Bidirectional Reflectance Distribution Function Values Research Articles

A modified version of BRDF model based on Kubelka-Munk theory for coating materials

The bidirectional reflectance distribution function (BRDF) can characterize the general optical property of object’s surface. The conventional BRDF model that a Lambertian constant volume scattering consideration has the limitation for the description of scattering characteristic of coating materials. Thus, a modified version of BRDF model is presented for coating materials with considering specular reflection and volume scattering based on the combination of the microfacet and Kubelka-Munk (K–M) theory. In this model, a mirror parameter, related to the surface roughness and reflectance, is introduced to adjust this model, and the volume scattering component is modeled following the K–M theory to make this new BRDF model more correspondence with physical interpretation. The simulation and measurement results for three kinds of coating samples show that the BRDF values simulated by the modified BRDF model are found in a good agreement with the measurements, and the model presented in this paper can improve the modeling accuracy effectively, which provides the theoretical support for remote sensing.

Fast Defect Inspection Based on Data-Driven Photometric Stereo

Fast inspection of a defect is a challenging task in mass production of curved surfaces, and photometric stereo (PS) utilizing multiple images from a single camera under a number of different illumination directions is a promising technique for this task due to its high sensitivity to surface normal perturbations. This paper adapts conventional PS and extends the technique to the inspection of non-Lambertian surfaces with high accuracy and efficiency. A data-driven PS is presented by establishing the Gaussian process (GP) model to represent the nonlinear reflectance behavior of various materials based on measured reflectance data sets. With the trained GP model, the surface normal can be estimated in two steps: prediction of bidirectional reflectance distribution function values under different light directions and the subsequent least-squares estimation of a surface normal. Comparison tests with other algorithms on the Mitsubishi Electric Research Laboratories data set and real workpieces with non-Lambertian materials show the superior accuracy and efficiency of the proposed method in surface normal estimation. After the surface normal of the workpiece is recovered, the defects can be detected by filtering out the perturbation of the surface normal. Experiments on steel and glossy polyester workpieces validate the efficacy of the proposed approach in detecting defects on curved non-Lambertian surfaces.

Modeling of radiation transport in coupled atmosphere-snow-ice-ocean systems

A radiative transfer model for coupled atmosphere-snow-ice-ocean systems (CASIO-DISORT) is used to develop accurate and efficient tools for computing the bidirectional reflectance distribution function (BRDF) of sea ice for a wide range of situations occurring in nature. These tools include a method to generate sea ice inherent optical properties (IOPs: single-scattering albedo, extinction optical depth, and scattering asymmetry parameter) for any wavelength between 300 and 4000 nm as a function of sea ice physical parameters including real and imaginary parts of the sea ice refractive index, brine pocket concentration and effective brine pocket size, air bubble concentration and effective air bubble size, volume fraction of ice impurities and impurity absorption coefficient, and sea ice thickness. The CASIO-DISORT code was used to compute look-up tables (LUTs) of the Fourier expansion coefficients of the BRDF as a function of angles of illumination and observation, sea ice IOPs, and ocean albedo. By interpolation in the LUTs one efficiently obtains accurate BRDF values. To include snow on the ice we modified DISORT2 to accept Fourier expansion coefficients for the BDRF as input instead of the BRDF itself, thereby reducing the computation time by a factor of about 60. The BRDF computed by CASIO-DISORT or retrieved from the LUTs applies to diffuse light only. To remedy this shortcoming we added a specular Gaussian beam component to the new BRDF tool and verified that it works well for BRDFs for bare and snow-covered sea ice.

Conspicuity tape for enhanced laser range finding

The signal from a laser range finder is greatly enhanced by attaching a retroreflector to the target. Low-cost, lightweight retroreflectors can be fabricated from conspicuity tape. This work reports the near-infrared retroreflection characteristics of conspicuity tape from bidirectional reflectance distribution function (BRDF) measurements at 904 nm. BRDF values approach 500 sr^-1 at near normal incidence. The BRDF test results are applied to predict the performance of alternate lightweight retroreflector designs suitable for tracking small helium balloons. The combination of a range finder and retroreflecting balloon enable a low-cost, high-performance method for wind profiling.

