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Electromagnetic Modeling in Microwave Remote Sensing
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Electromagnetic Modeling in Microwave Remote Sensing

A special issue of Remote Sensing (ISSN 2072-4292). This special issue belongs to the section "Engineering Remote Sensing".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 27646

Special Issue Editors

Dr. Pasquale Imperatore

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Guest Editor
National Research Council of Italy (CNR), Institute for Electromagnetic Sensing of the Environment (IREA), Naples, Italy
Interests: SAR processing; SAR interferometry; SAR calibration; SAR modeling; electromagnetic scattering; random layered media; parallel algorithms; high performance computing
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Joel T. Johnson

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Guest Editor
Department of Electrical and Computer Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210, USA
Interests: active microwave remote sensing, passive microwave remote sensing, microwave radiometry, electromagnetic theory, scattering from rough surfaces
Special Issues, Collections and Topics in MDPI journals
Dr. Francesco Soldovieri

E-Mail Website
Guest Editor
National Research Council of Italy (CNR), Institute for Electromagnetic Sensing of the Environment (IREA), Via Diocleziano 328, 80124 Naples, Italy
Interests: electromagnetic scattering; radar imaging; ground penetrating radar; data integration; non-invasive monitoring tools
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Daniele Riccio

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Guest Editor
Department of Electrical Engineering and Information Technology, Faculty of Engineering, University of Napoli Federico II, Via Claudio 21, 80125 Napoli, Italy
Interests: remote sensing; electromagnetic scattering; synthetic aperture radar; radar; microwave imaging
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

Microwave remote sensing offers a unique capability for monitoring the natural processes and available resources on our Planet, on both local and global scales. Notwithstanding the considerable progress made in the development of different classes of microwave sensors and the rich multidimensional information they can provide, the full interpretation and exploitation of the empirical data remains a challenging task. Finding a quantitative relation between the observables and the natural parameters is a key-problem in remote sensing, thus it has attracted much attention during last decades. Accordingly, electromagnetic modelling has a profound influence on the design of remote sensing applications, thus still posing challenging problems with theoretical, computational, and experimental relevance. Conversely, the way in which the knowledge about fundamental physics of the interaction between radiation and geo/bio-physical media is encoded, at a certain level of abstraction, by electromagnetic models has implications of deep semantic, ontological, and epistemological nature.

This special issue aims at highlighting recent progress in electromagnetic modelling and its application to microwave remote sensing, with relevance for geoscience and environmental investigations. We solicit contributions describing innovative formulations, model simulations, and application-oriented strategies for experimental data interpretation and geoscientific parameters retrieval. We invite researchers to contribute original research articles as well as review articles. 

Potential topics include but are not limited to the following:

  • Electromagnetic Scattering and Emission Theory
  • Forward Electromagnetic Models
  • Models of Discrete Random Media, Randomly Rough Surfaces, Inhomogeneous Random Media, and Random Layered Structures
  • Electromagnetic Modeling of the Sea, Land, Atmosphere, and Cryosphere
  • Microwave Inverse Problems and Retrieval Approaches
  • Computational Methods for electromagnetic scattering and emission simulation
  • Models and Applications for Microwave Imaging and Synthetic Aperture Radars (SAR)
  • Microwave Radiometry and Interference Mitigation
  • Near Range Radar in complex electromagnetic scenarios (e.g., Ground Penetrating Radar (GPR), Subsurface Imaging, Through-wall imaging)
  • Geo- and bio-physical parameter retrieval in operational and emerging microwave remote sensing applications.
  • Artificial Intelligence (AI) for microwave inverse problems
  • In-situ data analysis and Ground Validation
Dr. Pasquale Imperatore
Prof. Joel T. Johnson
Dr. Francesco Soldovieri
Prof. Daniele Riccio
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Remote Sensing is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Electromagnetic Wave Theory
  • Scattering and Emission
  • Electromagnetic Models
  • Inverse Problems
  • Microwave and Radar Imaging
  • Computational Electromagnetics
  • Synthetic Aperture Radar (SAR)
  • Microwave Radiometry
  • Artificial Intelligence (AI)

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Published Papers (9 papers)

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27 pages, 22251 KiB  
Article
Asymptotic Modeling of Three-Dimensional Radar Backscattering from Oil Slicks on Sea Surfaces
by Nicolas Pinel, Christophe Bourlier, Irina Sergievskaya, Nicolas Longépé and Guillaume Hajduch
Remote Sens. 2022, 14(4), 981; https://doi.org/10.3390/rs14040981 - 17 Feb 2022
Cited by 3 | Viewed by 1971
Abstract
This paper presents new results of a simulation of radar backscatter from oil slick areas on a real three-dimensional sea surface, based on a physical hydrodynamic model of surface wave damping in the presence of oil films, the local equilibrium model (MLB). To [...] Read more.
This paper presents new results of a simulation of radar backscatter from oil slick areas on a real three-dimensional sea surface, based on a physical hydrodynamic model of surface wave damping in the presence of oil films, the local equilibrium model (MLB). To solve this problem, the modelling was carried out by using the first-order small-slope approximation (SSA1) model. It presents the advantage of having a very good compromise between rapidity and accuracy of the calculation. The choice of the model is justified by solving the two-dimensional problem with several asymptotic methods and further comparing the results with a rigorous numerical method, based on the Method of Moments (MoM). Two approaches called “thin-layer” (TL) and “classical” were used to deal with the double layer (air/oil/sea) problem. The TL approach assumes that this double-layer problem can be seen locally as a Fabry–Pérot interferometer, which implies that the Kirchhoff-tangent plane approximation (KA) is valid. The classical approach consists in neglecting the presence of the oil layer for dealing with electromagnetic backscattering, which is valid for very thin oil films compared to the electromagnetic (EM) wavelength. It is shown that these two approaches have rather complementary validity domains: The TL approach is always valid for small observation angles, which makes it suitable for near nadir sensors such as altimeters, whereas the classical approach is valid for moderate observation angles, which makes it suitable for most satellite applications. The 3D modelling results are compared with C-band and X-band measured data (CSK experiment and OOW NOFO experiment) in VV polarization. The calculation takes into account that the oil film on the sea surface is mainly in an emulsion state. The results highlighted the relevance of the MLB hydrodynamic model, as well as the SSA1 EM model combined wit the classical approach, for quantifying NRCS in seas contaminated with marine oil or surfactants. The agreement is indeed very good in the X-band range. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
►▼ Show Figures

