Bidirectional Reflectance Distribution Function Research Articles

Mitigating illumination-, leaf-, and view-angle dependencies in hyperspectral imaging using polarimetry.

Abstract Automation of plant phenotyping using data from high-dimensional imaging sensors is on the forefront of agricultural research for its potential to improve seasonal yield by monitoring crop health and accelerating breeding programs. A common challenge when capturing images in the field relates to the spectral reflection of sunlight (glare) from crop leaves which, at certain solar incidences and sensor viewing angles, presents unwanted signals. The research presented here involves the convergence of two parallel projects to develop an algorithm which can use polarization data to decouple light reflected from the surface of the leaves and light scattered from the leaf's tissue. The first project is a mast-mounted hyperspectral imaging polarimeter (HIP) that can image a maize field across multiple diurnal cycles throughout a growing season. The second project is a multistatic fiber-based (MFB) Mueller matrix bidirectional reflectance distribution function (mmBRDF) instrument which measures the polarized light-scattering behavior of individual maize leaves. This data was fitted to an existing model using SCATMECH, which outputs parameters that were used to run Monte Carlo simulations. The simulated data were then used to train a shallow neural network which works by comparing unpolarized two-band vegetation index (VI) with linearly polarized data from the low-reflectivity bands of the VI. Using GNDVI and Red-edge Reflection Ratio (RERR) we saw an improvement of an order of magnitude or more in the mean error (ε) and a reduction spanning 1.5 to 2.7 in their standard deviation (εσ) after applying the correction network on the HIP sensor data.

Vicarious calibration of the Tropospheric Monitoring Instrument (TROPOMI) short-wave infrared (SWIR) module over the Railroad Valley Playa

Abstract. The short-wave infrared (SWIR) module of the Tropospheric Monitoring Instrument (TROPOMI) on board the ESA's Sentinel-5 precursor (S5p) satellite has been very stable during its 5 years in orbit. Calibration was performed on the ground, complemented by measurements during in-flight instrument commissioning. The radiometric response and general performance of the SWIR module are monitored by on-board calibration sources. We show that after 5 years in orbit, TROPOMI-SWIR has continued to show excellent performance with degradation of at most 0.1 % in transmission and having lost less than 0.3 % of the detector pixels. Independent validation of the instrument calibration, via vicarious calibration, can be done through comparisons with ground-based reflectance data. In this work, ground measurements at the Railroad Valley Playa, a valley in central Nevada that is often used as a reference for satellite measurements, are used to perform vicarious calibration of the TROPOMI-SWIR measurements. This is done using dedicated measurement campaigns as well as automated reflectance measurements within the RADCALNET programme. As such, TROPOMI-SWIR is an excellent test case to explore the methodology of vicarious calibration applied to infrared spectroscopy. Using methodology developed for the vicarious calibration of the OCO-2 and GOSAT missions, the absolute radiometry of TROPOMI-SWIR performance is independently verified to be stable down to ∼ 6 %–10 % using the Railroad Valley when both the absolute and relative radiometric calibrations are applied. Differences with the on-board calibration originate from the bidirectional reflection distribution function (BRDF) effects of the desert surface, the large variety in viewing angles, and the different sizes of footprints of the TROPOMI pixels. Vicarious calibration is shown to be an additional valuable tool in validating radiance-level performances of infrared instruments such as TROPOMI-SWIR in the field of atmospheric composition. It remains clear that for instruments of similar design and resolution to TROPOMI-SWIR, on-board calibration sources will continue to provide superior results due to the limitations of the vicarious calibration method.

Modified Model of Polarized Bidirectional Reflectance Distribution Function Used for Light Detection and Ranging (LiDAR)

In order to analyze the performance of a light detection and ranging system based on polarization modulation, it is necessary to theoretically analyze and model the polarization scattering characteristics of common target materials. In this paper, the shortcomings of the classical Hyde pBRDF (polarization bidirectional reflectance distribution function) model are analyzed. Based on the research results of many researchers in recent years, a new six-parameter pBRDF model is proposed. To verify the accuracy of the proposed model, this paper builds a measurement system for the polarization scattering characteristics of the target surface in the laser active imaging scene, and the polarization scattering characteristics of two common materials, namely a white paint coating and an aluminum plate, are measured. Based on the measurement results of the DOP (degree of polarization) of the scattered light of the target material and the BBO-FA (biogeography-based optimization-Firefly algorithm) algorithm, we performed inversion calculations on the key parameters of the target material. Using the parameters of the target material obtained via inversion, we use the model to simulate the Stokes vectors of the target and compare the simulated values of Stokes vectors with the measured values to verify the accuracy of the model. The verification results show that the simulation results of Stokes vectors are in good agreement with the measurement results for these two materials, and the introduction of various improvements to the model can effectively improve the accuracy of the model, which provides a tool for studying the performance parameters of a laser three-dimensional imaging system based on polarization modulation.

