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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.

A simple optical system is built to quickly realize partially coherent sources for directed energy applications. The apparatus implements a recently developed technique in which any uniformly correlated or Schell-model source can be generated by summing many statistically independent randomly tilted beams. This result means that only a tip-tilt or fast steering mirror (FSM) is needed to realize Schell-model sources, which in contrast to existing synthesis techniques, is both fast and flexible. A brief review of the theory necessary to understand and implement the tilt-only synthesis technique is presented. The FSM apparatus is then described. Lastly, experimental results of a Schell-model source are compared with theoretical predictions to validate both the synthesis technique and FSM apparatus.

At the Air Force Institute of Technology, we have developed a technique to estimate atmospheric turbulence parameters from the turbulence-induced random, differential motion of features in the time-lapse imagery of a distant target. The variance of differential motion is a path-weighted integral of the refractive index structure constant, ${\boldsymbol{C_{n}}}^{2}$ . The path weighting functions drop to zero at either ends of the path, their peak locations depending on feature sizes and separations. These weighting functions form a rich set and can be linearly combined to approximate a desired weighting function, such as that of a scintillometer or Fried's coherence diameter, $\boldsymbol{r}_{0}$ . The time-lapse measurements can thus mimic the measurements of any turbulence measuring instrument. Since this is a phase-based technique, it has the potential to estimate turbulence over long paths where irradiance based techniques suffer from saturation issues. The method has been validated earlier against scintillometer measurements over a 7 km path. In the present work, the method is used to obtain a direct estimate of $\boldsymbol{r}_{0}$ from the time-lapse imagery of a LED array. The $\boldsymbol{r}_{0}$ estimates are compared to those obtained from a co-located turbulence profiling instrument.

An experiment was conducted to study turbulence along a 149-km path between the Mauna Loa and Haleakala mountain tops using digital cameras and light-emitting diode (LED) beacons. Much of the path is over the ocean, and a large portion of the path is 3 km above sea level. On the Mauna Loa side, six LED beacons were placed in a roughly linear array with pair spacings from 7 to 62 m. From the Haleakala side, a pair of cameras separated by 83.8 cm observed these beacons. Turbulence along the path induces tilts on the wavefronts, which results in displacements of the LED spots in the images. The image motion is caused by unwanted noise sources such as camera platform motion. Differential motion between spots cancels much of this noise, and this differential motion is weighted by the turbulence along the path in different ways depending on the geometry between the sources and the cameras. A camera motion insensitive weighting function is developed to deal with this observational issue. A linear combination of these weighting functions is then used to generate a composite weighting function, which better rejects turbulence near the sources and receivers and is most sensitive to turbulence in the portion of the path out over the ocean. This technique is used to estimate turbulence in this region. The long range involved caused very strong scintillation in the image, which added new challenges to the data processing. A resulting estimate for Cn2 of 4 × 10 − 17 m − 2 / 3 is in good agreement with the Hufnagel–Valley HV5/7 model and the results of numerical weather modeling.

The Hartmann Turbulence Sensor (HTS) is an optical system capable of estimating several atmospheric turbulence parameters, such as Greenwood frequency, Fried’s coherence diameter and inner scale of turbulence. It primarily comprises of a 40 cm Meade telescope, a 32 x 32 Shack- Hartmann lenslet array, and a high-speed camera. The HTS estimates the turbulence parameters by measuring the local tilts of the aberrated wavefront coming from a laser source and incident at the pupil plane of the telescope. At the Air Force Institute of Technology (AFIT), a technique has been developed to measure the distribution of turbulence along an experimental path using the HTS and two laser sources of the same wavelength. By measuring the variances of the difference in wavefront tilts due to the two sources sensed by a pair of Hartmann subapertures with varying separations, turbulence information along the path can be extracted. The method relies on deriving a set of weighting functions, each weighting function dipping to zero at a range where the two sensing paths from the beacons to the subapertures intersect, thus canceling out the effect of turbulence at this location on the differential tilt signal. The analytical expression for the path weighting functions has been derived here. The technique has been applied to experimental data collected over a 500 m grassy path and the profiling results have been compared to a co-located scintillometer. This work will eventually aid in obtaining a better understanding of turbulence in the lower atmosphere and how it varies with height.

