Atmospheric Coherence Length Research Articles

Measurement of Atmospheric Coherence Length from a Shack–Hartmann Wavefront Sensor with Extended Sources

Free Space Optical Communication (FSOC) is a wireless communication method that utilizes laser beams for high speed and secure data transmission. Its performance is affected by various factors, among which atmospheric turbulence causes random fluctuations in the atmospheric refractive index, significantly impacting the reliability of communication links. The atmospheric coherence length is a key parameter describing the coherence properties of a laser signal as it propagates through the atmosphere, and accurately measuring it is crucial for assessing the quality of FSOC links. This paper proposes a novel strategy that utilizes extended sources directly as the information sources, combining the wavefront phase variance method with the extended source offset algorithm based on Shack–Hartmann wavefront sensors to directly measure atmospheric coherence length. Existing methods in extended scenarios typically rely on deploying laser beacons to aid in the calibration of atmospheric coherence length but setting up suitable beacons on horizontal communication links is challenging. Additionally, these approaches can be costly in terms of equipment and measurement expenses. Compared to traditional measurement methods, the algorithm proposed in this paper can measure directly based on extended scenarios in horizontal links, thereby effectively reducing system complexity and equipment costs. To verify the feasibility and effectiveness of this method, targeted simulations and experiments were conducted, and the results show that the coherence length measured by the algorithm is highly consistent with that measured by the Differential Image Motion Monitor (DIMM), with a deviation of less than 2% from actual values, effectively demonstrating the algorithm’s feasibility in coherence length assessment.

Research on integrated LiDAR and multi-parameter detection of atmospheric transmittance, turbulence, and wind

An integrated LiDAR system has been reported, which can be used for simultaneous detection of atmospheric transmittance, turbulence, and wind along the same path. Through the integrated design of optics and mechanics, the size and weight of the system were effectively reduced. The comprehensive detection distance of atmospheric transmittance, atmospheric coherence length, and radial wind had also been achieved at least 4 kilometers. Comparative experiments have demonstrated that the detection results of the integrated LiDAR system and the near-surface meteorological observation system have standard deviations of less than 0.03 km−1 for extinction coefficient, 0.2 m/s for wind velocity, and 7.15 × 10−14 m−2/3 for C 2 n (atmospheric refractive index structure parameter), thus verifying the accuracy of the system detection. The reliability of the integrated LiDAR system was validated through six consecutive nights of continuous detection experiments, measuring three parameters simultaneously. Through analysis, the influence laws among atmospheric transmittance, coherence length, and wind were preliminarily explored. Significant variations in wind velocity can induce substantial fluctuations in atmospheric coherence length, and it is positively correlated with atmospheric transmittance. The integrated LiDAR system can provide a variety of reliable real-time detection data for further research on the laser transmission process in the atmosphere.

Competition between turbulence and thermal blooming of coherent vortex beam array propagating in non-Kolmogorov marine atmosphere.

The competition between turbulence and thermal blooming significantly affects the propagation characteristics of laser beams in the atmosphere. Here, taking the propagation of a vortex beam array in a non-Kolmogorov marine atmosphere as an example, we have quantitatively analyzed the competition between turbulence and thermal blooming. The atmospheric coherence length is adopted to evaluate the turbulence strength, while a modified thermal distortion parameter is developed to evaluate the thermal blooming strength of vortex beam arrays in non-Kolmogorov turbulence. Results indicate that, in strong turbulence, there is a significant variation in the beam characteristics at the target plane as the spectral power law index increases, whereas this relationship exhibits a smoother change in weak turbulence. More interestingly, our results suggest that for a fixed aperture of laser emission systems, increasing the initial power density may not always lead to a higher average power density at the target plane, and there exists an optimal value no matter what the intensity of the turbulence is, i.e., weak, moderate, and strong turbulence. We hope these results may provide useful guidance for laser communication, laser power transmission, etc.