Figure 1

Figure 1
<p>Flowchart summarizing the methodology applied for calculating the EM scattering from clean/contaminated seas.</p> Full article ">Figure 2
<p>CSK experiment (March 2011)—Case 1 (10 March 2011, 17 h 51<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>): Detected oil spill in the ZPE area (<b>left</b>) and zoom over the detected oil spills (<b>right</b>).</p> Full article ">Figure 3
<p>CSK experiment (March 2011)—Case 2 (15 March 2011, 18 h 32<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>): Detected oil spill near the Ushant TSS (<b>left</b>) and zoom over the detected oil spill (<b>right</b>).</p> Full article ">Figure 4
<p>CSK experiment (March 2011)—Case 3 (11 February 2011, 05 h 41<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>): Detected oil spill in the ZPE area (<b>left</b>) and zoom over the detected oil spill (<b>right</b>).</p> Full article ">Figure 5
<p>OOW NOFO experiment (June 2011)—Case 1 (8 June 2011, 17 h 58<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>): ScanSAR Wide (X band) image in VV pol. with pollution in the upper left region (<b>left</b>) and zoom over the detected oil spills (<b>right</b>).</p> Full article ">Figure 6
<p>OOW NOFO experiment (June 2011)—Case 2 (9 June 2011, 21 h 28<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>): ASAR/ENVISAT (C band) image in VV pol. with pollution (<b>left</b>) and zoom over the detected oil spill (<b>right</b>).</p> Full article ">Figure 7
<p>OOW NOFO experiment (June 2011)—Case 3 (12 June 2011, 21 h 18<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>): ASAR/ENVISAT (C band) image in VV pol. zoomed over the detected oil spill.</p> Full article ">Figure 8
<p>Monostatic NRCS <math display="inline"><semantics> <mi>σ</mi> </semantics></math> (left hand-side figure) with respect to the observation angle <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>s</mi> </msub> </semantics></math> (deg.) according to scenario 4 described in [<a href="#B16-remotesensing-14-00981" class="html-bibr">16</a>] (<math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> m/s, V polarization, <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> GHz), for a light oil with thickness <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> mm, but with emulsified oil with equivalent relative permittivity <math display="inline"><semantics> <mrow> <msubsup> <mi>ϵ</mi> <mrow> <mi>r</mi> <mn>2</mn> </mrow> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msubsup> <mo>=</mo> <mn>17</mn> <mo>+</mo> <mn>4</mn> <mi>i</mi> </mrow> </semantics></math>: Comparison between clean and contaminated seas with the rigorous method, and with a contaminated sea by using the two simplifying approaches. The right hand-side figure shows, for a contaminated sea, the ratio between the NRCS of the simplifying approaches and of the rigorous method for light oil.</p> Full article ">Figure 9
<p>Monostatic NRCS <math display="inline"><semantics> <mi>σ</mi> </semantics></math> (in dB scale) with respect to the observation angle <math display="inline"><semantics> <msub> <mi>θ</mi> <mi>s</mi> </msub> </semantics></math> (in degrees) for <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>9.6</mn> </mrow> </semantics></math> GHz, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>4.5</mn> </mrow> </semantics></math> m/s, V polarization, and for a heavy oil with thickness <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> mm: Comparison between clean and contaminated seas, where SSA1 is compared with the rigorous numerical method for clean sea, and with the two simplifying “TL” and “cl.” approaches for contaminated sea. The left-hand side figure shows the numerical implementation of SSA1, whereas right-hand side figure shows the analytic implementation of SSA1.</p> Full article ">Figure 10
<p>Simulations for the same parameters as in <a href="#remotesensing-14-00981-f009" class="html-fig">Figure 9</a>, except for the oil film thickness: <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mo>μ</mo> </semantics></math>m, and comparison of the rigorous computation with different analytical asymptotic models (SSA1, WCAq, MSP, SPM, GOsh): in the first (upper) figure, comparisons for a clean sea, and in the second (lower) figure, comparisons for a contaminated sea with the classical approach.</p> Full article ">Figure 11
<p>CSK experiments: NRCS of SAR images of the 4 studied scenarios, as detailed in <a href="#sec2dot2-remotesensing-14-00981" class="html-sec">Section 2.2</a>: (<b>upper left</b>): scenario 1 (10 March 2011, 17 h 51<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>), (<b>upper right</b>): scenario 2 (15 March 2011, 18 h 32<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>), (<b>lower left</b>): scenario 3 (11 February 2011, 05 h 41<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>), (<b>lower right</b>): scenario 4 (10 March 2011, 17 h 51<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>).</p> Full article ">Figure 12
<p>Comparison of 3D analytical simulations with CSK experiments (March 2011): Scenario 1: average wind speed <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>6.3</mn> </mrow> </semantics></math> m/s (6 m/s on the top figure and 7 m/s on the bottom figure), average wind direction <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>+</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>27</mn> <mo>.</mo> <msup> <mn>6</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">Figure 13
<p>Isotropic slope spectra of associated to parameters of <a href="#remotesensing-14-00981-f012" class="html-fig">Figure 12</a> (6 m/s on the top figure and 7 m/s on the bottom figure), with representation of the Bragg wavenumbers for <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mrow> <mo>{</mo> <msup> <mn>30</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>45</mn> <mo>°</mo> </msup> <mo>,</mo> <msup> <mn>80</mn> <mo>°</mo> </msup> <mo>}</mo> </mrow> </mrow> </semantics></math>. The Lombardini et al. model [<a href="#B15-remotesensing-14-00981" class="html-bibr">15</a>] (which is usually called Marangoni damping effect) is also represented for comparison, for <math display="inline"><semantics> <mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> mN/m and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>D</mi> </msub> <mo>=</mo> <mrow> <mo>{</mo> <mn>0</mn> <mo>;</mo> <mn>0.05</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> rad/s.</p> Full article ">Figure 14
<p>Comparison of 3D analytical simulations with CSK experiments (March 2011): Scenario 2: <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>10.4</mn> </mrow> </semantics></math> m/s and <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <msup> <mn>149</mn> <mo>°</mo> </msup> </mrow> </semantics></math> (7 m/s and <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>149</mn> <mo>°</mo> </msup> </mrow> </semantics></math> on the top figure, and 10 m/s and <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>90</mn> <mo>°</mo> </msup> </mrow> </semantics></math> on the bottom figure), mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>41</mn> <mo>.</mo> <msup> <mn>0</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">Figure 15
<p>Comparison of 3D analytical simulations with CSK experiments (March 2011): Scenario 4: <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>6.4</mn> </mrow> </semantics></math> m/s (6 m/s on the top figure and 7 m/s on the bottom figure), <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>+</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, and mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>31</mn> <mo>.</mo> <msup> <mn>1</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">Figure 16
<p>Comparison of 3D analytical simulations with CSK experiments (March 2011): Scenario 3: <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math> m/s (corrected: 3 m/s on the top figure and 4 m/s on the bottom figure), <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>+</mo> <msup> <mn>160</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, and mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>50</mn> <mo>.</mo> <msup> <mn>1</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">Figure 17
<p>OOW NOFO experiment: NRCS of SAR images of the 3 studied scenarios, as detailed in <a href="#sec2dot2-remotesensing-14-00981" class="html-sec">Section 2.2</a>: upper: scenario 1 (8 June 2011, 17 h 58<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>), lower left: scenario 2 (9 June 2011, 21 h 28<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>), lower right: scenario 3 (12 June 2011, 21 h 18<math display="inline"><semantics> <msup> <mrow/> <mo>′</mo> </msup> </semantics></math>).</p> Full article ">Figure 18
<p>Comparison of 3D analytical simulations with Bergen experiments (June 2011): Scenario 2 (<math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>5.33</mn> </mrow> </semantics></math> GHz): <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>4.5</mn> </mrow> </semantics></math> m/s (4 m/s on the top figure and 5 m/s on the bottom figure), <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>+</mo> <msup> <mn>180</mn> <mo>°</mo> </msup> </mrow> </semantics></math>, and mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>34</mn> <mo>.</mo> <msup> <mn>1</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">Figure 19
<p>Comparison of 3D analytical simulations with Bergen experiments (June 2011): Scenario 3 (<math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>5.33</mn> </mrow> </semantics></math> GHz): <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>5.8</mn> </mrow> </semantics></math> m/s, <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>+</mo> <msup> <mn>90</mn> <mo>°</mo> </msup> </mrow> </semantics></math> (6 m/s and <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math> on the top figure, and 10 m/s and <math display="inline"><semantics> <mrow> <mo>+</mo> <msup> <mn>90</mn> <mo>°</mo> </msup> </mrow> </semantics></math> on the bottom figure), and mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>34</mn> <mo>.</mo> <msup> <mn>1</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">Figure 20
<p>Comparison of 3D analytical simulations with Bergen experiments (June 2011): Scenario 1 (<math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>9.6</mn> </mrow> </semantics></math> GHz): <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>10</mn> </msub> <mo>=</mo> <mn>2.6</mn> </mrow> </semantics></math> m/s, <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>−</mo> <msub> <mi>ϕ</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>−</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>60</mn> <mo>°</mo> </msup> </mrow> </semantics></math> on the top figure and <math display="inline"><semantics> <msup> <mn>0</mn> <mo>°</mo> </msup> </semantics></math> on the bottom figure), and mean incidence angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>48</mn> <mo>.</mo> <msup> <mn>0</mn> <mo>°</mo> </msup> </mrow> </semantics></math>. For the simulations, the SSA1 is represented, as well as the GOsh and SPM (3D versions).</p> Full article ">
26 pages, 10631 KiB  
Article
Simulation and Analysis of Electromagnetic Scattering from Anisotropic Plasma-Coated Electrically Large and Complex Targets
by Zhenmin Rao, Guoqiang Zhu, Siyuan He, Chao Li, Zewang Yang and Jian Liu
Remote Sens. 2022, 14(3), 764; https://doi.org/10.3390/rs14030764 - 7 Feb 2022
Cited by 5 | Viewed by 2321
Abstract
An efficient physical optics (PO) calculation method is proposed for the electromagnetic (EM) scattering of electrically large targets coated with magnetized plasma characterized by asymmetric tensor dielectric parameters. The outer surface of the arbitrarily shaped target is discretized into triangular elements. According to [...] Read more.
An efficient physical optics (PO) calculation method is proposed for the electromagnetic (EM) scattering of electrically large targets coated with magnetized plasma characterized by asymmetric tensor dielectric parameters. The outer surface of the arbitrarily shaped target is discretized into triangular elements. According to the principle of tangent plane approximation and by using the plane wave spectrum expansion method, the scattered field from one triangular element is derived as a double integral in the spectral domain. To obtain the solution in the spatial domain, the saddle point method is used to asymptotically calculate the integral. Then, the equivalent surface currents (ESCs) are constructed by calculating the surface field at the outer surface of the planar model, from which the PO solution is derived by using the Stratton–Chu integral. Moreover, to interpret the field propagation process in the plasma layer quantitatively, the total scattered field of the coated planar model is decomposed into the superposition of different mode field components. It is observed that the scattered fields demonstrate an inherent cross-polarization phenomenon due to the nonreciprocal constitutive relation of the plasma, which is a distinct feature and is different from the general anisotropic medium whose dielectric parameters can be diagonalized. The effectiveness of the proposed method is verified by numerical results. Furthermore, the proposed algorithm consumes less calculation time and memory as compared to commercial full solvers. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
►▼ Show Figures

