球極平面座標下微波背景輻射E/B 分割之分析

Abstract

宇宙微波背景輻射的極化可被分解為E type 與B type 兩個部分。當 觀測的天區很小時(小於十度)，我們可以用卡氏座標來分析資料並且 忽略資料背景的曲率。但如果我們想要分析來自更大天區的資料那麼 資料的背景曲率便不可忽略。我們使用球極平面投影的座標來達成此 目的。球極平面投影座標是一個對稱且正交的座標系統，並且在小天 區時逼近卡氏座標，因此我們能產生較準確的E 和B 模來分析背景天 區較大的資料。

The CMB polarization can be decomposed into E and B components. Usually when the portion of the sky is small enough(less than 10 degrees), we can analyze the field in Cartesian coordinates by taking the small-scale approximation and neglect the curvature effect. But if we want to analyze the field in a larger portion of the sky we must take the curvature into account. To include the curvature we introduce the stereographic coordinates for the sphere. It is an orthogonal symmetric coordinate that reduces to Cartesian coordinates in the small-sky limit. Hence we can generate more precise basis E and B modes and analyze the field in larger sky.