Quick Quality Assessment and Radiometric Calibration of C-SAR/01 Satellite Using Flexible Automatic Corner Reflector

Abstract

C-SAR/01, the successor of China’s Gaofen-3 Satellite, which launched on 23 November 2021, is the first synthetic aperture radar (SAR) satellite to be launched in China’s civil space infrastructure plan and has served as an invaluable data resource. Radiometric calibration and validation are prerequisites for the quantitative application of SAR data. In this study, the radiometric calibration experiments of C-SAR/01 data of the ultra-fine strip (UFS) and fine strip I (FSI) modes were conducted applying flexible automatic triangular trihedral corner reflectors deployed in Xilinhot SAR satellite calibration and validation site. Accordingly, the image quality and radiometric calibration accuracy were evaluated. The results show that the spatial resolution, peak sidelobe ratio, and integrated sidelobe ratio of UFS and FSI mode data of C-SAR/01 are better than those of the design indexes, and the calibration results from the integral method are more stable than those from the peak method. Furthermore, the standard deviation of the calibration constant for UFS mode data is 0.234 dB, with the relative and absolute calibration accuracies obtained as 0.233 and 0.532 dB, respectively, whereas the standard deviation calibration constant for FSI mode data is 0.198 dB, with its relative and absolute calibration accuracies evaluated as 0.199 and 0.333 dB, respectively.

1. Introduction

Synthetic aperture radar (SAR), actively emitting electromagnetic signals to ground targets, has all-day, all-weather ground observation capabilities, which is important for various applications, such as emergency disaster monitoring, agricultural monitoring, and land resource monitoring, with strict timeliness requirements [1]. Various space-borne SAR satellites, including ERS-1/2, Envisat ASAR, and Sentinel-1 of the European space agency (ESA); COSMO-SkyMed of the Italian space agency; Radarsat-2 of the Canadian space agency; and the German radar satellite–TerraSAR-X, have been launched and utilized continuously. In 2015, the National Medium- to Long-Term Civilian Space Infrastructure Development Plan (2015–2025) issued by the Chinese government, indicated that seven SAR satellites, including C-band, L-band, and S-band sensors, would be launched during the 13th Five-Year Plan. Among the first C-band SAR satellites, C-SAR/01, which adopts the working principle of the Gaofen-3 satellite, was launched on 23 November 2021. GaoFen-3 satellite of China is an important SAR satellite, and it has played a significant role in the application fields of marine monitoring, disaster mitigation, environmental protection, water conservancy, agriculture and meteorology, etc. C-SAR/01 is the first successor of GaoFen-3, which is designed to form C-band synthetic aperture radar (SAR) satellite constellation of China’s sea and land surveillance and monitoring system. This greatly enriches the SAR satellites data sources of China and presents new opportunities for quantitative applications of radar remote sensing, which is conducive towards satisfying the data requirements in various application fields. Additionally, after the launch of C-SAR/01, there is an urgent need to evaluate its performance and image quality.

Radiometric calibration, through which the relationship between perceived pixel values of SAR image data and geophysical information on the earth surface can be accurately established [2], is the prerequisite for the applications of SAR data quantification. Before quantitative application, the SAR system needs to undergo in-orbit radiometric calibration campaigns. During the five-month commissioning phase (CP), multiple radiometric calibrations of TerraSAR-X were performed at The German Aerospace Center (DLR) calibration field in south Germany and showed a relative calibration accuracy better than 0.4 dB and absolute calibration accuracy better than 0.7 dB [3]. After ESA’s radiometric refinement and 1.5 years of monitoring and analysis, the relative calibration accuracy of sentinel-1A for the interferometric wide swath (IW) mode, the main mode of Sentinel-1, has reached 0.3 dB [4]. During the Sentinel-1B commissioning phase, DLR performed a SAR system calibration on Sentinel-1B, and it has demonstrated a mean relative calibration accuracy of 0.25 dB and an absolute radiometric accuracy of 0.36 dB for the IW mode. During this period, the radiometric accuracy of the two SAR systems (i.e., S-1A and S-1B) was cross-checked and Sentinel-1A showed an absolute calibration accuracy of 0.38 dB [5]. Mayank D Mishra et al. performed an absolute calibration of Fine resolution stripmap 1 (FRS-1) and Medium resolution ScanSAR (MRS) modes of Radar Imaging SATellite (RISAT-1), which is India’s first indigenously developed C-band spaceborne SAR, by deploying triangular trihedral corner reflectors at various research sites in India, and the FRS-1 mode shows a relative radiometric calibration accuracy better than 0.9 dB, and the MRS mode shows a relative radiometric accuracy of 0.53 dB [6].

Radiometric calibration is generally implemented by two methods: point targets and distributed targets. Distributed targets have many features, such as known scattering characteristics, homogeneous stability and large area, and the most commonly used ones include the globally recognized Amazon rainforest and the Canadian boreal forest belt [7]. The selection conditions for distributed targets are stringent, and the radar cross-section (RCS) of natural point targets is different in different frequencies and incidence angles, which requires prior experimental measurements, so, in practice, artificial point targets are more feasible than other targets. In other words, radiometric calibration is more feasible through artificial point targets with known RCS. The in-orbit radiometric calibration campaigns of SAR systems, such as TerraSAR-X [3], Sentinel-1 [4,5], and RISAT-1 [6] have all used artificial point targets.

The commonly used artificial point targets include active radar calibrator (ARC) and corner reflector (CR), among which CR has become the mainstream of ground reference in radiometric calibration due to its simple structure, stable performance, ease of installation, and low cost. The triangular trihedral corner reflector has a wide beam width in the azimuth and elevation direction [8], which is suitable for cross-frequency calibration [2] and is a typical instrument for SAR radiometric calibration in practice. Zhou et al. used three types of corner reflectors for radiometric and geometric calibration of RADARSAT-2 satellite data and verified the accuracy of the results [9]. Praveen et al. performed absolute radiometric calibration and verified the calibration accuracy of RISAT-1 satellite data of fine resolution scan (FRS) mode, by using trihedral CR via the peak method [10]. Both studies yielded satisfactory results.

In the process of the radiometric calibration of SAR satellites employing the ground-based CRs, it is important to ensure that RCS presented by CR in the image conforms to the theoretical value [10], and this can be achieved by the following three aspects. First, by ensuring that the geometric structure and manufacturing accuracy of the corner reflector meet the requirements [11]; second, by ensuring a consistent direction between the ground CR and the incidence of radar beam during satellite transit; and third, by ensuring that the surrounding environment of CR deployment meets the requirements to minimize the influence of background clutter on the return signal of CR [12].

With the support of the Common Application Support Platform project for Land Observation Satellites of China’s Civil Space Infrastructure (CASPLOS_CCSI), based on the Xilinhot Climate Observatory, a SAR satellite calibration and validation site, which is currently under construction, is built through the technical deployment of automatic triangular trihedral CRs and ARCs developed by CASPLOS_CCSI. Additionally, during the experiment, flexible automatic triangular trihedral CR are mainly deployed in the Xilinhot Climate Observatory in a mobile way to support the ground-synchronous measurement experiments. Based on the Xilinhot SAR satellite calibration and validation site, utilizing flexible automatic triangular trihedral CRs, the present study aims make a quick assessment of the image quality and radiometric calibration accuracy of C-SAR/01, which is now in the commissioning phase, by performing the radiometric calibration of C-SAR/01 and evaluating the calibration accuracy, using the peak and integral methods, to ensure the accuracy of backscatter intensity measurements so that C-SAR/01 images can accurately reflect characteristics of feature targets, as well as to meet the requirements of quantitative applications for C-SAR/01 image radiometric performance, which provides a basis for the C-SAR/01 data quality assessment and quantitative applications.

This paper is organized as follows: Section 2 introduces the site and data in this experiment, Section 3 introduces the process and specific methods of radiometric calibration of this experiment, Section 4 assesses the quality of the experimental data, Section 5 describes the radiometric calibration results of the C-SAR/01 data, and Section 6 analyzes the radiometric calibration results of the C-SAR/01 data.

2. Study Area and Data

2.1. Experimental Area

The experimental area in this study is shown in Figure 1, and the experiments were conducted at the Xilinhot SAR satellite calibration and validation site of the CASPLOS_CCSI project. This site is located in Xilinhot, Inner Mongolia, and the underlying surface is a typical grassland with krylov needlegrass and leymus chinensis as the predominant species. The site was built to achieve a long period of monitoring of satellite performance and satisfy the needs of multiple SAR imaging modes, by means of fixed calibrator that can be remotely controlled, supplemented by a flexible calibrator, which was in the construction stage. In this time, the experimental site was concentrated in the Xilinhot Climate Observatory, as shown by yellow line in Figure 1, which had a flat terrain and was a vast area with an altitude of about 1090–1160 m. In this site, the types of surface coverage included grassland, rivers, low buildings, etc., and scattering characteristics of the background features were homogeneous and stable without interference from a strong target or electromagnetic signal, which can effectively reduce the interference from background clutter [12].

2.2. Remote Sensing Data

The C-SAR/01 satellite of China’s space infrastructure strategy was launched on 23 November 2021, employing a payload of C-band SAR with 5.4 GHz center frequency and 12 imaging modes, such as spot beam, strip, and TOPSAR (

Table 1. C-SAR/01 imaging mode.

Imaging Mode		Nominal Resolution /m	Imaging Swath /km	Polarization Mode
Spotlight (SL)		1	10	Single
Strip	Ultra-Fine Strip (UFS)	3	30	Single
	Fine Strip I (FSI)	5	50	Dual
	Fine Strip II (FSII)	10	100	Dual
	Standard Strip (SS)	25	130	Dual
	Quad Polarization Strip I (QPSI)	8	30	Full (Quad)
	Quad Polarization Strip II (QPSII)	25	40	Full (Quad)
Scan	Narrow ScanSAR (NSC)	50	300	Dual
	Wide ScanSAR (WSC)	100	500	Dual
	Global Observation (GLO)	500	650	Dual
Wave (WAV)		8	20	Full (Quad)
Expanded incidence angle (EXT)	Low Incidence	25	130	Dual
	High Incidence	25	80	Dual

) [13], which can acquire SAR images with a resolution of 1–500 m and swath of 10–650 km, from single to full polarization, to realize the monitoring of ocean and land resources.

The C-SAR/01 data used in this experiment are shown in

Table 2. Information of two C-SAR/01 satellite SLC images.

Date	Orbit Direction	Look Direction	Imaging Mode	Incidence Angle/°	Polarization	Nominal Resolution/m	Azimuth Pixel Size/m	Range Pixel Size/m
12 May 2022	Descending	Right	UFS	28.43~30.57	HH	3	1.669818	1.124222
15 May 2022	Ascending	Right	FSI	26.01~29.60	HH/HV	5	2.613357	1.124222

and both are single-look complex (SLC) images at Level-1A. The first scene data were acquired on 12 May 2022, in ultra-fine strip (UFS) mode HH polarization with a resolution of 3 m. The second image data were acquired on 15 May in the same year, using fine strip I (FSI) mode HH/HV dual-polarization with a resolution of 5 m. Seven automatic CRs were deployed on the site for synchronous measurements during the satellite imaging, and their distribution is shown in Figure 1 as red triangles, and the orange and red lines in Figure 1 represent the coverage areas of data acquired on 12 May and 15 May, respectively.

2.3. Ground Synchronous Measurement

Ensuring that the RCS of CR is in proximity to the theoretical value is indispensable in the radiometric calibration process. As previously mentioned, in addition to the environment in which CR is deployed, the mechanical imperfections of CR may introduce RCS deviation [11]. Deviations in the azimuth and elevation angle pointing of CR during satellite transit can also cause the RCS to vary from that of the theoretical value [14]. Therefore, the guarantee of the manufacture precision of CR used in the calibration experiment and its pointing accuracy during the synchronous experiment are critical.

2.3.1. Flexible Automatic Trihedral Corner Reflector

The seven ground-based calibration facilities used in this experiment were flexible automatic trihedral CRs developed by CASPLOS_CCSI, which can be moved easily. Each flexible automatic CR consisted of four parts: console, fixed base, triangular trihedral CRs, and the power control box (Figure 2), which transmitted signals to complete the adjustment of the CR alignment. The distribution of the flexible automatic CR on the 12 May UFS mode and 15 May FSI mode data are shown in Figure 3 and Figure 4, respectively.

Each CR inner leg length was 1000 mm, inner leg length deviation was less than ±3 mm, interplate orthogonality was less than ±0.2°, plate curvature was less than ±2 mm, and C-band RCS accuracy was better than 0.16 dB. The thermal deformation deviation of the inner leg length was less than ±3 mm, the deviation of the interplate orthogonality stability was less than ±0.1°, the deviation of the plate curvature stability was less than ±2 mm, the deviation of the elevation angle adjustment was less than ±0.1 °, the deviation of the azimuth angle adjustment was less than ±0.1°, and the stability of the C-band RCS was better than 0.1 dB.

2.3.2. Azimuth and Elevation Angle of CR Calculation

The peak RCS of the trihedral CR varied with the azimuth and elevation angles [14]. Therefore, the angles of CR were required to be consistent with the direction of the radar incident beam during the SAR satellite transit to ensure that the radar antenna received the peak RCS signal from the ground point target [15], thus maintaining the accuracy of the SAR satellite radiation calibration.

The orbital parameters of the C-SAR/01 were used to predict its position coordinates at transit [16]. Thereafter, the azimuth angle ${\phi }_S$ (orange arc line in Figure 5a) and incidence angle ${\theta }_S$ (green arc line in Figure 5b) of the satellite were calculated with the help of spatial geometry between the satellite and the ground, where the satellite azimuth angle ${\phi }_S$ is the azimuth of the ground equipment $—O$ pointing towards the satellite $—S$. Based on the relationship between the radar beam and satellite vector $\overrightarrow{V}$, the azimuth angle of CR ${\phi }_{\mathrm{CR}}$ was calculated by combining the satellite orbit and look directions, using a feature where the normal line $OE$ (orange straight line in Figure 5b) of the triangular trihedral CR $O-ABC$ was perpendicular to the bottom edge $BC$. By simulating various combinations of the satellite ascending–descending orbit and left–right look, the formula for calculating the CR azimuth angle ${\phi }_{\mathrm{CR}}$ was derived as Equation (1), and the geometric relationship between the satellite azimuth angle ${\phi }_S$ and the CR azimuth angle ${\phi }_{\mathrm{CR}}$ is shown in Figure 5a for the left look of the ascending orbit. Finally, the CR elevation angle ${\theta }_{\mathrm{CR}}$ (purple arc line in Figure 5b) was obtained from the geometric structure of the triangular trihedral CR $O-ABC$ as Equation (2).

$${\phi }_{\mathrm{CR}}={\phi }_S+90°$$

(1)

$${\theta }_{\mathrm{CR}}={\theta }_S-35.264°$$

(2)

2.3.3. Auxiliary Parameter Measurement

During the synchronization experiment, the real-time kinematic (RTK) of Starfish iRTK5 was applied to accurately acquire the latitude and longitude coordinates, as well as the elevation of the centers of the seven automatic CR deployed on the ground, where the accuracies of the RTK plane measurement and elevation were better than 10 and 15 mm, respectively. After the automatic CR is adjusted to the required azimuth and elevation angle through program control automatically, the azimuth and elevation angle of CR were reviewed using the traditional measurement method, i.e., using the north marker and level, respectively, to ensure the accuracy of the equipment alignment parameters (Figure 6a,b) and respond to the effectiveness of the automatic CR. Among them, the measurement accuracy of the north marker was 0.1°, and the measurement accuracy of the level was 0.2°.

3. Method

SAR radiometric calibration is a process of establishing the exact relationship between an image and ground target backscatter coefficients, which usually establishes the relationship between the image impulse response energy of the point target and its RCS through the overall radar system transfer parameter, i.e., the calibration constant [17].

The flow of the method used in this study is shown in Figure 7. Subsequent to the completion of satellite transit and ground synchronization experiment, the impulse response energy ${\epsilon }_p$ of the seven flexible CRs was first extracted from the C-SAR/01 image, and by combining this with the theoretical RCS of each CR, the absolute calibration constant $K$ was calculated. Using the calibration constant, the SLC data were absolutely calibrated to establish the quantitative relationship between the images and the radar backscattering coefficients.

3.1. SCR Analysis

To extract the response energy of the point target from the background clutter, the signal-to-clutter ratio (SCR) of the point target was first calculated and analyzed [18]. SCR is defined as the ratio of the peak power in the target impulse response to the average background clutter power estimated from the region close to the target and is used to measure the contrast of the point target with respect to the background clutter [2], as presented in Equation (3). If the point target SCR is greater than 20 dB, the effect of background noise on the calibration results is less than 0.5 dB [19], thus determining whether the point target SCR is greater than 20 dB, which is used as the reference standard towards employing the point target for radiation calibration.

$$\mathrm{SCR}=\frac{{\sigma }_{pq}^T}{{\sigma }_{pq}^C}=\frac{{\sigma }_{pq}^T\mathit{sin}\theta }{\langle {\sigma }_{pq}^C\rangle {\delta }_a{\delta }_r}$$

(3)

Here, ${\sigma }_{pq}^T$ represents the point target RCS, $\theta$ represents the local incidence angle of the point target, $\langle {\sigma }_{pq}^C\rangle$ represents the average background clutter RCS, and ${\delta }_a$ and ${\delta }_r$ represent the SAR image pixel space in the azimuth and range directions, respectively.

3.2. Point Target Response Energy Calculation

In point target-based SAR radiometric calibration, the extraction of the point target impulse response energy is a crucial step in the calculation of the calibration constants, and this is often achieved using the integral or peak method [20,21]. The integral method obtains the point target energy by integrating the impulse response over the specific region, while the peak method uses the product of the peak response of point target and area of the system resolution cell to obtain the energy.

The implementation of the peak method requires knowledge of the resolution unit of the SAR system [20]. The utilization of the method is, therefore, related to the focusing performance and image quality of the system [10]. The peak method formula for calculating impulse response energy based on the point target is:

$${\epsilon }_p=D{N}^{2}ar{\delta }_a{\delta }_r$$

(4)

where $D{N}^2$ represents the pixel intensity value of the point target; $a$ and $r$ denote the antenna 3 dB impulse response width (IRW) in the azimuth and range directions, respectively, ${\delta }_a$ and ${\delta }_r$ are the same as in Equation (3).

Compared to the peak method, which is sensitive to system focus and requires better image quality, the integral method is independent on the radar system focus and is not influenced by processor gain, scene, or processor partial coherence [21], and thus can be employed even if the image quality is unknown [22]. Furthermore, it has a wider range of application compared to the peak method.

When using the integral method to obtain the response energy of a point target, it is necessary to accurately determine the center position of the point target and select a suitable integration region around the center position. The precise determination of the point target center position and the appropriate selection of the integration region to both respond to the accuracy of the energy calculation and the calibration results. To address the problem, our team members Li et al.proposed a method to determine the point target center position based on the sliding window method [23]. This method introduces image context information and uses regional statistics to replace the traditional pixel-based positioning method, and the centroid of the sliding window with the largest sum is used as the centroid of the integration window [23]. Thus, the point target position and the integration window can be extracted more accurately.

The selection of the integration window is shown in Figure 8, where P represents the size of image pixel, and the orange cross region is the point target response energy integration region, and the green region is defined as the background energy integration region. In this study, the integration window was a rectangular area with a size of 32 × 32 pixels around the center point, obtained by the sliding window method.

The point target response energy is equal to the point target integration region energy minus the average clutter energy of the background region [12], and the specific calculation formula is:

$${\epsilon }_p=\left({\displaystyle \sum }_{i\in A}^{N_A}D{N}_i^2-\frac{N_A}{N_B}{\displaystyle \sum }_{i\in B}^{N_B}D{N}_i^2\right){\delta }_a{\delta }_r$$

(5)

where $D{N}_i^2$ is the intensity value of the point target pixel $i$, $N_A$ is the total number of image pixels in the point target energy integration region, $N_B$ is the number of image pixels in the background energy integration region, and ${\delta }_a$ and ${\delta }_r$ are the same as in Equation (3).

3.3. Calculation of the Calibration Constant

For point target $i$, the response energy calculated based on the C-SAR/01 image is ${\epsilon }_{p_i}$, RCS theoretical value ${\sigma }_{re{f}_i}$ and corresponding local incidence angle ${\theta }_i$ of the point target $i$ are known, and the calibration constant of point target $K_i$ is given as [17,22]:

$$K_i=\frac{{\epsilon }_{p_i}}{{\sigma }_{re{f}_i}}sin{\theta }_i$$

(6)

The average value of the calibration constants calculated for all point targets is usually used as the final calibration constants of data [17,22]:

$$K\left(dB\right)=10\ast lg\left(\frac{1}{N}{\displaystyle \sum }_{i=1}^N{K}_i\right)$$

(7)

After obtaining the calibration constants $K\left(dB\right)$, the Level-1A SLC data were converted into backscatter coefficient images, according to the calibration in Equation (8) of the GaoFen-3 series SAR satellite Level-1A data.

$${\sigma }_0\left(dB\right)=10\ast lg\left(D{N}^2\ast {\left(\frac{QV}{32767}\right)}^2\right)-K\left(dB\right)$$

(8)

Here, ${\sigma }_0\left(dB\right)$ is the value of the backscattering coefficient in dB, $D{N}^2$ is the intensity value calculated from the Level-1A image of C-SAR/01, satisfying the equation $D{N}^2=I^2+Q^2$, where $I$ and $Q$ represent the real part and the imaginary part, respectively, and $QV$ is the image quantization maximum.

4. Image Quality Assessment Results

In this study, we first extracted the impulse response function (IRF) of seven flexible CRs from SAR images and then evaluated the image quality of C-SAR/01 using spatial resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR) [2,24,25,26]. Spatial resolution is an important index for evaluating the ability of images to distinctly distinguish ground point targets, and it is usually expressed as IRW, which is the width between the −3 dB points on the impulse response function (IRF) main lobe peak [2], as shown in Figure 9, including resolution in range direction ${\rho }_r$ and azimuth direction ${\rho }_a$.

The specific calculation formula of resolution in range direction ${\rho }_r$ is [27]:

$${\rho }_r=\frac{c}{2f_{s}Lsin\theta }{N}_r$$

(9)

where $c$ is the speed of light, $f_s$ is sampling rate, $L$ is the interpolation multiplier, and $N_r$ is the distance of points between the points with intensities 3 dB below the maximum intensity of main lobe peak in range direction IRF, and $\theta$ is the radar beam incidence angle.

The specific calculation formula of resolution in azimuth direction ${\rho }_a$ is [27]:

$${\rho }_a=\frac{V_g}{f_{p}L}{N}_a$$

(10)

Here, $V_g$ is the velocity of the beam center pointing to the ground, $f_p$ is the pulse repetition frequency, $L$ is the interpolation multiple, and $N_a$ is the distance of points between the points with intensities 3 dB below the maximum intensity of main lobe peak in azimuth direction IRF.

PSLR is defined as the ratio of the highest intensity of the sidelobe to the peak of the main lobe in the point target IRF [2]. This is illustrated in Figure 9 and calculated in Equation (11). The PSLR describes the extent at which the weakly scattering point is masked by the strong scattering point [26].

$$\mathrm{PSLR}=10lg\frac{I_s}{I_m}$$

(11)

Here, $I_s$ represents the highest intensity of the sidelobe, and $I_m$ represents the peak intensity of the main lobe.

ISLR is defined as the ratio of the total energy in sidelobes to the main lobe energy on the point target IRF, as calculated in Equation (12). The ISLR measures the energy spilled from the main lobe to the sidelobe [26].

$$\mathrm{ISRL}=10lg\frac{E_S}{E_M}$$

(12)

Here, $E_S$ represents the total energy of the sidelobes; $E_M$ is the energy of the main lobe, while $E_S$ and $E_M$ is calculated as:

$$E_s={{\displaystyle \int }}_{-\infty }^a{\left|h\left(r\right)\right|}^{2}dr+{{\displaystyle \int }}_b^{\infty }{\left|h\left(r\right)\right|}^{2}dr$$

(13)

$$E_M={{\displaystyle \int }}_a^b{\left|h\left(r\right)\right|}^{2}dr$$

(14)

where the area within the integration limit $\left(a,b\right)$ corresponds to the main lobe region, and the area outside $\left(a,b\right)$ corresponds to the sidelobe region as the junction between the main lobe and the sidelobe.

CRs are usually visualized as dots or small crosses in SAR images. Interpolation is often employed to distinctly characterize point targets and their surrounding pixel points, so as to ensure accurate characterization, as well as measure their performance metrics. In this study, 8-fold fast Fourier transform (FFT) interpolation [23], which ensures both the computational efficiency and accuracy of results, was adopted to finely characterize CR impulse response within the 32 × 32 integration window obtained by the sliding window-based integral method. FFT interpolation is achieved mainly by one fast Fourier transform and one fast Fourier inverse transform, and its operation is divided into three main steps. Firstly, it involves computing the FFT of the original sequence $x\left(n,n\right)$ in $N\ast N$ size, as shown in Equation (15). Additionally, it involves constructing a new sequence $X_M\left(k_1,k_2\right)$ in length $M\ast M$ by $X_N\left(k_1,k_2\right),$ as shown in Equation (16). After that, it requires the performing of an inverse FFT of the sequence $X_M\left(k_1,k_2\right)$ to obtain $\widehat{x}\left(m,m\right)$, as shown in Equation (17).

$$X_N\left(k_1,k_2\right)={\displaystyle \sum }_{n_1=0}^{N-1}{\displaystyle \sum }_{n_2=0}^{N-1}x\left(n_1,n_2\right)exp\left\{-j2\pi \left(\frac{k_1{n}_1}{N}+\frac{k_2{n}_2}{N}\right)\right\} k_1, k_2, n_1,n_2\in \left[0,N-1\right]$$

(15)

$$X_M\left(k_1,k_2\right)=\left\{\begin{array}{c}{L}^2\times X_N\left(k_1,k_2\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}{k}_1\in \left[0,\frac{N-1}{2}\right],k_2\in \left[0,\frac{N-1}{2}\right]\hfill \\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} k_1\in \left[\frac{N-1}{2}+1,M-\frac{N-1}{2}-1\right],k_2\in \left[0,\frac{N-1}{2}\right]\hfill \\ L^2\times X_N\left(k_1-M+N,k_2\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em} k_1\in \left[\frac{N-1}{2}+1,M-1\right],k_2\in \left[0,\frac{N-1}{2}\right]\hfill \\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} k_1\in [0,M-1],k_2\in \left[\frac{N-1}{2}+1,M-\frac{N-1}{2}-1\right]\hfill \\ L^2\times X_N\left(k_1,k_2\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{k}_1\in \left[0,\frac{N-1}{2}\right],k_2\in \left[\frac{N-1}{2}+1,M-1\right]\hfill \\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} k_1\in \left[\frac{N-1}{2}+1,M-\frac{N-1}{2}-1\right],k_2\in \left[\frac{N-1}{2}+1,M-1\right]\hfill \\ L^2\times X_N\left(k_1-M+N,k_2\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{k}_1\in \left[\frac{N-1}{2}+1,M-1\right],k_2\in \left[\frac{N-1}{2}+1,M-1\right]\hfill \end{array}\right.$$

(16)

$$\widehat{x}\left(m_1,m_2\right)=\frac{1}{MM}{{\displaystyle \sum }}_{k_1=0}^{M-1}{{\displaystyle \sum }}_{k_2=0}^{M-1}{X}_M\left(k_1,k_2\right)exp\left\{+j2\pi \left(\frac{k_1{m}_1}{M}+\frac{k_2{m}_2}{M}\right)\right\}\hspace{1em}\hspace{1em}{k}_1, k_2, m_1,m_2\in \left[0,M-1\right]$$

(17)

Here, $L$ is the interpolation multiplier.

Figure 10 shows the one-dimensional IRF contours of the 3rd CR (CR-3) in range and azimuth directions for UFS and FSI mode data, where (a) and (b) correspond to the UFS mode and (c) and (d) correspond to the FSI mode. It can be seen that IRFs all show a shape similar to sinc function [28], which is consistent with the general rule of point target echo signal during SAR imaging.

According to the point target IRFs, the spatial resolution, PSLR, and ISLR of each point target on the two modes data were calculated, and the results are presented in

Table 3. Image quality parameters from each CR for UFS mode data on 12 May.

CR Number	Resolution (m)		PSLR (dB)		ISLR (dB)
	Range	Azimuth	Range	Azimuth	Range	Azimuth
CR-1	1.353	2.887	−22.195	−23.274	−21.802	−21.268
CR-2	1.388	2.862	−24.944	−23.353	−22.745	−19.93
CR-3	1.353	2.887	−22.087	−23.885	−21.554	−20.633
CR-4	1.370	2.887	−22.955	−24.332	−21.922	−21.083
CR-5	1.370	2.887	−22.204	−25.205	−21.259	−21.116
CR-6	1.353	2.862	−22.45	−23.386	−21.845	−18.792
CR-7	1.370	2.862	−22.988	−23.735	−21.842	−21.29
Mean	1.365	2.876	−22.832	−23.881	−21.853	−20.587

and

Table 4. Image quality parameters from each CR for FSI mode data on 15 May.

CR Number	Resolution (m)		PSLR (dB)		ISLR (dB)
	Range	Azimuth	Range	Azimuth	Range	Azimuth
CR-1	1.651	4.881	−23.047	−24.345	−21.831	−19.536
CR-2	1.616	4.760	−23.361	−24.533	−17.211	−20.467
CR-3	1.616	4.760	−22.63	−24.473	−21.464	−18.514
CR-4	1.599	4.801	−23.345	−22.544	−22.232	−19.786
CR-5	1.669	4.841	−24.303	−25.288	−21.699	−20.758
CR-6	1.669	4.841	−23.953	−22.465	−19.765	−17.352
CR-7	1.616	4.760	−25.154	−23.26	−22.62	−17.635
Mean	1.634	4.807	−23.685	−23.844	−20.975	−19.150

, respectively.

As shown in Table 3, for UFS mode data, the evaluated resolutions in range and azimuth directions are 1.365 and 2.876 m, respectively, which are better than that of the nominal resolution of 3 m. The evaluated PSLR in range and azimuth directions are −22.832 and −23.881 dB, respectively, which are better than that of the design index of C-SAR/01 of −22 dB. Lastly, the evaluated ISLR are −21.853 and −20.587 dB, which are better than that of the design index of −15 dB.

As shown in Table 4, for FSI mode data, the calculated resolutions in range and azimuth directions are 1.634 and 4.807 m, respectively, which are better than that of the nominal resolution of 5 m. The evaluated PSLR in range and azimuth directions are −23.685 and −23.844 dB, respectively, which are better than that of the design index of −22 dB. The calculated PSLR in range and azimuth directions are −20.975 and −19.150 dB, respectively, which are better than that of the design index of −15 dB.

5. Radiometric Calibration Processing Results

5.1. Point Target SCR Analysis

When using point targets to complete SAR image radiometric calibration, it is necessary to ensure that the point targets in SAR images are not markedly affected by background clutter. When SCR is greater than 20 dB, it can be inferred that the point target is effectively involved in the subsequent response energy calculation.

Using Equation (3) to calculate the SCR of each CR for the two modes’ data, the results are presented in

Table 5. Statistics of each CR for UFS and FSI mode data (/dB).

CR Number	UFS Data	FSI Data
CR-1	36.903	32.598
CR-2	38.181	33.866
CR-3	38.262	32.262
CR-4	37.398	34.88
CR-5	38.572	32.769
CR-6	37.678	32.109
CR-7	39.905	34.125
Mean	38.128	33.230

. The SCRs of CRs on the UFS mode data are all greater than 36 dB, and the mean is 38.128 dB. The SCRs of CRs on the FSI mode are all greater than 32 dB, and the mean is 33.230 dB. This implies that each CR can be used for the subsequent calculation of response energy and calibration constant.

5.2. Response Energy and Calibration Constant Calculation

In this study, the inner leg length of CR used is 1000 mm, and its theoretical RCS is calculated as [14]:

$${\sigma }_{refi}=10lg\left(\frac{4\pi a^4}{3{\lambda }^2}\right)$$

(18)

where ${\sigma }_{refi}$ is the peak RCS of the trihedral CR in dB square meters (dBsm), $a$ corresponds to the edge length of the corner reflector, $\lambda$ represents the wavelength of the C-SAR/01, which is 0.055517 m. Thus, the theoretical RCS of the corner reflector can be calculated as 31.332 dBsm.

The impulse response energy of each point target was calculated using the peak method and the sliding window-based integral method, respectively. Thereafter, the calibration constants of each point target were calculated according to Equation (6), obtaining the results shown in

Table 6. Response energy and calibration constant results of each point target for UFS mode data on 12 May.

