{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:27:33Z","timestamp":1760146053420,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T00:00:00Z","timestamp":1727308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the french national research council (CNRS)","award":["R-S24\/OT-0003-101-01"],"award-info":[{"award-number":["R-S24\/OT-0003-101-01"]}]},{"name":"the french space agency (CNES)","award":["R-S24\/OT-0003-101-01"],"award-info":[{"award-number":["R-S24\/OT-0003-101-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Synthetic aperture interferometry (SAI) is a signal processing technique that mixes the signals collected by pairs of elementary antennas to obtain high-resolution images with the aid of a computer. This note aims at studying the effects of the distance between the synthetic aperture interferometer and an observed scene with respect to the size of the antenna array onto the imaging capabilities of the instrument. Far-field conditions and near-field ones are compared from an algebraic perspective with the aid of simulations conducted at microwave frequencies with the Microwave Imaging Radiometer by Aperture Synthesis (MIRAS) onboard the Soil Moisture and Ocean Salinity (SMOS) mission. Although in both cases the signals kept by pairs of elementary antennas are cross-correlated to obtain complex visibilities, there are several differences that deserve attention at the modeling level, as well as at the imaging one. These particularities are clearly identified, and they are all taken into account in this study: near-field imaging is investigated with spherical waves, without neglecting any terms, whereas far-field imaging approximation is considered with plane waves according to the Van\u2013Citter Zernike theorem. From an algebraic point of view, although the corresponding modeling matrices are both rank-deficient, we explain why the singular value distributions of these matrices are different. It is also shown how the angular synthesized point-spread function of the antenna array, whose shape varies with the distance to the instrument, can be helpful for estimating the boundary between the Fresnel region and the Fraunhofer one. Finally, whatever the region concerned by the aperture synthesis operation, it is shown that the imaging capabilities and the performances in the near-field and far-field regions are almost the same, provided the appropriate modeling matrix is taken into account.<\/jats:p>","DOI":"10.3390\/rs16193584","type":"journal-article","created":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T06:55:52Z","timestamp":1727333752000},"page":"3584","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Comprehensive Comparison of Far-Field and Near-Field Imaging Radiometry in Synthetic Aperture Interferometry"],"prefix":"10.3390","volume":"16","author":[{"given":"Eric","family":"Anterrieu","sequence":"first","affiliation":[{"name":"Centre d\u2019\u00c9tudes Spatiales de la BIOsph\u00e8re (CESBIO), 13 Avenue Colonel Roche, 31400 Toulouse, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4570-5739","authenticated-orcid":false,"given":"Louise","family":"Yu","sequence":"additional","affiliation":[{"name":"Centre National d\u2019\u00c9tudes Spatiales (CNES), 18 Avenue Edouard Belin, 31400 Toulouse, France"}]},{"given":"Nicolas","family":"Jeannin","sequence":"additional","affiliation":[{"name":"Airbus Defence and Space (ADS), 31 Rue des Cosmonautes, 31400 Toulouse, France"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,26]]},"reference":[{"key":"ref_1","unstructured":"Balanis, C.A. (2005). Antenna Theory: Analysis and Design, John Wiley & Sons. [3rd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1109\/MAP.2017.2706648","article-title":"Fraunhofer and Fresnel Distances: Unified Derivation for Aperture Antennas","volume":"59","author":"Selvan","year":"2017","journal-title":"IEEE Antennas Propag. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Haupt, R.L. (2010). Antenna Arrays: A Computational Approach, John Wiley & Sons. [1st ed.].","DOI":"10.1002\/9780470937464"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1109\/36.673675","article-title":"Synthetic Aperture Radiometry Evaluated by a Two-Channel Demonstration Model","volume":"36","author":"Laursen","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/S0031-8914(34)90026-4","article-title":"Die Wahrscheinliche Schwingungsverteilung in Einer von Einer Lichtquelle Direkt Oder Mittels Einer Linse Beleuchteten Ebene","volume":"1","year":"1934","journal-title":"Physica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1016\/S0031-8914(38)80203-2","article-title":"The Concept of Degree of Coherence and its Application to Optical Problems","volume":"5","author":"Zernike","year":"1934","journal-title":"Physica"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Anterrieu, \u00c9., Lafuma, P., and Jeannin, N. (2022). An Algebraic Comparison of Synthetic Aperture Interferometry and Digital Beam Forming in Imaging Radiometry. Remote Sens., 14.","DOI":"10.3390\/rs14092285"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1029\/98RS00829","article-title":"Angular resolution of two-dimensional, hexagonally sampled interferometric radiometers","volume":"33","author":"Camps","year":"1998","journal-title":"Radio Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Duran, I., Lin, W., Corbella, I., Torres, F., Duffo, N., and Mart\u00edn-Neira, M. (2015, January 26\u201331). SMOS floor error impact and migation on ocean imaging. Proceedings of the IEEE International Geoscience And Remote Sensing Symposium (IGARSS 2015), Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7326048"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1109\/36.662749","article-title":"Radiometric sensitivity computation in aperture synthesis interferometric radiometry","volume":"36","author":"Camps","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1038\/158339b0","article-title":"Solar Radiation at 175 Mc\/s","volume":"158","author":"Ryle","year":"1946","journal-title":"Nature"},{"key":"ref_12","unstructured":"Born, M., and Wolf, E. (1999). Principles of Optics, Cambridge University Press and Assessment. [7th ed.]."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Thompson, A.R., Moran, J.W., and Swenson, G.W. (2017). Interferometry and Synthesis in Radio Astronomy, Springer International Publishing. [3rd ed.].","DOI":"10.1007\/978-3-319-44431-4"},{"key":"ref_14","unstructured":"Fischman, M.A., and England, A.W. (2000, January 24\u201328). A technique for Reducing Fringe Washing Effects in L-Band Aperture Synthesis Radiometry. Proceedings of the IEEE International Geoscience And Remote Sensing Symposium (IGARSS 2000), Honolulu, HI, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1049\/ip-rsn:19981670","article-title":"How Narrow is Narrowband?","volume":"145","author":"Zatman","year":"1998","journal-title":"IEE Proc.-Radar Sonar Navig."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Tanner, A.B., Lambrigsten, B.H., Gaier, T.M., and Torres, F. (August, January 31). Near Field Characterization of the GeoSTAR Demonstrator. Proceedings of the IEEE International Geoscience And Remote Sensing Symposium (IGARSS 2006), Denver, CO, USA.","DOI":"10.1109\/IGARSS.2006.654"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1029\/97RS02398","article-title":"Microwave Imaging of the Brightness Temperature Distribution of Extended Areas in the Near and Far Field Using Two-Dimensional Aperture Synthesis with High Spatial Resolution","volume":"33","author":"Peichl","year":"1998","journal-title":"Radio Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Liangbing, C., Qingxia, L., Zubiao, X., Ke, C., and Yaoting, Z. (2009, January 27\u201329). Near-Field Imaging of One-Dimensional Aperture Synthesis Radiometers. Proceedings of the IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless\nCommunications (MAPE 2009), Beijing, China.","DOI":"10.1109\/MAPE.2009.5355943"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2224","DOI":"10.1007\/s11431-011-4403-3","article-title":"Imaging Algorithm for Synthetic Aperture Interferometric Radiometer in Near Field","volume":"54","author":"Zhang","year":"2011","journal-title":"Sci. China Technol. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"D\u00edez-Garc\u00eda, R., and Mart\u00edn-Neira, M. (2016, January 11\u201314). Antenna spacing and pattern differences: Their impact in MIRAS reconstruction error. Proceedings of the 14th Specialist Meeting on Microwave Radiometry and Remote Sensing of the Environment (MicroRad 2016), Espoo, Finland.","DOI":"10.1109\/MICRORAD.2016.7530496"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fu, P., Hu, F., Hu, H., and Zheng, T. (October, January 26). A Wavenumber Domain Imaging Algorithm for Synthetic Aperture Interferometric Radiometry in Near-Field. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2020), Waikoloa, HI, USA.","DOI":"10.1109\/IGARSS39084.2020.9323395"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3606","DOI":"10.1109\/TMTT.2022.3175156","article-title":"A Near-Field Imaging Algorithm Based on Angular Spectrum Theory for Synthetic Aperture Interferometric Radiometer","volume":"70","author":"Fu","year":"2022","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_23","first-page":"1","article-title":"A Novel Imaging Method Using Fractional Fourier Transform for Near-Field Synthetic Aperture Radiometer Systems","volume":"19","author":"Hu","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wu, Y., Li, Y., Song, G., Dou, H., and Li, H. (2024). A Near-Field Imaging Method Based on the Near-Field Distance for an Aperture Synthesis Radiometer. Remote Sens., 16.","DOI":"10.3390\/rs16050767"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF00329903","article-title":"Brook Taylor and the method of increments","volume":"34","author":"Feigenbaum","year":"1985","journal-title":"Arch. Hist. Exact Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"193","DOI":"10.2528\/PIERB14011602","article-title":"Regularization Imaging Algorithm with Accurate G Matrix for Near-Field MMW Synthetic Aperture Imaging Radiometer","volume":"58","author":"Chen","year":"2014","journal-title":"Prog. Electromagn. Res. B"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Schnoering, G., Kawaguchi, T., and H\u00f6ller, C. (2024, January 6\u201310). Mixed Near-and Far-Field 2D Imaging with Sparse Arrays. Proceedings of the IEEE Radar Conference (RadarConf24), Denver, CO, USA.","DOI":"10.1109\/RadarConf2458775.2024.10548405"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1109\/TGRS.2004.830641","article-title":"The Visibility Function in Interferometric Aperture Synthesis Radiometry","volume":"42","author":"Corbella","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/TGRS.2008.916259","article-title":"The Flat Target Transformation","volume":"46","author":"Suess","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1109\/TGRS.2004.830940","article-title":"A Resolving Matrix Approach for Synthetic Aperture Imaging Radiometers","volume":"42","author":"Anterrieu","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, J., Zhu, X., Zhang, S., and Chen, X. (2018, January 6\u201310). General G-matrix imaging method for near-field millimeter-wave SAIR with any arrays. Proceedings of the IEEE International Wireless Symposium (IWS 2018), Chengdu, China.","DOI":"10.1109\/IEEE-IWS.2018.8400862"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hansen, P.C. (1998). Rank-Deficient and Discrete Ill-Posed Problems, Society for Industrial & Applied Mathematics. [1st ed.].","DOI":"10.1137\/1.9780898719697"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/36.843030","article-title":"Improved Image Reconstruction Techniques for Synthetic Aperture Radiometers","volume":"38","author":"Goodberlet","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","unstructured":"Golub, G.H., and Van Loan, C.F. (2013). Matrix Computations, Johns Hopkins University Press. [4th ed.]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1007\/BF01937276","article-title":"The Truncated SVD as a Method for Regularization","volume":"27","author":"Hansen","year":"1987","journal-title":"BIT Numer. Math."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1080\/00207390117151","article-title":"The Gibbs\u2019 Phenomenon","volume":"32","author":"Fay","year":"2001","journal-title":"Int. J. Math. Educ. Sci. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1109\/TGRS.2002.1176146","article-title":"Apodization Functions for 2D Hexagonally Sampled Synthetic Aperture Imaging Radiometers","volume":"40","author":"Anterrieu","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1109\/TGRS.2007.914809","article-title":"SMOS: The Payload","volume":"46","author":"McMullan","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1109\/TGRS.2008.916264","article-title":"SMOS: The Mission and the System","volume":"46","author":"Duesmann","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","unstructured":"Pivnenko, S., Nielsen, J.M., Cappellin, C., Lemanczyk, G., and Breinbjerg, O. (2007, January 23\u201328). High-Accuracy Calibration of the SMOS Radiometer Antenna Patterns at the DTU-ESA Spherical Near-Field Antenna Test Facility. Proceedings of the IEEE International Geoscience And Remote Sensing Symposium (IGARSS 2007), Barcelona, Spain."