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.

Generating Parametric BRDFs from Natural Language Descriptions

AbstractArtistic authoring of 3D environments is a laborious enterprise that also requires skilled content creators. There have been impressive improvements in using machine learning to address different aspects of generating 3D content, such as generating meshes, arranging geometry, synthesizing textures, etc. In this paper we develop a model to generate Bidirectional Reflectance Distribution Functions (BRDFs) from descriptive textual prompts. BRDFs are four dimensional probability distributions that characterize the interaction of light with surface materials. They are either represented parametrically, or by tabulating the probability density associated with every pair of incident and outgoing angles. The former lends itself to artistic editing while the latter is used when measuring the appearance of real materials. Numerous works have focused on hypothesizing BRDF models from images of materials. We learn a mapping from textual descriptions of materials to parametric BRDFs. Our model is first trained using a semi‐supervised approach before being tuned via an unsupervised scheme. Although our model is general, in this paper we specifically generate parameters for MDL materials, conditioned on natural language descriptions, within NVIDIA's Omniverse platform. This enables use cases such as real‐time text prompts to change materials of objects in 3D environments such as “dull plastic” or “shiny iron”. Since the output of our model is a parametric BRDF, rather than an image of the material, it may be used to render materials using any shape under arbitrarily specified viewing and lighting conditions.

Reconstruction of a large-scale realistic three-dimensional (3-D) mountain forest scene for radiative transfer simulations

ABSTRACT The realistic three-dimensional (3D) forest scene is an important input to 3D radiative transfer simulations, which are essential for analyzing the reflective properties of forest canopies. Previous studies utilized the voxel as an essential element to reconstruct the 3D forest scene, while they mainly focused on the small flattened areas and ignored the wood components. This study introduces a novel approach for reconstructing a realistic 3D mountain forest scene by incorporating branches into the voxel crown. To determine the optimal voxel size for simulating Bidirectional Reflectance Functions (BRFs) in a temperate deciduous mountain forest, this study reconstructed the forest scene using eight different voxel sizes, ranging from 30 to 100 cm with a step of 10 cm. Two forest scenes were examined to evaluate the impact of branches on radiative transfer simulations: one with branch voxel-based scenes and one without branches. The radiative transfer simulation is conducted using an efficient Monte Carlo path-tracing algorithm and has been implemented in the LargE-Scale remote sensing data and image Simulation framework (LESS) model, facilitating high-quality, large-scale simulations of forested environments. The finding revealed that the optimal voxel size for simulating BRFs in 30 m resolution is approximately 90 cm, smaller than the 100 cm used in flat areas. This study emphasized the significant impact of branches on the BRF simulations and underscored their critical role in scene reconstruction. The impact of branches is two-fold: branches themselves increase the simulated BRFs, whereas their shadows decrease them. Moreover, the effects of branches and their shadows decrease as the voxel size increases. The simulated spectral albedo exhibits maximum deviations of 0.71% and 1.04% in the red and NIR wavebands, respectively, while remaining below 0.2% in the blue waveband. Furthermore, the study suggests that if the precise branch architecture is unknown, constructing branches of the first generation is recommended to achieve better results. Additionally, the results demonstrate that the proposed scene achieves greater accuracy and robustness when compared to both the ellipsoid-based and the boundary-based scenes. The finding of this study can help researchers to better understand the underlying mechanisms driving the reflective properties of forest canopies, which can inform future studies and improve the accuracy of forest monitoring and ecological modeling.

