatial resolution, it is necessary to improve the hardware design in order to integrate with beam shaping system.

碩士
國立中央大學
光電科學與工程學系
101
Assignment of spots to the correct lenslet is critically important to a Shack Hartmann wavefront sensor. Conventional assignment-algorithm limits the amount of spots shift to be half the lenslet diameter, thereby limiting the dynamic range of the sensor. This work presents a quality-guided algorithm to extend the dynamic range of a Shack-Hartmann wavefront sensor. The proposed algorithm offers a high dynamic range and excellent robustness. The algorithm is tested on both simulated Shack-Hartmann spots and experimentally captured Shack-Hartmann spots.. The performance of the proposed algorithm is compared with existing algorithms. Results from simulation and from real-case data are analyzed. Any discrepancies are discussed.

Nonlinear microscopy, with its unique advantages over conventional confocal fluorescence microscopy, has been widely adopted to study biological processes at the cellular level. However, like all other high-resolution optical imaging techniques, nonlinear microscopy suffers from focal degradation due to optical aberrations in the sample as a result of refractive index mismatch. Optical aberrations distort the wavefront of the excitation beam, causing the focal spot to be larger than the diffraction limit. Since the fluorescence efficiency scales nonlinearly with the profile of the focusing excitation beam, aberrations further degrade the image brightness in addition to resolution. In this dissertation I describe the design, characterization and experimentation of an adaptive optics (AO) nonlinear laser scanning microscope implemented with open-loop control and an EMCCD-based Shack-Hartmann wavefront sensor (EMCCD SHWFS) for aberration compensation. Adaptive optics (AO), originally designed for ground-based astronomical observatories to correct for the aberrations from atmospheric turbulence while imaging distant stars and planets, has benefited many biomedical imaging platforms. We integrated a microelectromechanical system (MEMS) deformable mirror (DM) into our nonlinear laser scanning microscope. With an accurate open-loop control mechanism, which predicts the control voltages and generates a prescribed surface shape on the MEMS DM, known aberrations in the system can be compensated for with this computationally simple and inherently fast method. The use of a nonlinear guide star imbedded within the sample can reflect the sample aberration. However, the low level of nonlinear fluorescence signal is usually detected by photomultiplier tubes (PMT) and is below the sensitivity of a conventional charge-coupled device (CCD) based Shack-Hartmann wavefront sensor. This dissertation also describes the design of an EMCCD SHWFS to measure the wavefront distortion from the nonlinear guide star and aberration compensation from the skull bone marrow of a live mouse is demonstrated using the described system.

碩士
國立交通大學
光電系統研究所
107
In laser micromachining applications, the quality of the microstructural dependents on intensity and phase stability of the laser source. Recently, the Shack-Hartmann wavefront sensor (SHWS) has been widely used as the wavefront measuring technique. The laser beam incident to a microlens array (MLA) and is focused individually. By analyzing the shift of each focused points, SHWS can derive wavefront information of the incident laser beam. In this thesis, an MLA is directly fabricated on the protection window of a board-level camera via multiphoton polymerization (MPP) mechanism in the ultrafast laser system. With the combination of embedded platform and Wi-Fi transmission, miniaturized SHWS is achieved and can be used for laser source monitoring. The excitation source for MPP is an ultrafast laser of 780nm center wavelength. The objective lens is 20x, air-type, and with a numerical aperture of 0.75. By curing the optical adhesive, Norland Optical Adhesive 81 (NOA81), with the above system, the fabrication of MLA is realized. In femtosecond lasers, there is sufficient photon energy density in the focal volume. Therefore, energy transfer into monomers and produce free radicals. Through the connection of covalent bond, NOA81 is transferred into a transparent 3D solid structure inside a specific micrometer region. The miniature SHWS is equipped with a 5-megapixel (2592 × 1944) camera module. The design of MLA is based on Fresnel lenses rather than conventional plano-convex lenses. Thus, nearly 90% of fabrication time can be saved. Each sub-lens of the MLA is 61 μm in diameter and 5.98 μm in height. Currently, the miniature SHWS has a dynamic range of ± 14.29 π, a resolution of ±0.06 π, and a sensing range of 0.5 × 0.5 mm2. According to the lab-developed algorithm, the focal spots size is about 9.852 μm, which can achieve the requirement of the wavefront reconstruction algorithm and can be used in wavefront measurement.