Polarimetric Bidirectional Reflectance Distribution Function Research Articles

Active-illumination extension to the Priest and Meier pBRDF.

This paper develops a 3D vector solution for the scattering of partially coherent laser-beam illumination from statistically rough surfaces. Such a solution enables a rigorous comparison to the well-known Priest and Meier polarimetric bidirectional reflectance distribution function (pBRDF) [Opt. Eng.41(5), 988 (2002)10.1117/1.1467360]. Overall, the comparison shows excellent agreement for the normalized spectral density and the degree of polarization. Based on this agreement, the 3D vector solution also enables an extension to the Priest and Meier pBRDF that accounts for the effects of active illumination. In particular, the 3D vector solution enables the development of a closed-form expression for the spectral degree of coherence. This expression provides a gauge for the average speckle size based on the spatial-coherence properties of the laser source. Such an extension is of broad interest to long-range applications that deal with speckle phenomena.

Shape From Polarization With Distant Lighting Estimation.

This article presents a new approach for surface normal recovery from polarization images under an unknown distant light. Polarization provides rich cues of object geometry and material, but it is also influenced by different lighting conditions. Different from previous Shape-from-Polarization (SfP) methods, which rely on handcrafted or data-driven priors, we analytically investigate the benefits of estimating distant lighting for resolving the ambiguity in normal estimation from SfP using the polarimetric Bidirectional Reflectance Distribution Function (pBRDF) based image formation model. We then propose a two-stage learning framework that first effectively exploits polarization and shading cues to estimate the reflectance and lighting information and then optimizes the initial normal as the geometric prior. Leveraging the normal prior with the polarization cues from the input images, our network further generates the surface normal with more details in the second stage. We also present a data generation pipeline derived from the pBRDF model enabling model training and create a real dataset for evaluation of SfP approaches. Extensive ablation studies show the effectiveness of our designed architecture, and our approach outperforms existing methods in quantitative and qualitative experiments on real data.

Analysis of polarization characteristics of backscattered light and reflected light of underwater active light source

The analysis of the polarization characteristics of reflected light and backscattered light can provide theoretical support for the research on key technologies of underwater active light source polarization imaging. The influence of the parameters of different light sources, environments, and reflective targets on the characteristics of the reflected light was analyzed. The difference in the degree of polarization between the reflected light and the backscattered light was also determined. A Monte Carlo numerical simulation method based on a combination of Mie scattering theory and polarimetric bidirectional reflectance distribution function was used to establish underwater photon scattering and reflection-tracking models. Through simulation and analysis of the influence of the underwater environment system on the polarization characteristics of the backscattered photons and the reflected photons of different polarization types of the incident light, the following conclusions are drawn. First, in the same condition, the difference in polarization characteristics of backscattered and reflected light of circularly polarized light was larger than linearly polarized light. This is due to the better polarization-maintaining ability of circularly polarized light than linearly polarized light. Second, when various types of materials were used as reflective targets, the difference in their complex refractive indices changed the polarization of the reflected photons. And the complex refractive index had varying effects on the two types of polarized light.

Image-based acquisition and modeling of polarimetric reflectance

Realistic modeling of the bidirectional reflectance distribution function (BRDF) of scene objects is a vital prerequisite for any type of physically based rendering. In the last decades, the availability of databases containing real-world material measurements has fueled considerable innovation in the development of such models. However, previous work in this area was mainly focused on increasing the visual realism of images, and hence ignored the effect of scattering on the polarization state of light, which is normally imperceptible to the human eye. Existing databases thus only capture scattered flux, or polarimetric BRDF datasets are too directionally sparse (e.g., in-plane) to be usable for simulation. While subtle to human observers, polarization is easily perceived by any optical sensor (e.g., using polarizing filters), providing a wealth of additional information about shape and material properties of the object under observation. Given the increasing application of rendering in the solution of inverse problems via analysis-by-synthesis and differentiation, the ability to realistically model polarized radiative transport is thus highly desirable. Polarization depends on the wavelength of the spectrum, and thus we provide the first polarimetric BRDF (pBRDF) dataset that captures the polarimetric properties of real-world materials over the full angular domain, and at multiple wavelengths. Acquisition of such reflectance data is challenging due to the extremely large space of angular, spectral, and polarimetric configurations that must be observed, and we propose a scheme combining image-based acquisition with spectroscopic ellipsometry to perform measurements in a realistic amount of time. This process yields raw Mueller matrices, which we subsequently transform into Rusinkiewicz-parameterized pBRDFs that can be used for rendering. Our dataset provides 25 isotropic pBRDFs spanning a wide range of appearances: diffuse/specular, metallic/dielectric, rough/smooth, and different color albedos, captured in five wavelength ranges covering the visible spectrum. We demonstrate usage of our data-driven pBRDF model in a physically based renderer that accounts for polarized interreflection, and we investigate the relationship of polarization and material appearance, providing insights into the behavior of characteristic real-world pBRDFs.

