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Constrained by practical and economical considerations, one often uses seismic data with missing traces. The use of such data results in image artifacts and poor spatial resolution. Sometimes due to practical limitations, measurements may be available on a perturbed grid, instead of on the designated grid. Due to algorithmic requirements, when such measurements are viewed as those on the designated grid, the recovery procedures may result in additional artifacts. This paper interpolates incomplete data onto regular grid via the Fourier domain, using a recently developed greedy algorithm. The basic objective is to study experimentally as to what could be the size of the perturbation in measurement coordinates that allows for the measurements on the perturbed grid to be considered as on the designated grid for faithful recovery. Our experimental work shows that for compressible signals, a uniformly distributed perturbation can be offset with slightly more number of measurements.

Optical Confocal Holography is a combination of two well known concepts: confocal microscopy and optical (laser) holography. Confocal microscopy places an aperture at a conjugate focus to the specimen focus. This filters any rays that are not on the focus plane, allowing a 3-dimensional image of the specimen to be built up over a set of planes. Holography is the measurement of both the amplitude and phase characteristics of light. Typically most methods only measure the amplitude of the image. The phenomenon of interference allows the determination of the phase shift for a coherent source as well. The phase information is directly related to the index of refraction of a material, which in turn is a function of the temperature and composition. As a technique, confocal holography holds promise to better characterize many physical processes in materials science, such as combustion and convection. It also may contribute to the biological sciences by imaging low-contrast, weak-phase objects. Thanks to the ongoing, continued improvement in computer processing speed, it has recently become practical to interpret data from confocal holography microscopy with a computer. The objective of the microscope is to non-invasively measure the three-dimensional, internal temperatures and compositions (e.g. solute/solvent gradient) of a specimen. My contributions over the course of two years to the project were: generation and optimization of an optical design with a software package known as Zemax; sourcing and purchasing all components; formation of a CAD model of the microscope; experiments to characterize building vibrations and air currents; and the development of software in Visual Basic to simulate holograms and execute reconstruction algorithms for the specific application of confocal holography.

No description available.