A Review of Spaceborne High-Resolution Spotlight/Sliding Spotlight Mode SAR Imaging

Abstract

Spotlight/sliding spotlight modes can achieve higher resolution than the other imaging modes and are widely used in object detection and recognition applications. This paper reviews the progress of the spaceborne spotlight/sliding spotlight SAR imaging field. The three steps of the current spaceborne spotlight/sliding spotlight SAR imaging algorithm framework are discussed in this paper. These include the following: eliminating the azimuth spectral aliasing by azimuth deramp preprocessing; implementing imaging processing using imaging kernels (RD, CS, RMA, etc.); and degrading the back-folded phenomenon in the final focused image domain by reference function multiplication post-processing. The different imaging kernels, consisting of RD, CS, RMA, BAS, FS, and PFA, are presented. The phase errors in high-resolution spaceborne spotlight/sliding spotlight SAR imaging, especially the stop-and-go error, curved orbit error, and tropospheric delay error, are analyzed in detail. Furthermore, the autofocus methods are described. In addition, some new imaging SAR systems based on spotlight/sliding spotlight SAR mode, which have more advantages than the classic spaceborne spotlight/sliding spotlight SAR imaging, were shown in this paper. These include FMCW-based systems, multichannel systems, varying-PRF systems, and bistatic systems.

1. Introduction

The synthetic aperture radar (SAR) technique is already widely used in microwave remote sensing applications [1,2,3,4,5,6,7,8,9,10]. In a performance evaluation of the SAR system, wider swath is an important demand [11,12,13,14]. Current typical SAR algorithms include the time domain algorithm [15,16,17,18,19,20,21,22,23], frequency domain algorithm [24,25,26,27,28,29,30,31,32,33,34], and time frequency hybrid algorithm [35,36,37,38,39]. The classical time domain algorithms are based on the BP algorithm [15,16,17,18,19,20,21,22,23]. At present, the typical frequency domain algorithm is the range Doppler (RD) algorithm [24,25,26,27], chirp scaling (CS) algorithm [28,29,30,31], and range migration algorithm (RMA) [32,33,34]. As shown in Figure 1 and Figure 2, by steering the antenna radiation pattern, current spaceborne SAR imaging systems are operated in different modes (stripmap, scanSAR, spotlight, sliding spotlight, and terrain observation by progressive scans (TOPS)) [35,36]. The system is operated in scanSAR mode if a wider swath is required. As shown in Figure 1b, by controlling the elevation angles of the antenna, different sub-swaths are illuminated in scanSAR mode. Thus, the illumination time of each sub-swath in scanSAR mode is shorter than the swath of stripmap mode. Due to the antenna elevation patterns steering along multiple sub-swaths continuously, the azimuth imaging resolution of scanSAR mode is lower than stripmap mode. If a higher azimuth resolution is required, as shown in Figure 1c, spotlight mode can be used. A fixed imaging region is always illuminated by steering the antenna angle. Consequently, a longer illumination time and synthetic aperture length are obtained for this fixed imaging region. This results in a higher resolution for spotlight mode. As shown in Figure 2a, the sliding spotlight imaging mode adopts a lower antenna steering amplitude than spotlight mode. The antenna beam in the imaging scene will have a sliding movement. The rotation center of the sliding spotlight imaging mode will be outside the scene, which is different from the spotlight imaging mode. Therefore, sliding spotlight imaging mode has lower resolution but wider azimuth scene size than spotlight mode. Based on this, in spotlight or sliding spotlight imaging, the steering angle and the rotation center position of the antenna beam need to be designed according to the requirement of imaging resolution and scene size. However, the imaging algorithm of spotlight and sliding spotlight imaging can be the same. As shown in Figure 2b, TOPS mode operates oppositely compared to sliding spotlight imaging mode. Compared to stripmap mode, TOPS imaging mode increases the azimuth coverage size but degrades the azimuth resolution. In object detection and recognition applications, higher resolution is useful for describing more precise geometry structures and finer features of objects. This results in higher detection or recognition accuracy. As elaborated above, spotlight/sliding spotlight modes can obtain higher resolution than the other imaging modes. Thus, spotlight/sliding spotlight imaging modes are widely used in object detection and recognition applications.

Table 1. The number of spaceborne spotlight/sliding spotlight mode SAR imaging publications from 2014 to 2024.

Publication Topics	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	2024
Spaceborne spotlight/sliding spotlight mode SAR imaging	8	11	7	7	7	6	7	12	12	10	9

and

Table 2. The number of publications related to imaging methods, errors compensation methods, and new imaging systems in spaceborne spotlight/sliding spotlight mode SAR imaging from 2014 to 2024, respectively.

