Spectral Bidirectional Reflectance Distribution Function Research Articles

A Unified Physically Based Method for Monitoring Grassland Nitrogen Concentration with Landsat 7, Landsat 8, and Sentinel-2 Satellite Data

The increasing number of satellite missions provides vast opportunities for continuous vegetation monitoring, crucial for precision agriculture and environmental sustainability. However, accurately estimating vegetation traits, such as nitrogen concentration (N%), from Landsat 7 (L7), Landsat 8 (L8), and Sentinel-2 (S2) satellite data is challenging due to the diverse sensor configurations and complex atmospheric interactions. To address these limitations, we developed a unified and physically based method that combines a soil–plant–atmosphere radiative transfer (SPART) model with the bottom-of-atmosphere (BOA) spectral bidirectional reflectance distribution function. This approach enables us to assess the effect of rugged terrain, viewing angles, and illumination geometry on the spectral reflectance of multiple sensors. Our methodology involves inverting radiative transfer model variables using numerical optimization to estimate N% and creating a hybrid model. We used Gaussian process regression (GPR) to incorporate the inverted variables into the hybrid model for N% prediction, resulting in a unified approach for N% estimation across different sensors. Our model shows a validation accuracy of 0.35 (RMSE %N), a mean prediction interval width (MPIW) of 0.35, and an R2 of 0.50, using independent data from multiple sensors collected between 2016 and 2019. Our unified method provides a promising solution for estimating N% in vegetation from L7, L8, and S2 satellite data, overcoming the limitations posed by diverse sensor configurations and complex atmospheric interactions.

Universality in azimuthal asymmetry of anisotropic sea-ice reflectance.

We study the azimuthal asymmetry of the spectral bidirectional reflectance distribution function (BRDF) of an optically thick sea-ice layer. From radiative transfer modeling, we find that the azimuth-dependent part of the BRDF ceases to change rather rapidly with an increase in the optical thickness of the layer and tends to a nearly universal angular dependence, insensitive to the specific law of single scattering in the ice. The effect of the scattering phase function manifests itself only in the value of a pre-factor in the azimuth-dependent part of the BRDF. The universality stems from the refractive index mismatch at the air/ice interface and should occur for any natural ice containing large (compared to the wavelength) inclusions. The specified part of the BRDF is governed by sub-diffusive radiation transport and, at large illumination zenith angles, can make a noticeable contribution to the spectral albedo of the layer in the visible range.

Gonioreflectometer for measuring 3D spectral BRDF of horizontally aligned samples with traceability to SI

Present article describes a 3D gonioreflectometer developed at Aalto University for the measurement of spectral bidirectional reflectance distribution function (sBRDF) of horizontally aligned samples, needed to study sBRDF of sand from satellite calibration test sites. The new set-up incorporates three motorized arms that allow to measure in- and out-of-plane sBRDF. Illumination of the sample is provided by a supercontinuum laser coupled with laser line tunable filters and detection is performed with two types of photodiodes (Si and InGaAs) enabling collection of sBRDF in the spectral range from 450 nm to 1700 nm. The instrument is operated in the relative mode and its traceability to SI is achieved with the help of a 2D absolute reference gonioreflectometer available at Aalto University. The calibration procedure as well as system’s uncertainty estimation are described. The performance of the 3D gonioreflectometer is validated by measurements of a ceramic diffuse reflectance sample.

An efficient method for acquisition of spectral BRDFs in real-world scenarios

Modelling of material appearance from reflectance measurements has become increasingly prevalent due to the development of novel methodologies in Computer Graphics. In the last few years, some advances have been made in measuring the light-material interactions, by employing goniometers/reflectometers under specific laboratory’s constraints. A wide range of applications benefit from data-driven appearance modelling techniques and material databases to create photorealistic scenarios and physically based simulations. However, important limitations arise from the current material scanning process, mostly related to the high diversity of existing materials in the real-world, the tedious process for material scanning and the spectral characterisation behaviour. Consequently, new approaches are required both for the automatic material acquisition process and for the generation of measured material databases. In this study, a novel approach for material appearance acquisition using hyperspectral data is proposed. A dense 3D point cloud filled with spectral data was generated from the images obtained by an unmanned aerial vehicle (UAV) equipped with an RGB camera and a hyperspectral sensor. The observed hyperspectral signatures were used to recognise natural and artificial materials in the 3D point cloud according to spectral similarity. Then, a parametrisation of Bidirectional Reflectance Distribution Function (BRDF) was carried out by sampling the BRDF space for each material. Consequently, each material is characterised by multiple samples with different incoming and outgoing angles. Finally, an analysis of BRDF sample completeness is performed considering four sunlight positions and 16x16 resolution for each material. The results demonstrated the capability of the used technology and the effectiveness of our method to be used in applications such as spectral rendering and real-word material acquisition and classification.

