{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T18:09:19Z","timestamp":1770228559430,"version":"3.49.0"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Active radar calibrators (ARCs), also known as calibration transponders, are often used as reference targets for the absolute radiometric calibration of radar systems due to their large radar cross-sections (RCSs). Before such a transponder can be used as a reference target, the hardware itself has to be calibrated. A novel method, called the three-transponder method, was proposed some years ago to allow for RCS calibration of digital transponders without using any known RCS targets as reference. The first part of this paper refines the technique and presents the measurement setup as well as the results of a comprehensive measurement campaign performed to calibrate a single digital transponder. In this part of the paper, the results are validated and a comprehensive uncertainty analysis is performed to estimate the total RCS uncertainty associated with the presented measurement data. This uncertainty analysis follows the international standard \u201cGuide to the expression of uncertainty in measurement\u201d (GUM) and will derive expressions for all major sources of uncertainty. For the validation, the measurement results will be compared with full-wave electromagnetic simulations of trihedral corner reflectors; there is excellent agreement between the simulation and measurements.<\/jats:p>","DOI":"10.3390\/rs15082148","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T01:42:39Z","timestamp":1681954959000},"page":"2148","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Highly Accurate Radar Cross-Section and Transfer Function Measurement of a Digital Calibration Transponder without Known Reference\u2014Part II: Uncertainty Estimation and Validation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0650-9073","authenticated-orcid":false,"given":"Jens","family":"Reimann","sequence":"first","affiliation":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V., Institut f\u00fcr Hochfrequenztechnik und Radarsysteme, 82234 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3827-7932","authenticated-orcid":false,"given":"Anna Maria","family":"B\u00fcchner","sequence":"additional","affiliation":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V., Institut f\u00fcr Hochfrequenztechnik und Radarsysteme, 82234 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4902-5551","authenticated-orcid":false,"given":"Sebastian","family":"Raab","sequence":"additional","affiliation":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V., Institut f\u00fcr Hochfrequenztechnik und Radarsysteme, 82234 Wessling, Germany"}]},{"given":"Klaus","family":"Weidenhaupt","sequence":"additional","affiliation":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V., Institut f\u00fcr Hochfrequenztechnik und Radarsysteme, 82234 Wessling, Germany"}]},{"given":"Matthias","family":"Jirousek","sequence":"additional","affiliation":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V., Institut f\u00fcr Hochfrequenztechnik und Radarsysteme, 82234 Wessling, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0045-3726","authenticated-orcid":false,"given":"Marco","family":"Schwerdt","sequence":"additional","affiliation":[{"name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e.V., Institut f\u00fcr Hochfrequenztechnik und Radarsysteme, 82234 Wessling, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1109\/TGRS.2012.2201946","article-title":"High-Precision Assessment and Calibration of Polarimetric RADARSAT-2 SAR Using Transponder Measurements","volume":"51","author":"Touzi","year":"2013","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1109\/TGRS.2017.2745206","article-title":"A Polarimetric Active Transponder With Extremely Large RCS for Absolute Radiometric Calibration of SMAP Radar","volume":"56","author":"Sarabandi","year":"2018","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/TGRS.2009.2035308","article-title":"Final TerraSAR-X Calibration Results Based on Novel Efficient Calibration Methods","volume":"48","author":"Schwerdt","year":"2010","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3053","DOI":"10.1109\/JLT.2016.2535487","article-title":"Digital Compensation of Bandwidth Limitations for High-Speed DACs and ADCs","volume":"34","author":"Napoli","year":"2016","journal-title":"J. Light. Technol."},{"key":"ref_5","unstructured":"Jirousek, M., D\u00f6ring, B., Rudolf, D., Raab, S., and Schwerdt, M. (2014, January 3\u20135). Development of the highly accurate DLR \u201cKalibri\u201d Transponder. Proceedings of the 10th European Conference on Synthetic Aperture Radar, Berlin, Germany."