3D Wavelet-based Fusion Techniques for Biomedical Imaging

Hoy en día las técnicas de adquisición de imágenes tridimensionales son comunes en diversas áreas, pero cabe destacar la relevancia que han adquirido en el ámbito de la imagen biomédica, dentro del cual encontramos una amplia gama de técnicas como la microscopía confocal, microscopía de dos fotones, microscopía de fluorescencia mediante lámina de luz, resonancia magnética nuclear, tomografía por emisión de positrones, tomografía de coherencia óptica, ecografía 3D y un largo etcétera. Un denominador común de todas esas aplicaciones es la constante necesidad por aumentar la resolución y la calidad de las imágenes adquiridas. En algunas de dichas técnicas de imagen tridimensional se da una interesante situación: aunque que cada volumen adquirido no contiene información suficiente para representar el objeto bajo estudio dentro de los parámetros de calidad requeridos por algunas aplicaciones finales, el esquema de adquisición permite la obtención de varios volúmenes que representan diferentes vistas de dicho objeto, de tal forma que cada una de las vistas proporciona información complementaria acerca del mismo. En este tipo de situación es posible, mediante la combinación de varias de esas vistas, obtener una mejor comprensión del objeto que a partir de cada una de ellas por separado. En el contexto de esta Tesis Doctoral se ha propuesto, desarrollado y validado una nueva metodología de proceso de imágenes basada en la transformada wavelet disc¬reta para la combinación, o fusión, de varias vistas con información complementaria de un mismo objeto. El método de fusión propuesto aprovecha la capacidad de descom¬posición en escalas y orientaciones de la transformada wavelet discreta para integrar en un solo volumen toda la información distribuida entre el conjunto de vistas adquiridas. El trabajo se centra en dos modalidades diferentes de imagen biomédica que per¬miten obtener tales adquisiciones multi-vista. La primera es una variante de la micro¬scopía de fluorescencia, la microscopía de fluorescencia mediante lámina de luz, que se utiliza para el estudio del desarrollo temprano de embriones vivos en diferentes modelos animales, como el pez cebra o el erizo de mar. La segunda modalidad es la resonancia magnética nuclear con realce tardío, que constituye una valiosa herramienta para evaluar la viabilidad del tejido miocárdico en pacientes con diversas miocardiopatías. Como parte de este trabajo, el método propuesto ha sido aplicado y validado en am¬bas modalidades de imagen. En el caso de la aplicación a microscopía de fluorescencia, los resultados de la fusión muestran un mejor contraste y nivel de detalle en comparación con cualquiera de las vistas individuales y el método no requiere de conocimiento previo acerca la función de dispersión puntual del sistema de imagen. Además, los resultados se han comparado con otros métodos existentes. Con respecto a la aplicación a imagen de resonancia magnética con realce tardío, los volúmenes fusionados resultantes pre-sentan una mejora cuantitativa en la nitidez de las estructuras relevantes y permiten una interpretación más sencilla y completa de la compleja estructura tridimensional del tejido miocárdico en pacientes con cardiopatía isquémica. Para ambas aplicaciones los resultados de esta tesis se encuentran actualmente en uso en los centros clínicos y de investigación con los que el autor ha colaborado durante este trabajo. Además se ha puesto a libre disposición de la comunidad científica la implementación del método de fusión propuesto. Por último, se ha tramitado también una solicitud de patente internacional que cubre el método de visualización desarrollado para la aplicación de Resonancia Magnética Nuclear. Abstract Nowadays three dimensional imaging techniques are common in several fields, but es-pecially in biomedical imaging, where we can find a wide range of techniques including: Laser Scanning Confocal Microscopy, Laser Scanning Two Photon Microscopy, Light Sheet Fluorescence Microscopy, Magnetic Resonance Imaging, Positron Emission To-mography, Optical Coherence Tomography, 3D Ultrasound Imaging, etc. A common denominator of all those applications being the constant need for further increasing resolution and quality of the acquired images. Interestingly, in some of the mentioned three-dimensional imaging techniques a remarkable situation arises: while a single volume does not contain enough information to represent the object being imaged within the quality parameters required by the final application, the acquisition scheme allows recording several volumes which represent different views of a given object, with each of the views providing complementary information. In this kind of situation one can get a better understanding of the object by combining several views instead of looking at each of them separately. Within such context, in this PhD Thesis we propose, develop and test new image processing methodologies based on the discrete wavelet transform for the combination, or fusion, of several views containing complementary information of a given object. The proposed fusion method exploits the scale and orientation decomposition capabil¬ities of the discrete wavelet transform to integrate in a single volume all the available information distributed among the set of acquired views. The work focuses in two different biomedical imaging modalities which provide such multi-view datasets. The first one is a particular fluorescence microscopy technique, Light-Sheet Fluorescence Microscopy, used for imaging and gaining understanding of the early development of live embryos from different animal models (like zebrafish or sea urchin). The second is Delayed Enhancement Magnetic Resonance Imaging, which is a valuable tool for assessing the viability of myocardial tissue on patients suffering from different cardiomyopathies. As part of this work, the proposed method was implemented and then validated on both imaging modalities. For the fluorescence microscopy application, the fusion results show improved contrast and detail discrimination when compared to any of the individual views and the method does not rely on prior knowledge of the system’s point spread function (PSF). Moreover, the results have shown improved performance with respect to previous PSF independent methods. With respect to its application to Delayed Enhancement Magnetic Resonance Imaging, the resulting fused volumes show a quantitative sharpness improvement and enable an easier and more complete interpretation of complex three-dimensional scar and heterogeneous tissue information in ischemic cardiomyopathy patients. In both applications, the results of this thesis are currently in use in the clinical and research centers with which the author collaborated during his work. An imple¬mentation of the fusion method has also been made freely available to the scientific community. Finally, an international patent application has been filed covering the visualization method developed for the Magnetic Resonance Imaging application.

