Estimation of atmospheric parameters from time-lapse imagery

Jack E. McCrae Jr.; Santasri Basu; Steven T. Fiorino

doi:10.1117/12.2223986

13 May 2016 Estimation of atmospheric parameters from time-lapse imagery

Jack E. McCrae Jr., Santasri Basu, Steven T. Fiorino

Proceedings Volume 9833, Atmospheric Propagation XIII; 983303 (2016) https://doi.org/10.1117/12.2223986
Event: SPIE Defense + Security, 2016, Baltimore, MD, United States

Abstract

A time-lapse imaging experiment was conducted to estimate various atmospheric parameters for the imaging path. Atmospheric turbulence caused 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 C_n², 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. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions can be derived which relate the turbulence strength along the path to the shifts measured. 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 presume C_n² is constant along the path, then an estimate for r⁰ can 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 this approach would yield a poor estimator. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore-Penrose pseudo-inverse to create a new weighting function which yields the least-squares optimal linear combination of measurements for estimation of r0. This approach is carried out, and it is observed that this approach is somewhat noisy because the pseudo-inverse assigns weights much greater than one to many of the observations.

Citation Download Citation

Jack E. McCrae Jr., Santasri Basu, and Steven T. Fiorino "Estimation of atmospheric parameters from time-lapse imagery", Proc. SPIE 9833, Atmospheric Propagation XIII, 983303 (13 May 2016); https://doi.org/10.1117/12.2223986

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