Bidirectional Reflectance Distribution Function Measurements Research Articles

MSL goniospectrophotometer measurement model

Measurements of both hemispherical reflectance and the bidirectional reflectance distribution function (BRDF) are of interest to a wide range of industries including computer graphics, remote sensing, lighting design, and cosmetics. The scale of directional reflectance is often realised at national metrology institutes using goniospectrophotometers, and by integrating BRDF measurements made over the hemisphere, the scale of hemispherical reflectance can also be realised. This paper describes the measurement model for BRDF and hemispherical reflectance using the MSL goniospectrophotometer, which uses rotation stages to adjust the angle of the sample. The measurement model is applied to measurements of a white Spectralon sample and a white ceramic tile to demonstrate the performance of the instrument. The relative standard uncertainty in the BRDF of a white Spectralon sample at 550 nm is less than 0.1% for in-plane measurements, while the relative standard uncertainty in the hemispherical reflectance of a white Spectralon sample at 560 nm is 0.27%.

Effect of beryllium topography on BRDF measurements

The Bidirectional Reflectance Distribution Function (BRDF) of beryllium is important for a ray-tracing simulation to evaluate the effect of reflected light on optical diagnostics in the fusion device ITER. However, the BRDF for beryllium has not been investigated yet and is currently lacking. To fill this gap, this study measured BRDFs of beryllium specimens with different topographies using goniophotometers and optimized optical reflection models. Additionally, various surface topographic parameters were computed, and their correlation with parameters for the optical reflection models was explored. As a result, it was found that topographic parameters related to slope offer a certain correlation with the parameters of the reflection model. This can be useful for determining the optical reflection properties of materials for which direct BRDF measurements are not possible.

Design of an image-based BRDF measurement method using a catadioptric multispectral capture and a real-time Lambert calibration.

By utilizing a catadioptric system and a calibration Lambertian sample, a compact measurement method of bidirectional reflectance distribution function (BRDF) has been proposed for rapid and accurate measurement. With the help of an ellipsoidal dome mirror, a hyperboloid mirror, and a high-resolution camera, spatial reflectance distributions from reflected directions with a large field of view (FOV) can be obtained. The built-in Lambertian standard allows for real-time calibration to account for fluctuations in the illumination spectrum, effectively reducing the measurement drift and achieving a high accuracy. Moreover, a multispectral camera captures images at 8 spectral bands for accurate spectral color reconstruction from different directions. To verify the method, a prototype capable of fast, high-resolution measurements with a large FOV has been developed for characterizing the scattering properties of objects. It achieves a measured angular range up to 160°. Multispectral BRDF data for each sample can be obtained within 5 minutes with an angular resolution of less than 0.6°. Eight ceramic samples with different colors were selected for the verification of measurement accuracy, and their mean relative bias of BRDF measurement was found to be as low as 2.5%.

The Method of Multi-Angle Remote Sensing Observation Based on Unmanned Aerial Vehicles and the Validation of BRDF

The measurement of bidirectional reflectivity for ground-based objects is a highly intricate task, with significant limitations in the capabilities of both ground-based and satellite-based observations from multiple viewpoints. In recent years, unmanned aerial vehicles (UAVs) have emerged as a novel remote sensing method, offering convenience and cost-effectiveness while enabling multi-view observations. This study devised a polygonal flight path along the hemisphere to achieve bidirectional reflectance distribution function (BRDF) measurements for large zenith angles and all azimuth angles. By employing photogrammetry’s principle of aerial triangulation, accurate observation angles were restored, and the geometric structure of “sun-object-view” was constructed. Furthermore, three BRDF models (M_Walthall, RPV, RTLSR) were compared and evaluated at the UAV scale in terms of fitting quality, shape structure, and reflectance errors to assess their inversion performance. The results demonstrated that the RPV model exhibited superior inversion performance followed, by M_Walthall; however, RTLST performed comparatively poorly. Notably, the M_Walthall model excelled in capturing smooth terrain object characteristics while RPV proved applicable to various types of rough terrain objects with multi-scale applicability for both UAVs and satellites. These methods and findings are crucial for an extensive exploration into the bidirectional reflectivity properties of ground-based objects, and provide an essential technical procedure for studying various ground-based objects’ in-plane reflection properties.