A research on the spectral Bidirectional Reflectance Distribution Function measurement of tensile polyimide film rough surfaces

The reflection distribution function is important for calculating the scatter distribution on material surface. In order to calculate the light scatter distribution of the tensile polyimide, it is necessary to investigate the relationship between the Bidirectional Reflectance Distribution Function (BRDF) of tensile polyimide film with its surface roughness and the incident light, and test the fitting function to evaluate the BRDF. The measurement spectrum is from 300nm to 750nm. The measurement results show that the BRDF of polyimide film are different with the tensile stress, and the reflectance intensity in the reflective direction decreases with the increase of the tensile stress, increases with the wavelength of the incident light. The reflectance intensity is associated with the roughness changing of polyimide surfaces for the tensile stress, as the roughness increases with the more stress, and the intensity increases in the none reflective direction. The fitting precision is up to 95% applying with the T-S model compared with the classical Phong model. The research data can be used to evaluate the reflective intensity of pharmaceutical packaging film, medical light barrier film, thermal insulation film and other film materials.

Goniochromatic assessment of gray scales for color change.

The dependence of color differences on the illumination and viewing directions for two widely used gray scales for color change (SDCE and AATCC) was evaluated through measuring the spectral bidirectional reflectance distribution function (BRDF) by a gonio-spectrophotometer of metrological quality. Large incidence and viewing angles must be specially avoided using these gray scales because, in these conditions, color differences vary considerably from those established in ISO 105-A02 and ASTM D2616-12. While the visual appearance of the SDCE and AATCC gray scales for color change is similar, our results indicate that their goniochromatic properties are different. Finally, some recommendations regarding observation distance and illumination angle are given to correctly use these gray scales for visual experiments.

Attitude awareness of on-orbit space object based on analysis of time-series spectral signals

In order to estimate the attitude parameters of space objects under the condition of space-based long-distance observation, a hierarchical solving method based on the time-series spectral signal is proposed to estimate the parameters of surface reflection characteristics and the attitude of the space objects. The first step is to let the space object in three-axis stabilization state be equivalent to a two-facet model. Then multi-level fusion model of bidirectional reflectance distribution function (BRDF) is introduced to describe the spectral reflection characteristics of complex material surfaces. Based on the time-series spectral signal and its model, the product of area and spectral BRDF of the two-facet can be reconstructed. The second step is to set up the two-facet characteristic difference model to select the optimum wavelength based on the maximum of the difference thereby minimizing the influence of coupling characteristics on of the two-facet on attitude estimate. The third step is to construct the time-series spectral signal model under the change of object attitude. The objective function is defined as the error between the model data and the measured data, then the attitude parameter can be estimated using Levenberg-Marquardt algorithm. The simulation result shows that the method is more suitable for the object with cube body, and the error between inversion value and real value will increase as the phase angle and the detector noise increase. When signal-to-noise ratio is greater than or equal to 10, the inversion error is within 2%.

Versatile four-axis gonioreflectometer for bidirectional reflectance distribution function measurements on anisotropic material surfaces

The bidirectional reflectance distribution function (BRDF) data are essential for analyzing and modeling the material appearance of anisotropic surfaces. In order to acquire four-dimensional BRDF on the anisotropic material surfaces, a four-axis gonioreflectometer was designed and implemented. The instrument consists of a collimated, broadband light source, a four-axis rotation mechanism, a spectroradiometer, and a control system. The instrument is able to carry out spectral BRDF measurements over most of the incident and reflection hemispheres and the entire visible spectrum. One thousand twenty-four samples are obtained over the spectral range of 380 to 760 nm. The angular resolution of the BRDF measurement is <0.1 deg with good repeatability. A relative calibration method was adopted to obtain the absolute values of BRDFs. Various scanning schemes can be carried out by the instrument to scan the designated angular domains, enabling the instrument to capture material appearance with strong, distinctive anisotropic highlights and translucency. The obtained BRDF data of a textile sample demonstrate the instrument capability of capturing complex light scattering behaviors, including off-specular reflection peaks, off-plane reflection peaks, and backscattering. The designers of novel material appearance and computer graphics community will benefit from this work.

