The lens design is a fundamental but challenging problem, while modern lens design processes still follow the classic aberration optimization theory and need preliminary designs and experienced optical engineers to control the optimization process constantly. In this thesis, we develop a differentiable ray-tracing model and apply it to automatic lens design. Our method can do ray-tracing and render images with high accuracy, with the power to use the back-propagated gradient to optimize optical parameters. Different from traditional optical design, we propose to use the rendered images as the training criteria. The rendering loss shows superior results in optimizing lenses while also making the task easier. To remove the requirements of preliminary design and constant operations in conventional lens design, we propose a curriculum learning method that starts from a small aperture and field-of-view(FoV), gradually increases the design difficulty, and dynamically adjusts attention regions of rendered images. The proposed curriculum strategies empower us to optimize complex lenses from flat surfaces automatically. Given an existing lens design and setting all surfaces flat, our method can entirely recover the original design. Even with only design targets, our method can automatically generate starting points with flat surfaces and optimize to get a design with superior optical performance. The proposed method is applied to both spheric and aspheric lenses, both camera and cellphone lenses, showing a robust ability to optimize different types of lenses. In addition, we overcome the memory problem in differentiable rendering by splitting the differentiable rendering model into two sub-processes, which allows us to work with megapixel sensors and downstream imaging processing algorithms.

The field of computer graphics has made significant progress over the years, transforming from simple, pixelated images to highly realistic visuals used across various industries including entertainment, fashion, and video gaming. However, the traditional process of rendering images remains complex and time-consuming, requiring a deep understanding of geometry, materials, and textures. This thesis introduces a simpler approach through a machine learning model, specifically using Cycle-Consistent Adversarial Networks (CycleGAN), to generate realistic images and estimate global illumination in real-time, significantly reducing the need for extensive expertise and time investment. Our experiments on the Blender and Portal datasets demonstrate the model's ability to efficiently generate high-quality, globally illuminated scenes, while a comparative study with the Pix2Pix model highlights our approach's strengths in preserving fine visual details. Despite these advancements, we acknowledge the limitations posed by hardware constraints and dataset diversity, pointing towards areas for future improvement and exploration. This work aims to simplify the complex world of computer graphics, making it more accessible and user-friendly, while maintaining high standards of visual realism. / Master of Science / Creating realistic images on a computer is a crucial part of making video games and movies more immersive and lifelike. Traditionally, this has been a complex and time-consuming task, requiring a deep understanding of how light interacts with objects to create shadows and highlights. This study introduces a simpler and quicker method using a type of smart computer program that learns from examples. This program, known as Cycle-Consistent Adversarial Networks (CycleGAN), is designed to understand the complex play of light in virtual scenes and recreate it in a way that makes the image look real. In testing this new method on different types of images, from simpler scenes to more complex ones, the results were impressive. The program was not only able to significantly cut down the time needed to render an image, but it also maintained the fine details that bring an image to life. While there were challenges, such as working with limited computer power and needing a wider variety of images for the program to learn from, the study shows great promise. It represents a big step forward in making the creation of high-quality, realistic computer graphics more accessible and achievable for a wider range of applications.

