Cn2 Profile Research Articles

Developing MATLAB graphical user interface for acquiring single star SCIDAR data

To enhance operational efficiency and meet experimental demands, we have developed a graphical user interface (GUI) using MATLAB for Acquiring Single Star SCIDAR Data, leveraging the software’s integrated GUI Development Environment (GUIDE) tool. This interface streamlines the preprocessing and numerical computation of the power spectrum of atmospheric speckles while providing real-time graphical representations of atmospheric parameters, including the vertical profile of the refractive index structure function Cn2(h). It also incorporates parameters related to adaptive optics and high angular resolution, such as seeing, enabling immediate and instantaneous visual assessment of observational conditions. Furthermore, the novelty of this GUI lies in the ease of acquiring and processing data from various atmospheric parameters. The Single Star SCIDAR (Scintillation Detection and Ranging) method relies on analyzing the scintillation of light from single stars to assess the turbulent characteristics of the atmosphere. This assessment is based on the description provided by Cn2(h) derived from minimizing an objective function determined using the power spectrum of atmospheric speckles from single stars. For this purpose, a minimization algorithm called active-set is used.

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.

Single star SCIDAR: Atmospheric parameters profiling using the power spectrum of scintillation

Optical parameters of atmospheric turbulence have a significant impact on high angular resolution, adaptive optics, and site testing. The single star SCIDAR technique provides vertical profiles of these parameters, including the refractive index structure constant Cn2(h). Its is based on the analysis of single stars scintillation. This study introduces a new approach for real-time measurement of atmospheric parameters using the Single Star SCIDAR. The key element of this approach is the utilization of a modified power spectrum of atmospheric speckles, that have more significant variation with altitude. By using that modified power spectrum, an objective function is computed, and the minimization process is performed using the Active-Set algorithm. With this approach, we successfully obtained real-time vertical profiles of Cn2(h) with good accuracy. The processing takes approximately 3 s per profile, and the recovery rate (i.e. sum of Cn2(h)) is about 95%. The reliability of this approach is validated through simulation results and a comparison with data obtained from sounding balloons. These validations confirm the accuracy and credibility of this method, which can be useful in many practical applications.

Anisoplanatic optical turbulence simulation for near-continuous Cn2 profiles without wave propagation

Anisoplanatic optical turbulence simulation for near-continuous Cn2 profiles without wave propagation

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.

A Multi-Model Ensemble Pattern Method to Estimate the Refractive Index Structure Parameter Profile and Integrated Astronomical Parameters in the Atmosphere

In this study, we devised a constraint method, called multi-model ensemble pattern (MEP), to estimate the refractive index structure parameter (Cn2) profiles based on observational data and multiple existing models. We verified this approach against radiosonde data from field campaigns in China’s eastern and northern coastal areas. Multi-dimensional statistical evaluations for the Cn2 profiles and integrated astronomical parameters have proved MEP’s relatively reliable performance in estimating optical turbulence in the atmosphere. The correlation coefficients of MEP and measurement overall Cn2 in two areas are up to 0.65 and 0.76. A much higher correlation can be found for a single radiosonde profile. Meanwhile, the difference evaluation of integrated astronomical parameters also shows its relatively robust performance compared to a single model. The prowess of this reliable approach allows us to carry out regional investigation on optical turbulence features with routine meteorological data soon.

Novel Detection of Atmospheric Turbulence Profile Using Mie-Scattering Lidar Based on Non-Kolmogorov Turbulence Theory.