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cendes, Z. (July, January 26). The development of HFSS. Proceedings of the 2016 USNC-URSI Radio Science Meeting, Fajardo, PR, USA.","DOI":"10.1109\/USNC-URSI.2016.7588501"},{"key":"ref_7","first-page":"Nr\u2013171","article-title":"Erweiterte Momentenmethode zur Behandlung kompliziert aufgebauter und elektrisch grosser elektromagnetischer Steuprobleme","volume":"21","author":"Jakobus","year":"1995","journal-title":"Fortschrittsberichte VDI"},{"key":"ref_8","unstructured":"Raab, S., D\u00f6ring, B., Jirousek, M., Reimann, J., Rudolf, D., and Schwerdt, M. (2014, January 3\u20135). Comparison of Absolute Radiometric Transponder Calibration Strategies. Proceedings of the 10th European Conference on Synthetic Aperture Radar, Berlin, Germany."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rudolf, D., Raab, S., D\u00f6ring, B.J., Jirousek, M., Reimann, J., and Schwerdt, M. (2015, January 16\u201318). Absolute radiometric calibration of the novel DLR \u201cKalibri\u201d transponder. Proceedings of the 2015 German Microwave Conference, Nuremberg, Germany.","DOI":"10.1109\/GEMIC.2015.7107819"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Reimann, J., B\u00fcchner, A.M., Raab, S., Weidenhaupt, K., Jirousek, M., and Schwerdt, M. (2023). Highly Accurate Radar Cross-Section and Transfer Function Measurement of a Digital Calibration Transponder without Known Reference - Part I: Measurement and Results. Remote. Sens., 15.","DOI":"10.3390\/rs15041153"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"297","DOI":"10.2528\/PIERB14110406","article-title":"The Three-Transponder Method: A Novel Method for Accurate Transponder RCS Calibration","volume":"61","author":"Jirousek","year":"2014","journal-title":"Prog. Electromagn. Res. B"},{"key":"ref_12","unstructured":"Bureau International des Poids at Mesures (2008). Guide to the Expression of Uncertainty in Measurement, JCGM."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"128","DOI":"10.3390\/metrology2010009","article-title":"The GUM Tree Calculator: A Python Package for Measurement Modelling and Data Processing with Automatic Evaluation of Uncertainty","volume":"2","author":"Hall","year":"2022","journal-title":"Metrology"},{"key":"ref_14","unstructured":"(2023, April 14). Leica TS16 Data Sheet. Available online: https:\/\/leica-geosystems.com\/-\/media\/files\/leicageosystems\/products\/datasheets\/leica_viva_ts16_ds.ashx."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Doerry, A.W. (2008). Reflectors for SAR Performance Testing, Sandia National Laboratories. Technical Report SAND2008-0396.","DOI":"10.2172\/929123"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1214\/aoms\/1177729437","article-title":"Asymptotic Theory of Certain \u201cGoodness of Fit\u201d Criteria Based on Stochastic Processes","volume":"23","author":"Anderson","year":"1952","journal-title":"Ann. Math. Stat."},{"key":"ref_17","unstructured":"Raab, S., Doering, B.J., Rudolf, D., Reimann, J., and Schwerdt, M. (2016, January 6\u20139). Analysis of an Improved Temperature Management Concept for SAR System Calibration Transponders. Proceedings of the EUSAR 2016: 11th European Conference on Synthetic Aperture Radar, Hamburg, Germany."},{"key":"ref_18","unstructured":"(2023, April 14). R&S ZVA Vector Network Analyzer\u2014Operating Manual, Version 14.00 ed. Available online: https:\/\/www.rohde-schwarz.com\/webhelp\/zva_html_usermanual_en\/zva_html_usermanual_en.htm."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1109\/TGRS.2011.2162590","article-title":"Reference Target Correction Based on Point-Target SAR Simulation","volume":"50","author":"Doring","year":"2012","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1109\/TGRS.1984.350610","article-title":"Active Reflector for Radar Calibration","volume":"GE-22","author":"Brunfeldt","year":"1984","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_21","unstructured":"Raab, S., Schmidt, K., Weidenhaupt, K., Reimann, J., Buechner, A.M., and Schwerdt, M. (April, January 29). Absolute Radiometric Calibration of Broadband X-Band Transponders. Proceedings of the EUSAR 2021: 13th European Conference on Synthetic Aperture Radar, Online Event."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1109\/36.54363","article-title":"Synthetic aperture radar calibration using reference reflectors","volume":"28","author":"Gray","year":"1990","journal-title":"IEEE Trans. Geosci. Remote. Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/8\/2148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:18:55Z","timestamp":1760123935000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/8\/2148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,19]]},"references-count":22,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["rs15082148"],"URL":"https:\/\/doi.org\/10.3390\/rs15082148","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,19]]}}}