Mid-spatial frequency errors suppression strategy in micro-variable offset bonnet polishing based on direction angle–path step optimization

As a typical sub-aperture polishing technique, bonnet polishing tends to introduce mid-spatial frequency (MSF) errors, which significantly degrade the surface figure accuracy of optical components and the imaging quality of optical systems. To effectively suppress MSF errors in bonnet polishing, this paper proposes a strategy for suppressing MSF errors in micro-variable offset bonnet polishing based on direction angle-path step optimization. This method overcomes the limitations of traditional path optimization approaches by synergistically optimizing the direction angle and path step, thereby effectively mitigating the generation of mid-frequency errors. A quantitative relationship model between the rotation angle and path step of the tool influence function (TIF) and their frequency domain distribution is established, enabling active modulation and control of the error spectrum. Furthermore, by introducing random offset perturbations at dwell points, small fluctuations are introduced to disrupt the spatial coherence of the TIF, thus breaking the periodic structure of MSF errors. Simulation analysis and experimental results demonstrate that the optimized design of direction angle and path step can significantly reduce the amplitude of MSF errors under specific path step conditions. The root mean square (RMS) value of MSF errors is reduced from the initial 1.119 to 0.529 nm, achieving a reduction of 52.7%. With the introduction of random perturbations, the MSF error RMS further decreases to 0.389 nm, representing a 65.2% reduction from the initial value. This strategy does not rely on complex path planning and achieves efficient suppression of MSF errors through process parameter optimization alone, offering a practical and feasible technical approach for the manufacturing of high-precision optical components.