Interferometric Assessment of SAOCOM-1 TOPSAR Data

Satélite Argentino de Observación COn Microondas (SAOCOM-1) constellation operates in three acquisition modes: Stripmap (SM), Terrain Observation with Progressive Scans Synthetic Aperture Radar (TOPSAR) Narrow (TNA and TNB), and TOPSAR Wide (TW). Since repeat-pass SAOCOM-1 TOPSAR acquisitions are not synchronized, the generation of the related interferometric products is not guaranteed, as it happens instead for the synchronized repeat-pass TOPSAR acquisitions, such as those of Sentinel-1. In this work, we assess the suitability of SAOCOM-1 TOPSAR acquisitions for generating interferometric products. To this aim, we first discuss the constraints that must be fulfilled by the repeat-pass nonsynchronized TOPS acquisitions in order to make it feasible the generation of usable interferograms. Then, we verify whether SAOCOM-1 TOPSAR acquisitions fulfill these constraints. For this purpose, we present an analysis based on the use of a dataset composed by 18 TNB images relevant to a single subswath illuminating a region located in the southwest of Argentina. From this dataset, we were able to select 48 pairs that guarantee the spectral superposition needed for interferometric purposes. We verified that 50% of these 48 pairs fulfill the constraint required to avoid in the corresponding interferograms the presence of noncoherent azimuth stripes, whose azimuth extension depends on one side on the mis-synchronization percentage between the repeat-pass acquisitions and the other side on the overlapping percentage between adjacent bursts of the same acquisition. Summing up, the presented analysis proves the potential of SAOCOM-1 TOPSAR acquisitions to obtain interferometric products, despite the absence of bursts synchronization between repeat-pass acquisitions.


I. INTRODUCTION
S ATÉLITE Argentino de Observación COn Microondas (SAOCOM-1) is a spaceborne constellation developed by CONAE (Space Agency of Argentina), composed of two full-polarimetric synthetic aperture radar (SAR) (A and B) operating at a carrier frequency of 1.275 GHz (L-band).Both sensors operate in three acquisition modes: Stripmap (SM) [1], Terrain Observation with Progressive Scans SAR (TOPSAR) Narrow (TN), and TOPSAR Wide (TW) [2], which differ in coverage and spatial resolution [3].Data can be acquired in single/dual and quad polarizations.
Mission scope is mainly the generation of soil moisture maps to support agriculture in the wide Pampas Region of Argentina, profiting from the regional scale of the TOPSAR data.Consequently, a large amount of information acquired in TOPSAR mode is usually available [4].On the other side, SAR interferometry (InSAR) has not been defined in the specifications of the SAOCOM-1 mission for TOPSAR acquisitions, which are thus planned without burst synchronization.This means that in repeat-pass acquisitions, the radar is not constrained to observe a generic target on the ground always with the same squint angle, that is, with the same Doppler centroid (DC) [1].Therefore, an adequate spectral overlap between repeat-pass bursts relevant to the same area on the ground is not guaranteed.For this reason, the interferometric processing of SAOCOM-1 TOPSAR data is a challenging, sometimes unfeasible, task, generally more complex than that of SAOCOM-1 SM [5], [6], [7] data or that of synchronized TOPSAR data [8], [9], [10], [11].Within this context, evaluating the InSAR capabilities of SAOCOM-1 TOPSAR modes is of great interest, especially if we consider the great amount of available data acquired with these modes.In this work, we evaluate the suitability of SAOCOM-1 TOPSAR acquisitions for generating interferometric products.
To this aim, we first discuss the constraints that must be fulfilled by the repeat-pass nonsynchronized TOPS acquisitions in order to make it feasible the generation of usable interferograms (Section II).To do this, we introduce a metric to measure the mis-synchronization between repeat-pass bursts.Then, we show that depending on the amount of such mis-synchronization, two effects occur in the corresponding interferograms: coherence degradation and possible presence of totally incoherent azimuth stripes.Both effects are properly discussed and quantified in Sections II-A and II-B, respectively.
In Section III, we then verify whether SAOCOM-1 TOP-SAR acquisitions fulfill the constraints discussed in Section II.
To this aim, we present an analysis based on the use of a dataset composed by 18 TNB images relevant to a single subswath illuminating a region located in the southwest of Argentina.
Concluding remarks are reported in Section IV.