Spectral Reflectance Processing via Local Wavelength-Direction Correlations

The spectral bidirectional reflectance distribution function (BRDF) maps incident radiation of a surface to its outgoing counterpart at different wavelengths. This function plays a fundamental role in characterizing the various types of earth surfaces. Due to its high dimensionality, the measurements, analysis, and simulation of spectral BRDF are challenging. In this letter, we introduce a new method for processing spectral reflectance using the so-called data-adjacency, i.e., the correlation between adjacent wavelengths and viewing directions. The results show that the benefits of efficient representation, noise reduction, and analysis capability can all be integrated to the data.

An adaptive parameterization for efficient material acquisition and rendering

One of the key ingredients of any physically based rendering system is a detailed specification characterizing the interaction of light and matter of all materials present in a scene, typically via the Bidirectional Reflectance Distribution Function (BRDF). Despite their utility, access to real-world BRDF datasets remains limited: this is because measurements involve scanning a four-dimensional domain at sufficient resolution, a tedious and often infeasibly time-consuming process. We propose a new parameterization that automatically adapts to the behavior of a material, warping the underlying 4D domain so that most of the volume maps to regions where the BRDF takes on non-negligible values, while irrelevant regions are strongly compressed. This adaptation only requires a brief 1D or 2D measurement of the material's retro-reflective properties. Our parameterization is unified in the sense that it combines several steps that previously required intermediate data conversions: the same mapping can simultaneously be used for BRDF acquisition, storage, and it supports efficient Monte Carlo sample generation. We observe that the above desiderata are satisfied by a core operation present in modern rendering systems, which maps uniform variates to direction samples that are proportional to an analytic BRDF. Based on this insight, we define our adaptive parameterization as an invertible, retro-reflectively driven mapping between the parametric and directional domains. We are able to create noise-free renderings of existing BRDF datasets after conversion into our representation with the added benefit that the warped data is significantly more compact, requiring 16KiB and 544KiB per spectral channel for isotropic and anisotropic specimens, respectively. Finally, we show how to modify an existing gonio-photometer to provide the needed retro-reflection measurements. Acquisition then proceeds within a 4D space that is warped by our parameterization. We demonstrate the efficacy of this scheme by acquiring the first set of spectral BRDFs of surfaces exhibiting arbitrary roughness, including anisotropy.

Simple and fast approach to exploit the spectral reflection properties of liquid media.

Bidirectional reflectance distribution functions (BRDFs) are of importance for their wide applications. In this study, we presented a simple and fast approach to measure the spectral BRDF of both solid and liquid samples. Based on this approach, we fabricated a prototype and measured the BRDF value of some liquid samples such as water and NaCl solution at different wavelengths. According to the experimental data, we discussed the trend of the BRDF value of the NaCl solution of different concentrations. Then, the experimental data of the different NaCl solution at 637nm were used to invert the parameters of a five-parameter model. Additionally, we fitted the parameters as a polynomial.

A BRDF study on the visual appearance properties of titanium in the heating process

Bidirectional reflectance distribution function (BRDF) offers complete description of the spectral and spatial characteristics of opaque materials, i.e. the visual appearance properties of materials. In this letter, the visual appearance properties of titanium in the heating process are investigated by BRDF. The reliability of our results is verified by comparing the experimental data of polytetrafluoroethylene with the reference data. The in-plane spectral BRDF in visible region of heated commercial pure Ti at different incident and reflected zenith angles are measured. The experimental result indicates that the change tendency of BRDF vs. wavelength is not influenced by incident and reflected zenith angle, which implying that the colours of Ti may be pigment colouration rather than the structural colouration. Scanning electron microscopy (SEM) and the X-ray diffraction (XRD) testing are performed, and no titanium oxides are detected. The testing results imply that the colours may be generated by intermediate products during heated process. The powder samples are prepared, and the same colours as that of flake samples indirectly prove the validity of our conclusion. In addition, the spectral BRDF of optically smooth samples are measured, the results verify the reliability of our conclusion.

