TOPSAR: Terrain Observation by Progressive Scans

Transcription

1 1 TOPSAR: Terrain Observation by Progressive Scans F. De Zan, A. Monti Guarnieri Dipartimento di Elettronica ed Informazione - Politecnico di Milano Piazza Leonardo Da Vinci, Milano - Italy tel , fax monti@elet.polimi.it dezan@elet.polimi.it Abstract In this paper we introduce a novel (to our knowledge type of ScanSAR that solves the problems of scalloping and azimuth varying ambiguities. The technique employs a very simple counter rotation of the radar beam in the opposite direction to a SPOT: hence the name TOPS, our proposed acronym. After a short summary of the characteristics of the ScanSAR technique and its problems, we introduce TOPSAR, the technique of design, the limits, and a focusing technique. A synthetic example based on a possible future system follows. I. INTRODUCTION The simplified geometry of a typical ScanSAR-mode acquisition is shown in Fig. 1. A ScanSAR obtains wide swath coverage by periodically switching the antenna elevation beam to points in several range subswaths: three are shown in figures [1], [2]. The antenna beam switching implies that the sensor acquires a finite sequence of echoes, i.e. a burst, for each of the imaged subswaths. In each subswath the scan cyclically acquires bursts for a dwell time T D, repeated with a period T R (defined also as inter-burst time or cycle-time, and the ratio T F /T R (T F being the antenna footprint time, truncated to the lowest integer, gives the number of looks imaged: the higher the number of looks, the coarser the resolution. Here we will focus mainly on single-look, high resolution ScanSARs. sensor track T F for increasing range coverage, or for acquiring data in different polarizations, like in the ENVISAT AP mode. Wide range coverage would eventually lead to short revisit times in a LEO satellite, which is why the ScanSAR mode is of great interest in present day mission design. Thanks to this unique feature SRTM could map most of the earth in the interferometric mode during the short duration of the shuttle mission [3]. The wide-coverage-short-revisit-time makes ScanSAR quite attractive, particularly for interferometric applications [4]; however, there are drawbacks implied in its acquisition scheme that, in many cases, discourage its use. To better understand such drawbacks let us consider the acquisition of a single subswath, as shown in Fig. 2. In the figure, defines the slow time axis (azimuth, and its origin is assumed at the time instant corresponding to the center of the burst. The figure represents three point-like targets, P 1, P 2, P 3 located at different azimuths. These targets are illuminated by the antenna beam when the acquisition is turned on, and the resulting Impulse Response Function (IRF of the ScanSAR mode is sketched in the figure (the real part has been represented for simplicity, and we have assumed the monodimensional case, along azimuth. What is remarkable in a ScanSAR acquisition is the azimuth non-stationarity of the IRF: targets at different azimuths contribute as time windowed chirps with different central frequencies, due to the different delays, and different amplitude weighting, due to the Azimuth Antenna Pattern (AAP. Scan pattern T D /2 sub-swaths T D P 2 P 3 Fig. 1. Geometry of a typical 3 subswaths, high resolution ScanSAR. T R P 1 AAP T F /2 The burst mode acquisition, necessary to provide wide swath coverage, limits the Doppler history for each target to a ratio T D /T F with respect to an equivalent STRIPMAP SAR acquisition. As a consequence, the acquired target bandwidth is reduced by the same amount, and thus the azimuth resolution decreases. Azimuth resolution is the ScanSAR trade-off Fig. 2. ScanSAR acquisition geometry: the contribution of three targets has been represented to highlight the azimuth non-stationarities in both amplitudes and spectra. The change in the central frequency is the unavoidable con-