Researchers at the NASA Langley Research Center (LaRC) are developing a next-generation instrument for monitoring the Earth radiation budget (ERB) from low Earth orbit. This instrument is called the DEMonstrating the Emerging Technology for measuring the Earth's Radiation (DEMETER) instrument. DEMETER is a candidate to replace the Clouds and Earth's Radiant Energy System (CERES) instruments which currently monitor the ERB. LaRC has partnered with the Thermal Radiation Group at Virginia Tech to model and evaluate the thermal and optical design of the DEMETER instrument. The effort reported here deals with the numerical modeling of the optical and thermal radiative performance the DEMETER instrument. The numerical model is based on the Monte Carlo Ray-Trace (MCRT) method. The major optical components of the instrument are incorporated into the ray-trace model using 3-D surface equations. A CAD model of the instrument baffle is imported directly into the ray-trace environment using an STL triangular mesh. The instrument uses a single freeform mirror to focus radiation on the detector. A method for incorporating freeform surfaces into a ray-trace model is described. The development and capabilities of the model are reported. The model is used to run several ray-traces to compare two different quasi-black surface coatings for the DEMETER telescope baffle. Included is a list of future tests the Thermal Radiation Group will use the model to accomplish. / Master of Science / For decades NASA has used satellite-mounted scientific instruments to monitor the Earth radiation budget (ERB). The ERB is the energy balance of the planet Earth with its surroundings. Radiation from the sun is absorbed and reflected by the Earth. The Earth also emits radiation. The balance between these heat transfer components drives the planetary climate. Researchers at the NASA Langley Research Center (LaRC) are developing a new instrument for monitoring the ERB from low Earth orbit. This Earth observing instrument is called the DEMonstrating the Emerging Technology for measuring the Earth's Radiation (DEMETER) instrument. NASA has partnered with the Thermal Radiation Group at Virginia Tech to model and evaluate the thermal and optical design of the DEMETER instrument. The effort reported here deals with the numerical modeling of radiation heat transfer in the DEMETER instrument. The numerical model uses the Monte Carlo Ray-Trace (MCRT) method to evaluate the thermal and optical behavior of the DEMETER instrument. The development and capabilities of the model are reported. The model is used to run a series of simulations to compare the performance of two different quasi-black surface coatings for the DEMETER telescope baffle. Included is a list of future tasks the Thermal Radiation Group will accomplish using the model.

A Computação Gráfica, área em franco desenvolvimento, têm caminhado em busca da geração, cada vez mais rápida, de imagens mais realísticas. Os algoritmos que permitem a síntese de imagens realísticas demandam alto poder computacional, fazendo com que a geração deste tipo de imagem, de forma rápida, requeira o uso de computadores paralelos. Hoje, a técnica que permite gerar as imagens mais realísticas é o "ray tracing" . Os multicomputadores, por sua vez, são a arquitetura de computadores paralelos mais promissora na busca do desempenho computacional necessário às aplicações modernas. Esta dissertação aborda o problema da implementação do algoritmo de "ray tracing" em multicomputadores. A paralelização desta técnica para uso em computadores paralelos de memória distribuída pode ser feita de muitas formas diferentes, sempre envolvendo um compromisso entre a velocidade de processamento e a memória utilizada. Neste trabalho conceitua-se este problema e introduz-se ferramentas para a avaliação de soluções que levam em consideração a eficiência de processamento e a redundância no uso de memória. Também é apresentada uma nova taxonomia que, além de permitir a classificação de propostas para implementações de "ray tracing" paralelo, orienta a procura de novas soluções para este problema. O desempenho das soluções em cada classe desta taxonomia é avaliado qualitativamente. Por fim, são sugeridas novas alternativas de paralelização do algoritmo de "ray tracing" em multicomputadores. / Computer Graphics is headed today towards the synthesis of more realistic images, in less time. The algorithms used for realistic image synthesis demand high computer power, so that the synthesis of this kind of image, in short periods of time, requires the use of parallel computers. Nowadays, the technique that yields the most realistic images is ray tracing. On its turn, multicomputers are the most promising parallel architecture for reaching the performance needed in modern applications. This dissertation is on the problem of implementing the ray tracing algorithm on multicomputers. The parallelization of this technique on distributed memory parallel computers can take several forms, always involving a compromise between speed and memory. In this work, this problem is conceptualized and tools for evaluation of solutions that account for efficiency and redundancy, are introduced. It is also presented a new taxonomy that can be used for both the classification of parallel ray tracing proposals and for driving the search of new solutions to this problem. The performances of entries in each class of the taxonomy are qualitatively assessed. New alternatives for parallelizing the ray tracing algorithm on multicomputers, are suggested.