Research lines in Hyperthermia at the Bioinstrumentation Laboratory of the Centre for Biomedical Technology

The Bioinstrumentation Laboratory belongs to the Centre for Biomedical Technology (CTB) of the Technical University of Madrid and its main objective is to provide the scientific community with devices and techniques for the characterization of micro and nanostructures and consequently finding their best biomedical applications. Hyperthermia (greek word for “overheating”) is defined as the phenomenon that occurs when a body is exposed to an energy generating source that can produce a rise in temperature (42-45ºC) for a given time [1]. Specifically, the aim of the hyperthermia methods used in The Bioinstrumentation Laboratory is the development of thermal therapies, some of these using different kinds of nanoparticles, to kill cancer cells and reduce the damage on healthy tissues. The optical hyperthermia is based on noble metal nanoparticles and laser irradiation. This kind of nanoparticles has an immense potential associated to the development of therapies for cancer on account of their Surface Plasmon Resonance (SPR) enhanced light scattering and absorption. In a short period of time, the absorbed light is converted into localized heat, so we can take advantage of these characteristics to heat up tumor cells in order to obtain the cellular death [2]. In this case, the laboratory has an optical hyperthermia device based on a continuous wave laser used to kill glioblastoma cell lines (1321N1) in the presence of gold nanorods (Figure 1a). The wavelength of the laser light is 808 nm because the penetration of the light in the tissue is deeper in the Near Infrared Region. The first optical hyperthermia results show that the laser irradiation produces cellular death in the experimental samples of glioblastoma cell lines using gold nanorods but is not able to decrease the cellular viability of cancer cells in samples without the suitable nanorods (Figure 1b) [3]. The generation of magnetic hyperthermia is performed through changes of the magnetic induction in magnetic nanoparticles (MNPs) that are embedded in viscous medium. The Figure 2 shows a schematic design of the AC induction hyperthermia device in magnetic fluids. The equipment has been manufactured at The Bioinstrumentation Laboratory. The first block implies two steps: the signal selection with frequency manipulation option from 9 KHz to 2MHz, and a linear output up to 1500W. The second block is where magnetic field is generated ( 5mm, 10 turns). Finally, the third block is a software control where the user can establish initial parameters, and also shows the temperature response of MNPs due to the magnetic field applied [4-8]. The Bioinstrumentation Laboratory in collaboration with the Mexican company MRI-DT have recently implemented a new research line on Nuclear Magnetic Resonance Hyperthermia, which is sustained on the patent US 7,423,429B2 owned by this company. This investigation is based on the use of clinical MRI equipment not only for diagnosis but for therapy [9]. This idea consists of two main facts: Magnetic Resonance Imaging can cause focal heating [10], and the differentiation in resonant frequency between healthy and cancer cells [11]. To produce only heating in cancer cells when the whole body is irradiated, it is necessary to determine the specific resonant frequency of the target, using the information contained in the spectra of the area of interest. Then, special RF pulse sequence is applied to produce fast excitation and relaxation mechanism that generates temperature increase of the tumor, causing cellular death or metabolism malfunction that stops cellular division

