A technique for profiling of C over an atmospheric propagation path is proposed, developed and analyzed. The technique employs differential-tilt measurements to arrive at statistics which have unique weighting functions over the propagation path. These weighting functions are computed theoretically and used to derive a reconstructor matrix for C values throughout the path to be applied to an appropriate set of differential-tilt statistics. A candidate optical system is presented, and the performance of the profile reconstructor is analyzed. This study indicates that the relative error in the C estimates is approximately 5%. The relative error in estimating key atmospheric parameters such as the Fried parameter, isoplanatic angle, and the Rytov parameter from the reconstructed profiles is approximately 3%.

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We present a new approach for analyzing local power law processes and apply it to temperature measurements from the upper atmosphere. We segment the data and use the wavelet scale spectrum to estimate the parameters of the power law, the scale factor and the exponent. These parameters vary from segment to segment. Part of this variation is due to the non-stationarity of the data. Another part is due to estimation errors that depend on the segmentation. In this paper show h o w to remove e ectively these segmentation dependent v ariations.

The problem described in this paper deals with tracking the optical path perturbations introduced by the atmosphere when illuminating a target (missile) with laser light. Due to atmospheric irregularities, the optical path from an observer to an in-flight missile deviates from a straight line, and also changes in time. If the goal of the system is to point a laser beam at a specific point (or area) of the missile body for a given period of time, these optical path variations should be 'tracked' and compensated when pointing the laser beam. The laser beam should be pointed, not to the 'true' but to the 'apparent' location of the desired spot. In the actual system, the missile is illuminated with several lasers (forming a broad beam) , and an image of the missile (distorted through the atmosphere) is obtained from the backscattered light. This image contains all the information available about the optical path.The purpose of the work presented here is to estimate the 'apparent' location of five different spots of the missile (distributed evenly along the longitudinal axis, from the nose up to mid-body) from the backscattered images and 'a-priori' information that includes the size and speed of the missile. The data available is high-fidelity simulated data, and the apparent locations of the desired spots (over time) are known. Two approaches are considered here. The first approach is based on breaking the problem into two parts: a measurement part and an estimation part. For the measurement part, a Neural Network is used to 'infer' a mapping from the image to the apparent location of the points of interest (known for the simulated data). Those 'measured' locations are then used by a Kalman filter to estimate the apparent locations. The Kalman filter exploits the fact that the optical paths (from different spots along the longitudinal axis) are correlated in time. This correlation is caused by the missile's displacement through the atmosphere. The second approach is to compute the centroids of the images and use the resulting points as estimates of the apparent location of a point on the missile.For the first approach, simulation results show a noticeable decrease in the rms error of the apparent location estimates when compared to the 'average' location (mean value) . The second approach, while simple, was found to perform quite well.