Phase-based techniques to measure atmospheric turbulence have potential advantages when used over long ranges since they do not suffer from saturation issues as the irradiance-based techniques. The present work uses time-lapse imagery of a non-cooperative target from two spatially separated cameras to extract turbulence distribution along a path. By measuring the differential motion of pairs of extended features on the target, sensed by a single camera or between cameras, turbulence profiles can be obtained. Tracking the motion of extended features rather than point features allows estimation over a longer range. The approach uses a derived set of path weighting functions for differential tilt variances. The mathematical framework is discussed and the technique is applied to images collected of a multi-story building. Turbulence profiles over different slant paths are extracted from features at multiple levels of the building. This work will ultimately help in a better understanding of how turbulence varies with altitude in the surface layer.
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.
For effective turbulence compensation, especially in highly anisoplanatic scenarios, it is useful to know the turbulence distribution along a path. Irradiance-based techniques suffer from saturation when profiling turbulence over long ranges and hence alternate techniques are currently being explored. In an earlier work, a method to estimate turbulence parameters such as path weighted Cn2 and Fried’s coherence length r0 from turbulence induced random, differential motion of extended features in the time-lapse imagery of a distant target was demonstrated. A technique to measure the distribution of turbulence along an experimental path using the time-lapse imagery of a target from multiple cameras is presented in this work. The approach uses an LED array as target and two cameras separated by a few feet at the other end of the path imaging the LED board. By measuring the variances of the difference in wavefront tilts sensed by a single camera and between the two cameras due to a pair of LEDs with varying separations, turbulence information along the path can be extracted. The mathematical framework is discussed and the technique has been applied on experimental data collected over a 600 m approximately horizontal path over grass. A potentially significant advantage of the method is that it is phase based, and hence can be applied over longer paths. The ultimate goal of this work is to profile turbulence remotely from a single site using targets of opportunity. Imaging elevated targets over slant paths will help in better understanding how turbulence varies with altitude in the surface layer.