Measuring and Modeling the Bidirectional Reflection Distribution Function of Space Object's Surface Material

The characterization and temporal analysis of multispectral and hyperspectral data to extract the biophysical information of the Earth's surface can be significantly improved by understanding its aniosotropic reflectance properties, which are best described by a Bi-directional Reflectance Distribution Function (BRDF). The advancements in the field of remote sensing techniques and instrumentation have made hyperspectral BRDF measurements in the field possible using sophisticated goniometers. However, natural surfaces such as forest canopies impose limitations on both the data collection techniques, as well as, the range of illumination angles that can be collected from the field. These limitations can be mitigated by measuring BRDF in a virtual environment. This paper presents an approach to model the spectral BRDF of a forest canopy using the Digital Image and Remote Sensing Image Generation (DIRSIG) model. A synthetic forest canopy scene is constructed by modeling the 3D geometries of different tree species using OnyxTree software. The field collected spectra from the Harvard forest is used to represent the optical properties of the tree elements. The canopy radiative transfer is estimated using the DIRSIG model for specific view and illumination angles to generate BRDF measurements. A full hemispherical BRDF is generated by fitting the measured BRDF to a semi-empirical BRDF model. The results from fitting the model to the measurement indicates a root mean square error of less than 5% (2 reflectance units) relative to the forest's reflectance in the VIS-NIR-SWIR region. The process can be easily extended to generate a spectral BRDF library for various biomes.

Bidirectional Reflectance Distribution Functions (BRDFs) are well-known functions in computer graphics, and these special functions represent the surface reflectance of materials. BRDFs can be viewed as multivariate probability density function (pdf) of incoming photons leaving in a particular outgoing direction. However, constructing a multivariate probability distribution for modeling a given BRDF is difficult. A family of distributions, namely Copula distributions have been used to approximate BRDF. In this work, we employ the Pair-Copula constructions to represent the measured BRDF densities. As the measured BRDF densities have large storage needs, we use Wavelet transforms for a compact BRDF representation. We also compare the proposed BRDF representation with a number of well-known BRDF models, and show that our compact BRDF representation provides good approximation to measured BRDF data.

In fluorescent materials, light from a certain band of incident wavelengths is reradiated at longer wavelengths, i.e., with a reduced per-photon energy. While fluorescent materials are common in everyday life, they have received little attention in computer graphics. Especially, no bidirectional reradiation measurements of fluorescent materials have been available so far. In this paper, we extend the well-known concept of the bidirectional reflectance distribution function (BRDF) to account for energy transfer between wavelengths, resulting in a Bispectral Bidirectional Reflectance and Reradiation Distribution Function (bispectral BRRDF). Using a bidirectional and bispectral measurement setup, we acquire reflectance and reradiation data of a variety of fluorescent materials, including vehicle paints, paper and fabric, and compare their renderings with RGB, RGBxRGB, and spectral BRDFs. Our acquisition is guided by a principal component analysis on complete bispectral data taken under a sparse set of angles. We show that in order to faithfully reproduce the full bispectral information for all other angles, only a very small number of wavelength pairs needs to be measured at a high angular resolution.

The Bidirectional Reflectance Distribution Function (BRDF) of earth surface materials contains information relating to their physical structure and composition that cannot be inferred from their spectral properties alone. Knowledge of the BRDF is also critical to the accurate retrieval of earth surface albedo, since the BRDF describes the angular distribution of reflected radiation under given illumination conditions. Although the BRDF cannot be measured directly, it can be estimated using models of surface scattering in conjunction with reflectance data acquired at different viewing and illumination angles. The ability of a satellite sensor to characterise the BRDF of any point on the earth's surface is therefore dependent on (i) the range of view angles over which it is able to acquire data, (ii) the orbital characteristics of the satellite on which it is mounted, and (iii) the time period over which the data are recorded. This paper explores the BRDF sampling capabilities of several satellite sensors currently in operation (Landsat TM, SPOT HRV, NOAA AVHRR and ERS‐1 ATSR) or proposed for launch in the near future (MISR and MODIS). Sensors that are capable of off‐nadir viewing solely by virtue of having a wide field‐of‐view (e.g. NOAA‐AVHRR) or through across‐track pointing (e.g. SPOT‐HRV) provide a relatively sparse sample of the BRDF. On the other hand, future sensors with along‐track pointing, such as the MISR instrument of NASA's Earth Observing System (EOS), will provide a much more complete sample and are therefore better able to characterise the surface BRDF and albedo. Sensors such as these are also better equipped to obtain data at and around the ‘hot spot’ and, consequently, have the potential to extract detailed information on the biophysical properties of earth surface materials.