Advances in the Simultaneous Multiple Surface optical design method for imaging and non-imaging applications

Classical imaging optics has been developed over centuries in many areas, such as its paraxial imaging theory and practical design methods like multi-parametric optimization techniques. Although these imaging optical design methods can provide elegant solutions to many traditional optical problems, there are more and more new design problems, like solar concentrator, illumination system, ultra-compact camera, etc., that require maximum energy transfer efficiency, or ultra-compact optical structure. These problems do not have simple solutions from classical imaging design methods, because not only paraxial rays, but also non-paraxial rays should be well considered in the design process. Non-imaging optics is a newly developed optical discipline, which does not aim to form images, but to maximize energy transfer efficiency. One important concept developed from non-imaging optics is the “edge-ray principle”, which states that the energy flow contained in a bundle of rays will be transferred to the target, if all its edge rays are transferred to the target. Based on that concept, many CPC solar concentrators have been developed with efficiency close to the thermodynamic limit. When more than one bundle of edge-rays needs to be considered in the design, one way to obtain solutions is to use SMS method. SMS stands for Simultaneous Multiple Surface, which means several optical surfaces are constructed simultaneously. The SMS method was developed as a design method in Non-imaging optics during the 90s. The method can be considered as an extension to the Cartesian Oval calculation. In the traditional Cartesian Oval calculation, one optical surface is built to transform an input wave-front to an out-put wave-front. The SMS method however, is dedicated to solve more than 1 wave-fronts transformation problem. In the beginning, only 2 input wave-fronts and 2 output wave-fronts transformation problem was considered in the SMS design process for rotational optical systems or free-form optical systems. Usually “SMS 2D” method stands for the SMS procedure developed for rotational optical system, and “SMS 3D” method for the procedure for free-form optical system. Although the SMS method was originally employed in non-imaging optical system designs, it has been found during this thesis that with the improved capability to design more surfaces and control more input and output wave-fronts, the SMS method can also be applied to imaging system designs and possesses great advantage over traditional design methods. In this thesis, one of the main goals to achieve is to further develop the existing SMS-2D method to design with more surfaces and improve the stability of the SMS-2D and SMS-3D algorithms, so that further optimization process can be combined with SMS algorithms. The benefits of SMS plus optimization strategy over traditional optimization strategy will be explained in details for both rotational and free-form imaging optical system designs. Another main goal is to develop novel design concepts and methods suitable for challenging non-imaging applications, e.g. solar concentrator and solar tracker. This thesis comprises 9 chapters and can be grouped into two parts: the first part (chapter 2-5) contains research works in the imaging field, and the second part (chapter 6-8) contains works in the non-imaging field. In the first chapter, an introduction to basic imaging and non-imaging design concepts and theories is given. Chapter 2 presents a basic SMS-2D imaging design procedure using meridian rays. In this chapter, we will set the imaging design problem from the SMS point of view, and try to solve the problem numerically. The stability of this SMS-2D design procedure will also be discussed. The design concepts and procedures developed in this chapter lay the path for further improvement. Chapter 3 presents two improved SMS 3 surfaces’ design procedures using meridian rays (SMS-3M) and skew rays (SMS-1M2S) respectively. The major improvement has been made to the central segments selections, so that the whole SMS procedures become more stable compared to procedures described in Chapter 2. Since these two algorithms represent two types of phase space sampling, their image forming capabilities are compared in a simple objective design. Chapter 4 deals with an ultra-compact SWIR camera design with the SMS-3M method. The difficulties in this wide band camera design is how to maintain high image quality meanwhile reduce the overall system length. This interesting camera design provides a playground for the classical design method and SMS design methods. We will show designs and optical performance from both classical design method and the