Figure 1

Figure 1
<p>The model of an infinite plasma-coated PEC slab.</p> Full article ">Figure 2
<p>The propagation model of an infinite plasma-coated PEC slab.</p> Full article ">Figure 3
<p>The transmission relationship of the electric field in the plasma layer.</p> Full article ">Figure 4
<p>Reflection and transmission of EM wave from air to the surface of the plasma layer.</p> Full article ">Figure 5
<p>Reflection of EM wave on PEC substrate.</p> Full article ">Figure 6
<p>Reflection and transmission of EM waves from plasma layer into the air.</p> Full article ">Figure 7
<p>Model of the discrete complex target.</p> Full article ">Figure 8
<p>The perpendicular and parallel vectors <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mo>⊥</mo> <mi>i</mi> </msubsup> <mo>,</mo> <msubsup> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mo>/</mo> <mo>/</mo> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mo>⊥</mo> <mi>r</mi> </msubsup> <mo>,</mo> <msubsup> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mo>/</mo> <mo>/</mo> </mrow> <mi>r</mi> </msubsup> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>The reflection coefficients of the plasma-coated slab with a PEC substrate: (<b>a</b>) against the angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> incidence <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>0.1</mn> <mi>λ</mi> </mrow> </semantics></math>; (<b>b</b>) against the slab’s thickness <math display="inline"><semantics> <mi>d</mi> </semantics></math> <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <msup> <mrow> <mn>45</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">Figure 10
<p>Comparison of reflection coefficients of infinite PEC slab coated with different media: (<b>a</b>) plasma coating; (<b>b</b>) uniaxial media coating at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>c</b>) uniaxial media coating at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <msup> <mrow> <mn>45</mn> </mrow> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>Amplitude and phase of mode fields in lossless plasma coating: (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mi>R</mi> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <mi>R</mi> </mrow> </semantics></math>.</p> Full article ">Figure 12
<p>Amplitude and phase of mode fields in lossy plasma coating: (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mi>R</mi> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <mi>R</mi> </mrow> </semantics></math>.</p> Full article ">Figure 13
<p>The amplitude of mode fields in lossless plasma coating: (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mi>R</mi> <mo>|</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 14
<p>The phase of mode fields in lossless plasma coating: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <mi>R</mi> </mrow> </semantics></math>.</p> Full article ">Figure 15
<p>The amplitude of mode fields in lossy plasma coating: (<b>a</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mi>R</mi> <mo>|</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 16
<p>The phase of mode fields in lossy plasma coating: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <msup> <mi>R</mi> <mn>0</mn> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>∠</mo> <mi>R</mi> </mrow> </semantics></math>.</p> Full article ">Figure 17
<p>A <math display="inline"><semantics> <mrow> <mn>4</mn> <msub> <mi>λ</mi> <mn>0</mn> </msub> <mo>×</mo> <mn>5</mn> <msub> <mi>λ</mi> <mn>0</mn> </msub> </mrow> </semantics></math> plate coated with a plasma layer and its monostatic RCSs against angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math>. The layer’s thickness is <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>0.1</mn> <msub> <mi>λ</mi> <mn>0</mn> </msub> </mrow> </semantics></math>. The incident angle is <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. The relative permittivity tensor elements are <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>6</mn> </mrow> <mo>−</mo> <mn>3</mn> <mi>j</mi> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>4</mn> </mrow> <mo>−</mo> <mn>0.7</mn> <mi>j</mi> </mrow> </semantics></math>.</p> Full article ">Figure 18
<p>Models of plasma-coated cube and cylinder.</p> Full article ">Figure 19
<p>Monostatic RCSs from a PEC cube coated with (<b>a</b>) lossless and (<b>b</b>) lossy plasma layer. The relative permittivity tensor elements of the lossless and lossy plasma, respectively, are <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>6</mn> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>4</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>6</mn> <mo>−</mo> <mn>3</mn> <mi>j</mi> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>5</mn> <mi>j</mi> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>4</mn> <mo>−</mo> <mn>0</mn> <mrow> <mo>.</mo> <mn>7</mn> <mi>j</mi> </mrow> </mrow> </semantics></math>; the incident angle is <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">Figure 20
<p>Monostatic RCSs from a PEC cylinder coated with a plasma layer in (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>o</mi> <mi>y</mi> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>o</mi> <mi>z</mi> </mrow> </semantics></math> planes. The relative permittivity tensor elements of the lossless and lossy plasma, respectively, are <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>10</mn> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>10</mn> </mrow> <mo>−</mo> <mn>2</mn> <mi>j</mi> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>3</mn> </mrow> <mo>−</mo> <mn>4</mn> <mi>j</mi> </mrow> </semantics></math>.</p> Full article ">Figure 21
<p>The geometry of a plasma-coated missile and its observation planes.</p> Full article ">Figure 22
<p>Monostatic RCSs of the plasma-coated missile in (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>o</mi> <mi>y</mi> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>o</mi> <mi>z</mi> </mrow> </semantics></math> planes. The relative permittivity tensor elements of the lossless and lossy plasma, respectively, are <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>10</mn> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>10</mn> </mrow> <mo>−</mo> <mn>2</mn> <mi>j</mi> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>3</mn> </mrow> <mo>−</mo> <mn>4</mn> <mi>j</mi> </mrow> </semantics></math>.</p> Full article ">Figure 23
<p>The geometry of a plasma-coated aircraft and three observation planes.</p> Full article ">Figure 24
<p>Monostatic RCSs of the plasma-coated aircraft in three observation planes: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>o</mi> <mi>y</mi> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>o</mi> <mi>z</mi> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>y</mi> <mi>o</mi> <mi>z</mi> </mrow> </semantics></math>. The relative permittivity tensor elements of the lossless and lossy plasma, respectively, are <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>10</mn> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>3</mn> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mn>1</mn> </msub> <mrow> <mo>=</mo> <mn>10</mn> </mrow> <mo>−</mo> <mn>2</mn> <mi>j</mi> <mo>,</mo> <msub> <mi>ε</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mn>5</mn> <mi>j</mi> </mrow> <mo>,</mo> <msub> <mi>ε</mi> <mn>3</mn> </msub> <mrow> <mo>=</mo> <mn>3</mn> </mrow> <mo>−</mo> <mn>4</mn> <mi>j</mi> </mrow> </semantics></math>.</p> Full article ">
20 pages, 27520 KiB  
Article
The Role of Model Dimensionality in Linear Inverse Scattering from Dielectric Objects
by Gianluca Gennarelli, Giovanni Ludeno, Noviello Carlo, Ilaria Catapano and Francesco Soldovieri
Remote Sens. 2022, 14(1), 222; https://doi.org/10.3390/rs14010222 - 4 Jan 2022
Cited by 1 | Viewed by 2034
Abstract
This paper deals with 3D and 2D linear inverse scattering approaches based on the Born approximation, and investigates how the model dimensionality influences the imaging performance. The analysis involves dielectric objects hosted in a homogenous and isotropic medium and a multimonostatic/multifrequency measurement configuration. [...] Read more.
This paper deals with 3D and 2D linear inverse scattering approaches based on the Born approximation, and investigates how the model dimensionality influences the imaging performance. The analysis involves dielectric objects hosted in a homogenous and isotropic medium and a multimonostatic/multifrequency measurement configuration. A theoretical study of the spatial resolution is carried out by exploiting the singular value decomposition of 3D and 2D scattering operators. Reconstruction results obtained from synthetic data generated by using a 3D full-wave electromagnetic simulator are reported to support the conclusions drawn from the analysis of resolution limits. The presented analysis corroborates that 3D and 2D inversion approaches have almost identical imaging performance, unless data are severely corrupted by the noise. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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Figure 1

