Aspheric surface testing with a liquid compensatory interferometer

A simple method of testing deep aspheric surfaces is presented. The apparatus consists of a Twyman-Green interferometer and a liquid compensatory container. Two lenses, one with spherical surfaces and the other with a spherical surface and an aspheric surface, were tested by using this method. The device is very simple and easy to assemble. (C) 1998 Society of Photo-Optical Instrumentation Engineers.

Overview of the SMS design method applied to imaging optics

The Simultaneous Multiple Surfaces (SMS) was developed as a design method in Nonimaging Optics during the 90s. Later, the method was extended for designing Imaging Optics. We present an overview of the method applied to imaging optics in planar (2D) geometry and compare the results with more classical designs based on achieving aplanatism of different orders. These classical designs are also viewed as particular cases of SMS designs. Systems with up to 4 aspheric surfaces are shown. The SMS design strategy is shown to perform always better than the classical design (in terms of image quality). Moreover, the SMS method is a direct method, i.e., it is not based in multi-parametric optimization techniques. This gives the SMS method an additional interest since it can be used for exploring solutions where the multiparameter techniques can get lost because of the multiple local minima

Design and development of compact optical systems = Diseño y desarrollo de sistemas ópticos compactos

Esta tesis considera dos tipos de aplicaciones del diseño óptico: óptica formadora de imagen por un lado, y óptica anidólica (nonimaging) o no formadora de imagen, por otro. Las ópticas formadoras de imagen tienen como objetivo la obtención de imágenes de puntos del objeto en el plano de la imagen. Por su parte, la óptica anidólica, surgida del desarrollo de aplicaciones de concentración e iluminación, se centra en la transferencia de energía en forma de luz de forma eficiente. En general, son preferibles los diseños ópticos que den como resultado sistemas compactos, para ambos tipos de ópticas (formadora de imagen y anidólica). En el caso de los sistemas anidólicos, una óptica compacta permite tener costes de producción reducidos. Hay dos razones: (1) una óptica compacta presenta volúmenes reducidos, lo que significa que se necesita menos material para la producción en masa; (2) una óptica compacta es pequeña y ligera, lo que ahorra costes en el transporte. Para los sistemas ópticos de formación de imagen, además de las ventajas anteriores, una óptica compacta aumenta la portabilidad de los dispositivos, que es una gran ventaja en tecnologías de visualización portátiles, tales como cascos de realidad virtual (HMD del inglés Head Mounted Display). Esta tesis se centra por tanto en nuevos enfoques de diseño de sistemas ópticos compactos para aplicaciones tanto de formación de imagen, como anidólicas. Los colimadores son uno de los diseños clásicos dentro la óptica anidólica, y se pueden utilizar en aplicaciones fotovoltaicas y de iluminación. Hay varios enfoques a la hora de diseñar estos colimadores. Los diseños convencionales tienen una relación de aspecto mayor que 0.5. Con el fin de reducir la altura del colimador manteniendo el área de iluminación, esta tesis presenta un diseño de un colimador multicanal. En óptica formadora de imagen, las superficies asféricas y las superficies sin simetría de revolución (o freeform) son de gran utilidad de cara al control de las aberraciones de la imagen y para reducir el número y tamaño de los elementos ópticos. Debido al rápido desarrollo de sistemas de computación digital, los trazados de rayos se pueden realizar de forma rápida y sencilla para evaluar el rendimiento del sistema óptico analizado. Esto ha llevado a los diseños ópticos modernos a ser generados mediante el uso de diferentes técnicas de optimización multi-paramétricas. Estas técnicas requieren un buen diseño inicial como punto de partida para el diseño final, que será obtenido tras un proceso de optimización. Este proceso precisa un método de diseño directo para superficies asféricas y freeform que den como resultado un diseño cercano al óptimo. Un método de diseño basado en ecuaciones diferenciales se presenta en esta tesis para obtener un diseño óptico formado por una superficie freeform y dos superficies asféricas. Esta tesis consta de cinco capítulos. En Capítulo 1, se presentan los conceptos básicos de la óptica formadora de imagen y de la óptica anidólica, y se introducen las técnicas clásicas del diseño de las mismas. El Capítulo 2 describe el diseño de un colimador ultra-compacto. La relación de aspecto ultra-baja de este colimador se logra mediante el uso de una estructura multicanal. Se presentará su procedimiento de diseño, así como un prototipo fabricado y la caracterización del mismo. El Capítulo 3 describe los conceptos principales de la optimización de los sistemas ópticos: función de mérito y método de mínimos cuadrados amortiguados. La importancia de un buen punto de partida se demuestra mediante la presentación de un mismo ejemplo visto a través de diferentes enfoques de diseño. El método de las ecuaciones diferenciales se presenta como una herramienta ideal para obtener un buen punto de partida para la solución final. Además, diferentes técnicas de interpolación y representación de superficies asféricas y freeform se presentan para el procedimiento de optimización. El Capítulo 4 describe la aplicación del método de las ecuaciones diferenciales para un diseño de un sistema óptico de una sola superficie freeform. Algunos conceptos básicos de geometría diferencial son presentados para una mejor comprensión de la derivación de las ecuaciones diferenciales parciales. También