Estimation of Turbulence from Time-lapse Imagery

Atmospheric turbulence parameters are estimated for an imaging path based on time-lapse imaging results. Atmospheric turbulence causes frame-to-frame shifts of the entire image as well as parts of the image. The statistics of these shifts encode information about the turbulence strength (as characterized by Cn2, the refractive index structure function constant) along the optical path. The shift variance observed is simply proportional to the variance of the tilt of the optical field averaged over the area being tracked and averaged over the camera aperture. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions, which relate the turbulence strength along the path to the shifts measured, are derived. These weighting functions peak at the camera and fall to zero at the object. The larger the area observed, the more quickly the weighting function decays. One parameter we would like to estimate is r0 (the Fried parameter or atmospheric coherence diameter.) The weighting functions derived for pixel sized or larger parts of the image all fall faster than the weighting function appropriate for estimating the spherical wave r0. If we were to presume that Cn2 is constant along the path, then an estimate for r0 could be obtained for each area tracked, but since the weighting function for r0 differs substantially from that for every realizable tracked area, it can be expected that this approach would yield a poor estimate. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore–Penrose pseudoinverse to create a weighting function that yields the least-squares optimal linear combination of measurements for the estimation of r0. This approach is carried out for one example and is shown to give noisy results. A modified version of this approach that creates larger patches by averaging several smaller patches together solves this noise issue. This approach can also work to estimate other atmospheric parameters

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

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

Modeled and Measured Image-plane Polychromatic Speckle Contrast

The statistical properties of speckle relevant to short- to medium-range (tactical) active tracking involving polychromatic illumination are investigated. A numerical model is developed to allow rapid simulation of speckled images including the speckle contrast reduction effects of illuminator bandwidth, surface slope, and roughness, and the polarization properties of both the source and the reflection. Regarding surface slope (relative orientation of the surface normal and illumination/observation directions), Huntley’s theory for speckle contrast, which employs geometrical approximations to decrease computation time, is modified to increase accuracy by incorporation of a geometrical correction factor and better treatment of roughness and polarization. The resulting model shows excellent agreement with more exact theory over a wide range. An experiment is conducted to validate both the numerical model developed here and existing theory. A diode laser source with coherence length of 259±7  μm is reflected off of a silver-coated diffuse surface. Speckle data are gathered for 16 surface slope angles corresponding to speckle contrast between about 0.55 and 1. Taking the measured data as truth, both equations show error mean and standard deviation of less than 3%. Thus, the theory is validated over the range of this experiment

Estimation of Temporal Variations in Path-averaged Atmospheric Refractive Index Gradient from Time-lapse Imagery

The sea level vertical refractive index gradient in the U.S. Standard Atmosphere model is −2.7×10−8  m−1 at 500 nm. At any particular location, the actual refractive index gradient varies due to turbulence and local weather conditions. An imaging experiment was conducted to measure the temporal variability of this gradient. A tripod mounted digital camera captured images of a distant building every minute. Atmospheric turbulence caused the images to wander quickly, randomly, and statistically isotropically and changes in the average refractive index gradient along the path caused the images to move vertically and more slowly. The temporal variations of the refractive index gradient were estimated from the slow, vertical motion of the building over a period of several days. Comparisons with observational data showed the gradient variations derived from the time-lapse imagery correlated well with solar heating and other weather conditions. The time-lapse imaging approach has the potential to be used as a validation tool for numerical weather models. These validations will benefit directed energy simulation tools and applications

Feasibility of Obtaining Surface Layer Moisture Flux Using an IR Thermometer

This paper evaluates the feasibility of a method using a single hand-held infrared (IR) thermometer and a mini tower of wet and dry paper towels to psychometrically obtain surface layer temperature and moisture gradients and fluxes. Sling Psychrometers have long been standard measuring devices for quantifying the 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 m of the surface layer. This study explores a way to make multiple vertical psychrometric measurements with a single non-contact IR temperature sensor rather than using two in situ thermometers at each level. The surface layer dry- and wet-bulb temperatures obtained using an IR Thermometer 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. To evaluate the results obtained using this new approach, standard meteorological surface data are collected during each experiment, and moisture parameters are derived via psychrometric equations. The results indicate that, not only is the method possible and practical, but they suggest that the IR Thermometer method may provide more surface layer temperature and moisture gradient and flux sensitivity than other single instrument methods

