Bidirectional Reflectance Distribution Function Research Articles

Anisotropic Specular Image‐Based Lighting Based on BRDF Major Axis Sampling

AbstractAnisotropic specular appearances are ubiquitous in the environment: brushed stainless steel pans, kettles, elevator walls, fur, or scratched plastics. Real‐time rendering of these materials with image‐based lighting is challenging due to the complex shape of the bidirectional reflectance distribution function (BRDF). We propose an anisotropic specular image‐based lighting method that can serve as a drop‐in replacement for the standard bent normal technique [Rev11]. Our method yields more realistic results with a 50% increase in computation time of the previous technique, using the same high dynamic range (HDR) preintegrated environment image. We use several environment samples positioned along the major axis of the specular microfacet BRDF. We derive an analytic formula to determine the two closest and two farthest points from the reflected direction on an approximation of the BRDF confidence region boundary. The two farthest points define the BRDF major axis, while the two closest points are used to approximate the BRDF width. The environment level of detail is derived from the BRDF width and the distance between the samples. We extensively compare our method with the bent normal technique and the ground truth using the GGX specular BRDF.

Research on the Laser Scattering Characteristics of Three-Dimensional Imaging Based on Electro–Optical Crystal Modulation

In this paper, we construct a laser 3D imaging simulation model based on the 3D imaging principle of electro–optical crystal modulation. Unlike the traditional 3D imaging simulation method, this paper focuses on the laser scattering characteristics of the target scene. To accurately analyze and simulate the scattering characteristic model of the target under laser irradiation, we propose a BRDF (Bidirectional Reflectance Distribution Function) model fitting algorithm based on the hybrid BBO–Firefly model, which can accurately simulate the laser scattering distribution of the target at different angles. Finally, according to the fitted scattering characteristic model, we inverted the target imaging gray map. We used the laser 3D imaging restoration principle to reconstruct the 3D point cloud of the target to realize the laser 3D imaging of the target.

Influence of Target Surface BRDF on Non-Line-of-Sight Imaging

The surface material of an object is a key factor that affects non-line-of-sight (NLOS) imaging. In this paper, we introduce the bidirectional reflectance distribution function (BRDF) into NLOS imaging to study how the target surface material influences the quality of NLOS images. First, the BRDF of two surface materials (aluminized insulation material and white paint board) was modeled using deep neural networks and compared with a five-parameter empirical model to validate the method’s accuracy. The method was then applied to fit BRDF data for different common materials. Finally, NLOS target simulations with varying surface materials were reconstructed using the confocal diffusion tomography algorithm. The reconstructed NLOS images were classified via a convolutional neural network to assess how different surface materials impacted imaging quality. The results show that image clarity improves when decreasing the specular reflection and increasing the diffuse reflection, with the best results obtained for surfaces exhibiting a high diffuse reflection and no specular reflection.

High-Resolution Infrared Reflectance Distribution Measurement Under Variable Temperature Conditions.

The bidirectional reflectance distribution function (BRDF) can effectively characterize the reflectance properties of a target, which can be used to correct infrared remote sensing data and improve the accuracy of remote sensing measurements. When the surface temperature changes, the reflectance characteristics of the target usually change, and it is necessary to carry out BRDF measurements under variable temperature conditions. In this paper, a variable-temperature infrared BRDF measurement system based on a robotic arm is developed to realize high-resolution wide-temperature region measurement of BRDF. To improve the measurement accuracy, the shaping optical path was used to expand the laser beam, combined with the laser level to accurately adjust the three-dimensional coordinates of the robotic arm, and the dichotomy method is used to calibrate the detector nonlinearly. A portable heater suitable for the mechanical arm corner mechanism is developed, and fast and high-precision temperature control is realized by proportional integral derivative (PID) control. The specular and diffuse BRDF distributions were measured at room temperature to verify the effectiveness of the system. The BRDF distribution of SUS314 stainless steel samples with different roughness is measured during two temperature increases from 20 °C to 1000 °C, and the changing rule of BRDF under variable temperature environment is summarized, which provides technical support for evaluating the optical properties of high-temperature materials and improving the measurement accuracy of remote sensing data.

