INTERFEROMETRIC PROCESSING OF SLC SENTINEL-1 TOPS DATA

Raphael Grandin(1)

(1)Institut de Physique du Globe de Paris, Sorbonne Paris Cite, Univ Paris Diderot, CNRS, F-75005 Paris, France, Email:grandin@ipgp.fr

ABSTRACT

InSAR processing usually involves two successive steps:focusing and interferometry. Most public-domain InSARprocessing toolboxes are capable of performing both op-erations with data acquired in the standard Stripmapmode, starting from raw SAR data (level 0). How-ever, the focusing of burst-mode data, such as TOPS andScanSAR, requires substantial modifications to standardfocusing methods due to the particular spectral propertiesof these data. Anticipating on this potential difficulty fornon-expert users, the European Space Agency has chosento release Sentinel-1 TOPS data in a Single Look Com-plex format (level 1). The data are already focused usingstate-of-the-art processing techniques, with phase infor-mation preserved. Even so, the focusing method intro-duces an additional quadratic phase term in the azimuthdirection. In case of a small misregistration error betweena pair of images, this residual term leads to steep phaseramps in azimuth that are superimposed on the desired in-terferometric phase. Therefore, this quadratic phase termneeds to be removed from the SLC data prior to interfer-ogram calculation. Here, a pre-processing method allow-ing for compensating this phase term and simply feed-ing the corrected SLC data into a standard InSAR pro-cessing chain is described. The method consists of threesteps. The first step uses the metadata in order to recon-struct a continuous image in the azimuth direction, ac-counting for the small overlap between adjacent bursts(“stitching”). In the second step, multiplication of theimages by an appropriate phase screen is performed so asto cancel the azimuthal quadratic phase term (“deramp-ing”). The deramping operation uses the metadata, aswell as the azimuth time lag between the images deducedfrom sub-pixel image correlation, in order to determinesmall misregistration errors. Misregistration errors arecompensated using a simple affine relation deduced fromleast-square fitting of the azimuth offsets. Following thissecond step, the azimuth phase ramps are significantlyreduced in the corrected interferogram. The third stepconsists in refining the affine coefficients that account forthe misregistration error. The refinement is achieved bydifferencing the backward- and forward-looking interfer-ograms, exploiting the spectral diversity in burst over-lap regions (“spectral diversity”). This final step makesit possible to remove residual phase jumps across burstboundaries with the desired level of accuracy.

Key words: Sentinel-1 ; TOPS ; burst synchronization ;coregistration ; spectral diversity.

1. WIDE-SWATH BURST-MODE DATA

Azimuth spectral properties of burst-mode SAR data,such as ScanSAR [1] or TOPS [2], are significantly dif-ferent from those of Stripmap. In burst-mode, the systemobserves a series of sub-swaths by periodically steeringof the antenna in the elevation direction and transmit-ting a short succession of pulses gathered in the so-called“bursts”. As a consequence, a given target is imagedonly during a fraction of the equivalent stripmap syntheticaperture duration, thereby reducing its duration of illumi-nation. Therefore, the increased swath width comes at theexpense of azimuth resolution (Fig. 1).

Furthermore, the Doppler centroid of targets within anyburst becomes variable in azimuth. Due to the lattereffect, the impulse response function of standard burst-mode focusing methods includes a residual phase termthat exhibits a characteristic quadratic variation of the az-imuth phase. This phase term needs to be compensatedprior to using the phase for interferometric applications,a process referred to as “deramping” [3, 4].

Figure 1. Schematic representation of the TOPSAR ac-quisition mode (from [5]). The beam is steered peri-odically in range, in order to cover several sub-swaths,and progressively in azimuth, aft to fore, in order to in-crease the azimuth bandwidth, expand the footprint anddecrease scalloping.

_____________________________________ Proc. ‘Fringe 2015 Workshop’, Frascati, Italy 23–27 March 2015 (ESA SP-731, May 2015)

Figure 2. (a) Original phase of a Sentinel-1 TOPS SLC image. (b) Deramping function. (c) Corrected phase aftermultiplication by the deramping function. (d)-(e)-(f) show zooms in the area outlined by the white square in (a)-(b)-(c).For clarity, two successive bursts are shown over a small fraction of the swath width. The bursts are shown after stitching(i.e. burst overlap restored).

Here, a method for cancelling this phase term ispresented. The method uses timing information relativeto burst start and stop times that are usually provided withthe image metadata, as well as additional informationdeduced from sub-pixel correlation between master andslave images. The output of the method is a set of twocorrected images that can be subsequently ingested bya standard interferometric processing chain with onlyminimal modification. A particular emphasis is put onthe implementation of the method to Sentinel-1 TOPSdata provided in SLC format.

