Bidirectional Reflectance Distribution Function Model Research Articles

Bidirectional reflectance distribution function measurements and analysis of retroreflective materials

We compare the performance of various analytical retroreflecting bidirectional reflectance distribution function (BRDF) models to assess how they reproduce accurately measured data of retroreflecting materials. We introduce a new parametrization, the back vector parametrization, to analyze retroreflecting data, and we show that this parametrization better preserves the isotropy of data. Furthermore, we update existing BRDF models to improve the representation of retroreflective data.

Swift perspective shape matching algorithm based on Phong’s model for FPC stiffener bonding systems

Purpose – This paper aims to solve the issue of target positioning in auto stiffener bonder (ASB) systems for flexible printed circuits. Design/methodology/approach – The proposed approach uses Phong’s bidirectional reflectance distribution function (BRDF) model to simulate the reflection of light off a target in ASB systems to predict the current pose of the target based on image brightness, update the template, decrease the initial errors in the template and narrow down the search range. Findings – The experimental results indicate that the proposed approach can predict the inclination angle of the target with precision, presenting angle prediction errors of less than three degrees. Furthermore, with larger inclined angles, the overall matching errors were less than 1.5 pixels. Comparisons with the unmodified matching algorithm revealed that the proposed approach resulted in 65 per cent less calculation time for the algorithm and 14 per cent higher overall work efficiency in the ASB system. Originality/value – The edge-based perspective shape matching algorithm was modified using the Phong BRDF model and enhanced algorithm efficiency with the target pose prediction method while ensuring the precision and robustness of the system. The proposed approach has high potential value and can be expanded to recognition systems for objects with varying inclination angles and highly reflective surfaces.

Remote sensing of surface reflective properties: Role of regularization and a priori knowledge

Linear kernel-driven bidirectional reflectance distribution function (BRDF) models have been used for mapping albedo with single field-of-view satellite measurements such as Moderate Resolution Imaging Spectroradiometer (MODIS). Due to limited samplings and poor angular configurations available from these satellite remotely sensed data, BRDF models inversion is often plagued by numerical instability. In order to overcome the ill-posedness of the BRDF model inversion and robustly estimate terrestrial surface albedo, a regularization technique is employed for the cases where the number of observations is insufficient, or the angular distribution is poor. Emphasis is also placed on the combination of a priori knowledge with the regularized inversion. Numerical performances and case study results with ground measurements and MODIS observations suggest that the method is sound and robust for ill-posed BRDF inverse problems. The method presented in this study is promising for land surface reflective parameters retrieval even for regions where only sparse observations are available.

Bidirectional reflectance distribution function modeling of one-dimensional rough surface in the microwave band

In this study, the bidirectional reflectance distribution function (BRDF) of a one-dimensional conducting rough surface and a dielectric rough surface are calculated with different frequencies and roughness values in the microwave band by using the method of moments, and the relationship between the bistatic scattering coefficient and the BRDF of a rough surface is expressed. From the theory of the parameters of the rough surface BRDF, the parameters of the BRDF are obtained using a genetic algorithm. The BRDF of a rough surface is calculated using the obtained parameter values. Further, the fitting values and theoretical calculations of the BRDF are compared, and the optimization results are in agreement with the theoretical calculation results. Finally, a reference for BRDF modeling of a Gaussian rough surface in the microwave band is provided by the proposed method.

Effect of surface BRDF of various land cover types on geostationary observations of tropospheric NO<sub>2</sub>

Abstract. We investigated the effect of surface reflectance anisotropy, bidirectional reflectance distribution function (BRDF), on satellite retrievals of tropospheric NO2. We assume the geometry of geostationary measurements over Tokyo, which is one of the worst air-polluted regions in East Asia. We calculated air mass factors (AMF) and box AMFs (BAMF) for tropospheric NO2 to evaluate the effect of BRDF by using the radiative transfer model SCIATRAN. To model the BRDF effect, we utilized the Moderate Resolution Imaging Spectroradiometer (MODIS) products (MOD43B1 and MOD43B2), which provide three coefficients to express the RossThick–LiSparse reciprocal model, a semi-empirical and kernel-based model of BRDF. Because BRDF depends on the land cover type, we also utilized the High Resolution Land-Use and Land-Cover Map of the Advanced Land Observing Satellite (ALOS)/Advanced Visible and Near Infrared Radiometer type 2 (AVNIR-2), which classifies the ground pixels over Tokyo into six main types: water, urban, paddy, crop, deciduous forest, and evergreen forest. We first develop an empirical model of the three BRDF coefficients for each land cover type over Tokyo and then apply the model to the calculation of land-cover-type-dependent AMFs and BAMFs. Results show that the variability of AMF among the land types is up to several tens of percent, and if we neglect the reflectance anisotropy, the difference with AMFs based on BRDF reaches 10% or more. The evaluation of the BAMFs calculated shows that not considering BRDF will cause large errors if the concentration of NO2 is high close to the surface, although the importance of BRDF for AMFs decreases for large aerosol optical depth (AOD).

