Whilst the underlying mechanisms of atmospheric turbulence are complex, the observed effects on imaging can be described in simpler terms. In this thesis, I address the effects seen as geometric distortions in anisoplanatic imaging and propose new digital restorations techniques that are real-time capable and predictive. The anisoplanatic problem arises in wide-field telescopic imaging and in new ventures of astronomy such as giant telescopes that process wide-field imagery. The methods proposed here, both digital and digital-optical hybrid, remove the position dependent distortions as a precursor to image analysis. Previous existing digital restoration techniques have used a prototype formed by averaging an image time sequence for image registration where valuable high frequencies information is lost due to the low-pass filtering effect of averaging. The proposed techniques are capable of using any arbitrary frame in the sequence as prototype, thus circumventing the low pass filtering effect and also allowing real-time implementation. Furthermore, these techniques are made predictive by the use of Kalman filtering. The predictive capabilities of these techniques open a new path to the combination of digital processing and adaptive optics that can result in hybrid systems. The key to adoption of hybrid systems is to reduce the complexity and expense of the optics and couple this with digital processing prediction. To this end I also propose a new type of inexpensive and fast piezoelectric deformable mirror based on the vibration modes of circular PVDF membranes that exhibit striking similarities to Zernike polynomials. It requires only two electrodes for actuation and a very simple driving signal generator, therefore constituting an inexpensive and viable alternative to existing deformable mirrors. With the emergence of multi-conjugate adaptive optics (MCAO) and multiobject adaptive optics (MOAO) in astronomy, and the more demanding correction required for long range surveillance imaging, this inexpensive deformable mirror and the real-time capable digital algorithms are promising building blocks for a hybrid solution to the anisoplanatic imaging problem.

The use of efficient basis functions to model and represent flows with internal sharp velocity gradients, such as shocks or eddy microfronts, are investigated. This is achieved by analysing artificial data, observed atmospheric turbulence data and by the use of a Burgers' equation based spectral model. The concept of an efficient decomposition of a function into a basis set is presented and alternative analysis methods are investigated. The development of a spectral model using a generalized basis for the Burgers' equation is presented and simulations are performed using a modified Walsh basis and compared with the Fourier (trigonometric) basis and finite difference techniques. The wavelet transform is shown to be superior to the Fourier transform or the windowed Fourier transform in terms of defining the predominant scales in time series of turbulent shear flows and in 'zooming in' on local coherent structures associated with sharp edges. Disadvantages are found to be its inability to provide clear information on the scale of periodicity of events. Artificial time series of varying amounts of noise added to structures of different scales are analyzed using different wavelets to show that the technique is robust and capable of detecting sharp edged coherent structures such as those found in shear driven turbulence. The Haar function is used as a wavelet to detect ubiquitous zones of concentrated shear in turbulent flows sometimes referred to as microfronts. The location and organization of these shear zones suggest that they may be edges of larger scale eddies. A wavelet variance of the wavelet phase plane is defined to detect and highlight events and obtain measures of predominant scales of coherent structures. Wavelet skewness is computed as an indicator of the systematic sign preference of the gradient of the transition zone. Inverse wavelet transforms computed at the dilation corresponding to the peak wavelet variance are computed and shown to contain a significant fraction of the total energy contained in the record. The analysis of data and the numerical simulation results are combined to propose that the sharp gradients normally found in shear induced turbulence significantly affect the nature of the turbulence and hence the choice of the basis set used for the simulation of turbulence. / Graduation date: 1991

The statistics describing variations of turbulent motions within the so called inertial range of length scales depend on the scale over which the motions are varying and the "average" rate at which the turbulent kinetic energy is being dissipated on the molecular scale. This hypothesis stemmed from the similarity arguments published by A. N. Kolmogorov in 1941 and implies specific scaling relations between the average amplitude and length scale of turbulent motions. Turbulent motions agree to a good approximation with Kolmogorov scaling provided the fluid flow admits to the underlying assumptions. More recently it has been recognized that the large spatial variations in the rate of turbulent kinetic energy dissipation may be a partial explanation for deviations from Kolmogorov scaling. This recognition is due in part to the observation that the total volume occupied by turbulent motions of a given scale decreases as the scale decreases. These observations imply that active small scale turbulence is intermittent. This study aims to better understand how scaling relations describing more active regions are different from the relations describing turbulence where the small scales are less active. The thesis is that the relations are different. An 18 hour segment of wind data measured in near-neutral stratification 45 meters above a relatively flat ground is analyzed. There is virtually no trend in the mean wind speed, so the describing statistics are essentially stationary. Small scale activity is measured in terms of the difference in wind speed (structure function) at a separation distance of 1/16 of a second, which translates to about a meter. The differences in wind speed are raised to the sixth power and then averaged over 4 second (50 meter) windows. Non-overlapping windows containing a local maximum in the averaged sixth order structure function form one (MASC) ensemble of more active small scale samples and the local minima form another (LASC) ensemble of less active small scale samples. The variations in wind speed as a function of length scale within each ensemble are decomposed five different ways. Each of the five decompositions obey scaling relationships that are approximately linear in log-log coordinates. The MASC and LASC ensembles include 32% and 46% of the record, respectively. The turbulent kinetic energy as a function of scale falls off at a slower rate in the MASC ensemble versus the LASC ensemble and in magnitude the energy is greater at all scales in the MASC ensemble. This implies the transfer rate of turbulent kinetic energy toward small scales is more rapid on average in the MASC samples. Samples in the MASC ensemble occupied 30% less of the record, implying the flattening effect on the spectral slope exhibited by the samples contained in the MASC ensemble is less influential than the steepening influence of samples of the type in the LASC ensemble. The results are robust with respect to the choice of a basis set in representing the variance as a function of scale. / Graduation date: 1994

