Computation and Experiment on Linearly and Circularly Polarized Electromagnetic Wave Backscattering by Corner Reﬂectors in an Anechoic Chamber

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Article Computation and Experiment on Linearly and Circularly Polarized Electromagnetic Wave Backscattering by Corner Reﬂectors in an Anechoic Chamber

Mohammad Nasucha 1,2,*, Josaphat T. Sri Sumantyo 1, Cahya E. Santosa 1, Peberlin Sitompul 1, Agus H. Wahyudi 1, Yang Yu 1 and Joko Widodo 1

1 Center for Environmental Remote Sensing, Graduate School of Science and Engineering, Chiba University, Chiba 263-8522, Japan; [email protected] (J.T.S.S.); [email protected] (C.E.S.); [email protected] (P.S.); [email protected] (A.H.W.); aﬀ[email protected] (Y.Y.); [email protected] (J.W.) 2 Department of Informatics, Universitas Pembangunan Jaya, Tangerang Selatan 15413, Indonesia * Correspondence: [email protected]; Tel.: +81-070-4404-4451

Received: 22 August 2019; Accepted: 21 September 2019; Published: 24 September 2019

Abstract: Electromagnetic wave backscattering by corner reflectors in an anechoic chamber is studied using our developed computational tool. The tool applies the Finite-Difference Time-Domain (FDTD) method to simulate the propagation of the wave’s electric and magnetic fields. Experimental measurement in an anechoic chamber is also carried out as a comparison. The two results show agreement, including the finding that the backscatter intensity variation amongst the four circularly polarized modes is significantly smaller than the variation amongst the four linearly polarization modes.

Keywords: computation in radar; computation in synthetic aperture radar; backscattering by corner reﬂectors; simulation on circularly polarized electromagnetic waves

1. Introduction Understanding electromagnetic (EM) wave backscattering by corner reflectors is of interest to radar researchers. In particular, the backscattering of circularly polarized (CP) EM waves is of great interest. To study these CP EM waves, computations can be useful. The articles [1–9] report previously done computations on EM wave distribution in an anechoic chamber, but not in the context of backscattering by corner reflectors or in the context of CP EM waves. These works contributed to the development and performance improvement of the anechoic chamber. The articles [10–16] report computations and analyses on EM wave backscattering by corner reflectors. However, most of the reported computations for EM waves were done for non-polarized and linearly polarized waves. Until today, only [10] reports a computation on circularly polarized EM waves. It used the Method of Moments, and the report did not present any technical details about how the circular polarization was realized. To respond to this situation, our research aims to study circularly polarized EM wave backscattering by corner reflectors in an anechoic chamber through a computation using the Finite-Difference Time-Domain (FDTD) method. There has been no such work reported thus far. As an addition, we did the same computation for linearly polarized (LP) EM waves. An equivalent experiment has also been carried out to obtain a comparison.

Computation 2019, 7, 55; doi:10.3390/computation7040055 www.mdpi.com/journal/computation Computation 2019, 7, 55 2 of 17

Computation 2019, 7, x FOR PEER REVIEW 2 of 16 The simulation was done using our developed computational tool, called Anechoic Chamber SimulationThe simulation Tool Version was 1 (AST_V1).done using Both our thedeveloped simulation computational and the experiment tool, called were doneAnechoic for four Chamber target types,Simulation i.e., triangular Tool Version trihedral, 1 (AST_V1). horizontal Both plate the bar,simulation vertical and plate the bar, experiment and sphere, were and done for all for linear four polarizationtarget types, and i.e., alltriangular circular polarizationtrihedral, horizontal modes. plate bar, vertical plate bar, and sphere, and for all linearThe polarization remainder and ofthis all circular articleis polarization arranged as modes. follows: Section2 addresses the method, Section3 reportsThe the remainder results, Section of this4 discussesarticle is arranged the results, as and follows: Section Section5 summarizes 2 addresses the contentthe method, of all sections.Section 3 reports the results, Section 4 discusses the results, and Section 5 summarizes the content of all 2.sections. Method

2.1.2. Method The Measurement Plan The measurement plan is depicted in Figure1. This was the scenario to be followed by both the computation2.1. The Measurement and the experiment.Plan It can be described as follows: The measurement plan is depicted in Figure 1. This was the scenario to be followed by both the i. The cuboid anechoic chamber size shall be 6.5 (length) 4.0 (width) 2.4 m (height). computation and the experiment. It can be described as follows:× × ii. The distance between the transmitter (TX) and the receiver (RX) antennas shall be 0.8 m. i. The cuboid anechoic chamber size shall be 6.5 (length) × 4.0 (width) × 2.4 m (height). iii.ii. TheThe distance distance between between the the transmitter target (corner (TX) and reﬂector) the receiver and antennas (RX) antennas in the orthogonalshall be 0.8 m. direction iii. Theshall distance be 3.0 between m. the target (corner reflector) and antennas in the orthogonal direction shall iv. beThe 3.0 vectorm. network analyzer (VNA)’s port 1 shall feed signals to the TX antenna. v.iv. TheThe vector RX antenna network shall analyzer feed signals (VNA)’s to port the VNA’s 1 shall portfeed 2.signals to the TX antenna. vi.v. TheThe RX turntable antenna shallshall befeed controlled signals to by the the VNA’s turntable port controller. 2. vii.vi. TheBoth turntable the VNA shall and be the controlled turntable by controller the turntable can be controller. driven by the Personal Computer (PC). viii.vii. BothPhase the shiftersVNA and shall the be turntable provided controller for the TX can and be RX driven antennas by the in Personal the case of Computer circular polarization (PC). viii. Phaseand shallshifters be installedshall be provided correctly for eachthe TX mode, and RX i.e., antennas RX right-handed in the case TX of right-handed circular polarization (RR), RX andleft-handed shall be installed TX right-handed correctly for (LR), each RX mode, left-handed i.e., RX TX right-handed right-handed TX (LR), right-handed or RX left-handed (RR), RX left-handedTX left-handed TX right-handed (LL). Phase (LR), shifters RX will left-handed not be needed TX right-handed for linear polarization (LR), or RX modes,left-handed i.e., RXTX left-handedhorizontal TX(LL). horizontal Phase shifters (HH), RXwill vertical not be TX needed horizontal for (VH),linear RX polarization horizontal TXmodes, vertical i.e., (HV), RX horizontaland RX vertical TX horizontal TX vertical (HH), (VV). RX vertical TX horizontal (VH), RX horizontal TX vertical (HV), ix. andThe RX transmit vertical power TX vertical shall be(VV). 5 dBm for all measurement cases. x.ix. TheThe transmit target shallpower be shall placed be on5 dBm a turntable for all measurement in such a way cases. so that elevation angle θ = 0◦, and be x. Therotated target in shall such be a way placed so that on thea turntable aspect angle in suchφ changes a way fromso that90 elevationto 90 (negative angle θ and= 0°, positive and be − ◦ ◦ rotatedsigns respectivelyin such a way represent so that the the aspect left and angle the rightϕ changes sides from of the –90° target) to 90° with (negative 5◦ increments. and positive xi. signsThe respectively EM wave frequency represent shall the beleft chosen and the in ri suchght sides a way of so the that target) 5λ < withtarget 5° size increments.< 10λ. xi. The EM wave frequency shall be chosen in such a way so that 5λ < target size < 10λ.

