LWIR Polarimetric Imaging Process

• LWIR polarimetric imaging is a technique that maps the polarization state of thermal radiation (8–14 μm) to extract surface geometry and material properties.
• It integrates model-based inversion and learning-based approaches to convert polarization measurements into accurate surface normal estimations.
• Robust calibration with differential imaging corrects for system noise, enabling precise non-contact inspection and remote sensing even for specular objects.

Long-wave infrared (LWIR) polarimetric imaging is a measurement process that acquires spatially resolved maps of the polarization state of thermal radiation within the 8–14 μm spectrum. Owing to the opacity and emissivity of most materials in this band, LWIR polarimetric imaging captures both the polarization due to intrinsic thermal emission and the polarization resulting from reflected ambient LWIR, thereby yielding rich cues about surface geometry, material properties, and environmental interactions. The process is central to applications such as shape estimation for transparent or specular objects, material identification, remote sensing, and industrial inspection, particularly where visible-light approaches are ineffective.

1. Physical Polarization Model

LWIR polarimetric imaging in realistic scenarios must account for both emission and reflection components at the material surface. The emergent polarization signal is modeled as a linear combination of thermal emission (L_E) and reflected environmental radiation (L_R):

• Emission: Thermal photons generated within the body are transmitted through the surface with transmission coefficients $T_p$ and $T_s$ (for p- and s-polarizations), computed by the Fresnel equations.
• Reflection: Incident environmental LWIR is partially reflected as $R_p$ and $R_s$ components, also governed by Fresnel theory.

The emergent polarized radiance is thus:

$$L_p = R_p L_R + T_p L_E, \qquad L_s = R_s L_R + T_s L_E$$

Assuming unpolarized incident radiances, these terms simplify, enabling calculation of the degree of linear polarization (DoLP) and angle of linear polarization (AoLP):

$$\text{DoLP} = \left| \frac{L_p - L_s}{L_p + L_s} \right|, \qquad \text{AoLP} = \begin{cases} \text{mod}(\pi, \cdot), & L_p > L_s \ (\cdot + \pi/2) \bmod (\pi, \cdot), & L_p < L_s \end{cases}$$

This physically detailed model resolves prior deficiencies in LWIR shape-from-polarization (SfP) approaches, especially their neglect of the reflected component, thereby permitting accurate surface normal estimations even for objects transparent to visible light (2506.18217).

2. Surface Normal Recovery Strategies

Surface normals are estimated from LWIR polarimetric measurements using both analytic inversion and data-driven machine learning:

A. Model-Based Method

The analytic method exploits the non-linear relationship between DoLP and the surface zenith angle $\theta$. For a given refractive index and emission/reflection ratio, DoLP exhibits a well-characterized maximum (e.g., around $\theta \approx 79^{\circ}$), allowing for direct inversion in monotonic regions. Boundary conditions—assuming boundary normals point outward—resolve the inherent $\pi$-ambiguity in azimuth, propagating correct azimuth estimates inwards.

B. Learning-Based Approach

A neural network, utilizing a UNet backbone with Transformer layers, is trained on physically accurate synthetic LWIR images. Input features include polarization images at $0$, $\pi/4$, $\pi/2$, and $3\pi/4$, total radiance (s₀), and DoLP-related features derived from the Stokes parameters. The Forward imaging tensor incorporates terms such as:

$$L(\theta) = \frac{1}{2}(s_0 + s_1 \cos 2\theta + s_2 \sin 2\theta)$$

Training on simulated, physically correct data (using a custom Mitsuba3 renderer) enables the model to map polarization signatures directly to surface normals, robustly generalizing across material classes (2506.18217).

3. LWIR Polarimetric Imaging Process and Calibration

Accurate LWIR polarimetric imaging necessitates careful modeling and correction of system-level artifacts. The process is modeled as:

$I(\theta, s) = c^T M M(\theta) s + I_\text{off}$

• $s$ is the Stokes vector of the scene.
• $M(\theta)$ is the Mueller matrix of an ideal linear polarizer.
• $M$ models the microbolometer's polarimetric response (as a partial polarizer, with orientation-dependent gain).
• $c$ is the scalar gain.
• $I_\text{off}$ accounts for systematic noise and stray light.

A differential measurement strategy removes the additive offset by subtracting frames captured against a calibrated blackbody reference. The Stokes vector is recovered via least-squares estimation:

$s = (K^T K)^{-1} K^T I + s_b(T_\text{ref})$

where $K$ stacks the measurement matrices, and $I$ is the vector of differential images. This process, implemented with a rotating LWIR polarizer, uncooled microbolometer, and calibrated blackbody, yields reliable multi-angle measurements for robust polarimetric analysis (2506.18217).

4. Empirical Validation and the ThermoPol Dataset

The first real-world benchmark for LWIR SfP, the ThermoPol dataset, enables quantitative and qualitative assessment of new methods:

• Comprises 16 objects made from diverse materials (including LWIR-opaque but visible-transparent substrates).
• Acquisition ensures emission-dominated signals (object heating to $\sim$50°C), with ground-truth normals provided by accurately registered 3D scans of diffusely painted objects.
• Evaluations reveal that the learning-based approach achieves mean normal errors near 10°, outperforming direct model-inversion methods.
• The technique is robust to material type, surface finish, number of measurement angles, and environmental noise, providing accurate shape estimates even where visible-light cues fail (2506.18217).

5. Systematic Errors, Environmental Challenges, and Mitigations

LWIR polarimetric imaging is sensitive to several systematic factors:

• Sensor artifacts: Microbolometer drift and thermal noise introduce additive offsets ($I_\text{off}$), addressed via calibrated differential imaging.
• Stray light/reflections: These are mitigated by shielding and careful reference subtraction.
• Polarizer non-ideality: The camera's non-ideal polarimetric response is parameterized and incorporated into the recovery model.
• Acquisition speed: Accurate recovery is possible with as few as three measurement angles, potentially increasing throughput for time-sensitive or throughput-limited applications.

Experiments confirm the robustness of the system, demonstrating effective correction of systematic noise and retention of high accuracy even in uncontrolled lighting (2506.18217).

6. Implications and Applications

The integration of physically correct emission/reflection modeling, robust imaging hardware, and full-benchmark datasets represents a fundamental advance in LWIR polarimetric imaging:

• Enables passive 3D shape estimation for transparent and specular objects—a traditionally challenging regime for visible-light methods.
• Offers high accuracy across varied materials, illuminating a path forward in industrial metrology, non-contact inspection, and remote sensing.
• Establishes a reproducible framework and dataset for further research and benchmarking.

A plausible implication is that similar principles could be adapted for hyperspectral-polarimetric analysis in future LWIR systems, further expanding their domain of application.

7. Summary Table: Key Components in LWIR Polarimetric Imaging Process

Component	Function	Modeling/Correction
Emission/Reflection Mix	Determines observed polarization	Fresnel equations, linear combination (Lₚ, Lₛ)
Imaging Hardware	Acquisition of multi-angle measurements	Rotating polarizer, microbolometer sensor, calibrated blackbody
Data Processing	Extraction of Stokes vector, surface normal estimation	Model inversion or neural network regression (UNet+Transformer)
Calibration	Correction of offsets, system response	Differential imaging, characterization of $I_\text{off}$, gain, etc.
Data Benchmarking	Quantitative validation across materials	ThermoPol dataset, registered 3D ground truth

This process, rigorously grounded in physical modeling and experimental correction, defines the state-of-the-art for accurate, passive LWIR polarimetric imaging and surface shape estimation (2506.18217).