{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/45603"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/45603","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A comparison and study of the Born and Rytov expansions","abstract":"Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty years ago, a controversy has boiled over the regions of validity and relative merits of the methods. Although the methods fail for strong fluctuations and distant path lengths, these two perturbation methods are the only approaches available for weak fluctuations in a random in homogeneous media. The approximations have also been applied to the inverse problem for optical and acoustical tomography. The intent of this thesis is to investigate the work of previous authors and attempt to clarify the distinctions of each method. The conclusion will be reached that neither approximation is necessarily better than the other in general for all applications. A careful consideration of the problem following the points given should point towards the use of one approximation over the other.","abstract_html":"Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty years ago, a controversy has boiled over the regions of validity and relative merits of the methods. Although the methods fail for strong fluctuations and distant path lengths, these two perturbation methods are the only approaches available for weak fluctuations in a random in homogeneous media. The approximations have also been applied to the inverse problem for optical and acoustical tomography. The intent of this thesis is to investigate the work of previous authors and attempt to clarify the distinctions of each method. The conclusion will be reached that neither approximation is necessarily better than the other in general for all applications. A careful consideration of the problem following the points given should point towards the use of one approximation over the other.","abstract_has_math":false,"creators":["Bruce, Matthew F."],"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":["de Wolf, David A."],"committee_members":["Besieris, Ioannis M.","Kohler, Werner E."],"year":1993,"date_issued":"1993-08-19","date_published":"1993-08-19","updated_at":"2026-07-22T22:20:16Z","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-11102009-020128"],"render_values":[{"text":"etd-11102009-020128","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/45603","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["de Wolf, David A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Besieris, Ioannis M.","Kohler, Werner E."]},{"key":"dc:contributor.department","label":"Department","values":["Electrical Engineering"]},{"key":"dc:creator","label":"Author","values":["Bruce, Matthew F."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:49:24Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:49:24Z","2009-11-10"]},{"key":"dc:date.issued","label":"Date","values":["1993-08-19"]},{"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-11102009-020128"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/45603"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty years ago, a controversy has boiled over the regions of validity and relative merits of the methods. Although the methods fail for strong fluctuations and distant path lengths, these two perturbation methods are the only approaches available for weak fluctuations in a random in homogeneous media. The approximations have also been applied to the inverse problem for optical and acoustical tomography. The intent of this thesis is to investigate the work of previous authors and attempt to clarify the distinctions of each method. The conclusion will be reached that neither approximation is necessarily better than the other in general for all applications. A careful consideration of the problem following the points given should point towards the use of one approximation over the other."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A comparison and study of the Born and Rytov expansions"]}]}],"canonical_facts":{"dc:contributor.committeechair":["de Wolf, David A."],"dc:contributor.committeemember":["Besieris, Ioannis M.","Kohler, Werner E."],"dc:contributor.department":["Electrical Engineering"],"dc:creator":["Bruce, Matthew F."],"dc:date.accessioned":["2014-03-14T21:49:24Z"],"dc:date.available":["2014-03-14T21:49:24Z","2009-11-10"],"dc:date.issued":["1993-08-19"],"dc:description.abstract":["Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty years ago, a controversy has boiled over the regions of validity and relative merits of the methods. 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