FigureFigure 1.1. TheThe measurementmeasurement plan. plan. The The pyramidal pyramidal absorbers absorbers shall shall be be placed placed evenly evenly at at the the inner inner sides sides of allof all six six chamber’s chamber’s walls. walls.

Definitions of the elevation angle θ and the aspect angle ϕ are explained in Figure 2. The targets were corner reflectors of four different shapes: Trihedral, horizontal bar, vertical bar, and sphere. To make it realistic for practices, every target was chosen to be large enough compared to the wavelength

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Deﬁnitions of the elevation angle θ and the aspect angle φ are explained in Figure2. The targets

Computationwere corner 2019 reflectors, 7, x FOR PEER of four REVIEW diff erent shapes: Trihedral, horizontal bar, vertical bar, and sphere.3 of 16 To make it realistic for practices, every target was chosen to be large enough compared to the wavelength but not too large to be carried in a radar mission. Here Here we we use use the the term term “med “mediumium size” to specify that 5λ < targettarget size size < 1010λλ.. The The targets targets and and their their descriptions descriptions are are listed listed in in Table Table 11.. TheThe horizontalhorizontal andand thethe vertical plate bars are simply the same object, only having didifferentfferent standingstanding orientations.orientations.

Figure 2. Deﬁnitions of angles used in this work. The elevation angle θ is the angle between the target’s Figure 2. Definitions of angles used in this work. The elevation angle θ is the angle between the facing direction and the horizontal plane. The aspect angle φ is the electromagnetic (EM) wave incident target’s facing direction and the horizontal plane. The aspect angle ϕ is the electromagnetic (EM) wave angle in the azimuth point of view (in other words, the angle between the target’s facing direction and incident angle in the azimuth point of view (in other words, the angle between the target’s facing the vertical plane). Every measurement case in this study shall be done with θ = 0 and –90 φ 90 . direction and the vertical plane). Every measurement case in this study shall be done◦ with◦ θ≤ = 0°≤ and◦ –90° ≤ ϕ ≤ 90°. Table 1. List of targets and their descriptions.

No. TargetTable 1. List of targets and their descriptions. Description 1 Sphere A conducting thin-plate sphere having a diameter of 26 cm No.2 Target Trihedral A conducting thin-plate Description triangular trihedral having a width of 64 cm 13 Sphere Horizontal bar A conducting thin-plate A conducting sphere thin-plate having bara diameter of 4 63 cmof 26 cm × 24 Trihedral Vertical bar A conducting thin-plate The same triangular as target no.trihedral 3 but vertically having a positioned width of 64 cm 3 Horizontal bar A conducting thin-plate bar of 4 × 63 cm 2.2. The4 Method Vertical of Computation bar The same as target no. 3 but vertically positioned The computation was done systematically to fulfill the measurement plan specified in Section 2.1. 2.2. The Method of Computation A project definition, software requirement review, preliminary design review, and critical design review wereThe carried computation out before was coding done andsystematically implementation to fulfill [17 ].the The measurement critical design plan review specified (CDR) in Section of the 2.1.AST_V1 A project is presented definition, in Figures software3 and requirement4. The tool revi requiresew, preliminary default input design data, review, including and the critical permittivity design reviewand the were permeability carried out of freebefore space, coding and and the implemen relative permittivitytation [17]. (dielectricThe critical constant) design review and the (CDR) relative of thepermeability AST_V1 ofis thepresented air (because in Figures the transmission 3 and 4. The medium tool inrequires the experiments default in isput the air).data, However, including these the permittivityvalues can be and approximated the permeability by 1. Theof free tool space, needs and simulation the relative case-related permittivity data, (dielectric including constant) the anechoic and thechamber relative size; permeability the type,size, of the and air material(because properties the transmission of corner medium reflector; in the the experiments type and the is materialthe air). However,properties these of the values antennas; can the be distanceapproximated between by the 1. TXThe and tool RX needs antennas; simulation the distance case-related between data, the includingantennas andthe theanechoic corner chamber reflector; size; the polarizationthe type, size, mode and (eithermaterial HH, properties VH, HV, of VV, corner RR, LR, reflector; RL, or LL);the typeand theand Nyquist the material factor. properties The larger of the the Nyquist antennas; factor the chosen distance by thebetween user, thethe smallerTX and theRX FDTDantennas; cell sizethe distanceconfigured between by the the tool antennas will be, and and thus the thecorner more refle accuratector; the the polarization simulation resultsmode (either can be expectedHH, VH, toHV, be VV,while RR, more LR, computerRL, or LL); resources and the willNyquist be consumed. factor. The larger the Nyquist factor chosen by the user, the smaller the FDTD cell size configured by the tool will be, and thus the more accurate the simulation results can be expected to be while more computer resources will be consumed. The field distribution was simulated using the FDTD method by applying the Yee-grid configuration [18,19], employing an electric- and magnetic-fields update technique based on Maxwell equations [18–22], and realizing the energy-absorbing walls of the anechoic chamber with perfectly matched layers (PMLs) [20]. The real size of the anechoic chamber is 6.5 (length) × 4.0 (width) × 2.4 m (height). However, to minimize the usage of computer resources, the computation space domain was reduced to 4.2 (length) × 2.2 (width) × 2.0 m (height). The cuboid space domain was chosen in such a way that it is small enough but still contains all the objects of interest, i.e., the TX antenna, the RX antenna, and the corner reflector. This arrangement is valid because EM wave paths between the TX antenna and the corner reflector, and between the corner reflector and the RX antenna are “line of sight”. This computation space domain was realized by a Yee-grid consisting of 337 × 177 × 161 (9.6

Computation 2019, 7, x FOR PEER REVIEW 4 of 16 million)Computation cells,2019 ,where7, 55 the cell size was 1.25 × 1.25 × 1.25 cm. With a lambda of 10 cm (f = 3 GHz),4 this of 17 cell size corresponds to a Nyquist rate of 8, which is well above the minimum Nyquist rate, i.e., 2.

FigureFigure 3. 3. CriticalCritical design design review review of of Anechoic Anechoic Chamber Chamber Simulation Simulation Tool Tool Version Version 1 1 (AST_V1) (AST_V1) presented presented inin a a flow ﬂow chart chart (part (part 1). 1).

