Zernike多项式对空间高频相位拟合的改进方法  

Improvement Method for Fitting High-Frequency Phase by Zernike Polynomials

作　　者：陈丽霞[1] 胡小川[1] 韩开[1] 张彬[1] 

机构地区：[1]四川大学电子信息学院,四川成都610064

出　　处：《光学学报》2016年第3期117-124,共8页Acta Optica Sinica

基　　金：中国科学院自适应光学重点实验室基金(LAOF201303);四川省教育厅创新团队计划(13Td0048)

摘　　要：以随机相位屏构造光束波前畸变模型,运用不同阶数的Zernike多项式对其进行拟合。通过对比分析原始波前及拟合波前的功率谱密度,明确了波面拟合过程中Zernike多项式对波前中高频成分拟合存在的不足,进而提出了基于Zernike多项式的分块拟合方式加以改进。研究结果表明:在常规的拟合方式下,随着拟合阶数的增加,能准确反映的波前相位空间频率逐渐向高频范围扩展,但其扩展幅度并不大;此外,即使采用较高的拟合阶数,Zernike多项式也难以准确反映波前空间频率中的高频成分;而采用分块拟合方式后,Zernike多项式的拟合效果明显提升,并能有效反映畸变波前空间频率中的高频成分;在提高波面拟合精度上,增加分块数的效果明显优于增加Zernike多项式拟合阶数;对于分块拟合方式,当分块数一定时,增大子区域拟合所使用的Zernike阶数的拟合效果明显优于增大整体拟合所使用的Zernike阶数。A model for wave-front distortions is built up based on the random phase screen, and the wave-front is fitted by Zernike polynomials with different orders. By comparing and analyzing the power spectrum density （PSD） of the original wave-front and the fitted one, the correspomding relationship between the used orders of Zernike polynomials and the spatial frequency of the wave- front is obtained. Consequently, the insufficient of the conventional method for fitting high frequency phase by Zernike polynomials is revealed, and the local fitting method based on Zernike polynomials is further proposed. In this improvement method, the residual wave-front in the conventional fitting way is decomposed into many subdomains fitted by Zernike polynomials individually. The results indicate that, in the conventional fitting way, the range of spatial frequency of the wave-front that can be accurately described by Zernike polynomials increases gradually with the fitting order of Zernike polynomials, but the increment is modest; even fitted by Zernike polynomials with much higher order, it’s difficult to describe the high frequency components of the wave-front accurately. However, the spatial frequency of wave-front accurately described by Zernike polynomials obviously increases by using the local fitting way. In order to increase the fitting accuracy, increasing the number of subdomains is more superior than increasing the number of the used orders of Zernike polynomials. For the number of subdomains in the local fitting way is fixed, increasing the used orders of Zernike polynomials in subdomains makes more precise fit than increasing the number of overall fitted orders.

关 键 词：激光光学 ZERNIKE多项式 波面拟合 空间频率 

分 类 号：O439[机械工程—光学工程]