Feasibility, Design, and Deployment Requirements of TCR for ... - MDPI

remote sensing Technical Note

Feasibility, Design, and Deployment Requirements of TCR for Bistatic SAR Radiometric Calibration Qiaona Zheng 1,2, *, Yu Wang 1, * , Jun Hong 1 and Aichun Wang 3 1 2 3

*

Institute of Electronics, Chinese Academy of Sciences, National Key Laboratory of Science and Technology on Microwave Imaging, Beijing 100190, China; [email protected] University of Chinese Academy of Sciences, Beijing 100049, China China Center for Resources Satellite Data and Application, Beijing 100094, China; [email protected] Correspondence: [email protected] (Q.Z.); [email protected] (Y.W.); Tel.: +86-156-1153-2763 (Q.Z.); +86-10-5888-7524 (Y.W.)

Received: 13 July 2018; Accepted: 5 October 2018; Published: 10 October 2018







Abstract: The trihedral corner reflector (TCR) is widely used as the calibration device in monostatic synthetic aperture radar (SAR) calibration, and the performance of the TCR in radiometric calibration has been studied and verified in depth. As for the bistatic SAR system calibration problem, there have been few published studies. There is a lack of knowledge regarding the exact bistatic radar cross-section (RCS) pattern of TCR with different bistatic angles, and it is also not clear whether the TCR can be used as the calibration target in bistatic SAR. Moreover, the bistatic and monostatic radar cross-section (RCS) characteristics of the TCR are different, even if the bistatic angle is very small. Therefore, the feasibility, design, and deployment requirements of the TCR for bistatic SAR calibration should be carefully investigated. In this paper, we outline the theoretical and practical requirements that need to be satisfied when choosing appropriate calibration devices for bistatic radiometric calibration. Based on these requirements, we analyzed the bistatic RCS patterns using electromagnetic simulation, and concluded that the TCR is feasible for bistatic SAR calibration under relatively small bistatic angles (less than 6◦ ). The change of TCR boresight with the bistatic angle is not considered generally. However, we found that the TCR boresight and peak RCS will change with the bistatic angle. We have also proposed that the bistatic angle can be extended to 20◦ by taking the change of the TCR boresight into account. In this condition, we should get the TCR boresight according to the bistatic angle and then align it during the deployment. Both of these two conditions have their own unique advantages. Different error sources of TCR RCS from manufacture, misalignment, and deformation were investigated quantitatively with simulations, which can provide a theoretical basis for how to design a suitable TCR and guarantee the calibration accuracy for bistatic calibration. In addition, simulation results are different from those of monostatic calibration. Through experiments, we have further verified the feasibility by comparing the quality of bistatic SAR images and point target energy with several typical bistatic angles as the TCR boresight is considered or not. If the bistatic angle is larger than 6◦ , taking the TCR optimum boresight into account can improve imaging quality and point target energy. Keywords: bistatic SAR; trihedral corner reflector; radiometric calibration; RCS; electromagnetic simulation

1. Introduction The radiometric calibration theory and technique of the monostatic SAR system have been considerably improved in the past, and the relevant problem has been extensively studied and well understood [1–3]. Numerous canonical passive reflectors have been proven to be suitable as monostatic

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calibration targets such as spheres, dihedrals, and trihedrals. From the first decade of this century, great interest in the bistatic synthetic aperture radar (SAR) system has been arisen rapidly given its special merits in various microwave remote sensing applications [4–6]. However, for the bistatic SAR system, the calibration problem is significantly more complex, and limited bistatic SAR calibration theory and experiments have been reported in the literature. The main reason may be due to the lack of suitable calibration targets introduced by the bistatic SAR observation geometry. Therefore, the design of appropriate calibration targets and the investigation of their performances in the SAR image are the first and foremost issues in bistatic SAR radiometric calibration. At present, several bistatic calibration methods based on point targets have been proposed, which can be roughly divided into two categories. One idea is to use an active calibration target with a high radar cross-section (RCS) over a large frequency range that can be easily configured for different bistatic angles [7–9]; however, active calibration targets are expensive and complex to manufacture. The other view is to utilize passive calibration targets. In 2003, a passive cross-polarization bistatic calibration target was designed for RCS measurements [10]. Although this device performed well over a wide frequency range, it was very complicated to design and manufacture. Trihedral corner reflectors (TCRs) are generally considered not suitable for bistatic SAR calibration with large bistatic angles [11]. One bistatic SAR experiment has been reported using TCR, but failed to perform bistatic radiometric calibration [12], which may be due to the lack of an exact bistatic RCS pattern and not considering the design and deployment requirements. Theoretically, spheres can be considered as good calibration targets at arbitrary bistatic angles, but their relative low RCS restricts their practicability. The TCR is perhaps the most practical device for calibrating monostatic SAR systems. The monostatic RCS pattern of TCR has a 3-dB beamwidth of approximately 40◦ in both the azimuth and elevation dimensions, which means that it is much more tolerant to field alignment errors [13]. It is also relatively inexpensive to manufacture, and can be produced in large quantities. Consequently, the TCR have been used as the standard calibration target in monostatic SAR radiometric calibration for many years. However, knowledge on the bistatic calibration performance of TCR is inadequate or questionable; in particular, its feasibility for bistatic SAR with different bistatic angles is not so clear. Therefore, it is important and meaningful to analyze the TCR RCS characteristics, reexamine their feasibility, and subsequently analyze the design and deployment requirements of this classical passive calibration target in bistatic SAR radiometric calibration. The TCR has a very narrow bistatic pattern when the bistatic angle is used as an independent variable [8]. Therefore, it should be noted that the bistatic pattern discussed in this paper used the incident angle as an independent variable, rather than the bistatic angle, and we just analyzed the RCS characteristics of the TCR for bistatic SAR tandem mode radiometric calibration. The bistatic SAR tandem mode, whose transmitting and receiving antennas are spatially separated by a fixed distance (i.e., baseline) along the flight track of the SAR platform, can ensure that the bistatic angle is unchanged during the movement. One example for the tandem mode is the interferometric cartwheel [14]. Similarly, there are other distributed spaceborne SAR or constellation systems with a relatively small and fixed bistatic angles [15,16] along, across, or at the hybrid of the flight tracks. For example, TanDEM-X is the first genuinely bistatic SAR system in space, and the working mode includes monostatic, bistatic, and alternating bistatic mode. The first bistatic spaceborne SAR experiments was made as the bistatic angle is 1.8◦ , and then obtained the good quality bistatic image [17]. The Argentine SAOCOM constellation comprises two L-band satellites, SAOCOM-1A and SAOCOM-1B, which will be monitoring for the mitigation of the effects of natural disasters. This paper is structured as follows. Section 2 is devoted to outlining the requirements of the calibration target for radiometric calibration. The bistatic RCS pattern of the TCR is analyzed in Section 3 through electromagnetic simulations as the bistatic angle fixed in azimuth. Section 4 analyzes the various error factors of the TCR RCS quantitatively, including machining, deployment, and thermal deformation errors. In Section 5, the quality of the bistatic SAR images of the TCR with different bistatic angles are analyzed. The discussion and conclusions are finally drawn in Sections 6 and 7, respectively.

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2. Requirements of Calibration Target for Radiometric Calibration Knowing how to select a calibration target is critical when evaluating the feasibility of a certain calibration target for bistatic SAR radiometric calibration. The calibration targets, including passive corner reflectors and active calibration targets, play an important role in SAR radiometric calibration. In the following, we discuss the basic requirements that should be considered when designing suitable calibration targets for radiometric calibration, including the beamwidth, the stability of the RCS, and the signal-to-clutter ratio (SCR). These requirements are derived from monostatic SAR radiometric calibration in principle; however, they are also prerequisites for determining the feasibility of bistatic SAR calibration targets. 2.1. The Beamwidth Requirement For an antenna or reflector pattern, the beamwidth is a physical quantity that characterizes the angle range between certain power points (generally half power or so-called 3 dB) of the main lobe, when referenced to the peak effective radiated power of the main lobe. The wider the 3-dB beamwidth of a calibration target, the easier it is to align to the SAR antenna. The beamwidth requirement is that the beamwidth of the calibration target should be larger than the SAR antenna beamwidth, especially the azimuth beamwidth of the calibration target. Using the Sentinel-1 SAR calibration as an example, the first criterion can be expressed mathematically as follows [18]: BWcal > φa + ∆φy = BWSAR

(1)

where BWSAR is the beamwidth of the Sentinel-1 SAR antenna given by the sum of the SAR antenna azimuth beamwidth φa and the yaw attitude stability of antenna ∆φy ; and BWcal is the monostatic azimuth beamwidth of the calibration target, which should be larger with respect to the BWSAR . Obviously, Equation (1) is still valid for a bistatic situation, when BWcal stands for the bistatic azimuth beamwidth of the calibration targets. In fact, the TCR has a wide monostatic pattern (TCR RCS versus incident angle), but a very narrow bistatic pattern (TCR RCS versus bistatic angle) that is different from the pattern we usually define [8], and the 3-dB bistatic beamwidth can be written as: ◦

14.5 ϑ≈ a[m] · f [GHz]

(2)

where a is the length of the hypotenuse sides of the TCR, and f is the frequency. The 3-dB bistatic beamwidth is less than 4◦ for a 0.4-m TCR at X-band. It should be noted that the beamwidth and bistatic pattern discussed in this paper used the incident angle as an independent variable, and not the bistatic angle (angle between the incident and backscattered wave), if not specified. 2.2. The Stability of RCS Requirement The RCS of the target determines the power density returned to the radar for a particular power density incident on the target [19], so a natural requirement for a calibration target is that its RCS should be stable to allow radiometric calibration results with repeatability, where the stability of RCS refers to variation over frequency, due to the frequency having a great influence on the target RCS. For passive calibration targets, according to electromagnetic theory, the target RCS or backscattering characteristic can be divided into three regions, including the Rayleigh region (ka < 0.5), resonance region (0.5 < ka < 20), and optical region (ka > 20) [20], where k = 2π λ is the wavenumber, and a represents the feature size (e.g., radius of a sphere, interleg length of a TCR) of the passive target. Passive calibration targets will show a stable RCS when they work within the optical region. As shown in Figure 1, the target RCS is stable, and can be estimated accurately in the optical region. Therefore, the requirement for the stability of the RCS is that the feature size of the TCR must meet the optical region. We calculated that a > 0.1 can ensure RCS stability at the X-band.

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Therefore, the requirement for the stability of the RCS is that the feature size of the TCR must meet 4 of 19 the optical region. We calculated that a > 0.1 can ensure RCS stability at the X-band.

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0

Normalized RCS

-5

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-25 10

-2

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-1

10

0

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1

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2

ka

Figure ofof a perfectly conducting sphere normalized to the valuevalue πa2 . Figure 1.1.Radar Radarcross-section cross-section(RCS) (RCS) a perfectly conducting sphere normalized tooptics the optics 2 . Requirement π aSCR 2.3. The

To work as a calibration target, the target must be distinguished from the surrounding background 2.3. The SCR Requirement scatterers (often termed clutter), which means that the target must have a large enough RCS to ensure To work as a calibration target, the target must be distinguished from the surrounding sufficient visibility. The measure of visibility in a SAR image is the target SCR, and is defined as [13]: background scatterers (often termed clutter), which means that the target must have a large enough T sinin T of visibility RCS to ensure sufficient visibility. The measure σpq θi a SAR image is the target SCR, and is σpq (3) SCR = C  = D E defined as [13]: o p p σpq σpq a r

σ Tpq σ Tpq sin θi C o is the normalized = SCR (3) is the RCS of the calibration target, = σpqC is the background clutter RCS, σpq o p p σ σ pq pq a r clutter RCS (i.e., the clutter backgrounding coefficient), the subscript stands for the

T σpq

where average pq transmitted and received polarization of the radar signal, θi is the radar incident angle, and p a , pr are C o σ Tpq and σimages, where is the RCSsampling of the calibration background clutter RCS, σ pq is the the azimuth range interval oftarget, the SAR respectively. pq is the Generally, the SCR is directly related to radiometric calibration accuracy [21], as shown in Figure 2. normalized average clutter RCS (i.e., the clutter backgrounding coefficient), the subscript pq stands A SCR of at least 25 dB is desired to guarantee that the radiometric calibration error is less than 0.5 dB, which normally used a fundamental requirement for the SAR θ radiometric calibration experiment. for theistransmitted andas received polarization of the radar signal, i is the radar incident angle, and The bistatic backscattering coefficient of dry grass, when the radar incident angle is 20◦ , is likely to pa−, p10r dB are at thethe azimuth range interval of the SARtarget images, respectively. be X-bandand [22], and sampling we can obtain a calibration RCS of at least about 11 dBm2 whenGenerally, the SCR isthe 25SCR dB, is and the azimuth and range sampling interval are both m. In in practice, directly related to radiometric calibration accuracy [21], 0.5 as shown Figure the background reflections should be as small as possible. It is important to carefully consider 2. A SCR of at least 25 dB is desired to guarantee that the radiometric calibration error is less thanthe 0.5 deployment calibration targets restrict the influence of background clutter [23]. Remote Sens. 2018, 10, x FOR PEER REVIEW 5 of 19 dB, which isofnormally used as to a fundamental requirement for the SAR radiometric calibration

radiometric calibration error, Unit:dB

experiment. The bistatic backscattering coefficient of dry grass, when the radar incident angle is 20°, 0.8 is likely to be −10 dB at the X-band [22], and we can obtain a calibration target RCS of at least about 0.6 11 dBm2 when the SCR is 25 dB, and the azimuth and range sampling interval are both 0.5 m . In 0.4 practice, the background reflections should be as small as possible. It is important to carefully 0.2 consider the deployment of calibration targets to restrict the influence of background clutter [23]. 0

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-0.8

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Figure Figure 2. 2. Upper Upper (blue) (blue) and and lower lower (red) (red) limits limits of of the the radiometric radiometric calibration calibration errors errors vs. vs. signal-to-clutter signal-to-clutter ratio ratio (SCR). (SCR).

3. Bistatic RCS Characteristics To select and design proper calibration targets, knowledge of the bistatic RCS characteristics of calibration targets is indispensable according to the requirements listed in Section 2. The term RCS is

-0.4 -0.6 -0.8 -1 20

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SCR, Unit:dB

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Figure 2. Upper (blue) and lower (red) limits of the radiometric calibration errors vs. signal-to-clutter ratio (SCR).

3. Bistatic RCS Characteristics 3. Bistatic RCS Characteristics

To select and design proper calibration targets, knowledge of the bistatic RCS characteristics of select and design properaccording calibrationto targets, knowledge oflisted the bistatic RCS characteristics of is a calibrationTotargets is indispensable the requirements in Section 2. The term RCS calibration targets is indispensable according to the requirements listed in Section 2. The term RCS is measure of power scattered in a given direction when a target is illuminated by an incident wave from a measure of power scattered in a given direction when a target is illuminated by an incident wave radar. The RCS can be expressed by the electric field strength [20]: from radar. The RCS can be expressed by the electric field strength [20]:

Er |22 2 |E r 2 σσ== lim 4πR Rlim →∞ 4π R | Ein |22 R →∞

Ein

(4)

(4)

where Ein is the electric field strength of the incident wave impinging on the target, Er is the electric where Einofisthe thescattered electric field strength of the and incident impinging on the target, r is the field strength wave at the radar, R is wave the range from the radar to theEtarget. electric field strength of thetoscattered wave at the and radar, and R istarget the range fromHowever, the radar tothe the target target. RCS This definition applies both monostatic bistatic RCSs. This definition applies to both monostatic and bistatic target RCSs. However, the target RCSequal depends on the transmitting and receiving direction. Therefore, the bistatic RCS is generally not depends on the transmitting and receiving direction. Therefore, the bistatic RCS is generally not equal to the monostatic RCS. Figure 3 depicts both monostatic and bistatic radar configurations. A monostatic to the monostatic RCS. Figure 3 depicts both monostatic and bistatic radar configurations. A system uses a single location for both the transmitter and receiver, whereas a bistatic system locates monostatic system uses a single location for both the transmitter and receiver, whereas a bistatic the transmitter and receiver separately, and the angle between the transmitter and receiver is the system locates the transmitter and receiver separately, and the angle between the transmitter and bistatic angle.is the bistatic angle. receiver

Figure Themonostatic monostatic and and bistatic Figure 3. 3. The bistaticradar radarconfigurations. configurations.

At present, there have been manystudies studies on on monostatic monostatic RCSs forfor different types of targets, but but At present, there have been many RCSs different types of targets, little information on bistatic RCSs. The TCR is widely used as a calibration target in monostatic SAR little information on bistatic RCSs. The TCR is widely used as a calibration target in monostatic SAR radiometric calibration, but the characteristic of its real bistatic RCS, especially the exact bistatic RCS radiometric calibration, but the characteristic of its real bistatic RCS, especially the exact bistatic RCS pattern, is not clear in bistatic SAR calibration. In order to solve this problem, we considered two pattern, is not clear in bistatic SAR calibration. In order to solve this problem, we considered two approaches in the following: one based on the monostatic bistatic equivalence theorem, and the other was electromagnetic simulation at the X-band (9.6 GHz), and the TCR had inner-leg dimensions of 0.4 m to acquire stable RCS characteristics within the optical region.

3.1. Monostatic Bistatic Equivalence Theorem The monostatic bistatic equivalence theorem indicates that the bistatic RCS can be approximated β by the monostatic RCS measured on the bistatic angle bisector and measured at cos 2 times lower than the true frequency for small bistatic angles [24], which can be written by:     β β β σ f,α − ,α + ≈ σ f cos , α, α 2 2 2 where α is the incident angle and β is the bistatic angle.

(5)

α

is the incident angle and β is the bistatic angle. Consider a TCR with sides comprised of isosceles right triangles. With the geometry defined as per Figure 4, by using geometrical optics approximation theory, the RCS of a TCR can be formulated as [25]: Remote Sens. 2018, 10, 1610 6 of 19 where

σ (θ , ϕ ) =

4π

A 2 (θ , ϕ )

(6) λ Consider a TCR with sides comprised of isosceles right triangles. With the geometry defined as 2 per Figure 4, by using geometrical approximation theory, the RCS of a TCR can be formulated  optics 4c1c2  4  l  as [25]: if c1 + c2 ≤ c3  c3 4π   cσ1 (+θ,cϕ2 )+=  A2 (θ, ϕ) 2 A (θ , ϕ ) =  (7) (6) λ2 2   4  2  c31 c−2 2 c1 c+ c2 ≥ c3  i f c1 +ifc2 ≤ l  c1 +l 4c2 + 4c  3 c1 +c2 +cc 31 + c2 + c3  A2 (θ, ϕ) =    (7) 2  2 4  l c1 + c2 + c3 − i f c + c ≥ c 2 3 1 c1 + c2 + c3 where c1,c2,c3 are each assigned one of: where c1 , c2 , c3 are each assigned one of:

c1 c2 c3

2

c  cosθ 1    cos θ   = c θ sin ϕ  sin 2 = sin θ sin ϕ   sin θ cos ϕ   c 3  sin θ cos ϕ

(8)

(8)

A effective the radar length, is the effective aperture of a trihedral, is the elevation where where λ is λthe is radar wavewave length, A is the aperture of a trihedral, θ is the θ elevation angle, and ϕ angle, and is the azimuth angle. ϕ is the azimuth angle.

Figure 4. The monostatic RCS observation geometry of the trihedral corner reflector (TCR). Figure 4. The monostatic RCS observation geometry of the trihedral corner reflector (TCR).

As shown in Figure 5, the bistatic RCS azimuth patterns versus the azimuth angles of the TCR under different bistatic angles were simulated by using the monostatic bistatic equivalence theorem. It can be seen that the main lobe of the RCS patterns were very wide and flat, and the bistatic RCS values for different bistatic angles obtained by the monostatic bistatic equivalence theorem were similar to the monostatic RCS value near the peak. However, the azimuth angles corresponding to the peak RCS were different due to the monostatic RCS measured on the bistatic angle bisector.

RCS (dB) (dB) RCS

As As shown shown in in Figure Figure 5, 5, the the bistatic bistatic RCS RCS azimuth azimuth patterns patterns versus versus the the azimuth azimuth angles angles of of the the TCR TCR under under different different bistatic bistatic angles angles were were simulated simulated by by using using the the monostatic monostatic bistatic bistatic equivalence equivalence theorem. theorem. It It can can be be seen seen that that the the main main lobe lobe of of the the RCS RCS patterns patterns were were very very wide wide and and flat, flat, and and the the bistatic bistatic RCS RCS values values for for different different bistatic bistatic angles angles obtained obtained by by the the monostatic monostatic bistatic bistatic equivalence equivalence theorem theorem were were similar to the RCS to similar to2018, the monostatic monostatic RCS value value near near the the peak. peak. However, However, the the azimuth azimuth angles angles corresponding corresponding to Remote Sens. 10, 1610 7 of 19 the the peak peak RCS RCS were were different different due due to to the the monostatic monostatic RCS RCS measured measured on on the the bistatic bistatic angle angle bisector. bisector.

RCS pattern the the bistatic Figure The bistatic RCS azimuth of theon based on the equivalence monostatic bistatic Figure5. 5.5.The Thebistatic bistatic RCSazimuth azimuth patternof ofpattern theTCR TCRbased based onTCR themonostatic monostatic bistatic equivalencetheorem. theorem. equivalence theorem.

3.2. 3.2. FEKO FEKO Electromagnetic Electromagnetic Simulation Simulation 3.2. FEKO Electromagnetic Simulation FEKO FEKO is is aa simulation simulation software software for for three-dimensional three-dimensional (3D) (3D) structural structural electromagnetic electromagnetic field field FEKO is a simulation software for three-dimensional (3D) structural electromagnetic field analysis, analysis, and offers a variety of core algorithms such as the Method of Moments (MOM), Physical analysis, and offers a variety of core algorithms such as the Method of Moments (MOM), Physical and offers a variety of core algorithms such as the Method of Moments (MOM), Physical Optics (PO), Optics Optics (PO), (PO), Multilevel Multilevel Fast Fast Multipole Multipole Method Method (MLFMM), (MLFMM), Finite Finite Element Element Method Method (FEM), (FEM), Uniform Uniform Multilevel Fast Multipole Method (MLFMM), Finite Element Method (FEM), Uniform Theory of Theory Theoryof ofDiffraction Diffraction(UTD), (UTD),and andseveral severalof ofthe theabove abovealgorithms algorithmsare areused usedtogether. together.In Inaddition, addition,theoretical theoretical Diffraction (UTD), and several of the above algorithms are used together. In addition, theoretical analysis analysis or or simulation simulation computation computation has has been been used used as as aa standard standard for for RCS RCS analysis analysis and and evaluation evaluation of of the the analysis or simulation computation has been used as a standard for RCS analysis and evaluation of the calibration calibration target. target. Paper Paper [26] [26] has has concluded concluded that that FEKO’s FEKO’s RCS RCS is is more more reliable reliable and and accurate accurate than than the the results results calibration target. Paper [26] has concluded that FEKO’s RCS is more reliable and accurate than the of of the the normal normal anechoic anechoic chamber. chamber. So, So, we we give give the the results results of of FEKO FEKO electromagnetic electromagnetic simulation. simulation. Combining Combining results of the normal anechoic chamber. So, we give the results of FEKO electromagnetic simulation. the MOM with the MLFMA to calculate the RCS of TCR under different bistatic angles has the advantages the MOM with the MLFMA to calculate the RCS of TCR under different bistatic angles has the advantages Combining the MOM with the MLFMA to calculate the RCS of TCR under different bistatic angles of of shortening shortening the the calculation calculation time time and and having having aa high high accuracy. accuracy. The The bistatic bistatic RCS RCS observation observation geometry geometry of of has the advantages of shortening the calculation time and having a high accuracy. The bistatic RCS ϕ TCR is shown in Figure 6, where θ is the elevation angle, is the azimuth angle, and is the TCR is shown in Figure 6, where θ is the elevation angle, is the azimuth angle, and β is the observation geometry of TCR is shown in Figure 6, where θ is the elevation angle, ϕ is the β azimuth bistatic angle. We get the bistatic RCS azimuth pattern at different bistatic angles with angle bistaticand angle. the bistatic pattern RCS at different bistatic angles with the the elevation elevation angle angle, β isWe theget bistatic angle.RCS Weazimuth get the bistatic azimuth pattern at different bistatic angles fixed at 54.74° and the bistatic angle illustrated in the azimuth. ◦ fixed at 54.74° and the bistatic angle illustrated in the azimuth. with the elevation angle fixed at 54.74 and the bistatic angle illustrated in the azimuth.

Figure Figure 6. 6. The The bistatic bistatic RCS RCS observation observation geometry geometryof ofthe theTCR. TCR.

As shown in Figure 7, the bistatic RCS azimuth patterns of the TCR were simulated using the FEKO electromagnetic simulations. It can be seen that the main lobe of the bistatic RCS pattern became highly rippled and dramatically lower with the bistatic angle increasing. Furthermore, the peak RCS and beamwidth varied greatly for different bistatic angles, so even in the case of a small bistatic angle, the monostatic and bistatic RCS characteristics are different. However, the peak RCS for different

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RCS (dB)

As shown in Figure 7, the bistatic RCS azimuth patterns of the TCR were simulated using the FEKO electromagnetic simulations. It can be seen that the main lobe of the bistatic RCS pattern became highly rippled and dramatically lower with the bistatic angle increasing. Furthermore, the Remote Sens. 2018, 10, 1610 8 of 19 peak RCS and beamwidth varied greatly for different bistatic angles, so even in the case of a small bistatic angle, the monostatic and bistatic RCS characteristics are different. However, the peak RCS for different angles corresponded to different angles, which the same as the bistatic anglesbistatic corresponded to different azimuth angles,azimuth which was the same aswas the results obtained results by using the monostatic bistatic equivalence theorem. by usingobtained the monostatic bistatic equivalence theorem.

Figure 7. 7. The The bistatic bistatic RCS RCS azimuth azimuth pattern pattern of of the the TCR TCR based based on on FEKO FEKO electromagnetic electromagneticsimulations. simulations. Figure

By results of of the the FEKO FEKOelectromagnetic electromagneticsimulations simulations(see (seeFigure Figure7)7) and those By comparing comparing the results and those of of monostatic bistatic equivalence theorem Figure it was found peak thethe monostatic bistatic equivalence theorem (see(see Figure 5), 5), it was found thatthat thethe peak RCSRCS andand the the beamwidth of the two results were differentfor forthe thesame samebistatic bistatic angle. angle. The The TCR is specifically beamwidth of the two results were different specifically designed to be a backscatter, and the coherent addition of the waves work only in that direction. designed backscatter, and the coherent addition of the waves work only in that direction. In In most other directions, bistatic condition, there is very little scattering, in of allthe of most of of thethe other directions, i.e.,i.e., thethe bistatic condition, there is very little scattering, andand in all the other directions, scatter is less in backscatter the backscatter a narrow backscattering other directions, the the scatter is less thanthan in the [24].[24]. It hasIt ahas narrow backscattering lobe, lobe, with the beamwidth of the lobe proportional to the wavelength divided by a characteristic with the beamwidth of the lobe proportional to the wavelength divided by a characteristic length of length of the trihedral, so would the TCR be the worst casemonostatic for the monostatic bistatic equivalence the trihedral, so the TCR bewould the worst case for the bistatic equivalence theorem. theorem. Therefore, it is not suitable to use the equivalence theorem to compute the bistatic RCSFor of Therefore, it is not suitable to use the equivalence theorem to compute the bistatic RCS of TCR. TCR. thesethe reasons, the computation of the bistatic RCS characteristics inwere this paper theseFor reasons, computation of the bistatic RCS characteristics of the TCR of in the thisTCR paper based were based onelectromagnetic the FEKO electromagnetic on the FEKO simulations.simulations. ◦ , the ripples are too large and As As shown shown in in Figure Figure 7, 7, when when the the bistatic bistatic angle angle is is larger larger than than 66°, the ripples are too large and dramatic the peak peakRCS RCSpointing pointingofofthe theTCR TCR with SAR antenna’s boresight. Therefore, dramatic to align the with thethe SAR antenna’s boresight. Therefore, the the becomes unpredictable, which woulddegrade degradethe theSAR SARimage imagequality quality and and induce radiometric RCSRCS becomes unpredictable, which would radiometric ◦ , the bistatic RCS patterns of TCR are wide, with calibration calibration errors. errors. For For bistatic bistatic angles angles of of less less than than 66°, the bistatic RCS patterns of TCR are wide, with ◦ aa beamwidth beamwidth up up to to 30 30°,, so so itit satisfies satisfies the the beamwidth beamwidth requirement requirement of of the the calibration calibration target target when when the the bistatic SAR is working in tandem mode. On the other hand, the peak RCS is more than 15 dB, and bistatic SAR is working in tandem mode. On the other hand, the peak RCS is more than 15 dB, and also also satisfies satisfiesthe theSCR SCRrequirements requirementsthat thatwere werediscussed discussedininSection Section2.2. ◦ ◦ As is widely known, the TCR boresight of the maximum RCS is θ =RCS 54.74is, ϕ θ==45 for ,ϕ monostatic As is widely known, the TCR boresight of the maximum 54.74 = 45 for SAR. We got the bistatic RCS azimuth patterns (Figure 7) with the elevation angle fixed at 54.74◦ . monostatic SAR. We got the bistatic RCS azimuth patterns (Figure 7) with the elevation angle fixed The results of previous studies about TCR for bistatic SAR calibration may be obtained in this case [11]. at 54.74°. The results of previous studies about TCR for bistatic SAR calibration may be obtained in However, we found the elevation angle of the peak RCS for different bistatic angles are different, this case [11]. However, we found the elevation angle of the peak RCS for different bistatic angles are as shown in Figure 8a. The main lobe is gradually disappearing and the energy is moving to the different, as shown in Figure 8a. The main lobe is gradually disappearing and the energy is moving side lobe when the bistatic angle is greater than 20◦ , so we set 20◦ as the upper limit for the range of to the side lobe when the bistatic angle is greater than 20°, so we set 20° as the upper limit for the feasible bistatic angle. Then, we got the bistatic RCS azimuth patterns of the TCR as the elevation range of feasible bistatic angle. Then, we got the bistatic RCS azimuth patterns of the TCR as the angle corresponding to its individual peak RCS, as shown in Figure 8b. It can be seen that the bistatic elevation angle corresponding to its individual peak RCS, as shown in Figure 8b. It can be seen that RCS patterns are still wide and flat, even when the bistatic angle increases beyond 6◦ . These azimuth the bistatic RCS patterns are still wide and flat, even when the bistatic angle increases beyond 6°. patterns in Figure 8b are different from those of Figure 7, and the peak RCSs are larger than those of These azimuth patterns in Figure 8b are different from those of Figure 7, and the peak RCSs are larger Figure 7 at the same bistatic angle. So, we concluded that the TCR can be used as the bistatic calibration target as the bistatic angle increases below 20◦ . In this condition, we should align the TCR boresight

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than those of Figure 7 at the same bistatic angle. So, we concluded that the TCR can be used as the of 19 as the bistatic angle increases below 20°. In this condition, we should 9align the TCR boresight according to the bistatic angle during the deployment, instead of just fixing the elevation angle at 54.74°. However, the lower peak RCS will affect the SCR as the bistatic angle according to the bistatic angle during the deployment, instead of just fixing the elevation angle at become larger. 54.74◦ . However, the lower peak RCS will affect the SCR as the bistatic angle become larger.

Remote Sens. 2018, 10, 1610 bistatic calibration target

(a)

(b)

Figure Figure 8. 8. The bistatic RCS pattern of the TCR based on FEKO electromagnetic electromagnetic simulations simulations as as the the TCR TCR boresight boresight changes changes with with the the bistatic bistatic angle angle is is considered. considered. (a) The The bistatic bistatic RCS RCS elevation elevation pattern pattern of of the the TCR; TCR; (b) (b) the the bistatic bistatic RCS RCS azimuth azimuthpattern patternof ofthe theTCR. TCR.

Combined with the the electromagnetic electromagneticsimulation simulationresults resultsand andthe theabove above analysis, results Combined with analysis, thethe results cancan be be divided into two aspects. On the one hand, if we don’t consider the change of TCR boresight divided into two aspects. On the one hand, if we don’t consider the change of TCR boresight with the with the angle, bistaticthe angle, theisTCR not suitable for bistatic SAR calibration underlarge largebistatic bistatic angles. angles. bistatic TCR notissuitable for bistatic SAR calibration under Furthermore, the TCR meets the requirements of the calibration target for bistatic radiation calibration Furthermore, the TCR meets the requirements of the calibration target for bistatic radiation under the condition small bistatic angles (lessangles than 6◦(less ) when the SARbistatic is working inworking tandem calibration under theofcondition of small bistatic than 6°)bistatic when the SAR is mode. On the other we have the bistatic angle can angle be extended 20◦ by in tandem mode. Onhand, the other hand,also we proposed have also that proposed that the bistatic can be to extended taking thetaking change the TCR boresight into account. In summary, if the ifTCR is aligned withwith the to 20° by theof change of the TCR boresight into account. In summary, the TCR is aligned optimum boresight according to the bistatic angle during the deployment, it can also work at relatively the optimum boresight according to the bistatic angle during the deployment, it can also work at large bistatic angles at the cost at of the sacrificing the SCR. the SCR. relatively large bistatic angles cost of sacrificing 4. Error Factors of TCR RCS 4. Error Factors of TCR RCS In Section 3, the bistatic RCS characteristics of the TCR were analyzed, which indicated that the In Section 3, the bistatic RCS characteristics of the TCR were analyzed, which indicated that the TCR could meet the requirements listed in Section 2. For practical calibration of a bistatic SAR, it is TCR could meet the requirements listed in Section 2. For practical calibration of a bistatic SAR, it is very important to ensure the accurate RCS of the calibration targets. There are several error factors very important to ensure the accurate RCS of the calibration targets. There are several error factors that can introduce a change of RCS for the TCR, including that limited machining accuracy will mainly that can introduce a change of RCS for the TCR, including that limited machining accuracy will cause the interplate to be nonorthogonal and the interleg length to not reach the standard during the mainly cause the interplate to be nonorthogonal and the interleg length to not reach the standard manufacturing process. Moreover, the TCR deviates from the design route during the deployment, during the manufacturing process. Moreover, the TCR deviates from the design route during the or the attitude error (yaw, pitch, and roll) caused the deviation of the platform, which will result in deployment, or the attitude error (yaw, pitch, and roll) caused the deviation of the platform, which the pointing deviation. In addition, thermal deformation caused by the environment will also change will result in the pointing deviation. In addition, thermal deformation caused by the environment the interleg length. Proper control of the above errors will guarantee or improve the accuracy of the will also change the interleg length. Proper control of the above errors will guarantee or improve the bistatic SAR radiometric calibration. In order to meet the RCS accuracy requirement, we analyzed accuracy of the bistatic SAR radiometric calibration. In order to meet the RCS accuracy requirement, the error factors such as interplate orthogonality, machining error of length, pointing deviation, and we analyzed the error factors such as interplate orthogonality, machining error of length, pointing thermal deformation quantitatively with electromagnetic simulations. Furthermore, the machining deviation, and thermal deformation quantitatively with electromagnetic simulations. Furthermore, tolerance, deployment requirements for pointing, and deformation tolerance are recommended in the machining tolerance, deployment requirements for pointing, and deformation tolerance are this section. recommended in this section. 4.1. Interplate Orthogonality The interplate orthogonality means ensuring the angle between the two plates is 90◦ at their intersections, but in practical manufacturing, the plates need to be assembled together such as using welding or other techniques, so it is difficult to ensure the orthogonality between the two plates. When

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analyzing the bistatic RCS observation geometry of the TCR (see in Figure 6), points A and B move ◦ ◦ n outward or inward, and each point moves n /2 (n = 0, 0.1, 0.2, 0.3, 0.4, 0.5), respectively. In this condition, points A and B are still in the XOY plane, and OA = OB = b = 0.4 m; we can calculate the azimuth bistatic RCS pattern. Define ∆σ as the peak RCS reduction of the trihedral: ∆σ = σmax − σ

(9)

where σmax is the peak RCS of the ideal TCR, and σ is the peak RCS of the TCR with errors. The effect of the interplate angle deviations on RCS can be obtained, and we can also calculate the relationship between the interplate angle errors and the peak RCS errors, as shown in Figure 9.

Figure 9. The effect of interplate angle error on the RCS at different bistatic angles.

When only the angle between the two vertical plates is varied, we found that the RCS changes were negligible, as the interplate angle was smaller than 0.5◦ . For monostatic calibration, the interplate angle error will result in a reduction in RCS. However, the effect of interplate angle error on the RCS at different bistatic angles is irregular, which may be due to the complexity of the bistatic system, and the interplate angle error will change the original structure of the TCR. Even in the case of small bistatic angle (less than 6◦ ), the RCS errors are negative numbers, as the interplate angle is less than 90◦ (i.e., the interplate angle errors are negative numbers). The errors were more severe when the interplate angle was more than 90◦ , rather than less than 90◦ . The current level of machining can ensure the interplate angle error is less than 0.5◦ , and the maximum RCS error will not exceed 0.2 dB for different bistatic angles. Generally, the RCS loss of the TCR is about 0.23 dB if the interplate angle deviation is 0.5◦ for monostatic calibration [27]. So, RCS errors due to interplate angle errors are more severe for monostatic calibration at this machining level. Moreover, the interplate angle deviation will only cause a loss of RCS, and will not affect the beamwidth and stability requirements when the TCR is used as a bistatic calibration target. 4.2. Machining Error of Length The limited machining accuracy will also cause the length of the TCR to not be up to the standard. Figure 10 shows the curve with the machining errors of length and RCS errors. The absolute value of the RCS error is probably proportional to the machining error of length. Again, the changes were more severe when the length decreased rather than increased. In general, the current machining accuracy of length can be guaranteed up to 1 mm, and the relative RCS errors are less than 0.1 dB for different bistatic angles. Figure 10 also shows that a length error of less than 1 mm can result from an RCS error of less than 0.1 dB at the X-band for monostatic calibration, where the RCS error is a little larger than the result of bistatic calibration. Moreover, when the length error exceeds 2 mm, we found that only

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more severe when the length decreased rather than increased. In general, the current machining more severe whencan thebelength decreased increased. general, the less current accuracy of length guaranteed up torather 1 mm,than and the relative In RCS errors are thanmachining 0.1 dB for accuracy of length can be guaranteed up to 1 mm, and the relative RCS errors are less than dB an for different bistatic angles. Figure 10 also shows that a length error of less than 1 mm can result0.1 from different bistatic angles. Figure 10 also shows that a length error of less than 1 mm can result from an RCS error of less than 0.1 dB at the X-band for monostatic calibration, where the RCS error is a11little Remote Sens. 2018, 10, 1610 of 19 RCS error than dB atcalibration. the X-bandMoreover, for monostatic where the RCS errorwe is found a little larger than of theless result of0.1 bistatic whencalibration, the length error exceeds 2 mm, larger than the result of bistatic calibration. Moreover, when the length error exceeds 2 mm, we found that only the bistatic angle is 20°, and the RCS error is larger than that of the monostatic calibration. ◦ that only the bistatic angle is 20°, and the RCS error is larger than that of the monostatic calibration. the bistatic angle is 20 , and the RCS error larger than thatof of length the monostatic Similar to Similar to the interplate orthogonality, theismachining error does not calibration. affect the application Similar to the interplate orthogonality, the machining error of length does not affect the application the interplate orthogonality, the machining error of length does not affect the application of the TCR of the TCR for bistatic radiometric calibration. of the TCR for bistatic radiometric calibration. for bistatic radiometric calibration. 0.4

=0° =2° =0 ° =2 ° =4° =4 ° =6° =6 ° =8° =8 ° =10° =20° =10 °

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Figure 10. The effect of machining error of length on the RCS at different bistatic angles. Figure Figure 10. 10. The The effect effect of of machining machining error error of of length length on on the the RCS RCSat atdifferent differentbistatic bistaticangles. angles.

4.3. 4.3. Pointing Pointing Deviation Deviation 4.3. Pointing Deviation In it isit important to align the TCR with respect to the SAR antenna In radiometric radiometriccalibration, calibration, is important to align the boresight TCR boresight with respect to the SAR In radiometric calibration, it is important to align the TCR boresight with respect to the SAR antenna boresight. Either the attitude measurement errors of the SAR platform and antennas or the pointing of antenna boresight. Either the attitude measurement errors of the SAR platform and antennasthe or boresight. Either the attitude measurement errors the SAR platformand and antennas or the pointing of the TCR in the field will deployment cause the of pointing deviation final radiometric calibration the pointing ofdeployment the TCR inprocess the field process will causethe the pointing deviation and TCR inHere, the field process will cause the pointing deviation and the final radiometric calibration errors. we deployment focused on the latter from the view the TCR deployment the final radiometric calibration errors. Here, weoffocused on the latter requirements. from the view of the TCR errors. Here, we focused on the latter from the view of the TCR deployment requirements. Using a TCR with an interleg length of 0.4 m and a bistatic angle of 2° as an example, the bistatic deployment requirements. Using a TCR with an interleg length of 0.4 m and a bistatic angle of 2° as an example, the  bistatic ◦ a TCR of 0.4 m and a bistatic 2 as an example, θ ◦= 54.62the ,ϕbistatic = 44, peakUsing RCS is and thelength corresponding boresight is angle in theofdirection: 2 0 .2with 5 d Ban, interleg ◦ θ , ϕ54.62 44 , = peakRCS RCSisis20.25 andcorresponding the corresponding boresight is direction: in the direction: 20.25 peak dB, dB and the boresight is in the θ= = 54.62 = 44, ϕ, which which were obtained from, the simulation results in Figure 8. The bistatic RCS pattern was calculated were obtained from the simulation results in Figure The bistatic RCS pattern was calculated in the which were obtained from the results in 8. Figure 8. The bistatic RCS pattern was calculated   ◦ simulation ◦ 4050 ≤◦ϕ ≤ 50, and compared with theRCS. peakThe RCS. The contour in the range ≤ ◦θ and ≤ 60  , and compared range of 50 of 40 and with the peak contour map ofmap the ≤ θ50 ≤ 60 ≤ϕ≤ in the range of 50 ≤ θ ≤ 60 and 40 ≤ ϕ ≤ 50 , and compared with the peak RCS. The contour map of the azimuth and elevation misalignments is shown in Figure 11. azimuth and elevation misalignments is shown in Figure 11. of the azimuth and elevation misalignments is shown in Figure 11. 60

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Figure 11. The contour map of the RCS loss due to pointing deviation. Figure 11. The contour map of the RCS loss due to pointing deviation.

The RCS reduction becomes greater with the incident direction deviation from the optimum boresight increasing. As shown in Figure 12, we can also get the effect of the pointing deviation on the RCS for different bistatic angles. In the radiometric calibration, it is possible to control the pointing

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The RCS reduction becomes greater with the incident direction deviation from the optimum 12 of 19 boresight increasing. As shown in Figure 12, we can also get the effect of the pointing deviation on the RCS for different bistatic angles. In the radiometric calibration, it is possible to control the pointing ◦ and deviation within within 0.5 0.5°◦ generally. generally. Furthermore, Furthermore, an an azimuth azimuth deviation deviation of of less less than than 0.5 0.5° and elevation elevation deviation ◦ deviation of of less a deviation less than than 0.5° 0.5 could could introduce introduceno nomore morethan than0.5-dB 0.5-dBRCS RCSloss lossatatthe theX-band. X-band.However, However, ◦ pointing deviation of less than 0.5° in azimuth and elevation could make the resulting RCS within a pointing deviation of less than 0.5 in azimuth and elevation could make the resulting RCS within about 0.1 0.1 dB dB of of the the peak calibration [25]. [25]. By By comparing the two two results, results, we we found found about peak value value for for monostatic monostatic calibration comparing the that the theRCS RCSloss lossdue duetotopointing pointing deviation was more severe bistatic calibration. Moreover, the that deviation was more severe for for bistatic calibration. Moreover, the RCS RCSwas lossmore was severe more severe for elevation misalignments for misalignments, azimuth misalignments, so the loss for elevation misalignments than for than azimuth so the elevation elevation angle beas adjusted as accurately in deployment. angle should be should adjusted accurately as possibleasinpossible deployment.

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Figure 12. The Theeffect effect pointing deviation on RCS the RCS at different (a) Azimuth Figure 12. of of pointing deviation on the at different bistaticbistatic angles.angles. (a) Azimuth pointing pointing deviations and corresponding RCS (b)pointing elevationdeviations pointing deviations and corresponding deviations and corresponding RCS errors; (b)errors; elevation and corresponding RCS errors. RCS errors.

4.4. Thermal Deformation 4.4. Thermal Deformation The thermal deformation caused by environment mainly changes the length of the TCR, which The thermal deformation caused by environment mainly changes the length of the TCR, which is is similar to the machining error of length. The thermal deformation can be calculated according to similar to the machining error of length. The thermal deformation can be calculated according to the the temperature range, and then the relationship between thermal deformation and the temperature range, and then the relationship between thermal deformation and the corresponding corresponding bistatic RCS error can be obtained from Figure 10. Aluminum is commonly used for bistatic RCS error can be obtained from Figure 10. Aluminum is commonly used for the construction of the construction of plates; the linear thermal expansion coefficient of the aluminum 23 × 10−6 / ο C −6 /◦ C as is plates; the linear thermal expansion coefficient of the aluminum is 23 × 10 the measurement as the measurement temperature is 20 ο C . For the TCR with a length of 0.4 m, the length will change temperature is 20 ◦ C. For the TCR with a length of ο0.4 m, the length will change −0.552–0.368 mm −0.552–0.368 mm in the temperature range of −40 C to 60 ο C . According to Figure 10, it can be in the temperature range of −40 ◦ C to 60 ◦ C. According to Figure 10, it can be seen that the relative seen that the relative change on RCS is very small (less than 0.05 dB) for this temperature range. change on RCS is very small (less than 0.05 dB) for this temperature range. To sum up the errors in the above sections 4.1–4.4, it can be concluded that RCS errors due to To sum up the errors in the above Sections 4.1–4.4, it can be concluded that RCS errors due to interplate orthogonality and machining errors of length were more severe for monostatic calibration interplate orthogonality and machining errors of length were more severe for monostatic calibration under the current machining accuracy, and the thermal deformation is similar to the matching error under the current machining accuracy, and the thermal deformation is similar to the matching error of length. However, the effect of the pointing deviation on the RCS errors was more severe for bistatic of length. However, the effect of the pointing deviation on the RCS errors was more severe for calibration when the misalignment is the same. These results indicate that these error factors can bistatic calibration when the misalignment is the same. These results indicate that these error factors introduce different RCS errors for monostatic and bistatic calibration, so we cannot replace the can introduce different RCS errors for monostatic and bistatic calibration, so we cannot replace the conclusions of monostatic calibration with those of bistatic calibration. Moreover, these results will have conclusions of monostatic calibration with those of bistatic calibration. Moreover, these results will important reference values and guidance significance for guaranteeing the calibration accuracy for have important reference values and guidance significance for guaranteeing the calibration accuracy bistatic SAR calibration. for bistatic SAR calibration. 5. Simulation Simulation Experiments Experiments 5. One basic basic purpose purpose of of radiometric radiometric calibration calibration is is to to obtain obtain the the absolute calibration constant, constant, which which One absolute calibration is the the corresponding corresponding relation relation between between the the target target RCS RCS and and its its pixel pixel value value in in aa SAR SAR image. image. Therefore, is Therefore, either the accurate RCS or accurate pixel value is critical to calibration accuracy. We have described described either the accurate RCS or accurate pixel value is critical to calibration accuracy. We have the theoretical requirements, bistatic RCS characteristics, and error factors of the TCR RCS with the theoretical requirements, bistatic RCS characteristics, and error factors of the TCR RCS with electromagnetic simulations. In this section, based on the electromagnetic simulation results, bistatic

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electromagnetic simulations. In this section, based on the electromagnetic simulation results, bistatic SAR imaging simulation experiments were conducted to analyze the bistatic image quality and the pointimaging target energy, andexperiments these werewere compared withtoseveral bistatic angles as the SAR simulation conducted analyzetypical the bistatic image quality andTCR the boresight considered or not.were The compared bistatic SAR imaging are shown in Table 1 and point targetisenergy, and these with severalsystem typicalparameters bistatic angles as the TCR boresight imaging algorithm the Range–Doppler (RD) algorithm. isthe considered or not. Theisbistatic SAR imaging system parameters are shown in Table 1 and the imaging algorithm is the Range–Doppler (RD) algorithm. Table 1. System parameters used in the simulation dataset. Table 1. System parameters used in the simulation dataset.

Simulation Data Parameters Frequency 9.6 GHz (X-Band) Simulation Data Parameters Bandwidth 100(X-Band) MHz Frequency 9.6 GHz Pulse width μs Bandwidth 1001.5 MHz Pulse width µs4 m Altitude 21.5 × 10 Altitude 2× 104m/s m Velocity 150 Velocity 150 m/s Antenna azimuth beamwidth 0.5° Antenna azimuth beamwidth 0.5◦ Azimuth sampling rate 300 Hz Azimuth sampling rate 300 Hz Range samplingrate rate 120MHz MHz Range sampling 120

The SAR SAR image image quality quality of of aa point point target target isisaaprecondition preconditionthat thatdetermines determines whether whether to to use use this this The targetas asaacalibration calibrationtarget targetor ornot. not.The Themost most common commonimage imagequality quality parameters parametersfor forSAR SARimages imagesare are target the shape of the impulse response function (IRF). As for a point target, the IRF takes the form of the shape of the impulse response function (IRF). As for a point target, the IRF takes the form of aa Diracdelta deltafunction, function,and andthe theimage imagequality qualityparameters parametersof ofthe thepoint pointtarget targetare areshown shownininFigure Figure13. 13. Dirac

Figure 13. The image quality analysis parameters of the point target. Figure 13. The image quality analysis parameters of the point target.

The most important image quality parameters of the point target include [28]: (1) impulse response The most important image quality parameters of the point target include [28]: (1) impulse width (IRW); (2) peak side lode ratio (PSLR); and (3) integral side lobe ratio (ISLR). These features response width (IRW); (2) peak side lode ratio (PSLR); and (3) integral side lobe ratio (ISLR). These are often considered sufficient to judge the quality of the impulse response performance. The IRW features are often considered sufficient to judge the quality of the impulse response performance. The refers to the 3-dB width of the main lode, which is also known as image resolution. The PSLR and IRW refers to the 3-dB width of the main lode, which is also known as image resolution. The PSLR ISLR are related to the image contrast. PSLR is the ratio of the highest side lobe power to the peak and ISLR are related to the image contrast. PSLR is the ratio of the highest side lobe power to the of the response, and the PSLR is usually less than −13 dB. ISLR is the ratio of the energy contained peak of the response, and the PSLR is usually less than −13 dB. ISLR is the ratio of the energy in the side lobe to the energy contained in the main lobe of the impulse response, and the ISLR contained in the side lobe to the energy contained in the main lobe of the impulse response, and the is usually about −10 dB. The point target accounts for only one or two pixels in the SAR images. ISLR is usually about −10 dB. The point target accounts for only one or two pixels in the SAR images. Generally, the upsampling operation is a necessary pre-processing step in order to measure the above Generally, the upsampling operation is a necessary pre-processing step in order to measure the above parameters accurately. parameters accurately. The integral method is commonly used to obtain the absolute calibration constant by measuring The integral method is commonly used to obtain the absolute calibration constant by measuring the response of the targets. The integrated point target energy is mainly obtained by the difference the response of the targets. The integrated point target energy is mainly obtained by the difference between the energy of the point target in the integration area and the energy of the adjacent same between the energy of the point target in the integration area and the energy of the adjacent same background area. Typically, the region centered on the peak point is used to describe the target, which background area. Typically, the region centered on the peak point is used to describe the target, includes the target region and the background region [23]. which includes the target region and the background region [23].   Ncr Ecr = En − · Eclt (10) Nclt

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N  E cr  E n  N cr   E clt E cr  E n    Ncrclt  E clt  N clt 

(10) (10)

where En is the summed energy in the target region, Eclt is the energy in the background region, where En is the summed energy in the target region, Eclt is the energy in the background region, Ncr Eisn the Nenergy number of the samples in the target region, is the of samples in the where is the summed energy in the target region, Ecltand is the clt innumber the background region, N N is the number of the samples in the target region, and is the number of samples in clt is the number of samples in the region. Nbackground of the samples in the target region, and Nclt the crcris the number background region. In the following simulation experiments, the bistatic scattering data, containing amplitude and background region. In following simulation the data, containing and phase information, byexperiments, electromagnetic simulations were used the SAR amplitude echo simulation In the the followingobtained simulation experiments, the bistatic bistatic scattering scattering data, in containing amplitude and phase information, obtainedand byelectromagnetic electromagnetic simulations were used in the echo simulation and imaging processing, then the image quality parameters and point target energy were phase information, obtained by simulations were used in the SARSAR echo simulation and and imaging processing, and then the image quality parameters and point target energy were analyzed. The simulation results were shown figures 14–16 the consideration the TCR imaging processing, and then the image qualityinparameters andwithout point target energy were of analyzed. analyzed. The results were shown in figures 14–16 without consideration TCR2. boresight, andsimulation the image quality analysis parameters and point targetthe energy arethe shown inthe Table The simulation results were shown in Figures 14–16 without the consideration of TCRofboresight, boresight, and the image quality analysis parameters and point target energy are shown in Table 2. We can conclude that the main lobe of the TCR image became wider as the bistatic angle increased, and the image quality analysis parameters and point target energy are shown in Table 2. We can We can conclude the main of the TCR(i.e., image became wider asthe thepoint bistatic angle increased, which degrades the resolution of TCR the image IRW). Otherwise, target energy drops conclude that thethat main lobe of lobe the image became wider as the bistatic angle increased, which which degrades resolution of the image (i.e., IRW). the point target energy drops quickly with thethe bistatic angle increasing. Therefore, theOtherwise, increase bistatic angles will deteriorate degrades the resolution of the image (i.e., IRW). Otherwise, the point of target energy drops quickly with quickly with the bistatic angle increasing. Therefore, the increase of bistatic angles will deteriorate the quality of the bistatic SAR image and the point target energy. the bistatic angle increasing. Therefore, the increase of bistatic angles will deteriorate the quality of the the quality the bistatic SAR image andenergy. the point target energy. bistatic SARofimage and the point target Remote Sens. 2018, 10, 1610

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Figure 14. The simulation results for the 2° bistatic angle without the consideration of the TCR Figure 14. The The simulation results the 2° bistatic without consideration of optimum the profile TCR optimum boresight. (a) results The point target image afterangle upsampling 48the times; (b)ofthe Figure 14. simulation for for the 2◦ bistatic angle without the consideration theazimuth TCR boresight. (a) point image afterimage upsampling 48 times; (b)48 the azimuth profile basedprofile on the optimum (a) Theelectromagnetic point target after upsampling times; (b) the azimuth based onboresight. theThe results of target the simulation. resultson of the the results electromagnetic simulation. simulation. based of the electromagnetic

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Figure Figure15. 15.The Thesimulation simulationresults resultsfor for 6°bistatic bistaticangle anglewithout withoutthe theconsideration considerationofofthe theTCR TCRoptimum optimum boresight. (a) The point target image after upsampling 48 times; (b) the azimuth profile based on Figure 15. The resultsimage for 6°after bistatic angle without the consideration of profile the TCR optimum boresight. (a) simulation The point target upsampling 48 times; (b) the azimuth based onthe the results boresight. (a) The point targetsimulation. image after upsampling 48 times; (b) the azimuth profile based on the resultsofofthe theelectromagnetic electromagnetic simulation. 6◦

results of the electromagnetic simulation.

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Figure 16. The simulation (a) results for 20° bistatic angle without the consideration (b) of the TCR optimum boresight. (a) The point target image after upsampling 48 times; (b) the azimuth profile based on the Figure 16. results for Figure 16. The simulation results for20° 20◦bistatic bistaticangle anglewithout withoutthe theconsideration considerationof ofthe theTCR TCRoptimum optimum results ofThe thesimulation electromagnetic simulation. boresight. boresight. (a) (a)The The point pointtarget targetimage image after after upsampling upsampling48 48 times; times; (b) (b) the the azimuth azimuth profile profile based based on on the the results electromagnetic simulation. results of2.the the electromagnetic simulation. Tableof Image quality analysis parameters of the TCR. IRW: impulse response width, PSLR: peak side lode ratio, ISLR: integral side lobe ratio. Table 2. Image quality analysis parameters of the TCR. IRW: impulse response width, PSLR: peak side Table 2. Image quality analysis parameters of the TCR. IRW: impulse response width, PSLR: peak lode ratio, ISLR: integral side Range lobe ratio. Bistatic IRW (m) PSLR side lode Angle ratio, ISLR: integral side lobe ratio. Range ISLR Azimuth PSLR Azimuth ISLR Energy 2° 2.5521 −13.3511 −10.2050 −13.2756 −10.2737 49.8635 Bistatic Angle IRW (m) Range PSLR Range ISLR Azimuth PSLR Azimuth ISLR Energy Bistatic Angle IRW (m) Range PSLR Range ISLR Azimuth PSLR Azimuth ISLR Energy 6° 2.7604 −13.3257 −10.1887 −13.3436 −10.4011 44.1211 2◦ 2.5521 13.3511 −13.2756 −10.2737 2° 2.5521 −10.2050 −13.2756 −10.2737 49.8635 20° 3.4895 −−13.3511 −13.3577 −10.2050 −10.2092 −13.1612 −10.4430 49.8635 34.3275 ◦ 6 2.7604 −13.3257 −10.1887 −13.3436 −10.4011 44.1211 6° ◦ 2.7604 −13.3257 −10.1887 −13.3436 −10.4011 44.1211 20 3.4895 −13.3577 −10.2092 −13.1612 −10.4430 34.3275 3.4895 17–19, −13.3577 −10.2092 34.3275 As20° shown in figures the simulation results were−13.1612 obtained as the−10.4430 change of TCR boresight

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is considered, and image quality analysis parameters and point target energy of the TCR are shown As shown shown in in figures Figures17–19, 17–19,the thesimulation simulation resultswere wereobtained obtainedas asthe thechange changeof ofTCR TCR boresight boresight As in Table 3. As long as the bistatic angle is lessresults than 20°, the image quality was good, and the image is considered, considered, and and image image quality quality analysis analysis parameters parameters and and point point target target energy energy of of the the TCR TCR are are shown shown is quality analysis parameters could meet the general quality requirements. Otherwise, ◦ , theimage in Table 3. As long as the bistatic angle is less than 20 image quality was good, and the image incomparing Table 3. Asthe long as the bistatic thanangle 20°, the image 14 quality was good, andthat the whether image simulation resultsangle for theis2°less bistatic in figures and 17, it can be seen quality analysis parameters could meet the general image quality requirements. Otherwise, comparing quality analysis parameters could meet the general requirements. the TCR boresight is considered or not has little effect on image imagingquality when the bistatic angleOtherwise, is small (less the simulation results for the 2◦ bistatic angle in Figures 14figures and 17,14it and can 17, be seen that whether the TCR comparing the simulation results for the 2° bistatic angle in it be seen that whether than 6°). In addition, if the bistatic angle is larger than 6°, taking the TCRcan optimum boresight into boresight is considered or not has little effect on imaging when the bistatic angle is small (less than 6◦ ). the TCR boresight is considered or not has little effect on imaging when the bistatic angle is small (less account can improve the imaging quality and point target energy by comparing the parameters in In addition, if the bistatic angle is larger 6◦ , taking optimum accountinto can than 6°). 2Inand addition, if the bistatic anglethan is larger than the 6°, TCR taking the TCRboresight optimuminto boresight Tables 3. improvecan the improve imaging quality and point target by comparing thecomparing parametersthe in Tables 2 andin 3. account the imaging quality andenergy point target energy by parameters Tables 2 and 3.

(a)

(b)

Figure17.17.The Thesimulation simulation resultsfor for2◦2°bistatic bistaticangle anglewith withthe theconsideration consideration theTCR TCRoptimum optimum Figure results (a) (b)ofofthe boresight.(a) (a)The Thepoint pointtarget targetimage imageafter afterupsampling upsampling4848times; times;(b) (b)the theazimuth azimuthprofile profilebased basedononthe the boresight. Figure 17. The simulation results for 2° bistatic angle with the consideration of the TCR optimum results of the electromagnetic simulation. results of the electromagnetic simulation. boresight. (a) The point target image after upsampling 48 times; (b) the azimuth profile based on the results of the electromagnetic simulation.

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Figure 18. The simulation results for 6° ◦bistatic angle with the consideration of the TCR optimum Figure Figure 18. 18. The The simulation simulation results results for for 6° 6 bistatic bistatic angle angle with with the the consideration consideration of of the the TCR TCR optimum optimum boresight. (a) The point target image after upsampling 48 times; (b) the azimuth profile based on the boresight. boresight. (a) (a)The Thepoint pointtarget targetimage imageafter afterupsampling upsampling48 48times; times;(b) (b)the theazimuth azimuthprofile profile based based on on the the results of the electromagnetic simulation. results results of of the the electromagnetic electromagnetic simulation. simulation.

(a) (a)

(b) (b)

Figure Figure19. 19.The Thesimulation simulationresults resultsfor for20° 20◦bistatic bistaticangle anglewith withthe theconsideration considerationofofthe theTCR TCRoptimum optimum Figure 19. The simulation results for 20° bistatic angle with the consideration of the TCR optimum boresight. boresight.(a) (a)The Thepoint pointtarget targetimage imageafter afterupsampling upsampling4848times; times;(b) (b)the theazimuth azimuthprofile profilebased basedon onthe the boresight. (a) The point target image after upsampling 48 times; (b) the azimuth profile based on the resultsofofthe theelectromagnetic electromagneticsimulation. simulation. results results of the electromagnetic simulation. Table 3. Image quality analysis parameters of the TCR. Table 3. Image quality analysis parameters of the TCR. Table 3. Image quality analysis parameters of the TCR. Bistatic Angle IRW (m) Range PSLR Range ISLR Azimuth PSLR Azimuth ISLR Energy Bistatic Angle IRW (m) Range PSLR Range ISLR Azimuth PSLR Azimuth ISLR Energy Bistatic2◦Angle IRW (m) Range PSLR Range ISLR Azimuth Energy 2.6041 −13.3613 −10.2023 −13.2855 PSLR Azimuth −10.3628 ISLR 49.8637 2° ◦ 2.6041 −13.3613 −10.2023 −13.2855 −10.3628 49.8637 6 2.0313 −−13.3613 13.3295 −10.2343 −13.29544 −10.2122 47.5656 2° 2.6041 −10.2023 −13.2855 −10.3628 49.8637 6°20◦ 2.0313 −13.3295 −13.29544 −10.2122 47.5656 1.7187 − 13.3458 −−10.2343 10.3923 −13.29661 −10.1582 44.3411 6° 2.0313 −13.3295 −10.2343 −13.29544 −10.2122 47.5656 20° 1.7187 −13.3458 −10.3923 −13.29661 −10.1582 44.3411 20° 1.7187 −13.3458 −10.3923 −13.29661 −10.1582 44.3411

6. Discussion 6. Discussion 6. Discussion After discussing the requirements of SAR radiometric calibration for calibration targets in After discussing the requirements of SAR radiometric calibration for calibration targets in principle, feasibility the TCR forofbistatic SAR radiometric calibration at the X-band After the discussing the of requirements SAR radiometric calibration for calibration targetswas in principle, the feasibility of the TCR for bistatic SAR radiometric calibration at the X-band was investigated. electromagnetic SAR imaging simulation principle, the Both feasibility of the TCRsimulations for bistaticand SAR radiometric calibrationresults at thedemonstrated X-band was investigated. Both electromagnetic simulations and SAR imaging simulation results demonstrated that the TCRBoth can electromagnetic be used as a bistatic SAR calibration target forsimulation relatively results small bistatic angles investigated. simulations and SAR imaging demonstrated that the TCR◦ can be used as a bistatic SAR calibration target for relatively small bistatic angles (less (less than 6 ) if the boresight for different bistatic angles is not considered. Moreover, the bistatic that the TCR can be used as a bistatic SAR calibration target for relatively small bistatic angles angle (less than 6°) if the boresight ◦for different bistatic angles is not considered. Moreover, the bistatic angle can can be to 20 for bydifferent taking the change of the TCR boresight Moreover, into account, solved than 6°)extended if the boresight bistatic angles is not considered. thewhich bistatichas angle can be extended to 20° by taking the change of the TCR boresight into account, which has solved the the problem that the TCR is not suitable for a large bistatic angle [11]. However, the lower peak RCS be extended to 20° by taking the change of the TCR boresight into account, which has solved the problem that the TCR is not suitable for a large bistatic angle [11]. However, the lower peak RCS will will affect thethe SCR as the bistatic angle larger.angle In order design anthe appropriate TCR the problem that TCR is not suitable for becomes a large bistatic [11].toHowever, lower peak RCSaswill affect the SCR as the bistatic angle becomes larger. In order to design an appropriate TCR as the bistatic target, theangle interleg dimension must be large enoughan toappropriate ensure the target stable affect thecalibration SCR as the bistatic becomes larger. In order to design TCR as the bistatic calibration target, the interleg dimension must be large enough to ensure the target stable bistatic calibration target, the interleg dimension must be large enough to ensure the target stable RCS characteristics within the optical region. Furthermore, since the SCR is closely related to the RCS characteristics within the optical region. Furthermore, since the SCR is closely related to the

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RCS characteristics within the optical region. Furthermore, since the SCR is closely related to the radiometric calibration accuracy, if there is to be no more than a 0.5-dB measurement error, the SCR must be at least 25 dB. Otherwise, the target deployment sites should be chosen carefully to consider the clutter characteristics. To further prove the feasibility, the quality of the bistatic SAR images were compared with typical bistatic angles as the TCR boresight is considered or not. However, if the bistatic angle is larger than 6◦ , taking the TCR optimum boresight into account can improve the imaging quality and point target energy. The most important considerations when design a suitable TCR for bistatic calibration are the interplate orthogonality, the machining error of length, the pointing deviation, and the thermal deformation. Generally, the simulation results at the X-band imply that if an interplate angle deviation is less than 0.5◦ , the length error is less than 1 mm, and the pointing deviation is less than 0.5◦ , the resulting RCS will be within 0.5 dB of the peak value. Under the same accuracy, the requirements regarding those error factors for monostatic and bistatic calibration are different. The main motivation behind analyzing the TCR is that the bistatic RCS characteristics of the TCR are not so clear, and whether it can be used as a bistatic calibration target is questionable. Moreover, compared to active calibration targets and some passive calibration targets, the performance of TCR is that it is simple to manufacture, efficient to work, and has a relatively high bistatic RCS. Although we have analyzed how to design the TCR at the X-band, it can be easily extended to other bands that are similar to the bistatic SAR. In this paper, the feasibility of the TCR in bistatic tandem mode was validated, i.e., the mode where the bistatic angle appears in the azimuth (along track) direction. However, it was still valid if the bistatic angle was in the slant range (across track) direction or their hybrid. It must be admitted that the TCR does have limitations in bistatic SAR calibration. First, the feasibility of the TCR is limited to the mode that the bistatic angle is fixed. The bistatic SAR imaging modes are diversified, such as the tandem mode, translation invariant mode, constant velocity mode, and general mode [29]. However, the TCR has a very narrow bistatic pattern regarding the bistatic angles [8] and the 3-dB bistatic beamwidth corresponding to the bistatic angles is less than 4◦ for a 0.4-m TCR at the X-band, so it cannot be configured to calibrate all of the bistatic modes, especially bistatic modes with a large time-variable bistatic angle. Second, the TCR cannot be configured for all of the bistatic angles due to their rippled bistatic RCS pattern or lower SCR. We concluded that TCR can only be used as a radiometric calibration target for relatively small bistatic angles (less than 6◦ ). If the TCR is aligned with the optimum boresight, it can also work well, as the bistatic angle is less than 20◦ . For the time-variable bistatic angle or larger bistatic angle (more than 20◦ ), maybe we should analyze an active calibration target. 7. Conclusions The RCS characteristics and the requirements of radiometric calibration for bistatic SAR were analyzed based on the electromagnetic simulations. We concluded that the TCR could be used as a bistatic calibration target for relatively small bistatic angles (less than 6◦ ). TCR are generally considered not suitable for bistatic SAR calibration with large bistatic angles, but we have proposed that if we consider the TCR boresight changes with the bistatic angle, the bistatic angle can be extended to 20◦ . Both of these two conditions have their own advantages and disadvantages. If the change of TCR boresight with the bistatic angle is not considered, we just place it according to the TCR boresight of the monostatic calibration; however, it is not suitable for large bistatic angles (more than 6◦ ). In addition, the TCR was considered a good calibration target at a bistatic angle of less than 20◦ , but we need to know the optimum boresight in advance and align the TCR boresight with respect to the SAR antenna boresight during the deployment. To further verify the feasibility, bistatic SAR image quality and point target energy were analyzed. The importance of the study lies in that we can make full use of the advantages of the TCR, and then solve the problem of applicability and a design that is suitable TCR for bistatic radiometric calibration. Furthermore, the simulation results support that attention

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should be paid to ensure orthogonality between the three plates, interleg dimensions, and alignment, which will have reference value and guidance significance for the design and utilization of TCR RCS in bistatic SAR calibration. Author Contributions: J.H. played the leading role in preparing this article. Q.Z. performed the electromagnetic simulations and analyzed the data. Y.W. contributed to the structure and revision of this article and provided insightful comments and suggestions. A.W. provided valuable suggestions and revised the manuscript. Funding: This research work was partly supported by the NSFC (the National Natural Science Foundation of China, No. 61771453) and Equipment Development Department pre-research fund No. 6140416010202. Acknowledgments: Thanks go to Yuncheng Bu for providing some plotting supports. The authors would like to thank the anonymous reviewers for their meticulous work in enhancing the quality of this paper. Conflicts of Interest: The authors declare no conflict of interest.

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