Objective Laser beams propagating in turbulent atmosphere suffer from various factors such as diffraction, turbulence, aberration and jitter, which broaden the beam radius and significantly affect laser applications including laser propagation, communication and imaging. In recent years, researchers have made efforts to develop fast and high-precision methods for calculating far-field effective radius. Scaling laws and artificial intelligence models are commonly used for fast evaluation of laser beam propagation. However, comparison between these two methods is rarely reported. In this paper, the fast calculation method of far-field radius is studied, and the performance of the different models is compared in many aspects, hoping to provide reference for the selection and application of fast calculation methods for evaluation of laser atmospheric propagation.

Methods Firstly, numerical simulation is carried out by using wave optical program, and the scaling index of the scaling law is determined by genetic algorithm. Secondly, three AI (artificial intelligence) models, MLP, LightGBM and FTT, are selected to evaluate the effective radius of the far field, Additionally, two specific improvements are made to the FTT model (Fig.2). Then, the hyperparameters of AI models are determined by using TPE algorithm (Fig.3-4). Finally, three artificial intelligence models are constructed to evaluate the far-field effective radius (Fig.5).

Results and Discussions When the data is divided into 70% training set and 30% test set, the accuracy of the scaling law model and the three AI models are compared in the test set (Fig.1, Fig.6). The results show that the accuracy of the three artificial intelligence models is higher than that of the scaling law model, and the MFTT model has the highest accuracy with mean relative error of 1.36%. The effect of training set sample size on the evaluation accuracy of 4 models was studied (Fig.7). From the perspective of changing trend, the scaling law model is relatively stable, while the three AI models change sharply, which indicates that the accuracy of the AI model is more dependent on the amount of modeling data. When the training set ratio is greater than 8%, the accuracy of MFTT begins to be higher than that of the scaling law model, and the accuracy of MFTT is consistently higher than that of the other two models in the three AI models.The generalization ability of each model is compared under different propagation scenarios (Fig.8). The results show that the scaling law model and MFTT model have strong generalization ability, while the LightGBM and MLP model have poor generalization ability. The evaluation speed of each model is compared (Fig.9). The results show that all the models can evaluate the effective radius of the far field faster, in which the scaling law is the fastest.

Conclusions The far-field effective radius of Gaussian beam propagating through turbulent atmosphere has received much attention in engineering. This paper studies its fast calculation method. Based on the wave optics program, simulation of Gaussian beam propagating through turbulent atmosphere in multiple scenes is carried out, the scaling law model and three artificial intelligence models (LightGBM, MLP, MFTT） are constructed. The accuracy, generalization ability, the influence of the sample size and the speed of calculation of the scaling law model and three artificial intelligence models are compared. The results show that the accuracy of four models is influenced by the sample size of the training set. The accuracy of the scaling law model is the highest under the small sample size, and the accuracy of the MFTT model is the highest under the large sample size. When the data is divided into a 70% training set and a 30% test set, the mean relative error of the MFTT model is 1.36% under test set, MFTT has the best generalization ability and the scaling law model has the fastest calculation speed. This paper hopes to provide reference for the selection and application of fast calculation methods for evaluation of laser atmospheric propagation.