Correlations between Z-tilt, G-tilt, and centroid motion as a function of thresholding are studied through simulations and analyses. The Z-tilt, or Zernike tilt, is the first moment of the phase distribution over the aperture, while the G-tilt, or gradient tilt, is the average phase gradient over the aperture. It is found that raw centroid motion best correlates with G-tilt, but that even a small amount of thresholding makes Z-tilt the stronger correlation. The Zernike decomposition of the G-tilt is also presented. Using this decomposition, a theoretical value for the correlation between Z-tilt and G-tilt is determined. It is further demonstrated that the quad-cell signal best correlates with Z-tilt even though no thresholding is involved.

An expression is derived and studied that relates optical turbulence strength to the variance of the tilt difference between square apertures. This expression additionally depends upon the separation between the apertures and the direction in which tilts are measured. When a sensor, such as a Hartmann sensor, uses a lenslet array with square subapertures, the expression derived here is appropriate for computing the turbulence strength from the measured tilts. The expression derived here and the published expression for the equivalent circular aperture case are compared. Approximate expressions for this differential tilt variance are also derived.

The atmosphere’s surface layer (first 50–100 m above the ground) is extremely dynamic and is influenced by surface radiative properties, roughness, and atmospheric stability. Understanding the distribution of turbulence in the surface layer is critical to many applications, such as directed energy and free space optical communications. Several measurement campaigns in the past have relied on weather balloons or sonic detection and ranging (SODAR) to measure turbulence up to the atmospheric boundary layer. However, these campaigns had limited measurements near the surface. We have developed a time-lapse imaging technique to profile atmospheric turbulence from turbulence-induced differential motion or tilts between features on a distant target, sensed between pairs of cameras in a camera bank. This is a low-cost and portable approach to remotely sense turbulence from a single site without the deployment of sensors at the target location. It is thus an excellent approach to study the distribution of turbulence in low altitudes with sufficiently high resolution. In the present work, the potential of this technique was demonstrated. We tested the method over a path with constant turbulence. We explored the turbulence distribution with height in the first 20 m above the ground by imaging a 30 m water tower over a flat terrain on three clear days in summer. In addition, we analyzed time-lapse data from a second water tower over a sloped terrain. In most of the turbulence profiles extracted from these images, the drop in turbulence with altitude in the first 15 m or so above the ground showed a h m dependence, where the exponent m varied from −0.3 to −1.0, quite contrary to the widely used value of −4/3.

Surface layer optical turbulence values in the form of the refractive index structure function C n 2 are often calculated from surface layer temperature, moisture, and wind characteristics and compared to measurements from sonic anemometers, differential temperature sensors, and imaging systems. A key derived component needed in the surface layer turbulence calculations is the sensible heat value. Typically, the sensible heat is calculated using the bulk aerodynamic method that assumes a certain surface roughness and a friction velocity that approximates the turbulence drag on temperature and moisture mixing from the change in the average surface layer vertical wind velocity. These assumptions/approximations generally only apply in free convection conditions. To obtain the sensible heat, a more robust method, which applies when free convection conditions are not occurring, is via an energy balance method such as the Bowen ratio method. The use of the Bowen ratio––the ratio of sensible heat flux to latent heat flux––allows a more direct assessment of the optical turbulence-driving surface layer sensible heat flux than do more traditional assessments of surface layer sensible heat flux. This study compares surface layer C n 2 values using sensible heat values from the bulk aerodynamic and energy balance methods to quantifications from sonic anemometers posted at different heights on a sensor tower. The research shows that the sensible heat obtained via the Bowen ratio method provides a simpler, more reliable, and more accurate way to calculate surface layer C n 2 values than what is required to make such calculations from bulk aerodynamic method-obtained sensible heat.

Improvements to the Turbulence and Aerosol Research Dynamic Interrogation System (TARDIS) analysis are presented. This includes accounting for square sub-apertures and advanced noise reduction. Low signal-to-noise ratio (SNR) still presents challenges for accurate turbulence profiling.