Figure 1
<p>Geometry of the problem.</p> Full article ">Figure 2
<p>Scenario with a point target buried at (0, 0, 1) m in a homogeneous medium with relative permittivity <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. The blue circles denote the measurement points and the black square is the target.</p> Full article ">Figure 3
<p>Singular values (dB) of <math display="inline"><semantics> <mrow> <msup> <mrow> <munder accentunder="true"> <mstyle mathvariant="bold" mathsize="normal"> <munder accentunder="true"> <mi>A</mi> <mo>_</mo> </munder> </mstyle> <mo stretchy="true">¯</mo> </munder> </mrow> <mrow> <mn>3</mn> <mi>d</mi> </mrow> </msup> </mrow> </semantics></math> (blue curve) and <math display="inline"><semantics> <mrow> <msup> <mrow> <munder accentunder="true"> <mstyle mathvariant="bold" mathsize="normal"> <munder accentunder="true"> <mi>A</mi> <mo>_</mo> </munder> </mstyle> <mo stretchy="true">¯</mo> </munder> </mrow> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </msup> </mrow> </semantics></math> (red curve) matrices.</p> Full article ">Figure 4
<p>Optimal truncation index versus SNR for 3D (blue curve) and 2D (red curve) models.</p> Full article ">Figure 5
<p>L-curve for SNR = 0 dB (<b>left panel</b>) and 30 dB (<b>right panel</b>).</p> Full article ">Figure 6
<p>Three terms in Equation (21) and residue versus truncation index for 3D and 2D models: SNR = 0 dB (<b>left panel</b>). SNR = 30 dB (<b>right panel</b>).</p> Full article ">Figure 7
<p>Three terms in Equation (22) and norm of the solution versus truncation index for 3D and 2D models: SNR = 0 dB (<b>left panel</b>). SNR = 30 dB (<b>right panel</b>).</p> Full article ">Figure 8
<p>Spectral contents for different SNR levels obtained by means of Equation (20): 2D model (<b>upper panels</b>); 3D model (<b>lower panels</b>); color scale (−10, 0) dB.</p> Full article ">Figure 9
<p>Normalized amplitude of the PSF achieved for different SNR levels and for a point target placed at (0,0,1) m: 2D model (<b>upper panels</b>); 3D model (<b>lower panels</b>); color scale (0,1).</p> Full article ">Figure 10
<p>Cuts of the PSF achieved for different SNR levels and for a point target placed at (0,0,1) m: <math display="inline"><semantics> <mi>x</mi> </semantics></math>-cuts (<b>upper panels</b>). <math display="inline"><semantics> <mi>z</mi> </semantics></math> -cuts (<b>lower panels</b>). The red and blue lines refer to the 2D and 3D model, respectively.</p> Full article ">Figure 11
<p>Singular values (dB) of exact and far-field 3D/2D operators.</p> Full article ">Figure 12
<p>Optimal truncation index vs. SNR for 3D (blue curve) and 2D (red curve) far-field models of Equations (16) and (17).</p> Full article ">Figure 13
<p>Cuts of the PSF achieved for different SNR levels and for a point target placed at (0,0,1) m: <math display="inline"><semantics> <mi>x</mi> </semantics></math>-cuts (upper panels). <math display="inline"><semantics> <mi>z</mi> </semantics></math> -cuts (lower panels). The blue and red lines refer to the 3D and 2D far field models of Equations (16) and (17).</p> Full article ">Figure 14
<p>Simulated single-target scenario (<b>left panel</b>). Filtered data (<b>middle panel</b>). Average spectrum of the filtered data (<b>right panel</b>).</p> Full article ">Figure 15
<p>Normalized amplitude of the tomographic reconstructions vs. SNR achieved in the single-target scenario with 3D (<b>upper panels</b>) and 2D (<b>lower panels</b>) models. The dashed line circumference is the intersection of the spherical cavity with the investigation domain. Color scale (0, 1).</p> Full article ">Figure 16
<p>Simulated two-target scenario (<b>left panel</b>). Filtered data (<b>middle panel</b>). Average spectrum of the filtered data (<b>right panel</b>).</p> Full article ">Figure 17
<p>Normalized amplitude of the tomographic reconstructions vs. SNR achieved in the two-target scenario with the 3D model (<b>upper panels</b>) and 2D model (<b>lower panels</b>). The square is the cross-section of the parallelepiped cavity while the circumference is the projection of the spherical cavity on the investigation domain. Color scale (0, 1).</p> Full article ">Figure 18
<p>Normalized amplitude of the tomographic reconstructions vs. SNR achieved in the single-target scenario with the far-field 3D (<b>upper panels</b>) and 2D (<b>lower panels</b>) models of Equations (16) and (17). The square is the cross-section of the parallelepiped cavity while the circumference is the projection of the spherical cavity on the investigation domain. Color scale (0, 1).</p> Full article ">Figure 19
<p>Normalized amplitude of the tomographic reconstructions vs. SNR achieved in the two-target scenario with the far-field 3D (<b>upper panels</b>) and 2D (<b>lower panels</b>) models of Equations (16) and (17). The square is the cross-section of the parallelepiped cavity while the circumference is the projection of the spherical cavity on the investigation domain. Color scale (0, 1).</p> Full article ">
24 pages, 14020 KiB  
Article
SAR Imaging Distortions Induced by Topography: A Compact Analytical Formulation for Radiometric Calibration
by Pasquale Imperatore
Remote Sens. 2021, 13(16), 3318; https://doi.org/10.3390/rs13163318 - 22 Aug 2021
Cited by 10 | Viewed by 2824
Abstract
Modeling of synthetic aperture radar (SAR) imaging distortions induced by topography is addressed and a novel radiometric calibration method is proposed in this paper. An analytical formulation of the problem is primarily provided in purely geometrical terms, by adopting the theoretical notions of [...] Read more.
Modeling of synthetic aperture radar (SAR) imaging distortions induced by topography is addressed and a novel radiometric calibration method is proposed in this paper. An analytical formulation of the problem is primarily provided in purely geometrical terms, by adopting the theoretical notions of the differential geometry of surfaces. The novel and conceptually simple formulation relies on a cylindrical coordinate system, whose longitudinal axis corresponds to the sensor flight direction. A 3D representation of the terrain shape is then incorporated into the SAR imaging model by resorting to a suitable parametrization of the observed ground surface. Within this analytical framework, the area-stretching function quantitatively expresses in geometrical terms the inherent local radiometric distortions. This paper establishes its analytical expression in terms of the magnitude of the gradient of the look-angle function uniquely defined in the image domain, thus resulting in being mathematically concise and amenable to a straightforward implementation. The practical relevance of the formulation is also illustrated from a computational perspective, by elucidating its effective discrete implementation. In particular, an inverse cylindrical mapping approach is adopted, thus avoiding the drawback of pixel area fragmentation and integration required in forward-mapping-based approaches. The effectiveness of the proposed SAR radiometric calibration method is experimentally demonstrated by using COSMO-SkyMed SAR data acquired over a mountainous area in Italy. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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<p>Cylindrical coordinate system.</p> Full article ">Figure 2
<p>SAR imaging process: geometric scheme.</p> Full article ">Figure 3
<p>3D geometrical scheme of a ground surface patch: <math display="inline"><semantics> <mrow> <msup> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>n</mi> <mo>^</mo> </mover> </mstyle> <mo>′</mo> </msup> </mrow> </semantics></math> is the surface unit normal, <math display="inline"><semantics> <mrow> <msub> <mi>χ</mi> <mi>l</mi> </msub> </mrow> </semantics></math> is local incidence angle, <math display="inline"><semantics> <mi mathvariant="sans-serif">ω</mi> </semantics></math> is the projection angle, <math display="inline"><semantics> <mover accent="true"> <mi>z</mi> <mo>^</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mrow> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>a</mi> <mo>^</mo> </mover> </mstyle> <mo> </mo> <mrow> <mo>(</mo> <mrow> <mo>=</mo> <mstyle mathvariant="bold" mathsize="normal"> <mover accent="true"> <mi>x</mi> <mo>^</mo> </mover> </mstyle> </mrow> <mo>)</mo> </mrow> <mo> </mo> </mrow> </semantics></math>are the vertical and azimuth directions, respectively.</p> Full article ">Figure 4
<p>Schematic illustration of the discrete mapping for spatial transformation <math display="inline"><semantics> <mrow> <mstyle mathvariant="bold" mathsize="normal"> <mi>q</mi> </mstyle> <mo>=</mo> <mi>τ</mi> <mo stretchy="false">(</mo> <mstyle mathvariant="bold" mathsize="normal"> <mi>s</mi> </mstyle> </mrow> </semantics></math>), with <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>u</mi> <mo>,</mo> <mi>v</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mstyle mathvariant="bold" mathsize="normal"> <mi>q</mi> </mstyle> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>,</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>3 × 3 Grid kernel.</p> Full article ">Figure 6
<p>Processing Scheme.</p> Full article ">Figure 7
<p>Elevation (m) of the DEM: representation in the image space. The range direction is from left to right; the azimuth direction is from bottom to top.</p> Full article ">Figure 8
<p>The range direction is from left to right; the azimuth direction is from bottom to top: (<b>a</b>) Look Angle Function (LAF) (degree):<math display="inline"><semantics> <mrow> <mo> </mo> <mi>θ</mi> <mo>=</mo> <mi>θ</mi> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>,</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) a mask identifying (red) layover and (blue) shadow areas.</p> Full article ">Figure 9
<p>Magnitude of the (range-weighted) partial derivative of look-angle function along: (<b>a</b>) the azimuth direction (dB), <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <mi>r</mi> <mfrac> <mrow> <mo>∂</mo> <mi>θ</mi> </mrow> <mrow> <mo>∂</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>; (<b>b</b>) the range direction (dB), <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> <mrow> <mi>r</mi> <mfrac> <mrow> <mo>∂</mo> <mi>θ</mi> </mrow> <mrow> <mo>∂</mo> <mi>r</mi> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 10
<p>(<b>a</b>) Simulated radiometric-distortion image (dB) associated with the ground surface area; (<b>b</b>) local incidence angle (LIA) (degree): <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">χ</mi> <mi>l</mi> </msub> <mo>=</mo> <msub> <mi mathvariant="sans-serif">χ</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <mo>,</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>(<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mover accent="true"> <mi>σ</mi> <mo>˜</mo> </mover> <mo> </mo> <mn>0</mn> </msubsup> </mrow> </semantics></math> (dB) image obtained from SAR data without compensation of topography-induced radiometric distortions; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">σ</mi> <mo> </mo> <mn>0</mn> </msubsup> </mrow> </semantics></math> (dB) image obtained from SAR data including the compensation of topography-induced radiometric distortions. A mask identifying (red) layover and (blue) shadow areas is superimposed.</p> Full article ">Figure 12
<p>Distribution of the backscattering coefficient <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">σ</mi> <mo> </mo> <mn>0</mn> </msubsup> </mrow> </semantics></math> (dB): (<b>a</b>) obtained without compensation of topography-induced radiometric distortions; (<b>b</b>) obtained by including the compensation of topography-induced radiometric distortions.</p> Full article ">Figure 13
<p>Distribution of the local incidence angle (LIA) [degree].</p> Full article ">Figure 14
<p>Backscattering coefficient <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">σ</mi> <mo> </mo> <mn>0</mn> </msubsup> </mrow> </semantics></math> [dB] without the compensation of topography-induced distortions vs. local incidence angle [degree].</p> Full article ">Figure 15
<p>Backscattering coefficient <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="sans-serif">σ</mi> <mo> </mo> <mn>0</mn> </msubsup> </mrow> </semantics></math>(dB) after the compensation of topography-induced distortions vs. local incidence angle (degree).</p> Full article ">
18 pages, 4031 KiB  
Article
Full-Wave Modeling and Inversion of UWB Radar Data for Wave Propagation in Cylindrical Objects
by Lan Gao, Chiara Dachena, Kaijun Wu, Alessandro Fedeli, Matteo Pastorino, Andrea Randazzo, Xiaoping Wu and Sébastien Lambot
Remote Sens. 2021, 13(12), 2370; https://doi.org/10.3390/rs13122370 - 17 Jun 2021
Cited by 1 | Viewed by 2451
Abstract
The nondestructive characterization of cylindrical objects is needed in many fields, such as medical diagnostics, tree trunk inspection, or concrete column testing. In this study, the radar equation of Lambot et al. is combined with cylindrical Green’s functions to fully model and invert [...] Read more.
The nondestructive characterization of cylindrical objects is needed in many fields, such as medical diagnostics, tree trunk inspection, or concrete column testing. In this study, the radar equation of Lambot et al. is combined with cylindrical Green’s functions to fully model and invert ultra-wideband (UWB) ground-penetrating radar (GPR) data and retrieve the properties of cylindrical objects. Inversion is carried out using a lookup table (LUT) approach followed by local optimization to ensure retrieval of the global minimum of the objective function. Numerical experiments were conducted to analyze the capabilities of the developed inversion procedure to estimate the radius, permittivity, and conductivity of the cylinders. The full-wave model was validated in laboratory conditions on metallic and plastic pipes of different sizes. The adopted radar system consists of a lightweight vector network analyzer (VNA) connected to a single transmitting and receiving horn antenna. The numerical experiments highlighted the complexity of the inverse problem, mainly originating from the multiple propagation modes within cylindrical objects. The laboratory measurements demonstrated the accuracy of the forward modeling and reconstructions in far-field conditions. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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Figure 1

