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The case for high resolution multiple tau correlator 1. Triangular introduces systematic error. In low light conditions where photon counting technique is employed, one can't measure the instantaneous intensity due to the photon statistics. Instead, one counts the number of photons within a sample time, ts. In effect, this number of photons represents the intensity integrated over a period ts.Correlation function, G(t), is calculated as <n(0)n(t)>, where t is the average delay between the two bins. G(t) is the integral of the ideal correlation function, g(t), from t-ts to t+ts weighted by a triangular shape function.
In the case of an ideal exponential decay correlation function,
where The function
represents the systematic error introduced by the triangular average. 2. Systematic error comparison for multiple tau schemes Traditional multiple tau channel layout correlator calculates 16 data points at the smallest sample time, for example 12.5 ns. The sample time doubles every 8 data points. The delay times are (1, 2, …16)* 12.5ns, (9, 10..16)*25ns, (9,10,..16)*50ns, and so on. The sample time to delay time ratio is between 1/9 to 1/16 except for the first 8 data points. This is Multi Tau 16 (MT16) layout. MT32 channel layout means the first 32 data points are linear and the sample time doubles every 16 data points. The ratio of sample time to delay time is from 1/18 to 1/32. MT64 channel layout gives you first 64 linear data points and the sample time doubles every 32 data points. The ratio is between 1/34 to 1/64. The following figure shows the maximum systematic error as a function of x for MT16 (using 1/9 ratio), MT32 (1/17), and MT64 (1/33).
When x is small, all multiple tau correlators are sufficiently accurate. At larger x value, MT64 is has a smaller systematic error than MT32, which is also better than MT16. 3. High resolution products The high resolution correlation, Flex01-12D, gives you three choices.
Flex01-08D
For more information, please contact Jixiang Zhu, Correlator.com, 15 Colmart Way, Bridgewater, NJ 08807, 908-725-1244, 908-725-9851(fax) Jixiang@correlator.com, http://www.correlator.com |
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