Vertical Distribution of Optical Turbulence at the Peak Terskol Observatory and Mount Kurapdag

Atmospheric turbulence characteristics are essential in determining the quality of astronomical images and implementing adaptive optics systems. In this study, the vertical distributions of optical turbulence at the Peak Terskol observatory (43.27472°N 42.50083°E, 3127 m a.s.l.) using the Era-5 reanalysis and scintillation measurements are investigated. For the closest reanalysis grid node to the observatory, vertical profiles of the structural constant of the air refractive index turbulent fluctuations Cn2 were obtained. The calculated Cn2(z) vertical profiles are compared with the vertical distribution of turbulence intensity obtained from tomographic measurements with a Shack–Hartmann sensor. The atmospheric coherence length at the location of Terskol Peak was estimated. Using a combination of atmospheric models and paramaterization schemes of turbulence, Cn2(z) profiles at Mt. Kurapdag were obtained. The values of atmospheric coherence length at Peak Terskol are compared with estimated values of this length at the ten astronomical sites, including Ali, Lenghu and Daocheng.

Lidar signal processing method for atmospheric coherence length measurement based on the WD-ADMF

A denoising method applied to atmospheric coherent length lidar is proposed. Wavelet decomposition (WD) and the adaptive median filter (ADMF) are combined in this method. In this research, the effectiveness of the WD-ADMF has been verified through simulation and measurement. The results show that this filter algorithm, when applied to lidar data, improves the average peak signal-to-noise ratio (PSNR) and centroid error while maintaining data integrity such that the measurement of coherence length or the inference of C n 2 from coherence length more closely matches simulated truth and measured data.

A portable S-DIMM developed for preliminary measurement of seeing for Solar Site Survey: Theory and one case study

Imaging quality is highly important for astronomical observations. The imaging quality of a telescope depends not only on the capabilities of the telescope itself but also on its location. When distant stars pass the atmosphere, due to the presence of atmospheric turbulence, the imaging quality becomes degraded. The atmospheric coherence length is the most commonly used parameter to evaluate the influence of the local atmospheric turbulence on telescopes. It is used to describe the degree of atmospheric attenuation of image quality. For the preliminary estimation of atmospheric daytime seeing from a lot of candidate sites, we have developed a portable S-DIMM (PS-DIMM),which is mainly composed of a light-duty tracking mount, a 9 cm aperture lens barrel and a Canon 60D SLR camera. With the PS-DIMM the daytime seeing of a site can be well estimated by measuring the relative displacement variance of the edge positions at both ends of the Sun’s diameter. The principle of PS-DIMM is introduced in this paper. The simultaneous seeing measurements by it and the traditional S-DIMM were carried out at the Fuxian Lake Solar Station, showing a very well correlated between them but with an offset of 2.6 cm. In contrast to the traditional S-DIMM, PS-DIMM offers the advantages of reduced weight and enhanced portability. The utilization of PS-DIMM has played an important role in the early stages of the site survey for the next-generation solar telescopes.

Evaluation of atmospheric coherent length of free-space optical links by using phase fluctuation.

Atmospheric coherence length is one of the most crucial parameters for free-space optical (FSO) links, which can reflect the level of phase and amplitude fluctuations caused by the atmospheric turbulence. In this paper, we study the evaluation of the atmospheric coherence length of the FSO links. The analytical expression of atmospheric coherence length is rendered based on the phase fluctuation resulting from atmospheric turbulence by using the most realistic Bump model. The proposed method is validated theoretically with the Monte Carlo phase screen. Also, the experimental setup with respect to FSO links is established with the spatial light modulator to validate the method experimentally, wherein the fluctuated phase is collected by Shack-Hartmann sensor. The results show that the evaluation of atmospheric coherence length by the analytical expression is consistent with the theoretical prediction as well as the experimental measurement. Thus, the proposed method enables the accurate evaluation of atmospheric coherence length under various turbulence conditions, which can assist the performance analysis as well as design of free-space optical communication systems.

Research on piston error sensing for segmented mirrors under atmospheric turbulence.