NEW SURFACE REFLECTANCE MODEL WITH THE COMBINATION OF TWO CUBIC FUNCTIONS USAGE

In the article the model of light reflection based on the combination of two cubic bidirectional reflectance distribution functions is developed. The main components of color and the main requirements for reproducing the object`s glares are analyzed. The usage characteristics of Cook-Torrance, Bagher, Oren-Nayar, coupled Shirley reflection models are described. The advantages and disadvantages of the highly productive Blinn-Phong model are considered. The necessity of approximating the Blinn-Phong model by a function of low degree is justified. The characteristics of the cubic polynomial approximation of the Blinn-Phong model are determined. It was established that the main drawback of this approximation is a significant deviation of the function from the reference function in the glare’s attenuation zone. The combined function that combines two cubic functions is proposed. The first cubic function reproduces the glare’s epicenter, and the second replaces the specified function in the attenuation zone. A system of equations for calculating the coefficients of the second function was created. The formula for the connection point of two cubic functions is obtained. A graph of the developed combined model based on cubic functions is obtained. For the combined and original cubic functions a comparison of the maximum relative errors in the glare’s epicenter zone, the maximum absolute errors, and the relative errors at the inflection point was made. A three-dimensional plot of the absolute error of the combined cubic model from the Blinn-Phong model depending on the shininess and the angle value is built. Visualization results based on the combined and the original cubic functions are compared. It is confirmed that the proposed reflection model increases the realism of glare formation in the attenuation zone. The resulting combined reflection model provides a highly accurate approximation of the Blinn-Phong model and is highly efficient because the third power function is used.

One-shot reflectance direction color mapping for identifying surface roughness

Surface roughness, an important property of products, can be identified using the bidirectional reflectance distribution function (BRDF). A method to identify surface roughness is thus proposed using a one-shot reflectance direction color mapping imaging system. This imaging system can capture BRDF information across the entire field of view in one shot. Histograms of color variations in the captured images reveal that the surfaces with different roughness values on a metal piece can be identified even at a sub-micrometer scale.

BRDF representation in response to the build orientation in 3D-printed digital materials

Additively manufactured (AM) parts still lack a thorough understanding of their optical properties, particularly surface texture and reflectance characteristics at different viewing angles. This study examines the reflectance properties of material jetting (MJT) parts using bidirectional reflectance distribution functions (BRDFs). The visual appearance of the MJT parts was analyzed using a gonio-spectrophotometer at 328 unique incidence and viewing geometries for seven different wedge angles for build orientation (BO) from 0° to 90° at 15° intervals. The redundancy analysis (RDA) and principal component analysis (PCA) were used to study BO and to determine the prominent measurement geometries. The results indicate higher BOs resulted in more color and texture variation and rougher surfaces, with Sq 4.21 μm vertical compared to 1.42 μm for horizontal BOs. Furthermore, it affected the visual representation and parametric estimation of BRDF, where significantly lower luminance, more diffuse reflection, and less hue distribution were observed for all CMYK resins printed at higher BOs. Accordingly, vertically printed surfaces showed a wider near-to-specular luminance area than other BOs. An analysis of the bidirectional reflectance property suggests that a gonio-spectrophotometer can be embedded in the printing process and quality assurance in AM as a computationally efficient model.

A reproducible and replicable approach for harmonizing Landsat-8 and Sentinel-2 images

Clouds and cloud shadows significantly impact optical remote sensing. Combining images from different sources can help to obtain more frequent time series of the Earth’s surface. Nevertheless, sensor differences must be accounted for and treated before combining images from multiple sensors. Even after geometric correction, inter-calibration, and bandpass, disparities in image measurements can persist. One potential factor contributing to this phenomenon is directional effects. Bidirectional reflectance distribution function (BRDF) corrections have emerged as an optional processing method to soften differences in surface reflectance (SR) measurements, where the c-factor is one of the available options for this task. The c-factor efficiency is well-proven for medium spatial resolution products. However, its use should be restricted to images from sensors with a narrow view since it causes subtle changes in the processed images. There are currently a limited number of open tools for users to independently process their images. Here, we implemented the required tools to generate a Nadir BRDF-Adjusted Surface Reflectance (NBAR) product through the c-factor approach, and we evaluated them for a study area using Landsat-8 and Sentinel-2 images. Several comparisons were conducted to verify the SR and NBAR differences. Initially, a single-sensor approach was adopted and later a multi-source approach. Notably, NBAR products exhibit fewer disparities compared to SR products (prior to BRDF corrections). The results reinforce that the c-factor can be used to improve time series compatibility and, most importantly, provide the tools to allow users to generate the NBAR products themselves.