Acquisition and Application of Reflectance for Computer-Generated Images

In the field of computer graphics, accurate representation of material properties is crucial for rendering realistic imagery. This paper focuses on the bidirectional reflectance distribution function (BRDF) and its role in determining how materials interact with light. The authors review the state of the art in reflectance measurement systems, with a focus on BRDF and bidirectional texture function (BTF) measurement. They discuss practical limitations in measuring multi-dimensional functions and provide examples of how researchers have addressed these challenges. Additionally, they analyse various approaches to converting measured data into practical analytical functions for use in commercial rendering software, including data-driven methods such as neural networks and hybridized approaches.

Infrared BRDF measurement based on projection reconstruction with attenuated aperture filter effects

The Bidirectional Reflectance Distribution Function (BRDF) is a basic function that describes the spatial reflectivity of an opaque surface. Existing BRDF measurements are related to the size of the detector aperture because the values are not the true BRDF but an average over the aperture, and high spatial resolution and high SNR cannot be achieved simultaneously. In addition, the detection positions of the aperture cannot perfectly cover the entire hemisphere, and the measurement is not complete. In this paper, BRDF measurements were combined with projection reconstruction, and the mapping between the detected signals and the BRDF over a discrete hemispherical mesh was constructed. The spatial resolution of the reconstruction was the same as that of the discrete mesh, rather than the aperture size, and the aperture filter effect was attenuated. Simulations and a frosted gold plate measurement experiment were performed to verify the effectiveness of the proposed reconstruction method.

High Accuracy Solar Diffuser BRDF Measurement for On-Board Calibration in the Solar Reflective Band

In the solar reflective band, an on-board calibration method based on a solar diffuser (SD) can realize full aperture, full field of view, and end-to-end absolute radiometric calibration of optical remote sensors. The SD’s bidirectional reflectance distribution function (BRDF) is a key parameter that affects the accuracy of the on-board calibration. High-accuracy measurement of the SD BRDF is required in the laboratory before launch. Due to the uncertainty of the goniometer system, polarization effects, and other factors, the measurement uncertainty of the SD BRDF at large incident angles is much higher than that at a 0° incident zenith angle and 45° reflection zenith angle. In this paper, an absolute BRDF measurement facility is reported. The goniometric system consists of a high-brightness integrating sphere as a radiation source, a six-axis robot arm, and a large rotation stage. The measurement wavelength range was from 350 nm to 2400 nm. An improved data processing method based on the reciprocity theorem was proposed to reduce the measurement uncertainty of the SD BRDF at large incident angles. At an incident zenith angle of 75°, the improved data processing method reduced the measurement uncertainty of the SD BRDF by 52% at 410 nm to 480 nm, by 70% at 480 nm to 1000 nm, and by 20% at other bands compared to the absolute measurement method. The influence of the radiation source, goniometer system, detection system, and other factors on the measurement uncertainty are analyzed in this paper. The results show that the measurement uncertainty (coverage factor k = 2) of the SD BRDF was better than 1.04% at 350 nm to 410 nm, 0.60% at 410 nm to 480 nm, 0.43% at 480 nm to 1000 nm, and 0.86% at 1000 nm to 2400 nm.

