Optical Turbulence Model Research Articles

A Multifaceted Exploration of Atmospheric Turbulence and Its Impact on Optical Systems: Structure Constant Profiles and Astronomical Seeing

This study emphasizes the importance of conducting a comprehensive analysis considering the Cn2 atmospheric parameter for a reliable assessment of the seeing value. It highlights the use of the ECMWF ERA5 model to simulate pressure, temperature, and humidity profiles, enabling the evaluation of optical degradation. Accurate modeling and monitoring of temperature and humidity variables are emphasized for precise data in optical communication and astronomical observations. It also discusses the significance of optical turbulence models in understanding the impact of atmospheric turbulence on optical system performance. The validation of the selected Cn2 models is thoroughly analyzed. To evaluate the impact of the boundary layer on seeing conditions, three factors are considered. First, ERA5 data is used to simulate surface Cn2 values using the PAMELA model. Second, typical Cn2 values for specific dates in Redu are obtained. Finally, the thickness of the boundary layer, denoted as hbl, is calculated. This finding highlights the significant influence of the boundary layer on atmospheric seeing conditions and by incorporating Ibl into the models, a more accurate representation of the effects of the boundary layer on seeing quality is achieved.

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.

Hybrid optical turbulence models using machine-learning and local measurements.

Accurate prediction of atmospheric optical turbulence in localized environments is essential for estimating the performance of free-space optical systems. Macro-meteorological models developed to predict turbulent effects in one environment may fail when applied in new environments. However, existing macro-meteorological models are expected to offer some predictive power. Building a new model from locally measured macro-meteorology and scintillometer readings can require significant time and resources, as well as a large number of observations. These challenges motivate the development of a machine-learning informed hybrid model framework. By combining a baseline macro-meteorological model with local observations, hybrid models were trained to improve upon the predictive power of each baseline model. Comparisons between the performance of the hybrid models, selected baseline macro-meteorological models, and machine-learning models trained only on local observations, highlight potential use cases for the hybrid model framework when local data are expensive to collect. Both the hybrid and data-only models were trained using the gradient boosted decision tree architecture with a variable number of in situ meteorological observations. The hybrid and data-only models were found to outperform three baseline macro-meteorological models, even for low numbers of observations, in some cases as little as one day. For the first baseline macro-meteorological model investigated, the hybrid model achieves an estimated 29% reduction in the mean absolute error using only one day-equivalent of observation, growing to 41% after only two days, and 68% after 180days-equivalent training data. The data-only model generally showed similar, but slightly lower performance, as compared to the hybrid model. Notably, the hybrid model's performance advantage over the data-only model dropped below 2% near the 24 days-equivalent observation mark and trended towards 0% thereafter. The number of days-equivalent training data required by both the hybrid model and the data-only model is potentially indicative of the seasonal variation in the local microclimate and its propagation environment.

Analysis of atmospheric optical turbulence model— methods and progress

Stratification is a significant characteristic of atmospheric turbulence, especially high-altitude turbulence. At a fixed height, the real optical turbulence value fluctuates by 1–2 orders of magnitude or even greater on the average value. The turbulence profile model based on the observed data is a statistical average result. It can neither represent the stratification characteristics of an actual atmospheric turbulence profile nor have the prediction function, and can not fully meet the demand of optical engineering. Owing to the limitation of the capacity and speed of the computer, it is impossible to solve the Navier Stokes equation through direct numerical simulation (DNS) and large eddy simulation (LES) to predict the optical turbulence. The solution is to predict the conventional gas parameters through the mesoscale weather numerical prediction model MM5/ WRF, and then calculate the turbulence parameters through the turbulence parameterization scheme. In this paper, the prediction methods and research results of <inline-formula><tex-math id="M6">\begin{document}$ C_n^2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221986_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221986_M6.png"/></alternatives></inline-formula> in surface layer,boundary layer and free atmosphere layer are introduced. Tatarski formula is derived in detail from the turbulence kinetic energy prediction equation and the temperature fluctuation variance prediction equation, and the physical meaning and applicable conditions of the formula are summarized. The latest research progress of neural network prediction and Antarctic astronomical site selection is mainly introduced. The characteristics and differences among different models, such as the empirical model fitted with experimental data, the parameter model with conventional meteorological parameters based on Kolmogorov turbulence theory, the prediction model related to mesoscale meteorological model, and the neural network method based on data driving and so on, are analyzed. It is emphasized that Kolmogorov turbulence theory is the theoretical basis of the existing atmospheric optical turbulence parameter models.

