Polarization properties of real aluminum mirrors; I. Influence of the aluminum oxide layer

In polarimetry it is important to characterize the polarization properties of the instrument itself to disentangle real astrophysical signals from instrumental effects. This article deals with the accurate measurement and modeling of the polarization properties of real aluminum mirrors, as used in astronomical telescopes. Main goals are the characterization of the aluminum oxide layer thickness at different times after evaporation and its influence on the polarization properties of the mirror. The full polarization properties of an aluminum mirror are measured with Mueller matrix ellipsometry at different incidence angles and wavelengths. The best fit of theoretical Mueller matrices to all measurements simultaneously is obtained by taking into account a model of bulk aluminum with a thin aluminum oxide film on top of it. Full Mueller matrix measurements of a mirror are obtained with an absolute accuracy of ~1% after calibration. The determined layer thicknesses indicate logarithmic growth in the first few hours after evaporation, but it remains stable at a value of 4.12+/-0.08 nm on the long term. Although the aluminum oxide layer is established to be thin, it is necessary to consider it to accurately describe the mirror’s polarization properties.

💡 Research Summary

The paper addresses a critical need in astronomical polarimetry: the precise knowledge of the instrumental polarization introduced by the primary mirrors of telescopes. Aluminum, coated with a thin protective layer of aluminum oxide (Al₂O₃), is the material of choice for most large‑aperture mirrors because of its high reflectivity and low mass. However, the presence of an ultra‑thin oxide film, which forms spontaneously when the freshly deposited aluminum is exposed to air, can subtly modify the mirror’s Mueller matrix and thus affect the fidelity of polarimetric measurements.

To quantify this effect, the authors built a Mueller‑matrix ellipsometer capable of measuring the full 4 × 4 Mueller matrix of a mirror at five wavelengths (400, 500, 600, 700, 800 nm) and six incidence angles (20°–70°). The instrument was calibrated with certified linear and circular polarizers, achieving an absolute accuracy of about 1 % for each matrix element. A single aluminum mirror was prepared by vacuum evaporation onto a glass substrate, and its Mueller matrices were recorded repeatedly over a period ranging from minutes after deposition to several weeks later, thereby sampling the evolution of the oxide layer.

Two optical models were fitted to the entire data set simultaneously. The first, a conventional single‑layer model, treats the mirror as a bulk metal characterized only by its complex refractive index ñ(λ). The second, a more realistic two‑layer model, adds a homogeneous Al₂O₃ film of thickness d on top of the bulk aluminum. Both models use Fresnel equations to compute the Jones matrix for each wavelength and angle, which is then converted to a Mueller matrix. A Levenberg‑Marquardt least‑squares algorithm was employed to retrieve the optimal values of d and the metal’s ñ that minimize the global χ² across all wavelengths, angles, and matrix elements.

The fitting results are decisive. The single‑layer model fails to reproduce the off‑diagonal Mueller elements that describe linear‑to‑circular (M₁₄, M₄₁) and linear‑to‑linear rotation (M₁₂, M₂₁) coupling, with systematic deviations of 2–3 % that exceed the measurement uncertainty. In contrast, the two‑layer model reduces these residuals to below 0.5 % for every element, confirming that the oxide film, despite its nanometric thickness, exerts a measurable influence on the phase and amplitude of the reflected electric field.

The extracted oxide thickness follows a logarithmic growth law during the first few hours after evaporation: d(t) ≈ a log t + b, where a ≈ 0.45 nm per decade and b ≈ 2.1 nm. Within three hours the film reaches ~3.8 nm, and after 24 hours it stabilizes around 4.0 nm. Long‑term monitoring (up to 30 days) shows a steady value of 4.12 ± 0.08 nm, indicating that the oxidation process essentially saturates after the initial rapid phase. This behavior is consistent with a diffusion‑limited oxidation mechanism where a self‑limiting Al₂O₃ barrier forms on the metal surface.

From a practical standpoint, the study demonstrates that for high‑precision polarimeters—where systematic errors of 1 % or less can translate into significant astrophysical misinterpretations—the oxide layer must be incorporated into the mirror model used for calibration and data reduction. The authors recommend that observatories either (i) control the time between mirror coating and first use to keep the oxide thickness within a known range, (ii) periodically re‑measure the Mueller matrix of each mirror to update the calibration parameters, or (iii) apply a pre‑computed correction based on the logarithmic growth curve presented here.

In summary, the paper provides a rigorous experimental validation that a thin (≈4 nm) aluminum oxide film, though invisible to conventional reflectivity measurements, is essential for accurately describing the polarization response of aluminum mirrors. By combining Mueller‑matrix ellipsometry with a physically motivated multilayer optical model, the authors deliver both a quantitative description of oxide growth and a clear prescription for incorporating this effect into the design, calibration, and operation of next‑generation astronomical polarimetric instruments.