Active Polarimetric Measurements for Identification and Characterization of Space Debris

A bench-top polarimeter (λ = 1064 nm) is used to measure the polarimetric bidirectional reflectance distribution function of several common spacecraft materials in both bistatic and monostatic geometries. The Mueller matrix and polarimetric properties of each material were estimated as a function of the illumination and viewing angles. The findings expand upon previous research suggesting that active polarimetry may be useful for the remote characterization and identification of space debris.

Expression of the degree of polarization based on the geometrical optics pBRDF model.

An expression of the degree of polarization (DOP) based on the geometrical optics polarimetric bidirectional reflectance distribution function model is presented. In this expression, the DOP is related to the surface roughness and decreases at different reflection angles because diffuse reflection is taken into consideration. A shadowing/masking function introduced into the specular reflection expression makes the DOP values decrease as the angle of incidence or observation approaches grazing. Different kinds of materials were measured to validate the accuracy of this DOP expression. The measured results suggest that the errors of the DOP are reduced significantly, and the polarized reflection characteristics can be described more reasonably and accurately.

Modified polarimetric bidirectional reflectance distribution function with diffuse scattering: surface parameter estimation

The polarimetric bidirectional reflectance distribution function (pBRDF) describes the relationships between incident and scattered Stokes parameters, but the familiar surface-only microfacet pBRDF cannot capture diffuse scattering contributions and depolarization phenomena. We propose a modified pBRDF model with a diffuse scattering component developed from the Kubelka–Munk and Le Hors et al. theories, and apply it in the development of a method to jointly estimate refractive index, slope variance, and diffuse scattering parameters from a series of Stokes parameter measurements of a surface. An application of the model and estimation approach to experimental data published by Priest and Meier shows improved correspondence with measurements of normalized Mueller matrix elements. By converting the Stokes/Mueller calculus formulation of the model to a degree of polarization (DOP) description, the estimation results of the parameters from measured DOP values are found to be consistent with a previous DOP model and results.

Efficient polarimetric BRDF model.

The purpose of the present manuscript is to present a polarimetric bidirectional reflectance distribution function (BRDF) model suitable for hyperspectral and polarimetric signature modelling. The model is based on a further development of a previously published four-parameter model that has been generalized in order to account for different types of surface structures (generalized Gaussian distribution). A generalization of the Lambertian diffuse model is presented. The pBRDF-functions are normalized using numerical integration. Using directional-hemispherical reflectance (DHR) measurements, three of the four basic parameters can be determined for any wavelength. This simplifies considerably the development of multispectral polarimetric BRDF applications. The scattering parameter has to be determined from at least one BRDF measurement. The model deals with linear polarized radiation; and in similarity with e.g. the facet model depolarization is not included. The model is very general and can inherently model extreme surfaces such as mirrors and Lambertian surfaces. The complex mixture of sources is described by the sum of two basic models, a generalized Gaussian/Fresnel model and a generalized Lambertian model. Although the physics inspired model has some ad hoc features, the predictive power of the model is impressive over a wide range of angles and scattering magnitudes. The model has been applied successfully to painted surfaces, both dull and glossy and also on metallic bead blasted surfaces. The simple and efficient model should be attractive for polarimetric simulations and polarimetric remote sensing.

Results of a new polarimetric BRDF simulation of metallic surfaces

The polarimetric bidirectional reflectance distribution function (BRDF) can effectively model the polarimetric signatures of object surface, such as paints or metal. Meanwhile the simulation of this model can bring about more polarization information which may be beneficial to improve detection efficiency or target detection. In this paper, we reiterate the classical BRDF model and obtain the three-dimensional images of the polarimetric BRDF Mueller matrix components especially the off-diagonal elements in the actual scenario. Through the simulation, we achieve a preliminary understanding about the each components: the shapes of the components can be classified into two types, the components of the standard reflection Mueller matrix present obvious single apex, the others relating the depolarization present double peak. And some components have specific features about the incident angle. The relevant experiments have be designed and implemented to prove the correctness of the simulation. As well as the unimodal components, the bimodal components have been captured in the experiment for the first time. The preliminary interpretation about this bimodal structure has been given too.