Polarized spectral bidirectional reflectance distribution function in visible band based on Cauchy’s empirical dispersion equation

The polarized bidirectional reflectance distribution function (pBRDF) can describe the changes between the Stokes vectors of incident and reflected light. The existing model can only describe the spatial distribution of the target’s polarization characteristics at a single wavelength, so further research is needed for the description of the target’s polarized spectral characteristics. In this paper, a modified three-component polarized spectral bidirectional reflectance distribution function (pSBRDF) is proposed, which combines Fresnel equation in the specular reflection component with Cauchy’s empirical dispersion equation, by introducing the wavelength variable and dispersion constants that do not change with wavelength. The degree of the linear polarization (DoLP) of two types of coated fabric samples was measured at three incident angles and 400 to 760 nm wavelength. The error of the model in describing the spectral and the spatial distribution of DoLP are controlled within 0.00743 and 0.0757 respectively, which proves the accuracy of the model. This research provides the model basis for analysis of the target’s polarization characteristics and the theoretical basis for the application of polarization detection.

Influence of Vegetation Phenology on the Temporal Effect of Crop Fractional Vegetation Cover Derived from Moderate-Resolution Imaging Spectroradiometer Nadir Bidirectional Reflectance Distribution Function–Adjusted Reflectance

Moderate-Resolution Imaging Spectroradiometer (MODIS) Nadir Bidirectional Reflectance Distribution Function (BRDF)-Adjusted Reflectance (NBAR) products are being increasingly used for the quantitative remote sensing of vegetation. However, the assumption underlying the MODIS NBAR product’s inversion model—that surface anisotropy remains unchanged over the 16-day retrieval period—may be unreliable, especially since the canopy structure of vegetation undergoes stark changes at the start of season (SOS) and the end of season (EOS). Therefore, to investigate the MODIS NBAR product’s temporal effect on the quantitative remote sensing of crops at different stages of the growing seasons, this study selected typical phenological parameters, namely SOS, EOS, and the intervening stable growth of season (SGOS). The PROBA-V bioGEOphysical product Version 3 (GEOV3) Fractional Vegetation Cover (FVC) served as verification data, and the Pearson correlation coefficient (PCC) was used to compare and analyze the retrieval accuracy of FVC derived from the MODIS NBAR product and MODIS Surface Reflectance product. The Anisotropic Flat Index (AFX) was further employed to explore the influence of vegetation type and mixed pixel distribution characteristics on the BRDF shape under different stages of the growing seasons and different FVC; that was then combined with an NDVI spatial distribution map to assess the feasibility of using the reflectance of other characteristic directions besides NBAR for FVC correction. The results revealed the following: (1) Generally, at the SOSs and EOSs, the differences in PCCs before vs. after the NBAR correction mainly ranged from 0 to 0.1. This implies that the accuracy of FVC derived from MODIS NBAR is lower than that derived from MODIS Surface Reflectance. Conversely, during the SGOSs, the differences in PCCs before vs. after the NBAR correction ranged between –0.2 and 0, suggesting the accuracy of FVC derived from MODIS NBAR surpasses that derived from MODIS Surface Reflectance. (2) As vegetation phenology shifts, the ensuing differences in NDVI patterning and AFX can offer auxiliary information for enhanced vegetation classification and interpretation of mixed pixel distribution characteristics, which, when combined with NDVI at characteristic directional reflectance, could enable the accurate retrieval of FVC. Our results provide data support for the BRDF correction timescale effect of various stages of the growing seasons, highlighting the potential importance of considering how they differentially influence the temporal effect of NBAR corrections prior to monitoring vegetation when using the MODIS NBAR product.