Publication Topics	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	2024
Imaging methods	3	6	2	3	3	2	4	6	4	2	6
Errors and motions compensation methods	4	1	1	1	2	2	1	1	5	2	0
New imaging systems	1	4	4	3	2	2	2	5	3	6	3

present the number of journal and conference publications related to the topics of spaceborne spotlight/sliding spotlight mode SAR imaging from 2014 to 2024 (collected on 15 October 2024 from Engineering Village). From Table 1 and Table 2, we can see the research area of spaceborne spotlight/sliding spotlight mode SAR imaging is still developing in recent years and there are still some problems which need to be investigated.

Table 3. The main commercial SAR satellites which have spotlight/sliding spotlight mode.

Sattellite	Frequency Band	Spotlight Mode Resolution (m)	Coverage (km × km)	Country
RadarSat-2	C-band	1	18 × 8	Canada
COSMO-SkyMed	X-band	1	10 × 10	Italy
TerraSAR and TanDEM-X	X-band	Up to 0.25	10 × 5	Germany
ALOS-2	L-band	1	25 × 25	Japan
Capella	X-band	Up to 0.25	20 × 5 and 10 × 10	America
ICEYE	X-band	1	15 × 15	Finland
GF-3	C-band	1	10 × 10	China
HiSea-1	C-band	1	5 × 5	China

presents some parameters of the main commercial SAR satellites, which have spotlight/sliding spotlight mode. From Table 3, we can see the frequency bands of the current commercial SAR satellites mainly focus on L, C, and X bands. The spotlight resolution of them can be up to 1 m and higher. These current commercial SAR satellite data are already used for disaster monitoring, environment resources exploring, ocean observation, agricultural biomass estimation, digital elevation model (DEM) mapping, military reconnaissance, etc. This paper will review the progress of spaceborne spotlight/sliding spotlight SAR imaging field. Figure 3 is the structure of this paper.

2. Spaceborne Spotlight/Sliding Spotlight Imaging Methods

In spaceborne spotlight/sliding spotlight mode SAR, high-resolution of the imaging area can be achieved by increasing the azimuth bandwidth determined by antenna beam steering. The designed pulse repetition frequency (PRF) of the SAR system is designed at the limitation of range ambiguity. Therefore, the traditional stripmap SAR imaging algorithms, such as RD, CS, and RMA, cannot work in spotlight/sliding spotlight mode case because of the azimuth spectrum aliasing. Some methods were developed to solve this problem, such as the spectrum mosaicking method [37] and the subaperture method [38,39]. Generally, the instantaneous azimuth bandwidth after block processing follows the Nyquist sampling theory in the subaperture method [38,39]. However, the azimuth aliasing problem will exist for both the spectrum mosaicking method and subaperture methods when PRF is not high enough. Derotation operation-based full-aperture methods can overcome this problem effectively [40,41]. In the first step of full-aperture methods, by multiplying a reference function related to Doppler frequency modulation rate, i.e., derotation operation, the echoed data are resampled and transformed into a virtual azimuth time domain, which can meet the Nyquist sampling theory. In the second step of full-aperture methods, the traditional stripmap SAR imaging methods (based on different kernels, such as RD, CS, RMA, etc.) can be used for processing the resampled echoed data after derotation operation. This approach was named the two-step approach (TSA).

2.1. RD Kernel-Based Spaceborne Spotlight/Sliding Spotlight Imaging Method

In spaceborne spotlight/sliding spotlight mode SAR imaging, conventional hyperbolic range equation is not suitable to describe the range history accurately due to the curved earth surface and satellite orbit. Consequently, a higher order Doppler range model should be considered in spaceborne spotlight/sliding spotlight SAR. In [42], a fourth-order Doppler range model (DRM4) was proposed, which is more precise than conventional range equations in spaceborne low-earth-orbit SAR. In DRM4, a 2-D range–azimuth spectrum was derived, and then the corresponding spaceborne spotlight/sliding spotlight mode SAR imaging based on RD kernel was also developed [42]. As shown in Figure 4, the RD kernel-based spotlight/sliding spotlight method includes three steps. The first step removes azimuth aliasing. The second step is the extended RD algorithm based on DRM4 that considers the accurate azimuth modulation and range cell migration (RCM). The final step accomplishes wide swath imaging by segmenting multiple blocks along the range direction for compensating the cross-coupling phase accurately. From the simulation results shown in Figure 5, the approach based on the higher order compensated coupling phase focuses better than the lower order.