Analysis of scratch visibility on polymeric surfaces using 3D roughness measurement and the bidirectional reflectance distribution function (BRDF)

The evolution of visual aspect of polymers with wear is a fundamental problem in numerous industries. In this article, we study the visibility of scratches. Fifty parallel micro-scratches are performed on three samples differing only by their values of gloss. Scratches are much more visible on glossy samples than on mat ones, in agreement with previous works. To interpret these results, a bidirectional reflectance distribution function (BRDF) model is developed to compute the way a surface scatters light based on a roughness measurement described by a distribution of microfacet orientations. In this paper, this BRDF model is applied to investigate the influence of the scratches on the light scattering properties of a surface. Roughness measurements are performed on the surfaces before and after scratching. Then, the BRDFs are computed and compared to each other. The visibility of scratches strongly depends on how much they modify the roughness slope distribution function of the surface. Depending on the initial gloss of the surface, this leads to more or less contrast. Finally, a visibility criterion is proposed based on this contrast effect.

Three-dimensional measurement of fringe projection based on the camera response function of the quantified exposure time

Fringe projection technology is usually used for three-dimensional (3D) measurement, but there will be large errors when the measurement is overexposed or the surface is too dark. Polarizing filters can be used to eliminate the highlights of the image, but they may also cause the image to be too dark and affect the measurement accuracy. Otherwise, to ensure measurement accuracy, the complexity of the operation of the polarization system will be increased. In order to ensure the measurement accuracy and improve the measurement efficiency, a 3D measurement method of quantified exposure time is proposed in this paper, and the intensity response function of the light intensity captured by the camera and the exposure time is established, and more meaningful variable value intervals can be selected by the method of this paper. It can avoid the complex polarization bidirectional reflectance distribution function model, and the required exposure time can be calculated quantitatively within the already screened intervals. Then it is combined with the image fusion algorithm to generate the optimal fringe pattern. Experimental results demonstrate that this method significantly eliminates the effects of highlights in the image. The fuzzy transition area between the black and white fringes is effectively reduced, and the edge information of the fringes is correctly restored.

PROSPECULAR: A model for simulating multi-angular spectral properties of leaves by coupling PROSPECT with a specular function

Understanding the optical properties of leaves is of great importance for characterizing the relationships between leaf traits and remote sensing signals. The relationship between biochemical parameters and leaf spectral reflection has been widely established through PROSPECT, while surface structural parameters can be linked to leaf multi-angular reflection through Bidirectional Reflectance Distribution Function (BRDF) models. However, it's still challenging to characterize how leaf spectra response changes with different illumination and viewing geometries, in connection to both biochemical and surface structural traits. To address this challenge, we propose the model PROSPECULAR, which combines PROSPECT with a specular function determined by illumination-viewing geometry parameters, wavelength-dependent refractive index, and roughness. This model simulates spectral and multi-angular BRF and retrieves both leaf biochemical and surface structural parameters. The PROSPECULAR accounts for the wavelength dependence of the leaf surface refractive index in the specular function and separates the specular reflection from PROSPECT in the diffuse component calculation. The accuracy of PROSPECULAR's spectral simulation was assessed using a multi-angular dataset measured in the hemispherical space (42 viewing zenith angles (VZAs) at 20–50° source zenith angles (SZAs)). Then, the inversion accuracy of PROSPECULAR was validated using a multi-angular dataset measured in the principal plane (13 VZAs and 20–50° SZAs). The results showed that PROSPECULAR was able to simulate multi-angular BRF (RRMSE = 16.27%) when SZA was <50° and retrieve a unified set of biochemical parameters for each leaf sample using multi-angular BRF (RMSE of chlorophyll, water, dry matter, protein, and carbon-based constituents were 11.31 μg/cm2, 0.0029 g/cm2, 0.0022 g/cm2, 0.00096 g/cm2, and 0.0028 g/cm2, respectively). The agreement between the calculations and measurements of multi-angular BRF for various plant species indicated that PROSPECULAR is an effective leaf optical model. In contrast, the existing radiative transfer models (PROSPECT, PROCWT, PROCOSINE, and PROSDM) showed varying levels of accuracy in inverting biochemical parameters, depending on the VZA. The advantage of PROSPECULAR is its potential for characterizing both spectral and directional properties of leaves at arbitrary given illumination-viewing geometry and inverting leaf parameters using BRF data from several VZAs in the hemispherical space.

