Atmospheric refraction: Applied image analysis and experimental example for index profile with curvature

Abstract

In this work we consider atmospheric refractive bending and its effects on long-range imaging along a horizontal path. Refraction can impact the ability of a remote sensing or image system to accurately locate objects and determine their apparent proportions. We use a low-cost commercial camera operating in a time-lapse mode for refraction studies and have been recording images of a building that is 15.3 km west of the camera. Based on the paraxial ray equation, a solution for ray height and angle is obtained for a refractive index profile with curvature. A curved index profile can produce the effects of towering (stretching) and stooping (compression). The curvature parameter for the average atmospheric index profile between the camera and target can be derived from an analysis of the images collected by the camera system. We show example images where the building (33 m height) appears to stretch by 5.1 m and calculate a refractive index curvature parameter of 6.0x10 -5 m -2 .

Long-range propagation through inhomogeneous turbulent atmosphere: analysis beyond phase screens

“…It is an oversimplification, however, to assume that changes in the mean refractive index always correspond to larger-scale variations. For example, there is evidence that curvature features of certain sections of the vertical refractive index profile on the order of meters occur consistently at the same time of day and therefore may be considered deterministic and predictable [33,34]. On the other hand, turbulence gives rise to refractive index fluctuations over a wide range of scales.…”

“…As mentioned above, one may be able to predict and resolve the curvature of certain parts of the refractive index profile. In [33,34], the value of the curvature of the vertical refractive index profile in a region within about ten meters of the ground was deduced from measurements of the resulting apparant stretching of a building in time-lapse photographic images. While the profile changed significantly over the course of a day, the largest stretch for each day typically occurred at the same time of day, and the corresponding value of the curvature parameter was consistent over a five day period.…”

A Mitigation Method for Optical-Turbulence-Induced Errors and Optimal Target Design in Vision-Based Displacement Measurement

“…Thus, it will lose the structure’s real displacement information if it is applied for computer-based vision displacement measurement and reduce its accuracy. The second category relies on a stable background and uses fixed background objects as a reference, e.g., buildings, mountains, and bridge piers, of the image presenting the monitoring structure, thus mitigating the measurement error induced by optical turbulence in visual displacement measurements [ 21 , 22 , 23 ]. However, such a strategy is difficult to implement in practical engineering applications, as the optical turbulence increases with the measurement distance [ 24 ], making it difficult to find a stationary object in or near the same plane of the structure as a reference background.…”

Image shift due to atmospheric refraction: prediction by numerical weather modeling and machine learning

“…5 A similar system in Dayton, Ohio, was used by Basu et al 4 to investigate the temporal variations of the refractive index gradient. Time-lapse imagery has also been used to investigate the apparent stretch and compression of objects due to atmospheric refraction lensing effects 6 and the approach has also been applied to the estimation of turbulence strength. 7 The prediction of atmospheric refraction effects can be advantageous for many terrestrial optical applications where prior knowledge of the light's trajectory can improve the speed and accuracy of pointing and tracking functions.…”