Ph.D Thesis

Ph.D StudentSchwierz-Yosefzon Tatyana
SubjectTomography of a Product from a Projection: Influence of
Deviations of Ideal Symmetry
DepartmentDepartment of Quality Assurance and Reliability
Supervisors PROFESSOR EMERITUS Amos Notea
PROF. Moshe Deutsch


The increase importance of measuring systems for monitoring product quality in industry emphasizes the need for a general approach for characterization and optimal design. For this end Tomographic system is a highly desired measuring unit. The amount of information obtained by a tomographic image highly depends on the number of exposures or projections. In many cases, tomography based on a single projection is the only possibility. By applying Abel transform the linear attenuation coefficient distribution within the objects is attainable from a single projection radiography.

In the present study Abel transform was "extended" to reconstruct tomogrphic images for objects with shapes deviating from the cylindrical symmetry.

Two innovative methods for the reconstruction were developed, an analytical transform and a numerical approach (a recursive onion-peeling method). The methods were demonstrated for bi-parabolic hexagonal, triangular, rhombus and rectangular shape symmetry objects. The onion-peeling method was developed for objects whose cross section is representable by peels of constant density.

A generalized resolving power (r.p.) for measuring systems with complex reconstruction interpretational algorithms was developed. The advantage of this generalized r.p. is that knowledge of both the standard deviation and the analytical expression for the system response function is not required.

The developed methods are of the working-solution type. They were demonstrated on radiographic images generated by a microfocus system composed of a microfocus X-rays source, an image intensifier and 7 axial robot. The methods provide a logical and systematic approach to obtain the optimal design parameters of the system, limits of detection, resolving power, etc.