微球表面形貌检测中的偏心误差分析与修正

Analysis and correction of eccentricity errors in microsphere surface inspection

由于使用传统的误差修正方法进行微球形貌检测会有过大的残差,本文提出了一种新的偏心误差修正方法来提高微球表面形貌检测的精度和效率。在分析了横向偏心和轴向偏心引入光程差数学模型的基础上,推导了偏心误差的高阶近似模型,提出了小曲率半径下基于Zernike多项式拟合的偏心误差修正方法,并给出误差修正的流程及相关参数的标定方法。通过对2mm直径的微球的表面形貌检测验证了所提出误差修正方法的可行性和有效性。结果表明:相对于零条纹时的形貌误差基准,采用本文提出的方法修正后的残余形貌误差峰谷(PV)值为0.081 5λ,均方根(RMS)值为0.016 1λ,比传统方法修正效果更好,能够满足高精度微球形貌检测的需求。

When traditional error correction methods are used in microsphere surface inspection,it might show a larger residual.Therefore,this paper proposes a surface topography to correct the eccentricity of microsphere and to improve the measuring precision and efficiency.Based on the analysis of mathematic model of optical path difference introduced by the lateral and axial eccentricities,the high-order approximation model of eccentricity error was deduced.A eccentricity correction method for small sphere curvature radius was proposed on the basis of Zernike polynomials fitting.The correction flow was provided for illustrating the detail,and the corresponding calibration method of relative parameters was given.An experiment for the surface topography of a microphere with a diameter of 2mm was performed to verify the feasibility and effectiveness of the correction method.The experimental results relative to the standard profile data indicate that the proposed correction method offers the surface errors（peak-valley（PV）and root-mean-square（RMS）values）to be 0.081 5λand0.016 1λ,respectively,which are more excellent than that of the traditional methods.The method isable to meet the demand of high precise inspection of microspheres.