Figure 1
<p>Schematic representation of the considered cylindrically layered medium.</p> Full article ">Figure 2
<p>Model configuration for numerical experiments.</p> Full article ">Figure 3
<p>Detecting the cylindrical model with the lightweight radar system with vertical polarization.</p> Full article ">Figure 4
<p>Amplitude and phase of the (<b>a</b>) return loss transfer function (<b>b</b>) global transmission and reflection coefficient function and (<b>c</b>) feedback loss transfer function of the BBHA 9120D horn antenna as a function of frequency.</p> Full article ">Figure 5
<p>The effects of (<b>a</b>) radius and (<b>b</b>) relative permittivity on nonconductive cylindrical models.</p> Full article ">Figure 6
<p>The effects of (<b>a</b>) radius and (<b>b</b>) conductivity on conducting cylindrical models.</p> Full article ">Figure 7
<p>The objective function distribution of (<b>a</b>) PVC-1 with d equals 0.15 m, (<b>b</b>) PVC-2 with d equals 0.15 m, (<b>c</b>) PVC-3 with d equals 0.15 m, (<b>d</b>) PVC-1 with d equals 0.4 m, (<b>e</b>) PVC-2 with d equals 0.4 m, (<b>f</b>) PVC-3 with d equals 0.4 m.</p> Full article ">Figure 8
<p>The objective function distributions of metallic tubes with distances of (<b>a</b>) 0.15 m and (<b>b</b>) 0.4 m.</p> Full article ">Figure 9
<p>The comparison between the measured time domain signal and the modeled time domain signal of (<b>a</b>) PVC-1, (<b>b</b>) PVC-2, (<b>c</b>) PVC-3, (<b>d</b>) Metal-1, (<b>e</b>) Metal-2, (<b>f</b>) Metal-3 at position 0.15 m.</p> Full article ">Figure 10
<p>The comparison between the measured time domain signal and the computed time domain signal of (<b>a</b>) PVC-1, (<b>b</b>) PVC-2, (<b>c</b>) PVC-3, (<b>d</b>) Metal-1, (<b>e</b>) Metal-2, (<b>f</b>) Metal-3 at position 0.4 m.</p> Full article ">
25 pages, 4058 KiB  
Article
SCoBi Multilayer: A Signals of Opportunity Reflectometry Model for Multilayer Dielectric Reflections
by Dylan Boyd, Mehmet Kurum, Orhan Eroglu, Ali Cafer Gurbuz, James L. Garrison, Benjamin R. Nold, Manuel A. Vega, Jeffrey R. Piepmeier and Rajat Bindlish
Remote Sens. 2020, 12(21), 3480; https://doi.org/10.3390/rs12213480 - 23 Oct 2020
Cited by 5 | Viewed by 2799
Abstract
A multilayer module is incorporated into the Signals of Opportunity (SoOp) Coherent Bistatic Scattering model (SCoBi) for determining the reflections and propagation of electric fields within a series of multilayer dielectric slabs. This module can be used in conjunction with other SCoBi components [...] Read more.
A multilayer module is incorporated into the Signals of Opportunity (SoOp) Coherent Bistatic Scattering model (SCoBi) for determining the reflections and propagation of electric fields within a series of multilayer dielectric slabs. This module can be used in conjunction with other SCoBi components to simulate complex, bistatic simulation schemes that include features such as surface roughness, vegetation, antenna effects, and multilayer soil moisture interactions on reflected signals. This paper introduces the physics underlying the multilayer module and utilizes it to perform a simulation study of the response of SoOp-R measurements with respect to subsurface soil moisture parameters. For a frequency range of 100–2400 MHz, it is seen that the SoOp-R response to a single dielectric slab is mostly frequency insensitive; however, the SoOp-R response to multilayer dielectric slabs will vary between frequencies. The relationship between SoOp-R reflectivity and the contributing depth is visualized, and the results show that SoOp-R measurements can display sensitivity to soil moisture below the penetration depth. By simulation of simple soil moisture profiles with different wetting and drying gradients, the dielectric contrast between layers is shown to be the greatest contributing factor to subsurface soil moisture sensitivity. Overall, it is observed that different frequencies can sense different areas of a soil moisture profile, and this behavior can enable subsurface soil moisture data products from SoOp-R observations. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Representation of propagation and reflection processes within a discretized soil moisture profile.</p> Full article ">Figure 2
<p>Discretized soil moisture profile representation in SCoBi model and simulator package. Each profile is fit using defined dielectric constant values (shown as black points) over a discretized profile. For clarity, only the relative permittivity is shown.</p> Full article ">Figure 3
<p>(<b>a</b>) Real, (<b>b</b>) imaginary, and (<b>c</b>) magnitude square of the measured reflection coefficient. The color gradient shows the reflection coefficient values for soil moisture between 5% and 50%, and the cyan line shows the reflection coefficient values of water for the given frequency range. The black, dashed lines show the position of the commonly referenced SoOp-R sources, while the red dashed line shows the lower validation region of the Mironov dielectric model. All measurements are performed at normal incidence.</p> Full article ">Figure 4
<p>Behavior of (<b>a</b>) real and (<b>b</b>) imaginary dielectric constant for multiple soil moisture values as a function of frequency in addition to (<b>c</b>) penetration depth information from Equation (<a href="#FD6-remotesensing-12-03480" class="html-disp-formula">6</a>). The color gradient shows the dielectric constant for soil moisture between 5% and 50%, and the cyan line shows the dielectric constant of water for the given frequency range. The black dashed lines show the position of the commonly referenced SoOp-R sources, while the red dashed line shows the lower validation region of the Mironov dielectric model.</p> Full article ">Figure 5
<p>(Left column) Changes in reflectivity due to moving a secondary slab beneath a single dielectric slab and (right column) the corresponding penetration depth for each dual-slab configuration. Each row assumes that the first slab’s SM value is 20%, 30%, and 40% SM, respectively, and all simulations assume a second slab SM of 50% SM.</p> Full article ">Figure 6
<p>Frequency sweep of four two-layer profiles. The white lines represent the location of the second layer, the red line represent the penetration depth of the configuration, and the magenta line depicts where the transmittance reaches 10% of its original energy. The first slab SM is 10% for the upper four subplots and 30% for the lower four subplots. The second slab SM is 50% for all subplots.</p> Full article ">Figure 7
<p>Incidence angle sweep of four two-layer profiles at 370 MHz. The white lines represent the location of the second layer, the red line represent the penetration depth of the configuration, and the magenta line depicts where the transmittance reaches 10% of its original energy. The upper slab SM is 10% for the upper four subplots and 30% for the lower four subplots. The second slab SM is 50% for all subplots.</p> Full article ">Figure 8
<p>Relative difference between reflectivity measurements as a function of clay content within two soil slabs for different frequencies. The upper slab is 15 cm in height, and the second slab is semi-infinite. The top row of subplots show a configuration for SM values of 15% and 30% for Slabs 1 and 2, and the bottom row uses SM configurations of 30% and 15% for Slabs 1 and 2.</p> Full article ">Figure 9
<p>Example soil moisture profiles represented by polynomial-based equations indicated by the title of each subplot: (<b>a</b>,<b>d</b>,<b>g</b>) positive, linear soil moisture profiles; (<b>b</b>,<b>e</b>,<b>h</b>) negative, linear soil moisture profiles; and (<b>c</b>,<b>f</b>,<b>i</b>) second-order polynomial fits.</p> Full article ">Figure 10
<p>Elementary reflection coefficient in the subsurface of the soil moisture profiles of <a href="#remotesensing-12-03480-f009" class="html-fig">Figure 9</a>. Each subplot shares a common legend indicating the frequency of each reflection coefficient. Contributions from the air–surface interface are not depicted.</p> Full article ">Figure 11
<p>Intermediate reflection coefficient solution in the subsurface of the soil moisture profiles of <a href="#remotesensing-12-03480-f009" class="html-fig">Figure 9</a>. The reflection coefficient is initialized by the bottom-most elementary reflection coefficient and determined as the signal travels upward through the profile. Each subplot shares a common legend indicating the frequency of each reflection coefficient. Contributions from the air–surface interface are not depicted.</p> Full article ">
16 pages, 11401 KiB  
Article
Mapping and Assessment of Tree Roots Using Ground Penetrating Radar with Low-Cost GPS
by Lilong Zou, Yan Wang, Iraklis Giannakis, Fabio Tosti, Amir M. Alani and Motoyuki Sato
Remote Sens. 2020, 12(8), 1300; https://doi.org/10.3390/rs12081300 - 20 Apr 2020
Cited by 11 | Viewed by 5475
Abstract
In this paper, we have presented a methodology combining ground penetrating radar (GPR) and a low-cost GPS receiver for three-dimensional detection of tree roots. This research aims to provide an effective and affordable testing tool to assess the root system of a number [...] Read more.
In this paper, we have presented a methodology combining ground penetrating radar (GPR) and a low-cost GPS receiver for three-dimensional detection of tree roots. This research aims to provide an effective and affordable testing tool to assess the root system of a number of trees. For this purpose, a low-cost GPS receiver was used, which recorded the approximate position of each GPR track, collected with a 500 MHz RAMAC shielded antenna. A dedicated post-processing methodology based on the precise position of the satellite data, satellite clock offsets data, and a local reference Global Navigation Satellite System (GNSS) Earth Observation Network System (GEONET) Station close to the survey site was developed. Firstly, the positioning information of local GEONET stations was used to filter out the errors caused by satellite position error, satellite clock offset, and ionosphere. In addition, the advanced Kalman filter was designed to minimise receiver offset and the multipath error, in order to obtain a high precision position of each GPR track. Kirchhoff migration considering near-field effect was used to identify the three-dimensional distribution of the root. In a later stage, a novel processing scheme was used to detect and clearly map the coarse roots of the investigated tree. A successful case study is proposed, which supports the following premise: the current scheme is an affordable and accurate mapping method of the root system architecture. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Surveying scenario of the Metasequoia trees using the proposed 3D GPR system. (<b>b</b>) The low-cost GlobalSat GPS receiver used in this investigation.</p> Full article ">Figure 2
<p>Time-domain reflectometry (TDR) measurements of the soil moisture for the estimation of the subsurface velocity in the site.</p> Full article ">Figure 3
<p>Raw radargram of the tree root investigation using a 500 MHz RAMAC shielded antenna system.</p> Full article ">Figure 4
<p>(<b>a</b>) The location of the GEONET stations in Japan; (<b>b</b>) location of the investigation site and nearest GEONET Station.</p> Full article ">Figure 5
<p>(<b>a</b>) GPS receiver geometry with a reference station; (<b>b</b>) flowchart of the GPS receiver bias estimation and removal by use of the Kalman filter.</p> Full article ">Figure 6
<p>Moving trajectories of antennas recorded by the GlobalSat GPS receiver. (<b>a</b>) The record by the GlobalSat GPS receiver; (<b>b</b>) post-processing results.</p> Full article ">Figure 7
<p>Migrated vertical profiles along the survey direction. (<b>a</b>) Migrated profile at 0.8 m cross-survey direction; (<b>b</b>) migrated profile at 1.6 m cross-survey direction; (<b>c</b>) migrated profile at 2.4 m cross-survey direction; (<b>d</b>) migrated profile at 3.2 m cross-survey direction.</p> Full article ">Figure 8
<p>Migrated horizontal slices at different depths. Red lines indicate the detected roots in the migrated data set. (<b>a</b>) Migrated slice at 16-cm depth; (<b>b</b>) migrated slice at 19-cm depth; (<b>c</b>) migrated slice at 27.5-cm depth.</p> Full article ">Figure 9
<p>Migrated horizontal slices at different depths. Red lines indicate the detected roots in the migrated data set. (<b>a</b>) Migrated slice at 42-cm depth; (<b>b</b>) migrated slice at 59-cm depth; (<b>c</b>) migrated slice at 79.5-cm depth.</p> Full article ">Figure 10
<p>The coarse root detection in a 3D migrated cubic: (<b>a</b>) B-scan profile which contains a tree root. (<b>b</b>) Root extension tracking with the −3 dB positions of a local peak (survey direction). (<b>c</b>) Root extension tracking with the −3 dB positions of a local peak (cross-survey direction).</p> Full article ">Figure 11
<p>The reconstructed 3D root system: (<b>a</b>) View from the starting point; (<b>b</b>) view from the ending point.</p> Full article ">
19 pages, 5801 KiB  
Article
A Modified Model for Electromagnetic Scattering of Sea Surface Covered with Crest Foam and Static Foam
by Dongfang Li, Zhiqin Zhao, Yanwen Zhao, Yuan Huang and Zaiping Nie
Remote Sens. 2020, 12(5), 788; https://doi.org/10.3390/rs12050788 - 1 Mar 2020
Cited by 4 | Viewed by 3338
Abstract
With the increase of sea surface wind speed, whitecaps will appear on the sea surface. Generally, for Electromagnetic (EM) scattering of the foam-covered sea surface, medium-scale waves are used to replace the breaking waves of the real sea surface. Another treatment in computation [...] Read more.
With the increase of sea surface wind speed, whitecaps will appear on the sea surface. Generally, for Electromagnetic (EM) scattering of the foam-covered sea surface, medium-scale waves are used to replace the breaking waves of the real sea surface. Another treatment in computation is to adopt one of the whitecap coverages and fixed foam layer thickness. In fact, the evolution process of a breaking wave goes through two stages: stage A (crest foam) and stage B (static foam). In this paper, a geometric model of the sea surface covered with crest foam and static foam is established. The coverage ratio of stage A and stage B is proposed for the first time for a given sea state. In addition, different foam layer thickness distributions in each foam for various wind speeds are also considered. Based on the facet scattering theory of sea surface, this paper adopts the modified facet-based scattering model to deal with the scattering contribution of the sea surface and the effect of foam. Finally, in order to verify the accuracy of the geometric modeling and the scattering model of the sea surface, the EM backscattering of sea surface under different sea states are calculated. Simulation results show that the results of the proposed model are more consistent with the measured data than the results of the sea surface covered with individual crest foam or the sea surface covered with individual static foam. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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Figure 1

