Objective When laser propagates in the atmosphere, it is inevitable that a random change of the refractive index of the atmospheric turbulence causes laser spot broken and distorted, which seriously damages the laser beam quality. Under the conditions of weak- and strong-fluctuating media, the turbulence model has relatively rich theoretical research results. In view of the complexity of the turbulence itself, the current theory of light transmission in random media is not enough to perfectly present the far-field transmission characteristics of the laser spot in the strong-fluctuation region. As for the high-altitude laser transmission engineering applications, the spatial distribution of laser energy on the target surface and its temporal variation characteristics are vital for photoelectric system evaluation. However, the research of long-range high-altitude laser atmospheric transmission faces the following problems: first, there are few transmission tests in high-altitude areas; second, short-exposure laser spot data at high frame-rate sampling are rare; third, two-dimensional imaging methods to obtain more comprehensive laser statistical parameters are still lacking. In this study, we use a high-speed camera to perform laser spot tests at different distances in high-altitude areas. Using the laser short-exposure image data at sampling rate of 4000 frame·s ^-1, the change characteristics of short-exposure far-field laser spots in the turbulent atmosphere are qualitatively described, and the optical turbulence parameters such as ideal point scintillation indexes, aperture average factors, and inner scales are calculated. Our aim is to use the external field laser transmission test data to understand the spatial laser energy distribution on the target surface as well as its temporal variation characteristics under high-altitude conditions and to simultaneously determine its impact on the laser photoelectric system.

Methods The experiment is performed at an altitude of 3200 m in Gaomeigu, far from the underlying surface. The transmitting terminal is a 532 nm solid-state laser, while the receiving system is consisted of a high-speed CCD camera and a diffuse reflection screen. The camera is placed obliquely in front of the screen at ~9m, the transmitter is located in the balcony in the third floor of the Gaomeigu radar station at ~10m above the ground, and the receiver is located on the open ground at distances of 1, 2, 3, 4, and 4.7km from the transmitting terminal. The selected geographical location can ensure that most of the transmission paths are longer than 15m from the underlying surface and the maximum height is larger than 100m. In addition, the test is also performed in the canyon, far away from the underlying surface. The straight-line distance between two ends is ~2km, and the maximum link distance from the underlying surface is ~300m. The sampling rate of laser spot images is unified to 4000 frame·s ^-1, each image is 320pixel×240pixel, and the image accuracy is 8bit. For the acquired two-dimensional data of the laser spot, using the imaging method, the scintillation index under different receiving apertures is calculated, and subsequently polynomial fitting is used to obtain the ideal point scintillation index. With the former results, the refractive index structural parameters such as the path, aperture average factor, and inner scale can also be derived. Moreover, this method based on the calculation of the gray value of the light spot can also display the correlation coefficient between the power spectrum and its scaling rate as well as the spatial light intensity distribution.

Results and Discussion At a distance of 1km, with the playback of a short-exposure spot image at a sampling rate of up to 4000 frame·s ^-1, the broken laser spot shows a clear mesh-like morphological structure, and a few sharp bright spots are scattered. There are irregular shapes and different size holes inside the spot (Fig. 3). As time elapses, these flowing mesh-like structures and scattered bright spots undergo deformation and reconstruction. There is a certain unclear relationship between size of the reticulated texture and the scale of the turbulence. Using the light spot gray value data, the aperture average factor of different receiving radii on the target surface is obtained. The variation of the laser spot aperture average factor with the receiving aperture shows that the aperture average factor is not only a function of the aperture but also is related to the turbulence state (Fig. 6). The daily variation of Cn2 in high-altitude areas is relatively stable, showing a different trend from the “Mexican hat” trend near the ground at low altitudes (Fig. 7). The power spectral distributions of laser scintillation under different transmission distances show that the cutoff frequency of the power spectrum of a single pixel is generally higher than the average cutoff frequency of the circular domain, which indicates that the aperture smoothing effect of light intensity scintillation still exists in the frequency domain. The scaling rate obtained from the power spectrum shows a positive correlation trend with the ideal scintillation index (Figs. 9 and 11). Taking the spot centroid as the point of origin, the normalized spatial correlation coefficient of the light intensity fluctuations at the distance from the origin point shows that the spatial correlation radius increases with the increase of the scintillation index (Fig. 12). It is a completely different concept from the coherence length.

Conclusion The main purpose of designing this experiment is to find the transmission conditions far away from the underlying surface in high-altitude areas and to obtain the characteristics of the laser spot transmitted in high-altitude free atmospheric turbulence. Judging from the fact that there is no obvious “Mexican hat” structure in the daily variation trend of most transmission paths, the underlying surface on the transmission path has little influence, but there are still big differences between the real test conditions and high-altitude “free” atmosphere. In the future, we hope that we will have the opportunity to conduct high frame-rate laser spot image testing on higher and farther platforms to promote the understanding of laser transmission in free turbulent atmospheres.