Width of the specular peak perpendicular to the principal plane for rough surfaces

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.     

Directional statistics-based reflectance model for isotropic bidirectional reflectance distribution functions

We introduce a novel parametric bidirectional reflectance distribution function (BRDF) model that can accurately encode a wide variety of real-world isotropic BRDFs with a small number of parameters. The key observation we make is that a BRDF may be viewed as a statistical distribution on a unit hemisphere. We derive a novel directional statistics distribution, which we refer to as the hemispherical exponential power distribution, and model real-world isotropic BRDFs as mixtures of it. We derive a canonical probabilistic method for estimating the parameters, including the number of components, of this novel directional statistics BRDF model. We show that the model captures the full spectrum of real-world isotropic BRDFs with high accuracy, but a small footprint. We also demonstrate the advantages of the novel BRDF model by showing its use for reflection component separation and for exploring the space of isotropic BRDFs.     

Ray model of light scattering by flake pigments or rough surfaces with smooth transparent coatings

We derive expressions for the intensity and polarization of light singly scattered by flake pigments or a rough surface beneath a smooth transparent coating using the ray or facet model. The distribution of local surface normals is used to calculate the bidirectional reflectance distribution function (BRDF). We discuss the different distribution functions that can be used to characterize the distribution of local surface normals. The light-scattering model is validated by measurements of the BRDF and polarization by a metallic flake pigmented coating. The results enable the extraction of a slope distribution function from the data, which is shown to be consistent over a variety of scattering geometries. These models are appropriate to estimate or predict the appearance of flake pigment automotive paints.     

Surface temperature correction for active infrared reflectance measurements of natural materials

Land surface temperature algorithms for the moderate resolution imaging spectroradiometer satellite instrument will require the spectral bidirectional reflectance distribution function (BRDF) of natural surfaces in the thermal infrared. We designed the spectral infrared bidirectional reflectance and emissivity instrument to provide such measurements by the use of a Fourier transform infrared spectrometer. A problem we encountered is the unavoidable surface heating caused by the source irradiance. For our system, the effects of the heating can cause a 30% error in the measured BRDF The error caused by heating is corrected by temporally curve fitting the radiance signal. This curve-fitting technique isolates the radiance caused by reflected irradiance. With this correction, other factors dominate the BRDF error. It is now ~5% and can be improved further. The method is illustrated with measurements of soil BRDF.     

Geometrical considerations in analyzing isotropic or anisotropic surface reflections

The bidirectional reflectance distribution function (BRDF) represents the evolution of the reflectance with the directions of incidence and observation. Today BRDF measurements are increasingly applied and have become important to the study of the appearance of surfaces. The representation and the analysis of BRDF data are discussed, and the distortions caused by the traditional representation of the BRDF in a Fourier plane are pointed out and illustrated for two theoretical cases: an isotropic surface and a brushed surface. These considerations will help characterize either the specular peak width of an isotropic rough surface or the main directions of the light scattered by an anisotropic rough surface without misinterpretations. Finally, what is believed to be a new space is suggested for the representation of the BRDF, which avoids the geometrical deformations and in numerous cases is more convenient for BRDF analysis.     

Detailed analytical approach to the Gaussian surface bidirectional reflectance distribution function specular component applied to the sea surface

A statistical sea surface specular BRDF (bidirectional reflectance distribution function) model is developed that includes mutual shadowing by waves, wave facet hiding, and projection weighting. The integral form of the model is reduced to an analytical form by making minor and justifiable approximations. The new form of the BRDF thus allows one to compute sea reflected radiance more than 100 times faster than the traditional numerical solutions. The repercussions of the approximations used in the model are discussed. Using the analytical form of the BRDF, an analytical approximation is also obtained for the reflected sun radiance that is always good to within 1% of the numerical solution for sun elevations of more than 10 degrees above the horizon. The model is validated against measured sea radiances found in the literature and is shown to be in very good agreement.     

Instrument to measure the bidirectional reflectance distribution function of surfaces

A new instrument to measure the in situ bidirectional reflectance distribution function (BRDF) of surfaces is described. This instrument measures the BRDF for eight illumination angles from 0 to 65 deg, three colors (475, 570, and 658 nm), and at over 100 selected viewing angles. The viewing zenith angles range from 5 to 65 deg, and the azimuth angles, relative to the illumination direction, range from 0 to ?180 deg. Many tests of the system have been run and show that for flat surfaces the BRDF of a sample surface can be measured with a precision of 1-5% and an accuracy of 10% of the measured reflectance. The BRDF for a dry and wet sand sample is presented as a demonstration of the instrument.     