Ray tracing é um algoritmo para a síntese de imagens por computador. Suas características principais são a alta qualidade das imagens que proporciona (incorporando sombras, reflexões e transparências entre outros efeitos) e, por outro lado, a grande demanda em termos de processamento. O ray tracing parametrizado é um algoritmo baseado no ray tracing, que permite a obtenção de imagens com a mesma qualidade a um custo computacional dezenas de vezes menor, porém com restrições. Estas restrições são a necessidade de geração de um arquivo de dados inicial, cujo tempo de processamento é pouco maior que o do ray tracing convencional e a não possibilidade de alteração de qualquer parâmetro geométrico da cena. Por outro lado, a geração de versões da mesma cena com mudanças nos parâmetros ópticos (cores, intensidades de luz, texturas, reflexões, transparências, etc.) é extremamente rápida. Esta tese propõe extensões ao algoritmo de ray tracing parametrizado, procurando aliviar algumas de suas restrições. Estas extensões permitem alterar alguns parâmetros geométricos como a posição das fontes de luz, parâmetros de fontes de luz spot e mapeamento de revelo entre outros, mantendo o bom desempenho do algoritmo original. Também é estudada a paralelização do algoritmo e outras formas de aceleração do processamento. As extensões propostas permitem ampliar o campo de aplicação do algoritmo original incentivando sua adoção mais generalizada. / Ray tracing is an image synthesis computer algorithm. Its main features are the high quality of the generated images (which incorporate shadows, reflections and transparency, among other effects) and, on the other hand, a high processing demand. Parameterized ray tracing is an algorithm based on ray tracing which allows the synthesis of images with the same quality but tens of times faster than ray tracing, although with some restrictions. These restrictions are the requirement of generating a data file (which takes a little longer than standard ray tracing to create) and the fact that no geometric modifications are allowed. On the other side, the processing time for creating new versions of the image with changes only on optical parameters (colors, light intensities, textures, reflections, transparencies, etc.) is extremely fast. This Ph.D. dissertation proposes extensions to the parameterized ray tracing algorithm for diminishing its restrictions. These extensions allow changing some geometric parameters like the light source positions, spotlight parameters and bump-mapping among others, keeping the processing performance of the original algorithm. The parallelization of the algorithm is also focused as well as other performance enhancements. The proposed extensions enlarge the field of application of the original algorithm, encouraging more general adoption.

Battery life has been the slowest growing resource on mobile systems for several decades. Although much work has been done on designing new chips and peripherals that use less energy, there has not been much work on reducing energy consumption by removing energy intensive tasks from graphics algorithms. In our work, we focus on energy consumption of the ray tracing task because it is a resource-intensive, global-illumination algorithm. We focus our effort on ray tracing dynamic scenes, thus we concentrate on identifying the major elements determining the energy consumption of acceleration structures. We believe acceleration structures are critical in reducing energy consumption because they need to be built inexpensively, but must also be complex enough to boost rendering speed. We conducted tests on a Pentium 1.6 GHz laptop with GeForce Go 6800 GPU. In our experiments, we investigated various elements that modify the acceleration structure build algorithm, and we compared the energy usage of CPU and GPU rendering with different acceleration structures. Furthermore, the energy per frame when ray tracing dynamic scenes was gathered and compared to identify the best acceleration structure that provides a good balance between building energy consumption and rendering energy consumption. We found the bounding volume hierarchy to be the best acceleration structure when rendering dynamic scenes with the GPU on our test system. A bounding volume hierarchy is not the most inexpensive structure to build, but it can be rendered cheaply on the GPU while introducing acceptable energy overhead when rebuilding. In addition, we found the fastest algorithm was also the most inexpensive in terms of energy consumption. We propose an energy model based on this finding.