Large aperture ground-based segmented telescopes typically use electrical edge sensors to detect co-phase errors. However, complex observing environments can lead to zero-point drift of the edge sensors, making it challenging to maintain the long-term co-phase of the segmented primary mirror using only edge sensors. Therefore, employing optical piston error detection methods for short-term calibration of edge sensors can address the issue of zero-point drift in the sensors. However, atmospheric turbulence can affect calibration accuracy based on the observational target. To achieve high-precision calibration of electrical edge sensors, this study investigates the impact of atmospheric turbulence on optical piston error detection. Based on simulated results, it is found that the actual measured piston error in the presence of atmospheric turbulence is the difference between the average phases of the two segments. Subsequently, optical piston error detection experiments were conducted in a segmented mirror system under simulated turbulent conditions with varying turbulence intensities. Experimental studies have shown that the detection accuracy of the optical method is almost the same as without turbulence when using a detection aperture size that is 0.82 times the atmospheric coherence length and an exposure time of at least 40 ms. The root mean square of the cross-calibration is better than 3nm. These experimental results indicate that under conditions of good atmospheric seeing, the optical piston error detection method can meet the short-term calibration requirements of edge sensors by setting reasonable detection area size and exposure time. It may even be possible to directly use optical detection methods to replace edge sensors for real-time detection of piston errors.

A global turbulence model shows excellent atmospheric optical turbulence conditions over the Ethiopian plateau during non-rainy season

ABSTRACT A worldwide search is currently being conducted to determine the most appropriate sites for the next generation of large optical and infrared telescopes. Here, we report a global map of atmospheric optical turbulence-associated parameter (atmospheric coherence length) based on the fifth generation of European Centre for Medium Range Weather Forecasts re-analysis data set and results for atmospheric coherence lengths at European Southern Observatory and Tibetan Plateau locations (all at mid-latitudes). These confirm the accuracy of the global atmospheric optical turbulence model, but also the simulation result reveals that an excellent atmospheric calm site exist at the Ethiopian Plateau (at a latitude of ∼10°N) outside of the rainy season. The Ethiopian Plateau is the highest plateau in Africa, known as the ‘Roof of Africa’, with an average elevation of over 2500 m, and thus potentially provides good opportunities for astronomy and astrophysics. The median atmospheric coherence length at the Ethiopian Plateau was 17.7 cm and approximately 75 per cent of the time above 15.6 cm for dry conditions, indicating a very calm atmosphere. Although favourable atmospheric turbulence conditions at the Ethiopian Plateau were found from the global turbulence model, due to the complete lack of infrastructure it has never been visited, meaning that additional validation experiments are required.

A Computational Model of Cn2 Profile Inversion for Atmospheric Laser Communication in the Vertical Path.

In this paper, an atmospheric structure constant Cn2 model is proposed for evaluating the channel turbulence degree of atmospheric laser communication. First, we derive a mathematical model for the correlation between the atmospheric coherence length r0, the isoplanatic angle θ0 and Cn2 using the Hufnagel-Valley (HV) turbulence model. Then, we calculate the seven parameters of the HV model with the actual measured r0 and θ0 data as input quantities, so as to draw the Cn2 profile and the θ0 profile. The experimental results show that the fitted average Cn2 contours and single-day Cn2 contours have superior fitting performance compared with our historical data, and the daily correlation coefficient between the single-day computed θ0 contours and the measured θ0 contours is up to 87%. This result verifies the feasibility of the proposed method. The results validate the feasibility of the proposed method and provide a new technical tool for the inversion of turbulence Cn2 profiles.

Inversion Calculation of Atmospheric Refractive Index Structure Constant Based on Atmospheric Coherence Length and Isoplanatic Angle Measured in Nanshan, Xinjiang

Inversion Calculation of Atmospheric Refractive Index Structure Constant Based on Atmospheric Coherence Length and Isoplanatic Angle Measured in Nanshan, Xinjiang

Measuring atmospheric turbulence along folded paths using a laser-illuminated differential image motion monitor.

A laser-illuminated differential image motion monitor (DIMM) is presented that is able to measure the atmospheric coherence length r 0 along horizontal ground paths. This is accomplished by implementing a mono-static setup in which the transmitter and receiver are co-located and transmit to a retroreflective target. The impact of propagating along a folded path through the same volume of turbulent atmosphere is investigated in detail and the overall impact to angle-of-arrival measurements described. In addition, an outdoor test campaign was conducted to validate the findings by testing two commercial scintillometers and the laser DIMM side by side in both bi-static and mono-static configurations. Both analytical and experimental results show that under certain conditions, folded-path propagation can be treated identically to traditional single-path propagation.

