应用于大数值孔径、陡度非圆柱光学元件面形误差测量的非零位干涉拼接术研究

This project proposes a novel method called non-null stitching interferometry to get the full aperture map for a high aperture, steep acylindrical optics. Different from the conventional stitching interferometry, it does not need to carry out fringe-nulling routine for all subapertures, and the subaperture data is measured with non-null interferometry. The measurement process is carried out as following, to reduce the slope of the returned wavefront, the acylindrical surface was firstly divided into several subapertures, these subapertures should significantly overlap one another; each subaperture data is acquired with a small aperture cylindrical interferometer by using non-null interferometry; later, the tested acylindrical optics is rotated so as to measure the rest of the subaperture data; After data for every subaperture has been collected, a stitching algorithm is proposed to synthesize a full aperture map. There are three main themes related with this project: the first is to develop the interferometric theory so that we can get the subaperture data with non-null interferometry; the second theme is to propose a strategy for lattice design, and calculate the nominal movements; the third theme is to propose an acylindrical stitching algorithm, so that we can get the full aperture map for a high aperture, steep acylindrical optics. In this way, the fruits of the research not only will enrich the theory of stitching interferometry, but also will solve the measurement problem of high aperture, steep acylindrical optics. More importantly, it will provide a powerful tool to acquire the high accurate, high resolution, full aperture map for acylindrical optics.

本项目提出并研究“非零位干涉拼接术”，以获取大数值孔径、陡度非圆柱（如椭圆柱面、抛物柱面）光学元件的全口径面形误差。与传统的干涉拼接法不同，该项研究是采用非零位干涉法检测子孔径面形，测量前无需对每个子孔径精确调零。具体实现方式是：将非圆柱面划分为多个子孔径以降低返回波前的斜率（条纹密度），相邻子孔径间有局部重叠区，每次通过小口径的柱面干涉系统对子孔径进行非零位检测，然后通过转动非圆柱面测得全部子孔径面形，最后采用拼接技术获得全口径面形误差。项目的核心研究任务是：发展非圆柱面的非零位干涉测量理论，获得子孔径面形误差；提出子孔径划分的策略，确定子孔径的名义运动量；建立非圆柱面的干涉拼接模型，获得全口径面形误差。本项目的实施不仅可以丰富干涉拼接技术的理论成果，也有望解决大数值孔径、陡度非圆柱光学元件的面形检测难题，获得高精度、高分辨率、全口径的面形误差。

本项目瞄准了精密光学元件的面形误差检测的前沿方向，以可变零位补偿器和子孔径拼接技术的基本原理和方法为基础，开展了大数值孔径、陡度非圆柱光学元件的面形误差检测研究。通过3年研究攻关，主要取得的成果包括以下四个方面：.① 通过分析非圆柱光学元件的非圆柱度及其斜率，提出了子孔径宽度的确定方法，然后以子孔径宽度为基准对待测非圆柱光学元件划分子孔径，最后提出采用最小二乘拟合算法确定子孔径的最佳拟合圆柱轴线的位置参数，即为子孔径测量过程中的名义运动参数。.② 通过对圆柱坐标变换做一阶近似处理，提出了干涉拼接模型实现了柱状类零件的面形误差检测，获得了精密圆柱的360度面形误差，与轮廓仪测量结果相比较，采用本项目所提方法获得结果基本一致，但轴向分辨率更高。.③ 提出了勒让德傅里叶多项式，使得对柱状类光学零件检测时，相邻子孔径间无需重叠区，利用所提的勒让德傅里叶多项式对子孔径测量数据直接拟合，即可获得柱状零件的360度面形误差，所获结果与重叠拼接结果基本一致，但所提方法能够显著减少测量所需的子孔径数目，缩短测量时间。.④ 提出了基于旋转CGH的可变零位补偿器，能够产生大小可变的慧差，补偿非圆柱面干涉拼接测量中子孔径的回程误差，降低子孔径干涉图的条纹密度，获得可解析的干涉条纹图；同时与柱状零件的子孔径拼接算法结合，实现了数值孔径为0.45，最大非圆柱面度为81微米的抛物柱面透镜的全口径面形误差检测，所测结果与轮廓仪测量结果基本一致，但轴向分辨率更高。.上述研究成果实现大数值孔径、陡度非圆柱光学元件的面形误差检测，为精密光学元件的检测研究提供了新手段，丰富了干涉拼接测量理论。.在本项目经费的资助下，发表光学领域权威期刊论文6篇，其中中科院二区论文5篇，申请发明专利2项，其中1项已经授权，完成了项目的预期目标。