The Normalization of Surface Anisotropy Effects Present in SEVIRI Reflectances by Using the MODIS BRDF Method

A modified version of the MODerate resolution Imaging Spectroradiometer (MODIS) bidirectional reflectance distribution function (BRDF) algorithm is presented for use in the angular normalization of surface reflectance data gathered by the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) aboard the geostationary Meteosat Second Generation (MSG) satellites. We present early and provisional daily nadir BRDF-adjusted reflectance (NBAR) data in the visible and near-infrared MSG channels. These utilize the high temporal resolution of MSG to produce BRDF retrievals with a greatly reduced acquisition period than the comparable MODIS products while, at the same time, removing many of the angular perturbations present within the original MSG data. The NBAR data are validated against reflectance data from the MODIS instrument and in situ data gathered at a field location in Africa throughout 2008. It is found that the MSG retrievals are stable and are of high-quality across much of the SEVIRI disk while maintaining a higher temporal resolution than the MODIS BRDF products. However, a number of circumstances are discovered whereby the BRDF model is unable to function correctly with the SEVIRI observations—primarily because of an insufficient spread of angular data due to the fixed sensor location or localized cloud contamination.

Assimilating MODIS-based albedo and snow cover fraction into the Common Land Model to improve snow depth simulation with direct insertion and deterministic ensemble Kalman filter methods

This study assesses the analysis performance of assimilating the Moderate Resolution Imaging Spectroradiometer (MODIS)-based albedo and snow cover fraction (SCF) separately or jointly into the physically based Common Land Model (CoLM). A direct insertion method (DI) is proposed to assimilate the black and white-sky albedos into the CoLM. The MODIS-based albedo is calculated with the MODIS bidirectional reflectance distribution function (BRDF) model parameters product (MCD43B1) and the solar zenith angle as estimated in the CoLM for each time step. Meanwhile, the MODIS SCF (MOD10A1) is assimilated into the CoLM using the deterministic ensemble Kalman filter (DEnKF) method. A new DEnKF-albedo assimilation scheme for integrating the DI and DEnKF assimilation schemes is proposed. Our assimilation results are validated against in situ snow depth observations from November 2008 to March 2009 at five sites in the Altay region of China. The experimental results show that all three data assimilation schemes can improve snow depth simulations. But overall, the DEnKF-albedo assimilation shows the best analysis performance as it significantly reduces the bias and root-mean-square error (RMSE) during the snow accumulation and ablation periods at all sites except for the Fuyun site. The SCF assimilation via DEnKF produces better results than the albedo assimilation via DI, implying that the albedo assimilation that indirectly updates the snow depth state variable is less efficient than the direct SCF assimilation. For the Fuyun site, the DEnKF-albedo scheme tends to overestimate the snow depth accumulation with the maximum bias and RMSE values because of the large positive innovation (observation minus forecast).

Bidirectional reflectance distribution function based surface modeling of non-Lambertian using intensity data of light detection and ranging.

To provide a credible model for light detection and ranging (LiDAR) target classification, the focus of this study is on the relationship between intensity data of LiDAR and the bidirectional reflectance distribution function (BRDF). An integration method based on the built-in-lab coaxial laser detection system was advanced. A kind of intermediary BRDF model advanced by Schlick was introduced into the integration method, considering diffuse and specular backscattering characteristics of the surface. A group of measurement campaigns were carried out to investigate the influence of the incident angle and detection range on the measured intensity data. Two extracted parameters r and S(λ) are influenced by different surface features, which illustrate the surface features of the distribution and magnitude of reflected energy, respectively. The combination of two parameters can be used to describe the surface characteristics for target classification in a more plausible way.

