scansar focusing and interferometry andrea monti …...andrea monti guarnieri, claudio prati...

SCANSAR FOCUSING AND INTERFEROMETRY

Andrea Monti Guarnieri, Claudio PratiDipartimento di Elettronica e Informazione

Politecnico di MilanoPiazza L. da Vinci, 32 - 20133 Milano - Italy

e-mail: [email protected]; [email protected]

Abstract

We discuss an efficient phase preserving technique for ScanSAR focusing, used to obtain images suitable forScanSAR interferometry. Given two complex focused ScanSAR images of the same area, an interferogram canbe generated as for conventional repeat pass SAR interferometry. However, due to the non-stationary azimuthspectrum of ScanSAR images, the coherence of the interferometric pair and the interferogram resolution areaffected, both by the possible scan misregistration between two passes and by the terrain slopes along the azimuth.The resulting decorrelation can be significantly reduced by means of an azimuth varying filter, provided that someconditions on the scan misregistration are met. Finally, the SAR-ScanSAR interferometry is proposed: here thedecorrelation can always be removed with no resolution loss by means of the technique presented in the paper.

1 Introduction

ScanSAR is a Synthetic Aperture Radar with a swath coverage, in slant range, which is wider than that of con-ventional SAR systems. This coverage is achieved by scanning different swaths, i.e. by switching -on the fly- theantenna look angle into different positions [1]. The geometry of a two-beam and four-beam ScanSAR is shown inFig. 1 and compared with a conventional SAR. The ScanSAR sensor gets data from each of the Nsw sub-swaths,in a time interval TD (“dwell time”), that is approximately 1/Nsw times the time extent associated with the an-tenna beamwidth, TF . The same subswath is cyclically imaged every TR ≤ TF seconds (in the case of a singlelook for each scan cycle, as assumed here), to get coverage of the entire scene. The dwell time is slightly lowerthan TR/Nsw, due to the necessary antenna steering time [2]. ScanSAR raw data should be focused with a phasepreserving processor to obtain complex images suitable for ScanSAR interferometry (first proposed in [3]).

The spectral properties of ScanSAR data, and an efficient ScanSAR phase preserving focusing algorithm, arepresented in the following section [4, 5]. It will be shown that the ScanSAR complex focused images are character-ized by a non-stationary spectrum, that cyclically spans the entire azimuth bandwidth, which is equal to the pulserepetition frequency PRF .

In the third section, the generation of interferograms, either from repeated ScanSAR passes or by combiningSAR and ScanSAR passes, is considered. It will be shown that the coherence of the interferometric pair is affectedby the possible scan misregistration between two passes, the variation of the Doppler centroids and terrain slopesalong azimuth [3, 4, 5]. These effects are quantitatively evaluated, and a technique is proposed to cancel out most ofthe decorrelation. Experimental results are presented by simulating ScanSAR raw data obtained from ERS-1 SARdata.

2 Spectral properties of ScanSAR data

Two systems of coordinates will be used to get the expression of the ScanSAR pulse response: one for the “signaldomain” (i.e. the domain of the signals collected by the sensor), and one for the “data domain” (i.e. the position ofthe targets on the ground). In this paper, we refer to the signal domain coordinates (τ, t) for range and azimuth times(also known as “fast time” and “slow time”), and to the data domain coordinates (r0, ξ). The couple (r0, ξ) definesthe range and azimuth target location with respect to the sensor by identifying the closest approach distance, r0, and

1

the closest approach time, ξ (i.e. the zero-Doppler time instant). An example of the geometries of the broadsideSAR and ScanSAR systems is in Fig. 1.

The symbols used in the paper are summarized as follows:- (τ, t) and (r0, ξ) are the slant range and azimuth coordinates for signal and data domains;- f and fx are the range and azimuth frequencies, conjugate to (τ, t);- ω is the angular range frequency; ω0 = 2πf0 is the RF carrier, λ = 1/f0 the carrier wavelength;- R(t, r0) is the satellite-target distance;- v is the along-track satellite velocity.

2.1 Pulse response of ScanSAR systems

In the case of conventional SARs, the pulse response of a target located in (r0, ξ) can be approximated as follows[6]:

hSAR(τ, t; r0, ξ) = aβ

(v(t − ξ)

r0

)·

·δ(

τ − 2ΔR((t − ξ); r0)c

)· exp

(−j

(4πλ

ΔR((t − ξ); r0)))

(1)

The three terms on the right side of (1) have the following meaning:

[1] aβ is the antenna gain pattern. It depends on the angle β = vt/r0, shown in the geometry of Fig. 1.

