Optical-scintillation method of measuring turbulence inner scale

Utilization of high-speed imaging for atmospheric scintillation studies

Atmospheric scintillation studies have been traditionally undertaken utilizing nonimaging detection. When imaging devices are used, they typically detect the resultant signal at the receiver plane. Here, a high-speed camera has been utilized in atmospheric scintillation field trials, imaging a laser source (i.e., imaging the object plane) over a near ground path length of 1.5 km. The statistical nature of the acquired atmospheric scintillation data is characterized using a range of probability density functions. The exponentiated Weibull function was found to best describe the nature of scintillation over the broadest range of a scintillation index typical of atmospheric scintillation. A preliminary investigation into the relationship between the fit variables of three of the better-performing probability density functions and the scintillation index is presented, along with suggestions for future use of digital cameras in atmospheric scintillation studies.

Atmospheric Turbulence Study with Deep Machine Learning of Intensity Scintillation Patterns

A new paradigm for machine learning-inspired atmospheric turbulence sensing is developed and applied to predict the atmospheric turbulence refractive index structure parameter using deep neural network (DNN)-based processing of short-exposure laser beam intensity scintillation patterns obtained with both: experimental measurement trials conducted over a 7 km propagation path, and imitation of these trials using wave-optics numerical simulations. The developed DNN model was optimized and evaluated in a set of machine learning experiments. The results obtained demonstrate both good accuracy and high temporal resolution in sensing. The machine learning approach was also employed to challenge the validity of several eminent atmospheric turbulence theoretical models and to evaluate them against the experimentally measured data.

A Turbulence-Oriented Approach to Retrieve Various Atmospheric Parameters Using Advanced Lidar Data Processing Techniques

The article is aimed at presenting a semi-empirical model coded and computed in the programming language Python, which utilizes data gathered with a standard biaxial elastic lidar platform in order to calculate the altitude profiles of the structure coefficients of the atmospheric refraction index C N 2 ( z ) and other associated turbulence parameters. Additionally, the model can be used to calculate the PBL (Planetary Boundary Layer) height, and other parameters typically employed in the field of astronomy. Solving the Fernard–Klett inversion by correlating sun-photometer data obtained through our AERONET site with lidar data, it can yield the atmospheric extinction and backscatter profiles α ( z ) and β ( z ) , and thus obtain the atmospheric optical depth. Finally, several theoretical notions of interest that utilize the solved parameters are presented, such as approximated relations between C N 2 ( z ) and the atmospheric temperature profile T ( z ) , and between the scintillation of backscattered lidar signal and the average wind speed profile U ( z ) . These obtained profiles and parameters also have several environmental applications that are connected directly and indirectly to human health and well-being, ranging from understanding the transport of aerosols in the atmosphere and minimizing the errors in measuring it, to predicting extreme, and potentially-damaging, meteorological events.

Simulation of the microstructural characteristics of saltwater turbulence in a water tank

This study simulated the generation and evolution of saltwater turbulence within a water tank. By pouring fresh water over saltwater in the tank, a layer of saline water with a fixed gradient was created. Convective turbulence was then formed by heating the bottom of the tank. The temperatures at different heights were measured using eight thermocouples; thus, the average temperatures and temperature fluctuations at different heights were calculated. The salinity profile was obtained by moving a conductivity probe up and down to measure the conductivity. Two-dimensional light intensity grayscale images were recorded after transmitting a collimated laser beam through the water tank, after which the normalized variance and power spectra of the light intensity fluctuations at different heights were calculated. The results showed that the saltwater in the tank could be divided by height into two layers, namely, the mixed layer and entrainment zone, according to the profiles of the average temperature and average salinity under the experimental conditions. Different portions of the images showed different characteristics. The part corresponding to the saltwater mixed layer was similar to that corresponding to the mixed layer in the fresh water experiment. However, a two-peak structure was observed in the curve of the normalized light intensity spectrum calculated from the grayscale values in the part corresponding to the bottom of the entrainment zone, whereas a two-peak structure was not found in the light intensity fluctuation spectrum corresponding to the mixed layer. According to the refractive index fluctuation spectrum model, one peak was due to temperature fluctuations, and the other peak was due to salinity fluctuations. It can be concluded that the salinity contribution to the refractive index fluctuation in the entrainment zone was larger than that in the mixed layer. Moreover, spectral analysis showed that in the saltwater, the inner scale of turbulent temperature fluctuation was approximately 1.9 mm, while the inner scale of turbulent salinity fluctuation was approximately 0.1 mm. These findings will be helpful for us to understand the microstructural characteristics of seawater turbulence and guide the implementation of optical transmission experiments in seawater.