In metallic fusion devices, parasitic light originating from multiple reflections on the wall is a major problem for the interpretation of optical diagnostics. Strong stray light affects several optical diagnostics in ITER. One possibility to cope with this reflected light is to use photonic simulation, which can accurately predict the behavior of light within complex 3D geometry. A prerequisite is to get a good description of the reflection model, represented by the Bidirectional Reflectance Distribution Function (BRDF), based on optical measurements of in-vessel materials. To avoid complicated measurements using goniophotometer to get the BRDF, one possibility is to link surface optical properties and topography characteristics, such as roughness measurements, for example, using the classical Bennett’s formula. Measurements were performed using two experimental goniophotometers to fully characterize the BRDF of tungsten samples with different roughness values. Surface topography was measured using a three-dimensional laser scanning confocal microscope. Several parameters were extracted from these measurements including the arithmetic average roughness (Ra), the root mean square roughness (RMS), the Surface Inclination Angle Distribution and furthermore its mean value δm and the power spectral density (PSD). The correlations of BRDF model parameters deduced from the measurements are compared with the previous topographic parameters. The initial results on several tungsten samples show that Ra, which is the usual measure of surface roughness, is not the most suitable metric to link with the reflection behavior of the surface. In contrast, the PSD and the surface inclination angle are interesting metrics for describing the reflected light.

Using BRDF for radiance and luminance calculation

Artistic authoring of 3D environments is a laborious enterprise that also requires skilled content creators. There have been impressive improvements in using machine learning to address different aspects of generating 3D content, such as generating meshes, arranging geometry, synthesizing textures, etc. In this paper we develop a model to generate Bidirectional Reflectance Distribution Functions (BRDFs) from descriptive textual prompts. BRDFs are four dimensional probability distributions that characterize the interaction of light with surface materials. They are either represented parametrically, or by tabulating the probability density associated with every pair of incident and outgoing angles. The former lends itself to artistic editing while the latter is used when measuring the appearance of real materials. Numerous works have focused on hypothesizing BRDF models from images of materials. We learn a mapping from textual descriptions of materials to parametric BRDFs. Our model is first trained using a semi‐supervised approach before being tuned via an unsupervised scheme. Although our model is general, in this paper we specifically generate parameters for MDL materials, conditioned on natural language descriptions, within NVIDIA's Omniverse platform. This enables use cases such as real‐time text prompts to change materials of objects in 3D environments such as “dull plastic” or “shiny iron”. Since the output of our model is a parametric BRDF, rather than an image of the material, it may be used to render materials using any shape under arbitrarily specified viewing and lighting conditions.

An optimized Back-Propagation network (BP network) based on Genetic Algorithm (GA) was introduced to construct bidirectional reflectance distribution function (BRDF) model. To verify the performance of GA-BP network, two different kinds of space target materials were used for experiment. Based on the experimental data, we used GA to simulate the undetermined parameters of a five-parameter BRDF model, and used GA-BP network and BP network to construct a new BRDF model respectively. The fitting results manifest that the GA-BP network is suitable for construct a new BRDF model and outperforms the five-parameter BRDF model in speed and accuracy under the same condition.

Surface reflectance of real-world materials is now widely represented by the bidirectional reflectance distribution function (BRDF) and also by spatially varying representations such as SVBRDF and the bidirectional texture function (BTF). The raw surface reflectance measurements are typically compressed or fitted by analytical models, that always introduce a certain loss of accuracy. For its evaluation we need a distance function between a reference surface reflectance and its approximate version. Although some of the past techniques tried to reflect the perceptual sensitivity of human vision, they have neither optimized illumination and viewing conditions nor surface shape. In this paper, we suggest a new image-based methodology for comparing different anisotropic BRDFs. We use optimization techniques to generate a novel surface which has extensive coverage of incoming and outgoing light directions, while preserving its features and frequencies that are important for material appearance judgments. A single rendered image of such a surface along with simultaneously optimized lighting and viewing directions leads to the computation of a meaningful BRDF difference, by means of standard image difference predictors. A psychophysical experiments revealed that our surface provides richer information on material properties than the standard surfaces often used in computer graphics, e.g., sphere or blob.