The field distribution was simulated using the FDTD method by applying the Yee-grid configuration [18,19], employing an electric- and magnetic-fields update technique based on Maxwell equations [18–22], and realizing the energy-absorbing walls of the anechoic chamber with perfectly matched layers (PMLs) [20]. The real size of the anechoic chamber is 6.5 (length) 4.0 (width) 2.4 m × × (height). However, to minimize the usage of computer resources, the computation space domain was reduced to 4.2 (length) 2.2 (width) 2.0 m (height). The cuboid space domain was chosen in such × × a way that it is small enough but still contains all the objects of interest, i.e., the TX antenna, the RX antenna, and the corner reflector. This arrangement is valid because EM wave paths between the TX antenna and the corner reflector, and between the corner reflector and the RX antenna are “line of sight”. This computation space domain was realized by a Yee-grid consisting of 337 177 161 × × (9.6 million) cells, where the cell size was 1.25 1.25 1.25 cm. With a lambda of 10 cm (f = 3 GHz), × × this cell size corresponds to a Nyquist rate of 8, which is well above the minimum Nyquist rate, i.e., 2. In the computation, before the FDTD iteration, several procedures were carried out. The TX and RX antennas were synthesized, and targets were also synthesized and rotated according to the requested aspect angle φ. The transmitted power was converted to the transmitted voltage, transmitted wave intensity, and transmitted electric field. The transmitted electric field was represented in sinusoidal waves and fed carefully to the TX antenna by considering the requested mode of polarization.

Computation 2019, 7, 55 5 of 17 Computation 2019, 7, x FOR PEER REVIEW 5 of 16

Figure 4. CriticalCritical design design review review of AST_V1 presented in a flow ﬂow chart (part 2).

InFor the each computation, mode of linear before polarization, the FDTD iteration, i.e., RX Horizontal–TX several procedures Horizontal were carried (HH), out. RX Vertical–TXThe TX and RXHorizontal antennas (VH), were RX synthesized, Horizontal–TX and Verticaltargets were (HV), also or RX synthesized Vertical–TX and Vertical rotated (VV), according either theto the TX requestedhorizontal aspect or TX verticalangle ϕ antenna. The transmitted was fed with power the sinusoidalwas converted waves. to Fortheeach transmitted mode of voltage, circular polarization,transmitted wave i.e., RR, intensity, LR, RL, orand LL, transmitted more attention electric was field. required The since transmitted both the TXelectric horizontal field was and TXrepresented vertical antenna in sinusoidal needed waves to be fedand simultaneouslyfed carefully to with the TX the antenna same train by ofconsidering sinusoidal the waves, requested but of modedifferent of polarization. phases. ForDuring each the mode iteration of linear of thepolarization, FDTD calculation, i.e., RX Horizontal–TX the value of the Horizontal electric field (HH), arriving RX Vertical–TX at the RX Horizontalantenna was (VH), stored RX atHorizontal–TX every step. Upon Vertical completion (HV), or ofRX the Vertical–TX calculation Vertical iteration, (VV), the either set of the stored TX horizontalelectric field or values TX vertical was converted antenna towas the fed received with wavethe sinusoidal intensity andwaves. optionally For each received mode power.of circular The polarization,backscattered i.e., wave RR, intensity LR, RL, or in LL, dB wasmore calculated attention by:was required since both the TX horizontal and TX vertical antenna needed to be fed simultaneously with the same train of sinusoidal waves, but of Ir different phases. BS Intensity (dB) = 10 log( ) (1) It During the iteration of the FDTD calculation, the value of the electric field arriving at the RX whereantennaIt iswas the stored intensity at every of the transmittedstep. Upon wavecompletion and Ir isof thethe intensity calculation of the iteration, received the wave. set of Since stored the electricintensity field equals values the was voltage converted amplitude to the squared, received while wave the intensity voltage and is proportional optionally received to the electric power. field, The backscatteredthe backscattered wave wave intensity intensity in dB can was be calculated alternatively by: obtained by:

BS Intensity (dB) = 10 log( E)r (1) BS Intensity (dB) = 20 log( ) (2) Et where It is the intensity of the transmitted wave and Ir is the intensity of the received wave. Since the where E is the electric ﬁeld transmitted by the TX antenna and E is the electric ﬁeld received by the intensityt equals the voltage amplitude squared, while the voltager is proportional to the electric field, RX antenna. the backscattered wave intensity can be alternatively obtained by: The software has now become a graphical user interface (GUI) tool, namely AST_V1. The tool is currently capable of handling simulationsBS Intensity on EM (dB) wave = 20 backscattering log( ) in an anechoic chamber with(2) a size range of between 2 2 2 m to 20 20 20m in the frequency range of 3 to 8 GHz, with a full × × × × where Et is the electric field transmitted by the TX antenna and Er is the electric field received by the RX antenna.

Computation 2019, 7, x FOR PEER REVIEW 6 of 16

The software has now become a graphical user interface (GUI) tool, namely AST_V1. The tool is currently capable of handling simulations on EM wave backscattering in an anechoic chamber with Computation 2019, 7, 55 6 of 17 a size range of between 2 × 2 × 2 m to 20 × 20 × 20m in the frequency range of 3 to 8 GHz, with a full circle rotation turntable for the device under test (DUT), which has two horizontal dipole antennas circleand two rotation vertical turntable dipole forantennas. the device under test (DUT), which has two horizontal dipole antennas and two verticalThe AST_V1 dipole user antennas. interface’s appearance is shown in Figure 5. The four target types synthesized by theThe tool AST_V1 are shown user interface’s in Figure appearance6. Some visualiz is shownation in frames Figure5 during. The four a simulation target types are synthesized presented by in theFigure tool 7, are where shown target in Figure type6 =. Sometrihedral, visualization f = 3 GHz, frames polarization during amode simulation = RR, areθ = presented0°, and ϕ = in 0°. Figure In this7, wherefigure, targetthe target type structure,= trihedral, thef an=tenna3 GHz, structure, polarization and the mode electric= RR, fieldθ = distribution0◦, and φ = within0◦. In thisthe cuboid figure, the3D targetspace are structure, visualized the antennaby applying structure, one horizontal and the electric cutting field plane distribution and one or within two vertical the cuboid cutting 3D spaceplane(s). are visualized by applying one horizontal cutting plane and one or two vertical cutting plane(s). ItIt isis necessarynecessary toto mentionmention thatthat everyevery cuboidcuboid shownshown inin thethe figuresfigures visualizesvisualizes aa 3D3D spacespace thatthat isis smallersmaller thanthan thethe anechoicanechoic chamber,chamber, becausebecause itit representsrepresents onlyonly thethe FDTDFDTD spacespace domain.domain. ThisThis spacespace domain reduction technique technique is is applied applied to to reduce reduce computation computation time. time. The Thecomputation computation was done was donewith witha personal a personal computer computer that uses that an uses Intel an CORE Intel COREi7 processor i7 processor and a set and of a32 set GB of random 32 GB randomaccess memory access memory(RAM). (RAM). For future operations,operations, inin additionaddition toto thethe usage of dipole antennas, thethe tool can be equipped with more antennaantenna choices, choices, e.g., e.g., the the circularly circularly polarized polarized microstrip microstrip antenna antenna [23] that [23] can that handle can a frequencyhandle a rangefrequency of 4.83 range to 5.71of 4.83 GHz. to 5.71 If the GHz. tool If isthe modified tool is modified to handle to lower-frequencyhandle lower-frequency operations, operations, it can be it equippedcan be equipped with lower-frequency with lower-frequency antennas, antennas, e.g., the e.g., circularly the circularly polarized polarized microstrip microstrip antenna antenna [24] that [24] can handlethat can frequencies handle frequencies of around 2.2of GHz.around If it2.2 is intendedGHz. If toit dois simulationsintended to fordo higher simulations frequencies, for higher it can befrequencies, equipped with,it can forbe example,equipped the wi circularlyth, for example, polarized the microstrip circularly [polarized25] that can microstrip operate in [25] frequencies that can ofoperate around in 9.4frequencies GHz. of around 9.4 GHz.

