Physically based reflectance model utilizing polarization measurement

A surface bidirectional reflectance distribution function (BRDF) depends on both the optical properties of the material and the microstructure of the surface and appears as combination of these factors. We propose a method for modeling the BRDF based on a separate optical-property (refractive-index) estimation by polarization measurement. Because the BRDF and the refractive index for precisely the same place can be determined, errors cased by individual difference or spatial dependence can be eliminated. Our BRDF model treats the surface as an aggregation of microfacets, and the diffractive effect is negligible because of randomness. An example model of a painted aluminum plate is presented.     

Bidirectional reflectance distribution function of diffuse extreme ultraviolet scatterers and extreme ultraviolet baffle materials

Bidirectional reflectance distribution function (BRDF) measurements of a number of diffuse extreme ultraviolet (EUV) scatterers and EUV baffle materials have been performed with the Goddard EUV scatterometer. BRDF data are presented for white Spectralon SRS-99 at 121.6 nm; the data exhibit a non-Lambertian nature and a total hemispherical reflectance lower than 0.15. Data are also presented for an evaporated Cu black sample, a black Spectralon SRS-02 sample, and a Martin Optical Black sample at wavelengths of 58.4 and 121.6 nm and for angles of incidence of 15 degrees and 45 degrees. Overall Martin Optical Black exhibited the lowest BRDF characteristic, with a total hemispherical reflectance of the order of 0.01 and measured BRDF values as low as 2 x 10(-3) sr(-1).     

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.     

Comparison of two- and three-dimensional reconstruction methods in optical tomography

We present a three-dimensional (3D) image reconstruction scheme for optical near-infrared imaging of highly scattering material. The algorithm reconstructs the spatial distribution of the optical parameters of a volume Omega from transillumination measurements on the boundary of Omega. We test the performance of the method for a cylindrical object with embedded absorbing perturbation for a number of different source and detector arrangements. Furthermore, we investigate the effect of a mismatched reconstruction, using a two-dimensional (2D) reconstruction model to image a single plane of the object from 3D tomographic data obtained in a single plane. The motivation for the application of 2D models is their advantage in speed and memory requirements. We found that the difference in the measurement data between 2D and 3D models depends greatly on the measurement type used, giving a much better agreement for mean time-of-flight data than for dc intensity data. Image artifacts that are due to data model mismatches can therefore be significantly reduced by use of mean time data.     

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.     

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.     

Extreme ultraviolet scatterometer: design and capability

A scatterometer capable of plane-of-incidence bidirectional reflectance distribution function (BRDF) measurements at extreme ultraviolet wavelengths between 58.4 and 121.6 nm has been developed. This instrument has a lower measurement limit of approximately 10(-5) sr(-1), and it is able to accommodate angles of incidence between 10 degrees and 75 degrees . The scatterometer can measure scatter to within 1.5 degrees of the specular beam, and the scatter angle can be measured to within 0.1 degrees . The design, analysis, and performance of this instrument are discussed here. Scatter data, in the form of BRDF measurements, are presented for a 3000-line/mm grating and a flat chemical vapor deposited diamond sample.     

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.     

Emissivity Measurements on Metallic Surfaces with Various Degrees of Roughness: A Comparison of Laser Polarimetry and Integrating Sphere Reflectometry

Both integrating sphere reflectometry (ISR) as well as laser polarimetry have their advantages and limitations in their ability to determine the normal spectral emissivity of metallic samples. Laser polarimetry has been used for years to obtain normal spectral emissivity measurements on pulse-heated materials. The method is based on the Fresnel equations, which describe reflection and refraction at an ideally smooth interface between two isotropic media. However, polarimetry is frequently used with surfaces that clearly deviate from this ideal condition. Questions arise with respect to the applicability of the simple Fresnel equations to non-specular surfaces. On the other hand, reflectometry utilizing integrating spheres provides a measurement of the hemispherical spectral reflectance, from which the normal spectral emissivity can be derived. ISR provides data on spectral-normal-hemispherical reflectance and, hence, normal spectral emissivity for a variety of surfaces. However, the resulting errors are minimal when both the sample and the reference have a similar bidirectional reflectance distribution function (BRDF). In an effort to explore the limits of polarimetry in terms of surface roughness, room temperature measurements on the same samples with various degrees of roughness were performed using both ISR and a laser polarimeter. In this paper the two methods are briefly described and the results of the comparison are discussed.     

Bidirectional Reflectance Distribution Function of Rough Silicon Wafers

The trend towards miniaturization of patterning features in integrated circuits (IC) has made traditional batch furnaces inadequate for many processes. Rapid thermal processing (RTP) of silicon wafers has become more popular in recent years for IC manufacturing. Light-pipe radiation thermometry is the method of choice for real-time temperature monitoring in RTP. However, the radiation environment can greatly affect the signal reaching the radiometer. The bidirectional reflectance distribution function (BRDF) of rough silicon wafers is needed for the prediction of the reflected radiation that reaches the radiometer and for reflective RTP furnace design. This paper presents the BRDF measurement results for several processing wafers in the wavelength range from 400 to 1100 nm with the spectral tri-function automated reference reflectometer (STARR) at the National Institute of Standards and Technology (NIST). The rms roughness of these samples ranges from 1 nm to 1 m, as measured with an optical interferometric microscope. Correlations between the BRDF and surface parameters are obtained using different models by comparing theoretical predictions with experiments.     

