The objects with complex scattering properties with rough surfaces and heterogeneous media are widely used in various light-guiding devices, car dashboards, luminaires, and other illuminating systems as elements of scenes aimed to generate images with photorealistic quality. In most cases, such properties are described with Bi-directional Scattering Distribution Functions (BSDF). Typically, such functions are obtained with different measuring devices, like goniophotometers. However, the measurements of such functions are a complex task because of their multidimensional character and complex angular shape. At the present a lot of devices aimed at BSDF measurements have been developed, however all of them have a set of drawbacks, for example, it may be very complex construction, which makes such devices expensive in the manufacturing, or noticeable overall dimensions, what results in their inconvenient not portable usage, low speed of measurements. On the other side, other simpler category of BSDF measuring devices does not have sufficient accuracy, a restricted number of measurement directions, and a very restricted set of functions not allowing to measure such complex optical effects as polarization and fluorescence. In the given paper an original construction of the BSDF measuring device is considered, which does not have the mentioned drawbacks and combines most of the advantages of existing solutions. The proposed measurement setup has small overall dimensions, a simple and cheap construction keeping high accuracy and measurement speed, and a wide set of supported effects like polarization and fluorescence. The advantages of the developed measurement setup are proved with the accurate computer model based on BSDF obtained with the measurements of real samples.
The traditional bi-directional stochastic ray tracing with photon maps (BDPM) is a popular method for physically accurate lighting simulation. Although it has been improved by application of MIS there are still problems such as the optimal number of rays. The implementation of the BDPM runs progressively, iteration by iteration, tracing a number of light and camera paths and then merging them. The noise achieved after a fixed rum time does not always decrease with the number of rays, so there is some optimum. We produce the method of calculating the optimal number of rays. Variance of the contribution to luminance calculated by BDPM in one iteration depends on the number of rays via a relatively simple algebraic law, yet more sophisticated then for classic Monte Carlo because the merged paths are not statistically independent in BDPM. The noise after the given simulation time is determined by this variance divided by the number of iteration done within that time, so the law includes the average time spent on tracing one light and one camera ray. Expectedly for the optimal number of camera paths the resulting noise is homogeneous over the image. One can make relative or absolute noise to be homogeneous so we have a single value for the whole image. The resulting formula includes “time per camera/light ray” only as a weighted sum over all pixels which can be easily measured from a single trial tracing. With this optimal choice the noise is reduced considerably.
Simulation of light propagation in a dispersed medium is usually based upon continuous medium approximation, which is good when the distance between different ray hits much exceeds the particle size. But when the different ray events are not statistically independent, which violates the continuous medium approach. Current paper investigates the problem for automotive paints where the particles are thin planar flakes. We performed accurate ray optics simulation. Here subsequent light scattering events are correlated: if incident ray reached the given flake, then the probability that the reflected ray leaves the paint area without further scattering is higher than the probability of hitting a flake “on average”. If, however, the reflected ray hits the next flake while going upwards, then it will be reflected downwards and most likely hit the first flake again. After that the probability of hitting the same second flake is increased as compared to mean value. This increases the probability of uneven scattering while decreases that of even scattering. We demonstrate how this affects the total scattering and obtain some analytic estimates. We compare the bidirectional reflection function of paint surface calculated for the two models and show how the difference changes with concentration and flake size. It happens that a serious change is in the near-specular region. Some analytically derived “correction” terms can be applied to the continuous medium approach to move it towards the results of the explicit model. In some cases this improvement can be a due compromise with more expensive explicit one.
The authors present the raytracing-based method of the realistic image synthesis of the three-dimensional scenes with a complex environment containing gradient media. The proposed solution is based on the Runge-Kutta method and allows us to translate a ray to the specified distance in the free space with a gradient medium. The main specificity of the solution is the raytracing inside the medium with the complex boundary, including thousands (and sometimes millions) of geometry elements. So, an efficient way to find a ray intersection with the medium boundary becomes a serious problem. The authors designed an efficient solution for the construction of the adaptive geometry hierarchy which allows splitting the complex boundaries to the voxels with the reduced number of geometry elements and providing the fast raytracing procedure inside of the voxel. Special program interfaces to integrate the raytracing solutions to the rendering system were designed and realistic images of the scenes with gradient media were rendered. Moreover, the authors considered possible solutions for calculation of the luminance components inside of the medium with a gradient index of refraction. The investigation showed that the most efficient way of the luminance calculation is stochastic bidirectional ray tracing with a pair of photon maps. Realistic images of the scenes containing media with a gradient index of refraction were rendered.
We describe a method of tracing a backward (from camera) ray in a scene that contains birefrigent (uniaxial) media. The physics of scattering of an electromagnetic wave by a boundary between two media is well known and is a base for ray tracing methods; but processing of a backward ray differs from scattering of a “natural” forward ray. Say, when a backward ray refracts by a boundary, besides the energy transfer coefficient like for a forward ray, one must account for the radiance change due to beam divergence. We calculate this factor and prove it must be evaluated only for the first and the last media along the ray path while the contributions from the intermediate media mutually cancel. We present a closed numerical method that allows one to perform transformation of a backward ray on a boundary between two media either of which can be birefrigent. We hope it is more convenient and ready for usage in ray tracing engines than known publications. Calculation utilizes Helmholtz reciprocity to calculate directions of scattered rays and their polarization (i.e., Mueller matrices), which is advantageous over a straightforward “reverse” of forward ray transformation. The algorithm was integrated in the lighting simulation system Lumicept and allowed for an efficient calculation of images of scenes with crystal elements.
We describe an algorithm of tracing a backward (from camera) ray in a scene which contains birefrigent (uniaxial) media. The physics of scattering of an electromagnetic wave by a boundary between two media is well known and is a base for ray tracing algorithms; but processing of a backward ray differs from scattering of a “natural” forward ray. Say, when a backward ray refracts by a boundary, besides the energy transfer coefficient like for a forward ray one must account for the luminance change due to beam divergence. We calculate this factor and prove it must be evaluated only for the first and the last media along the ray path while the contributions from the intermediate media mutually cancel. In this paper we present a closed numerical method that allows to perform transformation of a backward ray on a boundary between two media either of which can be birefrigent. We hope it is more convenient and ready for usage in ray tracing engines that known publications. Calculation utilizes Helmholtz reciprocity to calculate directions of scattered rays and their polarization (i.e. Mueller matrices) which is advantageous over a straightforward “reverse” of forward ray transformation. The algorithm was integrated in the lighting simulation system Lumicept and allowed for an efficient calculation of images of scenes with crystal elements.
A physically accurate description of the optical properties of surfaces is the one of the most important requirements in optical simulation for both imaging and non-imaging optics. Uncertainty in the specification of the optical properties might influence the simulation image or the spatial distribution of radiation in optical system. One of the ways of describing the optical properties is using the Bidirectional Scattering Distribution Function (BSDF). As a rule, BSDF is measured by goniospectrophotometers, but sometimes it is not possible to perform such measurements. In some cases, the measurement should be done inside the material, but it is impossible to measure BSDF of the boundary there. One of the possible solutions is to measure the microrelief heights distribution by profile measurement machine or atomic force microscope and assign measured data for given model. But, not every optical design software solution has the ability to specify microrelief directly, while majority of them just have the ability to specify BSDF. In this article, authors show methods of BSDFs generation from measurements of the real microrelief in the form of spatial distribution of heights.
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