Imaging simulation of a dark field imperfection evaluation arrangement for spherical optical surface based on reverse ray tracing

Abstract Imaging simulation of a dark field imperfection evaluation arrangement for spherical optical surface is proposed on the basis of reverse ray tracing. A typical evaluation arrangement for optical element surface imperfections seen in reflection under dark field condition is introduced. As for thin lens, it is a common case that light spots naturally emerge in the field of view (FOV) and dark field condition is no longer satisfied because multiple optical surfaces reflect rays into the camera lenses. A virtual arrangement model composed of a camera model, sample and light geometries, optical properties is established to further discuss the imaging of various lenses and imperfection geometries. The finite aperture camera model is adopted to generate abundant reverse rays for dark field scattering imaging of imperfections such as scratches and digs. But only a small portion of emitted rays whose paths can be traced to lights during propagation will contribute to the final image. Image simulation is performed by solving illuminance integral equation with Monte Carlo techniques. Simulated images of various lens geometries show the bright spots with respect to radius of curvature and centre thickness, which are numerically evaluated by our own defined spot coefficient. To eliminate the blind spot area caused by multiple reflections, lights are switched in turn and an image sequence is captured. A result image with reduced blind area is obtained by image fusion based on the accurate prediction of spot size and location for each frame in sequence. Imaging experiments of 4 thin lenses show that the distributions of spots correspond well with our simulation and proposed fusion method can reduce the blind area for spherical surface inspection while remains high sensitive for imperfections.