Estimating Turbulence Distribution over a Heterogeneous Path Using Time‐lapse Imagery from Dual Cameras

Knowledge of turbulence distribution along an experimental path can help in effective turbulence compensation and mitigation. Although scintillometers are traditionally used to measure the strength of turbulence, they provide a path-integrated measurement and have limited operational ranges. A technique to profile turbulence using time-lapse imagery of a distant target from spatially separated cameras is presented here. The method uses the turbulence induced differential motion between pairs of point features on a target, sensed at a single camera and between cameras to extract turbulence distribution along the path. The method is successfully demonstrated on a 511 m almost horizontal path going over half concrete and half grass. An array of Light-Emitting Diodes (LEDs) of non-uniform separation is imaged by a pair of cameras, and the extracted turbulence profiles are validated against measurements from 3D sonic anemometers placed along the path. A short-range experiment with a heat source to create local turbulence spike gives good results as well. Because the method is phase-based, it does not suffer from saturation issues and can potentially be applied over long ranges. Although in the present work, a cooperative target has been used, the technique can be used with non-cooperative targets. Application of the technique to images collected over slant paths with elevated targets can aid in understanding the altitude dependence of turbulence in the surface layer

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. © 2013 Optical Society of Americ

Examining the Validity of Using a Gaussian Schell-Model Source To Model the Scattering of A Fully Coherent Gaussian Beam From A Rough Impedance Surface

Military applications that use adaptive optics (AO) often require a point source beacon at the target to measure and correct for wavefront aberrations introduced by atmospheric turbulence. However, turbulence prevents the formation of such a point beacon. The extended beacons that are created instead have finite spatial extents and exhibit varying degrees of spatial coherence. Modeling these extended beacons using a Gaussian Schell-model (GSM) form for the autocorrelation function would be a convenient approach due to the analytical tractability of Gaussian functions. We examine the validity of using such a model by evaluating the field scattered from a rough impedance surface using a full-wave computational technique called the method of moments (MoM). The MoM improves the fidelity of the analysis since it captures all the physics of the laser-target interaction, such as masking, shadowing, multiple reflections, etc. Two rough-surface targets with different roughness statistics are analyzed. The simulation results are verified with experimental bidirectional reflectance distribution function measurements. It is seen that for rough surfaces, in general, the scattered-field autocorrelation function is not of a GSM form. However, under certain conditions, modeling an extended beacon as a GSM source is legitimate. This analysis will aid in understanding the behavior of extended beacons and how they affect the overall performance of an AO system

Climate Change: Anticipated Effects on High-Energy Laser Weapon Systems in Maritime Environments

anticipated effects on high energy laser weapon systems in maritime environments. Journal of Applied Meteorology and Climatology, American Meteorological Society, 50, 153-166This study quantifies the potential impacts on ship-defense high-energy-laser (HEL) performance due to atmospheric effects in the marine boundary layer driven by recent observations and analysis of worldwide sea surface temperatures (SSTs). The atmospheric effects are defined using the worldwide probabilistic climatic database available in the High Energy Laser End-to-End Operational Simulation (HELEEOS) model, which includes an SST database for the period 1854–1997. A more recent worldwide sea surface temperature database was provided by the Naval Postgraduate School for the period 1990-2008. Mean differences and trends between the two SST databases are used to deduce possible climate change impacts on simulated maritime HEL engagements. The anticipated effects on HEL propagation performance are assessed at an operating wave-length of 1.0642 um across the world's oceans and mapped to a 1 degree x 1 degree grid. The scenario evaluated is near surface and nearly horizontal over a range of 5000 m in which anticipated clear-air maritime aerosols occur. Summer and winter scenarios are considered. In addition to realistic vertical profiles of molecular and aerosol absorption and scattering, correlated optical turbulence profiles in probabilistic (percentile) format are used