AC-SLODAR: measuring daytime normalized optical turbulence intensity distribution based on slope autocorrelation

Abstract

ABSTRACT In solar observations, the vertical distribution of turbulence can be detected with a multidirectional Shack–Hartmann wavefront sensor, based on SLODAR or S-DIMM+. By expressing the measured cross-correlation as a linear combination of theoretical correlation functions for various height layers, the distribution of turbulence intensity can be obtained through fitting. The theoretical correlation functions in different heights are employed to describe the slope correlation and calculated based on the phase structure function corresponding to classical turbulence statistical theories such as Kolmogorov or von Karman. However, for turbulence that does not obey classical theory, this deviation of the statistical characteristics would result in the measurement accuracy degradation of seeing profiles. A method, so-called AutoCorrelation-SLODAR (AC-SLODAR), is proposed. The feasibility of transforming cross-correlation into autocorrelation is analysed theoretically. Then, the autocorrelation function is calculated based on the actual data to avoid the deviation introduced by the theoretical turbulence statistical model. Extracting statistical characteristics from data also simplifies measurements, without requiring the evaluation of whether the data conforms to a particular classical statistical model. AC-SLODAR was validated with simulation data generated by the open-source emulator SOAPY. The measured error was reduced by 10 per cent compared with SLODAR for the situation of turbulence model deviation. The performance of AC-SLODAR was further compared with those of SLODAR based on the actual data collected in 2016 and 2017 on the New Vacuum Solar Telescope. The corresponding results of AC-SLODAR are consistent with those of SLODAR using a pre-evaluated turbulent model.