Overview: Since the groundbreaking discovery of gravitational waves, the scientific community has fervently pursued the exploration of low-frequency gravitational waves to glean deeper insights into the cosmos. The inherent limitations of ground-based conditions, however, pose formidable challenges for detectors in capturing gravitational waves below the 1 Hz threshold. Consequently, the imperative has shifted toward the deployment of space-based gravitational wave detectors as the paramount solution for effective low-frequency gravitational wave detection. At the crux of space-based gravitational wave detection lies the pivotal role of spaceborne telescopes. Given the expansive transmission distances spanning magnitudes of 10⁹ m between celestial constellations, the demand for nanoradian-level precision in telescope pointing accuracy becomes non-negotiable. The concomitant necessity for high-precision measurements and calibration emerges as a prerequisite for achieving the exacting standards of pointing accuracy in spaceborne telescopes dedicated to gravitational wave detection. To ameliorate the deleterious effects of pointing deviations on gravitational wave detection, this study strategically optimizes key parameters, including microlens structures, detector selection, and algorithmic frameworks, thereby achieving a breakthrough in high-precision pointing deviation measurements. Leveraging a low-density microlens array with extended sub-aperture focal lengths enhances the spatial scale of the light spot within each sub-aperture. This, coupled with detectors boasting a high signal-to-noise ratio, synergistically elevates the pointing detection accuracy of each discrete lens. Moreover, the paper introduces an innovative, Hartmann principle-based methodology for high-precision pointing deviation measurements, deploying a spatially reused paradigm across multiple sub-apertures. By aggregating measurement results from diverse sub-apertures, the approach effectively mitigates the influence of assorted random errors on measurement accuracy, thereby markedly enhancing the precision of pointing deviation measurements. Illustrating the efficacy of these methodologies, the paper exemplifies their application within the ambit of the "Tianqin Plan" for space-based gravitational wave detection. Employing numerical simulations and factoring in the design parameters of the Hartmann sensor, the study performs a meticulous analysis of pointing deviation measurement accuracy. Comparative analysis between single sub-aperture and sub-aperture correlation reuse technologies reveals a compelling enhancement in measurement accuracy, approximating a sevenfold improvement with the latter. The pointing deviation measurement accuracy achieved through sub-aperture correlation reuse technology is quantified at approximately 18.81 nanoradians. Considering the optical magnification inherent in spaceborne telescopes, estimated at around 30 times, the resultant pointing deviation measurement accuracy reaches an impressive 0.62 nanoradians. This design precision significantly surpasses the stipulated 1 nanoradian accuracy requirement for ground-based gravitational wave pointing deviation measurements. As a prudential measure, the proposed design incorporates a substantial margin to accommodate potential accuracy diminution attributable to external perturbations during empirical testing.

相位是描述光波状态的重要参数，但却无法直接观察。本文基于哈特曼探测器的波前快速探测功能，研究了光波相位三维显示的方法，并研制出相位三维显示系统。首先，利用Zemax软件对系统的光源、准直透镜等光学参数进行优化设计；然后，基于模式法波前重构理论，根据探测的Zernike多项式离焦量和像散项系数，实现了对3个不同类型镜片的相位三维显示，并给出相应屈光度的测量方法；最后，实验验证了光波相位的三维显示和屈光度测量的有效性，-2.00 D的近视镜测量值为-2.07 D，1.00 D的远视镜测量值为0.91 D，0.50 D的散光镜测量值为0.56 D。实验结果表明，此系统能够较准确地测量屈光矫正镜的屈光度，并实现相位的三维显示。本文设计的基于哈特曼探测器的相位三维显示方法具有更好的环境适应能力，便于研究者直观观测光的相位分布。

进行波前探测时，标准动物模型小鼠的眼底视网膜双层反射光会导致像差探测失效。为解决这一问题，本文提出了一种结合光学掩模调制的鼠眼像差测量方法，以期提高鼠眼波前像差测量精度。首先，根据鼠眼视网膜的关键参数，建立鼠眼波前像差探测的光学系统模型并进行光学仿真。然后，分析比较不同孔径的光学掩模对视网膜非目标层反射光束的遮拦效果，确定光学掩模参数与实验方案。最后，搭建鼠眼波前像差探测系统并开展在体鼠眼波前像差的测量实验。实验结果表明：0.5 mm孔径的光学掩模可以将鼠眼波前像差的测量均方根误差降低74.9%，与理论仿真的80%区域实现非目标层反射光遮拦效果近似。本文研究实现了对鼠眼视网膜非目标层反射光的有效遮拦，提升了鼠眼波前像差探测精度，为进一步实现鼠眼高分辨率成像奠定了基础。

微透镜阵列的衍射效应会影响夏克—哈特曼波前探测器的探测精度。本文根据惠更斯-菲涅耳衍射理论建立二维微透镜阵列衍射模型，模拟分析使用理想平行光入射微透镜阵列时在焦平面产生的二维衍射光斑阵列。然后，通过计算衍射光斑偏移一个像素的过程中质心的误差，确定最大质心计算误差。接着，利用模式法进行波前重构，获得波前探测误差。仿真结果显示：在偏移0.21和0.79个像素，即波面偏转0.03°和0.13°时，衍射导致的波前误差最大为0.125 λ。最后，实验验证了该误差计算方法的有效性。该研究结果可为夏克一哈特曼波前探测器的设计提供理论依据。

动态变化的大气湍流和观测目标的亮度的降低严重影响了夏克-哈特曼波前传感器（SHWFS）探测波前的精度。针对这两种复杂的观测条件，本文提出了一种以Transformer结构为基础的神经网络模型，它具有很好的全局建模能力，可以高精度地从SHWFS光斑阵列图像中重建波前。通过在动态变化的典型大气湍流相干长度r₀下进行仿真模拟，所提出的网络模型的残余波前RMS误差值稳定在0.010~0.024 μm之间。与已有的方法相比，本文方法能够更准确地重构波前像差。此外，本文方法的重构精度受导星或观测目标的亮度变化影响很小。因此，本文方法的重构精度对两种观测条件变化均具有较强的稳定性，为大口径天文光学望远镜的高分辨率成像提供了一种有前景的方法。

随着先进光学系统设计与制造的发展，大口径光学系统得到了广泛的应用。然而，大口径平面镜高精度面形的检测手段不足，限制了大口径平面镜的制造与应用。为实现大口径平面反射镜的高精度面形检测，提出一种夏克哈特曼扫描拼接检测平面镜面形的方法。对扫描拼接原理、波前重构算法进行了研究，建立了微透镜阵列成像的数学模型，验证了夏克哈特曼扫描拼接检测原理的可行性。针对一口径为150 mm的平面镜进行了扫描拼接检测实验，拼接得到的全口径面形为0.019λRMS(λ=635 nm)；与干涉检测结果对比，检测精度为0.008λRMS，结果表明该方法能够实现大口径平面反射镜的高精度检测。