2.2. CS Kernel-Based Spaceborne Spotlight/Sliding Spotlight Imaging Method

Spaceborne spotlight/sliding spotlight SAR in squint case is more complicated than broadside case in imaging due to special imaging geometry. The approximation assumptions used in the conventional broadside case of spaceborne spotlight/sliding spotlight SAR mode might not be available in squint case. Then, the corresponding spaceborne spotlight/sliding spotlight mode squint SAR is more difficult [43]. In [44], an extended nonlinear chirp scaling (ENLCS) algorithm was presented for a high squint case of spaceborne spotlight/sliding spotlight mode SAR. In the ENLCS algorithm, firstly, the linear range walk of the target is corrected for removing the linear part of RCM and mitigating the coupling component in the range–azimuth 2-D spectrum [44]. In order to finish the compensations of the residual RCM, second range compression (SRC) expression, and higher order range–azimuth coupling components, a bulk SRC is conducted. In the third step, an extended azimuth NLCS (ANLCS) operation is adopted so that the azimuth compression can be accomplished by equalizing the azimuth frequency modulation rate. The extended ANLCS has higher efficiency because only fast Fourier transform and complex multiplication are involved in the specific processing [44].

In the focused image based on TSA spotlight/sliding spotlight imaging methods, the aliasing problem may occur in the azimuth time domain. One three-step CS kernel-based approach, which modifies the reference function based on the unified-model-coefficient (UMC), can be used to solve the above aliasing phenomenon [45]. In [45], the range compensation is accomplished by an extended CS kernel first. Then, a nonlinear CS-based method was proposed by equalizing the Doppler rates at the same range distance so that the azimuth spatial variation is removed. This extends the depth-of-azimuth-focus (DOAF) and the processing efficiency is also improved. The three-step CS kernel-based spotlight/sliding spotlight imaging method consists of four parts mainly: azimuth preprocessing, range processing, azimuth processing, and geometric correction. Moreover, a hybrid CS algorithm (HCSA) [46] can also be used for squint sliding spotlight SAR processing. It integrates the modified CS (MCS) with the frequency CS (FCS) in the range–time domain. In the azimuth frequency domain, the frequency nonlinear CS (FNLCS) is combined [46]. In the hybrid CS (HCS), based on linear range walk correction (LRWC) and deramp operations, the Doppler frequency modulation rate is equalized. The aliasing problem of the azimuth time domain in the final focused image is also solved effectively. In the final step, the geometric distortion of the image is corrected. The block diagram of HCSA is shown in Figure 6. From the simulation results shown in Figure 7, we can see that the HCSA approach focuses better than the HCSA without FNLCSA.

2.3. RMA Kernel-Based Spaceborne Spotlight/Sliding Spotlight Imaging Method

Similarly to the three-step CS kernel-based spotlight/sliding spotlight imaging methods, three-step RMA kernel-based spaceborne spotlight/sliding spotlight imaging methods were proposed [47]. In [47], by using an azimuth convolution and data mosaic, the azimuth spectral aliasing phenomenon is resolved first. Afterward, a modified RMA is utilized to process the generated data of the first step. The final generated SAR image in the azimuth direction might be back-folded because the data resulting from the first step reduces along the azimuth time duration. One reference function can be introduced by multiplication to solve this problem in final SAR image post-processing. In this final step, the extended azimuth time duration data are limited generally, so that this full-aperture processing method is still efficient [47]. Moreover, in the case of high-squinted spaceborne spotlight/sliding spotlight SAR, due to the significant reduction in DOAF, Doppler parameter variations should be considered in the imaging method [48]. As shown in Figure 8, first, LRWC and range frequency-dependent derotation are added to remove the coupling component of the range–frequency domain related to the Doppler parameters. Then, a modified RMA is derived for precise focusing. In the third step, the deramp operation combined with improved nonlinear chirp scaling (INCS) is introduced to solve the back-folded phenomenon in the azimuth–time domain. The DOAF is also extended. Finally, geometry distortion caused by LRWC is corrected. From the simulation results shown in Figure 9, we can see that the modified RMA kernel-based algorithm focuses better than the modified CS kernel-based algorithm in the high-squinted spaceborne spotlight/sliding spotlight SAR case [48].

2.4. BAS-Based Spaceborne Spotlight/Sliding Spotlight Imaging Method

In [49], an imaging method was proposed which can process SAR data of sliding spotlight and TOPS modes simultaneously. The Doppler centroid variations in them are linear and the same. As discussed above, aliasing problem in the azimuth time domain still exists. An azimuth scaling operation is adopted to accomplish the processing in azimuth domain in [49]. In this approach, both sliding spotlight and TOPS modes use the common kernel. Furthermore, an efficient 2-D baseband azimuth scaling (2-D BAS) imaging algorithm presented in [50] can be used for the squinted case of spaceborne sliding spotlight and TOPS SAR modes simultaneously. First, the signal properties of SAR data in 2D range and azimuth directions were derived. Then, a parity-decomposition-based range equation (PDRE) was derived to build the model of targets range histories effectively. Then, a 2-D BAS algorithm is proposed to keep even symmetric component of PDRE but remove odd asymmetric component. This operation can eliminate the effect of squinted angle due to the antenna beam rotation. An even-order-multinomial perturbation function is introduced in the processing kernel for compensating phase modulation and high-order RCM variation in azimuth direction efficiently. The proposed method is efficient because only limited data are extended in azimuth–time domain. The post-processing in SAR image domain is needed for solving focused-domain folding phenomenon. The block diagram of a BAS imaging method for sliding spotlight mode is given in Figure 10. From the simulation results shown in Figure 11, we can see 2D BAS-based algorithm focuses better than the modified CS kernel-based algorithm in high-squinted spaceborne spotlight/sliding spotlight SAR case [50].