Plenoptic mapping for imaging and retrieval of the complex field amplitude of a laser beam

The plenoptic sensor has been developed to sample complicated beam distortions produced by turbulence in the low atmosphere (deep turbulence or strong turbulence) with high density data samples. In contrast with the conventional Shack-Hartmann wavefront sensor, which utilizes all the pixels under each lenslet of a micro-lens array (MLA) to obtain one data sample indicating sub-aperture phase gradient and photon intensity, the plenoptic sensor uses each illuminated pixel (with significant pixel value) under each MLA lenslet as a data point for local phase gradient and intensity. To characterize the working principle of a plenoptic sensor, we propose the concept of plenoptic mapping and its inverse mapping to describe the imaging and reconstruction process respectively. As a result, we show that the plenoptic mapping is an efficient method to image and reconstruct the complex field amplitude of an incident beam with just one image. With a proof of concept experiment, we show that adaptive optics (AO) phase correction can be instantaneously achieved without going through a phase reconstruction process under the concept of plenoptic mapping. The plenoptic mapping technology has high potential for applications in imaging, free space optical (FSO) communication and directed energy (DE) where atmospheric turbulence distortion needs to be compensated.

Method of estimation of turbulence characteristic scales

We propose an optical method that uses phase data of a laser beam obtained from a Shack-Hartmann sensor to estimate both the inner and outer scales of turbulence. The method is based on the sequential analysis of normalized correlation functions of Zernike coefficients. It allows the exclusion C(n)(2) from the analysis and reduces the solution of a two-parameter problem to a sequential solution of two single-parameter problems. The method has been applied to estimate the outer and inner scales of turbulence induced in the water cell.

Characterizing the propagation path in moderate to strong optical turbulence

In February 2005 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation and the University of Central Florida. A Gaussian beam was propagated along a horizontal 1500 m path near the ground. Scintillation was measured simultaneously at three receivers of diameters 1, 5, and 13 mm. Scintillation theory combined with a numerical scheme was used to infer the structure constant C2n, the inner scale l0, and the outer scale L0 from the optical measurements. At the same time, C2n measurements were taken by a commercial scintillometer, set up parallel to the optical path. The C2n values from the inferred scheme and the commercial scintillometer predict the same behavior, but the inferred scheme consistently gives slightly smaller C2n values.

Comment on "Heterodyne lidar returns in the turbulent atmosphere: performance evaluation of simulated systems"

The explanation proposed by Belmonte and Rye [Appl. Opt. 39, 2401 (2000)] for the difference between simulation and the zero-order theory for heterodyne lidar returns in a turbulent atmosphere is incorrect. The theoretical expansion the authors considered is not developed under a square-law structure-function approximation (random-wedge atmosphere). Agreement between the simulations and the zero-order term of the theoretical expansion is produced for the limit of statistically independent paths (bistatic operation with large transmitter-receiver separation) when the simulations correctly include the large-scale gradients of the turbulent atmosphere.

Effects of refractive turbulence on ground-based verification of coherent Doppler lidar performance

The effects of refractive turbulence on ground-based verification of the far-field performance of coherent Doppler lidar are determined with numerical simulation and compared with the first-order terms of a theoretical expansion. The collimated small-beam far-field test has better performance than the focused-beam test. For typical ground-based conditions, higher-order terms of the theoretical expansion are required for convergence.