[2] δ(τ) is the range compressed pulse. It is delayed by the antenna-target differential travel time. Here ΔR isdefined as follows:

ΔR(t − ξ; r0) = R(t − ξ; r0) − r0 � v2

2r0(t − ξ)2 (2)

[3] The complex exponential is the frequency dependent phase shift, proportional to the antenna-target travel timeΔR.

Notice that the pulse response hSAR is stationary in azimuth, since it depends on the offset t-ξ between the currentsatellite position t, and the closest approach time ξ.

The ScanSAR’s pulse response, hSS , is obtained by windowing the SAR pulse response hSAR with a squarewave wsc(t) that takes into account the illumination pattern in a given subswath:

wsc(t) =∞∑

k=−∞rect

(t

TD− kTR

)(3)

A smooth transition between the raising and trailing edges of the square-wave must be assumed (the transitiontime being longer than the carrier period), to avoid the generation of spurious transient harmonics in the raw-dataspectrum.If expressions (1) and (3) are combined, the following ScanSAR pulse response holds:

hSS(τ, t; ξ, r0) = hSAR(τ, t; ξ, r0) ·∞∑

k=−∞rect

(t

TD− kTR

)(4)

Unlike the SAR case, the ScanSAR pulse response (4) is not stationary in azimuth, since it depends both on thesatellite position t, and on the target’s closest approach time ξ. Notice that the amplitude of the Doppler history ofthe scatterers within a footprint (|ξ| ≤ TF /2), is weighted by the window:

|hSS(t, ξ)| =

{aβ( (t−ξ)v

r0) −TD

2 ≤ t ≤ TD2

0 elsewhere(5)

2

For example, the pulse responses of three targets at different azimuth positions are shown in Fig. 2. Here the timeorigin of the scanning pattern has been chosen so that the target at ξ = 0 appears at the center of the antennabeamwidth when the ScanSAR acquisition is switched on (see Fig. 3). It can be noted that the Doppler historyof each scatterer is observed in just one scanning cycle, except for the scatterers at the very edge of the antennaaperture, that are imaged twice in two subsequent scanning cycles.

The ScanSAR transfer function of a target located in (r0, ξ) can be derived by exploiting the SAR transferfunction, i.e. the 2D Fourier transform of (1) (derived in reference [6], by assuming the stationary phase principle):

HSAR(fx, f ; r0) � A1 · aβ

(λ

2vfx

)exp

(−j

π

fR(1 + f/f0)f2

x

), (6)

fR = −2v2/(λr0) being the Doppler Rate, and

fx =12π

dφ

dt= fR(t − ξ) (7)

the instantaneous frequency. The ScanSAR transfer function is then obtained by (5), (6) and (7):

HSS(fx, f ; r0, ξ) =

⎧⎨⎩ HSAR≡aβ( λ

2vfx) exp(−j πf2

x

fR(1+ ff0

)

)fR(ξ − TD

2 ) ≤ fx ≤ fR(ξ + TD2 )

0 elsewhere(8)

The ScanSAR azimuth spectrum is cyclostationary, since the Fourier transform of the pulse response spans the dataspectrum with periodicity Δfx = fRTR. The spectral shape depends on the target location in the acquisition timeslot, as shown in Fig. 2.b.

ξ

2 beamsScanSAR

4 beamsScanSAR

Acquisition time slot(for each beam)

TF TD

TR

tazimuth

sensortrack

full-resolutionSAR

ττslan

t rang

e

R(t

)

β

Figure 1: SAR and ScanSAR geometries.

2.2 ScanSAR data simulation.

Simulated ScanSAR data can be easily provided starting from either a raw or a range compressed SAR dataset, andby applying the time domain windowing in (3) (see [7]). A smooth cosinus transition, whose length is as short as afew pixel, can be used at the transition edges, since the time requested to steer the antenna in a different subswath isless than a sampling interval (if electric beam steering is assumed). For example, the data set used for the simulationshave been generated by ERS-1 SAR raw data. The window wsc(t) was designed to give a return time TR � 0.6 s (�85% of the synthetic aperture TF ), and a dwell time TD � TR/2 = 0.3 s, to simulate a 2-beam-1-look ScanSAR,whereas TD � 0.15 s was assumed for the 4-beam-1-look case. Results of processing these datasets are reported inthe following.