2.5. FS Kernel-Based and PFA-Based Spaceborne Spotlight/Sliding Spotlight Imaging Method

In [51], a frequency scaling algorithm (FSA) for spaceborne spotlight/sliding spotlight SAR full-aperture imaging was proposed. The processing steps include azimuth convolution for preprocessing, a modified FSA, and post-processing by azimuth convolution. Similarly to the three-step spotlight/sliding spotlight SAR imaging method based on CS or RMA kernel, an azimuth convolution preprocessing is operated in the first step. Next, an improved azimuth filter and a scaling factor were applied to realize RCMC and azimuth domain compression accurately. The final SAR focused image may be back-folded due to the compressed azimuth time domain. Therefore, in the final step, an azimuth convolution post-processing is introduced to eliminate aliasing in the azimuth time domain of SAR image after the FSA.

For spotlight/sliding spotlight SAR imaging, motion errors dependent on the range and curved range history need to be considered and compensated. The motion errors dependent on the range after RCMC could be handled by the parametric polar format algorithm (PPFA). In [52], a PPFA was proposed for widefield spotlight/sliding spotlight SAR imaging. The motion errors dependent on the range can be precisely corrected before RCMC by the proposed range-compressed domain motion compensation algorithm. After RCMC, an algorithm for correcting the curved range history accurately is conducted. Finally, by integrating azimuth variant phase error compensation, an azimuth wavenumber resampling is carried out to achieve a well-focused image.

As shown in

Table 4. Computational loads of different imaging algorithms.

Imaging Algorithm	The Computational Load
[47]	$\begin{array}{l}{N}_a^{\prime }{N}_r\left(34+15{\log }_2{N}_a^{\prime }+5{\log }_2{N}_r+4M_{\ker }\right)\\ +N_a{N}_r\left(6+5{\log }_2{N}_r+5{\log }_2{N}_a\right)\end{array}$
[45]	$N_a{N}_r\left(8+5{\log }_2{N}_r+4{\log }_2{N}_a\right)$
[48]	$N_a{N}_r\left(20+9{\log }_2{N}_r+5{\log }_2{N}_a\right)$

, different imaging algorithms have different computational loads. In Table 4, $N_r$ and $N_a$ are sampling numbers along range direction and azimuth direction, respectively. $M_{\ker }$ denotes the Stolt interpolation kernel length. $N_a^{\prime }$ denotes the extended sampling number along the azimuth direction. Although the proposed imaging algorithm in [48] has more computational load than [45], the imaging algorithm in [48] has higher accuracy than [45], especially in the highly squinted case.

As a kind of characteristic of an SAR image, the speckle effect degrades the SAR image quality. Essentially, speckle effect is related to the scattering property and the geometry shape of ground objects. In addition, noise in the echoed signal is related to the natural environment and the hardware configuration of the radar system. The imaging algorithm discussed above is an operation in the signal processing domain, which is evaluated quantitatively by resolution, peak side lobe ratio (PSLR), and integration side lobe ratio (ISLR) based on an ideal point target simulation. Therefore, the speckle effect and the noise in the echoed signal do not have direct relation to the imaging algorithm from the view of the physical mechanism. Based on this, the despeckle method used for stripmap mode SAR image filtering can also be adopted for the despeckle of spotlight/sliding spotlight SAR image. Figure 12 is the despeckle results of TerraSAR-X spotlight mode data using different methods [4]. From Figure 12, we can see the despeckle methods still show the effectiveness in spotlight SAR data.

In SAR imaging, the phase of the generated complex SAR image is useful in some applications, such as SAR interferometry. Currently, we do not have additional evaluation metrics for phase quality. However, PSLR and ISLR can reflect the phase quality to some degree qualitatively. In addition, the quality of SAR interferometry fringe can be used to evaluate the phase quality of the generated complex SAR image. Figure 13 is an SAR interferometric fringe map using TerraSAR-X staring spotlight mode data in one urban area. The TerraSAR-X staring spotlight mode data were also used for the experiment of multi-baseline SAR interferometry correlated synthesis image in [5]. In Figure 13, we can see the SAR interferometry fringes of some buildings are very clear and obvious. This verifies the effectiveness of the spotlight mode SAR imaging method in the TerraSAR-X imaging processer for keeping phase quality. The imaging method used for TerraSAR-X staring spotlight mode data processing is based on the typical imaging kernels elaborated above.