Research of the underwater polarization imaging process based on the Oren–Nayar polarization bidirectional reflection distribution function

Research of the underwater polarization imaging process based on the Oren–Nayar polarization bidirectional reflection distribution function

New Mie Scattering Diffuse Targets Development and Characterization

Abstract Earth science remote sensing observations require the detection and measurement of light originating from bright targets, such as clouds, and darker targets, such as an open ocean. This requirement drives the need to design, develop, and characterize improved calibration targets in support of current and future NASA instruments. New diffuse targets to be used as spectral albedo calibration standards were developed and characterized. The new targets based on fused silica or/and pressed and sintered Polytetrafluoroethylene (PTFE) were developed to be Earth scene specific. The various reflectance levels are achieved by modifying the material parameters, thickness, and surface finish. The new targets were characterized in cleanroom environment. We acquired high accuracy reflectance and transmittance data using a precision optical scatterometer and spectrophotometer located in the NASA Goddard Space Flight Center (GSFC) Diffuser Calibration Lab. The Total hemispherical reflectance (THR) and Bidirectional Reflectance Distribution Function (BRDF) were measured over the range of solar incident and scattered elevation and azimuthal angles typically realized on orbit by remote sensing instruments. We intend to space certify the new calibration targets after concluding on-orbit testing on the International Space Stations (ISS) scheduled for the second half of 2023.

Principal-plane BRDF of CO2 ice morphologies in controlled Mars polar conditions

Mars South Polar Residual Cap (SPRC) persists throughout the Southern hemisphere's warmest months. During the colder seasons, carbon dioxide (CO2) accumulates as ice on the surface of the planet, forming a seasonal cap during fall and winter and sublimating throughout spring. The seasonal cap and SPRC both exhibit unexpected reflectance properties that have not been explained. To better understand the Martian surface CO2 ice and how it affects Mars' geomorphology, atmosphere, and climate, it is imperative to corroborate laboratory experiments with orbital observations. This study uses a custom-designed goniometer for making reflectance measurements within the MARs Volatile and Ice evolutioN (MARVIN) environmental chamber, in which we can measure the Bidirectional Reflectance Distribution Function (BRDF) of different phases of CO2 under Mars polar conditions for the first time. This has the potential to explain present-day observations from orbit and enhance our understanding of the evolution of ice on Mars.

Single-image SVBRDF estimation with auto-adaptive high-frequency feature extraction

In this paper, we address the task of estimating spatially-varying bi-directional reflectance distribution functions (SVBRDF) of a near-planar surface from a single flash-lit image. Disentangling SVBRDF from the material appearance by deep learning has proven a formidable challenge. This difficulty is particularly pronounced when dealing with images lit by a point light source because the uneven distribution of irradiance in the scene interacts with the surface, leading to significant global luminance variations across the image. These variations may be overemphasized by the network and wrongly baked into the material property space. To tackle this issue, we propose a high-frequency path that contains an auto-adaptive subband “knob”. This path aims to extract crucial image textures and details while eliminating global luminance variations present in the original image. Furthermore, recognizing that color information is ignored in this path, we design a two-path strategy to jointly estimate material reflectance from both the high-frequency path and the original image. Extensive experiments on a substantial dataset have confirmed the effectiveness of our method. Our method outperforms state-of-the-art methods across a wide range of materials.

Retrieval of pseudo-BRDF-adjusted surface reflectance at 440 nm from the Geostationary Environmental Monitoring Spectrometer (GEMS)

Abstract. In satellite remote sensing applications, enhancing the precision of level 2 (L2) algorithms relies heavily on the accurate estimation of the surface reflectance across the ultraviolet (UV) to visible (VIS) spectrum. However, the mutual dependence between the L2 algorithms and the surface reflectance retrieval poses challenges, necessitating an alternative approach. To address this issue, many satellite algorithms generate Lambertian-equivalent reflectivity (LER) products as a priori surface reflectance data; however, this often results in an underestimation of these data. This study is the first to assess the applicability of background surface reflectance (BSR), derived using a semi-empirical bidirectional reflectance distribution function (BRDF) model, in an operational environmental satellite algorithm. This study pioneered the application of the BRDF model to hyperspectral satellite data at 440 nm, aiming to provide more realistic preliminary surface reflectance data. In this study, the Geostationary Environment Monitoring Spectrometer (GEMS) data were used, and a comparative analysis of the GEMS BSR and GEMS LER retrieved in this study revealed an improvement in the relative root mean squared error (rRMSE) accuracy of 3 %. Additionally, a time series analysis across diverse land types indicated a greater stability exhibited by the BSR than by the LER. For further validation, the BSR was compared with other LER databases using ground-truth data, yielding superior simulation performance. These findings present a promising avenue for enhancing the accuracy of surface reflectance retrieval from hyperspectral satellite data, thereby advancing the practical applications of satellite remote sensing algorithms.

