Symmetrical Normalization of Autocorrelation Function for Multi-Tau Photon Correlator

Abstract

Abstract: In view of using symmetrical normalization for smaller deviation than standard normalization for the multi-tau photon correlator in the whole delay time range but need more monitor channels. We suggest employing symmetrical normalization when the lag time larger than 16384 and standard normalization smaller than 16384. Deviation of symmetrical normalization and standard normalization was analyzed, results show that the deviation of symmetrical normalization is smaller in large lag time and have approximate deviation in small lag time. Measurements with standard polystyrene particles of 60 nm, 150 nm and 450 nm, the calculated average deviation and maximum deviation of two normalization estimators are similar in small lag time, but the average and maximum deviation of standard normalization are 19 to 37 times and 35 to 59 times larger than symmetrical in large time. We adopt nonnegative Tikhonov investigate inversion for 60 nm, 150 nm and 450 nm, the results suggest that the particles size distribution of symmetrical normalization is approach to the true particles size distribution in large lag time. Hence, employing symmetrical normalization in the appropriate dynamic range not only reduce the monitor channel, but also improve the statistical accuracy in large delay time range.