Figure 5.5. The appearance of the AST_V1 user interface.

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Figure 6. The four target types synthesized by the tool. In this figure, the elevation angle is 0° and Figure 6. The four target types synthesized by the tool. In this ﬁgure, the elevation angle is 0◦ and aspectFigure angle 6. The is fouralso 0°.target types synthesized by the tool. In this figure, the elevation angle is 0° and aspect angleangle isis alsoalso 00°.◦.

Figure 7. VisualizationVisualization during during a asimulation simulation (tri (trihedralhedral corner corner reflector, reﬂector, 3 GHz, 3 GHz, RR, RR, θ =θ 0°,= ϕ0 ◦=, 0°).φ = The0◦).

The3DFigure volume 3D 7. volume Visualization is visualized is visualized during by applying by a applyingsimulation a horizontal a horizontal(trihedral cutting corner cutting plane reflector, plane and andtwo 3 GHz,two vertical verticalRR, cuttingθ = cutting0°, ϕ planes: = 0°). planes: The (a) (Antennas3Da) Antennasvolume and is andvisualized target target visualization visualization by applying before beforea horizontal the the Fi Finite-Dinite-Difference cuttingﬀ planeerence andTime-Domain Time-Domain two vertical (FDTD) cutting calculation planes: (a) started,Antennas where and each target TX visualization and RX antenna before set theconsiste consisted Finite-Differenced of a horizontal Time-Domain and and a a vertical (FDTD) dipole dipole calculation antenna. antenna. (started,b–d) show where the each FDTD TX states and respectivelyrespectiveRX antennaly atatset stepssteps consiste 180,180,d 519,519, of a andand horizontal 11541154 ofof 1154.1154.and a vertical dipole antenna. (b–d) show the FDTD states respectively at steps 180, 519, and 1154 of 1154.

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2.3. The Method of Experiment The experiment was carried out thoroughly to fulﬁll the measurement plan speciﬁed in Section 2.1. It was done in the following sequence: i. The target, the TX antenna, and the RX antenna were placed properly according to Figure1. Each TX and RX antenna set consisted of a horizontal antenna and a vertical antenna. ii. Two phase shifters were provided to be used in the cases of circular polarization only (RR, LR, LR, LL). One phase shifter was used for the TX antenna, and another phase shifter was used for the RX antenna. iii. Before the measurements, the VNA conducted a calibration involving the measurement of the loss and time delay contributed by extended coax cables and connectors. iv. The VNA conducted the whole measurement cases, where

The transmit power was always set to 5 dBm. • The measurement mode was always set to Backscattering/Inverse Synthetic Aperture • Radar (ISAR). Equal measurements were done for the corner reﬂectors with shapes of sphere, trihedral, • horizontal bar, and vertical bar. For every target, measurements for all linear polarization modes (HH, VH, HV, VV) were • done consecutively. For every target and every linear polarization mode, measurements were done • consecutively for turntable angle = –90◦ until 90◦ with 5◦ increments, where for each of these turntable angles, measurements were done for f = 3 GHz until f = 9 GHz with 0.01 GHz increments. For every target, measurements for all circular polarization modes (RR, LR, RL, LL) were • done consecutively. For these cases, the two phase shifters were employed accordingly. For every target and every circular polarization mode, measurements were done • consecutively for turntable angle = –90◦ until 90◦ with 5◦ increments, where for each of these turntable angles, measurements were done for f = 3 GHz until f = 9 GHz with 0.01 GHz increments.

The EM wave feeding from port 1 of the VNA to the TX antennas and from the RX antenna to port 2 of the VNA, and the usage of the phase shifters for every polarization mode are described in Table2 (theoretical) and Table3 (practical). Et represents the amplitude of the transmitted electric field (at the TX antennas), whereas Er represents the amplitude of the received electric field (at the RX antennas). Here, the usage of Et, Er, and the sine function is only to describe the arrangements of phase shifting in the cases of circular polarization. The values of Et of different measurement cases were not necessarily the same, and the values of Er of different measurement cases were not necessarily the same either.

Table 2. Theoretical wave feeding, wave sensing and phase shifting for linearly polarized (LP) and circularly polarized (CP) modes.

Electric Field Sensing at Electric Field Feeding to Polarization (RX/TX) Horizontal Vertical Horizontal Vertical RX Antenna RX Antenna TX Antenna TX Antenna HH e(t) = Erin(2πft)- e(t) = Etsin(2πft)- VH - e(t) = Ersin(2πft) e(t) = Etsin(2πft)- HV e(t) = Ersin(2πft)-- e(t) = Etsin(2πft) VV - e(t) = Ersin(2πft)- e(t) = Etsin(2πft) RR e(t) = Ersin(2πft) e(t) = Ersin(2πft 0.5π) e(t) = Etsin(2πft) e(t) = Etsin(2πft + 0.5π) − LR e(t) = Ersin(2πft) e(t) = Ersin(2πft + 0.5π) e(t) = Etsin(2πft) e(t) = Etsin(2πft + 0.5π) RL e(t) = Ersin(2πft) e(t) = Ersin(2πft – 0.5π) e(t) = Etsin(2πft) e(t) = Etsin(2πft 0.5π) − LL e(t) = Ersin(2πft) e(t) = Ersin(2πft + 0.5π) e(t) = Etsin(2πft) e(t) = Etsin(2πft 0.5π) − Computation 2019, 7, 55 9 of 17

Table 3. Practical wave feeding, wave sensing, and phase shifting for LP and CP modes. Please notice the diﬀerent arrangements of phase shifting for the receiver (RX) right-handed transmitter (TX) right-handed (RR), RX left-handed TX right-handed (LR), RX left-handed TX right-handed (LR), or RX left-handed TX left-handed (LL) modes compared to Table3.