BRDF of human skin in the visible spectrum

PurposeSignificant research has been carried out in terms of development of new bidirectional reflectance distribution function (BRDF) instruments; however, there is still little research available regarding spectral BRDF measurements of human skin. This study aims to investigate the variation in human skin reflectance using a new fibre optic-based spectral-BRDF measurement device.Design/methodology/approachDesign of this system mainly involves use of multiple fibre optics to illuminate and detect light reflected from a sample, whereas a hemispherical dome was 3D printed to mount the fibres at various slant/tilt angles. To investigate the spectral differences in BRDF of human skin, 3 narrowband filters in the visible spectrum were used, whereas measurements were taken from the back of the hand for Caucasian and Asian skin types.FindingsThe experiments demonstrate that the BRDF of human skin varies with wavelengths in the visible spectrum and it is also different for Caucasian and Asian skin types. Both skin types exhibit off-specular reflection with increase in angle of incidence and show less variation with respect to viewing angles when the angle of incidence is normal to the surface.Research implicationsA database of spectral BRDF measurements of human skin will help not only in creating realistic skin renderings but also in development of novel skin reflectance models for biomedical and machine vision applications. The measurements would also provide means to validate the predictions from existing light transport/spectral simulation models for human skin and will ultimately help in the accurate diagnosis and simulation of various skin disorders.Originality/valueThe proposed system provides fast scatter measurements by utilising multiple fibres to detect light simultaneously at different angles while also allowing easy switching between incident light directions. Due to its flexible design and contact-based measurements, the device is independent of errors due to sample movements and does not require any image registration. Also, measurements taken from the device show that the BRDF of skin varies significantly in the visible spectrum and it is different for Caucasian and Asian skin types.

Overview of the 2015 Algodones Sand Dunes field campaign to support sensor intercalibration

Several sites from around the world are being used operationally and are suitable for vicarious calibration of space-borne imaging platforms. However, due to the proximity of these sites (e.g., Libya 4), a rigorous characterization of the landscape is not feasible, limiting their utility for sensor intercalibration efforts. Due to its accessibility and similarities to Libya 4, the Algodones Sand Dunes System in California, USA, was identified as a potentially attractive intercalibration site for space-borne, reflective instruments such as Landsat. In March 2015, a 4-day field campaign was conducted to develop an initial characterization of Algodones with a primary goal of assessing its intercalibration potential. Five organizations from the US and Canada collaborated to collect both active and passive airborne image data, spatial and temporal measurements of spectral bidirectional reflectance distribution function, and in-situ sand samples from several locations across the Algodones system. The collection activities conducted to support the campaign goal is summarized, including a summary of all instrumentation used, the data collected, and the experiments performed in an effort to characterize the Algodones site.

ESTABLISHING BRDF CALIBRATION CAPABILITIES THROUGH SHORTWAVE INFRARED.

Satellite instruments operating in the reflective solar wavelength region require accurate and precise determination of the Bidirectional Reflectance Distribution Functions (BRDFs) of the laboratory and flight diffusers used in their pre-flight and on-orbit calibrations. This paper advances that initial work and presents a comparison of spectral Bidirectional Reflectance Distribution Function (BRDF) and Directional Hemispherical Reflectance (DHR) of Spectralon, a common material for laboratory and on-orbit flight diffusers. A new measurement setup for BRDF measurements from 900 nm to 2500 nm located at NASA Goddard Space Flight Center (GSFC) is described. The GSFC setup employs an extended indium gallium arsenide detector, bandpass filters, and a supercontinuum light source. Comparisons of the GSFC BRDF measurements in the shortwave infrared (SWIR) with those made by the National Institute of Standards and Technology (NIST) Spectral Tri-function Automated Reference Reflectometer (STARR) are presented. The Spectralon sample used in this study was 2 inch diameter, 99% white pressed and sintered Polytetrafluoroethylene (PTFE) target. The NASA/NIST BRDF comparison measurements were made at an incident angle of 0° and viewing angle of 45°. Additional BRDF data not compared to NIST were measured at additional incident and viewing angle geometries and are not presented here. The total combined uncertainty for the measurement of BRDF in the SWIR range made by the GSFC scatterometer is less than 1% (k = 1). This study is in support of the calibration of the Radiation Budget Instrument (RBI) and Visible Infrared Imaging Radiometer Suit (VIIRS) instruments of the Joint Polar Satellite System (JPSS) and other current and future NASA remote sensing missions operating across the reflected solar wavelength region.

New earth system model for optical performance evaluation of space instruments.

