Objective With the advancement of high-power laser technology, the optical components that affect the system’s beam quality indicators are subjected to more stringent standards. Due to its properties of precise control of the surface shape and rapid development, computer-controlled optical surfacing technology has become an important processing method for creating high-quality optical components. Dual-rotor polishing technology, which is a type of computer-controlled small tool polishing technology, is one of them. It can achieve a steady and controllable removal function, which is vital in the surface processing of optical components. The removal function of Gaussian shape is ideal in computer-controlled optical surface cleaning. However, traditional dual-rotor motion polishing produces a substantial deviation from the Gaussian removal function and is not smooth enough, resulting in a mid-spatial-frequency error on the polished surface, which impacts the performance of the high-power laser system. The main cause of the mid-spatial-frequency error caused by small tools polishing is the simple repetition of the processing trajectory and the low precision of the removal function form. To address this issue, we have proposed a new small tool motion-polishing method that optimizes the two aspects of the removal function shape and processing trajectory to better suppress the mid-spatial-frequency error in this study.

Methods This study proposes an eccentric dual-rotor motion based on the traditional dual-rotor motion. The cross-sectional shape of the removal function through the center and the Gaussian curve are evaluated by establishing the motion model of the eccentric dual-rotor and using the goodness of fit as the evaluation index to optimize the removal function shape and obtain the range of process parameters that can produce the Gaussian removal function. To demonstrate the suppression effect of the removal function on the mid-spatial-frequency error, a mathematical model of the direction removal characteristic is proposed to evaluate how much removal direction a point on the removal function receives and whether the removal amount in each direction is uniform. The removal function of the dual-rotor motion and the eccentric dual-rotor motion are compared in the fixed-point polishing experiment. The suppressing effect of the dual-rotor motion and eccentric dual-rotor motion on the mid-spatial-frequency error is compared in grating track numerical control polishing experiment.

Results and Discussion A removal function that is closer to Gaussian shape than the motion of the dual-rotor is obtained from the optimization range of the simulation process parameters (Fig.5) and the fitted R²=0.9986. Comparison of simulation results of direction removal characteristic between dual-rotor motion and eccentric dual-rotor motion is shown(Fig. 8 and Table 2). It shows that the eccentric dual-rotor motion has better direction removal characteristic than the traditional dual-rotor motion, and theoretically has a better suppression effect on the mid-spatial-frequency error. The fixed-point polishing experiment compares the removal function shape of the traditional dual-rotor motion and the eccentric dual-rotor motion and obtaines the removal function shape, which is closer to the Gaussian removal function shape than the dual-rotor motion, the R²=0.9895 (Figs.10 and 11 and Table 3). The eccentric dual-rotor motion PSD curve obtained by the grating track numerical control polishing experiment is below the limit line, and the error ratio of eccentric dual-motor motion at frequency of 1 mm ^-1 and below is smaller than that of the motion of the dual-rotor, indicating that the eccentric dual-rotor removal function can better suppress the mid-spatial- frequency error (Figs.14 and 16), which verifies the correctness of the simulation analysis of the direction removal characteristic.

Conclusions The key parameters of the eccentric dual-rotor motion model were investigated and optimized theoretically in this study, and the Gaussian removal function of theoretical R²=0.9986 was obtained. The Gaussian removal function can theoretically be obtained within a considerable optimization range. Also the direction removal characteristic model is established, which shows that the removal function of the eccentric dual-rotor is more uniform and has a better suppression effect on the mid-spatial-frequency error. A fixed-point polishing experiment is used to examine the removal function of dual-rotor and eccentric dual-rotor. The eccentric dual-rotor motion obtains a removal function closer to the Gaussian shape than the dual-rotor motion, and its R²=0.9895. The effects of dual-rotor and eccentric dual-rotor motion on suppressing mid-spatial-frequency error are compared in the numerical control-grating track polishing experiment. Among them, the PSD curve of the dual-rotor motion partially exceeds the limit line, and the PSD curve obtained from the eccentric dual-rotor motion is below the limit line and has a better suppression effect on the mid-spatial-frequency error of less than 1 mm ^-1, indicating that the eccentric dual-rotor motion has a better suppression effect on the mid-spatial-frequency error. The above results verify the correctness of the direction removal characteristic and have guiding significance for the actual processing.