2 sequence of the one-to-one time-frequency mapping peculiar of the synthetic aperture, as the spectrum of a target at slow time would be centered on an azimuth-varying Doppler: f ( = k R (1 where we have assumed zero Doppler centroid and the azimuth time origin at the burst center. The instantaneous bandwidth, for each target, would be B a = k R T D (2 where k R is the Doppler rate. In the simplified rectilinear geometry we can approximate k R as follows: k R = 1 2 R( 2π 2 = 2v2 s (3 λr R being the closest approach distance, λ the wavelength and v s the sensor velocity. This space-varying spectrum must be taken into account when dealing with interferometric applications where perfect scan synchronization would be required to image in the two acquisitions the same spectrum from the same targets on the ground [5]. Besides this constraint, the sweeping of the Doppler spectrum has no further-drawbacks, when dealing with interferometric applications. Indeed, the major source of problems is the AAP weighting that varies from target to target, and also within the Doppler history of each target, as Fig. 2 shows. The figure shows the two way antenna pattern, usually approximated by a sinc 2 -like shape (a bell: ( ( L L G a (ψ( G sinc 2 λ ψ G sinc 2 v s (4 λ R Each target contributes to the burst for a small interval, = ±T D /2, much smaller than the footprint-time, T F, thus targets returns will be weighted by different slices of the AAP, depending on the azimuth location. This space-varying modulation causes several unwanted artifacts: - an annoying periodical modulation of the amplitude, or scalloping, that makes ScanSAR calibration a difficult task unless there is accurate knowledge of the Doppler centroid and noise floor [6]; - an azimuth varying resolution, ambiguity ratio and Noise Equivalent σ. These artifacts affect the targets at the edges of the antenna pattern, like P 1 and P 3 in Fig. 2, much more than those close to its center, like P 2. In a ScanSAR mission designed mainly for applications based on amplitude images there is an easy solution to the problem, simply increase the number of looksper-footprint. Indeed, this would reduce the geometric resolution by the same amount, and the effect would be compensated by the increase in the number of looks, hence improving the radiometric accuracy. In ENVISAT WSM, almost scallopingfree detected images are achieved by averaging three azimuth looks, and there is no need for azimuth antenna pattern compensation (that would require a very accurate Doppler centroid estimate. On the contrary, for an interferometric-oriented mission geometric resolution loss should be avoided, as this would introduce volume scattering decorrelation (for conventional interferometry, or reduce the signal-to-clutter ratio (for Permanent Scatterers applications [7], thus the design of 1-look-perfootprint is almost mandatory. Furthermore, the requirement of scan pattern alignment with respect to the same ground reference, necessary to avoid interferogram resolution loss [5], would cause in all the acquisitions, a systematic degradation of quality in the same ground locations (targets at the edge of the antenna beamwidth. This would be a major constraint in the design of such a system. II. TOPSAR MODE Let us now assume a quite different sensor that scans the image with very long bursts, and rotates the antenna throughout the acquisition from backward to forward, as shown in Fig. 3. We will define this sensor as Terrain Observation with Progressive Scan (TOPS, and note that it rotates the antenna opposite with respect to a SPOT, resulting in the opposite effect, say a worsening of the azimuth resolution. However the sensor gathers returns from a much longer strip than it would in a standard STRIPMAP mode within the same time span, so it can switch the antenna to targets pertaining to different subswaths or different polarizations 1. The task of reducing azimuth resolution is now performed by steering the antenna so the burst can be very long, even if some obvious limitations do apply (e.g., platform stability to span in subsequent passes at the very same Doppler frequencies for interferometric purposes and the design of an active antenna array with low grating lobes. Let us assume antenna rotation at a negative rate k ψ, anti- SPOT, so that its beam center points in the direction: ψ dc = k ψ with k ψ < (5 The target illumination is now computed, for the generic time, by taking this rotation into account (Fig. 3, and the AAP (4 becomes: ( vs G ar (ψ( G sinc 2 ( L λ = G sinc 2 ( L λ v s R + k ψ R ( 1 + R k ψ v s Each target will be illuminated by the steered antenna for a ground footprint that is equivalent to that of a fixed antenna, but shrunk by a factor: (6 α = 1 + R k ψ v s 1 (7 in other words this situation is equivalent to a STRIPMAP SAR with an antenna length L e = αl, that achieves an azimuth resolution α times coarser: ρ az αl/2. Note here that resolution loss is achieved by shrinking the footprint, rather than slicing it. Every target 2 experiences the same 1 A similar backward to forward scanning scheme is adopted in some military airborne system for wide-area moving target identification (MTI. 2 With the exclusion of those imaged at the edges of the burst, where impact is indeed minimal as the burst length increases, thus T B >> T D.

