Adaptive illumination applied to dark field defect detection of spherical optics

In the defect detection of spherical optical surfaces, illumination is critical for high-quality dark-field scattering imaging. In dark-field scattering imaging of spherical elements, it is hard to achieve correspondence between aperture angles and curvature radii, and continuously adjustable aperture angles are impractical for engineering applications. To solve these issues, a multi-level aperture angle matching scheme for annular light sources is proposed in this paper. Based on the Fresnel reflection law for marginal rays, the constraint relationship among the reflected light, the element’s radius, and the F-number of the imaging lens is derived under dark-field conditions. A dark-field imaging simulation model is established. The oblique incidence angle and diameter of the light source in the simulation are optimized. Within the F-number range of 6–14 for the imaging lens, the required aperture angle values for spherical elements to satisfy dark-field conditions are investigated. The boundary conditions for aperture angle variation and the critical radii of curvature corresponding to different F-numbers are determined. According to the boundary conditions, the aperture angles are set to 0°, 13°, 18° and 23.9°, and the corresponding element matching ranges for the four levels are defined. The results show that this graded scheme effectively resolves the difficulties in matching between aperture angles and curvature radii, as well as the poor engineering applicability of continuously adjustable angles. It enables full dark-field imaging and offers good engineering feasibility. Simulation-based mechanism analysis is mainly conducted in this paper, and preliminary experimental verification has been supplemented. The two parts together lay the foundation for a comprehensive research framework from simulation analysis to experimental validation.