On the manufacturing and metrology of rotationally symmetric aspheric and freeform surfaces using ray-traced fringe analysis and zernike polynomial reconstruction

Abstract In the numerical modeling of rotationally symmetric aspheric surfaces, artificial asymmetries often arise in the computed radius of curvature due to finite-difference approximations. These numerical artifacts, particularly along the X- and Y-axes, can distort two-dimensional curvature maps and compromise accuracy in high-precision optical applications. To address this limitation, we employ the Profile Rotation Model, which reconstructs a full two-dimensional curvature map by rotating a single one-dimensional surface profile through angular increments from 0° to 180°. This approach restores the surface’s inherent rotational symmetry and effectively eliminates spurious asymmetries. The model is applied to a 54 mm clear aperture, rotationally symmetric aspheric oblate ellipsoid, examined under both small- and large-sag conditions, with and without added measurement noise. Ray tracing is performed using a custom algorithm at both short and long wavelengths. For the small-sag surface at the short wavelength, surface reconstruction leverages a phase-wrapping algorithm in conjunction with the Profile Rotation Model. For the large-sag surface at the long wavelength, reconstruction utilizes a custom Zernike polynomial fitting algorithm enhanced by fringe-thinning analysis. Comparative results demonstrate that the Profile Rotation Model significantly reduces asymmetries and improves curvature consistency, especially in noisy and high-curvature regions. This approach is highly valuable for improving accuracy in optical design, fabrication, and metrology of aspheric surfaces.