Image-based bidirectional reflectance distribution function measurement

We present a new image-based process for measuring a surface's bidirectional reflectance rapidly, completely, and accurately. Requiring only two cameras, a light source, and a test sample of known shape, our method generates densely spaced samples covering a large domain of illumination and reflection directions. We verified our measurements both by tests of internal consistency and by comparison against measurements made with a gonioreflectometer. The resulting data show accuracy rivaling that of custom-built dedicated instruments.     

Directional-hemispherical reflectance for spectralon by integration of its bidirectional reflectance

The directional-hemispherical reflectance is obtained for Spectralon, the material chosen for onboard radiometric calibration of the multiangle imaging spectroradiometer, at laser wavelengths of 442, 632.8, and 859.9 nm. With p- and s-polarized incident light and for an angle of incidence of 45 degrees , the bidirectional reflectance distribution function was measured over a polar angle range of 1-85 degrees and a range of azimuthal angles of 0-180 degrees in 10 degrees increments. The resultant directional-hemispherical reflectance is found by integration to be 1.00 ? 0.01 at 442 nm, 0.953 ? 0.01 at 632.8 nm, and 0.956 ? 0.01 at 859.9 nm. The experimental methodology and the data analysis are presented together with a full discussion of the primary experimental errors.     

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.     

Reflectometer for measuring the bidirectional reflectance of rough surfaces

A fully automatic, four-axis gonioreflectometer is described. It has an angular accuracy of 0.3 degrees and a range of 90 degrees in both the theta(i) and the theta(r) zenith angles. The gonioreflectometer is simpler than previous designs because of its use of rotating arms rather than moving carriages to mount the optical components. Where possible, commercial components have been used to reduce the cost. A novel off-axis angular encoding scheme is also described.     

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.     

Simple algorithm for the measurement of absorption coefficients of a two-layered medium by spatially resolved and time-resolved reflectance

An inversion procedure for the recovery of absorption coefficients of a two-layered semi-infinite diffusive medium by use of time-resolved reflectance measured at two different source-detector distances is proposed. The inversion procedure is based on the property of the photon diffusion equation; i.e., the solution of the diffusion equation for the time-resolved reflectance measured at a longer source--detector distance coincides with that measured at a shorter one by a proper temporal, spatial, and intensity transformation. This inversion procedure, used together with the results of one set of Monte Carlo simulations, is validated as working well when the values of the scattering coefficients of the two layers and the thickness of the first layer are within a range of interest in tissue optics.     

Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements

The objective is to estimate the Rayleigh limit in bidirectional reflectance distribution function (BRDF) measurements caused by air in the laboratory, the wavelength, and the path length of light in the receiver field of view. Moreover, we intend to show the trend for the reduction of this limit by introducing a medium with small refractive index and by using a longer wavelength. Although the BRDF typically describes the angular distribution of scattered light from surfaces, the expression describing the equivalent BRDF caused by the optical scattering from gas molecules in the optical path is derived through the use of the Rayleigh scattering theory. The instrumentation is described, and the experimental results of the equivalent BRDF caused by gas scattering from molecules in clear air, nitrogen, and helium gases are reported. These results confirm the trends of the prediction.     

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.     

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.     

地震动的空间变化特性分析与修正相干模型

利用空间地震动相关性描述度量如相关、相干函数分析地震动在局部尺度内的相关性随空间距离、频率的变化规律。在此基础上,基于随机场基本理论对Harichandran-Vanmarcke模型进行了修正,在原一维模型基础上考虑了空间的二维因素,并通过Smart-1台阵event-40记录给出了模型参数的具体取值。     

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.     

Nonstationary multivariate process modeling through spatially varying coregionalization

Models for the analysis of multivariate spatial data are receiving increased attention these days. In many applications it will be preferable to work with multivariate spatial processes to specify such models. A critical specification in providing these models is the cross covariance function. Constructive approaches for developing valid cross-covariance functions offer the most practical strategy for doing this. These approaches include separability, kernel convolution or moving average methods, and convolution of covariance functions. We review these approaches but take as our main focus the computationally manageable class referred to as the linear model of coregionalization (LMC). We introduce a fully Bayesian development of the LMC. We offer clarification of the connection between joint and conditional approaches to fitting such models including prior specifications. However, to substantially enhance the usefulness of such modelling we propose the notion of a spatially varying LMC (SVLMC) providing a very rich class of multivariate nonstationary processes with simple interpretation. We illustrate the use of our proposed SVLMC with application to more than 600 commercial property transactions in three quite different real estate markets, Chicago, Dallas and San Diego. Bivariate nonstationary process inodels are developed for income from and selling price of the property. The work of the first and second authors was supported in part by NIH grant R01ES07750-06.     

Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution.     

Rayleigh scattering limits for low-level bidirectional reflectance distribution function measurements: corrigendum.

In previous research [C. C. Asmail et al. Appl. Opt. 33, 6084-6091 (1994)] an estimate was given of the low-level bidirectional reflectance distribution function (BRDF) limit due to Rayleigh scattering from the air molecules within the detector field of view. Although the underlying model was correct, a fault in the derivation led to a conclusion that contains an erroneous angular factor. A cosine factor in the equivalent BRDF derived by Asmail et al. [Appl. Opt. 33, 6084-6091 (1994)], which was considered unphysical in that treatment, is incorrect and can obscure the correction in certain circumstances. The treatment below calculates the scattered flux from the gas molecules in the field of view and compares it with the flux scattered from a sample in the same incident beam.     

Model of remote-sensing reflectance including bidirectional effects for case 1 and case 2 waters

A remote-sensing reflectance model based on a lookup table is proposed for use in analyzing satellite ocean color data in both case 1 and case 2 waters. The model coefficients are tabulated for grid values of three angles--solar zenith, sensor zenith, and relative azimuth--to take account of directional variation. This model also requires, as input, a phase function parameter defined by the contribution of suspended particles to the backscattering coefficient. The model is generated from radiative transfer simulations for a wide range of inherent optical properties that cover both case 1 and 2 waters. The model uncertainty that is due to phase function variability is significantly reduced from that in conventional models. Bidirectional variation of reflectance is described and explained for a variety of cases. The effects of wind speed and cloud cover on bidirectional variation are also considered, including those for the fully overcast case in which angular variation can still be considerable (approximately 10%). The implications for seaborne validation of satellite-derived water-leaving reflectance are discussed.     

Optical properties (bidirectional reflectance distribution function) of shot fabric

To study the optical properties of materials, one needs a complete set of the angular distribution functions of surface scattering from the materials. Here we present a convenient method for collecting a large set of bidirectional reflectance distribution function (BRDF) samples in the hemispherical scattering space. Material samples are wrapped around a right-circular cylinder and irradiated by a parallel light source, and the scattered radiance is collected by a digital camera. We tilted the cylinder around its center to collect the BRDF samples outside the plane of incidence. This method can be used with materials that have isotropic and anisotropic scattering properties. We demonstrate this method in a detailed investigation of shot fabrics. The warps and the fillings of shot fabrics are dyed different colors so that the fabric appears to change color at different viewing angles. These color-changing characteristics are found to be related to the physical and geometrical structure of shot fabric. Our study reveals that the color-changing property of shot fabrics is due mainly to an occlusion effect.     

Calibration of spatially phase-shifted DSPI for measurement of large structures

We present a method for the calibration of a spatially phase-shifted digital speckle pattern interferometer (SPS-DSPI), which was designed and built for the purpose of testing the James Webb space telescope (JWST) optical structures and related technology development structures. The need to measure dynamic deformations of large, diffuse structures to nanometer accuracy at cryogenic temperature is paramount in the characterization of a large diameter space and terrestrial based telescopes. The techniques described herein apply to any situation, in which high accuracy measurement of diffuse structures are required. The calibration of the instrument is done using a single-crystal silicon gauge. The gauge has four islands of different heights that change in a predictable manner as a function of temperature. The SPS-DSPI is used to measure the relative piston between the islands as the temperature of the gauge is changed. The measurement results are then compared with the theoretical changes in the height of the gauge islands. The maximum deviation of the measured rate of change of the relative piston in nm/K from the expected value is 3.3%.     

复合材料表面双向反射分布函数实验研究

为研究泡沫铝、铝基石墨纤维、镁基石墨纤维和碳纤维铝等特种复合材料的表面红外辐射及散射特性,测量了其表面双向反射分布函数(BRDF)值.利用自行研制的双向反射分布函数(BRDF)测试台,分别在0.6328、1.34、3.39 μm波段下,测量了上述材料在不同入射角下的表面双向反射分布函数值.实验结果表明:各种复合材料表面在可见光(0.6328 μm)波段的BRDF值分布在O.3区域内,且多呈镜反射状态;而在近中红外(1.34 μm和3.39 μm)波段的BRDF值分布在0.08区域内,呈现出一定的漫反射特征,且分布强度比可见光波段低很多,反映出各表面对各波段的吸收率不同.