Ray tracing é um algoritmo para a síntese de imagens por computador. Suas características principais são a alta qualidade das imagens que proporciona (incorporando sombras, reflexões e transparências entre outros efeitos) e, por outro lado, a grande demanda em termos de processamento. O ray tracing parametrizado é um algoritmo baseado no ray tracing, que permite a obtenção de imagens com a mesma qualidade a um custo computacional dezenas de vezes menor, porém com restrições. Estas restrições são a necessidade de geração de um arquivo de dados inicial, cujo tempo de processamento é pouco maior que o do ray tracing convencional e a não possibilidade de alteração de qualquer parâmetro geométrico da cena. Por outro lado, a geração de versões da mesma cena com mudanças nos parâmetros ópticos (cores, intensidades de luz, texturas, reflexões, transparências, etc.) é extremamente rápida. Esta tese propõe extensões ao algoritmo de ray tracing parametrizado, procurando aliviar algumas de suas restrições. Estas extensões permitem alterar alguns parâmetros geométricos como a posição das fontes de luz, parâmetros de fontes de luz spot e mapeamento de revelo entre outros, mantendo o bom desempenho do algoritmo original. Também é estudada a paralelização do algoritmo e outras formas de aceleração do processamento. As extensões propostas permitem ampliar o campo de aplicação do algoritmo original incentivando sua adoção mais generalizada. / Ray tracing is an image synthesis computer algorithm. Its main features are the high quality of the generated images (which incorporate shadows, reflections and transparency, among other effects) and, on the other hand, a high processing demand. Parameterized ray tracing is an algorithm based on ray tracing which allows the synthesis of images with the same quality but tens of times faster than ray tracing, although with some restrictions. These restrictions are the requirement of generating a data file (which takes a little longer than standard ray tracing to create) and the fact that no geometric modifications are allowed. On the other side, the processing time for creating new versions of the image with changes only on optical parameters (colors, light intensities, textures, reflections, transparencies, etc.) is extremely fast. This Ph.D. dissertation proposes extensions to the parameterized ray tracing algorithm for diminishing its restrictions. These extensions allow changing some geometric parameters like the light source positions, spotlight parameters and bump-mapping among others, keeping the processing performance of the original algorithm. The parallelization of the algorithm is also focused as well as other performance enhancements. The proposed extensions enlarge the field of application of the original algorithm, encouraging more general adoption.

A Computação Gráfica, área em franco desenvolvimento, têm caminhado em busca da geração, cada vez mais rápida, de imagens mais realísticas. Os algoritmos que permitem a síntese de imagens realísticas demandam alto poder computacional, fazendo com que a geração deste tipo de imagem, de forma rápida, requeira o uso de computadores paralelos. Hoje, a técnica que permite gerar as imagens mais realísticas é o "ray tracing" . Os multicomputadores, por sua vez, são a arquitetura de computadores paralelos mais promissora na busca do desempenho computacional necessário às aplicações modernas. Esta dissertação aborda o problema da implementação do algoritmo de "ray tracing" em multicomputadores. A paralelização desta técnica para uso em computadores paralelos de memória distribuída pode ser feita de muitas formas diferentes, sempre envolvendo um compromisso entre a velocidade de processamento e a memória utilizada. Neste trabalho conceitua-se este problema e introduz-se ferramentas para a avaliação de soluções que levam em consideração a eficiência de processamento e a redundância no uso de memória. Também é apresentada uma nova taxonomia que, além de permitir a classificação de propostas para implementações de "ray tracing" paralelo, orienta a procura de novas soluções para este problema. O desempenho das soluções em cada classe desta taxonomia é avaliado qualitativamente. Por fim, são sugeridas novas alternativas de paralelização do algoritmo de "ray tracing" em multicomputadores. / Computer Graphics is headed today towards the synthesis of more realistic images, in less time. The algorithms used for realistic image synthesis demand high computer power, so that the synthesis of this kind of image, in short periods of time, requires the use of parallel computers. Nowadays, the technique that yields the most realistic images is ray tracing. On its turn, multicomputers are the most promising parallel architecture for reaching the performance needed in modern applications. This dissertation is on the problem of implementing the ray tracing algorithm on multicomputers. The parallelization of this technique on distributed memory parallel computers can take several forms, always involving a compromise between speed and memory. In this work, this problem is conceptualized and tools for evaluation of solutions that account for efficiency and redundancy, are introduced. It is also presented a new taxonomy that can be used for both the classification of parallel ray tracing proposals and for driving the search of new solutions to this problem. The performances of entries in each class of the taxonomy are qualitatively assessed. New alternatives for parallelizing the ray tracing algorithm on multicomputers, are suggested.

