部分CMB图：角功率谱的偏差消除和最佳合并
Partial CMB maps: bias removal and optimal binning of the angular power spectrum
摘要：
我们提出了一种半解析方法来研究系统的影响和统计不确定性的计算角功率谱时，使用不完整的球面地图。计算出的功率谱尤其会损失角频率分辨率，可表示为δ_l ~ π/γ_max，其中γ_max是部分球面映射的有效最大范围。我们提出了一个校正算法，以减少系统的影响，估计C_l，从部分地图投影球谐Ylm（1，m）的基础上获得。我们已经推导出接近最佳的频带和加权函数在l-空间的功率谱计算使用小地图，和一个校正算法的部分掩盖球面地图，包含信息的角度相关的所有尺度。
英文摘要：
We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as δ_l ~ π/γ_max, where γ_max is the effective maximum extent of the partial spherical maps. We propose a correction algorithm to reduce systematic effects on the estimated C_l, as obtained from the partial map projection on the spherical harmonic Ylm(l,m) basis. We have derived near optimal bands and weighting functions in l-space for power spectrum calculation using small maps, and a correction algorithm for partially masked spherical maps that contain information on the angular correlations on all scales.
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