球面绝对检测方法的误差影响分析及实验研究

Error impact analysis and experimental research for absolute testing of spherical surfaces

球面绝对检测方法可以去除参考面面形误差的影响,从而提高了被检面的检测精度。在此高精度的检测中,被检面机构调整误差和环境扰动误差是影响检测结果的两个主要因素。将机构调整误差理解成一种特殊的面形误差,通过这一思路分析了该误差对最终检测结果的影响。为了提高检测精度,根据高阶离焦模型去除了调整误差中的离焦误差,并且设计了一种简易有效的旋转角度控制机构用来控制旋转错位误差。将环境扰动误差看作是随机误差,分析了该误差对三步检测每一步的影响,并采用多次测量取平均的办法减小其影响。基于Zygo干涉仪,使用六自由度高精度调整机构对精度优于λ/40的被检球面进行了绝对检测。绝对检测三步法测得的被检面面形误差的评价值小于单步法的测得结果对应的评价值,各评价值置信概率为0.99的置信区间长度很小,说明采用文中的装置和数据处理方法能实现绝对检测的高重复性和有效性。

Absolute surface testing method can eliminate the error caused by the reference surface and higher accuracy of the surface profile testing can be obtained. In surface test of high accuracy, the alignment error caused by mount for surface under test and the environmental perturbation error become two sensitive factors affecting the test results. In the process of error analysis, the alignment error was. regarded as a special surface profile in this article. In order to minimize the testing error, the defocus error was removed according to the mathematical model of high-order defocus error. Besides, a simple and effective device was designed to control the rotary error. The environmental perturbation error was considered as random error, so the influence on each step caused by the random error was analyzed and was reduced by averaging multiple measurements. Based on the high accuracy device of six freedoms and Zygo interferometer, a spherical surface with the precision above A/40 was tested. Evaluation values of surface error tested via absolute testing are smaller than those tested by single-step testing. Also, the narrow 0.99 confidence intervals are achieved. With the experimental device and data processing method, high repeatability and effectiveness of absolute testing can be realized.