SMS design method. Tolerance study is also given as the end of the chapter. Chapter 5 develops a two-stage SMS-3D based optimization strategy for a 2 freeform mirrors imaging system. In the first optimization phase, the SMS-3D method is integrated into the optimization process to construct the two mirrors in an accurate way, drastically reducing the unknown parameters to only few system configuration parameters. In the second optimization phase, previous optimized mirrors are parameterized into Qbfs type polynomials and set up in code V. Code V optimization results demonstrates the effectiveness of this design strategy in this 2-mirror system design. Chapter 6 shows an etendue-squeezing condenser optics, which were prepared for the 2010 IODC illumination contest. This interesting design employs many non-imaging techniques such as the SMS method, etendue-squeezing tessellation, and groove surface design. This device has theoretical efficiency limit as high as 91.9%. Chapter 7 presents a freeform mirror-type solar concentrator with uniform irradiance on the solar cell. Traditional parabolic mirror concentrator has many drawbacks like hot-pot irradiance on the center of the cell, insufficient use of active cell area due to its rotational irradiance pattern and small acceptance angle. In order to conquer these limitations, a novel irradiance homogenization concept is developed, which lead to a free-form mirror design. Simulation results show that the free-form mirror reflector has rectangular irradiance pattern, uniform irradiance distribution and large acceptance angle, which confirm the viability of the design concept. Chapter 8 presents a novel beam-steering array optics design strategy. The goal of the design is to track large angle parallel rays by only moving optical arrays laterally, and convert it to small angle parallel output rays. The design concept is developed as an extended SMS method. Potential applications of this beam-steering device are: skylights to provide steerable natural illumination, building integrated CPV systems, and steerable LED illumination. Conclusion and future lines of work are given in Chapter 9. Resumen La óptica de formación de imagen clásica se ha ido desarrollando durante siglos, dando lugar tanto a la teoría de óptica paraxial y los métodos de diseño prácticos como a técnicas de optimización multiparamétricas. Aunque estos métodos de diseño óptico para formación de imagen puede aportar soluciones elegantes a muchos problemas convencionales, siguen apareciendo nuevos problemas de diseño óptico, concentradores solares, sistemas de iluminación, cámaras ultracompactas, etc. que requieren máxima transferencia de energía o dimensiones ultracompactas. Este tipo de problemas no se pueden resolver fácilmente con métodos clásicos de diseño porque durante el proceso de diseño no solamente se deben considerar los rayos paraxiales sino también los rayos no paraxiales. La óptica anidólica o no formadora de imagen es una disciplina que ha evolucionado en gran medida recientemente. Su objetivo no es formar imagen, es maximazar la eficiencia de transferencia de energía. Un concepto importante de la óptica anidólica son los “rayos marginales”, que se pueden utilizar para el diseño de sistemas ya que si todos los rayos marginales llegan a nuestra área del receptor, todos los rayos interiores también llegarán al receptor. Haciendo uso de este principio, se han diseñado muchos concentradores solares que funcionan cerca del límite teórico que marca la termodinámica. Cuando consideramos más de un haz de rayos marginales en nuestro diseño, una posible solución es usar el método SMS (Simultaneous Multiple Surface), el cuál diseña simultáneamente varias superficies ópticas. El SMS nació como un método de diseño para óptica anidólica durante los años 90. El método puede ser considerado como una extensión del cálculo del óvalo cartesiano. En el método del óvalo cartesiano convencional, se calcula una superficie para transformar un frente de onda entrante a otro frente de onda saliente. El método SMS permite transformar varios frentes de onda de entrada en frentes de onda de salida. Inicialmente, sólo era posible transformar dos frentes de onda con dos superficies con simetría de rotación y sin simetría de rotación, pero esta limitación ha sido superada recientemente. Nos referimos a “SMS 2D” como el método orientado a construir superficies con simetría de rotación y llamamos “SMS 3D” al método para construir superficies sin simetría de rotación o free-form. Aunque el método originalmente fue aplicado en el diseño de sistemas anidólicos, se ha observado que gracias a su capacidad para diseñar más superficies y controlar más frentes de onda de entrada y de salida, el SMS también es posible aplicarlo a sistemas de formación de imagen proporcionando una gran ventaja sobre los métodos de diseño tradicionales. Uno de los principales objetivos de la presente tesis es extender el método SMS-2D para permitir el diseño de sistemas con mayor número de superficies y mejorar la estabilidad de los algoritmos del SMS-2D y SMS-3D, haciendo posible combinar la optimización con los algoritmos. Los beneficios de combinar SMS y optimización comparado con el proceso de optimización tradicional se explican en detalle para sistemas con simetría de rotación y sin simetría de rotación. Otro objetivo importante de la tesis es el desarrollo de nuevos conceptos de diseño y nuevos métodos en el área de la concentración solar fotovoltaica. La tesis está estructurada en 9 capítulos que están agrupados en dos partes: la primera de ellas (capítulos 2-5) se centra en la óptica formadora de imagen mientras que en la segunda parte (capítulos 6-8) se presenta el trabajo del área de la óptica anidólica. El primer capítulo consta de una breve introducción de los conceptos básicos de la óptica anidólica y la óptica en formación de imagen. El capítulo 2 describe un proceso de diseño SMS-2D sencillo basado en los rayos meridianos. En este capítulo se presenta el problema de diseñar un sistema formador de imagen desde el punto de vista del SMS y se intenta obtener una solución de manera numérica. La estabilidad de este proceso se analiza con detalle. Los conceptos de diseño y los algoritmos desarrollados en este capítulo sientan la base sobre la cual se realizarán mejoras. El capítulo 3 presenta dos procedimientos para el diseño de un sistema con 3 superficies SMS, el primero basado en rayos meridianos (SMS-3M) y el segundo basado en rayos oblicuos (SMS-1M2S). La mejora más destacable recae en la selección de los segmentos centrales, que hacen más estable todo el proceso de diseño comparado con el presentado en el capítulo 2. Estos dos algoritmos representan dos tipos de muestreo del espacio de fases, su capacidad para formar imagen se compara diseñando un objetivo simple con cada uno de ellos. En el capítulo 4 se presenta un diseño ultra-compacto de una cámara SWIR diseñada usando el método SMS-3M. La dificultad del diseño de esta cámara de espectro ancho radica en mantener una alta calidad de imagen y al mismo tiempo reducir drásticamente sus dimensiones. Esta cámara es muy interesante para comparar el método de diseño clásico y el método de SMS. En este capítulo se presentan ambos diseños y se analizan sus características ópticas. En el capítulo 5 se describe la estrategia de optimización basada en el método SMS-3D. El método SMS-3D calcula las superficies ópticas de manera precisa, dejando sólo unos pocos parámetros libres para decidir la configuración del sistema. Modificando el valor de estos parámetros se genera cada vez mediante SMS-3D un sistema completo diferente. La optimización se lleva a cabo variando los mencionados parámetros y analizando el sistema generado. Los resultados muestran que esta estrategia de diseño es muy eficaz y eficiente para un sistema formado por dos espejos. En el capítulo 6 se describe un sistema de compresión de la Etendue, que fue presentado en el concurso de iluminación del IODC en 2010. Este interesante diseño hace uso de técnicas propias de la óptica anidólica, como el método SMS, el teselado de las lentes y el diseño mediante grooves. Este dispositivo tiene un límite teórica en la eficiencia del 91.9%. El capítulo 7 presenta un concentrador solar basado en un espejo free-form con irradiancia uniforme sobre la célula. Los concentradores parabólicos tienen numerosas desventajas como los puntos calientes en la zona central de la célula, uso no eficiente del área de la célula al ser ésta cuadrada y además tienen ángulos de aceptancia de reducido. Para poder superar estas limitaciones se propone un novedoso concepto de homogeneización de la irrandancia que se materializa en un diseño con espejo free-form. El análisis mediante simulación demuestra que la irradiancia es homogénea en una región rectangular y con mayor ángulo de aceptancia, lo que confirma la viabilidad del concepto de diseño. En el capítulo 8 se presenta un novedoso concepto para el diseño de sistemas afocales dinámicos. El objetivo del diseño es realizar un sistema cuyo haz de rayos de entrada pueda llegar con ángulos entre ±45º mientras que el haz de rayos a la salida sea siempre perpendicular al sistema, variando únicamente la posición de los elementos ópticos lateralmente. Las aplicaciones potenciales de este dispositivo son varias: tragaluces que proporcionan iluminación natural, sistemas de concentración fotovoltaica integrados en los edificios o iluminación direccionable con LEDs. Finalmente, el último capítulo contiene las conclusiones y las líneas de investigación futura.

