Estimation of atmospheric parameters from time-lapse imagery

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 n 2 , 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 r 0 (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 r 0 . If we presume C n 2 is constant along the path, then an estimate for r 0 can be obtained for each area tracked, but since the weighting function for r 0 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 r 0 . 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.

Block matching and Wiener filtering approach to optical turbulence mitigation and its application to simulated and real imagery with quantitative error analysis

“…The exact amount of underestimation will depend on the block size, the particular C 2 n ðzÞ profile, and optical parameters. 36,37 Notwithstanding this, we have found that a fixed block size of B ¼ 15 pixels is effective for the range of turbulence conditions used in the simulated imagery. Furthermore, our results show that the corresponding residual RMS tilt factor is approximately a constant β ¼ 0.1 in the simulated imagery.…”

“…Thus, any block-based estimate will tend to underestimate the true tilt for a given point, by virtue of the spatial averaging effect. 36,37 Thus, we define a partial tilt correction operator ass −1 k;α ðx; yÞ½•. Applying this to the SE frames, and applying an ensemble mean, yields E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 2 4 ; 6 3 ; 2 9 4 fðx; yÞ ¼ hs −1 k;α ðx; yÞ½f k ðx; yÞi ¼ g α ðx; yÞ Ã h SE ðx; yÞ Ã zðx; yÞ ¼ h α ðx; yÞ Ã zðx; yÞ: (24) This result gives the rational for using h α ðx; yÞ as the degradation blur model for fully or partially tilt corrected imagery.…”

“…However, with increased size, there tends to be an increased underestimation of the true local motion from atmospheric tilt. 36,37 Thus, a balance is required. The exact amount of underestimation will depend on the block size, the particular C 2 n ðzÞ profile, and optical parameters.…”

“…Estimating this parameter from observed imagery is an active area of research. 30,36,37 In some applications, it may be possible to set this parameter manually, based on subjective evaluation of the restoration results.…”

Application of tilt correlation statistics to anisoplanatic optical turbulence modeling and mitigation

“…Some image-based methods have been developed that use a standard camera with specialized targets or sources [12,13]. Other methods are scene-based and use only the natural imagery acquired by an imaging sensor [14][15][16][17][18][19][20]. Methods that explicitly address camera or scene motion include [9,21].…”