Optical components made of anisotropic materials, such as crystal polarizers and crystal waveplates, are widely used in many complex optical system, such as display systems, microlithography, biomedical imaging and many other optical systems, and induce more complex aberrations than optical components made of isotropic materials. The goal of this dissertation is to accurately simulate the performance of optical systems with anisotropic materials using polarization ray trace. This work extends the polarization ray tracing calculus to incorporate ray tracing through anisotropic materials, including uniaxial, biaxial and optically active materials. The 3D polarization ray tracing calculus is an invaluable tool for analyzing polarization properties of an optical system. The 3×3 polarization ray tracing P matrix developed for anisotropic ray trace assists tracking the 3D polarization transformations along a ray path with series of surfaces in an optical system. To better represent the anisotropic light-matter interactions, the definition of the P matrix is generalized to incorporate not only the polarization change at a refraction/reflection interface, but also the induced optical phase accumulation as light propagates through the anisotropic medium. This enables realistic modeling of crystalline polarization elements, such as crystal waveplates and crystal polarizers. The wavefront and polarization aberrations of these anisotropic components are more complex than those of isotropic optical components and can be evaluated from the resultant P matrix for each eigen-wavefront as well as for the overall image. One incident ray refracting or reflecting into an anisotropic medium produces two eigenpolarizations or eigenmodes propagating in different directions. The associated ray parameters of these modes necessary for the anisotropic ray trace are described in Chapter 2. The algorithms to calculate the P matrix from these ray parameters are described in Chapter 3 for anisotropic ray tracing. This P matrix has the following characteristics: (1) Multiple P matrices are calculated to describe the polarization of the multiple eigenmodes at an anisotropic intercept. (2) Each P matrix maps the orthogonal incident basis vectors (Ê_m, Ê_n, Ŝ) before the optical interface into three orthogonal exiting vectors (a_m Ê'_m, a_n Ê'_n, Ŝ') after the interface, where a_m and a_n are the complex amplitude coefficients induced at the intercept. The ray tracing algorithms described in this dissertation handle three types of uncoated anisotropic interfaces isotropic/anisotropic, anisotropic/isotropic and anisotropic/anisotropic interfaces. (3) The cumulative P matrix associated with multiple surface interactions is calculated by multiplying individual P matrices in the order along the ray path. Many optical components utilize anisotropic materials to induce desired retardance. This important mechanism is modeled as the optical phase associated with propagation. (4) The optical path length OPL of an eigenpolarization along an anisotropic ray path is incorporated into the calculation of each P matrix. Chapter 4 presents the data reduction of the P matrix of a crystal waveplate. The diattenuation is embedded in the singular values of P. The retardance is divided into two parts: (A) The physical retardance induced by OPLs and surface interactions, and (B) the geometrical transformation induced by geometry of a ray path, which is calculated by the geometrical transform Q matrix. The Q matrix of an anisotropic intercept is derived from the generalization of s- and p-bases at the anisotropic intercept; the p basis is not confined to the plane of incidence due to the anisotropic refraction or reflection. Chapter 5 shows how the multiple P matrices associated with the eigenmodes resulting from propagation through multiple anisotropic surfaces can be combined into one P matrix when the multiple modes interfere in their overlapping regions. The resultant P matrix contains diattenuation induced at each surface interaction as well as the retardance due to ray propagation and total internal reflections. The polarization aberrations of crystal waveplates and crystal polarizers are studied in Chapter 6 and Chapter 7. A wavefront simulated by a grid of rays is traced through the anisotropic system and the resultant grid of rays is analyzed. The analysis is complicated by the ray doubling effects and the partially overlapping eigen-wavefronts propagating in various directions. The wavefront and polarization aberrations of each eigenmode can be evaluated from the electric field distributions. The overall polarization at the plane of interest or the image quality at the image plane are affected by each of these eigen-wavefronts. Isotropic materials become anisotropic due to stress, strain, or applied electric or magnetic fields. In Chapter 8, the P matrix for anisotropic materials is extended to ray tracing in stress birefringent materials which are treated as spatially varying anisotropic materials. Such simulations can predict the spatial retardance variation throughout the stressed optical component and its effects on the point spread function and modulation transfer function for different incident polarizations. The anisotropic extension of the P matrix also applies to other anisotropic optical components, such as anisotropic diffractive optical elements and anisotropic thin films. It systematically keeps track of polarization transformation in 3D global Cartesian coordinates of a ray propagating through series of anisotropic and isotropic optical components with arbitrary orientations. The polarization ray tracing calculus with this generalized P matrix provides a powerful tool for optical ray trace and allows comprehensive analysis of complex optical system.