3

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA




























ξ0 ξ1 ξ2

hsar

TRTf

wsc(t)

t

t

h(t;ξ1)

h(t;ξ2)

(a) (b)

H (f; ξ1)

H (f;0)

ffRTF/2

fRTD

0

fRξ1


















AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

















AAAAAAAAAAAAAAAAAAh(t;0)







AAAAAAAAAAAAAAAAAAA





























H (f; ξ2)

fRTRfRξ2

PRF

Figure 2: ScanSAR pulse responses of three targets at different azimuth (ξ), in the time domain (a) and in thetransformed domain (b).

3 ScanSAR focusing

Stripmap SAR focusing can be performed by filtering with the reference matched to (6):

Hr(fx, f ; r0) = exp(

jπ

fR(1 + f/f0)f2

x

)(9)

This processing can be easily extended to the ScanSAR case if computational efficiency is not crucial. First, theScanSAR range compressed data should be zero-padded in azimuth to fill up the time intervals when the acquisitionis switched off. Then the data can be focused in the same way as SAR data, e.g. by means of the matched phasereference (9).The spectrum of a focused target located in ξ can be computed by combining (8) and (9):

HSS(fx, f ; r0, ξ) · Hr(fx, f ; r0) ={

aβ( λ2v fx) fR(ξ − TD

2 ) ≤ fx ≤ fR(ξ + TD2 )

0 elsewhere(10)

This spectrum is bandpass, and its center frequency, fRξ, varies with the target azimuth position ξ (see Fig. 2.b).The focused target’s bandwidth is W = fRTD, i.e. approximately 1/Nsw times the SAR bandwidth, PRF, whichaccounts for the reduced ScanSAR azimuth resolution. The focusing technique discussed here thus gets Nsw timesoversampled data.

The cyclostationary spectral properties of ScanSAR focused data are shown in Fig. 4. A 4-beam-1-lookScanSAR was simulated, as shown in section 2.2, and then focused with the technique presented here. Then shorttime periodograms were computed at different azimuth positions. The time extent of each periodogram was muchlower than the synthetic aperture, TF . The resulting azimuth varying power spectrum density is reported in Fig.4.a. Notice the shift of the ScanSAR spectrum, due to the Doppler centroid fdc ≈ −200Hz. The azimuth-varyingpower of the focused image, aβ(λfx/(2v))2, that results from the interaction of the antenna pattern and the scanwindow, is shown in the Fig. 4.b. This could be compensated by a proper time domain equalization. In any case, anazimuth-varying SNR will occur.

3.1 Multiple-Look ScanSAR focusing.

The azimuth-varying SNR can be compensated by acquiring multiple looks, e.g. by imaging the same subswathmore than once during a synthetic aperture TF . If this is done, the return time TR should be reduced at least

4

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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

ξP

r0

TD

antenna footprint (TF)ξ0























AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

ξ1

TR
































t

0

OffOn

scanning pattern sensor track

Figure 3: ScanSAR geometry in the azimuth, range plane. Three scatterers at different azimuth positions and thecorresponding acquisition angular intervals are represented.

to a value TF /Nl, where Nl is the number of looks; at the same time the dwell time TD should be reduced bya factor Nl. Phase preserving focusing should then be performed on each look separately (e.g., by means of theabove mentioned technique), obtaining Nl complex images [8]. These images should be exploited to compute Nl

independent interferograms, which can then be coherently averaged to compensate for the azimuth varying SNR.The pulse bandwidth of a Nsw-beams-Nl-looks ScanSAR is the full SAR bandwidth, scaled by the inverse of

the beam-look product:Nlsw = Nl · Nsw, (11)

and the ScanSAR resolution worsens by the same amount. As an example, the ASAR wide-swath mode assumesNl = 3 looks and Nsw = 5 beams; in this case the look bandwidth is W = 50 Hz [9], which is less than 15 timesthe full SAR bandwidth.

3.2 Efficient ScanSAR focusing algorithms

The computational efficiency of the ScanSAR “standard focusing” previously discussed can be significantly im-proved if the amount of zero-padding is strongly reduced. Let us suppose we form an azimuth data strip of timeduration TP , which is slightly longer than TD, i.e. by zero-padding the data collected during the scanning cycle (therole played by TP − TD, i.e. the amount of zeroes to be added, will be clarified below). This short azimuth stripcan be focused by multiplying its Fourier transform by the matched SAR reference, Hr, in (9). One should be re-minded, however, that even if the acquisition time TD is much smaller than TF , the contributions of all the scatterersilluminated by the antenna are represented in the collected data (see Fig. 3). Thus, due to the low sampling rate inthe frequency domain, the contributions of the PRF · TD scatterers illuminated by the antenna are folded:

Nrep =⌈

TF + TD

Tp

⌉� Nlsw + 1 (12)

times, as Fig. 5.a shows (the “rounding to nearest integer” operator, �·�, has been introduced in (12) to include thecontribution of those targets whose echo is only partially contained in the strip of length TP ).

