光学元件面形误差的光滑延展算法

Smoothly extending algorithm for the surface error of optics

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 figuring technique,to improve the solution precision of the dwell time algorithm on the edge of the component,the initial surface of the error should be extended smoothly and limited.A curve surface extending algorithm was proposed which is based on the Gaussian curve.The character of smooth,limitary and parameter continuity were used.When the curve surface extending method was used in the dwell time solving process of a surface error with high frequency noise,the residual error of the dwell time algorithm on the edge was controlled.The ratio of the surface error constringency in the whole caliber reached 97% by RMS.The results show that the surface extending algorithm which based on the Gaussian curve can extend the surface error of optics smoothly.And it has good ability to oppose the noise disturbance.It improved the solution precision of the dwell time algorithm.