# Experimental Study on Phase Scintillation of Optical Transmission in Atmospheric Turbulence
## 3 Experimental Measurements  
The system schematic of this experiment is shown in Figure 3. The transmitter uses a solid-state laser with a wavelength of 532 nm, an output power of 200 mW, and a beam diameter of 5 mm as the light source. The laser emits the light source, which enters the atmospheric channel through the transmitting antenna (both the transmitting and receiving optical antennas are [PERSON] optical telescopes with an aperture of 105 mm). At the receiving end, the signal beam is received by the receiving antenna and passes through a collimating lens into a 4F beam-reducing and -collimating system composed of L1 (focal length: 135 nm) and L2 (focal length: 75 nm). Two polarizers are added in the middle of the beam-reducing and -collimating system to attenuate optical power and filter out the strong light reflected by objects. A wavefront sensor is placed behind the L2 lens for wavefront detection, and the measured information is output to a computer to observe the wavefront phase of the beam. The wavefront sensor used In this experiment Is the HASO4-FIRST Shack-Hartmann wavefront sensor manufactured by Imagine Optic (Orsay, France). It has an aperture size of 3.6 mm\({}^{2}\times\) 4.6 mm\({}^{2}\), with 32 \(\times\) 32 apertures. The sensor operates at wavelengths from 400 nm-1100 nm and a maximum acquisition frequency of 100 Hz. In order to accurately track turbulence, the sampling frequency of the sensor needs to satisfy the Nyquist sampling theorem, i.e., the sampling frequency must be at least twice the dominant frequency of the turbulence. For most atmospheric turbulent environments, the frame rate of modern Shack-Hartmann wavefront sensors is sufficient to track turbulence-induced changes in the environment and effectively measure wavefront aberrations induced by atmospheric turbulence [15]. The principle of operation of the Shack-Hartmann wavefront sensor is shown in the Figure 4. The Shack-Hartmann wavefront sensor consists of a beam reduction system, a microlens array, and a CCD, and the incident pupil is separated into many sub-apertures by the microlens array. Each microlens focuses the parallel light incident on it onto the detection range of the CCD to form a spot array. If the incident wavefront is an ideal planar wavefront, the spot formed by each microlens will fall accurately at its focal point. If there is an aberration in the incident wavefront, the spot formed by each microlens will be off its focal point in its focal plane. The subaperture spot offset of the measured wavefront relative to the reference wavefront reflects the slope of the wavefront of the incident wavefront within the subaperture. By measuring the offset of each sub-aperture spot, the phase of the incident wavefront over the full aperture range can be recovered by a dedicated algorithm. From the working principle of the Shack-Hartmann wavefront sensor, it can be seen that the wavefront detection accuracy of the Shack-Hartmann wavefront sensor mainly depends on the center-of-mass detection accuracy of each sub-aperture in the spot array. And the  
Figure 3: Experimental schematic diagram. magnitude of the wavefront aberration is related to the degree of deviation. In Figure 4, \(\Delta x\) and \(\Delta y\) are the offsets from the center reference point in the \(x\) and \(y\) directions respectively. The procedure for measuring wavefront aberrations is as follows:  
1. First, ensure that the Shack-Hartmann wavefront sensor is calibrated. Place the wavefront sensor at the receiving end of the beam propagation and adjust the optical path so that the incident beam passes precisely through the microlens array;
2. Second, the beam passes through atmospheric turbulence and is incident on the microlens array. Turbulence-induced wavefront aberrations shift the spot on the detector. Plots of the spot distribution at different points in time are collected to record the dynamics;
3. Center-of-mass probing was again performed on the distribution of light spots recorded by the detector.