Methods of Atmospheric Coherence Length Measurement

Free-space optical (FSO) communication possesses the advantages of high security, large information capacity, high-speed transmission, small terminal size, low power consumption, easy and flexible deployment, etc. It is a promising communication technique, and could be an alternative to optical fiber communication and traditional radio frequency (RF) communication. One of principal challenges that FSO faces is the susceptibility of the atmospheric channel, which is turbulent in nature. After the optical signals propagate over the atmospheric channel, their wavefronts suffer from deleterious perturbation, thus resulting in degradation in the performance of the FSO. This knowledge with respect to FSO links helps to optimize the system design and reduce the adverse effects of atmospheric turbulence. The atmospheric coherence length of FSO links reflects the atmospheric turbulence effects, and it is one of the key parameters of FSO systems. Measuring the atmospheric coherence length, as a result, is of great interest as well as importance to the FSO community. In this paper, several methods associated with atmospheric coherence length measurement are reviewed.

Simulation of spatial coherence of laser echo light field from random rough surface in turbulent atmosphere

According to the generalized Huygens-Fresnel principle, we derive the analytical formula for the complex degree of coherence of the echo light field under the von Karman atmospheric turbulence spectrum condition. Based on split-step beam propagation method of the turbulent phase screen and the target surface model, the fold pass propagation simulation of the laser in the turbulent atmosphere is realized. The dynamic speckle characteristics on the image plane are consistent with the experimental phenomenon. Firstly, the simulation results of the complex degree of coherence and phase structure function of the mirrored reflection echo light field are compared with the theoretical values, which verifies the correctness of the algorithm. Based on this, the complex degree of coherence of the echo light field reflected by the optical rough surface is calculated and analyzed. The results show that on a double-path turbulent flow path of 1.1 km, in other words, it transmits 2.2 km in unfolded mode, the spatial coherence of the echo light field is very sensitive to the root mean square value of height. When the root-mean-square value of height is close to the wavelength, the coherence is seriously degraded. When the correlation length of the target surface is much larger than the atmospheric coherence length, the coherence length of the echo light field is relatively close to the set spatial coherence length. When the correlation length of the target surface is close to the atmospheric coherence length, the influence of the rough surface of the target on the beam coherence cannot be ignored. When the correlation length of the target surface is much smaller than the atmospheric coherence length, the target surface characteristics have a dominant influence on the echo coherence, the spatial coherence of the light field is seriously degraded, and the echo is close to incoherent light. Considering the smooth target reflection surface, the greater the strength of turbulence, the faster the complex coherence decreases with space. The atmospheric coherence diameter <inline-formula><tex-math id="M1">\begin{document}${r_0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20212420_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20212420_M1.png"/></alternatives></inline-formula> can be calculated further according to the complex degree of coherence. For the Pearson correlation coefficient the simulation value and theoretical value are both 0.998, which indicates that the atmospheric coherence diameter calculated by the complex degree of coherence has a high correlation with the theoretical value. This research provides a theoretical basis for the coherent detection scheme of echoes from rough surfaces in the turbulent atmosphere. The simulation algorithm extracts the target surface features by analyzing the variation of the complex coherence of laser echo signals in the turbulent atmosphere with the spatial distance, and also provides a method of using the known target surface to obtain path turbulence information.

Influence of atmospheric turbulence on temporal coherence characteristics of received optical field

In the process of laser propagation in atmosphere, its coherence characteristics are reduced by turbulence, which further affects the efficiency and performance of coherent detection process. In this paper, atmospheric coherence time is defined to describe the fluctuation speed of laser field after atmospheric transmission. The relative size of atmospheric coherence time and coherence process duration time determines the performance of coherent detection process. According to the infinitely long phase screen technology, we simulate laser atmospheric transmission, and systematically study the influences of atmospheric parameters, transceiver parameters and wavelength on atmospheric coherence time. It is found that the atmospheric coherence time is positively correlated with wavelength, receiving aperture and atmospheric coherence length, and inversely proportional to wind speed, which shows that the atmospheric coherence time can be effectively improved by improving the optical design and changing the laser band, thus effectively reducing the disturbance caused by turbulence and improving the stability of the received light field. The atmospheric coherence time defined in this paper is an important parameter to measure the influence of turbulence on coherent detection. This study can provide a powerful reference for evaluating the influence of atmosphere on coherent detection process.

