弱透镜剪切测量中的椭圆加权HOLIC part3：弱透镜分析中图像矩的随机计数噪声效应
Elliptical Weighted HOLICs for Weak Lensing Shear Measurement part3:Random Count Noise Effect for Image's Moments in Weak Lensing Analysis
摘要：
这是第三篇用椭圆权函数（E-HOLIC）改进弱透镜分析中的系统误差的论文。在以前的论文中，我们已经成功地避免了错误，这取决于椭圆的背景图像。本文研究了背景图像的信噪比对系统误差的影响。我们发现，误差的来源是随机计数噪声，它来自泊松噪声的天空计数。随机计数噪声产生额外的矩和质心偏移误差，并且这些一阶在平均中被取消，但二阶没有被取消。推导了在测量图像矩和椭圆率时修正这些影响的公式，并用模拟图像验证了其有效性。我们发现，系统误差变得小于1%的物体与$S/N>3$的测量椭圆率。
英文摘要：
This is the third paper on the improvements of systematic errors in our weak lensing analysis using an elliptical weight function, called E-HOLICs. In the previous papers we have succeeded in avoiding error which depends on ellipticity of background image. In this paper, we investigate the systematic error which depends on signal to noise ratio of background image. We find that the origin of the error is the random count noise which comes from Poisson noise of sky counts. Random count noise makes additional moments and centroid shift error, and those 1st orders are canceled in averaging, but 2nd orders are not canceled. We derived the equations which corrects these effects in measuring moments and ellipticity of the image and test their validity using simulation image. We find that the systematic error becomes less than 1% in the measured ellipticity for objects with $S/N>3$.
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