High-accuracy measurements of snow Bidirectional Reflectance Distribution Function at visible and NIR wavelengths – comparison with modelling results

Abstract. High-accuracy measurements of snow Bidirectional Reflectance Distribution Function (BRDF) were performed for four natural snow samples with a spectrogonio-radiometer in the 500–2600 nm wavelength range. These measurements are one of the first sets of direct snow BRDF values over a wide range of lighting and viewing geometry. They were compared to BRDF calculated with two optical models. Variations of the snow anisotropy factor with lighting geometry, wavelength and snow physical properties were investigated. Results show that at wavelengths with small penetration depth, scattering mainly occurs in the very top layers and the anisotropy factor is controlled by the phase function. In this condition, forward scattering peak or double scattering peak is observed. In contrast at shorter wavelengths, the penetration of the radiation is much deeper and the number of scattering events increases. The anisotropy factor is thus nearly constant and decreases at grazing observation angles. The whole dataset is available on demand from the corresponding author.

Model and analysis of spectropolarimetric BRDF of painted target based on GA-LM method

Models based on microfacet were used to describe spectropolarimetric BRDF (short for bidirectional reflectance distribution function) with experimental data. And the spectropolarimetric BRDF values of targets were measured with the comparison to the standard whiteboard, which was considered as Lambert and had a uniform reflectance rate up to 98% at arbitrary angle of view. And then the relationships between measured spectropolarimetric BRDF values and the angles of view, as well as wavelengths which were in a range of 400-720 nm were analyzed in details. The initial value needed to be input to the LM optimization method was difficult to get and greatly impacted the results. Therefore, optimization approach which combines genetic algorithm and Levenberg-Marquardt (LM) was utilized aiming to retrieve parameters of nonlinear models, and the initial values were obtained using GA approach. Simulated experiments were used to test the efficiency of the adopted optimization method. And the simulated experiment ensures the optimization method to have a good performance and be able to retrieve the parameters of nonlinear model efficiently. The correctness of the models was validated by real outdoor sampled data. The parameters of DoP model retrieved are the refraction index of measured targets. The refraction index of the same color painted target but with different materials was also obtained. Conclusion has been drawn that the refraction index from these two targets are very near and this slight difference could be understood by the difference in the conditions of paint targets' surface, not the material of the targets.

Impact of cloud inhomogeneity on bi-directional reflectance

This paper uses SHDOM (Spherical Harmonics Discrete Ordinate Method) to calculate the nadir bidirectional reflectance distribution function (BRDF) of the cumulus and stratocumulus fields at the wavelengths of 0.67 μm and 2.13 μm, and discusses the impact of cloud inhomogeneity on BRDF. The cloud fields are adopted from I3RC Phase II, which are used to compare 3D radiative transfer models. The simulation results show that the cu field has 6% abnormal BRDF values (BRDF>1) with the increase of solar zenith angle. Further analyses show that grid cells whose BRDF is greater than one gather together at the local trough of the top of cloud. These regions can receive not only the direct incident solar beam, but also the beam scattered by the higher cloud of its neighborhood. Hence, the BRDF of those regions is enhanced. The abnormal BRDF phenomenon shows that the cloud inhomogeneity can result in inconsistency between satellite observation and plane parallel theory, implying that the reflectance observed by high resolution satellite is maybe enhanced by the cloud 3D effects. Thus one should take this fact into account when using the product retrieved by these data. The dominant solar zenith angles are quite large in the mid-high altitude area, and the impact of cloud inhomogeneity on these areas may be more significant.

Modelling the bidirectional reflectance distribution function (BRDF) of seawater polluted by an oil film

The Bi-directional Reflectance Distribution Function (BRDF) of both clean seawaters and those polluted with oil film was determined using the Monte Carlo radiative transfer technique in which the spectrum of complex refractive index of Romashkino crude oil and the optical properties of case II water for chosen wavelengths was considered. The BRDF values were recorded for 1836 solid angular sectors of throughout the upper hemisphere. The visibility of areas polluted with oil observed from various directions and for various wavelengths is discussed.

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).

Scattering by random particles on optical surfaces

An analytical technique has been developed for calculating the angle-resolved light scattering by contaminant particles on smooth opaque surfaces. The analytical method was tested by a comparison of measured and calculated bidirectional reflectance distribution function (BRDF) values for contaminated surfaces. BRDF values were calculated from particle sizes, shapes, and areal densities obtained from scanning electron microscope images of the contaminated surfaces by a Princeton gamma-tech image analyzer. Measured and calculated BRDF values agreed to within the uncertainty associated with the particle characterization process for most scattering angles.

