环形子孔径拼接技术检测大口径、高陡度光学非球面具有低成本、高效率的特点。提出一种基于最小二乘法和泽尼克多项式拟合的环形子孔径拼接方法检测高陡度光学非球面。研究了环形子孔径拼接算法的基本原理, 对环形子孔径的划分方式进行数学公式推导及参数运算, 建立被测非球面的有效数学模型。全口径的拼接结果与原始波面基本一致, 二者PV和RMS差值分别为0.015 1λ、0.004 7λ(λ为632.8 nm),残差的PV和RMS值为0.043 5λ、0.005 2λ, 验证该算法的有效性和准确性。

Annular sub-aperture stitching interferometry technology can test steep conformal aspheric surfaces with low cost and high efficiency without auxiliary null optics. The effective splicing algorithm was established based on simultaneous least-squares method and Zernike polynomial fitting. Firstly, the basic principle of the algorithm of the annular sub-aperture stitching was studied. Secondly, the mathematical formulas of the sub-aperture effective area were derived and the parameters of the sub-aperture effective area were calculated and optimized. Finally, the reasonable mathematical model was established. The detection method of annular sub-aperture stitching high steepness aspheric has been tested through on experimental verification. As a result, the surface map of the full aperture after stitching was consistent to the input surface map, the difference of PV error and RMS error between them is 0.015 1λ and 0.004 7λ(λ is 632.8 nm); the PV and RMS of residual error of full aperture phase distribution is 0.043 5λ and 0.005 2λ. The results conclude that this splicing model and algorithm were accurate and feasible.