The Giant Segmented Mirror Telescopes (GSMTs) including the Giant Magellan Telescope (GMT), the Thirty Meter Telescope (TMT), and the European Extremely Large Telescope (E-ELT), all have extreme adaptive optics (ExAO) instruments planned that will use pyramid wavefront sensors (PWFS). The ExAO instruments all have common features: a high-actuator-count deformable mirror running at extreme speeds (>1 kHz); a high-performance wavefront sensor (WFS); and a high-contrast coronagraph. ExAO WFS performance is currently limited by the need for high spatial sampling of the wavefront which requires large detectors. For ExAO instruments for the next generation of telescopes, alternative architectures of WFS are under consideration because there is a trade-off between detector size, speed, and noise that reduces the performance of GSMT-ExAO wavefront control. One option under consideration for a GSMT-ExAO wavefront sensor is a three-sided PWFS (3PWFS). The 3PWFS creates three copies of the telescope pupil for wavefront sensing, compared to the conventional four-sided PWFS (4PWFS), which uses four pupils. The 3PWFS uses fewer detector pixels than the 4PWFS and should therefore be less sensitive to read noise. Here we develop a mathematical formalism based on the diffraction theory description of the Foucault knife-edge test that predicts the intensity pattern after the PWFS. Our formalism allows us to calculate the intensity in the pupil images formed by the PWFS in the presence of phase errors corresponding to arbitrary Fourier modes. We use these results to motivate how we process signals from a 3PWFS. We compare the raw intensity (RI) method, and derive the Slopes Maps (SM) calculation for the 3PWFS, which combines the three pupil images of the 3PWFS to obtain the X and Y slopes of the wavefront. We then use the Object Oriented MATLAB Adaptive Optics toolbox (OOMAO) to simulate an end-to-end model of an AO system using a PWFS with modulation and compare the performance of the 3PWFS to the 4PWFS. In the case of a low read noise detector, the Strehl ratios of the 3PWFS and 4PWFS are within 0.01. When we included higher read noise in the simulation, we found a Strehl ratio gain of 0.036 for the 3PWFS using RI over the 4PWFS using SM at a stellar magnitude of 10. At the same magnitude, the 4PWFS RI also outperformed the 4PWFS SM, but the gain was only 0.012 Strehl. This is significant because 4PWFS using SM is how the PWFS is conventionally used for AO wavefront sensing. We have found that the 3PWFS is a viable WFS that can fully reconstruct a wavefront and produce a stable closed-loop with correction comparable to that of a 4PWFS, with modestly better performance for high read-noise detectors.

中文翻译：

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三棱锥波前传感器，第 1 部分：天文自适应光学的模拟和分析

巨型分段镜面望远镜 (GSMT) 包括巨型麦哲伦望远镜 (GMT)、三十米望远镜 (TMT) 和欧洲极大望远镜 (E-ELT)，都计划使用极端自适应光学 (ExAO) 仪器金字塔波前传感器 (PWFS)。ExAO 仪器都有共同的特点：以极快的速度 (>1 kHz) 运行的高致动器数量的可变形反射镜；高性能波前传感器（WFS）；和一个高对比度的日冕仪。ExAO WFS 性能目前受到波前高空间采样需求的限制，这需要大型探测器。对于用于下一代望远镜的 ExAO 仪器，正在考虑 WFS 的替代架构，因为在探测器尺寸、速度、和降低 GSMT-ExAO 波前控制性能的噪声。GSMT-ExAO 波前传感器正在考虑的一种选择是三边 PWFS (3PWFS)。与使用四个瞳孔的传统四边 PWFS (4PWFS) 相比，3PWFS 为波前传感创建了望远镜瞳孔的三个副本。3PWFS 使用的探测器像素比 4PWFS 少，因此对读取噪声的敏感度较低。在这里，我们开发了一种基于傅科刀口测试的衍射理论描述的数学形式，它预测 PWFS 后的强度模式。我们的形式允许我们在存在对应于任意傅立叶模式的相位误差的情况下计算由 PWFS 形成的瞳孔图像中的强度。我们使用这些结果来激发我们如何处理来自 3PWFS 的信号。我们比较了原始强度 (RI) 方法，并推导出 3PWFS 的斜率图 (SM) 计算，它结合了 3PWFS 的三个瞳孔图像以获得波前的 X 和 Y 斜率。然后，我们使用面向对象的 MATLAB 自适应光学工具箱 (OOMAO) 来模拟使用带调制的 PWFS 的 AO 系统的端到端模型，并将 3PWFS 的性能与 4PWFS 进行比较。在低读取噪声检测器的情况下，3PWFS 和 4PWFS 的斯特列尔比在 0.01 以内。当我们在模拟中包含更高的读取噪声时，我们发现使用 RI 的 3PWFS 比使用 SM 的 4PWFS 的斯特列尔比增益为 0.036，星等为 10。在相同的星等下，4PWFS RI 也优于 4PWFS SM，但是增益仅为 0.012 Strehl。这很重要，因为使用 SM 的 4PWFS 是 PWFS 常规用于 AO 波前感测的方式。我们发现 3PWFS 是一种可行的 WFS，它可以完全重建波前并产生稳定的闭环，其校正可与 4PWFS 相媲美，对于高读取噪声检测器具有适度更好的性能。