2. IMPULSE RESPONSE FUNCTION

The input SLC data are assumed to be preprocessed fromraw data using a standard procedure for range compres-sion, range cell migration correction (RCMC) and az-imuth compression. Since the pre-processing treats everysub-swath independently, it is sufficient to describe thepresent method for the processing of a single sub-swath.Sub-swath stitching can be performed in post-processing.

Assuming the data are processed to zero Doppler, and ne-glecting amplitude modulation due to the antenna patternin azimuth, the compressed target’s response in the origi-

nal focused SLC data is expressed as [5]:

sorig(η, τ) = A. sinc (Beff (η − η0))

× exp{

+jπkt(τ) (η − ηc(τ))2}

(1)where A is a constant, Beff is the effective azimuthbandwidth that dictates the azimuth resolution, kt is theDoppler centroid modulation rate in the focused SLCdata, τ is range (fast) time, η is the azimuth (slow) time,η0 is zero Doppler time of the target and ηc is the burstcenter time. The exponential term results in the phaseat the peak of the system’s impulse response envelope(here, at η = η0) being different from zero. The actu-ally retrieved phase will therefore not only include thecomplex reflectivity response of the pixel, as well as itsslant-range, but also an additional phase term that variesquadratically in azimuth. This azimuth phase term isevident in the Sentinel-1 SLC data provided by ESA(Figs. 2a. and 2d.).

The presence of this quadratic phase term poses a prob-lem for interferometry, since the steep azimuth phase gra-dients resulting from a quadratic evolution of the phaseare aliased over most of the duration of the burst, dueto the sampling at the relatively low pulse repetition fre-quency (PRF). This issue is most serious in TOPS modedue to the large azimuth bandwidth, but it also arises inScanSAR. Aliasing of the quadratic azimuth term leadsto amplitude and phase distortions when resampling theslave image during coregistration with the master image.Amplitude and phase artefacts in the resulting interfero-

grams are the signature of these distortions. Therefore,it is necessary to cancel the quadratic phase term prior tointerferogram formation.

3. PRINCIPLE OF DERAMPING

In order to remove the azimuth quadratic phase term, thephase can be multiplied in the image (time) domain byan appropriate compensation term. This operation is re-ferred to as “deramping”. The deramping function is de-signed to cancel the quadratic drift, so as to bring the az-imuth phase spectrum back to baseband:

sderamp(η, τ) = exp{−jπkt(τ) (η − ηref (τ))

2}

(2)

For Sentinel-1 TOPSAR (Fig. 1), the values of kt and ηccan be deduced from the metadata following the guide-lines provided in [6]. For our purposes, it suffices to men-tion that η is the zero-Doppler azimuth time centered inthe middle of the burst, i.e.:

η =

[−Nbu

2.q,+

Nbu2.q

](3)

where q is the azimuth sampling interval, given as theinverse of the pulse repetition frequency (q = 1

PRF ), andNbu is the number of samples is a burst. For Sentinel-1,Nbu is often constant over a given sub-swath. Noting thatthe above expression is ambiguous as it yields differentbounds for η depending on the even or odd nature ofNbu,the following expression is used, instead:

η = (lη − lη).q with lη = [1, Nbu] ∈ N (4)

where lη is the line index relative to the first line withinthe current burst. The above expression implies that az-imuth time η is referenced to the burst mid-time ηmid (i.e.η = 0 for η = ηmid), or, equivalently, to the burst starttime ηstart.

The reference time function ηref is given by:

ηref (τ) = ηc(τ)− ηc(0) with ηc(τ) = −fηc(τ)

ka(τ)(5)

where ηc is the burst center time, fηc is the Doppler cen-troid frequency and ka is the “classical” Doppler FM rate(i.e. corresponding to the stripmap case). The functionskt(τ), ka(τ) and fηc(τ) are provided for every burst as asequence of range polynomials in the metadata [6].

Deramping is an efficient method to reduce the quadraticphase term at first order. Unfortunately, due to inacurra-cies in Doppler centroid estimations, orbital parametersand DEM, perfect registration of a given target’s locationalong the azimuth (sensing) time axis is never achievedin practice. As a consequence, the azimuth time coor-dinate of a given pixel will not exactly match from one

acquisition to another. In other words, when two acquisi-tions are considered, the compressed response of a givenground target would actually be:

ssorig(η, τ) = smorig(η −∆ηlag, τ) (6)

where superscripts m and s refer to the master and slaveacquisitions, respectively, and ∆ηlag corresponds to thetime lag between the target’s illumination time in theslave acquisiton relative to the same time in the masterimage, with the time origins tied to the same location inspace. This time lag is the result of miregistrations inazimuth time.

