Objective Accurate measurement of beam quality is crucial to the evaluation of laser performance, and compared with the traditional method of measuring and then correcting after long-distance transmission, the beam quality after short-distance transmission is closer to the real situation at the export of the laser. When high-energy laser propagates in the air, as the power increases, the interaction with the air will also become more obvious, mainly reflected in atmospheric turbulence and thermal blooming effects, which will affect the distortion and expansion of the spot shape, leading to a decrease in beam quality. However, current simulations and experiments on high-power large-caliber laser transmission often involve long-distance transmission to obtain target power. After accounting for the effects of atmospheric turbulence and thermal blooming on the transmission path, they then deduce beam quality information for further evaluation. Due to the complexity and randomness of atmospheric turbulence and thermal blooming, as well as the inability to obtain real-time relevant parameters of each point on the transmission optical path, the deduction amount is much greater than the true value of the beam quality under poor atmospheric conditions, resulting in significant errors. Therefore, measuring beam quality directly at the system export, given the short transmission distance, is less affected by nonlinear effects such as atmospheric turbulence and thermal blooming, and thus produces more accurate results.

Methods Firstly, the theories regarding the atmospheric turbulence effect and thermal blooming effect in short-distance transmission were elaborated. Then, we simplified the optical path diagram for measuring beam quality (Fig.1), and established a model simulation based on this optical path diagram, by changing different environmental factors and conducting simulation experiments. Using a parallel light tube with a diameter of 700 mm, at a distance of 20 m, a Charge Coupled Device (CCD) was used to receive the focused spot and calculate its beam quality. While measuring the beam quality, a temperature pulsation meter was used to collect the indoor turbulence intensity during the experimental process, and methods for reducing turbulence intensity were analyzed.

Results and Discussions In the case of 20 m transmission, the beam quality \beta factor was severely affected by turbulence intensity C_n^2 , and the spot shape underwent significant distortion and expansion as turbulence increases (Fig.2). Further analysis was conducted on the variance of the \beta factors under different intensities of turbulence. The variance did not exceed 0.08% under weak turbulence, approximately 12.63% under moderate turbulence, and over 100% under strong turbulence (Fig.3). For lateral winds of different speeds, the difference in \beta factors was within 10%. For different relative humidity of the air, the difference in \beta factors did not exceed 15%. For different apertures, \beta factors increased with the increase of aperture size. In this case, the difference in \beta factors between different apertures was about 15% (Fig.4). When strong turbulence intensity is reached, the difference in \beta factors between different apertures could reach up to 80% (Fig.5). For different powers, the error in \beta factors calculation was within 2%. The beam transmission with different initial \beta factors was also simulated, and the beam quality measurement deviation of the laser system was less than 5% for the laser system with the air turbulence control intensity controlled below 1 \times 10^ - 14\;\textm^ - 2/3 and the beam quality \beta factor not less than 3 (Fig.6). Different transmission distance also had an impact on the \beta factors of laser beam quality. When the \beta factor measurements are stable in the moderate turbulent intervals for a transmission distance of 2 m, whereas it increases approximately linearly for 20 m (Fig.7). The actual measured beam quality of the 700 mm caliber collimator (Fig.8) was consistent with the simulation results (Fig.9). Collecting indoor turbulence intensity variation maps, both static and stirred air could achieve lower turbulence intensity values (Fig.10), which means that in actual measurement processes, atmospheric turbulence intensity can be reduced by stirring air to obtain more accurate values.

Conclusions This article introduces the research progress of high-power laser beam quality measurement. We separately discussed the effects of atmospheric turbulence and thermal blooming on laser transmission over short distances. After short distance transmission, the atmospheric turbulence effect has a greater impact on beam quality, and as C_n^2 increases, the \beta factors increases from 1.0848 to 8.9933. The influence of factors such as thermal blooming effect and humidity is minimal. In case of moderate and weak turbulence, the difference in \beta factors for different lateral wind speeds, relative air humidity, and power is within 3%. But for different apertures, when reaching C_n^2 \leqslant 10^ - 14\;\textm^ - 2/3 , the difference in \beta factors for different apertures is about 15%. When strong turbulence intensity is reached, the difference in \beta factors for different apertures can reach up to 80%. And in actual measurements, it has been verified that stirring air can also reduce atmospheric turbulence to a certain value. Therefore, it is necessary to minimize the disturbance of the air within the distance from the outlet to the beam splitter, making stirring air more practical. The \beta factors deviation is within 8% when C_n^2 \leqslant 10^ - 14\;\textm^ - 2/3 at 20 m transmission distance. The beam quality degradation after transmission is different for lasers with different initial factors, and the more excellent the initial beam quality is, the more serious the degradation is. The experimental results of this paper show that the beam quality measurement deviation of the high-power, large-caliber laser system with beam quality \beta factor not less than 3 is less than 5% by controlling the air turbulence control intensity below C_n^2 < 10^ - 14\;\textm^ - 2/3 , which provides a solution for the beam quality measurement of large-caliber laser export.