The bidirectional reflectance distribution function (BRDF) model developed by Torrance and Sparrow [J. Opt. Soc. Am. 57, 1105-1114 (1967)] is used to describe the specular reflection of rough surfaces. We compare this model with the BRDF measurements of four manmade surfaces with different roughnesses. The model can be used to describe the basic features of the measured BRDFs. We found that the width of the specular peak perpendicular to the principal plane decreases strongly with an increasing illumination zenith angle in the data as well as in the model. A model analysis shows that the width is approximately proportional to the cosine of the illumination angle theta(i), and the deviations are determined by the roughness of the surface. This relationship is accompanied by an increase in reflectance in the specular direction in the principal plane that is 1/cos theta(i) stronger than the increase for a perfectly smooth surface.

The bidirectional reflectance distribution function (BRDF) data are essential for analyzing and modeling the material appearance of anisotropic surfaces. In order to acquire four-dimensional BRDF on the anisotropic material surfaces, a four-axis gonioreflectometer was designed and implemented. The instrument consists of a collimated, broadband light source, a four-axis rotation mechanism, a spectroradiometer, and a control system. The instrument is able to carry out spectral BRDF measurements over most of the incident and reflection hemispheres and the entire visible spectrum. One thousand twenty-four samples are obtained over the spectral range of 380 to 760 nm. The angular resolution of the BRDF measurement is <0.1 deg with good repeatability. A relative calibration method was adopted to obtain the absolute values of BRDFs. Various scanning schemes can be carried out by the instrument to scan the designated angular domains, enabling the instrument to capture material appearance with strong, distinctive anisotropic highlights and translucency. The obtained BRDF data of a textile sample demonstrate the instrument capability of capturing complex light scattering behaviors, including off-specular reflection peaks, off-plane reflection peaks, and backscattering. The designers of novel material appearance and computer graphics community will benefit from this work.

Estimation of crop gross primary production (GPP): I. impact of MODIS observation footprint and impact of vegetation BRDF characteristics

We consider the flatland or 2D properties of the light field generated when a homogeneous convex curved surface reflects a distant illumination field. Besides being of considerable theoretical interest, this problem has applications in computer vision and graphics - for instance, in determining lighting and bidirectional reflectance distribution functions (BRDFs), in rendering environment maps, and in image-based rendering. We demonstrate that the integral for the reflected light transforms to a simple product of coefficients in Fourier space. Thus, the operation of rendering can be viewed in simple signal processing terms as a filtering operation that convolves the incident illumination with the BRDF. This analysis leads to a number of interesting observations for computer graphics, computer vision, and visual perception.

New phase function development and complete spectral radiative properties measurements of aerogel infused fibrous blanket based on simulated annealing algorithm

Silicon carbide formed by chemical vapor deposition is a promising material to use for lightweight, low-scatter mirrors. It can be made optically dense with a minimum of growth defects and stress birefringence, and it can be polished to a low-scatter finish that is comparable to the best high-quality fused-silica optics. Roughness values of 0.3 Å rms have been measured on a Zygo heterodyne profiler and under 1 Å rms on a Talystep mechanical-contact profiler. The optical constants measured in the wavelength range from 1.6–25 μm show that there is a reststrahlen band in the 10–13μm region and that the reflectance exceeds 94% at 12 μm. Total integrated scattering (TTS) at 0.647 μm can be as low as 1 × 10−6, corresponding to an rms roughness of 5.2 Å. Bidirectional-reflectance distribution function (BRDF) values of less than 5 × 10−6 at a scattering angle of 10 from the specular direction and approximately 3 × 10−6 at 25–80° from the specular direction have been measured at 0.633 μm. The integrated BRDF values yield a roughness in good agreement with that measured by TIS. These BRDF values are approximately 11 orders of magnitude down from the intensity of the specular beam. Data measured on silicon carbide samples from different sources and polished by different companies will be shown.