Estimation of Fried's Coherence Diameter from Differential Motion of Features in Time-lapse Imagery

Abstract

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.