Goniometer in the air: Enabling BRDF measurement of crop canopies using a cable-suspended plant phenotyping platform

The Bidirectional Reflectance Distribution Function (BRDF) quantifies the distribution of the spectral reflectance of a target surface at various viewing and illumination angles. In-field measurement of the BRDF of vegetation canopies improves the characterization of off-nadir measurements and informs radiative transfer models of canopy reflectance, where the Lambertian assumption does not hold. However, current field goniometers are unable to measure BRDF efficiently, especially for tall vegetation across the growing season because of the limitations of clearance, field accessibility, and flexibility of the sensor field of view. In this study, we explored the potential of using a large-scale cable-suspended field phenotyping system to quantify BRDF of the canopy reflectance at selected bands and Vegetation Indices (VIs) of maize and soybean canopies. The system performance benefited from the following conditions: no crop damage, full-season field accessibility of tall canopies, automatic measurement, and accurate positioning. Correlation analysis shows that a strong correlation exists among the reflectance, VIs, and the Green Pixel Fraction. The hemispheric distributions of the spectral reflectance at selected bands and VIs were quantified at multiple dates. Hot spots were observed in the backscatter direction at visible and near-infrared (NIR) bands at the largest sensor zenith angle around the Solar Principal Plane (SPP). In contrast, cold spots of the Normalized Difference Vegetation Index (NDVI) and its related VIs were observed in the backscatter direction around solar zenith angles. The row effect was found for the maize canopy at the NIR band and the Near-infrared reflectance of vegetation (NIRv). NDVI had the lowest anisotropy index values among investigated bands and VIs. This system could be further leveraged to generate rapid and detailed BRDF data at a high spatiotemporal resolution using multiple sensors.

Intercomparison of bidirectional reflectance distribution function measurements at in- and out-of-plane geometries.

In recent years, there has been a growing interest in the measurements of the bidirectional reflectance distribution function (BRDF) in industry and research and development. However, there is currently no dedicated key comparison to demonstrate the scale conformity. To date, scale conformity has been proved only for classical in-plane geometries, in comparisons between different national metrology institutes (NMIs) and designated institutes (DIs). This study aims at expanding that with nonclassical geometries, including, for the first time, to the best of our knowledge, two out-of-plane geometries. A total of four NMIs and two DIs participated in a scale comparison of the BRDF measurements of three achromatic samples at 550 nm in five measurement geometries. The realization of the scale of BRDF is a well-understood procedure, as explained in this paper, but the comparison of the measured values presents slight inconsistencies in some geometries, most likely due to the underestimation of measurement uncertainties. This underestimation was revealed and indirectly quantified using the Mandel-Paule method, which provides the interlaboratory uncertainty. The results from the presented comparison allow the present state of the BRDF scale realization to be evaluated, not only for classical in-plane geometries, but also for out-of-plane geometries.

Refractive index inversion method for metals based on circular polarization detection of light

Among many optical detection methods, the polarization detection method of light has been proven to be capable of providing outstanding, even unique sometimes, information of targets under test, this includes detecting objects that are difficult to be distinguished by the light intensity or spectrum information alone. However, as for materials identification, the current polarization detection method which usually uses linearly polarized light can only roughly distinguish metallic materials from non-metallic materials but cannot further differentiate among types of metallic materials. Note that the phase of a linearly polarized light may change after being reflected by a metal due to its complex refractive index, and the circular polarization information of the reflected light can be used to sense the phase change property of the metal, therefore, different types of metallic materials can be identified according to their characteristic circular polarization information due to their diverse complex refractive indices. In this paper, based on the circular polarization detection of light, a complex refractive index inversion method for metals is proposed accordingly, and experimental measurements and fitting estimations are carried out for different types of metallic materials using a Bidirectional Reflectance Distribution Function (BRDF) measurement equipment. The experimental results show that the method can accurately invert the complex refractive indices of different metals and distinguish different types of metal samples. Compared to the Mueller-matrix-based measurement method, the proposed method is computationally simple, needless of measuring a large number of parameters and performing complex calculations, it only needs to invert the results of twice measurements. In addition, it also has the advantages of high sensitivity, good stability and intuitive algorithm, which are valuable for identification applications of metallic materials.

Multistatic fiber-based system for measuring the Mueller matrix bidirectional reflectance distribution function.

