Reconstruction of long horizontal-path images under anisoplanatic conditions using multiframe blind deconvolution

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. This work explores the mean square error (MSE) performance of a multiframe blind deconvolution (MFBD) technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate, and severe turbulence conditions. Each set consisted of 1000 simulated turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. A Gaussian noise model-based MFBD algorithm reconstructs objects that showed as much as 40% improvement in MSE with as few as 14 frames and 30 Zernike coefficients used in the reconstruction, despite the presence of anisoplanatism in the data. An MFBD algorithm based on the Poisson noise model required a minimum of 50 frames to achieve significant improvement over the average MSE for the data set. Reconstructed objects show as much as 38% improvement in MSE using 175 frames and 30 Zernike coefficients in the reconstruction

Application of MFBD Algorithms to Image Reconstruction Under Anisoplanatic Conditions

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun-sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. My dissertation explores the performance of a multi-frame-blind-deconvolution technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios and compared to other speckle imaging techniques. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate and severe turbulence conditions. Each set consisted of 1000 simulated, turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. I will compare the mean-square-error (MSE) performance of speckle imaging methods and a maximum-likelihood, multi-frame blind deconvolution (MFBD) method applied to long-path horizontal imaging scenarios. Both methods are used to reconstruct a scene from simulated imagery featuring anisoplanatic turbulence induced aberrations. This comparison is performed over three sets of 1000 simulated images each for low, moderate and severe turbulence-induced image degradation. The comparison shows that speckle-imaging techniques reduce the MSE 46 percent, 42 percent and 47 percent on average for low, moderate, and severe cases, respectively using 15 input frames under daytime conditions and moderate frame rates. Similarly, the MFBD method provides, 40 percent, 29 percent, and 36 percent improvements in MSE on average under the same conditions. The comparison is repeated under low light conditions (less than 100 photons per pixel) where improvements of 39 percent, 29 percent and 27 percent are available using speckle imaging methods and 25 input frames and 38 percent, 34 percent and 33 percent respectively for the MFBD method and 150 input frames. The MFBD estimator is applied to three sets of field data and the results presented. Finally, a combined Bispectrum-MFBD Hybrid estimator is proposed and investigated. This technique consistently provides a lower MSE and smaller variance in the estimate under all three simulated turbulence conditions

Novel Methods in Computational Imaging with Applications in Remote Sensing

This dissertation is devoted to novel computational imaging methods with applications in remote sensing. Computational imaging methods are applied to three distinct applications including imaging and detection of buried explosive hazards utilizing array radar, high resolution imaging of satellites in geosynchronous orbit utilizing optical hypertelescope arrays, and characterization of atmospheric turbulence through multi-frame blind deconvolution utilizing conventional optical digital sensors. The first application considered utilizes a radar array employed as a forward looking ground penetrating radar system with applications in explosive hazard detection. A penalized least squares technique with sparsity-inducing regularization is applied to produce imagery, which is consistent with the expectation that objects are sparsely populated but extended with respect to the pixel grid. Additionally, a series of pre-processing steps is demonstrated which result in a greatly reduced data size and computational cost. Demonstrations of the approach are provided using experimental data and results are given in terms of signal to background ratio, image resolution, and relative computation time. The second application involves a sparse-aperture telescope array configured as a hypertelescope with applications in long range imaging. The penalized least squares technique with sparsity-inducing regularization is adapted and applied to this very different imaging modality. A comprehensive study of the algorithm tuning parameters is performed and performance is characterized using the Structure Similarity Metric (SSIM) to maximize image quality. Simulated measurements are used to show that imaging performance achieved using the pro- posed algorithm compares favorably in comparison to conventional Richardson-Lucy deconvolution. The third application involves a multi-frame collection from a conventional digital sensor with the primary objective of characterizing the atmospheric turbulence in the medium of propagation. In this application a joint estimate of the image is obtained along with the Zernike coefficients associated with the atmospheric PSF at each frame, and the Fried parameter r0 of the atmosphere. A pair of constraints are applied to a penalized least squares objective function to enforce the theoretical statistics of the set of PSF estimates as a function of r0. Results of the approach are shown with both simulated and experimental data and demonstrate excellent agreement between the estimated r0 values and the known or measured r0 values respectively