II. NONSYNCHRONIZED TOPSAR: EFFECTS ON THE INTERFEROGRAMS
Let start from the TOPS mode acquisition geometry [2], and consider the scene interburst time period T and the corresponding number of azimuth lines X , which can be expressed as wherein prf is the pulse repetition frequency.Note that the burst duration is approximately equal to T /N S , with N S being the number of subswaths of the considered acquisition burst mode.Moreover, the azimuth extension of the ground region relevant to each burst, say X g , can be expressed as X g = α X , where the factor α ≥ 1 accounts for the possible overlapping between adjacent bursts of the same acquisition.For the sake of simplicity, in the following, we will neglect the range dependence of α.
Turning to the repeat-pass scenario, let us consider two repeat-pass acquisitions that we name reference and secondary.Let consider two bursts, one for each acquisition, which include a generic illuminated target p.In the following, these two bursts are referred to as matching bursts.Let x ref p and x sec p be the azimuth lines corresponding to the target p in the two matching bursts.Let us define δx p as the shift between them and x p as its counterpart normalized to X Note that x p , which in the following is named as synchronization index, varies between 0, in the case of fully synchronized repeat-pass acquisitions, and 0.5, in the case of completely nonsynchronized ones.
In the absence of bursts synchronization, the interferograms computed by using TOPSAR data can be affected by two different effects: interferometric coherence degradation and the possible presence of totally incoherent azimuth stripes.In the following two subsections, we show how these effects can be quantified in terms of the synchronization index in (2).

A. Interferometric Coherence Reduction
This effect is due to the Doppler shift between matching bursts that are not aligned as in the synchronized TOPSAR case [2].To better analyze this effect, let us consider f ref DC, p and f sec DC, p [Hz], which are the DCs relevant to p in the reference and secondary images, respectively, and f DC, p be the corresponding Doppler separation The condition to be fulfilled to avoid complete spectral separation between the two matching bursts is wherein B az is the system Doppler bandwidth [Hz] [3].It can be easily shown that the synchronization index x p in ( 2) is related to the spectral separation f DC, p in (3) as follows: where k t, p is the DC rate [Hz/s] relevant to p in the considered acquisition burst mode [8], [12].According to (5), the condition in ( 4) can be translated into the following restriction in terms of synchronization index Note that the critical synchronization index x p,critical in (6) represents the maximum allowed value of the synchronization index that guarantees the spectral overlap between two matching bursts.It is noted that in the TOPS mode, k t, p > (N S B az /T ) [2], thus leading to the following weak upper bound for the critical synchronization index: where the last inequality comes from the consideration that the existing SAR systems based on TOPS mode exploit a number N S of subswaths at least equal to 3. From (7), it turns out that the critical synchronization index is well smaller than the limit 0.5 that marks the condition of completely nonsynchronized bursts.This means that within a generic dataset of nonsynchronized repeat-pass TOPS data, enforcement of condition ( 6) is not guaranteed: checking over this condition is thus mandatory to avoid the exploitation of data pairs useless for interferometric purposes.
As well known, the decorrelation introduced by the spectral separation f DC, p in (3) can be expressed in terms of interferometric coherence [1], say γ DC, p as wherein rect[•] is the rectangular pulse function.Using ( 5) and ( 6) in ( 8) leads to the following expression of the interferometric coherence in terms of synchronization index:

B. Decorrelation Stripes
Due to the Doppler frequency differences between the reference and secondary interfering bursts, in addition to the coherence degradation effect in (9), another effect corrupts the TOPS interferograms in the case of nonsynchronized acquisitions.Specifically, totally noncoherent azimuth stripes will unavoidably appear in the interferograms.To better clarify this aspect, let us refer to Fig. 1, where [Fig.1(a)] we have highlighted in red the overlapping areas between the adjacent bursts of the same acquisition.As can be seen in the figure, when generating the interferogram, the pixels [orange stripes in Fig. 1(a)] located at the end of the reference bursts (higher Doppler frequencies) interfere with those located at the beginning of the secondary bursts (lower Doppler frequencies).In correspondence to these pixels, the interferogram will be Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.totally noncoherent [blue stripes in Fig. 1(b)] since the corresponding frequency difference does not fulfill condition (4).In normalized notation, the condition to fulfill to avoid the appearance of these noncoherent stripes is wherein δx ov is the number of overlapping azimuth lines between adjacent bursts of the same acquisition.The normalized azimuth width of the noncoherent stripes is which holds when condition (10) is not satisfied.It is worth underlining that increasing the overlap between adjacent bursts of the same acquisition may allow avoiding the presence of these noncoherent azimuth stripes.Specifically, if x ov > max( x p,critical ), see (10), as it happens for instance for burst mode systems that exploit at least a twolook configuration [13], this effect is overcome.
This effect has also an important processing consequence.Indeed, TOPSAR interferograms usually present phase discontinuities between bursts.These residual phase jumps can be due to orbital inaccuracies, timing errors, or ionospheric relative azimuth shifts and are corrected by using the enhanced spectral diversity (ESD) algorithm [8], [11].As the algorithm estimates residual shifts from the spectral separation between the overlapping areas of adjacent bursts of the considered acquisitions, if those overlapping areas are noncoherent, which is the case of the blue stripes in Fig. 1, the ESD algorithm cannot be used.

