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Relations Between 3- and 4- Vectors and 3 x 3 and 4 x 4 Matrices

Boerner, Wolfgang-Martin and Danklmayer, Andreas and Mott, Harold and Cloude, Shane, R. (2006) Relations Between 3- and 4- Vectors and 3 x 3 and 4 x 4 Matrices. In: Proceeding of the International Workshop on Electromagnetic Wave Scattering (EWS), 11-13-11-24. International Workshop on Electromagnetic Wave Scattering (EWS), 2006-09-18 - 2006-09-22, Gebze, Turkey.

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In one of his last manuscripts Ernst Lüneburg stared at a systematic investigation between 3- and 4- vectors and the various matrix representations occurring in optical and radar polarimetry motivated by Prof. Mott´s exposition about the characteristic features and differences between Kronecker matrices, Kennaugh matrices and 3 x 3 and 4 x 4 covariance matrices. Although the development of this important transformation appears to have taken a long time to be accepted, first results described in this contribution by Ernst Lüneburg are rather promising. The considerations start with the Sinclair or Jones matrix of a coherent target in the linear (x, y) polarization basis and are focusing on the normalized voltage and power equations, knowing well that the optical brightness or radar voltage equations, respectively, are considered to be the cornerstone equations in optical and radar polarimetry. From the preliminary conclusions it appears that the covariance matrix formulation (as 4 x 4 and 3 x 3 matrix) is unable to produce any assessment about optimal power reception even in the coherent scatter case. This is quite in contrast to the Mueller/Kennaugh matrix formulation that involves the same second order matrix elements, but enables one to derive the optimal power reception polarization states.

Item URL in elib:https://elib.dlr.de/45236/
Document Type:Conference or Workshop Item (Paper, Poster)
Title:Relations Between 3- and 4- Vectors and 3 x 3 and 4 x 4 Matrices
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Boerner, Wolfgang-MartinUniversity of Chicago, UIC-ECE Communications, Sensing & Navigation Laboratory, USAUNSPECIFIED
Mott, HaroldUniversity of Alabama at TuscaloosaUNSPECIFIED
Cloude, Shane, R.AEL Consultants, UKUNSPECIFIED
Date:September 2006
Journal or Publication Title:Proceeding of the International Workshop on Electromagnetic Wave Scattering (EWS)
Refereed publication:No
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
Page Range:11-13-11-24
Gebze Institute of Technology, UNSPECIFIED
Keywords:Radar Polarimetry
Event Title:International Workshop on Electromagnetic Wave Scattering (EWS)
Event Location:Gebze, Turkey
Event Type:international Conference
Event Dates:2006-09-18 - 2006-09-22
Organizer:Gebze Institut of Technology
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W EO - Erdbeobachtung
DLR - Research area:Space
DLR - Program:W EO - Erdbeobachtung
DLR - Research theme (Project):W - Vorhaben SAR-Expert-Support-Lab (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Microwaves and Radar Institute > Microwave Systems
Microwaves and Radar Institute
Deposited By: Danklmayer, Dr.-Ing. Andreas
Deposited On:30 Oct 2006
Last Modified:27 Apr 2009 13:12

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