Bidirectionality effects can be a significant confounding factor when measuring hyperspectral reflectance data. The bidirectional reflectance distribution function (BRDF) can effectively characterize the reflectivity of surfaces to correct remote sensing measurements. However, measuring BRDFs can be time-consuming, especially when collecting Mueller matrix BRDF (mmBRDF) measurements of a surface via conventional goniometric techniques. In this paper, we present a system for collecting mmBRDF measurements using static optical fiber detectors that sample the hemisphere surrounding an object. The entrance to each fiber contains a polarization state analyzer configuration, allowing for the simultaneous acquisition of the Stokes vector intensity components at many altitudinal and azimuthal viewing positions. We describe the setup, calibration, and data processing used for this system and present its performance as applied to mmBRDF measurements of a ground glass diffuser.

Passive Terahertz Non-Line-of-Sight Imaging

We demonstrate the capability of the THz frequency (submillimeter wavelength) band to perform nonline-of-sight imaging by reflection from common rough surfaces. Active bidirectional reflectance distribution function measurements at 336 GHz show that surface roughness affects the strength, but not the width, of a specularly reflected beam of submillimeter-wavelength light. Uncooled passive direct-detection receivers built using high-frequency InP transistor technology achieve noise-equivalent temperature differences (NETD) ≤ 33 mK. One and two-dimensional, scanned single-pixel images made using such a passive receiver show that determination of the location, orientation, and pose of human targets can easily be made on surfaces whose specular component of reflectance is as low as 8%, without any algorithmic assistance. With such low instrumental NETD levels, the radiometric component of image quality is dominated by real fluctuations in the radiometric temperature of ordinary indoor backgrounds.

Measuring BRDF for curved surfaces based on parabolic reflection

In this study, we introduce a measurement method for the bidirectional reflectance distribution function (BRDF) for curved surfaces. Nearly all BRDF measurements assume that the target surface is planar. This is because if the object is non-planar, the reflection angle changes from position to position, making accurate measurement impossible. However, most real objects are curved. We have overcome this problem by applying the paraboloid reflection principle. If the curved target surface is a paraboloid, the light focused on its focal point is reflected as parallel light, as in a parabolic antenna. The BRDF can be measured as the deviation angle from this parallel light direction. Here, we demonstrate that this can significantly improve the BRDF measurement accuracy for curved surfaces.

BRDF LABORATORY MEASUREMENTS USING A CAMERA-AIDED SPECTRORADIOMETER

Abstract. Numerous natural surfaces observed using Remote Sensing do not reflect light as Lambertian surfaces. Instead, their reflection is highly dependent on two main directions: the direction of the light source and the observation viewing angle, which characterize the Bidirectional Reflectance Distribution Function (BRDF). The BRDF is one of the challenging main effects of remote sensing. Thus, studying the BRDF of various land cover surfaces is essential, and researchers invest many efforts to fulfill this objective. However, measuring the BRDF is tricky and requires unique instruments, e.g., the Gonioreflectometer. Unfortunately, the availability of such instruments is deficient, and they are costly and hard to maintain. Considering these limitations, we present a study and a new approach for measuring the BRDF of surfaces with a camera-aided spectroradiometer that simultaneously acquires an RGB image from the sensor location beside the spectral measurement. Then, we feed the Structure From Motion (SFM) process with the RGM images to retrieve the sensor locations. Next, we convert the sensor locations into the quantities needed for the BRDF measurement, i.e., zenith angles and distances relative to the measured sample. Finally, we apply a set of measurements under controlled conditions in a dark room designed for hyperspectral remote sensing studies to evaluate the proposed methodology. In particular, we experimented with three different material surfaces. The results clearly show the highly accurate sensor position derived by SFM, providing zenith angles and distance from the scene’s center with mean errors around one degree and 2.5 centimeters, respectively. In addition, the obtained spectra tell that the proposed approach is suitable for multiangular measurements of reflected light and studying the BRDF.

