Refraction in the lower troposphere: Higher order image distortion effects due to refractive profile curvature

There are many applications that rely on the propagation of light through the atmosphere - all of which are subject to atmospheric conditions. While there are obvious processes such as scattering due to particulates like clouds and dust that affect the received intensity of the radiation, the clear atmosphere can also cause significant effects. Refraction is a clear air effect that can cause a variety of phenomena such as apparent relocation, stretching and compression of objects when viewed through the atmosphere.;Recently, there has been significant interest in studying the refractive effects for low angle paths within the troposphere, and in particular, near-horizontal paths in the Earth's boundary layer, which is adjacent to the ground. Refractive effects in this case become problematic for many terrestrial optical applications. For example, the pointing of a free space optical communication or a remote sensing system can suffer wandering effects, high-resolution imagery can present distorted and/or dislocated targets, optical tracking of targets can be inaccurate, and optical geodetic surveying accuracy is also very sensitive to the effects of refraction.;The work in this dissertation was inspired by data from a time-lapse camera system that collects images of distant targets over a near-horizontal path along the ground. This system was used previously to study apparent diurnal image displacement and this dissertation extends that work by exploring the higher order effects that result from curvature in the vertical refractive index profile of the atmosphere. There are surprisingly few experiments involving atmospheric refractive effects that carefully correlate field data to analytical expressions and other factors such as meteorological data. In working with the time-lapse data, which is comprised of sequences of hundreds or thousands of images collected over durations of weeks or months, it is important to develop straightforward analysis techniques that can be applied to characterize the refractive effects.;To help with the time-lapse image refraction analysis process, a second order ray trace scheme has been developed. The ray trace is based on existing lens system tracing procedures, but is adapted for use with the atmospheric refractivity profile. The standard practice of ray tracing uses linear approximations through each element to obtain a ray path, however, the method described in this dissertation uses a quadratic correction term in order to more accurately and efficiently simulate the curvature of rays as they propagate through a gradient refractive index medium such as the atmosphere. Although a variety of finite element solutions have been implemented to describe ray trajectories in nonlinear refractive mediums, the new ray tracer described here is much easier to implement and provides quick, intuitive results. The method is tested against exact analytical ray height solutions for known profiles and was found to give nearly identical results. The ray trace was then applied to real atmospheric data and was found to give plausible results. The tay trace gives a visual aid in understanding the physical path the light takes in traversing the potential field. This will be beneficial in linking optical data to weather model data in an effort to develop a forecasting model for refraction. By selecting the correct boundary and initial conditions, we are able to model rays through the profile. Understanding the system will ultimately help in later analysis.;A primary objective of this dissertation is to expand on the work mentioned above on image dislocation and consider the effects of towering (stretching) and stooping (compression) in the imagery. These effects can be explained as a type of lensing by the atmosphere due to nonlinear gradients. To achieve towering and stooping, a curved vertical index profile is required. Where a positive lensing action by the medium causes some ray focusing, back projection from at the arrival angles shows the target viewed by an observer will appear stretched, or magnified (towering). Conversely, with a negative lensing action the target viewed will appear shortened or compressed (stooping). The lensing can be modeled with a parabolic refractive index profile and the curvature of the profile is characterized by the curvature parameter alpha (units: m-1). The objective of chapter 4 is to estimate the curvature parameter from an analysis of the images collected by the camera system. In effect, the camera acts as a device that measures ray angle of arrival so image changes that appear as a stretch can be related to changes in the curvature of the index profile.;Time-lapse images of the F & A Dairy products building in Las Cruces, NM (15.3 km range from the camera at the NMSU campus) were analyzed using a manual cursor-marking MATLAB script developed for this project. For several different dates, we found the largest stretches occur in the morning. For example, a comparison of two morning images separated by an hour shows the apparent height of the building in a second image gained about 34 pixels compared to the first image. The refractive index curvature change for this case is calculated and found to be alpha = 6.0 x 10-5 m-1 . As the day progressed the image slowly compressed back to the early morning size.;Optical measurements of the local index of refraction profile of the atmosphere have been made in the past but usually only for isolated events or time periods. There is little data to describe occurrence probabilities, spatial or temporal properties, or relative strength of effects for different seasons, or even durations of weeks. In this dissertation, time-lapse image data from two separate weeks were analyzed for daily stretching/compressing events and presented graphically. The results show a systematic trend of dramatic size changes in the morning and a slow progression to normal building size as the day continues.;Using the optical data presented in chapter 5 and the method for determining a in chapter 4, a method using analytical expressions is presented for determining the refractivity. After a solution is found, two checks are done to test the validity of the results. The first check is simulated in a ray trace model to verify the results are physically relevant and produce rays that can plausibly lead to the correct apparent building size. The second check is a comparison of the estimated gradient index profile from the inversion with the values of the numerical weather model.;Using the data from week of November 2014, a day from October 2014, and a day from the March 2015, the optical data was inverted to solve for the refractivity constants dh and z in order to recreate an approximate refractivity profile responsible for the observed stretching. Example values found for the constants are dh=21.49m and z=30m for November 26, 2014. The profile that is created by these constants was found to be fairly consistent with available weather model data.