Electric Field Sensing at Electric Field Feeding to Polarization (RX/TX) Horizontal Vertical Horizontal Vertical RX Antenna RX Antenna TX Antenna TX Antenna HH e(t) = Ersin(2πft)- e(t) = Etsin(2πft)- ComputationVH 2019, 7, x FOR PEER - REVIEW e(t) = Ersin(2πft) e(t) = Etsin(2πft)-9 of 16 HV e(t) = Ersin(2πft)-- e(t) = Etsin(2πft) VV - e(t) = Ersin(2 ft)- e(t) = Etsin(2 ft) Electric Field Sensing at π Electric Field Feeding to π RR e(t) = Etsin(2πft + 0.5π) e(t) = Ersin(2πft) e(t) = Etsin(2πft) e(t) = Etsin(2πft + 0.5π) Polarization (RX/TX) Horizontal Vertical Horizontal Vertical LR e(t) = Ersin(2πft) e(t) = Etsin(2πft + 0.5π) e(t) = Etsin(2πft) e(t) = Etsin(2πft + 0.5π) RX Antenna RX Antenna TX Antenna TX Antenna RL e(t) = Etsin(2πft + 0.5π) e(t) = Ersin(2πft) e(t) = Etsin(2πft + 0.5π) e(t) = Etsin(2πft) HH e(t) = Ersin(2πft) - e(t) = Etsin(2πft) - LL e(t) = Ersin(2πft) e(t) = Etsin(2πft + 0.5π) e(t) = Etsin(2πft + 0.5π) e(t) = Etsin(2πft) VH - e(t) = Ersin(2πft) e(t) = Etsin(2πft) - HV e(t) = Ersin(2πft) - - e(t) = Etsin(2πft) VV - e(t) = Ersin(2πft) - e(t) = Etsin(2πft) Please noticeRR that a right-handede(t) = Etsin(2πft + 0.5 circularlyπ) e(t) = Er polarizedsin(2πft) (RHCP)e(t) = Etsin(2π TXft) antennae(t) = Etsin(2 canπft + 0.5 beπ) realized by feeding the TX horizontalLR antennae(t) = Ersin(2 withπft) ae(t) train = Etsin(2 ofπ sineft + 0.5 wavesπ) e(t) = and Etsin(2 atπft the) e(t) same = Etsin(2 timeπft + 0.5 feedingπ) the TX RL e(t) = Etsin(2πft + 0.5π) e(t) = Ersin(2πft) e(t) = Etsin(2πft + 0.5π) e(t) = Etsin(2πft) vertical antenna withLL the 90◦ forward-shiftede(t) = Ersin(2πft) e(t) version = Etsin(2π offt + the0.5π) samee(t) = Et wavesin(2πft + train. 0.5π) Then,e(t) = Et uponsin(2πft) backscattering by a target, whenPlease expecting notice that at a the right-handed RX antenna, circularly an echo polarized with (RHCP) the same TX circularantenna can direction be realized (RHCP) by will be sensed properlyfeeding if the its TX vertical horizontal part antenna (the ﬁeld with senseda train of by sine the waves RX verticaland at the antenna) same time is feeding shifted the 90 TX◦ backward before thevertical summation antenna of with the horizontalthe 90° forward-shifted and vertical version parts. of Thisthe same is the wave reason train. for Then, the phase-shiftingupon backscattering by a target, when expecting at the RX antenna, an echo with the same circular direction direction of the RX vertical antenna being opposite to the TX vertical antenna in the RR case. In the case (RHCP) will be sensed properly if its vertical part (the field sensed by the RX vertical antenna) is of LR, the echoshifted received 90° backward at the before RX the antenna summation is expected of the hori tozontal have and the vertical opposite parts. directionThis is the reason to the for transmitted wave, andthe thus phase-shifting at the RXvertical directionantenna, of the RX vertical the echo ante isnna shifted being inopposite the same to the direction TX vertical as antenna the phase in shifting of the TX verticalthe RR case. antenna. In the case This of LR, is the the mainecho received message at the of RX Table antenna2. is expected to have the opposite direction to the transmitted wave, and thus at the RX vertical antenna, the echo is shifted in the same Unfortunately, the theoretical phase shifting described in Table2 requires two types of phase direction as the phase shifting of the TX vertical antenna. This is the main message of Table 2. shifters, i.e., +90 and 90 , for realization. When only the same type phase shifters are available for Unfortunately,◦ − the◦ theoretical phase shifting described in Table 2 requires two types of phase shifters, the experiment,i.e., +90° then and −90°, all CPfor realization. modes can When be only realized the same by type the phase technique shifters are described available for in the Table experiment,3. Somethen activities all CP modes that can took be realized place by during the technique the experiment described in Table are 3. presented in Figure8, whereas the Some activities that took place during the experiment are presented in Figure 8, whereas the physical appearances of the targets are depicted in Figure9. physical appearances of the targets are depicted in Figure 9.

Figure 8. SomeFigure activities8. Some activities that took that took place place during during the the experiment: (a) (Measuringa) Measuring the target the material’s target material’s dielectric constant,dielectric constant, (b) after (b) theafter antenna the antenna and and the the phasephase shifter shifter installation, installation, (c) the ( cphase) the shifter, phase and shifter, and (d) antenna–target(d) antenna–target horizontal horizontal alignment alignment using using a a laser laser liner.

Computation 2019, 7, 55 10 of 17 ComputationComputation 20192019,, 77,, xx FORFOR PEERPEER REVIEWREVIEW 1010 ofof 1616

FigureFigure 9.9. TargetsTargets availableavailable forfor experiments.experiments. TheThe cylinde cylindercylinderr is is not not partpart ofof thisthisthis report.report.report. During During the the measurement,measurement, thethe barbar cancan bebe positionedpositioned horizontallyhorizontally oror vertically.vertically.

3.3. Results Results ResultsResults ofofof bothbothboth simulation simulationsimulation and andand experiment experimentexperiment are arar presentedee presentedpresented here. here.here. Through ThroughThrough the thethe following followingfollowing graphs, graphs,graphs, the thebackscatteredthe backscatteredbackscattered EM waveEMEM wavewave intensity intensityintensity is depicted isis depicteddepicted for each foforr targeteacheach targettarget and each andand polarization eacheach polarizationpolarization mode. mode.mode. Every Every figureEvery presentsfigurefigure presentspresents (Figures (Figures (Figures10–13) the 10–13)10–13) measurement thethe measurementmeasurement results of a re targetresultssults where ofof aa thetargettarget results wherewhere of linear thethe resultsresults polarization ofof linearlinear and polarizationcircularpolarization polarization andand circularcircular can be polarizationpolarization compared. cancan From bebe thecompared.compared. same figure, FromFrom the thethe simulation samesame figure,figure, results thethe simulationsimulation and experimental resultsresults andresultsand experimentalexperimental of the same resultsresults target ofof can thethe be samesame compared targettarget cancan too. bebe In comparedcompared all figures, too.too. the InIn dotted allall figures,figures, lines thethe are dotteddotted scatter lineslines graphs, areare whereasscatterscatter graphs,graphs, the solid whereaswhereas lines are thethe their solidsolid second-order lineslines areare theirtheir polynomial second-ordersecond-order trendlines. polynomialpolynomial trendlines.trendlines.

