The statistics of ToF-SIMS data revisited and introduction of the empirical Poisson correction
The statistics of ToF-SIMS data revisited and introduction of the empirical Poisson correction
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DOI：
10.1002/sia.5955
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发表时间：
2016-04-01
影响因子：
1.7
通讯作者：
Smentkowski, Vincent S.
中科院分区：
文献类型：
--
作者：
Keenan, Michael R.;Smentkowski, Vincent S.
飞行时间二次离子质谱（ToF-SIMS）数据的生成涉及两个主要过程：二次离子产生和二次离子检测。如果测量的质谱的强度与所研究的物种的丰度成正比，则有助于解释ToF-SIMS数据。虽然二次离子产率通常被认为是一个线性过程，但离子检测不受探测器死区时间效应的影响。因此，人们设计了一些方法，试图对受死区时间影响的数据进行线性化或校正。在本文中，我们回顾了ToF-SIMS数据生成的统计数据，并证实了文献中的一份报告，即从所谓的泊松校正中估计的丰度是有偏差的。我们表明，这些修正只是渐近无偏的，严格的概率分析可以定量地解释观察到的偏差。确定了两个偏差来源，一个具有统计基础，另一个是由于高离子检测率下校正方程的形式。在此分析的基础上，我们提出了一个新的修正方程，即经验泊松修正，它在很大程度上消除了统计偏差。通过重新分析14个实验测量的数据集来说明所提出的校正的性能，这些数据集受到不同程度的死区时间效应的影响。版权所有：John Wiley & Sons， Ltd。
Generation of time-of-flight secondary ion mass spectrometry (ToF-SIMS) data involves two overarching processes: secondary ion production and secondary ion detection. The interpretation of ToF-SIMS data is facilitated if the intensities of the as-measured mass spectra are proportional to the abundances of the species under investigation. While secondary ion yield is normally taken to be a linear process, ion detection is not owing to detector dead-time effects. Consequently, methods have been devised that attempt to linearize, or correct, data that are affected by the dead time. In this article, we review the statistics of ToF-SIMS data generation and confirm a report in the literature that abundance estimates from so-called Poisson corrections are biased. We show that these corrections are only unbiased asymptotically and that a rigorous probabilistic analysis can quantitatively account for the observed bias. Two sources of bias are identified, one having a statistical basis and one due to the form of the correction equation at high ion detection rates. Based on insights gained from this analysis, we propose a new correction equation, the empirical Poisson correction, which largely eliminates the statistical bias. The performance of the proposed correction is illustrated by reanalyzing 14 experimentally measured datasets that suffer from varying levels of dead-time effects. Copyright (c) 2016 John Wiley & Sons, Ltd.