Investigation of Surface Defects in Optical Components Based on Reflection Mueller Matrix Spectroscopy

Nanoscale defects on the surface of ultra-precision optical elements seriously affect the beam quality in optical systems. In response to the challenge of detecting nanoscale defects on optical component surfaces, we propose a method for the detection and classification of various types of defects on optical component surfaces via reflection Mueller matrix spectroscopy (RMMS). Firstly, an electromagnetic scattering theoretical model for various types of defects on the surface of optical elements and the incident and scattered fields were established by combining the bidirectional reflection distribution function (BRDF) and the Rayleigh–Rice vector scattering theory. Then, the optimal conditions for RMMS measurements were determined by numerically simulating the BRDF. On this basis, the surface roughness and pockmarks of the optical test plate were simulated and analyzed via RMMS, and the results were verified experimentally; then, dirty particles and pockmarks above the surface of the optical element and subsurface bubble defects (SSBD) were simulated and analyzed via RMMS. The results showed that some elements of the Mueller matrix could significantly distinguish defects on the surface of the optical element with dimensions smaller than the visible wavelength, and the dimensions of various types of defects of the element could be inverted using the values of the Mueller matrix elements. This method provides a theoretical basis and reference for the detection and classification of various types of defects in precision optical components.

Space-Based THz Radar Fly-Around Imaging Simulation for Space Targets Based on Improved Path Tracing

Aiming at the space target detection application of a space-based terahertz (THz) radar, according to the imaging mechanism of broadband THz radars, a THz radar imaging simulation method based on improved path tracing is proposed. Firstly, the characterization method of THz scattering characteristics based on Kirchhoff’s approximation method is introduced. The multi-parameter THz bidirectional reflectance distribution function (THz-BRDF) models of aluminum (Al), white-painted Al, and polyimide film at 0.215 THz are fitted according to the theoretical data, with fitting errors below 4%. Then, the THz radar imaging simulation method based on improved path tracing is presented in detail. The simulation method utilizes path tracing to simulate parallelized THz radar echo signal data, considering multi-path energy scattering based on the THz-BRDF model. Finally, we conducted THz radar imaging simulation experiments. The influences in the imaging process of different fly-around motions are analyzed, and a comparison experiment is conducted with the fast-physical optics (FPO) method. The comparative results indicate that the proposed method exhibits richer and more realistic features compared with the FPO method. The simulation experiments results demonstrate that the proposed method can provide a data source for ground algorithm testing of THz radars, particularly in evaluating the target detection and recognition algorithm based on deep learning, providing strong support for the application of space-based THz radars in the future.

Impacts of clumping effect on canopy reflectance using 3D radiative transfer modeling

The product of leaf area index (LAI) and clumping index (CI) quantifies the effective leaf abundance and distribution across the landscape, and therefore, governs the radiation absorption, evapotranspiration, and carbon assimilation processes in the terrestrial ecosystems. Previous studies were mainly focused on developing inversion methods applicable to large scale for retrieving LAI and CI from multi-angular satellite observations. However, a few studies focused on quantifying the sensitivity of canopy bidirectional reflectance distribution function (BRDF) to changes in CI in a forward manner, hampering an accurate understanding of the relationship between CI and BRDF. In this study, we simulated how BRDF responds to changes in CI in Qinghai spruce (Picea crassifolia) forests based on a 3D radiative transfer model LESS and ground-measured data. We found that the LESS model effectively simulated the hot-spot, roof, and bowl-edge characteristics of the canopy BRDF by changing the sun-sensor geometry. We constructed forest scenes with variable CI (ranging from 0.4 to 0.8) to investigate the clumping effect on BRDF with different solar and observation angles. The red band bidirectional reflectance factor (BRF) showed higher sensitivity to changes in CI than that in the near-infrared (NIR) band. Canopy BRFs in the red band along the principal plane and cross principal planes measured in different seasons showed consistent sensitivity to changes in CI, suggesting that the red band BRF is helpful for CI inversion for forests with different levels of foliage clumping. In the NIR band, canopy BRFs along the principal plane measured in growing seasons [with solar zenith angle (SZA) &amp;lt;40°] and the cross principal plane measured in non-growing seasons (with SZA &amp;gt;40°) were sensitive to changes in CI in highly clumped forests (with CI ranging from 0.4 to 0.6). However, canopy BRF in the NIR band showed low sensitivity to changes in CI in highly clumped forests (CI &amp;lt;0.6), especially along the cross principal plane when SZA was approximately 10°. The simulated BRFs in the red and NIR bands showed relatively low sensitivity to changes in SZAs at a VZA of 40° and 0°, respectively. We highly recommend including the red band BRF for CI retrievals, and using a VZA of 40° in the red band and 0° in the NIR band may help reduce the CI estimation uncertainty caused by changes in SZA. This research provides a new perspective for understanding the sensitivity of multi-angular satellite data to changes in canopy structural characteristics of vegetation in global ecosystem studies and may help improve CI estimations using the multiangular optical remote sensing data.