Optical technique for inner-scale measurement: possible astronomical applications

We propose an optical technique that allows us to estimate the inner scale by measuring the variance of angle of arrival fluctuations of collimated laser beams of different sections w (i) passing through a turbulent layer. To test the potential efficiency of the system, we made measurements on a turbulent air flow generated in the laboratory, the statistical properties of which are known and controlled, unlike atmospheric turbulence. We deduced a Kolmogorov behavior with a 6-mm inner scale and a 90-mm outer scale in accordance with measurements by a more complicated technique using the same turbulent channel. Our proposed method is especially sensitive to inner-scale measurement and can be adapted easily to atmospheric turbulence analysis. We propose an outdoor experimental setup that should work in less controlled conditions that can affect astronomical observations. The inner-scale assessment might be important when phase retrieval with Laplacian methods is used for adaptive optics purposes.

Onset of strong scintillation with application to remote sensing of turbulence inner scale

Numerical simulation of propagation through atmospheric turbulence of an initially spherical wave is used to calculate irradiance variance σ(2)(I), variance of log irradiance σ(2)(ln I), and mean of log irradiance ?In I? for 13 values of l(0)/R(f) (i.e., of turbulence inner scale l(0) normalized by Fresnel scale R(F)) and 10 values of Rytov variance σ(2)(Rytov), which is the irradiance variance, including the inner-scale effect, predicted by perturbation methods; l(0)/R(f) was varied from 0 to 2.5 and σ(2)(Rytov) from 0.06 to 5.0. The irradiance probability distribution function (PDF) and, hence, σ(2)(I), σ(2)(In I), and ?ln I? are shown to depend on only two dimensionless parameters, such as l(o)/R(F) and σ(2)(Rytov). Thus the effects of the onset of strong scintillation on the three statistics are characterized completely. Excellent agreement is obtained with previous simulations that calculated σ(2)(I). We find that σ(2)(I), σ(2)(In I), and ?ln I? are larger than their weak-scintillation asymptotes (namely, σ(2)(Rytov), σ(2)(Rytov), and - σ(2)(Rytov)/2, respectively) for the onset of strong scintillation for all l(0)/R(f). An exception is that for the largest l(0)/R(f), the onset of strong scintillation causes σ(2)(ln I) to decrease relative to its weak-scintillation limit, σ(2)(Rytov). We determine the efficacy of each of the three statistics for measurement of l(0), taking into account the relative difficulties of measuring each statistic. We find that measuring σ(2)(I) is most advantageous, although it is not the most sensitive to l(0) of the three statistics. All three statistics and, hence, the PDF become insensitive to l(0) for roughly 1 < β0(2) < 3 (where β0(2) is σ (2)(Rytov) for l(0) = 0); this is a condition for which retrieval of l(0) is problematic.

Optical properties of a planar turbulent jet

A planar heated air jet was constructed. Its flow properties were characterized and shown to be both reproducible and in good agreement with the results of turbulence theory. The optical properties of the jet were studied with the help of a 632.8-nm He-Ne laser beam. The random phase modulations imposed on the wave front of the beam traversing the jet were measured by interferometric means, and their spectra and variance were determined. The one-dimensional phase fluctuation spectrum obeyed a -8/3 power law as predicted by theory, whereas the phase variance (?(2)) depended on the jet temperature and was studied for values to as high as 0.4 (rad)(2)).

Two-color correlation of atmospheric scintillation

We present the results of measurements of the correlation of scintillations of two colors of light made in the turbulent atmosphere. In strong path-integrated turbulence the correlation is below that predicted by the weak-turbulence theory. A phenomological theoretical approach is used to account for saturation effects. This simple theory provides a reasonable approximation to the correlation data. Thus, we conclude that saturation effects reduce the two-color correlation of atmospheric scintillation.

Aperture averaging of optical scintillations in the turbulent atmosphere

We have developed approximate expressions for the aperture-averaging factor of optical scintillation in the turbulent atmosphere. For large apertures and weak path-integrated turbulence with a small inner scale, the variance of signal fluctuations is proportional to the -7/3 power of the ratio of the aperture diameter to the Fresnel zone size. If the inner scale is large, the variance is proportional to the -7/3 power of the ratio of the aperture diameter to the inner scale. In strong path-integrated turbulence, two scales develop. That portion of the variance associated with the smaller scale is proportional to the -2 power of the ratio of the aperture diameter to the phase coherence length. That portion of the variance associated with the larger scale is proportional to the -7/3 power of the ratio of the aperture diameter to the scattering disk. These simple approximations are within a factor of 2 of the measurements.

