Abstract Time-dependent sub-aperture surface processing is widely used in industry for finishing of optical surfaces. It can often be viewed as the convolution process between a tool influence function (TIF, also known as footprint) and the equivalent dwell time derived from the velocity at discrete locations across the tool path. While the direct convolution problem has been extensively studied through numerical computation, this approach leads to limited and inaccurate prediction of the processed surface. Therefore, this paper proposes a simple and universal analytical model that uncovers the intrinsic relationship between process parameters and processed surface, and which has potential for a wide range of manufacturing processes. Furthermore, sensitivity of the process to TIF fluctuations is considered, which leads to highly accurate stochastic predictions of the processed surface waviness variation by Monte Carlo simulation. Experimental results in fluid jet polishing confirm correctness of the proposed analytical solution and effectiveness of the waviness prediction model. The presented solution provides a better understanding and insight into time-dependent sub-aperture surface processing and opens the door to efficiently tackling the related direct and inverse problem.

中文翻译：

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瞬态子孔径处理中表面形貌的分析和随机建模

摘要 瞬态亚孔径表面处理在工业中广泛用于光学表面的精加工。它通常可以被视为工具影响函数（TIF，也称为足迹）与从工具路径上离散位置的速度得出的等效驻留时间之间的卷积过程。虽然已经通过数值计算广泛研究了直接卷积问题，但这种方法导致对处理表面的预测有限且不准确。因此，本文提出了一种简单而通用的分析模型，揭示了工艺参数与加工表面之间的内在关系，具有广泛的制造工艺潜力。此外，还考虑了过程对 TIF 波动的敏感性，这导致通过蒙特卡罗模拟对处理后的表面波纹度变化进行高度准确的随机预测。流体射流抛光的实验结果证实了所提出的解析解的正确性和波纹度预测模型的有效性。所提出的解决方案提供了对时间相关子孔径表面处理的更好理解和洞察力，并为有效解决相关的正反问题打开了大门。