Hyperspectral-Polarimetric BRDF Dataset

• The hpBRDF dataset is a high-dimensional reflectance collection that records complete Mueller matrix data over dense spectral and angular grids, enabling precise analysis of material properties.
• It employs an integrated acquisition methodology using hyperspectral imaging and dual rotating retarders to capture full Stokes and polarization responses in a single shot.
• The dataset supports advanced applications such as physically-based rendering, remote sensing, and neural representation compression to accurately simulate light–material interactions.

A hyperspectral-polarimetric bidirectional reflectance distribution function (hpBRDF) dataset is a comprehensive measurement set that characterizes how real-world materials reflect light as a function of both wavelength (hyperspectral) and polarization, parameterized over a densely sampled set of incident and outgoing viewing directions. These datasets enable advanced modeling and simulation of light–material interactions by providing full Mueller matrix data across hundreds of spectral bands, thus supporting the joint analysis of spectral, angular, and polarimetric dependencies for scientific, engineering, and graphics applications.

1. Dataset Definition and Scope

The hpBRDF dataset, as established in "Hyperspectral Polarimetric BRDFs of Real-world Materials" (Moon et al., 17 Sep 2025), contains tabulated reflectance data where each measurement is a $4 \times 4$ Mueller matrix that fully describes the transformation of the polarization state of light upon reflection for a given pair of incident and outgoing directions and a specific wavelength. The data are acquired over a dense regular grid in both angular and spectral domains:

• Spectral coverage: The dataset spans 68 spectral bands from 414 nm (visible) to 950 nm (NIR), sampled at 8 nm intervals with an effective FWHM of ~10 nm.
• Angular sampling: The spatial-angular dimensions are parameterized using the Rusinkiewicz representation. Sampling comprises 361 bins in difference azimuth ($\phi_d$) and 91 bins each for difference elevation ($\theta_d$) and half-elevation ($\theta_h$). Each (φ, θ) tuple corresponds to a full Mueller matrix.
• Material diversity: 14 distinct spherical samples—including colored plastics, metals, dielectrics, and both rough and smooth finishes—were measured, each yielding a dense multidimensional hpBRDF.

A single material's dataset occupies on the order of 13 GB, reflecting the high dimensionality and physical completeness required for precise simulation and analysis.

2. Acquisition Methodology

The acquisition system employs several integrated imaging and optical modules to efficiently measure high-dimensional hpBRDF data:

• Imaging module: Utilizes a spherical sample and dense, image-based angular sampling. Observations across the visible hemisphere can be obtained by imaging the sample from a fixed viewpoint as the illumination direction is varied.
• Spectroscopy: Achieves single-shot acquisition of multiple wavelengths using a hyperspectral light-field camera. This camera features a microlens array, with each sub-region hosting a distinct narrow bandpass filter, enabling simultaneous capture of spatial and spectral information in a single exposure.
• Polarimetry: Implements broadband ellipsometric modulation using dual rotating retarders (DRR). A polarization state generator (PSG) and polarization state analyzer (PSA), each consisting of an ultra-broadband linear polarizer and an achromatic QWP, are rotated through multiple discrete angles to facilitate full-Stokes and Mueller matrix recovery.

The fundamental measurement sequence follows:

• Polarized light generation: $$s^{(\lambda)}_{\text{emitted}}(\theta) = R^{(\lambda)}(\theta) \cdot L \cdot s^{(\lambda)}$$, where $s^{(\lambda)}$ is the incident unpolarized Stokes vector, $L$ is the LP's Mueller matrix, and $R^{(\lambda)}(\theta)$ is the QWP's Mueller matrix at rotation $\theta$.
• After reflection, the light is analyzed by: $$s^{(\lambda)}_{\text{analyzed}}(\theta', \omega_o) = L \cdot R^{(\lambda)}(\theta') \cdot s^{(\lambda)}_{\text{captured}}(\theta, \omega_o)$$.
• The sensor measures $$f(\lambda, \theta, \theta') = [s^{(\lambda)}_{\text{analyzed}}(\theta', \omega_o)]_0$$, collecting sufficient modulated measurements to invert to a full Mueller matrix per (illumination, view, wavelength) tuple.

The dataset design allows rapid collection of tens of millions of measurement configurations with high physical accuracy, simultaneously covering wavelength, angular, and polarization domains.

