Investigating turbulence distribution in the lower atmosphere using time-lapse imagery from a camera bank.

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.

Thermal blooming with laser-induced convection: radial basis function simulation.

The propagation of a high energy laser through a nearly stagnant absorbing medium is studied. The absorption values and time scale of the problem are such that the laser induces convective heat currents transverse to the beam. These currents couple to the laser via the refractive index, causing time dependent thermal blooming. A numerical method is developed and applied to the model in [J. Electromagn. Waves Appl.33, 96 (2019)JEWAE50920-507110.1080/09205071.2018.1528183], using radial basis functions for spatial differencing, which allows for irregular point spacings and a wide class of geometries. Both the beam and laser-induced fluid dynamics are numerically simulated. These simulations are compared to a historical experiment of a 300 W laser in a smoke-filled chamber with good agreement; both cases include a crescent shaped spot at the target.

Implications of polarized pupil degradation due to focal shifts in dynamically ranged Rayleigh beacons.

A dynamically ranged pulsed Rayleigh beacon using sensed wavefronts across a system's pupil plane is proposed for tomographic quantification of the atmospheric turbulence strength. This method relies on relaying light from a telescope system's pupil plane to a wavefront sensor and having precise control of the light-blocking mechanisms to filter out scattered light from the unwanted scattering regions along the propagation path. To accomplish this, we tested and incorporated design features into the sensing system that we believe, to the best of our knowledge, are unique. Dynamically changing the range of the beacon source created focal shifts along the optical axis in the telescope sensing system. This effect induced polarization degradation in the optical pupil. As a result, polarization nonuniformity within the Pockels cell resulted in light leakages that corrupted the sensed data signals. To mitigate this unwanted effect, an analysis of the polarization pupil had to be completed for the range of possible Rayleigh beacon source distances, relating the change in polarization to the ability of a Pockels cell to function as an optical shutter. Based on the resultant polarization pupil analysis, careful design of the light relay architecture of the sensing system was necessary to properly capture sensed wavefront data from a series of intended ranges. Results are presented for the engineering design of the Turbulence and Aerosol Research Dynamic Interrogation System sensing system showing the choices made within the trade space and how those choices were made based on an analysis of the polarization pupil. Based on what we learned, recommendations are made to effectively implement a polarization-based Pockels cell shutter system as part of a dynamically ranged Rayleigh beacon system.

Speckle mitigation for wavefront sensing in the presence of weak turbulence.

When measuring atmospheric turbulence along the propagation path to an extended non-cooperative target, a wavefront sensor normally suffers from severe noise due to speckle. In this work, we quantify the benefits of speckle mitigation via polychromatic illumination for a Shack-Hartmann wavefront sensor. We obtain results over a wide range of conditions by using the spectral-slicing approach to polychromatic wave-optics simulations. To quantify speckle noise, even when turbulence is present, we introduce a metric involving racetrack-mode strength in slope-discrepancy space. The results show that polychromatic illumination greatly reduces speckle noise under realistic conditions. Even with near worst-case conditions, 15 coherence lengths per resolution cell reduce the wavefront-measurement error by 56%.

Polychromatic wave-optics models for image-plane speckle. 1. Well-resolved objects.

Polychromatic laser light can reduce speckle noise in wavefront-sensing and imaging applications that use direct-detection schemes. To help quantify the achievable reduction in speckle, this paper investigates the accuracy and numerical efficiency of three separate wave-optics methods. Each method simulates the active illumination of extended objects with polychromatic laser light. In turn, this paper uses the Monte Carlo method, the depth-slicing method, and the spectral-slicing method, respectively, to simulate the laser-object interaction. The limitations and sampling requirements of all three methods are discussed. Further, the numerical efficiencies of the methods are compared over a range of conditions. The Monte Carlo method is found to be the most efficient, while spectral slicing is more efficient than depth slicing for well-resolved objects. Finally, Hu's theory is used to quantify method accuracy when possible (i.e., for well-resolved objects). In general, the theory compares favorably to the simulation methods.

Polychromatic wave-optics models for image-plane speckle. 2. Unresolved objects.

Polychromatic laser light can reduce speckle noise in many wavefront-sensing and imaging applications. To help quantify the achievable reduction in speckle noise, this study investigates the accuracy of three polychromatic wave-optics models under the specific conditions of an unresolved object. Because existing theory assumes a well-resolved object, laboratory experiments are used to evaluate model accuracy. The three models use Monte-Carlo averaging, depth slicing, and spectral slicing, respectively, to simulate the laser-object interaction. The experiments involve spoiling the temporal coherence of laser light via a fiber-based, electro-optic modulator. After the light scatters off of the rough object, speckle statistics are measured. The Monte-Carlo method is found to be highly inaccurate, while depth-slicing error peaks at 7.8% but is generally much lower in comparison. The spectral-slicing method is the most accurate, always producing results within the error bounds of the experiment.

Enhanced, fast-running scaling law model of thermal blooming and turbulence effects on high energy laser propagation.

A new scaling law model is presented to rapidly simulate thermal blooming and turbulence effects on high energy laser propagation, producing results approaching the quality normally only available using wave-optics code, but at much faster speed. The model convolves irradiance patterns originating from two distinct scaling law models, one with a proficiency in thermal blooming effects and the other in turbulence. To underscore the power of the new model, results are verified for typical, realistic scenarios by direct comparison with wave optics simulation.

Physical optics solution for the scattering of a partially-coherent wave from a statistically rough material surface.

The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results.

Wavelength correction of refractivity variation measurements.

The index of refraction structure constant, Cn2 indicates how strongly the index of refraction varies in a region of the atmosphere. These variations usually arise through turbulent motions, creating an inhomogeneous distribution of species, density, temperature and pressure. Because the index of refraction also depends on wavelength, the measured value of Cn2 will depend on wavelength. This Cn2 difference generally becomes more pronounced as the difference in wavelength increases. This paper describes a technique for converting between measurements of Cn2 at different wavelengths, and gives an example for converting from centimeter to visible and near IR wavelengths.

A technique to measure optical properties of brownout clouds for modeling terahertz propagation.

Brownout, the loss of visibility caused by dust resultant of helicopter downwash, is a factor in the large majority of military helicopter accidents. As terahertz radiation readily propagates through the associated dust aerosols and is attenuated by atmospheric water vapor within short distances, it can provide low-profile imaging that improves effective pilot visibility. In order to model this application of terahertz imaging, it is necessary to determine the optical properties of obscurants at these frequencies. We present here a method of empirical calculation and experimental measurement of the complex refractive index of the obscuring aerosols. Results derived from terahertz time-domain spectral measurements are incorporated into the AFIT CDE Laser Environmental Effects Definition and Reference (LEEDR) software.