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在离子束抛光工艺中,为了提高驻留时间求解算法在工件边缘处的求解精度,需要对原始面形误差数据进行有界光滑延展。推导并提出了一种基于高斯曲线的曲面延展算法,该算法利用了高斯函数的有界性、光滑性和参数连续性。将该曲面延展算法应用于带有高频噪声的面形误差工件的驻留时间求解过程中,驻留时间算法在光学元件边缘处的残余误差得到了抑制,使得驻留时间算法在整个通光口径内的收敛率达到了97%(RMS)。这表明基于高斯曲线的曲面光滑延展算法能实现光学元件面形误差的光滑延展,并具有良好的抗噪声干扰能力,改善了驻留时间算法的求解精度。
In the ion beam polishing process, in order to improve the solution accuracy of the algorithm at the edge of the workpiece in order to improve the dwell time, the original surface shape error data needs to be bounded and smoothly extended. A Gaussian curve-based surface extension algorithm is derived and proposed. The algorithm takes advantage of the boundedness, smoothness and parameter continuity of the Gaussian function. In the process of solving the dwell time of the workpiece with the surface error of high-frequency noise, the residual error of the dwell time algorithm at the edge of the optical element is suppressed, so that the dwell time algorithm can be used in the whole light-passing The convergence rate within the caliber reached 97% (RMS). This shows that the Gaussian curve-based smoothing algorithm can smooth the surface error of optical elements and has a good anti-noise ability and improves the precision of the dwell time algorithm.