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摘要: 基于计算全息图（Computer-Generated Hologram，CGH）的非球面检测技术通过控制衍射光相位来生成所需要的参考波前，从而实现非球面的零位检测，近年来，该技术已经发展成为非球面的主流检测技术。对于CGH编码，采用传统编码方法实现高精度编码，其数据量往往高达几十甚至上百GB。因此，为同时确保编码精度高及编码数据量小，本文提出了一种变步长CGH编码方法。该方法首先通过寻找等相位面的方法得到CGH条纹分布，然后通过计算相位分布梯度选取不同的取样步长，使CGH能利用尽可能少的点实现高精度编码。利用变步长搜索的编码方法进行编码并制作了CGH对非球面样品进行检测，检测结果为3.142 nm （RMS）。为验证检测结果可信度，本文设计并制作了补偿器对同一非球面进行检测，其检测结果为3.645 nm （RMS）。对两检测结果点对点做差，RMS值为1.291 nm，结果表明该编码方法可满足非球面高精度检测需求。Abstract: In the field of aspheric testing, Computer-Generated Hologram (CGH) technology has been widely used. For CGH encoding, when applying the conventional encoding method to achieve highly accurate coding, it will use an amount of data that is often up to tens or even hundreds of GB. Therefore, in order to achieve high encoding accuracy with a small amount of encoded data, we propose a variable step size CGH encoding method. This method first obtains CGH fringe distribution through finding isophase surface, then selects different sampling steps by calculating the phase distribution gradient so that the CGH achieves high precision coding using as few points as possible. Finally, the method was used to CGH encode, then the resulting CGH was manufactured to test an aspheric surface. The test result is 3.142 nm (RMS). In order to verify the credibility of the test results, we design and make a compensator to test the same aspheric surface. The test result is 3.645 nm (RMS). The difference between the two results is 1.291 nm (RMS), and shows that the encoding method can meet the requirements of high-precision testing of aspheric surfaces.
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Key words:
- computer-generated hologram /
- CGH encoding /
- aspheric test
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图 1 CGH编码过程。（a）由相位轮廓干涉图计算相位函数；（b）条纹编码成多边形
Figure 1. CGH encoding process. (a) Wavefront phase function calculated by phase contour interferograms; (b) encoding the fringes into polygons
图 3 编码采样步长与编码偏差几何关系图
Figure 3. Geometric relationship between encoding sampling step and encoding deviation
图 7 标定光路示意图
Figure 7. Schematic diagram of calibration optical path of the CGH substrate error
图 11 两种方法的非球面检测结果对比
Figure 11. The test results of the aspheric mirror by proprosed method and zero compensator
图 12 CGH与补偿镜检测结果对比
Figure 12. Comparison of test results of CGH and null lens compensator
表 1 非球面参数
Table 1. Parameters of the aspheric lens
R D K A1 A2 −310.08 63 3.275 −2.148×10−8 −1.137×10−12 
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