Modeling and simulating the bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks

A high-efficiency anisotropic model for bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks (SWCOS) was proposed. This model was set by combining a BRDF model for anisotropic rough sea surface whose slopes follow Gaussian distribution and the two-beam inference theory of a thin film. We have simulated the BRDFs of oil slicks by using the above model and the measured complex refractive index data of Romashkino crude oil. In addition, the relationships between the BRDF of oil slicks and the wind speed of sea surface, thickness of oil slick, complex refractive index of crude oil and the incident zenith angle were analyzed. Also, the differences between optical characteristics of clean water and of polluted water were discussed in the context of the optical contrast of SWCOS. With high simulation speed and reliable simulation precision, this model provides a theoretical basis for rapid detection of oil spill.     

Measurement and Modeling of the Bidirectional Reflectance of SiO2 Coated Si Surfaces

An understanding of the variation of directional radiative properties of rough surfaces with dielectric coatings is important for temperature measurements and heat transfer analysis in many industrial processes. An experimental study has been conducted to investigate the effect of coating thickness on the bidirectional reflectance distribution function (BRDF) of rough silicon surfaces.Silicon dioxide films with thicknesses of 107.2, 216.5, and 324.6 nm were deposited using plasma-enhanced chemical vapor deposition onto the rough side of two Si wafers. The wafer surfaces exhibit distinct anisotropic characteristics as a result of chemical etching during the manufacturing process. A laser scatterometer measures the BRDF at a wavelength of 635 nm, after improvement of the signal-to-noise ratio. The slope distribution function obtained from the measured BRDF of uncoated Si surfaces was used in an analytical model based on geometric optics for rough surface scattering and thin-film optics for microfacet reflectance. The predicted BRDFs are in reasonable agreement with experimental results for a large range of coating thicknesses. The limitations of the geometric optics for modeling the BRDF of coated anisotropic rough surfaces in the specular direction are demonstrated. The results may benefit future radiative transfer analysis involving complicated surface microstructures with thin-film coatings.     

基于BRDF的在轨卫星反射特性

基于卫星的背景特性、材料特性、轨道特性及太阳帆板与卫星本体的相对运动特性,研究了在轨卫星的可见光反射特性.实验测量了三种卫星表面常用材料典型角度的双向反射分布函数,并构建了三种材料改进的SunBRDF模型.提出了一种单自由度运动的太阳帆板入射光线矢量计算方法.根据卫星的几何尺寸和表面材料特性,仿真获得了在轨卫星不同观测...     

Segmentation of rough surfaces using a polarization imaging system

A polarimetric vision system yielding a roughness-segmentation-based image is described. As a general principle, the bidirectional reflectance distribution function (BRDF) of a surface is assumed to be related to its local irregularities, i.e., its roughness. This BRDF is seen as the sum of a specular and a diffuse component. In this paper we propose to introduce polarization measurements in order to estimate this roughness parameter without requiring any assumption for the model of the diffuse component, nor is diffuse-specular separation required. Moreover, with the proposed method, the refractive indices of the observed objects are estimated at each pixel. Examples are given for quality control applications.     

Integrated three-dimensional shape and reflection properties measurement system

Creating accurate three-dimensional (3D) digitalized models of cultural heritage objects requires that information about surface geometry be integrated with measurements of other material properties like color and reflectance. Up until now, these measurements have been performed in laboratories using manually integrated (subjective) data analyses. We describe an out-of-laboratory bidirectional reflectance distribution function (BRDF) and 3D shape measurement system that implements shape and BRDF measurement in a single setup with BRDF uncertainty evaluation. The setup aligns spatial data with the angular reflectance distribution, yielding a better estimation of the surface's reflective properties by integrating these two modality measurements into one setup using a single detector. This approach provides a better picture of an object's intrinsic material features, which in turn produces a higher-quality digitalized model reconstruction. Furthermore, this system simplifies the data processing by combining structured light projection and photometric stereo. The results of our method of data analysis describe the diffusive and specular attributes corresponding to every measured geometric point and can be used to render intricate 3D models in an arbitrarily illuminated scene.     

Four-stream solution for atmospheric radiative transfer over a non-Lambertian surface

An analytical model characterizing the atmospheric radiance field over a non-Lambertian surface divides the radiation field into three components: unscattered radiance, single-scattering radiance, and multiple-scattering radiance. The first two components are calculated exactly. A δ-four-stream approximation is extended to calculate the azimuth-independent multiple-scattering radiance over a non-Lambertian surface, which is modeled by a statistical bidirectional reflectance distribution function (BRDF). Accuracy is assessed with respect to the exact results computed from a Gauss-Seidel iterative algorithm. Experiments comparing the results obtained with Lambertian and non-Lambertian surfaces show that incorporating the BRDF into the four-stream approximation significantly improves the accuracy in calculating radiance as well as radiative flux.     

Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and plane-polarized light

A Lambert surface would appear equally bright from all observation directions regardless of the illumination direction. However, the reflection from a randomly scattering object generally has directional variation, which can be described in terms of the bidirectional reflectance distribution function (BRDF). We measured the BRDF of a Spectralon white reflectance standard for incoherent illumination at 405 and 680?nm with unpolarized and plane-polarized light from different directions of incidence. Our measurements show deviations of the BRDF for the Spectralon white reflectance standard from that of a Lambertian reflector that depend both on the angle of incidence and the polarization states of the incident light and detected light. The non-Lambertian reflection characteristics were found to increase more toward the direction of specular reflection as the angle of incidence gets larger.     

Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics

The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly conducting surface with roughness and autocorrelation width comparable with the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a nonspecular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.     

Structured surface bidirectional reflectance distribution function reciprocity: theory and counterexamples

I address the question of whether the bidirectional reflectance distribution function (BRDF) of a structured surface has the same value when the incident and reflected angles are reversed. In particular, I examine the validity of some recent counterexamples and contrary measurements. On the basis of a new definition for structured surfaces, I conclude that the BRDF should be reciprocal. I show that designed counterexamples are flawed and suggest that measurements that do not exhibit reciprocity can be attributed to uncertainty and uncontrolled factors.     

Carbon aerogel: a new nonreflective material for the infrared

We present directional hemispherical reflectance (DHR) and bidirectional reflectance distribution function (BRDF) measurements of a carbon aerogel in the 2.5-14.3-microm infrared spectral region. The measured DHR is 1.0-1.2 +/- 0.2% throughout the 2.5-14.3-microm infrared wavelength region. When the incidence angle is increased from 8 degrees to 30 degrees off normal, the DHR increases by only 0.2%; i.e., performance does not significantly degrade as a result of illumination by off-normal infrared radiation. BRDF measurements, obtained at a wavelength of 10.6 microm, indicate that carbon aerogel exhibits Lambertian behavior. The carbon aerogel's BRDF value of 4 x 10(-3) sr(-1) is consistent with its measured DHR values. Gas adsorption and transmission-electron microscopy indicate a structure dominated by particles and pores of 相似文献   

Visible imaging characteristics of space targets oriented to on-orbit observation

This research presents the modelling and simulation method of the visible imaging characteristics for a space target. The surface of the space target is divided into facets in order to improve the modelling precision. Based on the consideration of the mixing-material of the solar panel, the measuring method of the equivalent BRDF is proposed, from which we achieve the measurement and modelling of the equivalent BRDF of the solar panel. To reflect the operate mode of the solar panel pointing to the sun, a calculation method of panel normal vector is proposed based on the principle of maximum light efficiency. The simulation of the detection signal is carried out according to the OTF and the photoelectric response model. The results show that the proposed modelling method can simulate the imaging characteristics of space targets with a complex structure, as well as correctly reflect the movement characteristics of the on-orbit satellite.     

Experimental validation of the MODTRAN 5.3 sea surface radiance model using MIRAMER campaign measurements

Radiometric images taken in mid-wave and long-wave infrared bands are used as a basis for validating a sea surface bidirectional reflectance distribution function (BRDF) being implemented into MODTRAN 5 (Berk et al. [Proc. SPIE5806, 662 (2005)]). The images were obtained during the MIRAMER campaign that took place in May 2008 in the Mediterranean Sea near Toulon, France. When atmosphere radiances are matched at the horizon to remove possible calibration offsets, the implementation of the BRDF in MODTRAN produces good sea surface radiance agreement, usually within 2% and at worst 4% from off-glint azimuthally averaged measurements. Simulations also compare quite favorably to glint measurements. The observed sea radiance deviations between model and measurements are not systematic, and are well within expected experimental uncertainties. This is largely attributed to proper radiative coupling between the surface and the atmosphere implemented using the DISORT multiple scattering algorithm.     

一种空间BRDF的编辑算法

双向反射分布函数（BRDF）一直是图形学中物体表面外观表现最通用的方法,空间BRDF是目前最优的一种BRDF,它只比标准RGB纹理多占用很小的存储空间,却达到了更加逼真的效果。但是,SBRDF的获取过程极为复杂和烦琐。该文提出了一种手工编辑SBRDF的算法,它不仅可以处理测量获取的SBRDF纹理,也可以利用标准的数字图像来实现SBRDF并进行更改。最后,通过实例渲染效果展示了该编辑工具的功效。