The leading difficulty in achieving the contrast necessary to directly image exoplanets and associated structures (e.g., protoplanetary disks) at wavelengths ranging from the visible to the infrared is quasi-static speckles (QSSs). QSSs are hard to distinguish from planets at the necessary level of precision to achieve high contrast. QSSs are the result of hardware aberrations that are not compensated for by the adaptive optics (AO) system; these aberrations are called non-common path aberrations (NCPAs). In 2013, Frazin showed how simultaneous millisecond telemetry from the wavefront sensor (WFS) and a science camera behind a stellar coronagraph can be used as input into a regression scheme that simultaneously and self-consistently estimates NCPAs and the sought-after image of the planetary system (exoplanet image). When run in a closed-loop configuration, the WFS measures the corrected wavefront, called the AO residual (AOR) wavefront. The physical principle underlying the regression method is rather simple: when an image is formed at the science camera, the AOR modules both the speckles arising from NCPAs as well as the planetary image. Therefore, the AOR can be used as a probe to estimate NCPA and the exoplanet image via regression techniques. The regression approach is made more difficult by the fact that the AOR is not exactly known since it can be estimated only from the WFS telemetry. The simulations in the Part I paper provide results on the joint regression on NCPAs and the exoplanet image from three different methods, called ideal, naïve, and bias-corrected estimators. The ideal estimator is not physically realizable (it is useful as a benchmark for simulation studies), but the other two are. The ideal estimator uses true AOR values (available in simulation studies), but it treats the noise in focal plane images via standard linearized regression. Naïve regression uses the same regression equations as the ideal estimator, except that it substitutes the estimated values of the AOR for true AOR values in the regression formulas, which can result in problematic biases (however, Part I provides an example in which the naïve estimate makes a useful estimate of NCPAs). The bias-corrected estimator treats the errors in AOR estimates, but it requires the probability distribution that governs the errors in AOR estimates. This paper provides the regression equations for ideal, naïve, and bias-corrected estimators, as well as a supporting technical discussion.

中文翻译：

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毫秒系外行星成像：II。回归方程和技术讨论

在从可见光到红外线的波长范围内实现直接成像系外行星和相关结构（例如原行星盘）所需的对比度的主要困难是准静态散斑（QSS）。QSS 很难在必要的精度水平上与行星区分开来，以实现高对比度。QSS 是自适应光学 (AO) 系统未补偿的硬件像差的结果；这些像差称为非常见路径像差 (NCPA)。2013 年，Frazin 展示了如何将来自波前传感器 (WFS) 和恒星日冕仪后面的科学相机的同步毫秒遥测用作回归方案的输入，该方案同时且自洽地估计 NCPA 和广受欢迎的行星图像系统（系外行星图片）。在闭环配置中运行时，WFS 测量校正后的波前，称为AO 残差(AOR)波前。回归方法的物理原理相当简单：当在科学相机上形成图像时，AOR 会同时模块 NCPA 产生的散斑以及行星图像。因此，AOR 可以用作通过回归技术估计 NCPA 和系外行星图像的探针。由于 AOR 并不完全已知，因此回归方法变得更加困难，因为它只能从 WFS 遥测中估计出来。第 I 部分论文中的模拟提供了来自三种不同方法的 NCPA 和系外行星图像联合回归的结果，称为理想的、朴素的, 和偏差校正估计器。理想的估计量在物理上是不可实现的（它可用作模拟研究的基准），但其他两个是。理想的估计器使用真实的 AOR 值（在模拟研究中可用），但它通过标准线性回归处理焦平面图像中的噪声。朴素回归使用与理想估计量相同的回归方程，不同之处在于它用 AOR 的估计值代替回归公式中的真实 AOR 值，这可能会导致有问题的偏差（但是，第一部分提供了一个示例，其中朴素估计对 NCPA 进行了有用的估计）。偏差校正估计器处理 AOR 估计中的错误，但它需要控制 AOR 估计中错误的概率分布。本文提供了理想的、朴素的、