Ray and Wave Aberrations Revisited: A Huygens-Like Construction yields Exact Relations

The optical aberrations of a system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersection measured in the image plane. The classical connection between the two descriptions is an approximation, the error of which has, so far, not been quantified analytically. We derive exact analytical equations for computing the wavefront surface, the aberrated ray directions, and the transverse ray aberrations in terms of the wave aberrations (OPD) and the reference sphere. We introduce precise conditions for a function to be an OPD function, show that every such function has an associated wavefront, and study the error arising from the classical approximation. We establish strict conditions for the error to be small. We illustrate our results with numerical simulations. Our results show that large numerical apertures and high-frequency OPD functions yield larger approximation errors.Comment: 12 pages, 10 Figures, JOSA A, vol. 33, no.

A Vignetting Model for Light Field Cameras with an Application to Light Field Microscopy

International audienceIn standard photography, vignetting is considered mainly as a radiometric effect because it results in a darkening of the edges of the captured image. In this paper, we demonstrate that for light field cameras, vignetting is more than just a radio-metric effect. It modifies the properties of the acquired light field and renders most of the calibration procedures from the literature inadequate. We address the problem by describing a model-and camera-agnostic method to evaluate vignetting in phase space. This enables the synthesis of vignetted pixel values, that, applied to a range of pixels yield images corresponding to the white images that are customarily recorded for calibrating light field cameras. We show that the commonly assumed reference points for microlens-based systems are incorrect approximations to the true optical reference, i.e. the image of the center of the exit pupil. We introduce a novel calibration procedure to determine this optically correct reference point from experimental white images. We describe the changes vignetting imposes on the light field sampling patterns and, therefore, the optical properties of the corresponding virtual cameras using the ECA model [1] and apply these insights to a custom-built light field microscope

Reconstruction and rendering of time-varying natural phenomena

While computer performance increases and computer generated images get ever more realistic, the need for modeling computer graphics content is becoming stronger. To achieve photo-realism detailed scenes have to be modeled often with a significant amount of manual labour. Interdisciplinary research combining the fields of Computer Graphics, Computer Vision and Scientific Computing has led to the development of (semi-)automatic modeling tools freeing the user of labour-intensive modeling tasks. The modeling of animated content is especially challenging. Realistic motion is necessary to convince the audience of computer games, movies with mixed reality content and augmented reality applications. The goal of this thesis is to investigate automated modeling techniques for time-varying natural phenomena. The results of the presented methods are animated, three-dimensional computer models of fire, smoke and fluid flows.Durch die steigende Rechenkapazität moderner Computer besteht die Möglichkeit immer realistischere Bilder virtuell zu erzeugen. Dadurch entsteht ein größerer Bedarf an Modellierungsarbeit um die nötigen Objekte virtuell zu beschreiben. Um photorealistische Bilder erzeugen zu können müssen sehr detaillierte Szenen, oft in mühsamer Handarbeit, modelliert werden. Ein interdisziplinärer Forschungszweig, der Computergrafik, Bildverarbeitung und Wissenschaftliches Rechnen verbindet, hat in den letzten Jahren die Entwicklung von (semi-)automatischen Methoden zur Modellierung von Computergrafikinhalten vorangetrieben. Die Modellierung dynamischer Inhalte ist dabei eine besonders anspruchsvolle Aufgabe, da realistische Bewegungsabläufe sehr wichtig für eine überzeugende Darstellung von Computergrafikinhalten in Filmen, Computerspielen oder Augmented-Reality Anwendungen sind. Das Ziel dieser Arbeit ist es automatische Modellierungsmethoden für dynamische Naturerscheinungen wie Wasserfluss, Feuer, Rauch und die Bewegung erhitzter Luft zu entwickeln. Das Resultat der entwickelten Methoden sind dabei dynamische, dreidimensionale Computergrafikmodelle

