标题： 基于空间引力波探测的倾斜-长度耦合远场波前误差估计 显示英文标题

标题： The estimation of far-field wavefront error of tilt-to-length distortion coupling in space-based gravitational wave detection

摘要： 在基于空间的引力波探测中，远场波前误差的估计是噪声减少的前提条件。泽尼克多项式被用来描述传输畸变光束的波前误差。两望远镜孔径之间的激光束传播是数值计算的。远场波前误差通过畸变高斯光束与参考无畸变高斯光束之间的峰谷相位偏差绝对高度来估算。结果显示，指向抖动与波前误差密切相关。此外，当抖动从100纳弧度减小到10纳弧度时，波前误差减少了十倍以上。在多参数最小化分析中，波前误差的最小值倾向于某些参数范围内的泽尼克多项式。一些泽尼克多项式与接收光束的波前误差有很强的相关性。当孔径直径增加到泽尼克[5,3]时，波前误差不是单调的，而是有波动的。然而，当臂长从10$^{-1}$兆公里增加到10$^3$兆公里时，波前误差几乎保持不变。当臂长从10$^{-1}$兆公里减少到10$^{-4}$兆公里（三个数量级）时，波前误差仅增加了一个数量级。在10$^{-4}$兆公里到10$^3$兆公里范围内，在泽尼克[5,3]和10纳弧度抖动的情况下，波前误差的最低限值从0.5飞米到0.015飞米。 显示英文摘要

摘要： In space-based gravitational wave detection, the estimation of far-field wavefront error of the distorted beam is the precondition for the noise reduction. Zernike polynomials is used to describe the wavefront error of the transmitted distorted beam. The propagation of a laser beam between two telescope apertures is calculated numerically. Far-field wavefront error is estimated with the absolute height of the peak-to-valley phase deviation between distorted Gaussian beam and a reference distortion-free Gaussian beam. The results show the pointing jitter is strongly related to the wavefront error. Furthermore, when jitter decreases 10 times from 100 to 10 nrad, wavefront error reduces for more than an order of magnitude. In the analysis of multi-parameter minimization, the minimum of wavefront error tends to Z[5,3] Zernike in some parameter ranges. Some Zernikes have a strong correlation with wavefront error of the received beam. When the aperture diameter increases at Z[5,3] Zernike, wavefront error is not monotonic and has oscillation. Nevertheless, wavefront error almost remains constant with the arm length increasing from 10$^{-1}$ Mkm to 10$^3$ Mkm. When the arm length decreases for three orders of magnitude from 10$^{-1}$ Mkm to 10$^{-4}$ Mkm, wavefront error has only an order of magnitude increasing. In the range of 10$^{-4}$ Mkm to 10$^3$ Mkm, the lowest limit of the wavefront error is from 0.5 fm to 0.015 fm, at Z[5,3] Zernike and 10 nrad jitter.