se presenta un procedimiento de solución numérica. La condición inicial está elegida como un grado de libertad adicional para controlar la superficie donde se forma la imagen. Basado en este enfoque, un diseño anastigmático se puede obtener fácilmente y se utiliza como punto de partida para un ejemplo de diseño de un HMD con una única superficie reflectante. Después de la optimización, dicho diseño muestra mejor rendimiento. El Capítulo 5 describe el método de las ecuaciones diferenciales ampliado para diseños de dos superficies asféricas. Para diseños ópticos de una superficie, ni la superficie de imagen ni la correspondencia entre puntos del objeto y la imagen pueden ser prescritas. Con esta superficie adicional, la superficie de la imagen se puede prescribir. Esto conduce a un conjunto de tres ecuaciones diferenciales ordinarias implícitas. La solución numérica se puede obtener a través de cualquier software de cálculo numérico. Dicho procedimiento también se explica en este capítulo. Este método de diseño da como resultado una lente anastigmática, que se comparará con una lente aplanática. El diseño anastigmático converge mucho más rápido en la optimización y la solución final muestra un mejor rendimiento. ABSTRACT We will consider optical design from two points of view: imaging optics and nonimaging optics. Imaging optics focuses on the imaging of the points of the object. Nonimaging optics arose from the development of concentrators and illuminators, focuses on the transfer of light energy, and has wide applications in illumination and concentration photovoltaics. In general, compact optical systems are necessary for both imaging and nonimaging designs. For nonimaging optical systems, compact optics use to be important for reducing cost. The reasons are twofold: (1) compact optics is small in volume, which means less material is needed for mass-production; (2) compact optics is small in size and light in weight, which saves cost in transportation. For imaging optical systems, in addition to the above advantages, compact optics increases portability of devices as well, which contributes a lot to wearable display technologies such as Head Mounted Displays (HMD). This thesis presents novel design approaches of compact optical systems for both imaging and nonimaging applications. Collimator is a typical application of nonimaging optics in illumination, and can be used in concentration photovoltaics as well due to the reciprocity of light. There are several approaches for collimator designs. In general, all of these approaches have an aperture diameter to collimator height not greater than 2. In order to reduce the height of the collimator while maintaining the illumination area, a multichannel design is presented in this thesis. In imaging optics, aspheric and freeform surfaces are useful in controlling image aberrations and reducing the number and size of optical elements. Due to the rapid development of digital computing systems, ray tracing can be easily performed to evaluate the performance of optical system. This has led to the modern optical designs created by using different multi-parametric optimization techniques. These techniques require a good initial design to be a starting point so that the final design after optimization procedure can reach the optimum solution. This requires a direct design method for aspheric and freeform surface close to the optimum. A differential equation based design method is presented in this thesis to obtain single freeform and double aspheric surfaces. The thesis comprises of five chapters. In Chapter 1, basic concepts of imaging and nonimaging optics are presented and typical design techniques are introduced. Readers can obtain an understanding for the following chapters. Chapter 2 describes the design of ultra-compact collimator. The ultra-low aspect ratio of this collimator is achieved by using a multichannel structure. Its design procedure is presented together with a prototype and its evaluation. The ultra-compactness of the device has been approved. Chapter 3 describes the main concepts of optimizing optical systems: merit function and Damped Least-Squares method. The importance of a good starting point is demonstrated by presenting an example through different design approaches. The differential equation method is introduced as an ideal tool to obtain a good starting point for the final solution. Additionally, different interpolation and representation techniques for aspheric and freeform surface are presented for optimization procedure. Chapter 4 describes the application of differential equation method in the design of single freeform surface optical system. Basic concepts of differential geometry are presented for understanding the derivation of partial differential equations. A numerical solution procedure is also presented. The initial condition is chosen as an additional freedom to control the image surface. Based on this approach, anastigmatic designs can be readily obtained and is used as starting point for a single reflective surface HMD design example. After optimization, the evaluation shows better MTF. Chapter 5 describes the differential equation method extended to double aspheric surface designs. For single optical surface designs, neither image surface nor the mapping from object to image can be prescribed. With one more surface added, the image surface can be prescribed. This leads to a set of three implicit ordinary differential equations. Numerical solution can be obtained by MATLAB and its procedure is also explained. An anastigmatic lens is derived from this design method and compared with an aplanatic lens. The anastigmatic design converges much faster in optimization and the final solution shows better performance.