5

00.2

0.40.6

0.81 0

200400

600800

10001200

14001600

−40

−20

0

Azimuth Power Spectrum (dB)

Off

On

0.2 0.4 0.6 0.80azimuth [s]

-3

-2.5

-2

-1.5

-1

-0.5

0

dB

(a) (b)

Figure 4: Azimuth-varying statistics of a focused ScanSAR image: (a) power spectrum density; (b) total power.

In other words, the focused pixel at a given azimuth is formed by the superposition of the echoes of the targetslocated at ξ + NTP (for N = 0 . . . Nrep − 1). Yet, these contributions are separated in the frequency domain by agap:

Δfg = |(fc2 − fc1) − fRTD| = |fR(TP − TD)| (13)

fc1 = frξ and fc2 = fr(ξ − TP ) being the central frequencies of the two targets spectra, and fRTD their bandwidth(see Fig.5.a). Thus, the resulting time domain aliasing can be removed by means of an azimuth varying filter1 whoseband is sketched in the Fig. 6.a. The filter should accommodate the Doppler rate variations with range. The filterselectivity can be reduced by increasing the frequency gap Δfg in (13), i.e. by increasing the amount of zero-paddingTP − TD.

The ScanSAR focusing introduced here can be summarized by the following steps:

(1) Padding the data strip acquired in a scan cycle with zero range lines up to a length TP ·PRF azimuth samples.

(2) Focusing the resulting strip by means of a SAR processor.

(3) Mosaicking Nrep copies of the focused strip / filtering to remove the time-domain aliasing. At this step a stripof Nrep · TP ·PRF azimuth samples is generated.

(4) Selecting the correct data portion, e.g. the central (TR + TP )PRF/Nlsw range lines.

There are two efficient ways to implement step (3): by operating in the time domain or in the frequency domain.The time domain approach, shown in the block diagram of Fig. 7, is accomplished by

(3.1) Mosaicking Nrep replicas of the focused sequence (no computational cost).

(3.2) Filtering the resulting large image with the azimuth-varying filter (see Fig. 6.a), to cancel the time-aliasedcontributions.

(3.3) Down-sampling the image, to get a pixel spacing close to the resolution, typically by a factor Nlsw.

Clearly, the last two steps should be done together to gain efficiencyThe frequency domain implementation of the azimuth varying filter leads to the following steps:

1A technique that exploits the same azimuth-varying filter, but for a different purpose (e.g. focusing SAR data when the Doppler centroidvaries linearly along azimuth) is presented in reference [10].

6

(3.1) Deramping the short azimuth strip (time extent TP ). This is done by multiplying the focused data by the linearfrequency vs azimuth phase operator [11]:

Hd(ξ) = exp(−j2π

(fR

2ξ2 − fdcξ

))ξ = −TP

2. . .

TP

2

As a result, the spectral contribution of all the scatterers in the strip are divided into Nrep blocks: one block iscentered on the Doppler centroid fdc, and the other blocks are frequency shifted by multiples of Δfc = fRTP

(see Fig. 5.b). The gap between adjacent blocks is Δfg.

(3.2) Fourier transforming the deramped strip in the azimuth direction.

(3.3) Computing Nrep looks by windowing, and inverse Fourier transforming short sequences of extent Δf =fRTP . The shapes of the spectral window (e.g. the filters’ masks) are represented in Fig. 5.c.

(3.4) Mosaicking the Nrep looks, in order to get the subsampled focused image.

It should be noted that since only one scanning interval is focused, the resolution changes for the scatterers at theedges of the antenna beam (e.g., referring to Fig 5.a, for ξ ≤ ξm and ξ ≥ ξM ). Thus, in order to get a stripmapScanSAR image with constant azimuth resolution, subsequent focused scanning intervals should be combined bymeans of an “overlap-add” technique.

3.3 Stripmap ScanSAR focusing.

The stripmap implementation of the ScanSAR focusing is achieved by focusing the data acquired in each scan cycleas shown in the previous subsection, and applying the “overlap-add” technique to the corresponding output blocks.This technique is illustrated in Fig. 6.b. The resulting processor can be efficiently implemented on a commonworkstation, because of the short azimuth kernel that fits in the core memory. One advantage of this technique isthat it exploits a conventional SAR processor, simply by adding a simple post-processing step to get the ScanSARfocused image.

