为获得三维面形的绝对分布,提出一种基于奇偶函数和Fourier级数的三球面面形重建方法。该方法在传统三球面法的测量基础上将测试面旋转90°后再次测量,将待测面面形分解为奇偶函数形式的正交基函数,并对于各正交基函数分别求解。利用实际面形进行算法仿真,面形残差均方根值(RMS)达到1.5λ/1000。将本文三球面法与两球面法、随机球法作比较,残差RMS最大为1.99 nm。针对实验中机构的旋转、平移、倾斜、离焦误差等进行量化分析,最大误差为0.90 nm。本文实现了球面三维面形绝对分布的检测,为多个球面镜的同步全口径检测提供了一种途径。

To obtain the absolute distribution of a three-dimensional surface, a method for three-sphere construction based on odd/even functions and the Fourier series is proposed. According to the traditional three-sphere method, the measurement of a test surface rotating by 90° is included in the combined experiments. Further, the surface shape distribution is decomposed into orthogonal basis functions in the odd/even form, and the functions are all solved individually. The algorithm is simulated based on the actual shape, and the root mean square (RMS) of the residual error reaches 1.5λ/1000. The proposed three-sphere method is also compared with the two-sphere method and the random ball method; the maximum residual RMS is 1.99 nm. The rotation, translation, tilt, and defocus errors of the adjustment mechanism during the experiments are quantitatively analyzed; a maximum error of 0.90 nm is revealed. The absolute distribution of the three-dimensional surface is detected in this study, enabling synchronous full-aperture detection of multiple spherical mirrors.