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1109\/TGRS.2002.1000330","article-title":"Two-dimensional synthetic aperture images over a land surface scene","volume":"40","author":"Bayle","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Talone, M., Gourrion, J., Sabia, R., Gabarr\u00f3, C., Gonzalez, V., Camps, A., Corbella, I., Monerris, A., and Font, J. (2010, January 25\u201330). SMOS\u2019 brightness temperatures validation: First results after the commisioning phase. Proceedings of the IEEE International Geoscience And Remote Sensing Symposium (IGARSS 2010), Honolulu, HI, USA.","DOI":"10.1109\/IGARSS.2010.5654257"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1384","DOI":"10.1109\/TGRS.2012.2184548","article-title":"The SMOS Soil Moisture Retrieval Algorithm","volume":"50","author":"Kerr","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1109\/TGRS.2008.915543","article-title":"Overview of the SMOS Sea Surface Salinity Prototype Processor","volume":"46","author":"Zine","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1086\/190688","article-title":"The Very Large Array","volume":"44","author":"Thompson","year":"1980","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1086\/324786","article-title":"The Cosmic Background Imager","volume":"114","author":"Padin","year":"2002","journal-title":"Publ. Astron. Soc. Pac."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1109\/TGRS.2004.840667","article-title":"MIRAS Reference Radiometer: A fully polarimetric noise injection radiometer","volume":"43","author":"Colliander","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_48","unstructured":"(2023, August 01). The MathWorks Inc.: Help Center. Available online: https:\/\/fr.mathworks.com\/help\/matlab\/ref\/eps.html."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/MSP.2008.930649","article-title":"Mean squared error: Love it or leave it? A new look at signal fidelity measures","volume":"26","author":"Wang","year":"2009","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_51","unstructured":"Torres, F., Abril, J., Nova, E., Broquetas, A., and Jofre, L. (2010, January 12\u201316). Far field condition in passive interferometry for security screening applications. Proceedings of IEEE the European Conference on Antennas and Propagation (EuCAP 2010), Barcelona, Spain."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Huber, P.J., and Ronchetti, E.M. (2009). Robust Statistics, John Wiley & Sons. [2nd ed.].","DOI":"10.1002\/9780470434697"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/LGRS.2008.2004722","article-title":"On the reduction of the systematic error in imaging radiometry by aperture synthesis: A new approach for the SMOS space mission","volume":"6","author":"Carfantan","year":"2009","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_54","unstructured":"Feynman, R.P., Leighton, R.B., and Sands, M. (2011). The Feynman Lectures on Physics, Vol. II: Mainly Electromagnetism and Matter, New Millennium ed., Basic Books."},{"key":"ref_55","unstructured":"Bracewell, R. (1999). The Fourier Transform and Its Applications, McGraw-Hill. [3rd ed.]."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/andp.19013090310","article-title":"Ueber das Gesetz der Energieverteilung im Normalspectrum","volume":"309","author":"Planck","year":"1901","journal-title":"Ann. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1080\/14786440009463878","article-title":"Remarks upon the Law of Complete Radiation","volume":"49","author":"Rayleigh","year":"1900","journal-title":"Philos. Mag."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/14786440509463348","article-title":"On the Partition of Energy between Matter and Aether","volume":"10","author":"Jeans","year":"1905","journal-title":"Philos. Mag."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/19\/3584\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:03:36Z","timestamp":1760112216000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/19\/3584"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,26]]},"references-count":58,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["rs16193584"],"URL":"https:\/\/doi.org\/10.3390\/rs16193584","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,9,26]]}}}