Angular Normalization of Land Surface Temperature and Emissivity Using Multiangular Middle and Thermal Infrared Data

This paper aimed at the case of nonisothermal pixels and proposed a daytime temperature-independent spectral indices (TISI) method to retrieve directional emissivity and effective temperature from daytime multiangular observed images in both middle and thermal infrared (MIR and TIR) channels by combining the kernel-driven bidirectional reflectance distribution function (BRDF) model and the TISI method. Four groups of angular observations and two groups of MIR and TIR channels with narrow and broad bandwidths were used to investigate the influence of angular observations and bandwidth on the retrieval accuracy. Model sensitivity analysis indicated that the new method can generally obtain directional emissivity and temperature with an error less than 0.015 and 1.5 K if the noise included in the measured directional brightness temperature (DBT) and atmospheric data was no more than 1.0 K and 10%, respectively. The analysis also indicated that 1) large-angle intervals among the angular observations and a larger viewing zenith angle, with respect to nadir direction, can improve the retrieval accuracy because those angle conditions can result in significant difference for components' fractions and DBT under different viewing directions; 2) narrow channels can produce better results than broad channels. The new method was finally applied to a multiangular MIR and TIR data set acquired by an airborne system, and a modified kernel-driven BRDF model was used for angular normalization to the surface temperature for the first time. The difference of the retrieved emissivity and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) emissivity was found to be approximately 0.012 in the study area.

Retrieval Spectral Albedo using red and NIR band of SPOT/VGT

Albedo is one of the critical parameters for understanding global climate change and energy/water balance. In this study, we used red and NIR reflectance from Satellite Pour I'Obervation de la Terre (SPOT)/Vegetation (VGT) S1 product. The product is preprocessed for users that they are atmospherically corrected using Simple Method Atmospheric Correction (SMAC) by Vision on Technology (VITO) for calculating broadband albedo. Roujean's Bi-directional Reflectance Distribution Function (BRDF) model is a semi-empirical method used for BRDF angular integration and inversion. Each kernel of Roujean's model was multi integrated by angle components (i.e., viewing zenith, solar zenith, and relative azimuth angle). Black-sky hemispherical function is integrated by observational angle; whereas, white-sky hemispherical efficient is integrated by incident angle. Estimated spectral albedo of red (<TEX>$0.61{\sim}0.68{\mu}m$</TEX>, B2) and near infrared (<TEX>$0.79{\sim}0.89{\mu}m$</TEX>, B3) have a good agreement with MODIS albedo products.

Analysis on Bidirectional Reflectance Distribution Function of Rough Earth Surface in Remote Sensing Imaging

In remote sensing imaging, bidirectional reflectance distribution function (BRDF) is powerful tool to describe light reflectance characteristic. Based on BRDF distribution of ground object, reflectance distribution in all directions will be calculated, and radiation difference of remote sensing imaging can be calibrated. This paper analyzes the several empirical / semi-empirical BRDF model suitable for the rough earth surface. The cement ground was selected as typical experiment topography, and the ground reflectance in all directions at different solar zenith angle was obtained. We compare measurement data to calculation results of three theoretical models, including five parameter model, Staylor &amp; Suttles model and Walthall model, and analyze and evaluate effectiveness of various models.

Modeling the BRDF from spectral reflectance measurements of metallic surfaces

The key quantity for expressing the directional optical effect of materials on the incident radiance is the bidirectional reflectance distribution function (BRDF). Our work is devoted to the BRDF spectral measurements, in order to render the synthetic images, mostly of the metallic paints. We measured the spectral reflectance off multiple paint samples then used the measured data to fit the analytical BRDF model, in order to acquire its parameters. Our contribution is in a mutual comparison and using the Cook–Torrance microfacet model as a fitting function for reflectance distribution evaluation. Results of analysis and the measurements were incorporated into the rendering process of car paint.

Optical roughness BRDF model for reverse Monte Carlo simulation of real material thermal radiation transfer.

Optical roughness was introduced into the bidirectional reflectance distribution function (BRDF) model to simulate the reflectance characteristics of thermal radiation. The optical roughness BRDF model stemmed from the influence of surface roughness and wavelength on the ray reflectance calculation. This model was adopted to simulate real metal emissivity. The reverse Monte Carlo method was used to display the distribution of reflectance rays. The numerical simulations showed that the optical roughness BRDF model can calculate the wavelength effect on emissivity and simulate the real metal emissivity variance with incidence angles.

Spectral scattering characteristics of space target in near-UV to visible bands

In this study, the spectral scattering characteristics of a space target are calculated in the near-UV to visible bands on the basis of measured data of spectral hemispheric reflectivity in the upper half space. Further, the bidirectional reflection distribution function (BRDF) model proposed by Davies is modified to describe the light scattering properties of a target surface. This modification aims to improve the characteristics identifying ability for different space targets. By using this modified Davies spectrum BRDF model, the spectral scattering characteristics of each subsurface can be obtained. A mathematical model of spectral scattering properties of the space target is built by summing all the contributing surface grid reflection scattering components, considering the impact of surface shadow effect.Moreover, the spectral scattering characteristics of the space target calculated with both the traditional and modified Davies BRDF models are compared. The results show that in the fixed and modified cases, the hemispheric reflectivity significantly affects the spectral scattering irradiance of the target.