Uncertainties in radiance calibrations of backscatter ultraviolet (BUV) instruments

Traditional radiance calibrations of solar backscatter ultraviolet (SBUV) instruments require a measurement of the bidirectional-reflectance distribution function (BRDF) of a flat-plate diffuser. To date the BRDF of the diffusers used for calibrating the Shuttle-borne SBUV instrument (SSBUV), has relied on an initial measurement of a sample plate coated with BaSO4 made by the National Institutes of Standards and Technology (NIST). Changes in the reflectance of the calibration diffusers were tracked over time with measurements of their total hemispherical reflectance. Preliminary comparisons of direct measurements of the BRDF using a new facility at the NASA/Goddard Space Flight Center, inferred BRDF values using an integrating sphere, and the NIST-based values, show significant inconsistencies. In general, direct measurements of BRDF values compare to within 1% of those inferred from integrating sphere measurements. However, these values differ from the NIST-based values by about 6%. These differences and their uncertainties are discussed. The results imply that SSBUV-measured vertical ozone profile values have an altitude-dependent error of between 3% and -12%, but there should be little effect on the measured total ozone values.

Prediction of the bidirectional reflectance-distribution function from atomic-force and scanning–tunneling microscope measurements of interfacial roughness

Computer codes that are based on Elson's theory for light scattering by interfacial roughness in multilayer coatings were used to predict the bidirectional reflectance-distribution function (BRDF) of several opaque coatings from surface-roughness profiles measured by either a scanning-tunneling microscope or an atomic-force microscope. The predictions usually agreed with measured BRDF values to within a factor of 2. The coatings consisted of single layers of Ag or Ni and dielectric stacks with up to three layers.

Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil

An analytical model of the bidirectional reflectance for optically semi‐infinite plant canopies has been extended to describe the reflectance of finite depth canopies with contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten‐parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single‐scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near‐infrared. Sensitivity tests were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single‐scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (> 2.5) these shifted to the two scattering phase function parameters for vegetation and the single‐scattering albedo of the vegetation. The three‐parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten‐parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting retrieved parameters and BRDFs are similar to those for the full sampling geometry, suggesting that the limited geometry of AVHRR measurements might be used to reliably retrieve BRDF and canopy albedo with this model.

Bidirectional reflectance and specularity of twelve spacecraft thermal control materials

Many spacecraft external payloads are sensitive to focused solar heating caused by specular reflections from exterior thermal control surfaces. This paper presents a method of calculating specularity using bidirectional reflectance distribution function (BRDF) input. Definitions are presented for directional and hemispherical specularity as a function of the conical half-angle surrounding the specular ray. Measured BRDF data are presented for commonly used thermal control materials including plastic films and paints. Angles of incidence range from 5 to 78 deg and data are taken both in and out of the plane of incidence. Most measurements are made at a wavelength of 0.488 /urn, though measurements for two white paints are also made at 1.06, 3.39, and 10.63 ftm. The BRDF values are found to increase with both angle of incidence and wavelength. A numerical code is described that integrates BRDF data to yield both directional and hemispherical specularity as a function of cone half-angle around the specular ray. Specularity results are presented for all 12 materials studied.

Scattering characteristics of Martin Black at 118 μm

BRDF (bidirectional reflectance distribution function) values for 0.000118 m radiation at different angles of incidence and different scattering angles from the Infrared Astronomical Satellite telescope baffle coated with Martin Black are presented. Data from scatterometer experiments are collected and the BRDF and beta - beta sub 0 (sin theta sub s - sin theta sub 0) values are calculated based on the geometry, the voltage readings, the attenuators in the beam, and the calculated reference levels. A composite curve of forward and backward scattering data for several angles of incidence shows a peak near the specular direction (beta - beta sub 0 = 0), which is the instrument profile reduced by the 20% specular reflection of the Martin Black. The nonspecular part of the reflectivity indicates the slightly specular but largely Lambertian character of the coating. Data for the specular reflectivity as a function of the incidence angle unexpectedly shows a decrease in the specular reflectance with increasing angle of incidence.