Sensing optical phase distortion via beatnote detection of a dual probe beam encoded with orbital angular momentum.

Laser based optical applications such as imaging, ranging, and wireless communications are susceptible to environmental distortions. Inferring the strength of these optical distortions is crucial to obtaining information about the environment in which the system is operating. Our technique of inferring environmental distortion strength leverages the spreading of light's orbital angular momentum (OAM) spectrum combined with heterodyne detection. A laser encoded with OAM can be decomposed into a basis set of helical modes that spreads upon interaction with optical distortions. This mode spreading is quantified using the OAM spectrum that can be measured using mode projection or mode sorting techniques. This new technique, to the best of our knowledge, provides benefits compared to the latter two OAM detection methods such as: low-frequency noise rejection, a simpler optical receiver, lower noise floor, and an inherent optical phase component. Central to the method is the heterodyne detection of the zeroth-order OAM coefficient of a superimposed two-beam, two-frequency, probe. The measured heterodyne signal power is seen to be proportional to the coupling power of each beam's OAM spectra. To test the idea, wave-optic simulations and experiments using spatial light modulators are implemented using a simplified optical turbulence model to represent the environment. The experimental implementation agrees well with simulated and theoretical results.

Measurements and Modeling of Optical Turbulence in the Coastal Environment

The goal of this study was to characterize optical turbulence in the near-coastal environment. Measurements to obtain the refractive index structure parameter and other meteorological data were taken over the course of a month along the shore of Monterey Bay. The results were compared to a new version of the Navy Vertical Surface Layer Model (NAVSLaM), a model of turbulence originally developed for maritime environments but now extended to terrestrial environments. The new version has not been previously validated by comparisons to experiments, particularly in a complex environment such as near the coastline. Our experimental results showed generally good agreement between measured and modeled levels of turbulence. Specifically, the differences between experimental and modeled values of the refractive index structure parameter were less than an order of magnitude in most conditions and followed the same diurnal trend. There were some greater differences during near-neutral conditions, but this is a known limitation of the model. Overall, this extended model appears to do a good job of predicting turbulence in this environment for the observed time period.

Optimal Prediction of Atmospheric Turbulence by Means of the Weather Research and Forecasting Model

The performance of ground-based astronomical observations and free-space optical communication (FSOC) systems suffers from atmospheric turbulence and meteorological conditions. The a priori knowledge of atmospheric conditions several hours before observations allows the programming of astronomical observations (flexible scheduling) to be optimized. In this paper, we present a prediction study based on the Weather Research and Forecasting (WRF) model. It allows the prediction and characterization of a useful set of meteorological parameters relevant to atmospheric physics (e.g., pressure, temperature, relative humidity, wind speed, and direction). Predicted parameters are then injected into an optical turbulence (OT) model to compute the refractive index structure constant C n 2. We performed sets of simulations for Cerro Pachon Observatory in Chile, using the data from the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR). The main goal is to quantify how accurately numerical weather prediction models can reproduce conditions over the complex terrain of the Cerro Pachon area. In order to produce a reliable forecast, meteorological prognostic skills need accurate representations of the physical parameterization options. Three widely used Planetary Boundary Layer (PBL) schemes and two Land Surface Models (LSM) were tested, analyzed, and compared in order to find the optimal WRF configuration. Predictions are compared to in situ measurements coming from balloon-borne radiosoundings. It is determined that the predicted C n 2 are in good agreement with the radiosoundings measurements with a mean relative error (MRE) under 6.4% at all altitudes when using balloon measurements to deduce some parameters such as the outer scale of turbulence L 0, which is used in the OT model. For a fully operational prediction, the MREs between the predictions and the measurements range from 1.4% to 8% according to the different ways to estimate the L 0 profiles. Seasonal statistics are also presented for different meteorological and turbulence parameters.