The efficiency of the focusing technique just proposed can be compared with the “standard ScanSAR” focus-ing, which is performed on the zero-padded dataset of Naz � PRF · TR azimuth samples (here assumed to berange-compressed). If we implement a wave-number domain algorithm, like the one in [12], two 2D FFT and 2complex multiplications for each sample (1 for filtering + 1 for Stolt interpolation) are required for focusing. Thecomputational cost, in terms of complex multiplications, is

N � PRF · TR(2 + log2(PRF · TR))Naz

≈ 2 + log2(PRF · TDNlsw) (14)

for each input data sample (1-look). Note that the output image comes at the SAR sampling rate, therefore is ∼ Nlsw

times oversampled. On the other hand, the computational cost of the implementation proposed here is the sum of thecost for processing a strip of N′

az = PRF · TP azimuth samples, + the post-processing, that requires one complexmultiplication for each input sample (for deramping), and forward + inverse FFT. If we assume TP = kTD (k ≥ 1),the total number of complex multiplications per sample is:

N ′ �PRF · TP

(3 + 3

2 log2(PRF · TP ) + 12 log2

(PRF ·TP

Nrep

))Naz

≈ k

Nlsw(3 + 2 log2(PRF · kTD) − log2 Nrep) (15)

The focused image comes sampled close to the Shannon limit. The gain in computational complexity grows with thefactor Nlsw as can be seen by comparing (14) and (15). As an example for a 4-beam-1-look ScanSAR, and assumingTP =3

2TD, the computational complexity is approximately half the cost of the standard SAR mode focusing, whereasfor the ASAR Wide-Swath Mode (Nlsw = 15) the cost is approximately 9 times less.

7

4 ScanSAR Interferometry

ScanSAR images from repeated satellite passes can be exploited for generating interferograms by means of the usualconjugate cross-multiplication of the images [3, 4, 5]. The main difference of ScanSAR interferometry with respectto the usual SAR interferometry is the possible scan misregistration between two passes. In this section the followingpoints will be shown:

i - A ScanSAR interferogram can be generated whenever the scan misregistration time ΔTD is smaller than thedwell time TD. The larger the ΔTD the higher the phase noise (the resolution in azimuth is not affected).

ii - The difference between the Doppler centroid of the two takes and the terrain azimuth slopes causes a relativeshift of the corresponding azimuth spectra. This shift can be consistent when compared to the effective bandwidth:W ∼ PRF/Nlsw, particularly when the number Nlswof looks × beams is large.

iii - The ScanSAR interferogram quality (signal to noise ratio) can be greatly improved by means of an azimuthvarying filtering of the images before their cross-multiplication.

For the sake of simplicity, we will discuss the principle of ScanSAR interferometry, assuming that the imagesare not subsampled in azimuth (as shown in the previous section to get an efficient focusing). The extension to thesubsampled images, is trivial.

4.1 Asynchronous Scanning Decorrelation (ASD)

The azimuth spectral support of one subswath is sketched in Fig. 8. An ideal rectangular antenna pattern has beenconsidered for simplicity. As already shown in section 3, the recovered azimuth bandwidth, whose central frequencylinearly changes along the azimuth direction (ξ), has the following expression:

W = fRTD =TD

TFPRF (16)

Let us now suppose we have a second image of the same subswath with the same dwell time TD and a scan mis-registration ΔTD. The azimuth spectral supports of the two ScanSAR images are shown in Fig. 9. From this figureit can be noted that the two supports partially overlap. The overlapped azimuth bandwidth Wi is proportional toΔTD (for ΔTD ≤ TD) as:

Wi =TD − ΔTD

TFPRF = (TD − ΔTD)fR (17)

The uncorrelated parts of the azimuth spectra reduce the interferometric pair coherence γ, together with the wellknown baseline (γB), temporal (γT ) and volume (γV ) decorrelation terms. Thus, the coherence of a ScanSARinterferometric pair can be expressed as follows:

γ = γB · γT · γV · γASD (18)

The last coherence term γASD, which is due to the Asynchronous Scanning Decorrelation (ASD), has the followingexpression (for ΔTD ≤ TD):

γASD =Wi

W= 1 − ΔTD

TD(19)

Since γASD might be dominant with respect to the other terms (especially when the number of subswaths used islarge) it should be eliminated by synchronizing the repeated scans or, whenever possible, by filtering out the noise,as described in the following section. For example, 2-beam and 4-beam (1-look) ScanSAR interferograms havebeen simulated by exploiting two ERS-1 interferometric passes (see section 2.2). Fig. 10 shows the interferometricfringes for synchronized scans, and for scan misalignment ΔTD = 0.8TD (e.g. γASD = 0.2). Notice the azimuthvariant SNR, that gives an almost uncorrelated vertical strip in the figures (e.g. the contribution of the targets locatedat the edges of the antenna beamwidth during the scan interval).