Research on the propagation of laser beams arraywith coherent and incoherent combination in dynamic atmosphere turbulence

High-power laser systems mostly use coherent or incoherent combined beams to achieve higher laser output power to satisfy the application. However, the far-field beam quality of laser will be reduced when propagating over atmosphere. Based on the propagation model of laser beams array, we use atmospheric coherence length, laser duration and average wind velocity to construct dynamic atmospheric turbulence which is characterized as a phase screen sequence. Meanwhile, considered as the indexes to evaluate beam quality, peak intensity and intensity in bucket are comparatively analysed in coherent and incoherent combined beams in far-field. The results indicate that in weaker turbulence circumstances, coherent combined beam has an advantage compared with the incoherent combined beams when laser duration is short, and coherent combination is more suitable for pulsed laser. With laser duration is increasing, the beam quality of incoherent and coherent combined beams both decrease and tend to be close. In stronger turbulence circumstances, the corresponding laser duration will be shorter when the beam quality of coherent combined beams is extraordinary close to that of incoherent combined beams. The researches can provide important data for high-power laser system to select the optimal beam combination mode to improve its performance.

Turbulence Models and Daily Variations Obtained by Bidirectional Atmospheric Coherent Length Measurements

Turbulence Models and Daily Variations Obtained by Bidirectional Atmospheric Coherent Length Measurements

Deep learning wavefront sensing method for Shack-Hartmann sensors with sparse sub-apertures.

In this letter, we proposed a deep learning wavefront sensing approach for the Shack-Hartmann sensors (SHWFS) to predict the wavefront from sub-aperture images without centroid calculation directly. This method can accurately reconstruct high spatial frequency wavefronts with fewer sub-apertures, breaking the limitation of d/r0 ≈ 1 (d is the diameter of sub-apertures and r0 is the atmospheric coherent length) when using SHWFS to detect atmospheric turbulence. Also, we used transfer learning to accelerate the training process, reducing training time by 98.4% compared to deep learning-based methods. Numerical simulations were employed to validate our approach, and the mean residual wavefront root-mean-square (RMS) is 0.08λ. The proposed method provides a new direction to detect atmospheric turbulence using SHWFS.

Mini-DIMM: theory analysis and experimental validation

The differential image motion monitor (DIMM) is a widely used instrument for measuring atmospheric coherence length. We studied the feasibility to miniaturize the classic DIMM. By adopting more accurate formulas, the geometry of the classic DIMM can be altered mildly. A mini-DIMM can be developed under this new geometry condition. For example, a mini-DIMM may consist of two 6-cm apertures, located close to each other. We present the validation experiment where astronomical seeing was measured simultaneously by a mini-DIMM and a standard DIMM. Comparisons with a standard DIMM show good agreement between the two instruments.

Measurement and analysis of atmospheric optical turbulence in Lhasa based on thermosonde

In this paper, we have analyzed the wind, temperature and optical turbulence index structure constant (Cn2) that are directly measured for the first time at Lhasa, Tibet. Unlike other mid-or-low latitude regions, the wind speed in Lhasa increases with the altitude according to the wind profiles, besides a strong wind speed near the tropopause. The temperature profiles indicate a large temperature change near the tropopause. The optical turbulence profiles show daily variation. When the altitude is below 12 km, except for individual points, the Cn2 values during morning and evening are basically in the same range of 10−17-10−15 m-2/3. When altitude is above 12 km, the intensity of turbulence during the morning in Lhasa is 1–2 orders of magnitude larger than that of the evening. In addition, we propose a turbulence profile model on the basis of Hufnagel-valley model to calculate the integrated values of the refractive index structure constants of the entire atmosphere, such as the Fried parameter, the seeing, the coherence time and the isoplanatic angle. The mean atmospheric coherence length r0 is 5.77 cm. Differences in these parameters between morning and evening also illustrate the stronger turbulence in the morning than evening.