高能激光大气传输性能评估技术

The actual effect of laser propagation in the atmosphere is not only related to its own propagation mechanism, but also closely related to atmospheric factors. Therefore, to accurately evaluate the effect of laser atmospheric propagation, it is not only necessary to carry out the mechanism research and establish the mathematical model of laser atmosoheric propagation, but also mecessary to carry out measurement, analysis and prediction of the optical characteristics of the atmosphere in the propagating process. Considering the complexity of the real atmospheric environment and the interaction of many factors, most of the researches adopt the physical experiment or the numerical simulation with controlled parameters to quantitatively reveal the influence of various atmospheric factors on laser propagation. Based on a large number of field measurements and the physical correlation analysis, the research of atmospheric optical characteristics focuses on the parametric modeling of optical turbulence. The development of the performance evaluation technology for the high energy laser was briefly introduced when propagating in the atmosphere at home and aboard, and its development trend for the practical application of high energy laser system in the future was pointed out.

Effects of intermittency and stratification on the evaluation of optical propagation

To evaluate the effects of intermittency and stratification on propagation of laser beams, we analyze experimental radiosonde profiles using complete ensemble empirical mode decomposition. First, we extract intermittency and stratification at different scales from the original Cn2 profiles. Second, we establish an intrinsic optical turbulence model (IOTM), which includes fine structures. Third, we calculate several turbulence moments using IOTM. The results quantitatively evaluate the effects of variations at different scales on typical parameters relevant to optical turbulence effects.

Analysis of an optical turbulence profile using complete ensemble empirical mode decomposition.

We obtain an intrinsic optical turbulence model using a data-driven method named complete ensemble empirical mode decomposition. First, the measured profile of a refractive index structure parameter is decomposed into a set of intrinsic mode functions and a residue. The components are tested against white noise to determine the statistical significance. Meanwhile, the physical meanings of the IMFs are revealed using meteorological data that agrees with previous research. Second, the effect of noisy oscillations, quasi-cyclical variations, and the trend on the overall profile are evaluated by the variance contribution rate. Third, the intrinsic optical turbulence model is defined. The combination of different IMFs with the residue forms intrinsic optical turbulence profiles, by which the stratification structures on different scales are embedded into the model. Comparison with other models highlights the virtue of the intrinsic optical turbulence model.

Investigation of Hill's optical turbulence model by means of direct numerical simulation.

For almost four decades, Hill's "Model 4" [J. Fluid Mech. 88, 541 (1978) has played a central role in research and technology of optical turbulence. Based on Batchelor's generalized Obukhov-Corrsin theory of scalar turbulence, Hill's model predicts the dimensionless function h(κl(0), Pr) that appears in Tatarskii's well-known equation for the 3D refractive-index spectrum in the case of homogeneous and isotropic turbulence, Φn(κ)=0.033C2(n)κ(-11/3) h(κl(0), Pr). Here we investigate Hill's model by comparing numerical solutions of Hill's differential equation with scalar spectra estimated from direct numerical simulation (DNS) output data. Our DNS solves the Navier-Stokes equation for the 3D velocity field and the transport equation for the scalar field on a numerical grid containing 4096(3) grid points. Two independent DNS runs are analyzed: one with the Prandtl number Pr=0.7 and a second run with Pr=1.0 . We find very good agreement between h(κl(0), Pr) estimated from the DNS output data and h(κl(0), Pr) predicted by the Hill model. We find that the height of the Hill bump is 1.79 Pr(1/3), implying that there is no bump if Pr<0.17 . Both the DNS and the Hill model predict that the viscous-diffusive "tail" of h(κl(0), Pr) is exponential, not Gaussian.

近海面大气光学湍流计算模型的比较与改进

近海面大气光学湍流计算模型的比较与改进

Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non Kolmogorov strong turbulence

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received signal, affecting link performance. Most theoretical treatments have been described by Kolmogorov's power spectral density model through weak turbulence with constant wind speed. However, several experiments showed that Kolmogorov theory is sometimes incomplete to describe atmospheric turbulence properly, especially through the strong turbulence with variable wind speed, which is known to contribute significantly to the turbulence in the atmosphere. We present an optical turbulence model that incorporates into variable wind speed instead of constant value, a non-Kolmogorov power spectrum that uses a generalized exponent instead of constant standard exponent value 11/3, and a generalized amplitude factor instead of constant value 0.033. The free space optical communication performance for a Gaussian beam wave of scintillation index, mean signal-to-noise ratio<SNR>, and mean bit error rate <BER>, have been derived by extended Rytov theory in non-Kolmogorov strong turbulence. And then the influence of wind speed variations on free space optical communication performance has been analyzed under different atmospheric turbulence intensities. The results suggest that the effects of wind speed variation through non-Kolmogorov turbulence on communication performance are more severe in many situations and need to be taken into account in free space optical communication. It is anticipated that this work is helpful to the investigations of free space optical communication performance considering wind speed under severe weather condition in the strong atmospheric turbulence.