Figure 1
<p>Foam coverage and foam thickness at different wind speeds. (<b>a</b>) Foam coverage models for crest foam and static foam. (<b>b</b>) Foam thickness distributions for crest foam and static foam.</p> Full article ">Figure 2
<p>Foam coverage at different wind speeds. (<b>a</b>) The ratio of crest foam and static foam. (<b>b</b>) Comparison of the Hwang model and the new whitecap coverage summed by crest foam and static foam.</p> Full article ">Figure 3
<p>The sea spectrum for various wind speeds.</p> Full article ">Figure 4
<p>The whitecap coverage in the sea surface. (<b>a</b>) The sea surface without foam. (<b>b</b>) The sea surface covered with crest foam only. (<b>c</b>) The sea surface covered with static foam only. (<b>d</b>) The sea surface covered with the proposed distribution of crest foam and static foam for <span class="html-italic">U</span><sub>10</sub> = 10 m/s. (<b>e</b>) The sea surface covered with the proposed distribution of crest foam and static foam for <span class="html-italic">U</span><sub>10</sub> = 15 m/s.</p> Full article ">Figure 4 Cont.
<p>The whitecap coverage in the sea surface. (<b>a</b>) The sea surface without foam. (<b>b</b>) The sea surface covered with crest foam only. (<b>c</b>) The sea surface covered with static foam only. (<b>d</b>) The sea surface covered with the proposed distribution of crest foam and static foam for <span class="html-italic">U</span><sub>10</sub> = 10 m/s. (<b>e</b>) The sea surface covered with the proposed distribution of crest foam and static foam for <span class="html-italic">U</span><sub>10</sub> = 15 m/s.</p> Full article ">Figure 5
<p>(<b>a</b>) The dielectric constant of seawater. (<b>b</b>) The dielectric constant of sea surface covered with foam.</p> Full article ">Figure 6
<p>The scattering model of the sea surface covered with the foam layer. (1), (2), (3) and (4) represent the four scattering contributions for Electromagnetic (EM) scattering model.</p> Full article ">Figure 7
<p>The scattering of foam layer varying with foam layer thickness for <span class="html-italic">θ<sub>i</sub></span> = 10° and <span class="html-italic">θ<sub>i</sub></span> = 60°.</p> Full article ">Figure 8
<p>Comparison results of Normalized RCS (NRCS) by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam, and the measured data from JOSS-I model. <span class="html-italic">f</span> = 4.455 GHz, <span class="html-italic">U</span><span class="html-italic"><sub>10</sub></span> = 7.7 m/s. (<b>a</b>) VV polarization. (<b>b</b>) HH polarization.</p> Full article ">Figure 9
<p>Comparison results of NRCS by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam, and the measured data from JOSS-I model. <span class="html-italic">f</span> = 4.455 GHz, <span class="html-italic">U</span><span class="html-italic"><sub>10</sub></span> = 10.5 m/s. (<b>a</b>) VV polarization. (<b>b</b>) HH polarization.</p> Full article ">Figure 10
<p>Comparison results of NRCS by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam and the measured data from JOSS-I model. <span class="html-italic">f</span> = 8.91 GHz, <span class="html-italic">U</span><span class="html-italic"><sub>10</sub></span> = 12.5 m/s. (<b>a</b>) VV polarization. (<b>b</b>) HH polarization.</p> Full article ">Figure 11
<p>Comparison results of NRCS by the proposed model, the sea surface covered with crest foam only, the sea surface covered with static foam only, the sea surface covered half crest foam and half static foam and the measured data from 4FRS model. <span class="html-italic">f</span> = 8.91 GHz, U<span class="html-italic"><sub>10</sub></span> = 16 m/s. (<b>a</b>) VV polarization. (<b>b</b>) HH polarization.</p> Full article ">