In recent times, there has been a growing interest in measuring atmospheric turbulence over long paths. Irradiance based techniques such as scintillometry, suffer from saturation and hence commercial scintillometers have limited operational ranges. In the present work, a method to estimate path weighted C n 2 from turbulence induced random, differential motion of extended features in the time-lapse imagery of a distant target is presented. Since the method is phase based, it can be applied to longer paths. The method has an added advantage of remotely sensing turbulence without the need for deployment of sensors at the target location. The imaging approach uses a derived set of path weighting functions that drop to zero at both ends of the imaging path, the peak location depending on the size of the imaging aperture and the relative sizes and separations of the features whose motions are being tracked. For sub-aperture sized features and separations, the peaks of the weighting functions are closer to the target end of the path. For bigger features and separations, the peaks are closer to the camera end. Using different sized features separated by different amounts, a rich set of weighting functions can be obtained. These weighting functions can be linearly combined to produce a desired weighting function such as that of a scintillometer or that of r 0 . The time-lapse measurements can thus mimic the measurements of a scintillometer or any other instrument. The method is applied to both simulated and experimentally obtained imagery and some validation results with a scintillometer is shown as well.

In [Opt. Lett.42, 1512 (2017)OPLEDP0146-959210.1364/OL.42.001512], the authors present a new class of non-uniformly correlated sources with circular coherence. They also describe a basic experimental setup for synthesizing this class of sources, which uses the Van Cittert-Zernike theorem. Here, we present an alternative way to analyze these sources and a different way to generate them.

In a previous paper [Opt. Express22, 31691 (2014)] two different wave optics methodologies (phase screen and complex screen) were introduced to generate electromagnetic Gaussian Schell-model sources. A numerical optimization approach based on theoretical realizability conditions was used to determine the screen parameters. In this work we describe a practical modeling approach for the two methodologies that employs a common numerical recipe for generating correlated Gaussian random sequences and establish exact relationships between the screen simulation parameters and the source parameters. Both methodologies are demonstrated in a wave-optics simulation framework for an example source. The two methodologies are found to have some differing features, for example, the phase screen method is more flexible than the complex screen in terms of the range of combinations of beam parameter values that can be modeled. This work supports numerical wave optics simulations or laboratory experiments involving electromagnetic Gaussian Schell-model sources.

A Hartmann Turbulence Sensor was employed along a 200 meter path over a grassy field to investigate turbulence anisotropy. This sensor was based on a 16″ telescope with a 32 × 32 subaperture array featuring 700 active subapertures and a camera operating as fast as 8000 frames/sec. Data was recorded at different times of the day over the course of a 5-week period in 3–12 hour capture periods. Anisotropy was gauged by both differences between horizontal and vertical tilt variances observed on subapertures and also on variances of tilt differences between subaperture pairs. This latter differential tilt approach is expected to be largely immune to base disturbances. Unsurprisingly, during the day the turbulence appeared to be largely isotropic. During the evening neutral events, (at times near sunset) the turbulence showed a statistically significant anisotropy with tilt variances and differential tilt variances in the vertical direction exceeding those on the horizontal by roughly 5%. The anisotropy observed is consistent with the atmosphere being arranged into a vertically layered structure. At times near sunrise, where limited data was collected, this effect appeared to be weaker. No clear conclusions are drawn for the nighttime case, where while the turbulence was generally lower than that seen during the day, the measures of anisotropy appeared to be quite noisy. The results of this experiment are in general agreement with those of Sanchez et al. (referenced herein), who used a largely identical instrument at Kirtland AFB, NM, but with an environment and collection geometry which were quite different. Most models of surface layer turbulence presume isotropic conditions, this research shows that this presumption isn't always correct and a small correction is all that would be needed to create more realistic models.

Investigating the time-evolution of partially-coherent sources is necessary for certain optical coherence effects. Several simulation approaches have been developed, many of which can only treat cross-spectrally pure sources. However, some significant source types are not cross-spectrally pure. This paper reviews two methods for the synthesis of time-evolving sources which need not be pure. Both involve filtering matrices of uncorrelated Gaussian random numbers. One method requires control of both amplitude and phase, while the other only requires phase control. The utility of the methods for non-cross-spectrally pure sources is demonstrated for the first time. The source is generated by passing coherent light through two different diffusers which move at the same speed but in opposite directions. Simulation results for the time-evolving field are shown. Further, the coherence functions of the synthesized field are compared to theory for validation.