Figure 10. Backscatter intensity of a medium-sized trihedral (w/λ = 6.4): (a) Simulation result of LP, FigureFigure 10.10. BackscatterBackscatter intensityintensity ofof aa medium-sizedmedium-sized trihedraltrihedral ((ww//λλ == 6.4):6.4): ((aa)) SimulationSimulation resultresult ofof LP,LP, (b) simulation result of CP, (c) experimental result of LP, and (d) experimental result of CP. ((bb)) simulationsimulation resultresult ofof CP,CP, ((cc)) experimentalexperimental resultresult ofof LP,LP, andand ((dd)) experimentalexperimental resultresult ofof CP.CP.

Computation 2019, 7, 55 11 of 17 Computation 2019, 7, x FOR PEER REVIEW 11 of 16 Computation 2019, 7, x FOR PEER REVIEW 11 of 16

. . FigureFigure 11. 11.Backscatter Backscatter intensity intensity of of a a medium-sized medium-sized horizontalhorizontal bar ((l/ ((l/λ == 6.3,6.3, w/w/λλ == 0.4):0.4): (a ()a Simulation) Simulation Figure 11. Backscatter intensity of a medium-sized horizontal bar ((l/λ = 6.3, w/λ = 0.4): (a) Simulation resultresult of LP,of LP, (b )(b simulation) simulation result result of of CP, CP, ( c(c)) experimental experimental result of of LP, LP, and and (d (d) )experimental experimental result result of ofCP. CP. result of LP, (b) simulation result of CP, (c) experimental result of LP, and (d) experimental result of CP.

FigureFigure 12. 12.Backscatter Backscatter intensityintensity of of a a medium-sized medium-sized vertical vertical bar bar((l/λ ((l = /6.3,λ = w6.3,/λ =w 0.4):/λ = (a0.4):) Simulation (a) Simulation result Figure 12. Backscatter intensity of a medium-sized vertical bar ((l/λ = 6.3, w/λ = 0.4): (a) Simulation result resultof LP, of LP,(b) simulation (b) simulation result result of CP, of (c CP,) experimental (c) experimental result resultof LP, ofand LP, (d and) experimental (d) experimental result of result CP. of CP. of LP, (b) simulation result of CP, (c) experimental result of LP, and (d) experimental result of CP.

Computation 2019, 7, 55 12 of 17 Computation 2019, 7, x FOR PEER REVIEW 12 of 16

Figure 13. Backscatter intensity of a medium-sized sphere (d/λ = 6.8): (a) Simulation result of LP, Figure 13. Backscatter intensity of a medium-sized sphere (d/λ = 6.8): (a) Simulation result of LP, (b) (b) simulation result of CP, (c) experimental result of LP, and (d) experimental result of CP. simulation result of CP, (c) experimental result of LP, and (d) experimental result of CP. 4. Discussion 4. Discussion The measurement was done for 64 cases, i.e., two types of test (simulation and experiment), four differentThe measurement targets, and eight was didonefferent for 64 polarization cases, i.e., two modes. types Furthermore, of test (simulation every and case experiment), was done for four 37 didifferentfferent angles.targets, Asand shown eight differ in theent figures, polarization for every modes. measurement Furthermor case,e, every a second-order case was polynomialdone for 37 trendlinedifferent angles. was drawn. As shown Despite in the opportunityfigures, for ev toery address measurement many possible case, a comparisonssecond-order amongst polynomial the cases,trendline the obviouswas drawn. trends Despite are discussed the opportunity here. to address many possible comparisons amongst the cases, the obvious trends are discussed here. 4.1. Relationship between Backscatter Intensity and Aspect Angle 4.1. Relationship between Backscatter Intensity and Aspect Angle A relationship between backscatter intensity and aspect angle happens for the trihedral cases, as shownA relationship in [13] and between as indicated backscatter by the intensity studies and in [as10pect,14]. angle The happens study in for [13 the] showed trihedral proof cases, that as theshown strongest in [13] backscatter and as indicated intensity by happensthe studies when in [10,14]. the EM The wave study comes in [13] from showed the direction proof that thethe trihedralstrongest facesbackscatter (aspect intensity angle = 0happens◦). The studies when inthe [ 10EM,14 ]wave investigated comes from the e fftheects direction of trihedral that plate the damagetrihedral to faces the backscatter (aspect angle intensity, = 0°). butThe implicitly studies in also [10,14] showed investigated that, for an the ideal effects trihedral, of trihedral the strongest plate backscatterdamage to intensitythe backscatter occurs intensity, when the but EM implicitly wave comes also from showed the directionthat, for thatan ideal the trihedral trihedral, faces the direction.strongest backscatter The result ofintensity our simulation occurs when on the the trihedralEM wave showed comes from agreement the direction with this that phenomenon, the trihedral wherefaces direction. the backscatter The intensityresult of of our most simulation polarization on modes the returnedtrihedral to showed the maximum agreement when thewith aspect this anglephenomenon, was around where 0◦ the. The backscatter simulation intensity resulted of most in the polarization same trends modes for the returned horizontal to the bar maximum and the verticalwhen the bar, aspect where angle the maximumwas around backscatter 0°. The simulation intensities resulted happened in whenthe same the trends aspect anglefor the was horizontal 0◦, and thebar minimumand the vertical backscatter bar, where intensities the maximum occurred backscatter when the intensities aspect angle happened was 90◦ .when The samethe aspect trend angle was demonstratedwas 0°, and the consistently minimum forbackscatter both linear intensities polarization occurred and circular when the polarization. aspect angle A diwasfferent 90°. trendThe same was showntrend was in the demonstrated case of the sphere, consistently where the for backscatter both linear intensity polarization graph wasand flat. circular This canpolarization. be explained A bydifferent the fact trend that was in the shown simulation in the wecase used of the a perfect sphere, sphere where model, the backscatter and this geometry intensity wasgraph exactly was flat. the sameThis can for allbe aspectexplained angles. by the fact that in the simulation we used a perfect sphere model, and this geometry was exactly the same for all aspect angles. The experiment showed the same trend for most linear polarization modes of the trihedral, horizontal bar, and vertical bar, although with less curving degrees compared to the simulation

Computation 2019, 7, 55 13 of 17

The experiment showed the same trend for most linear polarization modes of the trihedral, horizontal bar, and vertical bar, although with less curving degrees compared to the simulation results. For the trihedral, the convex curve (maximum at φ = 0◦ and minimum at φ = 90◦) occurred for the VH, HV, and VV cases. For the horizontal bar, the convex curve occurred for the VH and VV cases. For the vertical bar, a less obvious convex curve occurred for the VH and VV cases. The sphere resulted in flat backscatter intensity lines for all linear polarization cases, which was the same as the simulation results. The results of the experiments for the circular polarization modes unexpectedly differed. All of these cases resulted in a flat curve, meaning that the backscatter intensity value was not related to the aspect angle. The reason for this anomaly is yet unknown and should be subject to further investigation.