Optical Turbulence Measurements and Models for Mount John University Observatory

AbstractSite measurements were collected at Mount John University Observatory in 2005 and 2007 using a purpose-built scintillation detection and ranging system. C2N(h) profiling indicates a weak layer located at 12–14 km above sea level and strong low altitude turbulence extending up to 5 km. During calm weather conditions, an additional layer was detected at 6–8 km above sea level. V(h) profiling suggests that tropopause layer velocities are nominally 12–30m s−1, and near-ground velocities range between 2 and 20m s−1, dependent on weather. Little seasonal variation was detected in either C2N(h) and V(h) profiles. The average coherence length, r0, was found to be 7±1 cm for the full profile at a wavelength of 589 nm. The average isoplanatic angle, θ0, was 1.0±0.1 arcsec. The mean turbulence altitude, , was found to be 2.0±0.7 km above sea level. No average in the Greenwood frequency, fG, could be established due to the gaps present in the V(h) profiles obtained. A modified Hufnagel-Valley model was developed to describe the C2N(h) profiles at Mount John, which estimates r0 at 6 cm and θ0 at 0.9 arcsec. A series of V(h) models were developed, based on the Greenwood wind model with an additional peak located at low altitudes. Using the C2N(h) model and the suggested V(h) model for moderate ground wind speeds, fG is estimated at 79 Hz.

The inertial range “outer scale” and optical turbulence

The crucial parameter used to calculate turbulence effects upon light waves propagating through the atmosphere is known as the structure constant, \(c_n^2\) . As Tatarski has shown, this parameter depends upon the “outer scale” of the inertial sub-range of the turbulence. Recently there have been successful predictions of astronomical “seeing” conditions at Mauna Kea Astronomical Observatory which have increased interest in this subject and in the use of the so-called “Dewan Optical Turbulence Model”. In the case of the Air Force, there has been a longstanding need for such optical turbulence prediction, especially in the stratosphere. In the past researchers have used a relation due to Tatarski, (which plays a prominent role in this model) in order to deduce values of the “outer scale” from \(c_n^2\) measurements. When doing this, they have been surprised to find values very much smaller than expected. The goal of the paper is to explain this unexpected result. As we will show, this result can be explained by two factors: (a) the average turbulent layer thicknesses are smaller than originally believed, and, more importantly, (b) only a minor fraction of the stratosphere is turbulent. In order to arrive at this conclusion, we used the high-resolution (10 m) wind profiles that were originally used to formulate the previously mentioned optical turbulence model.

Toward increasing the accuracy and realism of future optical turbulence calculations

Due to the increased use of laser and ground-to-satellite communications the need for reliable optical turbulence information is growing. Optical turbulence information is important because it describes an atmospheric effect that can degrade the performance of electromagnetic systems and sensors, e.g., free-space optical communications and infrared imaging. However, analysis of selected past research indicates that there are some areas (i.e., data and models) in which optical turbulence information is lacking. For example, line-of-sight optical turbulence data coupled with atmospheric models in hilly terrain, coastal areas, and within cities are few in number or non-existent. In addition, the bulk of existing atmospheric computer models being used to provide estimates of optical turbulence are basically one-dimensional in nature and assume uniform turbulence conditions over large areas. As a result, current optical turbulence theory and models may be deficient and in error for inhomogeneous (nonuniform) turbulence conditions, such as those that occur in urban environments or environments with changing topography and energy budgets. While it is anticipated that theoretical advances in environmental physics (and like disciplines) will be a catalyst for much new work this area, in the interim, we suggest that some very practical computational research can be performed to extend existing low-atmospheric turbulence and micrometeorological calculations beyond current limitations.

Modeling and measurements of atmospheric optical turbulence over land

The effects of atmospheric turbulence on optical system performance depend primarily on the refractive index structure parameter C2n and the inner scale ?0. A simple model for C2n and ?0 is described and experimentally tested. The model, based on the Monin-Obuhkov similarity theory, was developed by Thiermann and is valid in the atmospheric surface layer over land. The inputs to the model are standard meteorological parameters plus solar irradiance and parameters that characterize the local terrain. Model results are compared with measurements of C2n and ?0 made with a laser scintillometer at a height of 1.8 m. The performance of the model was found to be good during unstable daytime conditions.