插值点扩散函数各向异性
Interpolating point spread function anisotropy
摘要：
计划中的宽场弱透镜测量预计将把剪切场的统计误差减少到前所未有的水平。相比之下，像那些由与点扩散函数（PSF）的卷积引起的系统误差将不会受益于该缩放效应，并且将需要非常精确的建模和校正。虽然已经设计了许多方法来执行PSF校正本身，但到目前为止，PSF形状及其在仪器视场中的空间变化的建模引起的关注要少得多。然而，这一步是至关重要的，因为PSF只在恒星位置上是已知的，而校正必须在天空中的任何位置上进行。因此，可靠的插值方案是强制性的，并且流行的方法是使用低阶二元多项式。在本文中，我们评估其他四个经典的空间插值方法的基础上样条（B样条），反距离加权（IDW），径向基函数（RBF）和普通克里格（OK）。在2010年引力透镜精度测试（GREAT 10）模拟数据的Star挑战部分上对这些方法进行了测试，并与经典的多项式拟合（Polyfit）进行了比较。我们还测试了我们所有的插值方法，独立于PSF的建模方式，通过插值GREAT 10星场本身（即，PSF参数在起始位置处是精确已知的）。在这种情况下，我们发现RBF是明显的赢家，紧随其后的是其他本地方法，IDW和OK。整体方法，Polyfit和B样条，在很大程度上落后，特别是在（地面）湍流PSF的领域。在非湍流PSF的字段中，所有插值器达到PSF系统$σ_{sys}^2$的方差优于未来天基调查预期的$1\times10^{-7}$上限，局部插值器的性能优于全局插值器。
英文摘要：
Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). We also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics $σ_{sys}^2$ better than the $1\times10^{-7}$ upper bound expected by future space-based surveys, with the local interpolators performing better than the global ones.
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