III. MATERIALS AND STUDY CASE
The test site is located in the southwest of Argentina.It was selected due to the relatively large amount of available SAOCOM-1 TOPSAR data, acquired in TNB and dual-pol mode.We show the results related to the subswath 5 (S5DP).
The SAR dataset consists of 18 ascending images acquired between 27 December 2019 and 4 February 2022.Each image is composed by a varying number of bursts from 12 to 14, where the common area of the whole dataset comprises only five bursts.
It is observed that computing the interferograms from nonsynchronized TOPSAR data mainly follows the same steps already presented in the literature for processing synchronized TOPSAR interferometric pairs.However, some care must be taken in the selection of matching bursts and interburst phase shift removal.These implementation details, not being the focus of this work, are addressed in Appendixes I and II.
We processed scene pairs whose perpendicular baseline is not greater than 2000 m, that is, less than a third of the critical baseline [1] for the system parameters and near the orbital tube of 2500 m for the processed dataset.Furthermore, we allowed DC difference smaller than the system Doppler bandwidth in order to test the limits of this nonsynchronized TOPS system (i.e., 202 Hz [3]).
According to ( 6) and (10), the synchronization index between the pairs to be considered must be less than ∼ 0.15 to obtain Doppler spectrum overlap and less than ∼ 0.07 to avoid interburst noncoherent stripes.
By doing so, we computed a total of 48 interferograms, whose properties are summarized in Table I.In 24 of them (50%), the condition in ( 10) is fulfilled resulting in coherent interferograms without noncoherent stripes.The top row in Fig. 2 shows three selected cases (highlighted in bold in Table I), where good coherence can be appreciated.
In the remaining 24 interferograms, the condition in ( 10) is not satisfied, resulting in the scenario shown in Fig. 1.Three representative cases (highlighted in bold in Table I) are shown in the bottom row of Fig. 2. Note the noncoherent stripes aligned with the bursts' transitions, particularly noticeable in interferograms 21 and 42.Note also the good coherence in these interferograms, although the Doppler separation between matching bursts (150.5 and 145.7 Hz) is close to the system Doppler bandwidth (202 Hz).
In some cases, i.e., interferograms 18, 24, 25, 31, 32, 34, 47, and 48, decorrelation linked to f DC, p alone produces a lower coherence than the actually observed (see the last column in  I).This can be attributed to the used coherence estimator, which overestimates the values when coherence is low [14].
Despite the good results in terms of coherence, there are phase artifacts affecting many interferograms.In particular, there are residual phase ramps that can be related to errors in the orbital ephemerides, which is a known issue [5], and ionospheric effects that can produce azimuthal phase ramps indistinguishable from those derived from orbital uncertainty [15], [16].This kind of artifact, assuming a purely orbital cause, can be dealt with by using the approach proposed in [17], which estimates and applies orbital corrections before the interferogram formation.We applied it to our dataset, resulting in the corrected interferograms shown in Fig. 3. Notice that the orbital correction is also applicable to the interferograms with interburst phase discontinuities.In these cases, orbital corrections are computed by considering only a single burst and propagating them to the whole interferogram.Obviously, these phase jumps limit the potential use of the entire interferogram reducing to a single burst the effective area that can be investigated.IV.CONCLUSION This work demonstrates that it is possible to systematically obtain coherent interferograms from SAOCOM-1 data acquired in TOPSAR modes, although bursts synchronization has not been foreseen for these SAOCOM-1 modes.
Out of a time series of 18 acquisitions, we were able to compute 48 interferograms that compose a well-connected interferometric dataset, as can be seen by analyzing Table I, with the potential of being useful for computing deformation time series.
The main open issue is that many interferograms present phase biases that cannot be corrected using the ESD algorithm due to SAOCOM-1 lack of synchronization and noncoherent stripes, which cannot be straightforwardly removed.An approach to address this problem, which is a matter of current study and future work, is to take benefit from the overlapping area between consecutive subswaths for estimating the phase offsets between adjacent bursts.
Finally, we remark that the proposed approach has been applied to a single subswath (S5DP).However, it is highlighted that the same procedure is applicable to the other subswaths (S6DP and S7DP) that compose the acquisitions, given that the Doppler bandwidth (∼212 and ∼225 Hz) is even wider than that considered in our test case (∼202 Hz).

