反射镜是光学仪器的核心元件,其面形的精密测量一直是研究领域的重要内容。利用光场调控产生大小灵活可变的空间周期性分布的光学点阵,并提出了一种基于二维光学点阵形变实现面形快速测量的方法。结合几何光学和空间三维变换理论,建立了二维光学点阵几何形变量与反射镜三维面形的数学关联模型,并提出了基于点阵质心的面形重构算法,研究分析了测量方法的测量范围和单像素点分辨率,并对反射镜进行了多倾角的实验测试,实现了对直径为10.5 mm的反射镜的亚微米级的测量。通过将测试数据与商用干涉仪的测量数据进行比较,验证了所提方法的可行性。该方法具有测量精度高、速度快和适应强等特点。

A reflector is the core element of optical instruments, and the precision measurement of its shape has always been an important part of research areas. A method for rapid shape measurement based on the deformation of two-dimensional optical lattice is proposed based on the variable spatial periodic distribution optical lattice generated by the modulation of optical fields. Based on the theory of geometric optics and space three-dimensional transformation, a mathematic correlation model between a two-dimensional optical lattice deformation and a three-dimensional shape of reflector is established. A surface reconstruction algorithm based on lattice centroid is proposed. The measurement range and single pixel resolution of the proposed measurement method are analyzed. The multi-dip angle experiments are carried out, and a submicron measurement of the reflector with a diameter of 10.5 mm is achieved. The feasibility of the method is verified when we compare the test data with the measurement data of the commercial interferometer. In addition, the method has the characteristics of high precision, fast speed and strong adaptability.