Enhanced mid-spatial frequency error suppression through multi-directional randomized path superposition processing

Mid-spatial frequency (MSF) errors significantly degrade the imaging performance of optical systems; the important source of MSF is the regular processing path. Pseudo-random paths are effective in reducing MSF errors by sub-aperture polishing tools. However, the current random path still exhibits noticeable directionality, and the surface will still retain regular textures with certain directionality after processing. Therefore, this paper proposes what we believe to be a novel tree-growth randomized path generation (TRPG) algorithm emulating natural tree branching patterns, along with a multi-directional randomized path (MDRP) superposition processing method that incorporates random directionality. These approaches aim to further enhance the disorder of the path and improve the suppression of MSF errors. Both theoretical and experimental results show that single-pass random path and fixed-direction random path (FDRP) superposition processing produce significant characteristic frequencies. In contrast, no characteristic frequencies are observed after MDRP superposition processing. This indicates that the random path superposition processing with random directionality offers a more significant advantage in suppressing MSF errors.