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15 pages, 3125 KiB  
Technical Note
Link Budget Analysis for GNSS-R Sea Surface Return in Arbitrary Acquisition Geometries Using BA-PTSM
by Gerardo Di Martino, Alessio Di Simone, Antonio Iodice and Daniele Riccio
Remote Sens. 2022, 14(3), 520; https://doi.org/10.3390/rs14030520 - 22 Jan 2022
Cited by 2 | Viewed by 2216
Abstract
In this article, we present a link budget analysis for Global Navigation Satellite System (GNSS) signals scattered off the sea surface in arbitrary acquisition geometries. The aim of our study is to investigate the reliability of the Geometrical Optics (GO) scattering model, which [...] Read more.
In this article, we present a link budget analysis for Global Navigation Satellite System (GNSS) signals scattered off the sea surface in arbitrary acquisition geometries. The aim of our study is to investigate the reliability of the Geometrical Optics (GO) scattering model, which accurately describes sea surface scattering at and near the specular reflection direction, in properly modeling the sea surface return in far-from-specular acquisition geometries, which are of interest for maritime surveillance purposes and where GO is expected to fail. To this end, we adopted the recent Bistatic Anisotropic Polarimetric Two-Scale Model (BA-PTSM), which revealed good agreement with advanced scattering models, such as the second-order Small Slope Approximation (SSA2), regardless of the acquisition geometry, with the advantage of a reduced computational complexity. Numerical results have been derived for both circular polarization channels and for both spaceborne and airborne GNSS-Reflectometry (GNSS-R). It has been shown that, as long as conventional GNSS-R processing is assumed, GO can be safely adopted for simulation and analysis of spaceborne GNSS-R data regardless of the acquisition geometry and sea state, whereas more accurate scattering models, e.g., BA-PTSM, should be used for airborne receivers in far-from-specular configurations. Full article
(This article belongs to the Special Issue Electromagnetic Modeling in Microwave Remote Sensing)
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Figure 1