3. Errors and Motions Compensation in Spaceborne Spotlight/Sliding Spotlight Imaging Model

3.1. Autofocus Imaging Methods for Errors and Motions Compensation

A well-focused SAR imaging result requires accurate measuring positions of the radar so that the echoed radar data can be processed coherently. However, the atmospheric propagation effects and motion measurement error of the flight platform bring disturbances to SAR imaging processing [53,54]. The above phase errors cause two kinds of degradations during SAR imaging, i.e., residual RCM and azimuth phase error (APE) [55]. Generally, the residual RCM is neglected when the imaging resolution is not very high or the motion measurement error is small. Namely, only APE needs to be compensated in the above cases. However, as the measurement error increases or the imaging resolution improves, the aforementioned approximation is not available. Both the residual RCM and APE need to be considered in the SAR imaging model.

By integrating two-step scaling transform (TSST) with structure-aided 2-D autofocus, a spotlight SAR imaging algorithm was developed for the squinted angle case [56]. As shown in Figure 14a, an azimuth–time nonlinear scaling transform (ATNST) and a modified range–frequency linear scaling transform (MRFLST) were first developed to degrade the echoed signal coupling between the azimuth–time domain and the range–frequency domain. Furthermore, during MRFLST implementation, fast Fourier transforms (FFTs) and complex multiplications, which do not have interpolation, were involved to improve efficiency. Meanwhile, in order to avoid range frequency spectrum aliasing, a constant scaling factor was selected as a criterion. Then, in the TSST, the prior structure information of 2-D phase error, which is caused by the atmospheric propagation effect and the motion measurement error, is studied for phase error corrections. Finally, a 2-D autofocus SAR imaging approach was proposed by combining the range frequency fragmentation technique and the obtained structure of 2-D phase error.

Doppler aliasing always happens in spotlight/sliding spotlight SAR imaging. The accuracy of motion compensation during SAR imaging will be affected greatly by Doppler aliasing. The subaperture (SA) approach is an effective strategy to avoid Doppler aliasing. However, the SA approach will meet the stitching problem between different subapertures. As aforementioned, the TSA-based full-aperture method not only avoids the above stitching problem but also eliminates the Doppler aliasing. In [57], a 2-D frequency domain autofocus approach integrated with TSA was presented. As shown in Figure 14b, coarse focusing imaging and dealiasing are performed first. Then, the phase error expressions are analyzed and derived. Therefore, the prior structure information of the phase errors is obtained accurately. After this, the common 2-D phase errors are inverted. Finally, the autofocus method of the full-aperture data are accomplished in the 2-D frequency domain without aliasing. From the autofocus comparison results shown in Figure 15 and Figure 16, we can see the proposed TSST with the structure-aided 2-D autofocus algorithm and the 2-D autofocus combined with the TSA focus better than the traditional phase gradient autofocus (PGA) algorithms [56,57].

Nevertheless, for spaceborne spotlight/sliding spotlight mode SAR processing, the traditional TSA combined with the autofocus technique still faces a number of difficulties. For instance, when inverse Fourier transformation of the azimuth frequency spectrum is operated in the slow time domain, aliasing may occur, which disturbs the correction of the tropospheric phase or residual motion errors. An extended TSA combined with the autofocus technique was proposed to address these problems [58]. The processing steps include the following: pulse compression and one stage motion compensation; range frequency-dependent SPECAN and azimuth frequency spectrum resampling; RCM correction in the azimuth frequency domain using the traditional SAR imaging kernel; full-aperture azimuth scaling with the range-dependent scaling cancelation of Doppler history; estimating and compensating the residual errors in the slow time domain; and focusing on the azimuth domain and correcting geometric distortion.

In spaceborne spotlight/sliding spotlight mode SAR, phase errors between the adjacent antenna beams may occur because of the switching errors of the discrete azimuth antenna beam. An estimated method of phase errors based on image contrast maximization criteria was proposed for compensation of image focusing [59]. In addition, a troposphere delay was introduced in the echoed signal. These phase errors and delays will influence the final image quality. The phase errors caused by antenna beam steering in the azimuth direction can also be estimated and compensated by another method, Newton entropy minimization (N-EM) [60]. N-EM algorithm combined with the subaperture imaging approach can estimate the phase errors of the antenna beams.