Turbulence can cause effects such as light intensity fluctuations and phase fluctuations when a laser is transmitted in the atmosphere, which has serious impacts on a number of optical engineering application effects and on climate improvement. Therefore, accurately obtaining real-time turbulence intensity information using lidar-active remote sensing technology is of great significance. In this paper, based on residual turbulent scintillation theory, a Mie-scattering lidar method was developed to detect atmospheric turbulence intensity. By extracting light intensity fluctuation information from a Mie-scattering lidar return signal, the atmospheric refractive index structure constant, Cn2, representing the atmospheric turbulence intensity, could be obtained. Specifically, the scintillation effect on the detection path was analyzed, and the probability density distribution of the light intensity of the Mie-scattering lidar return signal was studied. It was verified that the probability density of logarithmic light intensity basically follows a normal distribution under weak fluctuation conditions. The Cn2 profile based on Kolmogorov turbulence theory was retrieved using a layered, iterative method through the scintillation index. The method for detecting Kolmogorov turbulence intensity was applied to the detection of the non-Kolmogorov turbulence intensity. Through detection using the scintillation index, the corresponding C˜n2 profile could be calculated. The detection of the C˜n2 and Cn2 profiles were compared with the Hufnagel-Valley (HV) night model in the Yinchuan area. The results show that the detection results are consistent with the overall change trend of the model. In general, it is feasible to detect a non-Kolmogorov turbulence profile using Mie-scattering lidar.

Improving Hufnagel-Andrews-Phillips model for prediction [formula omitted] using empirical wind speed profiles

Using reanalysis database of wind speed at higher altitudes acquired from the national centers for environment prediction and national centers for atmospheric research for one year 2019, the vertical profiles of optical turbulence represented by refractive index structure parameter (Cn2) were derived for two times (night and day) at twelve free-cloud days. Their dates are 4, 15 and 26 January, 7, 15 and 26 April, 2, 15 and 30 July and 2, 13 and 27 October which represent the seasons: winter, spring, summer and autumn, respectively. The Cn2 profiles extending from lower altitudes up to 25 km were calculated by the modification of single height Hufnagel-Andrews-Phillips model through establishment empirical functions for vertical variation of wind speed as functions of only height. The results show that wind profiles have highest values at night and are mostly obeyed the higher polynomial functions. In winter and spring the Cn2 profiles have significant peak values at 11 km elevation, while in another seasons the near ground Cn2 were largest and then steep decreasing at higher heights.

Optical Turbulence Characteristics in the Upper Troposphere–Lower Stratosphere over the Lhasa within the Asian Summer Monsoon Anticyclone

The high elevation, complex topography, and unique atmospheric circulations of the Tibetan Plateau (TP) make its optical turbulence characteristics different from those in low-elevation regions. In this study, the characteristics of the atmospheric refractive index structure constant (Cn2) profiles in the Lhasa area at different strength states of the Asian summer monsoon anticyclone (ASMA) are analyzed based on precious in situ sounding data measured over the Lhasa in August 2018. Cn2 in the upper troposphere–lower stratosphere fluctuates significantly within a few days during the ASMA, particularly in the upper troposphere. The effect of the ASMA on Cn2 varies among the upper troposphere, tropopause, and lower stratosphere. The stronger and closer the ASMA is to Lhasa, the more pronounced is the “upper highs and lower lows” pressure field structure, which is beneficial for decreasing the potential temperature lapse rate. The decrease in static stability is an important condition for developing optical turbulence, elevating the tropopause height, and reducing the tropopause temperature. However, if strong high-pressure activity occurs at the lower pressure layer, such as at 500 hPa, an “upper highs and lower highs” pressure field structure forms over the Lhasa, increasing the potential temperature lapse rate and suppressing the convective intensity. Being almost unaffected by low-level atmospheric high-pressure activities, the ASMA, as the main influencing factor, mainly inhibits Cn2 in the tropopause and lower stratosphere. The variations of turbulence intensity in UTLS caused by ASMA activities also have a great influence on astronomical parameters, which will have certain guiding significance for astronomical site testing and observations.

