方域斜率子孔径拼接及其精度理论分析

Subaperture Slope Stitching on Square Region and Its Accuracy Theoretical Analysis

子孔径拼接方法在大口径光学元件检测中发挥着重要的作用,关于子孔径拼接精度研究也受到广泛重视。子孔径斜率数据可由哈特曼探测器测得,被测光学元件上每个子孔径上的斜率数据通过最小二乘法进行拼接。测量过程中,测量数据不可避免含有随机噪声,这将影响拼接参数(如倾斜)的不确定度。推导了误差传递公式及评价拼接精度的公式,并分别计算了并行拼接和串行拼接中任意子孔径上每一点的拼接误差。在0.06s的随机噪声下,拼接斜率的统计误差与理论误差之间的差别在10-9 rad量级。模拟实验结果证实了所提出的拼接精度公式的正确性,可以用来评价拼接精度,并从理论上给出了并行拼接误差小于串行拼接误差的原因。

Subaperture stitching method plays an important role in large aperture optical element testing.Meanwhile,the accuracy of subaperture stitching has been paid attention.The data on subaperture in this paper is collected by Hartmann test device or Hartmann-Shack wavefront senor or other slope data measuring equipment.The slope data on each subaperture of test optical component is connected by the linear least squares fitting routine in this paper.Importantly,the error transfer formulas are deduced when the measurement data is polluted by the random noise,which will affect the uncertainty of stitching parameters such as tilt or defocus.The accuracy formulas for stitching evaluation,which can be used to calculate the stitching error of each point on each subaperture for parallel mode and the serial mode,are derived mathematically.Under the random noise of 0.06 s,the difference between the statistical error of the slope and theoretical error is rad magnitude.The result shows that the stitching accuracy formulas proposed are verified and they can be used to evaluate stitching accuracy.The reason why the error of the parallel stitching mode is less than that of the serial stitching mode can begiven theoretically.