In this study, a new global earth system model is introduced for evaluating the optical performance of space instruments. Simultaneous imaging and spectroscopic results are provided using this global earth system model with fully resolved spatial, spectral, and temporal coverage of sub-models of the Earth. The sun sub-model is a Lambertian scattering sphere with a 6-h scale and 295 lines of solar spectral irradiance. The atmospheric sub-model has a 15-layer three-dimensional (3D) ellipsoid structure. The land sub-model uses spectral bidirectional reflectance distribution functions (BRDF) defined by a semi-empirical parametric kernel model. The ocean is modeled with the ocean spectral albedo after subtracting the total integrated scattering of the sun-glint scatter model. A hypothetical two-mirror Cassegrain telescope with a 300-mm-diameter aperture and 21.504 mm × 21.504-mm focal plane imaging instrument is designed. The simulated image results are compared with observational data from HRI-VIS measurements during the EPOXI mission for approximately 24 h from UTC Mar. 18, 2008. Next, the defocus mapping result and edge spread function (ESF) measuring result show that the distance between the primary and secondary mirror increases by 55.498 μm from the diffraction-limited condition. The shift of the focal plane is determined to be 5.813 mm shorter than that of the defocused focal plane, and this result is confirmed through the estimation of point spread function (PSF) measurements. This study shows that the earth system model combined with an instrument model is a powerful tool that can greatly help the development phase of instrument missions.

Polarimetric multispectral bidirectional reflectance distribution function measurements using a Fourier transform instrument

Fourier optics system have already been recognized as an efficient solution to measure rapidly multispectral bidirectional reflectance distribution function (BRDF) of any kind of surface with very high angular resolution. This capacity is useful to study complex BRDF behaviors in particular for anisotropic surfaces. Measurement of the BRDF polarization dependence is useful to understand better the scattering processes involved in the different types of samples. In the proposed paper we show that polarimetric spectral BRDF (pBRDF) measurements are also possible using such instruments. We evaluate the accuracy of the system using black glass surface. Examples of pBRDF measurements on different types of samples (color shifting paints, car paints and gloss reference samples) are presented.

Color characterization of coatings with diffraction pigments.

Coatings with diffraction pigments present high iridescence, which needs to be characterized in order to describe their appearance. The spectral bidirectional reflectance distribution functions (BRDFs) of six coatings with SpectraFlair diffraction pigments were measured using the robot-arm-based goniospectrophotometer GEFE, designed and developed at CSIC. Principal component analysis has been applied to study the coatings of BRDF data. From data evaluation and based on theoretical considerations, we propose a relevant geometric factor to study the spectral reflectance and color gamut variation of coatings with diffraction pigments. At fixed values of this geometric factor, the spectral BRDF component due to diffraction is almost constant. Commercially available portable goniospectrophotometers, extensively used in several industries (automotive and others), should be provided with more aspecular measurement angles to characterize the complex reflectance of goniochromatic coatings based on diffraction pigments, but they would not require either more than one irradiation angle or additional out-of-plane geometries.

A novel approach to modeling spacecraft spectral reflectance

Simulated spectrometric observations of unresolved resident space objects are required for the interpretation of quantities measured by optical telescopes. This allows for their characterization as part of regular space surveillance activity. A peer-reviewed spacecraft reflectance model is necessary to help improve the understanding of characterization measurements. With this objective in mind, a novel approach to model spacecraft spectral reflectance as an overall spectral bidirectional reflectance distribution function (sBRDF) is presented. A spacecraft’s overall sBRDF is determined using its triangular-faceted computer-aided design (CAD) model and the empirical sBRDF of its homogeneous materials. The CAD model is used to determine the proportional contribution of each homogeneous material to the overall reflectance. Each empirical sBRDF is contained in look-up tables developed from measurements made over a range of illumination and reflection geometries using simple interpolation and extrapolation techniques. A demonstration of the spacecraft reflectance model is provided through simulation of an optical ground truth characterization using the Canadian Advanced Nanospace eXperiment-1 Engineering Model nanosatellite as the subject. Validation of the reflectance model is achieved through a qualitative comparison of simulated and measured quantities.

Consistency analysis of multidimensional gonio-spectrophotometric measurements in interlaboratory comparisons

The spectral bidirectional reflectance distribution function (BRDF) is the key quantity to specify the spectral reflectance of materials for any condition of irradiation and detection, and its characterization is quite important for surfaces with a high dependence on these conditions, such as iridescent coatings. In order to evaluate the calibration and measurement capabilities (CMC) of National Metrology Institutes with the ability to measure the spectral BRDF, a case study interlaboratory comparison is in progress. Spectral BRDF has both spectral and geometric dependence, and this multidimensionality must be treated in the comparison to provide useful information to the participants about their CMCs. A data analysis method for the comparison is presented in this work, which was tested by simulations for different scenarios. The proposed method assesses whether the experimental data from each participant are consistent with those from the others. Finally, one-dimensional and multidimensional degrees of equivalence are defined, which should allow systematic deviations of spectral and geometric nature to be identified.