Real-time all-frequency global illumination with radiance caching

Global illumination (GI) plays a crucial role in rendering realistic results for virtual exhibitions, such as virtual car exhibitions. These scenarios usually include all-frequency bidirectional reflectance distribution functions (BRDFs), although their geometries and light configurations may be static. Rendering all-frequency BRDFs in real time remains challenging due to the complex light transport. Existing approaches, including precomputed radiance transfer, light probes, and the most recent path-tracing-based approaches (ReSTIR PT), cannot satisfy both quality and performance requirements simultaneously. Herein, we propose a practical hybrid global illumination approach that combines ray tracing and cached GI by caching the incoming radiance with wavelets. Our approach can produce results close to those of offline renderers at the cost of only approximately 17 ms at runtime and is robust over all-frequency BRDFs. Our approach is designed for applications involving static lighting and geometries, such as virtual exhibitions.

Bidirectional reflectance distribution function measurements of characterized Apollo regolith samples using the visible oxford space environment goniometer

AbstractA laboratory study was performed using the Visible Oxford Space Environment Goniometer in which the broadband (350–1250 nm) bidirectional reflectance distribution functions (BRDFs) of two representative Apollo regolith samples were measured, for two surface roughness profiles, across a range of viewing angles—reflectance: 0–70°, in steps of 5°; incidence: 15°, 30°, 45°, and 60°; and azimuthal: 0°, 45°, 90°, 135°, and 180°. The BRDF datasets were fitted using the Hapke BRDF model to (1) provide a method of comparison to other photometric studies of the lunar regolith and (2) to produce Hapke parameter values which can be used to extrapolate the BRDF to all angles. Importantly, the surface profiles of the samples were characterized using an Alicona 3D® instrument, allowing two of the free parameters within the Hapke model, φ and , which represent porosity and surface roughness, respectively, to be constrained. The study determined that, for , the 500–1000 μm size‐scale is the most relevant for the BRDF. Thus, it deduced the following “best fit” Hapke parameters for each of the samples: Apollo 11 rough— = 0.315 ± 0.021, = 0.261 ± 0.007, and = 0.039 ± 0.005 (with = 21.28° and φ = 0.41 ± 0.02); Apollo 11 smooth— = 0.281 ± 0.028, = 0.238 ± 0.008, and = 0.032 ± 0.006 (with = 13.80° and φ = 0.60 ± 0.02); Apollo 16 rough— = 0.485 ± 0.155, = 0.155 ± 0.083, and = 0.135 ± 0.007 (with = 21.69° and φ = 0.55 ± 0.02); Apollo 16 smooth— = 0.388 ± 0.057, = 0.063 ± 0.033, and = 0.221 ± 0.011 (with = 14.27° and φ = 0.40 ± 0.02). Finally, updated hemispheric albedo functions were determined for the samples, which can be used to set laboratory measured visible scattering functions within thermal models.

Investigating the evolution of road surface descriptors according to observation angles using a database of the reflection properties of urban materials

For road lighting design, road surface descriptors like the degree of lightness Q0 and specular factor S1 are derived from reflection properties (or Bidirectional Reflectance Distribution Function (BRDF)) of road surfaces. However, these BRDF are based on outdated road surface characteristics and are also partial (they are called r-tables) because only the motorist’s 1° observation angle is considered. Thus, the need to have full BRDF measurements of current road surfaces available. This paper proposes to use a recently released open source database of measured whole BRDF by means of our in-lab gonioreflectometer to investigate the performance of Q0 and S1 according to observation angles. We first compare descriptors obtained from measured and interpolated r-tables and find a good accuracy, especially for Q0. Then we propose a model for these descriptors function of the observation angle, and find quite an accurate fitting. Finally, we suggest a methodology for the classification of road surfaces which equally considers Q0, S1 and the observation angles, and propose a tentative classification of road surfaces based, not in terms of their materials, but rather in terms of their usage-driven performance.