Two-wavelength adaptive optics (AO), where sensing and correcting (from a beacon) is performed at one wavelength $\lambda_\text{B}$ and compensation and observation (after transmission through the atmosphere) is performed at another $\lambda_\text{T}$, has historically been analyzed and practiced assuming negligible irradiance fluctuations (i.e., weak scintillation). Under these conditions, the phase corrections measured at $\lambda_\text{B}$ are robust over a relatively large range of wavelengths, resulting in a negligible decrease in AO performance. In weak-to-moderate scintillation conditions, which result from distributed-volume atmospheric aberrations, the pupil-phase function becomes discontinuous, producing what Fried called the ``hidden phase'' because it is not sensed by traditional least-squares phase reconstructors or unwrappers. Neglecting the hidden phase has a significant negative impact on AO performance even with perfect least-squares phase compensation. To the authors' knowledge, the hidden phase has not been studied in the context of two-wavelength AO. In particular, how does the hidden phase sensed at $\lambda_\text{B}$ relate to the compensation (or observation) wavelength $\lambda_\text{T}$? If the hidden phase is highly correlated across $\lambda_\text{B}$ and $\lambda_\text{T}$, like the least-squares phase, it is worth sensing and correcting; otherwise, it is not. Through a series of wave optics simulations, we find an approximate expression for the hidden-phase correlation coefficient as a function of $\lambda_\text{B}$, $\lambda_\text{T}$, and the scintillation strength. In contrast to the least-squares phase, we determine that the hidden phase (when present) is correlated over a small band of wavelengths centered on $\lambda_{\text{T}}$. Over the range $\lambda_\text{B},\lambda_\text{T} \in \left[1,3\right] \text{ } \mu\text{m}$ and in weak-to-moderate scintillation conditions (spherical-wave log-amplitude variance $\sigma_\chi^2 \in \left[0.1,0.5\right]$), we find the average hidden-phase correlation linewidth to be approximately $\text{0.35} \text{ } \mu\text{m}$. Consequently, for $\left|\lambda_\text{B}-\lambda_\text{T}\right|$ greater than this linewidth, including the hidden phase does not significantly improve AO performance over least-squares phase compensation.

Propagation and imaging models in combination with NWP and radiative effects can be used to estimate system performance. This presentation describes using local sensors to enhance model performance and considers data obtained during recent eclipse. Full-text article not available; see video presentation

Wind speed and sonic temperature measured with ultrasonic anemometers are often utilized to estimate the refractive index structure parameter C n 2 , a vital parameter for optical propagation. In this work, we compare four methods to estimate C n 2 from C T 2 , using the same temporal sonic temperature data streams for two separated sonic anemometers on a homogenous path. Values of C n 2 obtained with these four methods using field trial data are compared to those from a commercial scintillometer and from the differential image motion method using a grid of light sources positioned at the end of a common path. In addition to the comparison between the methods, we also consider appropriate error bars for C n 2 based on sonic temperature considering only the errors from having a finite number of turbulent samples. The Bayesian and power spectral methods were found to give adequate estimates for strong turbulence levels but consistently overestimated the C n 2 for weak turbulence. The nearest neighbors and structure function methods performed well under all turbulence strengths tested.

The sonic anemometer makes rapid measurements of air temperature and wind velocity which are then used to quantify atmospheric turbulence. Turbulence strength is estimated from the parameters of a curve fit to a structure function computed from the measured data. This procedure was carried out for both experimental and simulated data and the differences between the results obtained were examined. Averaging effects due to the measurement interval caused changes in both measured and simulated results mostly represented by an offset in the simple theoretical structure function. An additional offset was observed in the simulated results due to frequencies cut off by the simulation method. This study also examined the effect of the finite sample length on the computed power spectrum and structure function. This effect appears to be unimportant for the Kolmogorov power spectrum usually presumed here, but it is shown that non-Kolmogorov power spectra don’t necessarily produce accurate results even in simulation.

Interdependence of atmospheric aerosol particle formation, ambient sensible and latent heat flux and implications for optical turbulence are studied. Nano-aerosol particle counters, Energy Balance and Aerodynamic methods are used to enhance potential Machine Learning applications.

Non-stationary turbulence is simulated by modulating the results from stationary simulation. Aliasing the Kolmogorov spectrum improves the results. It is demonstrated that there is an optimal number of samples to estimate the turbulence strength.

In an earlier work, we demonstrated a method to profile turbulence using time-lapse imagery of a distant target from five spatially separated cameras. Extended features on the target were tracked and by measuring the variances of the difference in wavefront tilts sensed between cameras due to all pairs of target features, turbulence information along the imaging path could be extracted. The method is relatively low cost and does not require sophisticated instrumentation. Turbulence can be sensed remotely from a single site without deployment of sources or sensors at the target location. Additionally, the method is phase-based, and hence has an advantage over irradiance-based techniques which suffer from saturation issues. The same concept has been applied to understand how turbulence changes with altitude in the surface layer. Short exposure images of a 30 m tall water tower were analyzed to obtain turbulence profiles along the imaging path. The experiment was performed over two clear days from mid-morning to early afternoon. The turbulence profiles show a drop in turbulence with altitude as expected. However, the rate at which turbulence decreased with altitude was different close to the ground from at higher altitudes.

