光纤和波导对准过程中边缘高精度线性拟合

High-precision Linear Fitting of Edges in Alignment of Fiber and Waveguide

对已有边缘直线检测算法无法满足波导器件边缘的高精度检测需要。基于最小二乘的基本思想,提出了一种拟合系数收敛的直线逼近方法。首先分析了拟合系数与样本空间线性相关性的关系并根据拟合系数建立了非随机误差的判断模型;然后在非随机误差有限可分且足够大的假设条件下,证明了总体样本空间存在方差小于总体方差且只与随机误差有关的样本子空间;最后基于残差关系提出直线拟合逼近的新方法。实验结果表明,与传统直线检测方法比较,新算法能精确地检测出受损边缘,角度误差小于0.01°。新方法具有拟合精度高,抗边缘噪声影响能力强,拟合系数收敛快的特点,达到微电子,光电子封装等领域高精度线性检测的需要。

High-precision edge detection of fiber and waveguide chip is an important basis for the position and posture adjustment of waveguide alignment. Considering that the conventional edge line detection algorithms can not meet the need of high-precision detection of waveguide devices edge, a new fitting method of linear approximation based on the idea of least squares was introduced, where the coefficient converged to zero. First of all, factor analysis of relationship between the fitting function coefficient and the linear correlation coefficient was undertaken, and a assessment model of non-random error was established. Then, under the hypothesis that non-random errors was assumed to be large enough and was limited in small enough regions, a subspace, which belonged to a general sample space and only have random errors, was proved to have less variance than that of the general sample space. Finally, based on the relationship of residuals of the linear approximation, a new fitting method was proposed. The experiment results showed that the new algorithm accurately detected the linear edge which was damaged and the angle error was less than 0.01 degree. Therefore, the new method has some excellent characteristics, e.g. high precision, anti-impact ability on errors, and fast convergence of fitting coefficients, and it can meet the need of high-precision fields, such as auto micro-electronics and opto-electronics packaging.