3.2. Compensation Approaches of Stop-and-Go, Curved Orbit, and Troposheric Delay Errors

In spaceborne SAR imaging processing, there is the assumption that the platform does not move during signal transmission and reception. This is called start–stop or stop-and-go approximation [61,62,63]. It includes two parts. The first one is the “slow-time” part, which is related to the satellite motion between transmission and reception. The “slow-time” approximation part is regarded as a linear azimuth phase ramp in the range–Doppler domain after RCMC. Its expression can be written as follows [61]:

$$H_{SS}^{slow}\left(f_a,r\right)=\exp \left[j\cdot 2\pi \cdot {\displaystyle \frac{r}{c}}\cdot f_a\right]$$

(1)

where $r$ is the range vector, $c$ is the speed of light, and $f_a$ is the azimuth–frequency vector. The azimuth time over the range of targets is constant after this correction. The second stop-and-go approximation effect is the “fast-time” part, i.e., the Doppler effect. It represents the satellite motion during the transmission and reception of the chirp signal itself. This “fast-time” effect is space invariant and is compensated using the following [61] equation:

$$H_{SS}^{fast}\left(f_a,f_r\right)=\exp \left[j\cdot 2\pi \cdot {\displaystyle \frac{f_a}{K_r}}\cdot f_r\right]$$

(2)

where $f_r$ is the range frequency and $K_r$ represents the chirp rate. The phase errors caused by stop-and-go approximation should be compensated before SAR imaging processing.

In most spaceborne or airborne SAR imaging algorithms, the flight path of the carrier platform is always assumed to be linear. However, in spaceborne SAR, this approximation will fail when the imaging resolution is very high. At this case, the difference between the real curved orbit of the satellite and the approximated linear orbit should be considered to be compensated. A possibility correction approach is performed when by multiplied with the following phase [61]:

$$H_{OCO1}\left(t,f_r;r_{ref}\right)=\exp \left[j\cdot {\displaystyle \frac{4\pi }{c}}\cdot \left(f_0+f_r\right)\cdot \delta r_{hyp}\left(t;r_{ref}\right)\right]$$

(3)

where $\delta r_{hyp}$, the line-of-sight approximation error of the range history, is calculated for a reference target in the center of the scene. Considering the compensation calculated by (3) is only effective for midrange, a second-order range-dependent OCO may be necessary. This residual error can be corrected by [61,64,65] the following equation:

$$H_{OCO2}\left(t,r\right)=\exp \left[j\cdot {\displaystyle \frac{4\pi }{\lambda }}\cdot \left(\delta r_{hyp}\left(t;r\right)-\delta r_{hyp}\left(t;r_{ref}\right)\right)\right]$$

(4)

In addition, the equivalent acceleration range model proposed in [66] could also describe the curved spaceborne orbit precisely. Then, based on this new range model, a velocity scaling algorithm was proposed, which can meet the requirement of very high-resolution. Moreover, in [67], a spaceborne spotlight/sliding spotlight mode SAR imaging method using subaperture coherent superposition in the image domain was proposed, which also considers the curved orbit error compensation model. In order to alleviate azimuth spectrum aliasing, the echoed data are divided into subapertures first [67]. After that, based on the azimuth time scaling transformation, higher order phase correction, and combining the phase transition function, the 2-D space variance of the equivalent velocity model due to the difference between the real curved orbit and linear orbit approximation can be eliminated. Then, in each subaperture, the dechirp function is adopted and the corresponding partial-resolution subaperture image is obtained. Finally, in the image domain, these subaperture images are superposed coherently and one full-resolution image is achieved. Moreover, in order to accelerate the SAR imaging efficiency, the subaperture data recording and imaging processing are synchronized together [67].

In spaceborne SAR, an undesired phase delay on the order of 2–4 m caused by the troposphere is added to the transmitted and echoed electromagnetic signal. This should be compensated in spaceborne SAR but does not need to be considered in airborne SAR. The zenith path delay through the troposphere can be modeled by a quadratic [68] or an exponential [69,70] function, which is related to the target height. The troposphere phase delay can be given by the following equation:

$$\Delta R_{tropo}\left(t;r_{ref}\right)={\displaystyle \frac{Z\cdot \exp \left[-h\left(r_{ref}\right)/H\right]}{\cos \theta \left(r_{ref}\right)\cdot \cos {\alpha }_i\left(t;r_{ref}\right)}}={\displaystyle \frac{\Delta R_{tropo}^{ref}\left(t;r_{ref}\right)}{\cos {\alpha }_i\left(t;r_{ref}\right)}}$$

(5)

where $\theta$ is the look angle, $h$ is the altitude of the target, $H$ is the reference height, $Z$ is the constant zenith path delay; ${\alpha }_i$ is the incident azimuth angle. In Figure 17, $\alpha$ is the squint angle in the slant range plane. $\Delta R_{tropo}^{ref}$ is the tropospheric delay at zero-Doppler. $h_{tropo}$ is the troposphere height.

The processing steps of spaceborne spotlight/sliding spotlight SAR imaging is shown in Figure 18, which includes the corrections of the phase errors or delays mentioned above [61]. These compensations can be suitable for any focusing kernel. From the corrections comparison results shown in Figure 19, we can see a corner reflector (CR) after processing using the processing chain shown in Figure 18 with the corrections focuses better than without the corrections.