Correction of sub-pixel topographical effects on land surface albedo retrieved from geostationary satellite (FengYun-2D) observations

The Qinghai-Tibetan Plateau is characterised by a very strong relief which affects albedo retrieval from satellite data. The objective of this study is to highlight the effects of sub-pixel topography and to account for those effects when retrieving land surface albedo from geostationary satellite FengYun-2D (FY-2D) data with 1.25km spatial resolution using the high spatial resolution (30 m) data of the Digital Elevation Model (DEM) from ASTER. The methodology integrates the effects of sub-pixel topography on the estimation of the total irradiance received at the surface, allowing the computation of the topographically corrected surface reflectance. Furthermore, surface albedo is estimated by applying the parametric BRDF (Bidirectional Reflectance Distribution Function) model called RPV (Rahman-Pinty-Verstraete) to the terrain corrected surface reflectance. The results, evaluated against ground measurements collected over several experimental sites on the Qinghai-Tibetan Plateau, document the advantage of integrating the sub-pixel topography effects in the land surface reflectance at 1km resolution to estimate the land surface albedo. The results obtained after using sub-pixel topographic correction are compared with the ones obtained after using pixel level topographic correction. The preliminary results imply that, in highly rugged terrain, the sub-pixel topography correction method gives more accurate results. The pixel level correction tends to overestimate surface albedo.

Absolute Calibration of Optical Satellite Sensors Using Libya 4 Pseudo Invariant Calibration Site

The objective of this paper is to report the improvements in an empirical absolute calibration model developed at South Dakota State University using Libya 4 (+28.55°, +23.39°) pseudo invariant calibration site (PICS). The approach was based on use of the Terra MODIS as the radiometer to develop an absolute calibration model for the spectral channels covered by this instrument from visible to shortwave infrared. Earth Observing One (EO-1) Hyperion, with a spectral resolution of 10 nm, was used to extend the model to cover visible and near-infrared regions. A simple Bidirectional Reflectance Distribution function (BRDF) model was generated using Terra Moderate Resolution Imaging Spectroradiometer (MODIS) observations over Libya 4 and the resulting model was validated with nadir data acquired from satellite sensors such as Aqua MODIS and Landsat 7 (L7) Enhanced Thematic Mapper (ETM+). The improvements in the absolute calibration model to account for the BRDF due to off-nadir measurements and annual variations in the atmosphere are summarized. BRDF models due to off-nadir viewing angles have been derived using the measurements from EO-1 Hyperion. In addition to L7 ETM+, measurements from other sensors such as Aqua MODIS, UK-2 Disaster Monitoring Constellation (DMC), ENVISAT Medium Resolution Imaging Spectrometer (MERIS) and Operational Land Imager (OLI) onboard Landsat 8 (L8), which was launched in February 2013, were employed to validate the model. These satellite sensors differ in terms of the width of their spectral bandpasses, overpass time, off-nadir-viewing capabilities, spatial resolution and temporal revisit time, etc. The results demonstrate that the proposed empirical calibration model has accuracy of the order of 3% with an uncertainty of about 2% for the sensors used in the study.

An Improved Method For Retrieving Land Surface Albedo Over Rugged Terrain

Land surface albedo is a very important parameter, which can be derived from a bidirectional reflectance distribution function (BRDF) model with angular integration of BRDF in a particular distribution of downward solar irradiance. The Algorithm for MODIS Bidirectional Reflectance Anisotropic of Land Surface (AMBRALS) utilizes a kernel-driven BRDF model to retrieve land surface albedo, but it does not take into account the topographic effect. This letter proposed an improved method by adding topographic factor to the AMBRALS, which removes the topographic effect on land surface reflectance and considers the topographic effect in retrieving land surface albedo. This method is applied to the HJ-1A/B CCD land surface reflectance data to retrieve the land surface albedo. The results are compared with those from the AMBRALS and with the ground measurements. The comparison results show that the proposed method performs well in general and better than the AMBRALS over rugged area.

