{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/41910"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/41910","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Rough surface scattering under Gaussian beam illumination and the Kirchhoff approximation","abstract":"In this thesis, an analysis of the scattering of a rough perfect electric conductor (PEC) surface under illumination by a Gaussian beam using the Kirchhoff approximation is presented. The analysis assumes a source distribution which yields a Gaussian beam solution as a radiated field. This field is used to excite a current density on the surface using the Kirchhoff approximation. A vector potential approach utilizes this current to calculate the fields scattered by the surface. The analysis is carried out for the backscatter case and near-normal incidence in order to reduce the final numerical evaluation to a two-dimensional integration. The normalized radar cross-section (NRCS) is calculated and compared with the result for plane wave illumination. The analysis explores the effects of varying the source aperture size, rough surface correlation length and rms height on the NRCS. An asymptotic evaluation of the mean squared field is presented, as well as the mathematical form of the fourth moment of the scattered field. As a further study, the NRCS of a rough surface under a Gaussian tapered plane wave illumination is presented. The interplay of the beam spot and correlation length for such illuminated surfaces is discussed.","abstract_html":"In this thesis, an analysis of the scattering of a rough perfect electric conductor (PEC) surface under illumination by a Gaussian beam using the Kirchhoff approximation is presented. The analysis assumes a source distribution which yields a Gaussian beam solution as a radiated field. This field is used to excite a current density on the surface using the Kirchhoff approximation. A vector potential approach utilizes this current to calculate the fields scattered by the surface. The analysis is carried out for the backscatter case and near-normal incidence in order to reduce the final numerical evaluation to a two-dimensional integration. The normalized radar cross-section (NRCS) is calculated and compared with the result for plane wave illumination. The analysis explores the effects of varying the source aperture size, rough surface correlation length and rms height on the NRCS. An asymptotic evaluation of the mean squared field is presented, as well as the mathematical form of the fourth moment of the scattered field. As a further study, the NRCS of a rough surface under a Gaussian tapered plane wave illumination is presented. The interplay of the beam spot and correlation length for such illuminated surfaces is discussed.","abstract_has_math":false,"creators":["Tyeryar, Keith Allen"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Electrical Engineering","degree_department":"Electrical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1993,"date_issued":"1993","date_published":"1993","updated_at":"2026-07-22T22:20:23Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04072009-040449"],"render_values":[{"text":"etd-04072009-040449","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/41910","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Electrical Engineering"]},{"key":"dc:creator","label":"Author","values":["Tyeryar, Keith Allen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:32:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:32:49Z","2009-04-07"]},{"key":"dc:date.issued","label":"Date","values":["1993"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04072009-040449"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/41910"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, an analysis of the scattering of a rough perfect electric conductor (PEC) surface under illumination by a Gaussian beam using the Kirchhoff approximation is presented. The analysis assumes a source distribution which yields a Gaussian beam solution as a radiated field. This field is used to excite a current density on the surface using the Kirchhoff approximation. A vector potential approach utilizes this current to calculate the fields scattered by the surface. The analysis is carried out for the backscatter case and near-normal incidence in order to reduce the final numerical evaluation to a two-dimensional integration. The normalized radar cross-section (NRCS) is calculated and compared with the result for plane wave illumination. The analysis explores the effects of varying the source aperture size, rough surface correlation length and rms height on the NRCS. An asymptotic evaluation of the mean squared field is presented, as well as the mathematical form of the fourth moment of the scattered field. As a further study, the NRCS of a rough surface under a Gaussian tapered plane wave illumination is presented. 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