APPENDIX A
In this appendix, we clarify how to select matching bursts in nonsynchronized TOPS datasets.
The lack of synchronization in SAOCOM-1 TOPSAR data implies that there is not a common time frame for bursts acquired in repeat-pass acquisitions, which is useful for recognizing corresponding bursts [8].Therefore, bursts of different acquisitions do not always cover the same ground area.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
For the sake of simplicity, let us consider only two acquisitions.Two scenarios are possible: the reference bursts can be directly aligned with the secondary bursts [see Fig. 4(a)] or not [see Fig. 4(b) and (c)].To deal with both scenarios, a common burst reference frame must be defined.To this aim, we identify the middle range point of the first line (azimuth time), in both images and for each burst, and we translate these tie points into a geocentric Cartesian system using the orbital information.Then, we compute the Euclidean distance from each tie point of the reference bursts to all the tie points of the secondary bursts: the pair with the lowest distance will present the largest azimuth spectral overlap, thus defining the searched burst matching.
Note that to correctly address the possibility that a generic burst is not present in one of the two acquisitions, this distance should be computed by considering the tie points of all the reference and secondary bursts.To better clarify this aspect, let us refer to the example of Fig. 4(c).In this case, if for the reference acquisition, we used only the tie point of B1, we would match this burst B1 and the secondary burst B1 (red arrow).This, however, would be not correct since, actually, the reference burst B2 matches the secondary burst B1 (green arrow).

APPENDIX B
In this appendix, we briefly summarize the rationale of the ESD algorithm in [8] and describe how we implement it.
The interburst phase discontinuities are usually compensated by using the ESD algorithm proposed in [8].It exploits the spectral separation between the overlapping areas of adjacent bursts in the considered acquisitions for estimating residual geometrical shifts.The formulation in [8] assumes that the estimated phase offset is essentially the same in all consecutive bursts.Thus, the residual shift is estimated as the average ratio between the phase offset and the Doppler frequency differences at all the pixels in the superposition areas [8] wherein ⟨•⟩ indicates the average value, ˆ y is an approximation for the estimation of the residual shift, ϕ ESD, p is the phase offset at pixel p, and f ovl DC, p stands for the DC frequency difference in the overlap area for each burst.
We introduced a slight modification for accounting for nonstationary cases where nonrigid corrections need to be used [8], such as interferograms affected by strong azimuth gradients introduced by the ionosphere [15].We estimated one phase offset value per burst transition and used them to compute the following cumulative interferometric phase function: which we directly apply to the interferogram as an additional phase correction.In (13), b is the burst number, the index i identifies the interchannel overlapping areas, and ϕ ESD i is the mean phase difference in the ith interchannel overlapping area computed as in [8].

Fig. 1 .
Fig. 1.(a) Sketch of a co-registered pair of images composed by three bursts.For each acquisition, the overlapping area between adjacent bursts is depicted in red.For each couple of interferometric matching bursts, orange stripes are characterized by a Doppler frequency difference greater than the Doppler bandwidth, due to the azimuth shift between acquisitions.(b) Sketch of the corresponding interferogram.Noncoherent stripes (depicted in blue in correspondence to the orange stripes) appear after the interferogram formation because of the Doppler frequency difference.

Fig. 4 .
Fig. 4. Relevant to nonsynchronized TOPSAR data.Reference and secondary acquisitions consist of a number of bursts labeled with B1 and B2 ∼BN identifiers.Matching bursts are colored alike.Bursts highlighted with red crosses have no correspondence in the other acquisition.Green arrows highlight the minimum Euclidean distance between the reference and the secondary bursts.(a) Reference bursts are directly aligned with secondary bursts.(b) and (c) Reference bursts are not directly aligned with secondary bursts.

TABLE I LIST
OF THE 48 INTERFEROGRAMS COMPUTED