Estimation of turbulence from time-lapse imagery

Abstract

Abstract. Atmospheric turbulence parameters are estimated for an imaging path based on time-lapse imaging results. Atmospheric turbulence causes 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 2 n , 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 and averaged over the camera aperture. By presuming this turbulence follows the Kolmogorov spectrum, weighting functions, which relate the turbulence strength along the path to the shifts measured, are derived. 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 were to presume that C 2 n is constant along the path, then an estimate for r 0 could 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 that this approach would yield a poor estimate. Instead, the weighting functions for a number of different patch sizes can be combined through the Moore-Penrose pseudoinverse to create a weighting function that yields the least-squares optimal linear combination of measurements for the estimation of r 0 . This approach is carried out for one example and is shown to give noisy results. A modified version of this approach that creates larger patches by averaging several smaller patches together solves this noise issue. This approach can also work to estimate other atmospheric parameters. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Estimation of atmospheric turbulence using differential motion of extended features in time-lapse imagery

“…This technique was used in Ref. 10 to get an unbiased estimate of r 0 from the motion of image patches of two different sizes. Here it is shown that the weighting functions for differential patch-averaged tilt variances can be used to better reproduce the weighting functions for the spherical wave r 0 and a scintillometer.…”

“…Path-averaged C 2 n was estimated from turbulence-induced random motion of different parts of the building. 9,10 In this work, a scheme to directly estimate turbulence parameters such as pathweighted C 2 n and Fried's coherence diameter r 0 , from the differential motion of target features is described. The differential mode of measurement cancels the effect of any common mode disturbance such as platform vibrations.…”

“…The camera is at z ¼ 0 and the target is at z ¼ 7000 m.Optical Engineering104108-7 October 2018 • Vol. 57(10)…”

“…Differences in the two profiles are possibly due to estimation errors resulting from moving shadows and poor image contrast during early morning and late afternoon.Optical Engineering104108-8 October 2018 • Vol. 57(10)…”

“…Differences in the two profiles are possibly due to estimation errors resulting from moving shadows, contrast change in neighboring images due to changing cloud cover, and poor image contrast during early morning and late afternoon.Optical Engineering104108-9 October 2018 • Vol. 57(10) for that separation.For July 20, 12 patches of 1∕e diameter 16 cm (14 pixels) from different parts of the 4 target posters were used. This resulted in four pairs of patches of separation 1.16 m (100 pixels) and four pairs of patches with separation 4.79 m (412 pixels) from each image.…”