Many problems in physics involve imaging objects with high spatial frequency content in a limited amount of time. The limitation of available experimental data leads to the infamous problem of diffraction limited data which manifests itself by causing ringing in the image. This ringing is due to the interference phenomena in optics and is known as the Gibbs phenomenon in engineering. Present techniques to cope with this problem include filtering and regularization schemes based on minimum norm or maximum entropy constraints. In this paper, a new technique based on object modeling and estimation is developed to achieve superresolution reconstruction from partial Fourier transform data. The nonlinear parameters of the object model are obtained using the singular value decomposition (SVD)-based all-pole model framework, and the linear parameters are determined using a standard least squares estimation method. This technique is capable, in principle, of unlimited resolution and is robust with respect to Gaussian white noise perturbation to the measured data and with respect to systematic modeling errors. Reconstruction results from simulated data and real magnetic resonance data are presented to illustrate the performance of the proposed method.
The details of a model used to predict the scattering of a plane polarized wave by a spherical particle as observed with a microscope are presented. The model accounts for the effect of a refractive interface on the outgoing scattered field and determines the image produced by a lens with high numerical aperture. The predictions of the model are verified by direct comparison with the experimentally observed scattering from polystyrene spheres in a fluid.
A light extinction tomography technique has been developed to monitor ice water clouds upstream of a direct connected engine in the Propulsion Systems Laboratory (PSL) at NASA Glenn Research Center (GRC). The system consists of 60 laser diodes with sheet generating optics and 120 detectors mounted around a 36-inch diameter ring. The sources are pulsed sequentially while the detectors acquire line-of-sight extinction data for each laser pulse. Using computed tomography algorithms, the extinction data are analyzed to produce a plot of the relative water content in the measurement plane. To target the low-spatial-frequency nature of ice water clouds, unique tomography algorithms were developed using filtered backprojection methods and direct inversion methods that use Gaussian basis functions. With the availability of a priori knowledge of the mean droplet size and the total water content at some point in the measurement plane, the tomography system can provide near real-time in-situ quantitative full-field total water content data at a measurement plane approximately 5 feet upstream of the engine inlet. Results from ice crystal clouds in the PSL are presented. In addition to the optical tomography technique, laser sheet imaging has also been applied in the PSL to provide planar ice cloud uniformity and relative water content data during facility calibration before the tomography system was available and also as validation data for the tomography system. A comparison between the laser sheet system and light extinction tomography resulting data are also presented. Very good agreement of imaged intensity and water content is demonstrated for both techniques. Also, comparative studies between the two techniques show excellent agreement in calculation of bulk total water content averaged over the center of the pipe.
In the context of helical cone-beam CT, Danielsson et al. discovered that for each point interior to the cylindrical surface containing a given helix, there is exactly one line segment passing through the point which intersects two points less than one turn apart on the helix. This segment is called a π-line. A new constructive algebraic proof of this result is presented along with a fast algorithm to compute the endpoints of the π-line through an arbitrary point in the interior of the helix cylinder. This proof exposes the geometry of the decomposition of a cylinder interior as a disjoint union of π-lines.
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