A tutorial on the physics of light and image shading.

This paper provides an overview of the many different ways that light interacts with surfaces in the natural environment to provide useful information for visual perception. It begins with a discussion of how the concept of light has evolved over the course of human history. It then considers a wide variety of optical phenomena including Lambert's laws of illumination, the effects of microscopic surface structure on patterns of reflection, the bidirectional reflectance distribution function, the refraction of transmitted light, chromatic dispersion, thin film interference, sub-surface scattering, the Fresnel effects, indirect illumination from multiple reflections, caustics, and the structure of the light field. The primary goal of this discussion is to provide the necessary background information to help students and young researchers more easily understand the scientific literature on the perception of 3D shape and material properties from patterns of image shading.

Feasibility of satellite vicarious calibration using HYPERNETS surface reflectances from Gobabeb and Princess Elisabeth Antartica sites

The HYPERNETS project developed a new hyperspectral radiometer (HYPSTAR®) integrated in automated networks of water (WATERHYPERNET) and land (LANDHYPERNET) bidirectional reflectance measurements for satellite validation. In this paper, the feasibility of using LANDHYPERNET surface reflectance data for vicarious calibration of multispectral (Sentinel-2 and Landsat 8/9) and hyperspectral (PRISMA) satellites is studied. The pipeline to process bottom of atmosphere (BOA) surface reflectance HYPERNETS data to band-integrated top of atmosphere (TOA) reflectances and compare them to satellite observations is detailed. Two LANDHYPERNET sites are considered in this study: the Gobabeb HYPERNETS site in Namibia (GHNA) and Princess Elizabeth Base in Antarctica (PEAN). 36 near-simultaneous match-ups within 1 h are found where HYPERNETS and satellite data pass all quality checks. For the Gobabeb HYPERNETS site, agreement to within 5% is found with Sentinel-2 and Landsat 8/9. The differences with PRISMA are smaller than 10%. For the HYPERNETS Antarctica site, there are also a number of match-ups with good agreement to within 5% for Landsat 8/9. The majority show notable disagreement, i.e., HYPERNETS being over 10% different compared to satellite. This is due to small-scale irregularities in the wind-blown snow surface, and their shadows cast by the low Sun. A study comparing the HYPERNETS measurements against a bidirectional reflectance distribution function (BRDF) model is recommended. Overall, we confirm data from radiometrically stable HYPERNETS sites with sufficient spatial and angular homogeneity can successfully be used for vicarious calibration purposes.

Efficient Photon Beam Diffusion for Directional Subsurface Scattering.

Real-time subsurface scattering techniques are widely used in translucent material rendering. Among advanced methods that rely on the bidirectional scattering-surface reflectance distribution function (BSSRDF), screen space algorithms exhibit limited translucency, while existing large-distance methods are inefficient and yield poor illumination details. To address these limitations for better large-distance scattering, we develop a novel algorithm by extending the photon beam diffusion (PBD) model within the light view and screen space. Unlike surface irradiance in prior methods, we incorporate the refracted beam in the medium into real-time scattering estimation, presenting a new consideration for photon beam utilization. Concretely, we store all photon beam samples in light view textures and utilize an adaptive sampling pattern for beam sample selection in large filtering kernel sizes. This can reduce the sample count based on surface attributes. In screen space, virtual sources are derived from samples to estimate PBD contributions, with an approximation that preserves boundary conditions. To avoid possible overestimation, we implement correction factors that scale contributions, effectively aligning our results with path-tracing references. Through these reformulations, our efficient PBD generates results closest to references among existing methods. The experiments accurately represent better front-face illumination details and backlit translucency effects, while significantly accelerating performance compared to previous large-distance methods.