We build on well-accepted work to theoretically consider the impact of measurement time on accuracy of reported CT2 and Cn2 values. These results are applied to measured sonic anemometer data.

The Turbulence and Aerosol Research Dynamic Interrogation System (TARDIS) is an optical sensing system that is based on dynamically changing the range between the collecting sensor and Rayleigh beacon during a static period of relatively unchanging turbulence-induced wavefront perturbations. In the past, obtaining measurement-based estimates of the turbulence strength profile from TARDIS was based around collating segmented refractive index structure parameter, Cn2 values traced to specific layers of the atmosphere. These values were developed from Fried parameter segments, which were deduced from differential tilt variance measurements from neighboring subapertures on the Shack-Hartmann wavefront sensor. In this work, we will exploit the crossings between the sensing paths from the different beacon locations (during a static period) to the wavefront sensor subapertures to derive turbulence profiles along the path. The differential tilt variance between a pair of subapertures due to a pair of beacons at two different ranges in a crossed sensing path configuration has a unique turbulence weighting function associated with it which depends on the geometry of the beacons and the subapertures. By using these unique path weighting functions along with the corresponding measured differential tilt variances for all configurations where the sensing paths cross, Cn2 profiles along the path can be constructed. The derivation of the weighting functions will be discussed and derived profiles will be compared to measurements from other profiling instruments such as MZA’s DELTA-Sky and to numerical weather prediction models.

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.

Turbulence strength can be estimated from sonic anemometer data using both time-domain and frequency-domain approaches; these techniques are compared here. Atmospheric turbulence has a strong impact on both laser propagation and long-range imaging. Measurement of turbulence is thus important for predicting optical system performance. The ultrasonic anemometer is an attractive instrument for making point measurements of turbulence in support of optical experiments. It makes rapid measurements of air temperature and wind speed. These measurements are then processed to produce estimates of turbulence strength as well as the turbulence outer scale. There are two main routes for estimating turbulence from these measurements. In a frequency-domain approach, the temporal power spectrum of the temperature measurements is fit to a -5/3 power-law, since turbulence is expected to obey this Kolmogorov power spectrum at least within some inertial range. In a time-domain approach, the structure function of the temperature measurement is computed, and this structure function is fit to a 2/3 power-law. This is the structure function predicted for the Kolmogorov power spectrum. Because these different approaches use the temperature measurements quite differently, there are some differences in the results obtained. With the frequency domain approach, the desired power law expected to be observed for frequencies in the middle of the range used, while with the time-domain approach, the desired functional form is only seen for the shortest separations in time. These two approaches are used to analyze experimental data collected in field experiments at Wright-Patterson AFB at heights of 2.64 and 5 meters above the ground. Because these two approaches use the same data in different ways some differences in the results obtained can be d. The reasons for these differences in the results will be discussed.

Sonic anemometers have been used extensively to measure virtual temperature fluctuations associated with turbulence and thereby determine the temperature structure function parameter. While it is common to utilize the temperature power spectrum in such an analysis, it is similarly possible to use a structure function based approach. In this work, we consider the details involved and benefits/disadvantages of processing by each method.

Psychrometric measurements via sling psychrometers have long been the standard for quantifying thermodynamics of near-surface atmospheric gas-vapor mixtures, specifically moisture parameters. However, these devices are generally only used to measure temperature and humidity at one near-surface level. Multiple self-aspirating psychrometers can be used in a vertical configuration to measure temperature and moisture gradients and fluxes in the first 1-2 meters of the surface layer. This study evaluates the feasibility of a method using infrared (IR) imagery, and a mini-tower of wet and dry paper towels to psychometrically obtain surface layer temperature and moisture gradients and fluxes. First, the possible utility of using a single IR thermometer/detector to evaluate moisture and heat fluxes near the surface was explored, and it was found that the single IR sensor could be used to sense wet- and dry-bulb temperature changes of 0.7 K and 0.6 K respectively over vertical distances as small as 50 cm, thus allowing surface layer temperature and moisture gradients/fluxes to be quantified. The feasibility of this single IR detector method to provide with reasonable certainty values of surface layer heat and moisture fluxes suggests the technique could be exploited with more efficiency and accuracy with a calibrated imaging IR camera or sensor array. The surface layer dry- and wet-bulb temperatures obtained using an MWIR camera system are compared to Kestrel 4000 Weather Meter and Bacharach sling psychrometer measurements under various atmospheric conditions and surface types to test the viability of the method. Uncertainty statistics are calculated and evaluated to quantify effectiveness.