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.

Deciduous tree reconstruction algorithm based on cylinder fitting from mobile terrestrial laser scanned point clouds

Vector reconstruction of objects from an unstructured point cloud obtained with a LiDAR-based system (light detection and ranging) is one of the most promising methods to build three dimensional models of orchards. The cylinder fitting method for woody structure reconstruction of leafless trees from point clouds obtained with a mobile terrestrial laser scanner (MTLS) has been analysed. The advantage of this method is that it performs reconstruction in a single step. The most time consuming part of the algorithm is generation of the cylinder direction, which must be recalculated at the inclusion of each point in the cylinder. The tree skeleton is obtained at the same time as the cluster of cylinders is formed. The method does not guarantee a unique convergence and the reconstruction parameter values must be carefully chosen. A balanced processing of clusters has also been defined which has proven to be very efficient in terms of processing time by following the hierarchy of branches, predecessors and successors. The algorithm was applied to simulated MTLS of virtual orchard models and to MTLS data of real orchards. The constraints applied in the method have been reviewed to ensure better convergence and simpler use of parameters. The results obtained show a correct reconstruction of the woody structure of the trees and the algorithm runs in linear logarithmic time

Optimization of Dengue immunoassay by label-free interferometric optical detection method

In this communication we report a direct immunoassay for detecting dengue virus by means of a label-free interferometric optical detection method. We also demonstrate how we can optimize this sensing response by adding a blocking step able to significantly enhance the optical sensing response. The blocking reagent used for this optimization is a dry milk diluted in phosphate buffered saline. The recognition curve of dengue virus over the proposed surface sensor demonstrates the capacity of this method to be applied in Point of Care technology.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.

Stabilisation of low softening point petroleum pitch fibres by HNO3

This paper deals with the stabilisation of low softening point pitch fibres obtained from petroleum pitches using HNO3 as oxidising agent. This method presents some advantages compared with conventional methods: pitches with low softening point (SP) can be used to prepare carbon fibres (CF), the stabilisation time has been reduced, the CF yields are similar to those obtained after general methods of stabilisation, and the initial treatments to increase SP when low SP pitches are used to prepare CF, are avoided. The parent pitches were characterised by different techniques such as diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), elemental analysis and solvent extraction with toluene and quinoline. The interaction between HNO3 and the pitch fibres, as well as the changes occurring during the heat treatment, have been followed by DRIFTS.

Stabilisation of low softening point petroleum pitch fibres by iodine treatment

A method using iodine has been developed for the stabilisation of low softening point (SP) pitch fibres that avoids air stabilisation in the production of carbon fibres (CF). The interaction between iodine and petroleum pitches has been studied by following the changes in the hydrogen content, aromatic or aliphatic, during the heat treatment of iodine-treated pitch fibres. Two low SP petroleum pitches were used and the iodine-treated pitch fibres were analysed by TGA, DSC, DRIFT, XPS and SEM. The results confirm that using this novel method pitches with low SP can be used to prepare CF with two advantages, compared with conventional methods. The stabilisation time is considerably reduced and treatments to increase the SP, usually required when low SP pitches are used to prepare CF, can be avoided.

New method for designing distillation columns of multicomponent mixtures

This paper presents a series of calculation procedures for computer design of ternary distillation columns overcoming the iterative equilibrium calculations necessary in these kind of problems and, thus, reducing the calculation time. The proposed procedures include interpolation and intersection methods to solve the equilibrium equations and the mass and energy balances. The calculation programs proposed also include the possibility of rigorous solution of mass and energy balances and equilibrium relations.

Optimizing the number of stations in arrays measurements: experimental outcomes for different array geometries and the f-k method