Pre-Launch Calibration of the Bidirectional Reflectance Distribution Function (BRDF) of Ultraviolet-Visible Hyperspectral Sensor Diffusers

An Ultraviolet-Visible Hyperspectral Sensors (UVS) instrument is an ultraviolet-visible imaging spectrograph equipped with two-dimensional charge-coupled device detectors. It records both the spectrum and the swath perpendicular to the flight direction, offering a wide 112° swath. This configuration enables global daily ground coverage with high spatial resolution. The absolute values of in-orbit solar irradiance can be evaluated using the bidirectional reflectance distribution function (BRDF), with the measurement accuracy directly affecting the accuracy of constituent inversion. This paper outlines the calibration process for the BRDF of the UVS, detailing the calibration methods and equipment used. It also proposes a BRDF model and discusses key coefficients. The accuracy levels of the UVS in the UV1, UV2, and VIS channels were 2.162%, 2.162%, and 2.173%, respectively.

Directional Applicability Analysis of Albedo Retrieval Using Prior BRDF Knowledge

Surface albedo measures the proportion of incoming solar radiation reflected by the Earth’s surface. Accurate albedo retrieval from remote sensing data usually requires sufficient multi-angular observations to account for the surface reflectance anisotropy. However, most middle and high-resolution remote sensing satellites lack the capability to acquire sufficient multi-angular observations. Existing algorithms for retrieving surface albedo from single-direction reflectance typically rely on land cover types and vegetation indices to extract the corresponding prior knowledge of surface anisotropic reflectance from coarse-resolution Bidirectional Reflectance Distribution Function (BRDF) products. This study introduces an algorithm for retrieving albedo from directional reflectance based on a 3 × 3 BRDF archetype database established using the 2015 global time-series Moderate Resolution Imaging Spectro-radiometer (MODIS) BRDF product. For different directions, BRDF archetypes are applied to the simulated MODIS directional reflectance to retrieve albedo. By comparing the retrieved albedos with the MODIS albedo, the BRDF archetype that yields the smallest Root Mean Squared Error (RMSE) is selected as the prior BRDF for the direction. A lookup table (LUT) that contains the optimal BRDF archetypes for albedo retrieval under various observational geometries is established. The impact of the number of BRDF archetypes on the accuracy of albedo is analyzed according to the 2020 MODIS BRDF. The LUT is applied to the MODIS BRDF within specific BRDF archetype classes to validate its applicability under different anisotropic reflectance characteristics. The applicability of the LUT across different data types is further evaluated using simulated reflectance or real multi-angular measurements. The results indicate that (1) for any direction, a specific BRDF archetype can retrieve a high-accuracy albedo from directional reflectance. The optimal BRDF archetype varies with the observation direction. (2) Compared to the prior BRDF knowledge obtained through averaging method, the BRDF archetype LUT based on the 3 × 3 BRDF archetype database can more accurately retrieve the surface albedo. (3) The BRDF archetype LUT effectively eliminates the influence of surface anisotropic reflectance characteristics in albedo retrieval across different scales and types of data.

Asymmetry in the Diurnal Variation of Land Surface Albedo and Its Impacts on Daily Mean Albedo Estimation

AbstractDaily mean albedo, a crucial variable of the earth radiation budget, is significantly affected by the diurnal variation of land surface albedo (DVLSA). The DVLSA typically exhibits asymmetry, thereby affecting the estimation of the daily mean albedo. However, the asymmetry in the DVLSA is generally ignored in daily mean albedo estimation. In this study, we investigated the influencing factors of the asymmetry in the DVLSA and evaluated its impacts on estimating the daily mean albedo based on field observations and simulated data. Our findings reveal that the asymmetry in the DVLSA varies among land cover types, with forests exhibiting more pronounced asymmetry compared to croplands, grasslands, and bare soil. The diurnal variation of the atmospheric conditions is the primary factor controlling the asymmetry in the DVLSA, with that of land surface conditions being a secondary factor. Neglecting the asymmetry in the DVLSA leads to estimation error in daily mean albedo, particularly pronounced during winter. The relative error of daily mean albedo can exceed 10% when the mean asymmetry index of diffuse irradiance fraction reaches 40%. However, the DVLSA retrieved from the satellite Bidirectional Reflectance Distribution Function product inadequately captures asymmetry, resulting in a relative error of approximately 13.7% in estimating daily mean albedo.