Single optical surface imaging designs with unconstrained object to image mapping

In this work, novel imaging designs with a single optical surface (either refractive or reflective) are presented. In some of these designs, both object and image shapes are given but mapping from object to image is obtained as a result of the design. In other designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the examples considered, the image is virtual and located at infinity and is seen from known pupil, which can emulate a human eye. In the first introductory part, 2D designs have been done using three different design methods: a SMS design, a compound Cartesian oval surface, and a differential equation method for the limit case of small pupil. At the point-size pupil limit, it is proven that these three methods coincide. In the second part, previous 2D designs are extended to 3D by rotation and the astigmatism of the image has been studied. As an advanced variation, the differential equation method is used to provide the freedom to control the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a curved object surface have been obtained. Finally, this anastigmatic differential equation method has been extended to 3D for the general case, in which freeform surfaces are designed.

Osiris— The optical, spectroscopic and infrared remote imaging system for the Rosetta orbiter

The scientific objectives, design, and implementation of the Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) for the International Rosetta Mission are described. The instrument comprises two camera systems with a common electronics box. A narrow angle camera will provide high resolution images of the structure and morphology of the nucleus of a comet. A wide angle camera with high straylight rejection and dynamic range will be used to investigate the innermost coma and the emission process at the surface of the comet. An infrared imaging system, which dramatically enhances the scientific return has been included in the narrow angle camera at little extra cost.

Combination of optical and on-destructivemechanicaltechniques for the measurement of maturity in peach

Increasing consumer dissatisfaction related with lack of ripeness in peach has been repeatedly reported since 1990 to the present day. There is thus, a great interest in improving the assessment of peach maturity, currently based on Magness Taylor firmness (destructive, highly variable, and time consuming) and colour (not reliable for highly coloured varieties). The present research studies as an alternative several non-destructive (ND) measurements, based on multispectral imaging, visible spectra, and low mass impact response. Their relationship with maturity, as well as the potential of their combination was studied. As a result, two rather independent (R2 = 0.3) groups of non-destructive measurements, chlorophyll related optical indexes and low mass impact (LMI) measurements, were identified. Optical measurements showed the best behaviour for assessing maturity at harvest, while LMI measurements reflected handling incidences, showing a promising potential to be used to control transport and postharvest handling.