Rainbow Particle Imaging Velocimetry

National audienceWe introduce a new approach for snapshot imaging of time-resolved, non-stationary 3D fluid flows. Based on Particle Imaging Velocimetry (PIV), a well-established technique for fluid flow analysis, we propose a novel approach for spectral encoding of the third dimension. To do so, we illuminate the flow volume with a stack of monochromatic light planes at different wavelengths (rainbow) : we call this novel approach Rainbow-PIV. With a single camera, we can record the third dimension, this is a completely new approach compared to the state-of-the-art

Ray and Wave Aberrations Revisited: A Huygens-Like Construction Yields Exact Relations

International audienceThe aberrations of an optical system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersections measured in the image plane. The classical connection between the two descriptions is an approximation, the error of which has, so far, not been quantified analytically. We derive exact analytical equations for computing the wavefront surface, the aberrated ray directions, and the transverse ray aberrations in terms of the wave aberrations (OPD) and the reference sphere. We introduce precise conditions for a function to be an OPD function, show that every such function has an associated wavefront, and study the error arising from the classical approximation. We establish strict conditions for the error to be small. We illustrate our results with numerical simulations. Our results show that large numerical apertures and OPD functions with strong gradients yield larger approximation errors

Refractive Index Dependent Bidirectional Scattering Distribution Functions

Wir untersuchen die Wirkung des Eintauchens von realen Materialien in Medien mit unterschiedlichem Brechindex. In der Theorie sollte das Reflektanz-Verhalten eines Materials, das in den umgebenden Medien mit unterschiedlichen Brechungsindizes eingetaucht wird,durch die Fresnel-Gleichungen vorhergesagt werden. Wie wir jedoch zeigen, folgt nur eine Unterklasse von Materialien diesem theoretischen Modell. In der Realität zeigen viele Materialien unerwartete Effekte wie stärker lokalisierte Highlights oder eine deutliche Zunahme von spekularer Reflexion durch Mikrogeometrie. In unseren Experimenten haben wir herausgefunden, dass diese Effekte ziemlich stark variieren, und keines der bestehenden BRDF-Modelle das realistisch wiedergeben. Wir schlagen ein neues, parametrisches Modell vor, dass den Brechungsindex berücksichtigt. Wir fitten unsere Messergebnisse an das Modell und erhalten so Parameter zur Beschreibung der Reflektanz verschiedener Medien.We investigate the effect of immersing real-world materials into media of different refractive indices. In theory, the reflective and transmissive behavior of a material that is immersed into surrounding media with different refractive indices should be predicted by the Fresnel equations. However, as we show, %\todo{Ivo}{} only a subclass of materials follows this theoretical model. In reality, many materials exhibit unexpected effects such as stronger localized highlights or a significant increase in the glossy reflection due to microgeometry. In our experiments we found that the variation of these effects can be quite strong, and none of the existing BRDF models realistically reproduce these effects seen in reality. We propose a new, parametric model that takes refractive index changes into account. We fit measurements of different materials and present results to demonstrate the importance of BRDF changes for submerged objects

An Introduction to Optimization Techniques in Computer Graphics

International audienceBackground: Many students in Computer Science do not have a sufficient background in applied mathematics to employ state-of-the-art optimization techniques and to judge the outcome of such techniques critically (e.g. regarding the stability/quality/accuracy of their output). At the same time, the use of optimization techniques in computer graphics is becoming ubiquitous. Treating optimization algorithms as a black box yields sub-optimal results at best. At worst, stability issues and convergence problems may prevent the solution of a problem or impede the general application of a method to a wide range of input, i.e. beyond the set of examples shown in a paper. The course will draw attention to these aspects and to current best practices. This will enable participants to judge articles that use optimization schemes critically and improve their own skill set

An Equivalent F-Number for Light Field Systems: Light Efficiency, Signal-to-Noise Ratio, and Depth of Field

International audienceThe paper discusses the light efficiency and SNR of light field imaging systems in comparison to classical 2D imaging. In order to achieve this goal, I define the "equivalent f-number" as a concept of capturing the light gathering ability of the light field system. Since the f-number, in classical imaging systems, is conceptually also linked with the depth-of-field, I discuss an appropriate depth-of-field interpretation for light field systems