Turbulence Detection in the Atmospheric Boundary Layer Using Coherent Doppler Wind Lidar and Microwave Radiometer

The refractive index structure constant (Cn2) is a key parameter used in describing the influence of turbulence on laser transmissions in the atmosphere. Three different methods for estimating Cn2 were analyzed in detail. A new method that uses a combination of these methods for continuous Cn2 profiling with both high temporal and spatial resolution is proposed and demonstrated. Under the assumption of the Kolmogorov “2/3 law”, the Cn2 profile can be calculated by using the wind field and turbulent kinetic energy dissipation rate (TKEDR) measured by coherent Doppler wind lidar (CDWL) and other meteorological parameters derived from a microwave radiometer (MWR). In a horizontal experiment, a comparison between the results from our new method and measurements made by a large aperture scintillometer (LAS) is conducted. The correlation coefficient, mean error, and standard deviation between them in a six-day observation are 0.8073, 8.18 × 10−16 m−2/3 and 1.27 × 10−15 m−2/3, respectively. In the vertical direction, the continuous profiling results of Cn2 and other turbulence parameters with high resolution in the atmospheric boundary layer (ABL) are retrieved. In addition, the limitation and uncertainty of this method under different circumstances were analyzed, which shows that the relative error of Cn2 estimation normally does not exceed 30% under the convective boundary layer (CBL).

Improving on Atmospheric Turbulence Profiles Derived from Dual Beacon Hartmann Turbulence Sensor Measurements

Atmospheric turbulence is an inevitable source of wavefront distortion in all fields of long range laser propagation and sensing. However, the distorting effects of turbulence can be corrected using wavefront sensors contained in adaptive optics systems. Such systems also provide deeper insight into surface layer turbulence, which is not well understood. A unique method of profile generation by a dual source Hartmann Turbulence Sensor (HTS) technique is introduced here. Measurements of optical turbulence along a horizontal path were taken to create Cn2 profiles. Two helium-neon laser beams were directed over an inhomogeneous horizontal path and captured by the HTS. The measured differential tilt variances imposed on the laser wavefronts were used in conjunction with a set of computed weighting functions to profile the turbulence over the sensing path. The weighting function matrix is inherently ill-conditioned, therefore, Tikhonov regularization was applied to produce accurate Cn2 profiles. A distribution of sonic anemometers and a co-located boundary layer scintillometer (BLS) collected independent Cn2 measurements to add confidence to the HTS profiles. The Cn2 profiles generated by this approach agree very well with the auxiliary anemometer and scintillometer measurements. This method of producing turbulence profiles may be useful in future multi-conjugate adaptive optics applications.

Near ground horizontal high resolution Cn2 profiling from Shack-Hartmann slopeand scintillation data.

Coupled slope and scintillation detection and ranging (CO-SLIDAR) is a very promising technique for the metrology of near ground Cn2 profiles. It exploits both phase and scintillation measurements obtained with a dedicated wavefront sensor and allows profiling on the full line of sight between pupil and sources. This technique is applied to an associated instrument based on a mid-IR Shack-Hartmann wavefront sensor coupled to a 0.35 m telescope, which observes two cooperative sources. This paper presents what we believe is the first comprehensive description of the CO-SLIDAR method in the context of near-ground optical turbulence metrology. It includes the presentation of the physics principles underlying the measurements of our unsupervised Cn2 profile reconstruction strategy together with the error bar estimation on the reconstructed values. The application to data acquired in a heterogeneous rural landscape during an experimental campaign in Lannemezan, France, demonstrates the ability to obtain profiles with a sampling pitch of about 220 m over a 2.7 km line of sight. The retrieved Cn2 profiles are presented and their variability in space and time is discussed.

On the isoplanatic patch size in High Angular Resolution Techniques

To reach a high performance with an adaptive optics system, we need a calibration using a reference source. This latter should be located in the same isoplanatic domain as the science source. Different techniques and methods have been developed leading to estimations of the isoplanatic patch but all are model-dependent. We developed a new technique for the estimation of the isoplanatic angle based on an extended object. This technique is now part of our new turbulence profile monitor PML (Profiler of Moon Limb) based on the observation of the Moon limb or Sun edge. The first statistics of the isoplanatic angle with this new technique are presented and compared to the exiting techniques based on scintillation measurements or other turbulence parameters such as Fried parameter and/or C2n profile.