An optical study of human ocular dimensions

Many workers have studied the ocular components which occur in eyes exhibiting differing amounts of central refractive error but few have ever considered the additional information that could be derived from a study of peripheral refraction. Before now, peripheral refraction has either been measured in real eyes or has otherwise been modelled in schematic eyes of varying levels of sophistication. Several differences occur between measured and modelled results which, if accounted for, could give rise to more information regarding the nature of the optical and retinal surfaces and their asymmetries. Measurements of ocular components and peripheral refraction, however, have never been made in the same sample of eyes. In this study, ocular component and peripheral refractive measurements were made in a sample of young near-emmetropic, myopic and hyperopic eyes. The data for each refractive group was averaged. A computer program was written to construct spherical surfaced schematic eyes from this data. More sophisticated eye models were developed making use of linear algebraic ray tracing program. This method allowed rays to be traced through toroidal aspheric surfaces which were translated or rotated with respect to each other. For simplicity, the gradient index optical nature of the crystalline lens was neglected. Various alterations were made in these eye models to reproduce the measured peripheral refractive patterns. Excellent agreement was found between the modelled and measured peripheral refractive values over the central 70o of the visual field. This implied that the additional biometric features incorporated in each eye model were representative of those which were present in the measured eyes. As some of these features are not otherwise obtainable using in vivo techniques, it is proposed that the variation of refraction in the periphery offers a very useful optical method for studying human ocular component dimensions.

Modelling ocular monochromatic aberrations using schematic eyes with homogeneous optical media

Previous research has indicated that schematic eyes incorporating aspheric surfaces but lacking gradient index are unable to model ocular spherical aberration and peripheral astigmatism simultaneously. This limits their use as wide-angle schematic eyes. This thesis challenges this assumption by investigating the flexibility of schematic eyes comprising aspheric optical surfaces and homogeneous optical media. The full variation of ocular component dimensions found in human eyes was established from the literature. Schematic eye parameter variants were limited to these dimensions. The levels of spherical aberration and peripheral astigmatism modelled by these schematic eyes were compared to the range of measured levels. These were also established from the literature. To simplify comparison of modelled and measured data, single value parameters were introduced; the spherical aberration function (SAF), and peripheral astigmatism function (PAF). Some ocular components variations produced a wide range of aberrations without exceeding the limits of human ocular components. The effect of ocular component variations on coma was also investigated, but no comparison could be made as no empirical data exists. It was demonstrated that by combined manipulation of a number of parameters in the schematic eyes it was possible to model all levels of ocular spherical aberration and peripheral astigmatism. However, the unique parameters of a human eye could not be obtained in this way, as a number of models could be used to produce the same spherical aberration and peripheral astigmatism, while giving very different coma levels. It was concluded that these schematic eyes are flexible enough to model the monochromatic aberrations tested, the absence of gradient index being compensated for by altering the asphericity of one or more surfaces.

Evaluation of videokeratoscopy

The present thesis evaluates various aspects of videokeratoscopes, which are now becoming increasingly popular in the investigation of corneal topography. The accuracy and repeatability of these instruments has been assessed mainly using spherical surfaces, however, few studies have assessed the performance of videokeratoscopes in measuring convex aspheric surfaces. Using two videokeratoscopes, the accuracy and repeatability of measurements using twelve aspheric surfaces is determined. Overall, the accuracy and repeatability of both instruments were acceptable, however, progressively flatter surfaces introduced greater errors in measurement. The possible reasons for these errors are discussed. The corneal surface is a biological structure lubricated by the precorneal tear film. The effects of variations in the tear film on the repeatability of videokeratoscopes have not been determined in terms of peripheral corneal measurements. The repeatability of two commercially available videokeratoscopes is assessed. The repeatability is found to be dependent on the point of measurement on the corneal surface. Typically, superior and nasal meridians exhibit poorest repeatability. It is suggested that interference of the ocular adnexa is responsible for the reduced repeatability. This localised reduction in repeatability will occur for all videokeratoscopes. Further, comparison with the keratometers and videokeratoscopes used show that measurements between these instruments are not interchangeable. The final stage of this thesis evaluates the performance of new algorithms. The characteristics of a new videokeratoscope are described. This videokeratoscope is used to test the accuracy of the new algorithms for twelve aspheric surfaces. The new algorithms are accurate in determining the shape of aspheric surfaces, more so than those algorithms proposed at present.

3D-form metrology of arbitrary optical surfaces by absorption in fluids

We present an imaging technique for the 3D-form metrology of optical surfaces. It is based on the optical absorption in fluids situated between the surface and a reference. An improved setup with a bi-chromatic light source is fundamental to obtain reliable topographic maps. It is able to measure any surface finish (rough or polished), form and slope and independently of scale. We present results focused on flat and spherical optical surfaces, arrays of lenses and with different surface finish (rough-polished). We achieve form accuracies from several nanometers to sub-lambda for sag departures from tens to hundred of microns. Therefore, it seems suitable for the quality control in the production of precision aspheric, freeform lenses and other complex shapes on transparent substrates, independently of the surface finish.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.