离轴椭圆柱面镜测量方法及调整误差分析

Measurement Method and Alignment Error Analysis of Off-Axis Elliptical Cylindrical Mirror

为了实现对离轴椭圆柱面镜面形的高精度检测,提出一种无像差点法和计算全息法相结合的混合式干涉测量方法。针对离轴椭圆柱面镜的特殊面形,将由平面镜与计算全息图(CGH)高度集合而成的标准柱面镜(TC)的出射柱面波作为检测光,并将光轴移至入射一侧的椭圆焦点与离轴椭圆柱面镜中心的连线方向,以减少测量光路的相对口径。再利用椭圆的一对无像差共轭点,实现干涉测量。将离轴椭圆柱面镜作为光轴上具有6个自由度的空间刚体,推导出误差分离矩阵。从波像差理论出发,推算出调整量引起的调整误差的各部分参数,确定了干涉测量方法中的调整量。实验结果表明,该测量方法可以有效地实现离轴椭圆柱面镜形貌的测量,利用误差分离矩阵可以推导出调整误差参数,便于进一步的系统误差分析与校正。

To achieve high-precision detection of surface shapes of off-axis elliptical cylindrical mirrors, this paper proposed hybrid interferometry integrating the aberration-free point method and the computer-generated hologram(CGH) method. In view of the special surface shapes of off-axis elliptical cylindrical mirrors, the emergent cylindrical wave of a typical cylindrical(TC) mirror, a highly integrated element composed of a plane mirror and a CGH, was used as the detection light. The optical axis was oriented to be in alignment with the line connecting the elliptical focus on the incident side and the center of the off-axis elliptical cylindrical mirror for a smaller relative aperture of the measurement optical path. Then, interferometry was implemented through the pair of aberration-free conjugate points of the ellipse. With the off-axis elliptical cylindrical mirror regarded as a spatial rigid body with six degrees of freedom on the optical axis, an error separation matrix was deduced. The wavefront aberration theory was applied to derive the parameters of the alignment error brought by the alignment amount and to determine the alignment amount in interferometry. The experimental results show that this method offers an effective measurement of the surface shape of the off-axis elliptical cylindrical mirror, and the parameters of the alignment error can be deduced via an error separation matrix, which paves the way for further analysis and correction of the system error.