8

Besides the decorrelation, the scan mis-registration introduces a loss of resolution in the complex interferogram.The increase in the interferogram resolution can be expressed by the ratio between the common bandwidth forsynchronized acquisitions and the common bandwidth for misaligned acquisitions, e.g. (W/Wi) = (1/γASD). Thesize of a resolution cell (a pixel) on the ground also increases by the same factor, and decorrelation may result as thecontribution of non stationarities, like slope changes within the same pixel.

azimuth, ξ

TD

fc0

fc2

TP

(a)

f

fc1

f

fc0

fc1

fc2

Δfc

(b)

BA

PRF

I

II

III

(c)

Δfg

Δfg

TPξm ξM

Figure 5: (a) Azimuth spectral support of the data focused within the short strip of time duration TP , for a 4-beamScanSAR. The time-domain folding of the darker blocks is caused by the low sampling in the frequency domain.(b) The same spectral support after deramping: the contribution of the three blocks, overlapped in the time domain,are separated in the frequency domain. (c) Masks of the filters required to separate the three blocks.

Up to now, we assumed the same Doppler centroid for the two interferometric images. However, if the two im-ages were acquired with a different Doppler centroid, Δfdc (e.g. due to a different antenna pointing), the expression(17) of the overlapped bandwidth becomes:

Wi = (TD − ΔTD)fR + Δfdc (20)

Therefore, a change in the Doppler centroid of Δfdc can be regarded as an equivalent scan misalignment ΔT′D =

Δfdc/fR.

4.2 Eliminating the ASD term

The decorrelation term created by the scan misregistration γASD can be avoided by filtering out the incorrelatedpart of the images’ spectra. It is clear from Fig. 9 that the central frequency of the band-pass filters, which allowsthe taking of only the common part of the spectra has the same linear variation of the filters used in the focusingstep. Once ΔTD is known, the first image should be band-pass filtered with a bandwidth Wi and with the followingcentral frequency:

fo1 = (ξ′ + ΔTD)fR, (21)

9

ξ′ being the azimuth coordinate of the first image (again the reference azimuth has been chosen in the middle of thedwell time TD). The central frequency used to filter the second image has the following expression:

fo2 = (ξ′′ − ΔTD)fR (22)

ξ′′ being the azimuth coordinate of the second image.If the effect of terrain slopes - detailed in the next section - is not relevant, the ASD can be easily cancelled by

windowing the two raw datasets by the product of the two scan patterns wsc1, wsc2 in order to keep only the commonspectral contributions (the mid grey areas in Fig. 9) [8].

The decorrelation reduction achieved with the proposed data processing can be clearly appreciated by comparingfigures 11 and 12. In the cases illustrated, two interferometric ScanSAR acquisitions with a ΔTD that is halfthe dwell time TD were simulated. As a result the coherence histogram derived from the misaligned ScanSARacquisitions is scaled with respect to the one derived for SAR (e.g. for aligned ScanSAR acquisitions) of the factorgiven in (18,19). The position of the coherence histogram peak, for example, is approximately halved. Howevernotice that most of the decorrelation is recovered by performing the azimuth varying filtering.

The ASD can be theoretically removed whenever there is a common band Wi > 0 i.e. γASD > 0 in (19). Thiscondition implies:

ΔTD < TD

orΔTD > TR − TD

⇒ΔTD < TR

Nlsw

or

ΔTD > TR

(1 − TR

Nlsw

) for 0 ≤ TD ≤ TR, (23)

derived from (19), taking into consideration the periodicity of the acquisition. Notice that for the 2-beam-1-lookScanSAR (Nlsw = 2), condition (23) is met with ∼ 100% of the times for random acquisitions, and 50% of thetimes for a 4-beam-2-look system. The first system seems to be a good candidate for ScanSAR interferometry. Whenthe beam-look product is large, stringent constraints on the scan acquisition synchronizations should be assumed.For example, the 5-beam-3-look ASAR requires an along track synchronization error of less than 140 m to obtaina common bandwidth, Wi > 0. However, that limit should be reduced to obtain an acceptable interferogramresolution.

