Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Battery energy; Ray tracing; GPU; Dynamic scene; Acceleration structure. Includes bibliographical references (73-74 leaves ).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Mobile devices; uniform grid; KdTree; BVH; mobile; GPGPU; energy; GPU; computer graphics; ray tracing. Includes bibliographical references (leaves 75-77).

Ulm, Univ., Diss., 2002.

Erlangen-Nürnberg, Diss., 2010.

Techn. Hochsch., Diss., 2003--Aachen.

Techn. University, Diss., 2003--Darmstadt.

The health, safety, comfort and productivity of a room’s occupants is greatly influenced by the sound field within it. An acoustical engineer is often consulted during the design of a room to prevent or alleviate unwanted acoustical problems. Prediction models are often used to find the most cost-effective solution to a given acoustical problem. The accuracy of sound-field prediction varies with the particular model, as do the parameters predicted. Most models only predict sound-pressure levels. Many only predict energetic quantities, ignoring wave phase and, therefore, interference and modal effects in rooms. A ray-tracing model, capable of predicting sound-pressure level, reverberation time and lateral energy fraction was translated into MATLAB code and modified to increase accuracy by including phase. Modifications included phase effects due to path length travelled and phase changes imparted by surface reflections as described by complex reflection coefficients. Further modifications included predicting steady-state and transient sound-intensity levels, providing information on the direction of sound-energy flow. The modifications were validated in comparison with free-field theory and theoretical predictions of sound fields in the presence of a single surface. The complex reflection coefficients of four common building materials were measured using two methods—an impedance tube and the spherical-decoupling method. Using these coefficients, the modified program was compared with experimental data measured in configurations involving one or more surfaces made of these materials, in an anechoic chamber, a scale-model room, and a full-scale office space. Prediction accuracy in the anechoic chamber, and in the presence of a single reflecting surface, greatly improved with the inclusion of phase. Further comparison with full-scale rooms is required before the accuracy of the model in such rooms can be evaluated definitively. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The computation of traveltimes plays a critical role in the conventional implementations of Kirchhoff migration. Finite-difference-based methods are considered one of the most effective approaches for traveltime calculations and are therefore widely used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging. In this thesis, I improved the accuracy of the solution of the linearized eikonal equation by constructing a linear system of equations (LSE) based on finite-difference approximation, which is of second-order accuracy. The ill-conditioned LSE is initially regularized and subsequently solved to calculate the traveltime update. Numerical tests proved that this method is as accurate as the second-order eikonal solver. Later arrivals are picked using ray tracing. These traveltimes are binned to the nearest node on a regular grid and empty nodes are estimated by interpolating the known values. The resulting traveltime field is used as an input to the linearized eikonal algorithm, which improves the accuracy of the interpolated nodes and yields a local ray-based traveltime. This is a preliminary study and further investigation is required to test the efficiency and the convergence of the solutions.

Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the anellipticity parameter and the symmetry axis azimuth in inhomogeneous background media. Specifically, our expansion assumes an inhomogeneous elliptically anisotropic background medium, which may be obtained from well information and stacking velocity analysis in HTI media. This formulation has advantages on two fronts: on one hand, it alleviates the computational complexity associated with solving the HTI eikonal equation, and on the other hand, it provides a mechanism to scan for the best fitting parameters without the need for repetitive modeling of traveltimes, because the traveltime coefficients of the expansion are independent of the perturbed parameters.

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.