基于非均匀采样的五棱镜阵列扫描测量大口径准直波前

Scanning Measurement of Large Aperture Collimated Wavefront with Pentaprism Array Based on Nonuniform Sampling

五棱镜扫描法通过沿扫描方向连续采集子孔径光束会聚点的坐标,由斜率反演波前分布,是检测大口径准直波前的常用方法。在传统的一维五棱镜扫描法的基础上,提出添加多个五棱镜,形成一组并联的五棱镜和一组串联的五棱镜,实现了一种基于非均匀采样的五棱镜阵列扫描测量大口径准直波前三维分布的方法。该方法通过三个平行于扫描方向的并联五棱镜同时测量准直波前X方向的斜率,三个垂直于扫描方向的串联五棱镜同时测量准直波前Y方向的斜率,采用Zernike多项式中4~11项的导函数拟合测量得到的斜率,继而获得用Zernike多项式表征的准直波前三维分布。该方法只需要一次扫描测量,就能同时获得待测波前三条线上的斜率,避免了传统方法测量全口径准直波前时需要在X、Y方向进行的多次扫描,优化了扫描机构,缩短了扫描检测时间,实现了全口径准直波前的快速检测。通过仿真验证了使用待测波前三条线上斜率复原待测波前的可行性与准确性。应用该方法对1 m口径准直波前进行了检测,并与干涉法检测结果进行了对比,两种方法得到的准直波前数值与分布形式基本一致,证明了该方法的可行性。

Objective Collimated wavefront is an important parameter to estimate the quality of optical systems such as collimator,i nterferometer,and camera lens.Pentaprism scanning method is a conventional method to detect large aperture collimated wavefront by continuously collecting the coordinates of the focus of sub-aperture beams along the scanning direction and retrieving the wavefront distribution from the slope of the wavefront.The traditional pentaprism scanning method can only measure the wavefront distribution on one line of the collimated wavefront,and cannot obtain the full aperture aberration distribution of the wavefront.In order to obtain the full aperture aberration distribution of the wavefront,it is necessary to conduct multiple scans to obtain the slopes of multiple lines of the wavefront.This scanning method is often used for the surface shape detection of large aperture flat optical elements,through rotating the optical flat and measuring the slope of the surface in polar coordinates.However,the method is not suitable for measuring the collimated wavefront of the optical system.To measure the full aperture collimated wavefront,two pentaprism scanning systems in the X and Y directions,respectively,are generally required.The scanning mechanisms are complex,time-consuming,and vulnerable to environmental disturbances.In this paper,pentaprism array is proposed to simplify the scanning mechanism,shorten the scanning detection time of the full aperture collimated wavefront,and realize the rapid detection of the collimated wavefront.Methods Based on the traditional one-dimensional pentaprism scanning method,we propose to add multiple pentaprisms t o form a group of parallel pentaprisms and a group of series pentaprisms,and realize a pentaprism array scanning based on nonuniform sampling to measure the three-dimensional distribution of large aperture collimated wavefront.Three parallel pentaprisms parallel to the scanning direction are used to measure the slope of the collimated wavefront in the X direction,and simultaneously three series pentaprisms perpendicular to the scanning direction are used to measure the slope of the collimated wavefront in the Y direction.All the pentaprisms move along the scanning direction simultaneously.Thus,this method only needs one scanning measurement process to obtain the slopes of the three lines of the wavefront simultaneously.It avoids the process of multiple scanning in the X and Y directions when measuring the full aperture collimated wavefront by the traditional method.The measured slope is fitted with the derivative function of the 4th--11th terms in the Zernike polynomials,and then the three-dimensional distribution of the collimated wavefront is represented by the Zernike polynomials.Only low order aberrations of the wavefront can be fitted since the low sampling rate in the Y direction.Results and Discussions The feasibility and accuracy of using the slopes of the three lines of the wavefront to r econstruct the wavefront are verified by simulations,in which the reconstruction errors of the collimated wavefront with the pentaprism array are peak-to-valley(PV)value of 0.058λand root-mean-square(RMS)value of 0.009λ(Fig.3).The analysis for robustness of the proposed method is also given(Fig.4).The proposed method is used to detect the collimated wavefront with the aperture of 1 m(Fig.5).After correcting the mechanical scanning errors,the PV and RMS values of the measured wavefront are 2.495λand 0.448λ,respectively.As a comparison,detection of the wavefront is also carried out with interferometry,with which the PV and RMS values of the measured wavefront are 2.752λand 0.496λ,respectively.The retrieved collimated wavefront results obtained by the two methods are basically consistent,with nearly the same values and distribution form,which proves the feasibility of this method(Fig.9).The uncertainty analysis of the pentaprism array scanning method is carried out,including uncertainty of spot centroid detection,uncertainty of the rail straightness and uncertainty of environmental disturbance.The combined uncertainty of the proposed method is 0.035λ.Conclusions Based on the traditional pentaprism scanning method,in this paper we propose a pentaprism array scanning m ethod based on nonuniform sampling to measure the large aperture collimated wavefront.It solves the problem of complex and time-consuming scanning mechanism for the traditional pentaprism scanning method to detect the full aperture three-dimensional aberration distribution of large aperture collimated wavefront.This method measures the slope of the collimated wavefront in the X direction through three pentaprisms in parallel and the slope in the Y direction through three pentaprisms in series,and fits the low order aberration of the wavefront through the derivative of Zernike polynomials.The proposed method is simulated and analyzed,and the collimated wavefront with the aperture of 1 m is detected.The detection results are compared with the collimated wavefront measured by interferometry.The low order aberration distributions of the collimated wavefront measured by the two methods are basically consistent with the numerical value,which proves the feasibility and accuracy of the proposed method.The uncertainty analysis of the pentaprism array scanning method is also carried out,which demonstrates the measurement accuracy of the proposed method.