4.3 Effect of the azimuth slopes

The effect of the azimuth slopes of the terrain on the image reflectivity spectrum can be studied using the geometryshown in Fig. 13: there a constant sloped terrain with an azimuth slant angle α is represented. For squint angles≈ 0, the transmitted wavelength λ is projected on the terrain scaled by a factor 1/(sin α cos θ), θ being the lookangle. The corresponding azimuth ground wavenumber (i.e. in the direction L in the figure) is: kL = 4π/λL =4π sinα cos θ /λ.The second interferometric image is gathered with a look angle θ + Δθ, the ground terrain spectrum is thus shiftedby:

ΔkL � ∂k

∂θΔθ =

4πf0

cΔθ sin θ sin α =

4πf0

c

Bn

r0sin θ sin α, (24)

Bn being the normal baseline. The corresponding azimuth spectrum shift is:

Δkx � ΔkL

cos α=

4πf0

c

Bn

r0sin θ tan α (25)

If we define ρB to be the ratio between the current baseline, and the “critical” baseline, fixed by the system rangebandwidth, BR:

ρB =Bnmax

Bn=

BRf0

r0 tan θ

Bn, (26)

then the following expression of the azimuth spectral shift (given in Hz) holds:

Δfx =Δkx

2πv =

2BR

cvρB sin θ tan θ tan α (27)

10

The azimuth spectral shift in (27) is usually ignored in SAR interferometry, since it is much smaller than the azimuthbandwidth. Yet, it can be significant in ScanSAR system, where the azimuth bandwidth is reduced proportionallyto the beams-looks product, Nlsw. Take, for example, the ASAR case. If we assume a look angle of θ = 40o anda normal baseline Bn = 1

4Bmax, from (27) we get a shift Δfx = 22 Hz for an azimuth slope of 100. This shift isindeed a small fraction of the SAR azimuth bandwidth (∼ 1500 Hz), yet it is approximately 45% of the ScanSARazimuth bandwidth (50 Hz, [9]). For perfectly aligned scans, that shift contributes to the image coherence (in (18)),with a factor γASD = 0.45, and the resolution is more than doubled.

In the case of misaligned acquisitions, the common bandwidth Wi can be increased or reduced on a slopedterrain, depending on the signs of the scan error ΔTD and of the shift Δfx, induced by the azimuth slope. Thecoherence coefficient γASD is then modified as predicted by (19), but uses Wi + Δfx instead of Wi for the commonbandwidth. The slope dependent decorrelation can be cancelled out by tuning the central frequency of the filters,in (21,22), and the filter bandwidth, according to the expression (27). Yet, the possible resolution loss cannot berecovered.

4.4 ScanSAR-SAR interferometry.

The decorrelation due to asynchronous scanning and terrain slopes and the resolution loss can be avoided if oneScanSAR survey is combined with a SAR survey got from the same mission, under a sufficiently close view angle.In that case, the decorrelation that comes from the non overlapped bandwidth can be removed by filtering the SARdata with the azimuth varying filter specified in the previous section. If the effect of slopes is minimal, it is sufficientto apply the scanning pattern wsc(t) used by the ScanSAR acquisition to the SAR raw data.

The mixed SAR-ScanSAR interferometry is particularly helpful for those missions where scanning alignmentrequirements would be barely met, like for ASAR.

TD TF ≈ TR

fDC

ξ

fPR

F

TR-TD TD

TR

(a)

(b)

Figure 6: (a) Azimuth spectral support of the filter required to solve the time-domain aliasing. Notice that the filtershould be actually folded in the frequency domain due to the azimuth sampling, PRF . (b) Overlap-add scheme forfocusing continuous image strips.

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Raw / Range compressed

data

ZeroPad

Full resolutionfocusing

(SAR processor)

Mosaicking N images

Azimuth variantFiltering

time-domainaliased image

Focusedimage

Figure 7: Schematic diagram of the efficient phase preserving focusing technique proposed in the paper.

azimuth

azimuth

f

start stop

W

TD

TF

PRF

Figure 8: ScanSAR azimuth spectral support of one subswath.

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spectrum from the first pass

spectrum from the second pass

common spectrum

azimuthWi

TD

TF

f ΔTD

PRF

Figure 9: ScanSAR spectrum supports of the same subswath in two repeated passes. The azimuth axis of the firstimage is used as the common reference. The spectral support of the first image (i.e. the same of figure 8) is shownin light gray. The spectral support of the second image is shown in dark gray. The intersection of the two supports isshown in mid gray.

