Matrix Bidirectional Reflectance Distribution Function Research Articles

Mitigating Illumination-, Leaf-, and View-Angle Dependencies in Hyperspectral Imaging Using Polarimetry

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 that, at certain solar incidences and sensor viewing angles, presents unwanted signals. The research presented here involves the convergence of 2 parallel projects to develop a facile algorithm that 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 Mueller matrix bidirectional reflectance distribution function (mmBRDF) instrument which measures the polarized light-scattering behavior of individual maize leaves. The mmBRDF data was fitted to an existing model, which outputs parameters that were used to run simulations. The simulated data were then used to train a shallow neural network which works by comparing unpolarized 2-band vegetation index (VI) with linearly polarized data from the low-reflectivity bands of the VI. Using GNDVI and red-edge reflection ratio 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 ( ϵ σ ) after applying the correction network on the HIP sensor data.

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.

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

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

Estimating surface orientation from microfacet Mueller matrix bidirectional reflectance distribution function models in outdoor passive imaging polarimetry

Representative examples from 3 years of measurements from JPL’s ground-based multiangle spectropolarimetric imager (GroundMSPI) are compared to a Mueller matrix bidirectional reflectance distribution function (mmBRDF). This mmBRDF is used to model polarized light scattering from solar illuminated surfaces. The camera uses a photoelastic-modulator-based polarimetric imaging technique to measure linear Stokes parameters in three wavebands (470, 660, and 865 nm) with a ±0.005 uncertainty in degree of linear polarization. GroundMSPI measurements are made over a range of scattering angles determined from a fixed viewing geometry and varying sun positions over time. This microfacet mmBRDF model predicts an angle of the linear polarization that is consistently perpendicular to the scattering plane and therefore is only appropriate for rough surface types. The model is comprised of a volumetric reflection term plus a specular reflection term of Fresnel-reflecting microfacets. The following modifications to this mmBRDF model are evaluated: an apodizing shadowing function, a Breon or Gaussian microfacet scattering density function, and treating the surface orientation as an additional model parameter in the specular reflection term. The root-mean-square error (RMSE) between the GroundMSPI measurements and these various forms of the microfacet mmBRDF model is reported. Four example scenes for which a shadowed-Breon microfacet mmBRDF model yields realistic estimates of surface orientation, and the lowest RMSE among other model options are shown.

Full four-dimensional and reciprocal Mueller matrix bidirectional reflectance distribution function of sintered polytetrafluoroethylene.

We measured the Mueller matrix bidirectional reflectance distribution function (BRDF) of a sintered polytetrafluoroethylene (PTFE) sample over the scattering hemisphere for six incident angles (0°-75° in 15° steps) and for four wavelengths (351 nm, 532 nm, 633 nm, and 1064 nm). The data for each wavelength were fit to a phenomenological description for the Mueller matrix BRDF, which is an extension of the bidirectional surface scattering modes developed by Koenderink and van Doorn [J. Opt. Soc. Am. A.15, 2903 (1998)JOAOD60740-323210.1364/JOSAA.15.002903] for unpolarized BRDF. This description is designed to be complete, to obey the appropriate reciprocity conditions, and to provide a full description of the Mueller matrix BRDF as a function of incident and scattering directions for each wavelength. The description was further extended by linearizing the surface scattering mode coefficients with wavelength. This data set and its parameterization provides a comprehensive on-demand description of the reflectance properties for this commonly used diffuse reflectance reference material over a wide range of wavelengths.

Depolarization of diffusely reflecting man-made objects

The polarization properties of light scattered or diffusely reflected from seven different man-made samples are studied. For each diffusely reflecting sample an in-plane Mueller matrix bidirectional reflectance distribution function is measured at a fixed bistatic angle using a Mueller matrix imaging polarimeter. The measured profile of depolarization index with changing scattering geometry for most samples is well approximated by an inverted Gaussian function. Depolarization is minimum for specular reflection and increases asymptotically in a Gaussian fashion as the angles of incidence and scatter increase. Parameters of the Gaussian profiles fitted to the depolarization data are used to compare samples. The dependence of depolarization on the incident polarization state is compared for each Stokes basis vector: horizontal, vertical, 45 degrees, 135 degrees, and right- and left-circular polarized light. Linear states exhibit similar depolarization profiles that typically differ in value by less than 0.06 (where 1.0 indicates complete depolarization). Circular polarization states are depolarized more than linear states for all samples tested, with the output degree of polarization reduced from that of linear states by as much as 0.15. The depolarization difference between linear and circular states varies significantly between samples.