Gonioreflectometric properties of metal surfaces

Angularly resolved measurements of scattered light from surfaces can provide useful information in various fields of research and industry, such as computer graphics, satellite based Earth observation etc. In practice, empirical or physics-based models are needed to interpolate the measurement results, because a thorough characterization of the surfaces under all relevant conditions may not be feasible. In this work, plain and anodized metal samples were prepared and measured optically for bidirectional reflectance distribution function (BRDF) and mechanically for surface roughness. Two models for BRDF (Torrance–Sparrow model and a polarimetric BRDF model) were fitted to the measured values. A better fit was obtained for plain metal surfaces than for anodized surfaces.

Investigation of limits of applicability of the pBRDF model for active polarimeters

The polarimetric bidirectional reflectance distribution function is modeled for active polarimeters. The applicability boundaries of the model are determined based on the comparison of the simulated and experimental data.

Determining the complex index of refraction of an unknown object using turbulence-degraded polarimetric imagery

A novel index-of-refraction material-characterization technique using passive polarimetric imagery degraded by atmospheric turbulence is presented. The method uses a variant of the LeMaster and Cain (J. Opt. Soc. Am. A 25(9), 2170-2176 (2008)) blind-deconvolution algorithm to recover the true object (i.e., the first Stokes parameter), the degree of linear polarization, and the polarimetric-image point spread functions. Nonlinear least squares is then used to find the value of the complex index of refraction that best fits the theoretical degree of linear polarization, derived using a polarimetric bidirectional reflectance distribution function, to the turbulence-corrected degree of linear polarization. To verify the proposed material-characterization technique, experimental results of two painted metal samples are provided and analyzed. C

Spectro-polarimetric bidirectional reflectance distribution function determination of in-scene materials and its use in target detection applications

For sensing systems that characterize the spectro-polarimetric radiance reaching the camera, the origin of the sensed phenomenology is a complex mixture of sources. While some of these sources do not contribute to the polarimetric signature, many do such as the polarization state of the downwelled sky radiance, the target and background p-BRDF(polarimetric bidirectional reflectance distribution function), the polarization state of the upwelled path radiance, and the sensor Mueller matrix transfer function. In this paper we derive portions of the p-BRDF in terms of both the spectral diffuse and polarimetric specular components of the reflectance using an in-scene calibration technique. This process is applied to simulated data, laboratory data, and data from a field collection. Spectra of a car panel for clean and contaminated states derived using laboratory data are injected into a hyperspectral image cube. It is shown how this target can be identified using a target specific tracking vector derived from its polarimetric signature as it moves between spatial locations within a scene.

A geometrical optics polarimetric bidirectional reflectance distribution function for dielectric and metallic surfaces

A polarimetric bidirectional reflectance distribution function (pBRDF), based on geometrical optics, is presented. The pBRDF incorporates a visibility (shadowing/masking) function and a Lambertian (diffuse) component which distinguishes it from other geometrical optics pBRDFs in literature. It is shown that these additions keep the pBRDF bounded (and thus a more realistic physical model) as the angle of incidence or observation approaches grazing and better able to model the behavior of light scattered from rough, reflective surfaces. In this paper, the theoretical development of the pBRDF is shown and discussed. Simulation results of a rough, perfect reflecting surface obtained using an exact, electromagnetic solution and experimental Mueller matrix results of two, rough metallic samples are presented to validate the pBRDF.

Polarimetric microfacet scattering theory with applications to absorptive and reflective surfaces

We investigate the polarimetric scattering properties of highly absorbing and highly reflective rough surfaces in the IR. We obtain Muel- ler matrix measurements from these surfaces and compare the data to a Fresnel model. From the data, we determine that a rough, highly absorb- ing surface has a higher degree of polarization compared to a rough, highly reflective surface. In addition, we present a full polarimetric ver- sion of the microfacet model and discuss its properties. This closed-form result for the polarimetric bidirectional reflectance distribution function (BRDF) is derived from the microfacet model. © 2002 Society of Photo-Optical

Polarimetric bidirectional reflectance distribution function of glossy coatings

An analytic expression is derived for the angle-dependent polarimetric bidirectional reflectance distribution function (BRDF) of a glossy coating consisting of a Lambertian reflector covered by a specular dielectric layer. This model conforms to all the requirements of a real BRDF and explains the angular dependence of the polarized BRDF measurements of a glossy paint. Two common assumptions about the properties of paint coatings are shown to be incorrect: Multiple scattering by paint pigments will seldom completely depolarize the reflected energy, and, even when it does, the first surface and the volume scattering cannot be completely separated based on polarization alone. Guidelines for using the model to separate first-surface and volume scattering components are proposed.