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5 Conclusions

An efficient focusing technique for ScanSAR images has been presented. This technique operates on one small dataset at a time (i.e. the data collected during the dwell time), thus allowing real-time implementation possibilities.Repeat pass ScanSAR interferometry has been analyzed. Due to the azimuth varying nature of the ScanSAR imagesspectrum, an accurate synchronization of the repeated scanning cycles is necessary to generate low noise interfero-grams. However, it has been shown that even if the scanning cycles show just a partial overlap, the AsynchronousScanning Decorrelation term can be eliminated by means of an azimuth varying band pass filter. Furthermore, thatfilter can be designed to reduce the decorrelation due to the azimuth slope of the terrain, which can be noticed par-ticularly with low-resolution ScanSAR systems. The same technique can be exploited to generate interferogramsbetween SAR and ScanSAR images.

6 Acknowledgments

The authors would like to thank prof. Fabio Rocca for his input.

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References

[1] Moore, et. al. “Scanning Spaceborne Synthetic Aperture Radar with integrated Radiometer”, IEEE trans. AESvol. AES-17, no. 3, pp. 410–421, 1981.

[2] A. Currie, M.A. Brown “Wide-swath SAR”, IEE Proc.-F, vol. 139, no. 2, pp. 123–135, Apr. 1992.

[3] A. Monti Guarnieri, C. Prati, F. Rocca, “Interferometry with SCANSAR” EARSeL newsletter, Dec, 1994.

[4] A. Monti Guarnieri, C. Prati, F. Rocca. “Frequent observation of surface motions using ScanSAR andGeoSAR”, proc. The Space Congress (Bremen, Germany), 23–25 May, 1995.

[5] A. Monti Guarnieri, C. Prati, F. Rocca. “Interferometry with ScanSAR”, proc. IGARSS ’95 (Florence, Italy),10–14 Jul, 1995, vol. 1, pp. 550-553, 1995

[6] R. Bamler, “A comparison of Range-Doppler and Wavenumber Domain SAR focusing Algorithms”, IEEEtrans. Geosci. and Remote Sensing vol. 30, no 4, Jul 1992, pp. 706–713.

[7] K. Eldhuset, et. al. “ScanSAR simulation and processing using ERS-1 data”, proc. IGARSS ’94 (Pasadena,CA), 8–12 Aug, 1994, vol. 2, pp. 1184–1186, 1994.

[8] R. Bamler, “Adapting Precision Standard SAR Processors to ScanSAR”, proc. IGARSS ’95 (Florence, Italy),10–14 Jul, 1995, vol. 3, pp. 2051–2053, 1995.

[9] Y. L. Desnos “Envisat Ground Segment: ASAR processing and product quality requirements” European SpaceAgency, Report No. PO-RS-ESA-GS-00245, Feb. 1995.

[10] C. Prati and F. Rocca, “Focusing SAR Data with Time-Varying Doppler Centroid”, IEEE trans. Geosci. andRemote Sensing vol. 30, no 3, May 1992, pp. 550–559.

[11] J. C. Curlander, R. N. McDonough, “Synthetic Aperture Radar systems and signal processing”, J. Wiley &Sons, 1991.

[12] C. Cafforio, C. Prati and F. Rocca, “Full resolution focusing of SEASAT SAR images in the frequency-wavenumber domain”, Int. J. Rem. Sens., vol. 12, no. 3, pp. 491–510, 1991.

[13] F. Gatelli et al. “The wavenumber shift in SAR interferometry”, IEEE Trans. on Geosci. and Remote Sensing,Vol. 32, no. 4, Jul 1994.

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(a)

(c)

(b)

(d)

Figure 10: ScanSAR interferograms simulated by ERS-1 SAR data: 2-beam-1-look ScanSAR, with sinchronizedscans (a), and sinchronization error 80% of the dwell time (ΔTD=60 ms) (b); 4-beam-1-look ScanSAR, withsinchronized scans (c), and sinchronization error 80% of the dwell time (ΔTD=30 ms) (d).

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(a) (b) (c)

Figure 11: (a) ScanSAR interferometry with no filtering. (b) ScanSAR interferometry with ASD filtering. (c) SARinterferometry (B = PRF/4).

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0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

4

Coherence (%)

Figure 12: Coherence histograms before and after eliminating ASD. The coherence histogram of the equivalentISAR system with the same bandwidth of ScanSAR is drawn for reference.

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azimuth

θ L

λ α

θ

λL

λL=λ/(cosθ sinα)

Figure 13: Geometry of a SAR (or ScanSAR) system imaging a target on the ground slanted in azimuth of an angleα. Notice the dependence of the ground wavelength λL on the slope.

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scansar focusing and interferometry andrea monti …...andrea monti guarnieri, claudio prati...

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