任意掩模球面上各向同性场的调和分析
Harmonic analysis of isotropic fields on the sphere with arbitrary masks
摘要：
从最大尺度的星系调查中获得约束是具有挑战性的，因为调查掩模只允许大角度模式的部分测量。这使来自谐波空间2点函数的信息远离对角线，并引入模式之间的耦合。在本文中，我们推导出一个自定义的本征基适用于任何特定的调查几何形状，使所有的信息都保留在对角线上。以有点复杂的像素和选择函数窗口为代价，结果是具有简单散粒噪声的对角2点函数，以及高斯随机场情况下的对角协方差矩阵。我们推导出的基础上的表面上的一个球体，我们用它来构建一个3D球面傅里叶-贝塞尔功率谱估计假设的调查几何形状，是可分离的角度和径向方向。
英文摘要：
Obtaining constraints from the largest scales of a galaxy survey is challenging due to the survey mask allowing only partial measurement of large angular modes. This scatters information from the harmonic-space 2-point function away from the diagonal and introduces coupling between modes. In this paper, we derive a custom eigenbasis adapted to any particular survey geometry so that all information is retained on the diagonal. At the expense of a somewhat complex pixel- and selection-function-window, the result is a diagonal 2-point function with a simple shot noise, and a diagonal covariance matrix in the case of a Gaussian random field. We derive the basis on the surface of a sphere, and we use it to construct a 3D spherical Fourier-Bessel power spectrum estimator assuming a survey geometry that is separable in the angular and radial directions.
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