光谱完美主义：光子噪声限制萃取Optical Fiber Spectroscopy的理论框架
Spectro-Perfectionism: An Algorithmic Framework for Photon Noise-Limited Extraction of Optical Fiber Spectroscopy
摘要：
我们描述了一种新的算法，用于从光纤光谱仪的二维（2D）数字图像中“完美”提取一维光谱，基于精确的原始像素数据的2D前向建模。该算法对任意复杂的二维点扩散函数（PSF）都是正确的，而传统的最优提取算法只对有限类可分离的PSF是正确的。该算法的结果在统计上独立的提取样本的1D光谱，并保持完整的原生分辨率的2D光谱仪没有退化。统计误差和提取的光谱的1D分辨率都被准确地确定，允许任何模型光谱与数据的正确卡方比较。使用一个模型PSF中发现的红色通道的斯隆数字巡天摄谱仪，我们比较我们的算法的性能的横截面为基础的最佳提取，也表明我们的方法允许coaddition和前景估计进行作为一个组成部分的提取步骤。这项工作证明了当前和下一代多光纤光谱仪即使在强烈的夜空前景下也能用于微弱星系的调查。我们描述了处理的微妙之处所产生的光纤到光纤的串扰，讨论了一些可能的挑战，部署我们的方法来分析一个全面的调查，并指出，我们的算法可以推广到一个最佳的方法，纠正和天文成像数据的组合。
英文摘要：
We describe a new algorithm for the "perfect" extraction of one-dimensional spectra from two-dimensional (2D) digital images of optical fiber spectrographs, based on accurate 2D forward modeling of the raw pixel data. The algorithm is correct for arbitrarily complicated 2D point-spread functions (PSFs), as compared to the traditional optimal extraction algorithm, which is only correct for a limited class of separable PSFs. The algorithm results in statistically independent extracted samples in the 1D spectrum, and preserves the full native resolution of the 2D spectrograph without degradation. Both the statistical errors and the 1D resolution of the extracted spectrum are accurately determined, allowing a correct chi-squared comparison of any model spectrum with the data. Using a model PSF similar to that found in the red channel of the Sloan Digital Sky Survey spectrograph, we compare the performance of our algorithm to that of cross-section based optimal extraction, and also demonstrate that our method allows coaddition and foreground estimation to be carried out as an integral part of the extraction step. This work demonstrates the feasibility of current- and next-generation multi-fiber spectrographs for faint galaxy surveys even in the presence of strong night-sky foregrounds. We describe the handling of subtleties arising from fiber-to-fiber crosstalk, discuss some of the likely challenges in deploying our method to the analysis of a full-scale survey, and note that our algorithm could be generalized into an optimal method for the rectification and combination of astronomical imaging data.
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