Array measurements have become a valuable tool for site response characterization in a non-invasive way. The array design, i.e. size, geometry and number of stations, has a great influence in the quality of the obtained results. From the previous parameters, the number of available stations uses to be the main limitation for the field experiments, because of the economical and logistical constraints that it involves. Sometimes, from the initially planned array layout, carefully designed before the fieldwork campaign, one or more stations do not work properly, modifying the prearranged geometry. Whereas other times, there is not possible to set up the desired array layout, because of the lack of stations. Therefore, for a planned array layout, the number of operative stations and their arrangement in the array become a crucial point in the acquisition stage and subsequently in the dispersion curve estimation. In this paper we carry out an experimental work to analyze which is the minimum number of stations that would provide reliable dispersion curves for three prearranged array configurations (triangular, circular with central station and polygonal geometries). For the optimization study, we analyze together the theoretical array responses and the experimental dispersion curves obtained through the f-k method. In the case of the f-k method, we compare the dispersion curves obtained for the original or prearranged arrays with the ones obtained for the modified arrays, i.e. the dispersion curves obtained when a certain number of stations n is removed, each time, from the original layout of X geophones. The comparison is evaluated by means of a misfit function, which helps us to determine how constrained are the studied geometries by stations removing and which station or combination of stations affect more to the array capability when they are not available. All this information might be crucial to improve future array designs, determining when it is possible to optimize the number of arranged stations without losing the reliability of the obtained results.

A new approach for semi-automatic rock mass joints recognition from 3D point clouds

Rock mass characterization requires a deep geometric understanding of the discontinuity sets affecting rock exposures. Recent advances in Light Detection and Ranging (LiDAR) instrumentation currently allow quick and accurate 3D data acquisition, yielding on the development of new methodologies for the automatic characterization of rock mass discontinuities. This paper presents a methodology for the identification and analysis of flat surfaces outcropping in a rocky slope using the 3D data obtained with LiDAR. This method identifies and defines the algebraic equations of the different planes of the rock slope surface by applying an analysis based on a neighbouring points coplanarity test, finding principal orientations by Kernel Density Estimation and identifying clusters by the Density-Based Scan Algorithm with Noise. Different sources of information —synthetic and 3D scanned data— were employed, performing a complete sensitivity analysis of the parameters in order to identify the optimal value of the variables of the proposed method. In addition, raw source files and obtained results are freely provided in order to allow to a more straightforward method comparison aiming to a more reproducible research.

Geometric 3D point cloud compression

The use of 3D data in mobile robotics applications provides valuable information about the robot’s environment but usually the huge amount of 3D information is unmanageable by the robot storage and computing capabilities. A data compression is necessary to store and manage this information but preserving as much information as possible. In this paper, we propose a 3D lossy compression system based on plane extraction which represent the points of each scene plane as a Delaunay triangulation and a set of points/area information. The compression system can be customized to achieve different data compression or accuracy ratios. It also supports a color segmentation stage to preserve original scene color information and provides a realistic scene reconstruction. The design of the method provides a fast scene reconstruction useful for further visualization or processing tasks.

FFT Interpolation From Nonuniform Samples Lying in a Regular Grid

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed “the missing samples problem” in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial and provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti’s The paper includes numerical assessments of the method’s stability and complexity.

Discontinuity spacing analysis in rock masses using 3D point clouds

The complete characterization of rock masses implies the acquisition of information of both, the materials which compose the rock mass and the discontinuities which divide the outcrop. Recent advances in the use of remote sensing techniques – such as Light Detection and Ranging (LiDAR) – allow the accurate and dense acquisition of 3D information that can be used for the characterization of discontinuities. This work presents a novel methodology which allows the calculation of the normal spacing of persistent and non-persistent discontinuity sets using 3D point cloud datasets considering the three dimensional relationships between clusters. This approach requires that the 3D dataset has been previously classified. This implies that discontinuity sets are previously extracted, every single point is labeled with its corresponding discontinuity set and every exposed planar surface is analytically calculated. Then, for each discontinuity set the method calculates the normal spacing between an exposed plane and its nearest one considering 3D space relationship. This link between planes is obtained calculating for every point its nearest point member of the same discontinuity set, which provides its nearest plane. This allows calculating the normal spacing for every plane. Finally, the normal spacing is calculated as the mean value of all the normal spacings for each discontinuity set. The methodology is validated through three cases of study using synthetic data and 3D laser scanning datasets. The first case illustrates the fundamentals and the performance of the proposed methodology. The second and the third cases of study correspond to two rock slopes for which datasets were acquired using a 3D laser scanner. The second case study has shown that results obtained from the traditional and the proposed approaches are reasonably similar. Nevertheless, a discrepancy between both approaches has been found when the exposed planes members of a discontinuity set were hard to identify and when the planes pairing was difficult to establish during the fieldwork campaign. The third case study also has evidenced that when the number of identified exposed planes is high, the calculated normal spacing using the proposed approach is minor than those using the traditional approach.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.