Distortion-corrected Fourier ellipsometry for thin-film characterization on tilted and curved optical surfaces

Accurate characterization of thin films on tilted and curved optical components, such as spherical lenses, is a critical challenge in advanced optical manufacturing. Conventional ellipsometry assumes a locally planar measurement region with a well-defined surface normal, leading to measurement deviations when surface tilt or curvature alters the local incidence geometry. Consequently, film thickness on curved components is often inferred indirectly from simultaneously coated planar witness samples, which fail to accurately reflect the actual thickness distribution. To address this issue, a distortion-corrected Fourier ellipsometry (FE) method is proposed for direct thin-film characterization on tilted and curved surfaces. A geometrical reflection model and a corresponding distortion correction algorithm are established to restore the correspondence between Fourier plane (FP) coordinates and the incident-azimuthal angle field by reconstructing the ideal horizontal FP light field. A snapshot FE system with a microscale illumination spot is developed to satisfy the local planar approximation and acquire angle-resolved ellipsometric information. Experiments on tilted bare planar CaF 2 substrates, tilted planar HfO 2 -coated CaF 2 samples, and an HfO 2 -coated plano-convex CaF 2 lens verify geometric correction, accurate thin-film metrology, and curved-surface thickness mapping, respectively. The proposed method improves the ellipsometric-parameter RMSE by 32.7% for the substrates, maintains sub-nanometer thickness RMSE for tilted planar films at tilt angles up to 15°, in agreement with a commercial ellipsometer , and achieves reference-based thickness RMSEs below 1 nm across 30 measurement positions in the inner, middle, and outer regions of the curved lens. These results demonstrate the feasibility of distortion-corrected FE for high-precision thin-film metrology on tilted and curved optical surfaces.