Greenwood frequency measurement of atmospheric turbulence by phase difference method

To measure the Greenwood frequency of the atmospheric turbulence accurately, the validity of phase difference method and the selection of the sampling points and the sampling frequency of the Shack-Hartmann wavefront sensor(S-H WFS) have been studied. Firstly, the principle of the phase difference method and the noise elimination algorithm are given. Secondly, the effects of the sampling points of S-H WFS and the statistical times of Greenwood frequency on the measurement accuracy are investigated. The experimental results show that, while both the sampling points and the statistical times are more than 400, the Greenwood frequency can be measured accurately. Thirdly, the influence of the measurement noise is considered and the result shows that the deviation error of the measured value is reduced from 30% to 0.6% with the noise removed. Fourthly, the repeatability of the phase difference method is measured. It is shown that the deviation RMS error is 1.9 Hz which is 3% of the ideal value. Therefore, the Greenwood frequency can be measured accurately with the phase difference method. Based on the above results, the Greenwood frequency of the atmospheric turbulence is measured and analyzed with the range of 8-108 Hz. It indicates that the measured value is almost the same as theoretical value without consideration of the disturbance of the air in the Lab. At last, the relation between the sampling frequency of S-H WFS and the Greenwood frequency is investigated. It can be seen that the sampling frequency of the S-H WFS should be increased if the measured Greenwood frequency is enlarged. Furthermore, an empirical formula is achieved to calculate the needed sampling frequency of the S-H WFS. In a word, all the results show that, when it meets the demand of sampling points, sampling frequency and statistical times, the phase difference method can be used to measure the Greenwood frequency of atmospheric turbulence accurately.