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.     

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.     

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   

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.     

Laboratory-based bidirectional reflectance distribution functions of radiometric tarps

Laboratory-based bidirectional reflectance distribution functions (BRDFs) of radiometric tarp samples used in the vicarious calibration of Earth remote sensing satellite instruments are presented in this paper. The results illustrate the BRDF dependence on the orientation of the tarps' weft and warp threads. The study was performed using the GSFC scatterometer at incident zenith angles of 0 degrees, 10 degrees, and 30 degrees; scatter zenith angles from 0 degrees to 60 degrees; and scatter azimuth angles of 0 degrees, 45 degrees, 90 degrees, 135 degrees, and 180 degrees. The wavelengths were 485 nm, 550 nm, 633 nm, and 800 nm. The tarp's weft and warp dependence on BRDF is well defined at all measurement geometries and wavelengths. The BRDF difference can be as high as 8% at 0 degrees incident angle and 12% at 30 degrees incident angle. The fitted BRDF data show a very small discrepancy from the measured ones. New data on the forward and backscatter properties of radiometric tarps are reported. The backward scatter is well pronounced for the white samples. The black sample has well-pronounced forward scatter. The provided BRDF characterization of radiometric tarps is an excellent reference for anyone interested in using tarps for radiometric calibrations. The results are NIST traceable.     

Assessment of a bidirectional reflectance distribution correction of above-water and satellite water-leaving radiance in coastal waters

Water-leaving radiances, retrieved from in situ or satellite measurements, need to be corrected for the bidirectional properties of the measured light in order to standardize the data and make them comparable with each other. The current operational algorithm for the correction of bidirectional effects from the satellite ocean color data is optimized for typical oceanic waters. However, versions of bidirectional reflectance correction algorithms specifically tuned for typical coastal waters and other case 2 conditions are particularly needed to improve the overall quality of those data. In order to analyze the bidirectional reflectance distribution function (BRDF) of case 2 waters, a dataset of typical remote sensing reflectances was generated through radiative transfer simulations for a large range of viewing and illumination geometries. Based on this simulated dataset, a case 2 water focused remote sensing reflectance model is proposed to correct above-water and satellite water-leaving radiance data for bidirectional effects. The proposed model is first validated with a one year time series of in situ above-water measurements acquired by collocated multispectral and hyperspectral radiometers, which have different viewing geometries installed at the Long Island Sound Coastal Observatory (LISCO). Match-ups and intercomparisons performed on these concurrent measurements show that the proposed algorithm outperforms the algorithm currently in use at all wavelengths, with average improvement of 2.4% over the spectral range. LISCO's time series data have also been used to evaluate improvements in match-up comparisons of Moderate Resolution Imaging Spectroradiometer satellite data when the proposed BRDF correction is used in lieu of the current algorithm. It is shown that the discrepancies between coincident in-situ sea-based and satellite data decreased by 3.15% with the use of the proposed algorithm. This confirms the advantages of the proposed model over the current one, demonstrating the need for a specific case 2 water BRDF correction algorithm as well as the feasibility of enhancing performance of current and future satellite ocean color remote sensing missions for monitoring of typical coastal waters.     

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.     

Sensing polarization with variable coherence tomography

Variable coherence tomography (VCT) was recently developed by Baleine and Dogariu for the purpose of directly sensing the second-order statistical properties of a randomly scattering volume [J. Opt. Soc. Am. A21, 1917 (2004)]. In this paper we generalize the theory of VCT to include polarized inputs and anisotropic scatterers. In general the measurement of the scattered coherency matrix or Stokes vector is not adequate to describe the scattering, as these quantities depend on the coherence state of the incident beam. However, by controlling the polarized coherence properties of the source beam, VCT can be generalized to probe the polarimetric scattering properties of objects from a single-point Stokes vector or coherency matrix measurements. With polarized VCT, we are able to design a method that can measure analogous information to the polarimetric bidirectional reflection distribution function (BRDF), but do it from monostatic data. This capability would allow the BRDF to be measured remotely without having to adjust either the incident or observation angle with respect to the target.     

多角度测量系统实现室外BRDF测量

为了实现室外BRDF的准确测量,设计了多角度测量系统.测量系统包括一台自动测量架和两台ASD(Analytical Spectral Devices)公司生产的野外型光谱仪,光谱仪的光谱分辨率为3nm,一台光谱仪固定在测量架平台上测量目标各方向反射,另一台光谱仪放置在地面上同时测量漫反射板反射.应用该系统进行了室外草地的测量实验,测量整个周期(66个方向点)用时10min,测量主平面(间隔5°,共31个方向点)用时2.5min.测量结果显示目标的反射为非朗伯性,并在主平面的反射方向性最强烈.     

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions.