Optimizing Fitting Statistics in Photon Correlation Spectroscopy

J. Shaumeyer, R. Gammon
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引用次数: 1

Abstract

We have performed an experiment to test our understanding of the run time, T, necessary to achieve a specified precision in the value of the intensity coherence time, τc, extracted from correlation functions taken in the strong signal limit, and to test predictions for the values of some experimental parameters that optimize the precision. Using ensembles of 10 correlation functions taken at 5 different choices of sample time, we found that the ensemble estimators for the error in τc were well described by the expression δτ/τ c =4.2/T/τ c , in agreement with the work of Degiorgio and Lastovka (1971). The sample times used were chosen so that the number of coherence times spanned by the 128 channels of the correlator, α, covered the range 1 ≤ α ≤ 16; in this range, we found no evidence of a minimum in δτ/τc to suggest an optimum value of α. These results were independent of whether we used three-parameter or two-parameter least-squares fits to extract τc. However, we did find that the two fits gave systematically different values of τc, and both show a similar dependence on α.
光子相关光谱学中拟合统计的优化
我们进行了一个实验,以测试我们对运行时间T的理解,T是在强信号极限中从相关函数中提取的强度相干时间τc值达到指定精度所必需的,并测试对优化精度的一些实验参数值的预测。使用5种不同采样时间下的10个相关函数的集合,我们发现τc误差的集合估计可以用δτ/τ c =4.2/T/τ c的表达式很好地描述,这与Degiorgio和Lastovka(1971)的工作一致。选取采样次数,使相关器的128个通道所跨越的相干次数α在1≤α≤16范围内;在这个范围内,我们发现没有证据表明δτ/τc有一个最小值来表示α的最佳值。这些结果与我们是否使用三参数或两参数最小二乘拟合来提取τc无关。然而,我们确实发现这两种拟合给出了系统不同的τc值,并且都显示出对α的相似依赖。
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