IMAGE-BASED BRDF MEASUREMENT

Abstract. One of the most challenging effects of remote sensing is landcover materials' Bidirectional Reflectance Distribution Function (BRDF). A wide range of approaches and measuring methods address the BRDF in various studies. However, there is a requirement for an accurate measurement setup and costly special equipment. Furthermore, the measurements and calculations are applied to model the BRDF for a single point on the object's surface. Considering these limitations, we propose a new modular framework and methodology for measuring, modeling, and analyzing the BRDF without the need for unique instruments. Instead, we suggest acquiring multiple overlapping images in a simple and time-saving way, sampling the desired object's Region Of Interest (ROI) in one image and automatically tracking it in the other images. Experimental results using laboratory data acquired under controlled conditions clearly show the advantages of our framework in retrieving the camera positions, tracking ROIs in the different images, and accurately measuring the BRDF of various land-cover types. Moreover, we observed the variability of the obtained measurements before and after applying the kernel-driven approach to minimize the BRDF effect. The results show that the applied correction reduces this variability significantly, indicating the high accuracy of measuring the directional reflectance using the proposed approach.

A new snow bidirectional reflectance distribution function model in spectral regions from UV to SWIR: Model development and application to ground-based, aircraft and satellite observations

A generalized and flexible snow Bidirectional Reflectance Distribution Function (BRDF) model is proposed to describe the snow anisotropic properties in the spectral ranges from UltraViolet (UV) to Short-Wave InfraRed (SWIR). The new development belongs to the Fast and Accurate Semi-analytical Model of Atmosphere-surface Reflectance (FASMAR) family. FASMAR is developed, applied to and validated by ground-, aircraft- and satellite observations. FASMAR is a kernel-driven BRDF model. It contains four major kernels: isotropy kernel, asymptotic radiative transfer kernel, single-scattering kernel, and auxiliary kernels. These kernels enable FASMAR to characterize the angular-dependent scattering features and wavelength-dependent absorbing patterns of the snow BRDF properties. The comparison between FASMAR and RossThick-LiSparseReciprocal-Snow (RTLSRS) model were performed using radiative transfer simulations, ground-, aircraft- and satellite observations at selected wavelengths 380, 480, 670, 870, 1220, and 2200 nm. For Solar Zenith Angle (SZA) smaller than 70°, FASMAR shows somehow better accuracy compared to the RTLSRS model. FASMAR’s accuracy keeps quite stable for large SZAs (SZA larger than 70°). The relative difference between FASMAR calculations and radiative transfer simulations is within 5% for wavelengths between 380 and 2200 nm. A similar accuracy of FASMAR is observed compared to aircraft BRDF measurements, with a relative difference of less than 5%. FASMAR also shows good agreement with ground-based and satellite observations, with correlation coefficients larger than 0.9 and relative errors smaller than 2% for UV–vis and 4% for NIR-SWIR spectral ranges. The comparisons additionally reveal that the accuracy of FASMAR is not strongly affected by the a priori knowledge of the snow grain size. FASMAR can provide snow BRDF estimation with good accuracy in spectral regions from UV to SWIR under all observation/illumination geometries. FASMAR is used support the operational retrieval of the snow properties from satellite observations.

Bidirectional Reflectance Distribution Function (BRDF)-Based Coarseness Prediction of Textured Metal Surface

Because coarseness has a remarkable effect on visual appearance, there has been an increasing demand for measuring quantitative coarseness based on an explicit algorithm, especially in industry. However, even in BYK-mac, a reliable measurement device for high correlation with visual inspection, its results are not clearly defined and not traceable to international standards. In addition, previous studies requiring a captured image of a sample that is sensitive to capturing conditions are not appropriate to apply to industrial sites. Therefore, in this paper, a novel method for predicting coarseness by measuring only the color and the bidirectional reflectance distribution function (BRDF) is presented. The proposed method generates images using illumination optical analysis by applying the BRDF, which is insensitive to the capturing conditions, so it can be reliably applied to industrial sites with various measurement disturbances. The proposed coarseness prediction workflow was verified based on a comparison of the predicted coarseness values of 56 samples with seven levels of roughness for each of the eight colors and the measured values using BYK-mac. Images generated from illumination optical analysis through BRDF of the prepared sample showed lower brightness on the rougher surface, similar to the BRDF measurement results. The results of the measurement and comparison show that the coarseness orders for each color are similar to each other and that the coarseness variations according to roughness levels are also similar, with a coefficient of determination, R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , of 0.9374.