Processing Pipeline for Digitalizing the Lineage Tree of Early Zebrafish Embryogenesis from Multiharmonic Imaging

The reconstruction of the cell lineage tree of early zebrafish embryogenesis requires the use of in-vivo microscopy imaging and image processing strategies. Second (SHG) and third harmonic generation (THG) microscopy observations in unstained zebrafish embryos allows to detect cell divisions and cell membranes from 1-cell to 1K-cell stage. In this article, we present an ad-hoc image processing pipeline for cell tracking and cell membranes segmentation enabling the reconstruction of the early zebrafish cell lineage tree until the 1K-cell stage. This methodology has been used to obtain digital zebrafish embryos allowing to generate a quantitative description of early zebrafish embryogenesis with minute temporal accuracy and μm spatial resolution

Imaging systems application of multichannel configurations

While multichannel configurations are well established for non-imaging applications, they have not been used yet for imaging applications. In this paper we present for the first time some of multichannel designs for imaging systems. The multichannel comprises discontinuous optical sections which are called channels. The phase-space representation of the bundle of rays going from the object to the image is discontinuous between channels. This phase-space ray-bundle flow is divided in as many paths as channels there are but it is a single wavefront both at the source and the target. Typically, these multichannel systems are at least formed by three optical surfaces: two of them have discontinuities (either in the shape or in the shape derivative) while the last is a smooth one. Optical surfaces discontinuities cause at the phase space the wave front split in separate paths. The number of discontinuities is the same in the two first surfaces: Each channel is defined by the smooth surfaces in between discontinuities, so the surfaces forming each separate channel are all smooth. Aplanatic multichannel designs are also shown and used to explain the design procedure.

Advances in the SMS design method for imaging optics

In this work, two SMS algorithms are presented for an objective design with different selected ray-bundles: three meridian ray-bundles (3M) and one meridian and two skew ray-bundles (1M-2S), the latter from pin hole point of view, provides a better sampling of the phase space. Results obtained with different algorithms will be compared.

Progress in the SMS design method for imaging optics

In this work, two SMS algorithms are presented for an objective design with different selected ray-bundles: three meridian ray-bundles (3M) and one meridian and two skew ray-bundles (1M-2S), the latter from pin hole point of view, provides a better sampling of the phase space. Results obtained with different algorithms will be compared

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

Computational methods to create and analyze a digital gene expression atlas of embryo development from microscopy images