4. New Imaging Systems in Spaceborne Spotlight/Sliding Spotlight SAR Mode

4.1. Multichannel Spotlight/Sliding Spotlight SAR Models

In spaceborne spotlight/sliding spotlight mode SAR, due to the limitation of the system PRF, high-resolution and large-scale coverage could not be obtained simultaneously. The azimuth multichannel technique can alleviate PRF restriction by sampling additional azimuth echoed signals. This can be regarded as spatial sampling steps decreasing along the azimuth direction. As shown in Figure 20, in sliding spotlight SAR, the azimuth multichannel technique can achieve high-resolution and wide swath imaging simultaneously [71,72,73,74,75,76]. In multichannel sliding spotlight SAR mode, there are still some problems. First, the conventional azimuth multichannel stripmap mode SAR imaging algorithms did not work very well in sliding spotlight mode due to an extended Doppler bandwidth led by a progressive steering beam. Second, the phase characteristics of the multichannel system between spotlight/sliding spotlight mode and stripmap mode are different because of the Doppler centroid varying. Third, in the spaceborne multichannel spotlight/sliding spotlight SAR imaging system, the reference function adopted in the full-aperture imaging approach is designed according to the layout of the phased array antenna system. Some azimuth multichannel sliding spotlight mode imaging methods were proposed to address these issues [71,72,73,74,75,76]. First, in order to avoid an unambiguous Doppler spectrum, the raw data needs to be operated by a deramping function in each channel. Afterward, the single-channel sliding spotlight SAR imaging algorithm is carried out for each channel. Finally, post-processing after focusing is performed to alleviate back-folded phenomenon in the SAR image domain [73]. The GaoFen-3 imaging results are presented in [73,74,76]. From the comparison results shown in Figure 21, we can see the dual-channel sliding spotlight SAR imaging method, which considers the phase mismatch due to the antenna beam switching focus better than without the phase mismatch [74].

In the spaceborne azimuth multichannel sliding spotlight SAR imaging, the classical channel phase error estimation algorithms for stripmap SAR mode are unable to be directly used because of Doppler centroid varying and wider Doppler bandwidth. To solve these problems, a deramping-based approach extends the classical methods used in stripmap SAR mode to sliding spotlight SAR mode [76]. The Doppler centroid variation could be removed by multiplying a corresponding deramp phase for each channel. Simultaneously, the resulting Doppler bandwidth also decreases. Therefore, the signal spectral characteristics of multichannel sliding spotlight SAR are converted to the same as stripmap SAR mode. Then, the classical estimation methods of the channel phase error of stripmap SAR can be applied to the multichannel sliding spotlight SAR case subsequently. The dual-channel sliding spotlight mode GaoFen-3 SAR imaging results demonstrate the performance of the proposed method [76].

4.2. FMCW-Based Spotlight/Sliding Spotlight Systems

In a classical SAR system, the pulse system is generally adopted. With the carrier signal frequency band increasing, the system also requires higher peak transmitting power. The SAR system using frequency modulated continuous wave (FMCW) transmitting and receiving mechanism needs lower peak transmitting power. It will reduce the hardware cost for the transmitter [77,78]. However, in an FMCW-based SAR system, the “stop-and-go” approximation model is not available because of the continuous changes in the transmitted and received signals as the platform moves. An FMCW SAR imaging algorithm for sliding spotlight mode was proposed in [79]. First, azimuth deramp preprocessing is carried out for eliminating the aliasing of the azimuth frequency spectrum; then, ωk kernel is used for the imaging processing of FMCW SAR echoed signal; finally, in post-processing for focusing the SAR image, azimuth deramp operation is utilized to avoid the aliasing in the image domain [79]. Figure 22 presents the FMCW-based sliding spotlight mode imaging results as shown in broadside case and squinted case, respectively. In the simulation shown in Figure 22, the center frequency and bandwidth are 35 Ghz and 6 Ghz, respectively. We can see the imaging results focus well from Figure 22.