Evaluation of semi-empirical BRDF models inverted against multi-angle data from a digital airborne frame camera for enhancing forest type classification

Forest mapping based on remote sensing data usually relies on purely spectral information ignoring that the observed signal may be substantially influenced by angular effects. On the other hand, it is known that for forest canopies the variation of reflectance with the sun-view-geometry is significant. The study examines different approaches to extract spectro-directional information from airborne imagery and explores its use in forest type classification. The images were acquired in a standard aerial survey. They were taken with a common forward and side overlap with the result that each point on the ground is observed from several view directions.To obtain directional information that might be useful in forest type classification, two widely used semi-empirical models of the bidirectional reflectance distribution function (BRDF) were tested, i.e., the Rahman–Pinty–Verstraete model (RPV; with 3 and 4 parameters) (Rahman et al., 1993) and the RossThick-LiSparse model (RTLS; with 3 and 5 parameters) (Wanner et al., 1995). For each sample plot, observations from at least 10 view directions were available. The models were inverted against the observations applying a look-up table approach. The estimated model parameters were used 1) directly as explanatory variables in the classification, and 2) to estimate the bidirectional reflectance factor (BRF) for selected sun-view-geometries, referred to as modeled BRFs. The BRFs also served as explanatory variables in the classification. For the classification the Random Forests classifier was used.Both models proved to provide information that can be successfully used in forest type classification outperforming conventional (single-angle) multi-spectral data. The 3-parameter version of the RPV model was found most effective. Compared to the conventional dataset, the overall classification accuracy increased from 72% (kappa: 0.64) to 85% (kappa: 0.81), when the parameters of this model were used as explanatory variables. The 4-parameter version of RPV and the 5-parameter version of RTLS fitted the observed data more accurately than the corresponding 3-parameter versions. However, the classification accuracies obtained with the estimated model parameters were significantly lower than those obtained with the 3-parameter models. All tested models yielded higher classification accuracies with the modeled BRFs than with the model parameters. Again, the highest classification accuracy was obtained with the RPV-3P model (overall accuracy: 92%; kappa: 0.89). The classification accuracy varied with the sun-view-geometry. These differences could partly be explained by the angular sampling scheme and partly by the models' capability to estimate the reflectance at angles that were not observed.

ACT: A leaf BRDF model taking into account the azimuthal anisotropy of monocotyledonous leaf surface

Leaf reflectance of monocotyledons generally displays a strong azimuthal anisotropy due to the longitudinal orientation of the veins. The Cook and Torrance (CT) bidirectional reflectance distribution function model was adapted to account for this distinctive feature. The resulting ACT (Anisotropic Cook and Torrance) model is based on the decomposition of the roughness parameter into two perpendicular components. It is evaluated on sorghum (Sorghum halepense) and wheat (Triticum durum) leaf BRF (Bidirectional Reflectance Factor) measurements acquired using a conoscope system. Results show that the ACT model fits the measurements better than azimuthally isotropic surface models: the root mean square error computed over all the BRF measurements for both leaves decreases from ≈0.06 for the Lambertian model to ≈0.04 for the CT model and down to ≈0.03 for the ACT model. The adjusted value of the refraction index is plausible (n≈1.32) for both leaves while the retrieved roughness values perpendicular to the veins (sorghum=0.56; wheat=0.46) is about two times larger than that parallel to the veins (sorghum=0.27; wheat=0.18). Nonetheless, the observed residual discrepancies between the ACT model simulations and the measurements may be explained mainly by the Lambertian assumption of the volume scattering.

Correction of Reflectance Anisotropy Effects of Vegetation on Airborne Spectroscopy Data and Derived Products

Directional effects in airborne imaging spectrometer (IS) data are mainly caused by anisotropic reflectance behavior of surfaces, commonly described by bi-directional reflectance distribution functions (BRDF). The radiometric and spectral accuracy of IS data is known to be highly influenced by such effects, which prevents consistent comparison of products. Several models were developed to approximate surface reflectance anisotropy for multi-angular observations. Few studies were carried out using such models for airborne flight lines where only a single observation is available for each ground location. In the present work, we quantified and corrected reflectance anisotropy on a single airborne HyMap flight line using a Ross-Li model. We stratified the surface in two vegetation structural types (different in vertical structuring) using spectral angle mapping, to generate a structure dependent set of angular observations. We then derived a suite of products [indices (structure insensitive pigment index, normalized difference vegetation index, simple ratio index, and anthocyanin reflectance index) and inversion-based (SAIL/PROSPECT-leaf area index, Cw, Cdm, Cab)] from corrected and uncorrected images. Non-parametric analysis of variance (Kruskal-Wallis test) showed throughout significant improvements in products from corrected images. Data correction resulting in airborne nadir BRDF adjusted reflectance (aNBAR) showed uncertainty reductions from 60 to 100% (p-value = 0.05) as compared to uncorrected and nadir observations. Using sparse IS data acquisitions, the use of fully parametrized BRDF models is limited. Our normalization scheme is straightforward and can be applied with illumination and observation geometry being the only a priori information. We recommend aNBAR generation to precede any higher level airborne IS product generation based on reflectance data.