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arXiv 1602.05486astro-ph.IM
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利用同时光瞳平面和焦平面遥测进行系外行星成像的统计框架,第II部分:作为波前传感器场函数的科学照相机图像

A Statistical Framework for Utilization of Simultaneous Pupil Plane and Focal Plane Telemetry for Exoplanet Imaging, Part II: The Science Camera Image as a Function of the Wavefront Sensor Field

Richard A. Frazin

摘要:

为了超越超大望远镜(ELT)时代系外行星差分成像的局限性,本系列的第一篇论文建立了一个严格的全偏振框架,用于确定科学相机(SC)图像,给出了湍流波前和光学系统多个平面中的未知像差。本文建立在论文I中开发的结构上,以严格地表达偏振SC图像中的波前传感器(WFS)上的场冲击,从而提供了两个子系统中的测量之间的直接连接。该公式允许SC图像被写入WFS测量的函数,包括以下未知量,其原则上可以通过统计推断来估计:非共路像差(NCPA)、WFS增益误差、分束器下游的像差和行星图像。它表明,WFS的偏差误差是数学上等价的NCPA。因此,在具有处理WFS偏差和增益的能力的情况下,该方法不应对WFS校准问题过度敏感。重要的是,这个公式包括随机过程,代表噪声测量的SC图像,噪声WFS测量,和高频分量的波前WFS是不敏感的。结果表明,波前误差由于噪声在WFS测量有一个方便的半解析表示WFS测量算子的奇异函数。此外,这些过程的一阶和二阶统计量被指定,从而为本系列后面的论文中描述的统计推断方法的应用奠定了基础。

英文摘要:

In an effort to transcend the limitations of differential imaging of exoplanets in the era of extremely large telescopes (ELTs), the first paper in this series established a rigorous, fully polarimetric framework for determining the science camera (SC) image given a turbulent wavefront and unknown aberrations in multiple planes the optical system. This article builds on the structure developed in Paper I in order to rigorously express the polarimetric SC image in terms of the field impinging on the wavefront sensor (WFS), thereby providing a direct connection between the measurements made in both subsystems. This formulation allows the SC image to be written as a function of the WFS measurements, including the following unknown quantities which can, in principle, be estimated via statistical inference: the non-common path aberration (NCPA), WFS gain errors, aberrations downstream of the beamsplitter, and the planetary image. It is demonstrated that WFS bias error is mathematically equivalent to NCPA. Thus, with the ability to treat WFS bias and gains, the method should not be overly sensitive to WFS calibration problems. Importantly, this formulation includes stochastic processes that represent noisy measurement of the SC image, noisy WFS measurements, and high-frequency components of the wavefront to which the WFS is insensitive. It is shown that wavefront error due to noise in the WFS measurements has a convenient semi-analytical representation in terms of the WFS measurement operator's singular functions. Further, the first and second order statistics of these processes are specified, thereby setting the stage for the application of statistical inference methods to be describe in later papers in this series.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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