Improving atmospheric CO2 retrieval based on the collaborative use of Greenhouse gases Monitoring Instrument and Directional Polarimetric Camera sensors on Chinese hyperspectral satellite GF5-02

ABSTRACT The Greenhouse Gas Monitoring Instrument (GMI) onboard the Chinese hyperspectral satellite GF5–02 can provide abundant observations of global atmospheric CO2, which plays an important role in climate research. CO2 retrieval precision is the key to determining the application value of the GMI. To reduce the influence of atmospheric scattering on retrieval, we combined the Directional Polarimetric Camera (DPC) data on the same satellite to improve the anti-interference ability of GMI CO2 retrieval and ensure its retrieval precision. To realize the reliability and feasibility of the collaborative use of the GMI and DPC, this paper designs the pointing registration method of the GMI based on coastline observations, the spatial resolution matching method and the collaborative cloud screening method of the GMI and DPC observations. Combined with the DPC, which supplied the spectral data and aerosol product, the retrieval ability of the coupled bidirectional reflectance distribution function CO2 retrieval (CBCR) method developed for GMI CO2 retrieval was improved, with the retrieval efficiency of CO2 products increasing by 27%, and the CO2 retrieval precision increasing from 3.3 ppm to 2.7 ppm. Moreover, collaborative use not only guaranteed the GMI’s ability to detect global and area CO2 concentration distribution characteristics, such as significant concentration differences between the Northern and Southern Hemispheres in winter and high CO2 concentrations in urban agglomeration areas caused by human activities, but also extended the GMI’s potential for monitoring anomalous events, such as the Tonga volcanic eruption.

Radiometric Cross-Calibration of Wide-Field-of-View Cameras Based on Gaofen-1/6 Satellite Synergistic Observations Using Landsat-8 Operational Land Imager Images: A Solution for Off-Nadir Wide-Field-of-View Associated Problems

The Gaofen-1 satellite is equipped with four wide-field-of-view (WFV) instruments, enabling an impressive spatial resolution of 16 m and a combined swath exceeding 800 km. These WFV images have shown their valuable applications across diverse fields. However, achieving accurate radiometric calibration is an essential prerequisite for establishing reliable connections between satellite signals and biophysical, as well as biochemical, parameters. However, observations with large viewing angles (&gt;20°) pose new challenges due to the bidirectional reflectance distribution function (BRDF) effect having a pronounced impact on the accuracy of cross-radiation calibrations, especially for the off-nadir WFV1 and WFV4 cameras. To overcome this challenge, a novel approach was introduced utilizing the combined observations from the Gaofen-1 and Gaofen-6 satellites, with Landsat-8 OLI serving as a reference sensor. The key advantage of this synergistic observation strategy is the ability to obtain a greater number of image pairs that closely resemble Landsat-8 OLI reference images in terms of geometry and observation dates. This increased availability of matching images ensures a more representative dataset of the observation geometry, enabling the derived calibration coefficients to be applicable across various sun–target–sensor geometries. Then, the geometry angles and bidirectional reflectance information were put into a Particle Swarm Optimization (PSO) algorithm incorporating radiative transfer modeling. This PSO-based approach formulates cross-calibration as an optimization problem, eliminating the reliance on complex BRDF models and satellite-based BRDF products that can be affected by cloud contamination. Extensive validation experiments involving satellite data and in situ measurements demonstrated an average uncertainty of less than eight percent for the proposed cross-radiation calibration scheme. Comparisons of top-of-atmosphere (TOA) results calibrated using our proposed scheme, the previous traditional radiative transfer modeling using MODIS BRDF products for BRDF correction (RTM-BRDF) method, and official coefficients reveal the superior accuracy of our method. The proposed scheme achieves a 36.99% decrease in root mean square error (RMSE) and a 38.13% increase in mean absolute error (MAE) compared to official coefficients. Moreover, it achieves comparable accuracy to the RTM-BRDF method while eliminating the need for MODIS BRDF products, with a decrease in RMSE exceeding 14% for the off-nadir WFV1 and WFV4 cameras. The results substantiate the efficacy of the proposed scheme in enhancing cross-calibration accuracy by improving image match-up selection, efficiently removing BRDF effects, and expanding applicability to diverse observation geometries.

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.