NeRFactor

We address the problem of recovering the shape and spatially-varying reflectance of an object from multi-view images (and their camera poses) of an object illuminated by one unknown lighting condition. This enables the rendering of novel views of the object under arbitrary environment lighting and editing of the object's material properties. The key to our approach, which we call Neural Radiance Factorization (NeRFactor), is to distill the volumetric geometry of a Neural Radiance Field (NeRF) [Mildenhall et al. 2020] representation of the object into a surface representation and then jointly refine the geometry while solving for the spatially-varying reflectance and environment lighting. Specifically, NeRFactor recovers 3D neural fields of surface normals, light visibility, albedo, and Bidirectional Reflectance Distribution Functions (BRDFs) without any supervision, using only a re-rendering loss, simple smoothness priors, and a data-driven BRDF prior learned from real-world BRDF measurements. By explicitly modeling light visibility, NeRFactor is able to separate shadows from albedo and synthesize realistic soft or hard shadows under arbitrary lighting conditions. NeRFactor is able to recover convincing 3D models for free-viewpoint relighting in this challenging and underconstrained capture setup for both synthetic and real scenes. Qualitative and quantitative experiments show that NeRFactor outperforms classic and deep learning-based state of the art across various tasks. Our videos, code, and data are available at people.csail.mit.edu/xiuming/projects/nerfactor/.

Uncertainty analysis for CCD-augmented CASI® BRDF measurement system

This work presents a measurement uncertainty analysis for a system designed to simultaneously capture specular in-plane and out-of-plane bidirectional reflectance distribution function (BRDF) data with high spatial resolution by augmenting the Complete Angle Scatter Instrument (CASI®) with a charge-coupled device (CCD) camera. Various scatter flux, incident flux, scatter angle, and detector solid angle uncertainty contributions are considered and evaluated based on imperfectly known system parameters. In particular, incident flux temporal fluctuation, detector noise and non-linearity, and out-of-plane aperture misalignment considerations each require significant adjustment from original CASI® uncertainty analysis, and expressions for neutral density (ND) filter, scatter angle, and solid angle uncertainties each require new formulations. Ultimately, ND filter uncertainty produces the largest contribution for the augmented system—at least when using unrefined worst-case tolerances—followed by solid angle uncertainty and pixel non-linearity. Total BRDF uncertainty and its contributing terms are compiled for several measurement scenarios, and compared with those from original analyses for single-pixel detectors. In particular, when ND filter uncertainty can be ignored or mitigated, total BRDF uncertainty values are comparable to those for the original system.

Data-driven algorithm to classify the degree of isotropy in the bidirectional reflectance distribution function

The bidirectional reflectance distribution function (BRDF) is used to describe reflectances of materials by calculating the ratio of the reflected radiance to the incident irradiance. While it was found that the isotropic models maintained symmetry about ϕs = π, such symmetry was not maintained about the θs = θi axis, except for close to the specular peak. This led to the development of a data-driven metric for how isotropic a BRDF measurement is. Research efforts centered around developing an algorithm that could determine material anisotropy without having to fit to models. This algorithm was tested using high fidelity data (containing off-axis BRDFs), which was collected via a modified Complete Angle Scatter Instrument (CASI®) with a CCD array detector. The algorithm accurately characterized the degree of isotropy for four out of five materials and worked for cases where the BRDF is higher than 100 sr − 1. This algorithm is intended to improve BRDF characterization, and the applications of light curve analysis, scene generation, and remote sensing.