CR Number	Theoretical RCS (/dBsm)	Integral Method		Peak Method
		Response Energy (/dB)	Calibration Constant (/dB)	Response Energy (/dB)	Calibration Constant (/dB)
CR-1	31.332	65.988	31.565	62.56	28.138
CR-2	31.332	66.655	32.246	63.603	29.193
CR-3	31.332	66.588	32.185	62.552	28.15
CR-4	31.332	66.555	32.142	62.844	28.43
CR-5	31.332	66.606	32.195	63.08	28.669
CR-6	31.332	66.419	31.s997	63.165	28.744
CR-7	31.332	66.736	32.314	63.091	28.669
Mean response energy/dB		66.507		62.985
Mean calibration constants/dB		32.092		28.57
Standard deviation of calibration constants/dB		0.234		0.342

and

Table 7. Response energy and calibration constant results of each point target for FSI mode data on 15 May.

CR Number	Theoretical RCS (/dBsm)	Integral Method		Peak Method
		Response Energy (/dB)	Calibration Constant (/dB)	Response Energy (/dB)	Calibration Constant (/dB)
CR-1	31.332	66.891	32.195	61.854	27.158
CR-2	31.332	66.628	31.917	61.506	26.795
CR-3	31.332	66.459	31.745	61.178	26.464
CR-4	31.332	66.744	32.043	61.248	26.547
CR-5	31.332	67.077	32.379	62.046	27.348
CR-6	31.332	66.679	31.995	61.711	27.027
CR-7	31.332	66.931	32.24	61.788	27.097
Mean response energy/dB		66.773		61.619
Mean calibration constants/dB		32.073		26.919
Standard deviation of calibration constants/dB		0.198		0.304

.

As shown in Table 6, for the UFS mode image, the average of response energy obtained by the sliding window-based integral method is 66.507 dB, and the mean value of the calibration constant is 32.092 dB, whereas the mean of response energy obtained by the peak method is 62.985 dB, and the mean value of the calibration constant is 28.57 dB. The standard deviation of the calibration constants calculated by the integral and peak methods are 0.233 and 0.342 dB, respectively. Figure 11a shows the distribution of the calibration constants for UFS data calculated by the peak and the sliding window-based integral method.

As shown in Table 7, for the FSI mode image, the mean of response energy obtained by the sliding window-based integral method is 66.773 dB, and the mean value of the calibration constant is 32.073 dB. In contrast, the mean of response energy obtained by the peak method is 61.619 dB, and the mean value of calibration constant is 26.919 dB. The standard deviation of the calibration constants obtained by the integral method is 0.198 dB, and that of the peak method is 0.304 dB. Figure 11b presents the distribution of the calibration constants for FSI data calculated by the peak and sliding window-based integral methods.

5.3. Backscattering Coefficient Calculation and Calibration Accuracy Analysis

According to Equation (8), the calibration constants obtained by the peak method and the integral method shown in Table 6 and Table 7 were used to radiometrically calibrate the two modes of SAR data, and the backscattering coefficient images of the SAR data were obtained. The RCS of each CR were extracted from the images, and the calibration accuracy was evaluated via the relative calibration accuracy and absolute calibration accuracy indexes [24].

The relative calibration accuracy is defined as the standard deviation of a set of reference point targets with the same theoretical RCS in the calibration site [9,22,24], and it is calculated as follows:

$$\Delta RCA=\sqrt{{\displaystyle \sum }_{i=0}^{N-1}\frac{{(\widehat{\sigma }-{\overline{\sigma }}_c)}^2}{N}}$$

(19)

where $\Delta RCA$ is the relative calibration accuracy, ${\overline{\sigma }}_c$ is the average of $N$ point target RCS measurements, and $\widehat{\sigma }$ is the single point target RCS measurement.

The absolute calibration accuracy is defined as the maximum of the absolute value of the difference between the RCS measurement and the theoretical value of each CR, and it is expressed as follows:

$$\Delta ACA=Max\left|{\widehat{\sigma }}_i-{\sigma }_i\right|$$

(20)

where $\Delta ACA$ is the absolute calibration accuracy and ${\widehat{\sigma }}_i$ and ${\sigma }_i$ are the RCS measurements and theoretical RCS of the point target $i$, respectively.

Extracted from the UFS data on 12 May 2022, the RCS measurements and calibration accuracy of each point target are shown in

Table 8. Each point target RCS and accuracy analysis for UFS mode data on 12 May.

CR Number	Theoretical RCS/dBsm	Integral Method		Peak Method
		Measurements /dBsm	Difference /dBsm	Measurements /dBsm	Difference /dBsm
CR-1	31.332	30.8	−0.532	30.886	−0.446
CR-2	31.332	31.48	0.148	31.942	0.61
CR-3	31.332	31.42	0.088	30.898	−0.434
CR-4	31.332	31.376	0.044	31.178	−0.154
CR-5	31.332	31.429	0.097	31.417	0.085
CR-6	31.332	31.231	−0.101	31.492	0.16
CR-7	31.332	31.549	0.217	31.418	0.086
Relative calibration accuracy		0.233		0.343
Absolute calibration accuracy		0.532		0.61

, where the relative calibration accuracy from the integral method is 0.233 dB and that from the peak method is 0.343 dB. The absolute calibration accuracies obtained by the integral and peak methods are 0.532 and 0.61 dB, respectively.

Extracted from the FSI data on 15 May 2022, the RCS measurements and calibration accuracy of each point target are shown in

Table 9. Each point target RCS and accuracy analysis for FSI mode data on 15 May.

