Error analysis and measurement methods of curved optical element surface defects dark-field imaging inspection system based on multi-axis kinematics

In surface defect dark-field inspection of the curved optical element, the camera field of view (FOV) is much smaller than the aperture of the element, so the images of different positions on the element surface, which are also called sub-aperture images, need to be collected and stitched to obtain the whole surface image of the element. It is usually achieved by controlling multi-axis motion guide rails to make relative motion between camera and optical element. During sub-aperture images collection, there is not only relative translation between camera and optical element, but also optical element spin and swing with its optical axis for curved optical element. The motion errors of each motion axis will make sub-aperture scanning path deviate its predetermined path. Hence, it will lead to the dislocation of the stitching image, and will cause defects break and dislocation in stitching image, which will largely affect the optical element surface quality quantitative evaluation. Since multi-axis kinematics (MAK) is a mathematical model which is often used to describe the motion of objects located in multi-axis system, such as numerical control machine and mechanical arm. The multi-axis kinematics error analysis (MAKEA) model is put forward in this paper and applied in the optical element surface defects dark-field imaging inspection system. The effect of all axis motion errors including optical axis motion errors to sub-aperture scanning path has been specifically simulated and analyzed. The simulation result indicates that the optical axis swing error caused by assembly is the main error of dark-field imaging system, whereupon a swing angle assembly error measurement (SAAEM) method by measuring the optical axis positions of different thickness spherical optical elements is proposed. By adjusting the motor of the element optical axis swing, the optical axis swing error can be compensated. The sub-aperture images stitching experiment is carried out to verify the validity of optical axis swing error compensation. Results show the situation of sub-aperture images stitching dislocation is improved. The root-mean-square-error (RMSE) of sub-aperture images scanning path after error compensation is nearly 1/20 of the RMSE before compensation. •An error analysis model of complicated multi-axis equipment for curved optical element surface defects inspection based on multi-axis kinematics is established.•The main error source is founded by compared all error source