Effects of saturation on the optical scintillometer

Measurements of the level of turbulence C(2)(n) have been successfully performed with the optical scintillometer. The success of this instrument is based on the observed fact that the variance of aperture averaged scintillation is described by weak scattering theory even for conditions in which strong scintillation is observed for point detectors. However, for sufficiently long propagation paths, the aperture averaged variance is affected by strong scattering. The effects of strong scattering are calculated theoretically and compared to experimental results. The physics of this regime are discussed and the important parameters investigated. The new range of validity of the optical scintillometer is discussed.

Aperture size and bandwidth requirements for measuring strong scintillation in the atmosphere

Irradiance statistics were simultaneously measured with five apertures of four different sizes and also with five different bandwidths under conditions of strong path-integrated turbulence to determine aperture size and bandwidth requirements. The probability density function and the second and third moments are considered. Good measurements of these statistics can be made with detector apertures near the wave coherence length and with bandwidths near the ratio of the transverse wind velocity to the wave coherence length under these conditions.

Estimation of the parameters of the atmospheric turbulence spectrum using measurements of the spatial intensity covariance

Estimates of the level of turbulence C(2)(n) and the inner scale of turbulence lambda(0) are obtained from measurements of the spatial covariance of laser scintillation in weak scattering conditions. Boundary layer turbulence is widesense nonstationary over time scales of <1 min but becomes locally wide-sense stationary on time scales of 2 min. The interpretation of the measurements is very sensitive to the form of the turbulence spectrum in the dissipation region.

Aperture averaging effects on the two-color correlation of scintillations

The scintillation two-color correlation coefficient was measured using a variable aperture. The correlation, at constant aperture, vs turbulence strength and the aperture averaging effects at constant turbulence strength were obtained. The results show a strong decrease or correlation with increasing turbulence strength and a moderate increase with increasing aperture. These results cannot be accounted for by a constant shape turbulence spectrum. It is shown that a turbulence strength-dependent inner scale can explain most of the results using the Rytov approximation.

Comparison of scintillation methods for measuring the inner scale of turbulence

One method of inner scale measurement uses the irradiance variance of a diverging monochromatic wave (the irradiance being obtained through a small aperture at the receiver position) and the irradiance variance of a large-aperture C(2)(n) scintillometer. The ratio of these two variances depends on the inner scale of turbulence l(0) but not on the refractive-index structure parameter C(2)(n). Another method uses the bichromatic correlation of irradiances from waves having two different wavelengths, transmitted through a common small aperture (the irradiance being obtained through a small aperture at the receiver position) and the two corresponding monochromatic irradiance variances. The ratio of the bichromatic correlation to the geometric mean of the two monochromatic variances depends on l(0) but not on C(2)(n). A third method is to obtain the ratio of the two monochromatic variances without using the bichromatic correlation. These methods are compared graphically using calculations based on an accurate atmospheric refractive-index spectrum. A scaling analysis is performed to determine the minimum number of parameters needed to describe the methods. It is suggested that systematic errors, rather than signal-to-noise limitations, determine the accuracy with which inner scale is measured. The effects of refractive-index dispersion between the two wavelengths must be taken into account. The results indicate that the bichromatic method has advantages when l(0) less, similar0.6 radicalL/k, whereas the method using small and large apertures has the advantage when l(0) greater, similar0.6 radicalL/k were L is the propagation path length and k is the optical wave number.

Sample size influence on optical scintillation analysis. Analytical treatment of the higher-order irradiance moments

The statistical distribution of the experimentally obtained higher-order moments of optical scintillation probability density is studied. It is shown that this distribution is strongly dependent on the size of the data sample. At reasonable sample sizes the correct estimation of the theoretical value is improbable. At practically available sample sizes the region of the most probable values of the estimated higher-order moment is almost independent of the scintillation probability density function (PDF). The distinction between the candidate PDFs is almost impossible at reasonable sample sizes.