Photon correlation spectroscopy of the small amount of data based on auto-regressive power spectrum

Dynamic light scattering (DLS) technology is a powerful approach for measuring ultrafine particle size. The correlation method and photon correlation spectroscopy (PCS) are two methods of DLS technology. However, measurement accuracy of the correlation method and PCS based on traditional power spectrum is lower under the condition of the small amount of measurement data. For measurement problem of the small amount of data, PCS based on auto-regressive (AR) power spectrum is proposed in this paper. According to existing small amount of measurement data, this method can forecast subsequent data by an AR model, and then estimate the power spectrum of the data, which can achieve the measurement accuracy of the large amount of data. Besides, the optimal fast Fourier transform (FFT) points of 50 nm-1000 nm particles are obtained by analyzing the mean square error (MSE) of the AR power spectrum and its theoretical power spectrum in different FFT points. The results of simulation and experiment data demonstrate that the AR power spectrum method might serve as an effective approach to PCS measurement problem with the small amount of data.