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.
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.
In the long-term production and processing practice, China's optical manufacturing industry has formed a coexistence model with traditional optical classical polishing and high-speed polishing. China’s optical experts are familiar with many optical standards such as the US military standard, German standard, ISO10110, and China national standard, promote optical elements production which can meet the needs of high precision instruments. High efficiency production methods are used to lay a foundation for meeting the market demands of China and other countries. The application of virtual prototyping methods, the emergence of a large number of professional optical specialists, and the popularization of advanced processing and testing equipment have all contributed to the development of China's optical industry. The number, shape and type of the optical components and test requirements are critical to the mass production of the optical components. An optical manufacturer’s sustainable operations not only depend on professional lens design, but also rely on advanced processing and testing equipment, effective cost control management and China's mature industrial chain. In this paper, we analyze the current state and characteristics of China's optical industry from the aspects of component design, processing methods, optical standards, processing and inspection equipment, and cost control. The cost information is valid for China. We propose a way to optimize a mass production cost which is based on the complexity of the optical system. As result it makes it possible to produce complex optical systems in China. To demonstrate the efficiency of the proposed method of analysis, we present examples of the lenses produced.
The paper describes the use of stochastic ray tracing methods for synthesizing of photorealistic images, formed by optical systems of augmented reality devices, that combines image synthesized by the optoelectronic device with the surrounding environment. As the result of the research, new methods are proposed that make it possible to increase the efficiency and preserve the physical correctness of stochastic ray tracing methods in the task of the photorealistic images synthesis formed by optical systems. The authors show that in such cases the methods of direct stochastic ray tracing are more effective for visual modeling of the augmented reality picture on an example of the head-up display (HUD) optical system. The proposed approaches allow to combine direct, inverse and bi-directional stochastic ray tracing methods in one calculation. The work is illustrated by examples of the synthesized images observed in HUD optical systems.
The problems of using stray light visualization for the effective analysis and design of complex optical systems are considered. Examples of real applications are given where the use of the light propagation criterion in conjunction with the visual representation of the ray path makes it possible to effectively analyze complex optical design problems. The suggested solution allows not only to visualize source of the stray light in the optical system but alto to render the image on the detector taking into account diffuse scattering on all illuminated surfaces.
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.
Physically accurate lighting simulation requires precise account of the optical properties (BSDF) which are usually measured using gonio-spectrophotometer. In this paper, the authors analyzed the accuracy of BSDF shape measured for later use of measurements in special software for photorealistic visualization and virtual prototyping. Visual and numerical analysis were done. In the first case we look at the sample image rendered under specified lighting conditions, replacing its properties on measurement results and visually estimate the similarity (or difference). In the second case we compare the results of simulation of spatial or angular radiance distribution with results of corresponding radiometric measurements.
Typical results of the optic simulation are images generated on the virtual sensors of various kinds. As a rule, these images represent two-dimensional distribution of the light values in Cartesian coordinates (luminance, illuminance) or in polar coordinates (luminous intensity). Using the virtual sensors allows making the calculation and design of different kinds of illumination devices, providing stray light analysis, synthesizing of photorealistic images of three-dimensional scenes under the complex illumination generated with optical systems, etc.
Based on rich experience in the development and practical using of computer systems of virtual prototyping and photorealistic visualization the authors formulated a number of basic requirements for the visualization and analysis of the results of light simulations represented as two-dimensional distribution of luminance, illuminance and luminous intensity values. The requirements include the tone mapping operators, pseudo color imaging, visualization of the spherical panorama, regression analysis, the analysis of the image sections and regions, analysis of pixel values, the image data export, etc. All those requirements were successfully satisfied in designed software component for visual analysis of the light simulation results. The module "LumiVue" is an integral part of "Lumicept" modeling system and the corresponding plug-in of computer-aided design and support for CATIA product. A number of visual examples of analysis of calculated two-dimensional distribution of luminous intensity, illuminance and luminance illustrate the article. The examples are results of simulation and design of lighting optical systems, secondary optics for LEDs, stray light analysis, virtual prototyping and photorealistic rendering.
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