CR Number	Theoretical RCS/dBsm	Integral Method		Peak Method
		Measurements /dBsm	Difference /dBsm	Measurements /dBsm	Difference /dBsm
CR-1	31.332	31.45	0.118	31.56	0.228
CR-2	31.332	31.171	−0.161	31.197	−0.135
CR-3	31.332	30.999	−0.333	30.866	−0.466
CR-4	31.332	31.297	−0.035	30.949	−0.383
CR-5	31.332	31.633	0.301	31.75	0.418
CR-6	31.332	31.249	−0.083	31.43	0.098
CR-7	31.332	31.495	0.163	31.5	0.168
Relative calibration accuracy		0.199		0.304
Absolute calibration accuracy		0.333		0.466

, where the relative calibration accuracy from the integral method is 0.199 dB, and that from the peak method is 0.304 dB. The absolute calibration accuracies obtained by the integral and peak methods are 0.333 and 0.466 dB, respectively.

6. Discussion

After making a quick assessment of the image quality and radiometric calibration accuracy of the UFS and FSI mode of C-SAR/01 data, we have got the above experimental results and conducted analysis on them.

According to experimental results in Table 5, the SCRs of each CR on the UFS and FSI mode of C-SAR/01 data are all greater than 32 dB. The result indicates that the background environment of the site is relatively homogeneous and the backscattering intensity is weak, which is suitable for the calibration and validation of SAR satellites. According to the results of calibration constants of the UFS and FSI mode in Table 6 and Table 7, the standard deviations of the calibration constants calculated by the integral method are always better than that calculated by peak methods. Furthermore, in Figure 11a,b, it can be seen that the calibration constants of each point target calculated by the integral method (green line) fluctuate less than those calculated by the peak method (blue line). Additionally, looking at the relative calibration accuracy and absolute calibration accuracy shown in Table 8 and Table 9, it can be seen that the results from the integral method are always better than that from peak methods. Thus, the stability of the integral method is better than that of the peak method, and the former method got higher calibration accuracy in high-resolution SAR images.

Compared to the results in Table 8 and Table 9 with the design indexes of C-SAR/01 relative calibration accuracy and absolute calibration accuracy, which are 1.0 dB and 1.5 dB [24], respectively, it can be seen that relative calibration accuracy and absolute calibration accuracy of both UFS and FSI mode, which are better than 0.343 dB and 0.61 dB, respectively, are better than the design indexes. In addition, in terms of radiometric applications, the relative calibration accuracy and absolute calibration accuracy of C-SAR/01 in the UFS and FSI modes are satisfied requirements of the geophysical parameter measurement for radiometric calibration accuracy, which are 0.5 dB for the relative and 1 dB for the absolute calibration, in different applications, including ice classification, ice motion, wind speed over ocean, soil motion, surface roughness, vegetation mapping/monitoring, etc. [2]. At the same time, the calibration accuracy of C-SAR/01 also meets the main application requirements of Gaofen-3 satellite in the ocean, disaster reduction, water conservancy, meteorology, etc. [24]. Therefore, C-SAR/01 data will play an important role in various fields after radiometric calibration in the future.

However, the above experimental results of the UFS and FSI mode of C-SAR/01 are different; they include the spatial resolution, PSLR, ISLR, SCR, calibration constant, and relative and absolute calibration accuracy, etc. It may be caused by a different imaging mode, different elevation orbit and left–right view, different imaging time, etc., which requires more in-depth analysis.

7. Conclusions

Radiometric calibration is the cornerstone towards performing quantitative applications for SAR satellite data. In this study, based on the flexible automatic trihedral CR deployed at the Xilinhot SAR satellite calibration and validation site, the radiometric calibration of the UFS and FSI mode data of C-SAR/01 employing the sliding window-based integral and peak methods was performed as quickly. The calibration results obtained by the two methods were compared and analyzed. The results show that the spatial resolution, PSLR and ISLR of the UFS, and FSI mode data of C-SAR/01 are better than those of the design indexes, and the calibration results of the integral method are more stable than those of the peak method. Statistically, the standard deviation of the calibration constants of the UFS mode was evaluated as 0.234 dB, the relative calibration accuracy as 0.233 dB, and the absolute calibration accuracy as being 0.532 dB. Furthermore, the standard deviation of the calibration constants of the FSI mode was calculated as 0.198 dB, the relative calibration accuracy as 0.199 dB, and the absolute calibration accuracy as being 0.333 dB. The results satisfy the design indexes of C-SAR/01 and meet the requirements of quantitative applications for C-SAR/01 image radiometric performance.

Subsequently, our team will conduct a two months ground synchronous measurement experiment in the Xilinhot SAR satellite calibration and validation site, with 15 automatic trihedral CRs and ARCs in an RCS range of 35~55 dB to perform radiometric calibration of C-SAR/01 in different imaging modes in order to obtain more SAR data and more accurately and comprehensively understand the performance of the C-SAR/01 satellite. Now, the Xilinhot SAR satellite calibration and validation site used for this experiment is still under construction. The site will be built into a larger range of calibration sites to meet the needs of a wider range of imaging modes, with a fixed deployment of remotely controllable automatic CR and ARC to form a long-term, cyclical operational service capability. At the same time, the experimental method of realizing the complete SAR radiometric calibration process based on remotely controllable calibrators is investigated from the calculation of the calibrator orientation to the ground-synchronous measurement experiment and then to the SAR image radiometric calibration, so as to achieve the purpose of long-term monitoring of satellite radiometric calibration performance to ensure the quality and stability of SAR data.