Should this time lag be incorrectly accounted for dur-ing deramping, a residual quadratic phase term would re-main superimposed on the desired interferometric phase.This residual phase term corresponds to the differencebetween two slightly misaligned quadratic phase terms,which yields a linear phase ramp in azimuth expressedas:

φ(η, τ = 0) = 2π kt(0) ∆ηlag

(η +

∆ηlag2

)(7)

where τ = 0 has been assumed for simplicity. Theresidual azimuth phase slope is therefore proportionalto the time lag ∆ηlag (Fig. 3). For values typical ofSentinel-1 IW mode (kt = 1.7 kHz, Nbu = 1629,q = 2.055 msec), a misregistration error of 0.1 azimuthpixels (i.e. ∆ηlag = 0.1 ∗ q) induces a 2.4π phase stepat burst junction. Similar values were reported for TOPSinterferometry with TerraSAR-X [7].

In order to assess and correct these misregistrations, anaccurate method has been proposed by [7]. The methodrelies on exploitation of the spectral diversity in burstoverlap regions, following the ideas introduced by [8]forthe accurate coregistration of burst-mode data.

Alternatively, a more simple method is here introduced.Instead of using the phase information to achieve coreg-istration, it is possible to use the actual offset in theSLC images between the location of every target in themaster and slave image. This offset can be determinedby means of a sub-pixel correlation, which is a routinestep in the standard procedure of interferometric calcu-lation. As shown below, although less accurate than

Figure 3. The slope of azimuth phase ramps induced byimperfect synchronization of master and slave acquisi-tions are proportional to the temporal lag between burstcentre times in the two acquisitions.

the Enhanced Spectral Diversity (ESD) method [7], theproposed method allows for substantially decreasing az-imuth phase artefacts and thereby provide useful resultsfor standard interferometric applications.

4. PROPOSED METHOD

4.1. Step 1: burst stitching

In the first step, the standard deramping function (Eq. 2)is applied to both master and slave images (Fig. 4). Themultiplication by the deramping function is carried outfor each burst separately.

The deramped bursts are then shifted by an appropri-ate number of azimuth samples ∆p so as to account forthe azimuth overlap between successive bursts. Shifted

Figure 4. Workflow of the method.

bursts are then mosaicked to produce a continuous image.This step is here termed “burst stitching”. The azimuthshift ∆pi for burst number i is found by computing thedifference between, on one hand, the number of azimuthpixels corresponding to the time difference between sens-ing of the first pulse of the current burst ηi0 and sensing ofthe first burst in the previous burst ηi−10 , and, on the otherhand, the number of samples within current burst N i

bu:

∆pi = (ηi0− ηi−10 )/q−N ibu < 0 (for i > 1) (8)

For Sentinel-1, the sensing time of the first line of anyburst is provided in the metadata in two forms: eitherreferenced to an absolute time reference (i.e. UTC time)or relative to the ascending node crossing time. Since thesatellite evolves on a sun-synchronous orbit, any of thesetwo times can be used, as only time differences duringthe course of the acquisition are relevant. We found ∆pi

to be close to an integer:∣∣∆pi − int(∆pi)∣∣ ≈ 10−3 (9)

This characteristic of burst pacing stemps from the re-sampling of the data on a regular grid that is operated aspart SLC generation [5]. A regular sampling implies thatsuccessive bursts can be, in good approximation, stitchedby applying a simple translation by an integer number ofazimuth samples. Therefore, a sophisticated resamplingscheme is unnecessary at that stage.

We note that the number of pixels corresponding to theoverlap region changes by a few pixels from one burstto another (i.e. ∆pi 6= ∆pj for i 6= j), as well as fromone acquisition to another for a given pair of consecutivebursts (i.e. ∆pm,i 6= ∆ps,i). In other words, the first lineof burst number i in the slave image does not necessarilycorrespond to the first line of burst number i in the masterimage. As a consequence, the burst mid-times ηmid thatare used to reference the azimuth time η in Eq. 4 will notmatch in general. This burst-to-burst and acquisition-to-acquisition integer shift will be used in the next step toaccount for burst centre misalignment.