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<p>Conventional (LHCP-forward-scattering, red box) vs. unconventional (RHCP-backscattering, green box) GNSS-R.</p> Full article ">Figure 2
<p>Scattering geometry and reference system.</p> Full article ">Figure 3
<p>SNR in RL polarization for a spaceborne GNSS-R receiver obtained using BA-PTSM (solid lines) and GO (dashed lines) for wind speed 5 m/s (blue lines), 15 m/s (red lines), and 25 m/s (green lines). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>120</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>150</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>180</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>SNR in RR polarization for a spaceborne GNSS-R receiver obtained using BA-PTSM (solid lines) and GO (dashed lines) for wind speed 5 m/s (blue lines), 15 m/s (red lines), and 25 m/s (green lines). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>120</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>150</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>180</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>SNR in RL polarization for an airborne GNSS-R receiver obtained using BA-PTSM (solid lines) and GO (dashed lines) for wind speed 5 m/s (blue lines), 15 m/s (red lines), and 25 m/s (green lines). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>120</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>150</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>180</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>SNR in RR polarization for an airborne GNSS-R receiver obtained using BA-PTSM (solid lines) and GO (dashed lines) for wind speed 5 m/s (blue lines), 15 m/s (red lines), and 25 m/s (green lines). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>120</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>e</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>150</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>f</b>) <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>s</mi> </msub> <mo>=</mo> <msup> <mn>180</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p> Full article ">
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