4.3. Bistatic Spotlight/Sliding Spotlight Models

The stripmap mode bistatic SAR (BiSAR) configurations mainly include two types: translational-variant BiSAR and translational-invariant BiSAR [80,81]. RD, CS, and RMA kernel-based monostatic algorithms can also be modified for the translational-invariant BiSAR imaging case. Due to the difference between monostatic and bistatic configurations, additional range variance needs to be considered in the modified algorithms [82,83,84,85]. Translational-variant BiSAR, consisting of one stationary platform [86], bistatic forward-looking [87], and other nonequal-speed and nonparallel configurations, needs the other compensations for varied phase errors along the azimuth direction [88,89,90,91,92]. The aforementioned BiSAR imaging models are generally limited to the uniform straight trajectory. Furthermore, the bistatic spotlight synthetic aperture radar (BSSAR) [93,94,95,96,97] imaging technique has a potential application ability in reconnaissance. In [93], the resolution characteristic of the sliding spotlight geostationary earth orbit spaceborne–airborne bistatic (GEO SA-Bi) SAR system was analyzed. Firstly, the common azimuth coverage and coherent accumulated time are investigated theoretically. Then, the GEO SA-Bi SAR resolution is computed accurately by using the gradient method. As shown in Figure 23, the imaging model of sliding spotlight mode GEO low-earth-orbit bistatic SAR (GEO-LEO BiSAR) was studied in [96]. At the assumption of equivalent circular orbit trajectory, a bistatic range model was proposed to describe the range history of sliding spotlight mode GEO-LEO BiSAR [96]. Then, based on this model, an imaging method was presented to decrease the 2-D spatial variance and obtain the imaging results accurately. First, due to the influence of beam steering and azimuth variation in the Doppler centroid, a two-step preprocessing method was implemented to alleviate Doppler aliasing. Then, considering satellite motion parameters vary along the azimuth direction due to the influence of the curved trajectory, azimuth trajectory scaling was derived to solve this problem. As shown in Figure 24, by using TerraSAR-X as a transmitter, the spaceborne/stationary bistatic SAR (SS-BiSAR) imaging results were implemented in [94]. From Figure 24, we can see different angles have obvious scattering differences for the same ground object. The bistatic GEO SAR system, which means a geosynchronous SAR is used as the transmitter and a ground stationary instrument is used as the receiver, is shown in [95]. The imaging geometry structure of bistatic GEO SAR and the corresponding flowing diagram are presented in Figure 25. In addition to the conventional imaging kernels, a subaperture (SA) parametric polar format algorithm (PFA) could also be utilized for BSSAR imaging [97].

4.4. Varying-PRF Spotlight/Sliding Spotlight Models

The PRF variation can alleviate the contradictions between wide swath and high-resolution. The staggered PRF, i.e., a periodic PRF variation strategy, which is set in the multiple sub-swaths illuminated by different elevation beams, can obtain an ultra-wide swath [98,99]. On the other hand, PRF in spotlight/sliding spotlight SAR mode is required to adapt slant range variation and decrease serious range migration, so that ultra-high-resolution can be obtained. The advantages of varying-PRF spotlight/sliding SAR mode [100,101,102,103,104,105,106,107] consist of more uniform signal ambiguity, higher data efficiency, and wider effective swath width. In the preprocessing steps of varying-PRI spotlight/sliding spotlight SAR imaging shown in [101], the echoed data are sampled on a regular grid so that uniform sampling is applied. Furthermore, the Doppler frequency spectrum is studied to verify the non-ideal focusing effectiveness of the proposed SAR imaging methods. In the varying-PRF spotlight/sliding spotlight SAR, the pulse durations are transmitted variedly [101]. The correlation among the operation modes of the SAR system, data preprocessing approach, and the imaging results is presented in Figure 26. Figure 27 is the corresponding imaging results of varying-PRF spotlight mode SAR, which are focused well using the corresponding imaging processing approaches. In [100], a continuously varying pulse repetition interval (CVPRI)-based method was utilized in spotlight/sliding spotlight SAR. This can overcome the problem of azimuth variation and realize high-resolution wide swath imaging. In this proposed method, a modified equivalent squint range model (MESRMTE8) and its accuracy were analyzed. Then, the spatial variation properties of the MESRM-TE8 were investigated. Subsequently, the SAR imaging processing in the azimuth frequency domain of a large scene is realized. In CVPRI, the high-order phase modulation is compensated by a modified scaling approach combined with the imaging method. This extended scaling method can also correct the back-folded phenomenon of azimuth time in the spotlight/sliding spotlight SAR image domain.

5. Conclusions

This paper reviews the progress of the spaceborne spotlight/sliding spotlight SAR imaging field. Current spaceborne spotlight/sliding spotlight SAR imaging algorithm framework includes three steps: eliminate the azimuth spectral aliasing by azimuth deramp preprocessing; implement imaging processing using imaging kernels (RD, CS, RMA, etc.); and degrade the back-folded phenomenon in the final focused image domain by reference function multiplication post-processing. The phase errors caused by the unsteady motion of the platform and the random errors can be compensated by autofocus methods. In spaceborne spotlight/sliding spotlight SAR imaging, the stop-and-go error, curved orbit error, and troposheric delay error should be considered and compensated. In addition, considering the new requirements in the spaceborne spotlight/sliding spotlight SAR imaging field (such as lower peak transmitting power, high-resolution and wide swath obtaining simultaneously, better observation effectiveness, etc.), some new imaging SAR systems were developed, such as the FMCW-based system, multichannel system, varying-PRF system, and bistatic system.

Although the current research on spaceborne spotlight/sliding spotlight SAR imaging algorithms is relatively mature, there are still many problems which need to be investigated further. The development from a bistatic system to a multi-static system can make the radar obtain the scattering information of the ground objects from different view angles. Further, the information fusion of different polarizations, frequency bands, look angles, and satellite orbits for the extraction of more features is an important demand in object detection applications.