After appropriate shift in azimuth, burst overlap regionsare split into two parts. The mid-time of the burst overlapregion in the master image is used to place the burst sepa-ration for both the master and slave images. This way, theforward-looking phase is not mixed with the backward-looking phase.

4.2. Step 2: gross deramping using sub-pixel offsets

In a second step, the actual time lag between the mas-ter and slave image is corrected by taking into accountpixel offsets. After sub-pixel correlation of the slave im-age against the master image, an affine transformationis determined by least-squares fitting of the pixel offsets(Fig. 5). The affine transformation consists in translatingpixels with coordinates (x, y) in the original slave image

Figure 5. Offsets between the master and slave imagemeasured from incoherent cross-correlation. The leftpanels correspond to the range offsets, while the rightpanels correspond to the azimuth offsets. The upper pan-els show the offsets as a function of the range coordinatewithin the master image, whereas the lower panels repre-sent the same offsets as a function of azimuth coordinate.The red line shows the fitted variation of the azimuth off-set as a function of azimuth in the affine transformationapplied during coregistration. The slope indicates an az-imuth stretching of the slave image with respect to themaster image.

to a new location given by coordinates (x′, y′) in the re-sampled slave image. The coordinates are related accord-ing to the matrix operation:[

x′

y′

]=

[A BD E

] [xy

]+

[CF

](10)

Since only the azimuth translation is of interest here,the azimuth time offset ∆ηoff associated with the affinetransformation is given by:

∆ηoff (x, y) = (y′ − y).q = (a+ bx+ cy).q

with

{a = Fb = Dc = (E − 1)

(11)

At this point, the time coordinates η are not yet synchro-nized. Indeed, due to variations in the length of the burstoverlap regions, the mid-time of any burst in the mas-ter image ηmmid does not exactly match with the mid-timeof the corresponding burst in the slave image ηsmid. In-deed, as mentioned above, the burst sensing start time ofa given burst ηistart generally differs by an integer numberof azimuth samples between the slave and master images(Eq. 8). The initial time difference at the beginning ofthe image acquisition, ηs,1start − η

m,1start, can be understood

as the predicted offset at the top of the image. However,due to the regular sampling of the SLC, this predicted off-set should only change by an integer number of azimuthpixels across burst transitions, and otherwise remain con-stant in burst interiors. In contrast, computation of actual

offsets between images by means of sub-pixel correlationdemonstrates that the images are slightly distorted. In or-der to account for these distortions, an additional term isadded (Fig. 6):

∆ηishift = (ηs,1start − ηm,1start)− (ηs,istart − η

m,istart) (12)

In Eq. 12, the second term in braces corresponds to thetime difference between burst sensing start time for thecurrent burst i in slave and master images. The first termis introduced to account for the initial time difference atthe beginning of the image acquisition, i.e. the predictedtime offset at the top of the image. The above formula al-lows for cancelling this predicted offset throughout theimage, which will be replaced by the measured offset∆ηoff .

Finally, the full expression of the deramping function thatis applied to the slave image reads:

s′deramp(η, τ) = exp{−jπkt(τ) (η −∆ηlag − ηref (τ))

2}

∆ηlag = ∆ηshift + ∆ηoff(13)

Using this expression, burst deramping and stitching isagain applied to the original slave SLC image (Fig. 4).

The master and slave images are then ready for interfer-ometric processing. At this stage, residual phase rampsare significantly reduced in the corrected interferograms.This demonstrates that the accuracy of the misregistra-tion error, which depends on the quality of sub-pixel off-

Figure 6. Sketch showing the spatial / temporal relation-ship between the centre times ηmid of one burst as seenin the master and slave images. In the master image, thecentre time ηmmid is referenced to a time origin that differsfrom the time origin used to index the centre time in theslave image ηsmid. This difference corresponds to the off-set between the two origin times, which can be resolvedby means of a sub-pixel correlation. Furthermore, theburst mid-time in the master image does not correspondto the same azimuth line as the burst centre time in theslave image, resulting in an additional shift by an integernumber of azimuth lines between the two burst centres.The sum of these two tems (offset and shift) yields theappropriate time lag that should be included in the der-amping function of the slave image so as to compensatefor the slightly different time origins.

sets determined from the amplitude image, is already rel-atively good. Accordingly, the performance of the sub-pixel correlation depends on surface conditions.

4.3. Step 3: refined deramping using spectral diver-sity

Although the corrected images already yield interfero-grams with a reasonable quality, the above method isstill insufficiently accurate for high-precision applica-tions, such as monitoring of slow tectonic deformation.Imperfection of the coregistration can be observed inplaces where sub-pixel offsets have yielded ambiguousresults, resulting in a poor estimation of the affine coef-ficients. These residual errors are manifested as phasejumps across burst boundaries.