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 C n 2 ( 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.

Partially coherent beams (PCBs) of light can be highly directional, as from lasers, yet resistant to speckle and scintillation, as from LEDs. Generating PCBs with separate optical components for beam shaping and spatial coherence is complicated, and fundamentally limited. The authors control both shape and coherence using liquid-crystal spatial light modulators, and can produce two different classes of PCBs using the same simple optical setup. This work is immediately applicable in such diverse fields as medicine, directed energy, free-space optical communication, and manufacturing.

Accurate characterization of atmospheric turbulence is useful for performance assessment of optical systems operating in real environments and for designing systems to mitigate turbulence effects. Irradiance-based techniques such as scintillometry, suffer from saturation, and hence commercial scintillometers have limited operational ranges. A method to estimate turbulence parameters, such as path weighted Cn2 and Fried’s coherence diameter r0 from turbulence-induced random, differential motion of extended features in the time-lapse imagery of a distant target is presented. Since the method is phase-based, it can be applied to longer paths. It has an added advantage of remotely sensing turbulence without the need for deployment of sensors at the target location. The approach uses a derived set of path weighting functions that drop to zero at both ends of the imaging path, the peak location depending on the size of the imaging aperture, and the relative sizes and separations of the features whose motions are being tracked. Using different sized features separated by different amounts, a rich set of weighting functions can be obtained. These weighting functions can be linearly combined to approximate a desired weighting function such as that of a scintillometer or that of r0 in inhomogeneous turbulence. The time-lapse measurements can thus mimic the measurements of a scintillometer or any other instrument. The method is applied to images captured along two different paths, and the estimates are compared to co-located scintillometer measurements.

The near real-time synthesis of a non-uniformly correlated partially coherent source using a low-actuator-count deformable mirror is demonstrated. The statistical optics theory underpinning the synthesis method is reviewed. The experimental results of a non-uniformly correlated source are presented and compared to theoretical predictions. A discussion on how deformable mirror characteristics such as actuator count and pitch affect source generation is also included.

High-spatial-frequency optical fields or sources are often encountered when simulating directed energy, active imaging, or remote sensing systems and scenarios. These spatially broadband fields are a challenge in wave optics simulations because the sampling required to represent and then propagate these fields without aliasing is often impractical. To address this, two spatial filtering techniques are presented. The first, called Fresnel spatial filtering, finds a spatially band-limited source that, after propagation, produces the exact observation plane field as the broadband source over a user-specified region of interest. The second, called statistical or quasihomogeneous spatial filtering, finds a spatially band-limited source that, after propagation and over a specified region of interest, yields an observation plane field that is statistically representative of that produced by the original broadband source. The pros and cons of both approaches are discussed in detail. A wave optics simulation of light transiting a ground glass diffuser and then propagating to an observation plane in the near-zone is performed to validate the two filtering approaches.

A fast, flexible and efficient method for generating partially coherent sources is presented. It is shown that the Schell-model (uniformly correlated) and non-uniformly correlated sources can be produced quickly using a fast steering mirror and low-actuator-count deformable mirror, respectively. The statistical optics theory underpinning the proposed technique is presented and discussed. Simulation results of two Schell-models and one non-uniformly correlated source are presented and compared to the theory to test the new approach.

Time-evolving simulation of sources with partial spatial and temporal coherence is sometimes instructive or necessary to explain optical coherence effects. Yet, existing time-evolving synthesis techniques often require prohibitive amounts of computer memory. This paper discusses three methods for the synthesis of continuous or pulsed time-evolving sources with nearly arbitrary spatial and temporal coherence. One method greatly reduces computer memory requirements, making this type of synthesis more practical. The utility of all three methods is demonstrated via a modified form of Young's experiment. Numerical simulation and laboratory results for time-averaged irradiance are presented and compared with theory to validate the synthesis techniques.