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.     

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.     

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.     

Modeling the bidirectional reflectance of emissive displays

The reflection properties of a display device influence the available contrast and affect the perception of subtle detail. The display reflection characteristics of flat-panel displays (FPDs) are appropriately described by a six-dimensional bidirectional reflectance distribution function (BRDF). I describe a Monte Carlo method for modeling the bidirectional reflectance of multilayer emissive structures used in electronic display devices. I estimate the complete BRDF using a one-dimensional angular distribution function of the luminance. I apply the method to model typical high-performance cathode-ray tube and FPD structures. I find that, for the BRDF signatures of cathode-ray tubes characterized by a specular and a quasi-Lambertian components, the estimated values for the specular and diffuse reflection coefficients agree well with low-resolution experimental measurements conducted with a rotation arm and a collimated probe. I show that emissive FPDs with thin-film organic layers on reflective substrates can exhibit a predominant specular peak broadened by short-range light scattering.     

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.     

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.     

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   

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.     

Specular, diffuse, and polarized light scattered by two wheat canopies

Using polarization measurements, the reflectance factor R(theta(i),phi(i),theta(r),phi(r)) of two wheat canopies is divided into components due to specularly and diffusely reflected light. The data show that two key angles may be predicted, the angle of the polarizer for minimum flux and the angle of incidence of sunlight specularly reflected by a leaf to a sensor. The results show that specular reflection is a key aspect to radiation transfer by two canopies. Results suggest that the advent of heading in wheat may be remotely sensed from polarization measurements of the canopy reflectance.     

Variational estimation of inhomogeneous specular reflectance and illumination from a single view

Estimating the illumination and the reflectance properties of an object surface from a few images is an important but challenging problem. The problem becomes even more challenging if we wish to deal with real-world objects that naturally have spatially inhomogeneous reflectance. In this paper, we derive a novel method for estimating the spatially varying specular reflectance properties of a surface of known geometry as well as the illumination distribution of a scene from a specular-only image, for instance, recovered from two images captured with a polarizer to separate reflection components. Unlike previous work, we do not assume the illumination to be a single point light source. We model specular reflection with a spherical statistical distribution and encode its spatial variation with a radial basis function (RBF) network of their parameter values, which allows us to formulate the simultaneous estimation of spatially varying specular reflectance and illumination as a constrained optimization based on the I-divergence measure. To solve it, we derive a variational algorithm based on the expectation maximization principle. At the same time, we estimate optimal encoding of the specular reflectance properties by learning the number, centers, and widths of the RBF hidden units. We demonstrate the effectiveness of the method on images of synthetic and real-world objects.     

Influence of orientation of rough grooves on spectral reflectivity of a surface in the thermal radiation wavelength range

Roughness is one of the principal factors influencing reflectance of a surface that takes place in radiation heat transfer. In the present work, we investigate the influence of the orientation of single-oriented roughness grooves on the directed–directed spectral reflectance of surfaces within the wavelength range of 0.2–20.0 μm. The surfaces have a mean square deviation of the roughness (σ) of 0.2 μm and 2.0 μm and the areas exceed the size of the incident light beam. The angles of reflection are equal to the angles of incidence and are equal to 50° and 70°. The degree of influence of the groove orientation on the reflectance is defined as the ratio of the reflectances of one and the same surface with the grooves oriented parallel and perpendicular to the plane of incidence. In the theoretical investigation, we engage the unidimensionally rough surface model. An experimental study by means of physical modeling was performed: the degree of influence of the groove orientation on the spectral reflection of the surface was estimated, within the investigated wavelength range, according to the degree of influence of the groove orientation on the monochromatic reflectance of the reference ground surfaces within the σ-range of 0.01–4.33 μm on the wavelength 0.405 μm. The studies performed show that the spectral range of the groove orientation influence on the surface reflectance increases with an increase in σ and a decrease in the angle of incidence; the degree of that influence has a maximum the value of which increases with the increase in the angle of incidence. We determine the conditions of agreement of the theory and the experiment.     

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.     

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.     

Surface bidirectional reflection distribution function and the texture of bricks and tiles

We study and analyze properties underlying the visual appearance of materials such as the surface bidirectional reflection distribution function and texture. The spatial distribution of scattered light in relation to the incident light determines the surface appearance and can be partly specified by the bidirectional reflection distribution function, which is defined as the directionally dependent ratio of radiance to irradiance. We perform gonioradiometric measurements on samples of bricks and tiles. To describe the reflection mechanisms in the surfaces under study, we combine models of specular and diffuse reflectance from rough surfaces and fit them to the experimental data. We also collect images and determine the textural differences in the surface appearance, resulting from the variation in the illumination direction and the viewing directions.     

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.     

Enhanced specular peaks in diffuse light scattering from weakly rough metal surfaces

We employ Monte Carlo techniques based on the reduced Rayleigh equations to study an enhanced specular peak that appears in the light scattered from weakly rough metal surfaces. This peak is not associated with the specular reflection but instead appears, with finite angular width, at the specular angle of the mean diffusely scattered intensity. As is the case with backscattering enhancement, the specular peak arises from the interference of contributions of multiple-scattering processes related to surface plasmon polariton excitation. We demonstrate that the specular peak is seen clearly for surface roughness that has a conventional Gaussian power spectrum. Further, we show that the peak appears more distinctly for roughness whose power spectrum has a new rectangular form, which is proposed here with the intent of better isolation of the scattering processes essential to the specular peak. Finally, for a pair of rough surfaces that have appropriately correlated surface roughness, it is found that the cross correlation of scattered amplitudes presents a well-isolated specular peak, which directly demonstrates the constructive interference that produces the effect.     

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.     

Reflectance and scattering properties of highly absorbing black appliqués over a broadband spectral region

I present angle-dependent directional hemispherical reflectance (DHR) and bidirectional reflectance distribution function (BRDF) measurements of three highly absorbing black appliqués in the 250-2000-nm broadband spectral region. DHR measurements of Energy Science Laboratories, Inc. (ESLI), Rippey, and Rodel appliqués were obtained at incidence angles of 8 degrees , 50 degrees , and 70 degrees . For an incidence angle of 8 degrees , the ESLI appliqué exhibited the lowest DHR value of 0.3% across this entire spectral region, whereas the Rippey and Rodel had DHR values of 1.5% and 2.0-2.5%, respectively. In-plane BRDF measurements of the appliqués, obtained at a wavelength of 633 nm and incidence angle of 10 degrees , yielded Lambertian profiles from -80 degrees to +80 degrees with values ranging from ~10(-3) sr(-1) for the ESLI, 6 x 10(-3) sr(-1) for the Rippey, and 9 x 10(-3) sr(-1) for the Rodel appliqué. In addition, rms surface roughness and correlation lengths for the Rippey and the Rodel appliqués were determined. The in-plane BRDF data were used to estimate the reflected specular component from Beckmann's scattering theory, and excellent agreement was found.     

Small-angle goniometry for backscattering measurements in the broadband spectrum

We present experiments on spectral bidirectional reflectance distribution function (BRDF) effects at backscatter and discuss the feasibility of new methods for laboratory and field simulations of remote sensing of land surfaces. The extreme sharpness of the intensity peak allows both directional and comparative experimental spectral studies of hot spots. We demonstrate wavelength-dependent features in the hot-spot reflectance signatures that facilitate extension of spectral and directional BRDF measurements of natural targets (such as forest understories and ice surfaces) into retroreflection to exploit their hot-spot characteristics in the interpretation of spaceborne and airborne data.     

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.