These phase jumps can be interpreted as the difference,in slant-range time, between on one hand, the forward-looking sensor-to-ground slant range just before (above)a given burst boundary, and on the other hand, thebackward-looking slant-range just after (below) the burstboundary. In case of significant ground displacementsbetween two diachronic acquisitions, this difference isproportional to the ground motion in the azimuth direc-tion. This is the concept behind the so-called “multiple-aperture” interferometry method, which can be appliedby splitting the beam in two parts in the Stripmap mode[9].

Alternatively, it is possible to achieve a precise coregis-tration by exploiting the proportionality between the pixeloffset and the residual phase difference, according to theso-called “spectral diversity” method [8, 7]. In burst-mode, this difference between the forward and backwardinterferometric phases is due to the squint difference inburst overlap regions, which equals ∼ 2◦ for Sentinel-1. Since the forward- and backward-looking phases areboth provided in the original SLC product, this differencecan be readily measured after multilooking the cross-interferogram (Fig. 7.a). The phase difference ∆φsd isrelated to the misregistration error ∆ηsd according to:

∆φsd = 2π ∆fovl ∆ηsd mod[2π] (14)

where ∆fovl is the Doppler frequency difference in theburst overlap region. This frequency difference can be de-duced from the azimuth distance ∆povl between the mid-dle positions of two successive bursts, counted in numberof pixels:

∆fovl = kt∆povl q with ∆povl = Nbu+Novl

2(15)

where kt stands for the Doppler centroid modulation rateaveraged over the image and Novl is the number of az-imuth pixels in a burst overlap region (typically∼ 10% ofthe burst length Nbu). In practice, the phase retrieved inthe cross-interferogram ∆φsd is observed to vary slowlyacross the image. A first order polynomial surface (i.e.a straight plane) can be used to fit the retrieved phase

Figure 7. Refinement of the lag estimation using spectraldiversity. The top row shows the phase retrieved in thecross-interferogram over eight successive burst overlapregions. For clarity, the phase in non-overlap regions isnot shown. The middle row shows the first-order poly-nomial surface adjustment. The bottom row shows theresidual.

(Fig. 7.b). This way, the affine coefficients in Eq. 11can be refined by accounting for the residual lag deducedfrom spectral diversity:

∆ηsd(x, y) = (a′ + b′x+ c′y).q (16)

Accordingly, a higher order polynomial surface could beused to improve the fit to the observed phase evolutionalong azimuth and range. Nevertheless, the linearity ofEq. 16 has the advantage of providing suitable conditionsfor combining a large number of images within a networkof interferograms without requiring that every pair shouldbe computed.

Finally, the lag term in the deramping function (Eq. 13)is updated using the refined estimate provided by spectraldiversity:

∆η′lag = ∆ηlag + ∆ηsd (17)

The slave SLC is deramped a third time using the aboveexpression, and the interferogram can be recalculated(Fig. 7.c).

An example of the resulting interferograms obtained us-ing the proposed method is presented in Fig. 8. Phasejumps across burst boundaries, as well as across sub-swaths, are significantly reduced.

5. CONCLUDING REMARKS

This study demonstrates that, despite the rule-of-thumpaccuracy of 0.1 pixel achieved by the sub-pixel correla-tion method, it is possible to derive a misregistration er-ror with sufficient accuracy to substantially reduce resid-ual phase ramps. This suggests that the large support en-abled by the correlation estimation performed across thefull image allows for determining affine coefficients in

Figure 8. Sentinel-1A TOPS interferogram computed with the proposed method. The interferogram covers a highlycoherent area in the Mojave desert, western USA.

Eq. 10 with sufficient accuracy to derive the actual off-set induced by image misregistration with a much betteraccuracy than achieved on a single correlation window.Furthermore, the short revisit time of Sentinel-1 shouldguarantee that little surface changes occur in practice,leading to good coherence and reliable sub-pixel offsetretrievals. In spite of being less accurate than the ESDmethod, the proposed method has the advantage of sim-plicity and reasonable efficiency. Accordingly, the accu-racy of the method depends on the quality of the retrievedoffset field, but also relies on the high percentage of burstsynchronization achieved by the Sentinel-1 system.

ACKNOWLEDGMENTS

This work has been supported by CNRS-PNTS (grant n◦PNTS-2015-09).

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