3. Data Analysis and Physical Parameterization

The hpBRDF dataset admits physically rigorous analysis that reveals the dependencies of material reflection on spectra, polarization, material class, and geometry. For each Mueller matrix at a fixed configuration, Lu–Chipman decomposition separates the overall interaction into fundamental physical quantities:

• Diattenuation (polarization-dependent transmission/reflectance; matrix $M_P$)
• Polarizance (ability to create polarization from unpolarized light; vector $P$)
• Depolarization (loss or mixing of polarization)
• Retardance (phase shift between s- and p-polarizations; $M_R$)

Material and surface distinctions are directly visible in these decomposed parameters. For example, analysis of the retardance submatrix elements (e.g., $M_{R,13}$, $M_{R,23}$, $M_{R,31}$, $M_{R,32}$) enables discrimination between metallic and dielectric surfaces, based on sign inversion and off-diagonal dominance. Diattenuation and polarization preservation trends reveal how colored plastics and other materials modulate spectro-polarimetric properties as a function of wavelength, often in nontrivial ways that defy intensity-only analysis.

The methodology supports both pointwise analysis (at given parameter tuples) and global examination via dimension reduction. Principal Component Analysis (PCA) over the Mueller matrix-valued domain reveals low-rank structure, with high variability and complexity in the angular domain and smoother spectral variation.

4. Rendering and Compact Neural Representations

The hpBRDF dataset facilitates physically accurate rendering across spectral and polarization domains. Using the dense Mueller matrix data, rendering pipelines (e.g., Mitsuba 3) can synthesize scenes under varied spectral illuminants and polarizations, producing not only intensity images but also maps of predicted polarization properties (e.g., degree of polarization, angular orientation, ellipticity) across the visible and NIR regimes.

Given the massive data volume, compact parameterizations are essential. Two strategies are demonstrated:

• Principal Component Compression: PCA projection onto leading eigencoefficients enables lossy, physically meaningful compression, with principal patterns interpretable as variations in polarization or angular phenomena.
• Implicit Neural Representation: A neural network, parameterized as a continuous function of (incident angle, outgoing angle, wavelength), predicts the $4\times 4$ Mueller matrix at any query point. This method achieves substantial reduction in storage (e.g., 146 kB versus 13 GB) while providing continuous interpolation and smoothness, circumvents lookup artifacts, and supports high-quality, differentiable forward simulation.

Comparison with analytical pBRDF models illustrates that while classical parametric models can match intensity (e.g., sRGB) appearance, they consistently fail to reproduce crucial polarization subtleties, particularly in the off-diagonal retardance elements.

5. Applications and Use Cases

The hpBRDF dataset underpins a new class of research and engineering applications that require rigorous spectral and polarimetric information:

• Physically-based and inverse rendering: Enables joint optimization or simulation of scene appearance under any spectral and polarization conditions, advancing realism and supporting material identification.
• Remote sensing and material inspection: The high-dimensional "fingerprint" enables advanced classification, detection of surface or composition anomalies, and improved quality control.
• Sensor and display development: Supports the design of polarization-aware cameras, photonic devices, and computational photography pipelines that exploit joint spectro-polarimetric cues.
• Dataset-based scientific studies: Facilitates detailed analysis of the spectral and polarization responses of real-world materials, especially for the validation or development of novel light transport and reflectance models.

Furthermore, the dataset’s hybrid data-driven and analytical modeling support paves the way for integration into broader AI pipelines—serving as ground-truth for neural reflectance models and spectral-polarimetric field regression.

6. Limitations and Future Directions

Current limitations of the hpBRDF dataset are determined by both hardware and reconstruction methodology:

• Acquisition trade-offs: The spatial resolution per spectral channel is reduced due to the multiplexing inherent in the hyperspectral light-field camera. Additionally, the measurement system is limited to isotropic or near-isotropic samples due to geometric constraints.
• Data completion: Certain configurations yield missing or occluded Mueller matrix entries; basic inpainting with 3D Gaussian convolution is used. There is an open opportunity to incorporate physically-informed regularization or trainable data-driven inpainting methods for improved consistency.
• Model accuracy: While implicit neural representations achieve high fidelity, further accuracy can be obtained by further refining model capacity and learning methodologies, possibly leveraging physically inspired priors.

Future efforts are anticipated to include broader material and geometry diversity, support for anisotropic BRDFs, system upgrades for higher channel resolution, and further advances in neural modeling—potentially yielding real-time, accurate, compact hpBRDF evaluation for graphics, vision, and scientific simulation.

Table: Key Data Dimensions for hpBRDF Dataset

Dimension	Range / Format	Description
Wavelength	414–950 nm (68 bands, 8 nm step)	Spectral axis; visible + NIR
Angular Sampling	361 × 91 × 91 bins (φ_d, θ_d, θ_h)	Dense angular parameterization
Data per bin	$4 \times 4$ Mueller matrix	Complete polarization mapping
Materials	14 samples	Plastics, dielectrics, metals
Data per material	~13 GB	High-dimensional storage footprint

Careful consideration of these axes is essential for both raw data analysis and effective modeling or compression. This structure ensures that advanced simulations and analyses can fully leverage the complexity and richness of real-world light–matter interaction.