Este trabalho apresenta uma proposta de aplicação da técnica de ray-tracing bidirecional em ambientes esféricos, contendo fontes luminosas puntiformes. Trata-se de um trabalho que discorre no contexto da área de Síntese de Imagens Realísticas dentro da Computação Gráfica. O trabalho tem como principal contribuição a definição e o desenvolvimento de uma técnica para simular o fenômeno físico de refração da luz proveniente das fontes luminosas puntiformes da cena. A Síntese de Imagens Realísticas é uma das principais áreas de aplicação e pesquisa da Computação Gráfica. Uma imagem realística é uma imagem que incorpora os efeitos da luz que interage com objetos fisicamente reais. A dificuldade fundamental para a síntese de imagens realísticas se encontra na complexidade do mundo real, que apresenta uma infinidade de graduações de cores, texturas, reflexões, sombras, etc. Para a criação destas imagens realísticas, percorre-se um grande número de estágios, englobando métodos de modelagem, definição da posição de visualização, remoção de elementos ocultos, efeitos de reflexão e refração, e assim por diante. O trabalho está organizado da seguinte forma. Inicialmente, faz-se um estudo aprofundado da Óptica, área da Física que estuda o comportamento da luz no mundo real. A seguir, são apresentados algoritmos que simulam este comportamento da luz, enfatizando-se o algoritmo de rastreamento de raios (ray-tracing). Discute-se a seguir os principais problemas relacionados a simulação de objetos transparentes na Computação Gráfica. Então, uma proposta para a simulação em ambientes esféricos da refração da luz que provem diretamente das fontes luminosas puntiformes da cena a apresentada. Esta proposta baseia-se na utilização do algoritmo de rastreamento bidirecional de raios. O algoritmo apresentado é composto de duas fases. Na primeira etapa, são geradas as fontes secundarias de luz. Na segunda etapa, utiliza-se a informação obtida na primeira etapa para simular a refração da luz que provem diretamente das fontes luminosas da cena. As fontes secundarias de luz tem sua origem na utilização dos objetos esféricos transparentes como lentes esféricas convergentes. A fonte luminosa secundaria localiza-se no ponto imagem da lente, considerando-se como ponto objeto a fonte luminosa puntiforme original. A localização da fonte luminosa secundaria é obtida através da equação dos pontos conjugados. Também armazena-se uma informação relacionada com a área de atuação da fonte luminosa secundaria (angulo de espalhamento). 0 angulo de espalhamento é essencial para que, na segunda fase do algoritmo, seja possível identificar se o ponto atual é iluminado ou não pela fonte secundaria em questão. Finalizando, são geradas imagens tanto no protótipo implementado quanto em um algoritmo de ray-tracing convencional. Os resultados obtidos são comparados em nível de realismo e tempo de execução. / This work presents a proposal of using the bidirectional ray tracing method in spherical modeling environments containing punctual light sources. This project was developed within the field of Computer Graphics, more precisely in the area of synthesis of realistic images. The main contribution of this work is the definition and the development of a method that simulates the light refraction proceeding from localized light sources in the scene. The synthesis of realistic images is one of the main areas of application and research in Computer Graphics. A realistic image is an image that contains light effects interacting with physically real objects. The major difficulty for rendering realistic images is the complexity of the real world, with several color graduations, textures, reflections, shadows, etc. For this rendering, many steps like modeling methods, definition of visualization position, hidden-surface algorithms, reflection and refraction effects, and so forth, are developed. At first, this work presents a study about Optics, the area of Physics that studies the behaviour of light in the real world. In sequence, algorithms that simulate that behaviour are presented, with special attention to ray tracing method. After that, the principal problems of the simulation of transparency in Computer Graphics are discussed. So, a proposal for simulation of the light refraction proceeding from light source in spherical modeling environment, is presented. This proposal is based on use of the bidirectional ray tracing algorithm. This algorithm is divided in two main stages. In the first stage, the secondary light sources are generated. In the second stage, the information about the secondary light sources is utilized to simulate the light refraction directly proceeding from light sources of the scene. The secondary light sources are originated from transparent spherical objects like convergent spherical lenses. The position of the secondary light source is the image point of the lens, corresponding to punctual light source like object point. The position of the secondary light source is calculated by the equation of the conjugated points. Also the information about the scattering angle of the secondary light source is stored. The scattering angle is essential, in first stage of algorithm, to establish if the current point is illuminated by any secondary light source. Finally, images are generated both in the implemented prototype as in conventional ray tracing. The final results of this work are evaluated based on realism and runtime.