Saturation Behaviors in Deep Turbulence

Distributed-volume atmospheric turbulence near the ground significantly limits the performance of incoherent imaging and coherent beam projection systems operating over long horizontal paths. Defense, military and civilian surveillance, border security, and target identification systems are interested in terrestrial imaging and beam projection over very long horizontal paths, but atmospheric turbulence can blur the imagery and aberrate the laser beam such that they are beyond usefulness. While many post-processing and adaptive optics techniques have been developed to mitigate the effects of turbulence, many of these techniques do not work as expected in stronger volumetric turbulence, or in many cases don\u27t work at all. For these techniques to be effective or next generation techniques to be developed, a better theoretical understanding of deep turbulence is necessary. In an attempt to improve understanding of deep turbulence, this work explores the saturation behavior of two features of deep turbulence; the anisoplanatic error and the branch-point density. In this work, the behavior of the anisoplanatic error over long horizontal and slant paths, where the angular extent of the scene is many times greater than the isoplanatic angle, is characterized by developing generalized expressions for the total, piston-removed, and piston-and-tilt-removed anisoplanatic error in non-Kolmogorov turbulence with a finite outer scale. As an outcome of this work it can be concluded that in many cases the anisoplanatic error saturates to a value less than 1 rad$^2$. This means that while not actually infinite, the piston-removed and piston-and-tilt-removed isoplanatic angle is often significantly larger than expected. Additionally, power law exponent, outer scale size, scene geometry, and source model play a large part in determining the effective isoplanatic angle. The limit imposed on the system by the anisoplanatic error is much less severe than predicted by classical isoplanatic angle expression, but only if we include the interplay of piston and/or global tilt removal, a finite outer scale, accurate image formation models, and realistic turbulence profiles. Additionally, in this work wave-optics simulations are used to model the branch-point density as a function of turbulence strength, sampling grid resolution, and inner scale. Another outcome of this work is that increasing grid resolution and turbulence strength cause the branch-point density to grow without bound, when no inner scale is used. When a non-zero inner scale is used, via a Hill spectrum, the growth of the branch-point density is significantly reduced as a function of increasing Rytov variance and saturates as a function of increasing inner scale

proceedings of a workshop held at Göttingen September 27 - 29, 2006

An international workshop entitled: Modern Solar Facilities - Advanced Solar Science was held in Göttingen from September 27 until September 29, 2006. The workshop, which was attended by 88 participants from 24 different countries, gave a broad overview of the current state of solar research, with emphasis on modern telescopes and techniques, advanced observational methods and results, and on modern theoretical methods of modelling, computation, and data reduction in solar physics. This book collects written versions of contributions that were presented at the workshop as invited or contributed talks, and as poster contributions.Vom 27. bis 29. September 2006 fand in Göttingen ein internationaler Workshop zum Thema: Modern Solar Facilities - Advanced Solar Science statt, der von 88 Teilnehmern aus 24 verschiedenen Ländern besucht wurde und der einen breiten Überblick über den gegenwärtigen Stand der sonnenphysikalischen Forschung gab, unter Betonung moderner Teleskope und Techniken, fortschrittlicher Beobachtungsmethoden und Ergebnisse, sowie zu modernen theoretischen Verfahren der Modellierung, Berechnung und Datenreduktion in der Sonnenphysik. Dieser Band fasst die schriftlichen Versionen von Beiträgen zusammen, die auf der Konferenz als eingeladene oder angemeldete Vorträge, sowie als Posterbeiträge präsentiert worden sind.conferenc

Investigations of small-scale magnetic features on the solar surface

Solar activity is controlled by the magnetic field, which also causes the variability of the solar irradiance that in turn is thought to influence the climate on Earth. The magnetic field manifests itself in the form of structures of largely different sizes. This thesis concentrates on two types of the smallest known magnetic features: The first part studies the properties of umbral dots, dot-like bright features in the dark umbra of a sunspot. The obtained umbral dot properties provide a remarkable confirmation of the results of recent magneto-hydrodynamical simulations. Observations as well as simulations show that umbral dots differ from their surroundings mainly in the lowest photospheric layers, where the temperature is enhanced and the magnetic field is weakened. In addition, the interior of the umbral dots displays strong upflow velocities which are surrounded by weak downflows. This qualitative agreement further strengthens the interpretation of umbral dots as localized columns of overturning convection. The second part of the thesis investigates bright points, which are small-scale brightness enhancements in the darker intergranular lanes of the quiet Sun produced by magnetic flux concentrations. Observational data obtained by the balloon-borne solar telescope SUNRISE are used in this thesis. For the first time contrasts of bright points in the important ultraviolet spectral range are determined. A comparison of observational data with magneto-hydrodynamical simulations revealed a close correspondence, but only after effects due to the limited spectral and spatial resolution were carefully included. 98% of the synthetic bright points are found to be associated with a nearly vertical kilo-Gauss field.Comment: PhD thesis, Braunschweig University, 209 pages; ISBN 978-3-942171-73-1, uni-edition GmbH 201

Mean squared error performance of MFBD nonlinear scene reconstruction using speckle imaging in horizontal imaging applications

Terrestrial imaging over very long horizontal paths is increasingly common in surveillance and defense systems. All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. This paper explores the Mean-Square-Error (MSE) performance of a multi-frame-blind-deconvolution-based reconstruction technique using a non-linear optimization strategy to recover a reconstructed object. Three sets of 70 images representing low, moderate and severe turbulence degraded images were simulated from a diffraction limited image taken with a professional digital camera. Reconstructed objects showed significant, 54, 22 and 14 percent improvement in mean squared error for low, moderate, and severe turbulence cases respectively