4.2. Standard Deviations of CPs and LPs It is in our interest to understand the behaviors of circularly polarized EM waves when hitting a target. Here, their backscatter intensities were observed at an aspect angle of 0◦. It was interesting to ﬁnd that the backscatter intensities of CP modes varied less signiﬁcantly compared to the backscatter intensities of LP modes. This phenomenon is presented in Table4.

Table 4. Comparison of the standard deviations of CPs and LPs for every target: (a) According to the simulation, and (b) according to the experiment.

(a) Simulation: CP’s vs. LP’s St. Dev. (φ = 0◦) (b) Experiment: CP’s vs. LP’s St. Dev. (φ = 0◦) Backscatter Intensity Backscatter Intensity Target Standard Deviation (σ) Target Standard Deviation (σ) Of All LP Modes Of All CP Modes Of All LP Modes Of All CP Modes Trihedral 3.00 1.13 Trihedral 8.11 1.30 Horizontal Bar 1.55 0.11 Horizontal Bar 8.88 1.50 Vertical Bar 2.59 0.66 Vertical Bar 8.38 0.91 Sphere 2.09 0.33 Sphere 2.19 0.87

According to the simulation, the standard deviations of CP modes of the trihedral, the horizontal bar, the vertical bar, and the sphere were 1.13, 0.11, 0.66, and 0.33, respectively, which were significantly smaller than the standard deviations of the LP modes, i.e., 3.00, 1.55, 2.59, and 2.09, respectively. The same trend happened in the experiment, where the standard deviations of CP modes of each target were 1.30, 1.50, 0.91, and 0.87, which were significantly smaller than the standard deviations of the LP modes, i.e., 8.11, 8.88, 8.38, and 2.19. This means that the simulation and the experiment show agreement in returning standard deviations for CP modes that are significantly smaller than the standard deviations of LP modes. This phenomenon, in our understanding, can be explained as follows:

The RX sensor of an LP system employs either a horizontally or vertically polarized antenna, so it • receives only one component of the backscattered waves (either horizontal or vertical). In this way, the values of backscattered wave intensity for each possible mode, i.e., HH, VH, HV, and VV, are potentially significantly different from each other. The RX sensor of a CP system employs both horizontally and vertically polarized antennas plus • a phase shifter, where it receives both horizontal and vertical components of the backscattered waves and sums them up (after shifting the phase of one of the two). Due to this summation mechanism, the resulting values of backscattered wave intensity for each possible mode, i.e., RR, LR, RL, and LL, are less significantly different from each other compared to the LP case. Please be reminded that the backscattered waves off a radar object consist of both horizontal and vertical components (likely with different intensity). The differences of the backscattered wave intensities of RR, LR, RL, and LL modes are merely determined by the phase-shifting manner. Computation 2019, 7, 55 14 of 17

4.3. Backscatter Intensity Diﬀerences amongst LP Modes As discussed in Section 4.2, both the simulation and the experiment showed that the standard deviation of the backscatter intensity of linearly polarized EM waves was relatively large. It means that both the simulation and the experiment could diﬀerentiate between the backscatter intensities of each HH, VH, HV, and VV case. The details of the variations shown by LP modes (φ = 0◦) are presented in Table5, and the details of the CP modes are also presented as a comparison.

Table 5. Backscatter intensity diﬀerences amongst LP modes compared to CP modes: (a) Simulation and (b) experiment. Please notice that the backscatter intensities of CP modes varied less signiﬁcantly compared to LP modes. The ones shaded in green are the largest values of each target for the LP modes.

(a) Simulation: Backscatter Intensity Diﬀerences amongst All Polarization Modes (φ = 0◦) Backscatter of LP Modes [dB] Backscatter of CP Modes [dB] HH VH HV VV St. Dev. RR LR RL LL St. Dev. Trihedral 81.15 88.85 86.22 82.74 3.00 83.04 82.95 85.37 85.13 1.13 − − − − − − − − Horizontal Bar 81.08 85.38 83.45 83.92 1.55 85.62 85.70 85.41 85.49 0.11 − − − − − − − − Vertical Bar 84.43 85.29 79.89 79.56 2.59 80.85 81.04 79.55 79.74 0.66 − − − − − − − − Sphere 80.54 76.64 74.95 78.50 2.09 89.56 89.61 88.91 88.94 0.33 − − − − − − − − (b) Experiment: (a) Backscatter Intensity Diﬀerences amongst All Polarization Modes (φ = 0◦) Backscatter of LP Modes [dB] Backscatter of CP Modes [dB] HH VH HV VV St. Dev. RR LR RL LL St. Dev. Trihedral 65.39 84.75 85.56 76.79 8.11 66.53 65.71 68.41 64.93 1.30 − − − − − − − − Horizontal Bar 65.54 89.53 83.98 80.13 8.88 65.20 65.16 68.67 65.23 1.50 − − − − − − − − Vertical Bar 78.80 88.13 82.77 65.47 8.38 64.53 66.06 66.37 64.29 0.91 − − − − − − − − Sphere 75.44 72.92 70.87 76.48 2.19 86.55 84.60 84.36 85.59 0.87 − − − − − − − −

The results of the simulation can be described as the following. For the trihedral, HH returned the largest value ( 81.15 dB) whereas VH returned the smallest value ( 88.85 dB). For the horizontal − − bar, HH returned the largest value ( 81.08 dB) whereas VH returned the smallest value ( 85.38 dB). − − For the vertical bar, the VV case resulted in the largest value ( 79.56 dB) whereas VH resulted in the − smallest value ( 85.29 dB). For the sphere, HV returned the largest value ( 74.95 dB) whereas HH − − returned the smallest value ( 80.54 dB). − The experimental results can be described as the following. For the trihedral, HH returned the largest value ( 65.39 dB) whereas HV returned the smallest value ( 85.56 dB). For the horizontal bar, − − HH resulted in the largest value ( 65.54 dB) whereas VH resulted in the smallest value ( 89.53 dB). − − For the vertical bar, VV returned the largest value ( 65.47 dB) whereas VH returned the smallest − value ( 88.13 dB). For the sphere, HV returned the largest value ( 70.87 dB) whereas VV returned the − − smallest value ( 78.50 dB). − It is interesting to ﬁnd that the simulation results agreed with the experimental results for the largest backscatter intensity values of every target (shaded in green). HH, HH, VV, and HV were the polarization modes where the trihedral, the horizontal bar, the vertical bar, and the sphere resulted in its largest backscatter intensities, respectively, in both the simulation and the experiment. This conveys important information that (i) the medium-sized sphere tends to reverse EM wave polarization, (ii) the medium-sized trihedral tends to retain the polarization, theoretically because of the double reﬂection (reverse then reverse again), (iii) the medium-sized horizontal bar tends to strongly backscatter horizontally polarized EM waves while retaining their polarity, and (iv) the medium-sized vertical bar tends to strongly backscatter vertically polarized EM waves while retaining their polarity. Computation 2019, 7, x FOR PEER REVIEW 14 of 16

As discussed in Section 4.2, both the simulation and the experiment showed that the standard deviation of the backscatter intensity of linearly polarized EM waves was relatively large. It means that both the simulation and the experiment could differentiate between the backscatter intensities of each HH, VH, HV, and VV case. The details of the variations shown by LP modes (ϕ = 0°) are presented in Table 5, and the details of the CP modes are also presented as a comparison.

