A polarization-aware physics-based rendering (PBR) engine uses a Mueller matrix (MM)-valued polarized bidirectional reflectance distribution function (pBRDF) as a characterization of a given material's polarized light scattering behavior. To evaluate the ability of the pBRDF to predict polarized light scattering, this work creates a validation loop between pBRDF characterization, scene renderings, and MM imaging of scenes. A conventional method for pBRDF sampling is MM imaging of spherical objects so that many scattering geometries are simultaneously captured. This pBRDF serves as input to a polarization-aware PBR engine for rendering arbitrary object shapes and illumination geometries. In this work, spheres and the components of a Cornell box are 3D-printed to create a set of shapes made of the same material. Then a validation loop is created where the pBRDF from sphere MM measurements are used for polarimetric renderings which are compared to MM images of the Cornell box. The generalization of the pBRDF is tested using different shapes for measurement or polarimetric rendering. For example, multiple surface interactions inside the Cornell box will create polarimetric effects that are not observed by measuring spheres. The pBRDF's ability to generalize varying lighting geometries and adjacency effects will be tested.
Closed-form solutions for shape-from-polarization (SfP) generally assume either purely specular or purely diffuse polarized light scattering models. However, polarized light scattering from real-world objects is a mixture of both of these processes. This work makes use of a closed-form expression for polarized light scattering model which combines specular and diffuse contributions. In prior work, we have demonstrated the broad applicability of a triply-degenerate (TD) model which decouples depolarization from the dominant Mueller-Jones matrix (MJM). The depolarization is controlled by a single parameter and the MJM encodes the polarization-dependent properties (e.g. diattenuation, polarizance). In this work, SfP information content is explored using our model for the MJM term which combines diffuse and specular polarization to simulate single-view, noise-free Mueller images. A merit function for simultaneous estimates of per-pixel surface normal and absolute depth is proposed. Cross-sections of this merit function are shown to be convex along depth and contain erroneous ambiguities for the surface normal. While ambiguities in surface normal estimates are well known for existing SfP approaches, these cross-sections show a kind of ambiguity unique to our model. Through investigation of the idealized scenario of an exactly-known pBRDF model and noise-free, infinitely precise polarimetric measurements, we found that simultaneous depth and shape estimation is achievable.
Integrated optical models allow for accurate prediction of the as-built performance of an optical instrument. Optical models are typically composed of a separate ray trace and diffraction model to capture both the geometrical and physical regimes of light. These models are typically separated across both open-source and commercial software that don’t interface with each other directly. To bridge the gap between ray trace models and diffraction models, we have built an open-source optical analysis platform in Python called Poke that uses commercial ray tracing APIs and open-source physical optics engines to simultaneously model scalar wavefront error, diffraction, and polarization. Poke operates by storing ray data from a commercial ray tracing engine into a Python object, from which physical optics calculations can be made. We present an introduction to using Poke, and highlight the capabilities of two new propagation modules that add to the utility of existing scalar diffraction models. Gaussian Beamlet Decomposition is a ray-based approach to diffraction modeling that allows us to integrate physical optics models with ray trace models to directly capture the influence of ray aberrations in diffraction simulations. Polarization Ray Tracing is a ray-based method of vector field propagation that can diagnose the polarization aberrations in optical systems. Poke has been recently used to study the next generation of astronomical observatories, including the ground-based Extremely Large Telescopes (TMT, GMT, ELT) and a 6 meter space telescope (6MST) early concept for NASA’s Habitable Worlds Observatory.
Polarized light-matter interactions are mathematically described by the Mueller matrix (MM)-valued polarized bidirectional reflectance distribution function (pBRDF). A pBRDF is parameterized by 16 degrees of freedom that depend upon scattering geometry. A triple degenerate (TD) MM assumption reduces the degrees of freedom to eight: one for reflectance, six for non-depolarizing properties, and one for depolarization. When the non-depolarizing dominant process is known or assumed (e.g., Fresnel reflection), the degrees of freedom are further reduced to two. For a given material, if the TD model is appropriate and the dominant non-depolarizing process is known, then these two degrees of freedom can be estimated from as few as two polarimetric measurements. Thus, the MM can be extrapolated from a reduced number of measurements. The primary contribution of this work is the development and demonstration of a linear estimator for an MM’s dominant eigenvalue (i.e., single depolarization parameter) that requires fewer measurements than a full MM reconstruction. MM extrapolations from single snapshot acquisitions with a Sony Triton 5.0MP polarization camera are performed at 30 acquisition geometries and two wavelengths on an ensemble of LEGO bricks treated to have varying surface roughness. These extrapolated MMs are compared with MMs reconstructed from a complete dual rotating retarder Mueller imaging polarimeter. The flux error mean and mode are 11.06% and 1.03%, respectively, despite a 10 × reduction in the number of polarimetric measurements.
An object’s polarimetric bidirectional reflection distribution function (pBRDF) is fully parameterized by the 16 degrees of freedom of a Mueller matrix (MM) at each scattering geometry. A common pBRDF approximation to reduce the degrees of freedom is as a weighted sum of a Fresnel reflection term and an ideal depolarizer term. The weights on these terms represent fractional specular and diffuse reflection and are typically fit independently. Any MM for which the smallest three eigenvalues of the Cloude MM decomposition are identical,1 can be rewritten as a convex sum of a dominant non-depolarizing MM and an ideal depolarizer.2, 3 Therefore, the fractional contribution of each term in this pBRDF model is a single depolarization parameter which corresponds to the largest eigenvalue.2 The reduced degrees of freedom for pBRDFs described by this single depolarization parameter create an opportunity to utilize partial polarimetry. The primary contribution of this work is a linear estimator for a MM’s dominant eigenvalue which requires fewer measurements than a full MM reconstruction. Despite reducing the number of simulated measurements by a factor of 10, partial-polarimetry and full Mueller polarimetry eigenvalue estimates are comparable. Root-mean-squared error (RMSE) averaged over acquisition geometry for eigenvalues of a white and a gray balance card were 0.027 and 0.025 respectively for 4 polarimetric measurements, and 0.019 and 0.032 respectively for 40 polarimetric measurements. MM extrapolations from measurements with a commercial off-the-shelf linear Stokes camera are performed at 25 acquisition geometries on an ensemble of LEGO bricks treated to have varying surface roughness. Averaged over the acquisition geometries, the partial-polarimetry extrapolated MMs achieve a 7.3% minimum and 15.1% maximum flux discrepancy from full-polarimetry reconstructed MMs over the varying surface textures. This work demonstrates the first approach, known to the authors, for extrapolating depolarizing MMs.
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