Focal-plane Cn2(h) profiling based on single-conjugate adaptive optics compensated images

Knowledge of the atmospheric turbulence in the telescope line-of-sight is crucial for wide-field observations assisted by adaptive optics (AO), for which the Point Spread Function (PSF) becomes strongly elongated due to the anisoplanatism effect. This one must be modelled accurately to extrapolate the PSF anywhere across the Field of view (FOV) and improve the science exploitation. However, anisoplanatism is a function of the Cn2(h) profile, that is not directly accessible from single conjugate AO telemetry. One may rely on external profilers, but recent studies have highlighted more than 10% of discrepancies with AO internal measurements, while we aim better than 1% of accuracy for PSF modelling. To tackle this existing limitation, we present the Focal plane profiling (FPP), as a $C_n^2(h)$ profiling method that relies on post-AO focal plane images. We demonstrate such an approach complies with a 1%-level of accuracy on the $C_n^2(h)$ estimation and establish how this accuracy varies regarding the calibration stars magnitudes and positions in the field. We highlight that photometry and astrometry errors due to PSF mis-modelling reaches respectively 1% and 50{\mu}as using FPP on a Keck baseline, with a preliminary calibration using a star of magnitude H=14 at 20". We also validate this concept using Canadas NRC-Herzberg HENOS testbed images in comparing FPP retrieval with alternative $C_n^2(h)$ measurements on HeNOS. The FPP approach allows to profile the $C_n^2(h)$ using the SCAO systems and improve significantly the PSF characterisation. Such a methodology is also ELT-size compliant and will be extrapolated to tomographic systems in a near future.

A new model for the profiles of optical turbulence outer scale and Cn2 on the coast

Atmospheric optical turbulence severely restricts the performances of electro-optical systems. The turbulent atmosphere causes the intensity of a light beam to fluctuate or scintillate, leads the light beam to wander and makes the images randomly displace, which directly relates to the refractive index structure parameter Cn2. Therefore the knowledge of Cn2 is essential to evaluate and to predict the effects of optical turbulence on electro-optical imagery systems. During the period from December 13, 2016 to January 2, 2017, 30 sets of sounding data, which include temperatures, humidities, pressures, wind speeds, wind directions and atmospheric refractive index structure parameters, are obtained by using a self-developed meteorological radiosonde for turbulence at Marine Meteorological Science Experiment Base at Bohe of Maoming. On the basis of the HMNSP99 outer scale model, an atmospheric optical turbulence outer scale formula of Maoming is obtained by fitting the sounding data. At the same time, the experimental data of the turbulence profiles are statistically averaged, and then based on the Hufnagel-Valley model, a statistical model is obtained, which is appropriate to the variation of the turbulence profile on the coast. According to Tatarski turbulence parameterization and the Maoming outer scale formula, the new estimated Cn2 values are compared with their experimental observations and the results from other already defined models, respectively. Statistical analysis shows that the overall correlation coefficients of log10(Cn2) between observed values and estimated values by using the new fitting Maoming outer scale formula, the HMNSP99 model, the Dewan model and the Coulman model are 0.924, 0.848, 0.763 and 0.651, respectively. Also, both the trends and magnitudes for these four outer scale models are consistent with each other. The errors of the above four outer scale models are very small:their overall average absolute errors and average relative errors are 0.514 and 2.963%, 0.627 and 3.612%, 0.943 and 5.439%, 0.766 and 4.417%, respectively, and the error of the Maoming outer scale model is smallest. The reliabilities and validities of the new outer scale and Cn2 models are further verified. In addition, it is found that the occurrence of upper air optical turbulence is closely related to wind shear and temperature gradient. The results support the prediction of the atmospheric optical turbulence profile required for electro-optical engineering on the coast.

Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis

We present a numerical wave propagation method for simulating imaging of an extended scene under anisoplanatic conditions. While isoplanatic simulation is relatively common, few tools are specifically designed for simulating the imaging of extended scenes under anisoplanatic conditions. We provide a complete description of the proposed simulation tool, including the wave propagation method used. Our approach computes an array of point spread functions (PSFs) for a two-dimensional grid on the object plane. The PSFs are then used in a spatially varying weighted sum operation, with an ideal image, to produce a simulated image with realistic optical turbulence degradation. The degradation includes spatially varying warping and blurring. To produce the PSF array, we generate a series of extended phase screens. Simulated point sources are numerically propagated from an array of positions on the object plane, through the phase screens, and ultimately to the focal plane of the simulated camera. Note that the optical path for each PSF will be different, and thus, pass through a different portion of the extended phase screens. These different paths give rise to a spatially varying PSF to produce anisoplanatic effects. We use a method for defining the individual phase screen statistics that we have not seen used in previous anisoplanatic simulations. We also present a validation analysis. In particular, we compare simulated outputs with the theoretical anisoplanatic tilt correlation and a derived differential tilt variance statistic. This is in addition to comparing the long- and short-exposure PSFs and isoplanatic angle. We believe this analysis represents the most thorough validation of an anisoplanatic simulation to date. The current work is also unique that we simulate and validate both constant and varying Cn2(z) profiles. Furthermore, we simulate sequences with both temporally independent and temporally correlated turbulence effects. Temporal correlation is introduced by generating even larger extended phase screens and translating this block of screens in front of the propagation area. Our validation analysis shows an excellent match between the simulation statistics and the theoretical predictions. Thus, we think this tool can be used effectively to study optical anisoplanatic turbulence and to aid in the development of image restoration methods.

Retrieval of Cn2 profile from differential column image motion lidar using the regularization method

We develop a regularization-based algorithm for reconstructing the Cn2 profile using the profile of Fried’s transverse coherent length (r0) of differential column image motion (DCIM) lidar. This algorithm consists of fitting the set of measured data to a spline function and a two-stage inversion method based on regularized least squares QR-factorization (LSQR) in combination with an adaptive selection method. The performance of this algorithm is analyzed by a simulated profile generated from the HV5/7 model and experimental DCIM lidar data. Both the simulation and experiment support the presented approach. It is shown that the algorithm can be applied to estimate a reliable Cn2 profile from DCIM lidar.

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.

Simultaneous observations of structure function parameter of refractive index using a high-resolution radar and the DataHawk small airborne measurement system

Abstract. The SOUSY (SOUnding SYstem) radar was relocated to the Jicamarca Radio Observatory (JRO) near Lima, Peru, in 2000, where the radar controller and acquisition system were upgraded with state-of-the-art parts to take full advantage of its potential for high-resolution atmospheric sounding. Due to its broad bandwidth (4 MHz), it is able to characterize clear-air backscattering with high range resolution (37.5 m). A campaign conducted at JRO in July 2014 aimed to characterize the lower troposphere with a high temporal resolution (8.1 Hz) using the DataHawk (DH) small unmanned aircraft system, which provides in situ atmospheric measurements at scales as small as 1 m in the lower troposphere and can be GPS-guided to obtain measurements within the beam of the radar. This was a unique opportunity to make coincident observations by both systems and to directly compare their in situ and remotely sensed parameters. Because SOUSY only points vertically, it is only possible to retrieve vertical radar profiles caused by changes in the refractive index within the resolution volume. Turbulent variations due to scattering are described by the structure function parameter of refractive index Cn2. Profiles of Cn2 from the DH are obtained by combining pressure, temperature, and relative humidity measurements along the helical trajectory and integrated at the same scale as the radar range resolution. Excellent agreement is observed between the Cn2 estimates obtained from the DH and SOUSY in the overlapping measurement regime from 1200 m up to 4200 m above sea level, and this correspondence provides the first accurate calibration of the SOUSY radar for measuring Cn2.

Utilizing the Kantorovich metric for the validation of optical turbulence predictions

In this Letter, via idealized and realistic case studies, we have documented the limitations of several conventional metrics in validating Cn2 profile predictions. We have introduced the (normalized) Kantorovich metric as a viable alternative and demonstrated its prowess.