Also issued as a Ph.D. thesis in the Dept. of Electrical Engineering, 1971. / Bibliography: p. 93-95.

In this thesis work, the background of atmospheric turbulence degradation in imaging was reviewed and two aspects are highlighted: blurring and geometric distortion. The turbulence burring parameter is determined by the atmospheric turbulence condition that is often unknown; therefore, a blur identification technique was developed that is based on a higher order statistics (HOS). It was observed that the kurtosis generally increases as an image becomes blurred (smoothed). Such an observation was interpreted in the frequency domain in terms of phase correlation. Kurtosis minimization based blur identification is built upon this observation. It was shown that kurtosis minimization is effective in identifying the blurring parameter directly from the degraded image. Kurtosis minimization is a general method for blur identification. It has been tested on a variety of blurs such as Gaussian blur, out of focus blur as well as motion blur. To compensate for the geometric distortion, earlier work on the turbulent motion compensation was extended to deal with situations in which there is camera/object motion. Trajectory smoothing is used to suppress the turbulent motion while preserving the real motion. Though the scintillation effect of atmospheric turbulence is not considered separately, it can be handled the same way as multiple frame denoising while motion trajectories are built.

The turbulent atmosphere degrades images of objects viewed through it by introducing random amplitude and phase errors into the optical wavefront. Various methods have been devised to obtain true images of such objects, including the shift-and-add method, which is examined in detail in this work. It is shown theoretically that shift-and-add processing may preserve diffraction-limited information in the resulting image, both in the point source and extended object cases, and the probability of ghost peaks in the case of an object consisting of two point sources is discussed. Also, a convergence rate for the shift-and-add algorithm is established and simulation results are presented. The combination of shift-and-add processing and Wiener filtering is shown to provide excellent image restorations.

M. Tech. Electrical Engineering. / Aims to perform a comparative analysis of algorithms developed to restore sequences degrade by the effects of atmospheric turbulence with the focus placed on the removal of heat scintillation.

No description available.

No description available.

The Coriolis force has a subtle, but significant impact on the dynamics of geophysical and astrophysical flows. The Rossby number, Ro, is the nondimensional parameter measuring the relative strength of the Coriolis term to the nonlinear advection terms in the equations of motion. When the rotation is strong, Ro goes to zero and three-dimensional flows are observed to two-dimensionalize. The broad aim of this work is to examine the effect of the strength of rotation on the nonlinear dynamics of turbulent homogeneous flows. Our approach is to decompose the rotating turbulent flow modes into two classes: the zero-frequency 2-dimensional (2D) modes; and the high-frequency inertial waves (3D). / First, using numerical simulations of decaying turbulence over a large range of Ro we identified three regimes. The large Ro regime is similar to non-rotating, isotropic turbulence. The intermediate Ro regime shows strong 3D-to-2D energy transfers and asymmetry between cyclones (corotating) and anticyclones (couter-rotating), whereas at small Ro regime these features are much reduced. / We then studied discreteness effects and constructed a kinematic model to quantify the threshold of nonlinear broadening below which the 2D-3D interactions critical to the intermediate Ro regime are not captured. These results allow for the improvement of numerical studies of rotating turbulence and refine the comparison between results obtained in finite domains and theoretical results derived in unbounded domains. / Using equilibrium statistical mechanics, we examined the hypothesis of decoupling predicted in the small Ro regime. We identified a threshold time, t☆ = 2/Ro2, after which the asymptotic decoupling regime is no longer valid. Beyond t ☆, we show that the quasi-invariants of the decoupled model continue to constrain the system on the short timescales. / We found that the intermediate Ro regime is also present in forced turbulence and that interactions responsible for it are nonlocal. We explain a steep slope obtained in the 2D energy spectrum by a downscale enstrophy transfer. The energy of the 2D modes is observed to accumulate in the largest scales of the domain in the long-time limit. This is reminiscent of the "condensation" observed in classical forced 2D flows and magnetohydrodynamics.