Table 5. Backscatter intensity differences amongst LP modes compared to CP modes: (a) Simulation and (b) experiment. Please notice that the backscatter intensities of CP modes varied less significantly compared to LP modes. The ones shaded in green are the largest values of each target for the LP modes.

(a) Simulation: Backscatter Intensity Differences amongst All Polarization Modes (ϕ = 0°) Backscatter of LP Modes [dB] Backscatter of CP Modes [dB]

HH VH HV VV St. Dev. RR LR RL LL St. Dev. Trihedral −81.15 −88.85 −86.22 −82.74 3.00 −83.04 −82.95 −85.37 −85.13 1.13 Horizontal Bar −81.08 −85.38 −83.45 −83.92 1.55 −85.62 −85.70 −85.41 −85.49 0.11 Vertical Bar −84.43 −85.29 −79.89 −79.56 2.59 −80.85 −81.04 −79.55 −79.74 0.66 Sphere −80.54 −76.64 −74.95 −78.50 2.09 −89.56 −89.61 −88.91 −88.94 0.33 (b) Experiment: (a) Backscatter Intensity Differences amongst All Polarization Modes (ϕ = 0°) Backscatter of LP Modes [dB] Backscatter of CP Modes [dB]

HH VH HV VV St. Dev. RR LR RL LL St. Dev. Trihedral −65.39 −84.75 −85.56 −76.79 8.11 −66.53 −65.71 −68.41 −64.93 1.30 Horizontal Bar −65.54 −89.53 −83.98 −80.13 8.88 −65.20 −65.16 −68.67 −65.23 1.50 Vertical Bar −78.80 −88.13 −82.77 −65.47 8.38 −64.53 −66.06 −66.37 −64.29 0.91 Sphere −75.44 −72.92 −70.87 −76.48 2.19 −86.55 −84.60 −84.36 −85.59 0.87

The results of the simulation can be described as the following. For the trihedral, HH returned the largest value (−81.15 dB) whereas VH returned the smallest value (−88.85 dB). For the horizontal bar, HH returned the largest value (−81.08 dB) whereas VH returned the smallest value (−85.38 dB). For the vertical bar, the VV case resulted in the largest value (−79.56 dB) whereas VH resulted in the smallest value (−85.29 dB). For the sphere, HV returned the largest value (−74.95 dB) whereas HH returned the smallest value (−80.54 dB). The experimental results can be described as the following. For the trihedral, HH returned the largest value (−65.39 dB) whereas HV returned the smallest value (−85.56 dB). For the horizontal bar, HH resulted in the largest value (−65.54 dB) whereas VH resulted in the smallest value (−89.53 dB). For the vertical bar, VV returned the largest value (−65.47 dB) whereas VH returned the smallest value (−88.13 dB). For the sphere, HV returned the largest value (−70.87 dB) whereas VV returned the smallest value (−78.50 dB). It is interesting to find that the simulation results agreed with the experimental results for the largest backscatter intensity values of every target (shaded in green). HH, HH, VV, and HV were the polarization modes where the trihedral, the horizontal bar, the vertical bar, and the sphere resulted in its largest backscatter intensities, respectively, in both the simulation and the experiment. This conveys important information that (i) the medium-sized sphere tends to reverse EM wave polarization, (ii) the medium-sized trihedral tends to retain the polarization, theoretically because of the double reflection (reverse then reverse again), (iii) the medium-sized horizontal bar tends to strongly backscatter horizontally polarized EM waves while retaining their polarity, and (iv) the Computation 2019, 7, 55 15 of 17 medium-sized vertical bar tends to strongly backscatter vertically polarized EM waves while retaining their polarity. 5. Summary 5. Summary The work reported in this article can be summarized as follows: The work reported in this article can be summarized as follows: ▪ TheThe measurement measurement was was done done for for four four different different medium medium-sized-sized targets, targets, eight eight different different polarization polarization modemodes,s, and and 37 different 37 different angles, angles, by by simulation simulation and and experiment experiment,, where where,, in in this this study study,, medium medium-sized-sized waswas defined defined as 5λ as < 5 λtarget< target size size < 10λ.< 10 λ. The simulation was done using our developed tool, AST_V1, that simulates electromagnetic field propagation using the FDTD method. The experiment was done in our anechoic chamber. The simulation results mostly agreed with previous studies that the backscatter intensity relates to the target’s aspect angle, where the largest backscatter intensity was obtained when the aspect angle is 0◦ and the least backscatter intensity was obtained when the aspect angle is 90◦. The simulation agreed with the experiment in the observation of circularly polarized EM waves, where the circular polarization resulted in significantly smaller backscatter intensity standard deviation compared to the linear polarization. This can also mean that the circular polarization provided more stable backscattering. The simulation to some extent agreed with the experiment in the observation of linearly polarized EM waves, where HH, HH, VV, and HV were the polarization modes where the trihedral, the horizontal bar, the vertical bar, and the sphere resulted in the largest backscatter intensity, respectively. This finding confirms the understanding that:

A sphere tends to reverse EM wave polarization, • A trihedral tends to retain the EM wave polarization, • A horizontal bar tends to strongly backscatter horizontally polarized EM waves while • retaining their polarity, and A vertical bar tends to strongly backscatter vertically polarized EM waves while retaining • their polarity. However, please note that other polarization modes also exist, with less intensity. • The computation was done with the FDTD cell size of 1.25 1.25 1.25 cm. The accuracy of the × × computation results can potentially be improved by reducing the cell size.

Author Contributions: Conceptualization, M.N.; data curation, M.N., C.E.S., P.S., A.H.W., and Y.Y.; formal analysis, M.N.; funding acquisition, J.T.S.S.; investigation, M.N. and J.W.; methodology, M.N., J.T.S.S., P.S., Y.Y., and J.W.; project administration, J.T.S.S.; resources, J.T.S.S., C.E.S., P.S., and A.H.W.; software, M.N.; supervision, J.T.S.S.; validation, P.S.; visualization, M.N.; writing—original draft, M.N.; writing—review & editing, J.T.S.S. and P.S. Funding: This research has been funded by the Chiba University Strategic Priority Research Promotion Program FY2016-FY2018. Acknowledgments: The authors would like to convey gratitude to the Mitsubishi Corporation International Student Scholarship as well as the Ministry of Research, Technology, and Higher Education of the Republic of Indonesia (Kemenristekdikti) for their support to the study. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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