Abstract The creation of atlases, or digital models where information from different subjects can be combined, is a field of increasing interest in biomedical imaging. When a single image does not contain enough information to appropriately describe the organism under study, it is then necessary to acquire images of several individuals, each of them containing complementary data with respect to the rest of the components in the cohort. This approach allows creating digital prototypes, ranging from anatomical atlases of human patients and organs, obtained for instance from Magnetic Resonance Imaging, to gene expression cartographies of embryo development, typically achieved from Light Microscopy. Within such context, in this PhD Thesis we propose, develop and validate new dedicated image processing methodologies that, based on image registration techniques, bring information from multiple individuals into alignment within a single digital atlas model. We also elaborate a dedicated software visualization platform to explore the resulting wealth of multi-dimensional data and novel analysis algo-rithms to automatically mine the generated resource in search of bio¬logical insights. In particular, this work focuses on gene expression data from developing zebrafish embryos imaged at the cellular resolution level with Two-Photon Laser Scanning Microscopy. Disposing of quantitative measurements relating multiple gene expressions to cell position and their evolution in time is a fundamental prerequisite to understand embryogenesis multi-scale processes. However, the number of gene expressions that can be simultaneously stained in one acquisition is limited due to optical and labeling constraints. These limitations motivate the implementation of atlasing strategies that can recreate a virtual gene expression multiplex. The developed computational tools have been tested in two different scenarios. The first one is the early zebrafish embryogenesis where the resulting atlas constitutes a link between the phenotype and the genotype at the cellular level. The second one is the late zebrafish brain where the resulting atlas allows studies relating gene expression to brain regionalization and neurogenesis. The proposed computational frameworks have been adapted to the requirements of both scenarios, such as the integration of partial views of the embryo into a whole embryo model with cellular resolution or the registration of anatom¬ical traits with deformable transformation models non-dependent on any specific labeling. The software implementation of the atlas generation tool (Match-IT) and the visualization platform (Atlas-IT) together with the gene expression atlas resources developed in this Thesis are to be made freely available to the scientific community. Lastly, a novel proof-of-concept experiment integrates for the first time 3D gene expression atlas resources with cell lineages extracted from live embryos, opening up the door to correlate genetic and cellular spatio-temporal dynamics. La creación de atlas, o modelos digitales, donde la información de distintos sujetos puede ser combinada, es un campo de creciente interés en imagen biomédica. Cuando una sola imagen no contiene suficientes datos como para describir apropiadamente el organismo objeto de estudio, se hace necesario adquirir imágenes de varios individuos, cada una de las cuales contiene información complementaria respecto al resto de componentes del grupo. De este modo, es posible crear prototipos digitales, que pueden ir desde atlas anatómicos de órganos y pacientes humanos, adquiridos por ejemplo mediante Resonancia Magnética, hasta cartografías de la expresión genética del desarrollo de embrionario, típicamente adquiridas mediante Microscopía Optica. Dentro de este contexto, en esta Tesis Doctoral se introducen, desarrollan y validan nuevos métodos de procesado de imagen que, basándose en técnicas de registro de imagen, son capaces de alinear imágenes y datos provenientes de múltiples individuos en un solo atlas digital. Además, se ha elaborado una plataforma de visualization específicamente diseñada para explorar la gran cantidad de datos, caracterizados por su multi-dimensionalidad, que resulta de estos métodos. Asimismo, se han propuesto novedosos algoritmos de análisis y minería de datos que permiten inspeccionar automáticamente los atlas generados en busca de conclusiones biológicas significativas. En particular, este trabajo se centra en datos de expresión genética del desarrollo embrionario del pez cebra, adquiridos mediante Microscopía dos fotones con resolución celular. Disponer de medidas cuantitativas que relacionen estas expresiones genéticas con las posiciones celulares y su evolución en el tiempo es un prerrequisito fundamental para comprender los procesos multi-escala característicos de la morfogénesis. Sin embargo, el número de expresiones genéticos que pueden ser simultáneamente etiquetados en una sola adquisición es reducido debido a limitaciones tanto ópticas como del etiquetado. Estas limitaciones requieren la implementación de estrategias de creación de atlas que puedan recrear un multiplexado virtual de expresiones genéticas. Las herramientas computacionales desarrolladas han sido validadas en dos escenarios distintos. El primer escenario es el desarrollo embrionario temprano del pez cebra, donde el atlas resultante permite constituir un vínculo, a nivel celular, entre el fenotipo y el genotipo de este organismo modelo. El segundo escenario corresponde a estadios tardíos del desarrollo del cerebro del pez cebra, donde el atlas resultante permite relacionar expresiones genéticas con la regionalización del cerebro y la formación de neuronas. La plataforma computacional desarrollada ha sido adaptada a los requisitos y retos planteados en ambos escenarios, como la integración, a resolución celular, de vistas parciales dentro de un modelo consistente en un embrión completo, o el alineamiento entre estructuras de referencia anatómica equivalentes, logrado mediante el uso de modelos de transformación deformables que no requieren ningún marcador específico. Está previsto poner a disposición de la comunidad científica tanto la herramienta de generación de atlas (Match-IT), como su plataforma de visualización (Atlas-IT), así como las bases de datos de expresión genética creadas a partir de estas herramientas. Por último, dentro de la presente Tesis Doctoral, se ha incluido una prueba conceptual innovadora que permite integrar los mencionados atlas de expresión genética tridimensionales dentro del linaje celular extraído de una adquisición in vivo de un embrión. Esta prueba conceptual abre la puerta a la posibilidad de correlar, por primera vez, las dinámicas espacio-temporales de genes y células.

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Electrically tunable delay for trains of optical pulses

A technique to implement an electrically tunable delay line with high bandwidth for trains of ultrashort optical pulses is presented. The system is based on the temporal self-imaging effect in fiber gratings and electrooptic modulation.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.