3 TABLE I TYPICAL PARAMETERS OF THE TARGET SPACEBORNE SENSOR OPERATING IN BURST-ACQUISITION MODE. Parameter Symbol Value Unit Wavelength λ 5.66 cm Sensor Velocity (equivalent v s 68 m/s Antenna Length (along track L 1 m Sensor height (over earth H 627 km Azimuth Resolution ρ a 2 m Antenna footprint L F 4 km Number of subswaths N s 3 parameters, but we still maintain the approximate geometry shown in Fig. 1 as this would lead to a much simpler description with minimal impact on true performance. TABLE II TYPICAL SWATH-DEPENDENT PARAMETERS VALUES, COMPUTED AT MID-RANGE FOR EACH SUBSWATH. Swath IS1 IS2 IS3 PRF (Hz k r (Hz/s Incidence angle ( o Swath Depth, ground (km Slant range (km Fig. 3. TOPSAR acquisition geometry. In both figures are represented some of the repeated positions along the orbit of the sensor and the corresponding radiation patterns. (a sketch of the three subswaths scanning scheme; (b scanning in one of the subswaths: each target is illuminated by the antenna for an equivalent footprint that is α times smaller than the physical one. AAP weighting, and ambiguities becomes stationary in azimuth, and the same happens for azimuth resolution and SNR, and there is no scalloping at all. The azimuth varying Doppler is still there, and a wider total bandwidth is spanned, roughly α times the PRF, but this would not call for an increase in PRF as the instantaneous antenna beamwidth is the same as for full resolution SAR in that antenna rotation is small compared to azimuth sampling. III. TOPSAR ACQUISITION The paper focuses mainly on the design of a high resolution space-borne sensor in TOPSAR mode intended mainly for interferometric applications. The target mission is a C-band sensor orbiting at 63 km over the ground, with an orbit repeat time of 14 days, and a large swath coverage of 3 km, with an azimuth resolution of 2 m. Swath coverage is essential to a short revisit time, and this prompts the burst mode. The most relevant parameters are listed in Tab. III: this mission does not correspond to any current one, but it could be an interesting proposal for the future. The swath-dependent parameters are shown in Tab. III, and were computed by simulating an elliptical sensor orbit and assuming ellipsoidal earth. In the following we will use these The raw data support in the slow-time / Frequency Domain (TFD is outlined in Fig. 4 for both the usual ScanSAR and the proposed TOPSAR. In the figure four targets, P 1 P 4 are represented in their zero-doppler time, whereas their Doppler histories are shown by thin lines with negative slopes, equal to the Doppler rate, k R. The TFD supports are represented by the shaded blocks: the shading recalls the AAP weighting. In ScanSAR mode, the AAP is fixed and results in a rectangular TFD support for the raw data, whereas in TOPSAR mode the antenna pointing sweeps with time, introducing a Doppler centroid rate 3 : k a = ( 2vs λ sin (ψ dc( 2v s λ k ψ (8 that is responsible for the up-right slant TFD support in Fig. 4.b. Comparison of Figs. 4.a and 4.b reveals the different effect of the AAP in the two cases: the targets at different azimuth experience the same illumination in TOPSAR and an azimuthvarying illumination in ScanSAR, leading in this latter case to the cited artifacts (scalloping, azimuth varying ambiguities, SNR and resolution. Furthermore, the TOPSAR burst is much longer, hence the loss due to edges effects (evidenced as useless data in the figure, and the rank (the number of pulses lost at each subswath switching is minimized. 3 We assume here first order approximations, where Doppler rate is constant, and we neglect its dependence on the cosine of the squint angle. In a real case we would account for this when computing the proper antenna steering law.

4 and T B T D, then (1 can be approximated as follows: k a T B k R (N s 1 T B (11 that imposes a lower bound on the antenna steering k a = k R (N s 1 For the N s = 3 subswath TOPSAR the frequency sweep of the antenna should be roughly double the Doppler rate, and would result in a resolution loss of a factor three, with respect to a full resolution SAR, that is consistent with (6,7 where: Fig. 4. TFD support for burst mode acquisitions: a conventional footprintsliced ScanSAR, b the proposed shrunk-swath TOPSAR. The staircase behavior shown here suggests possible quantization of the antenna steering law. The dwell time, T D should be designed to meet the desired azimuth resolution (ρ az. If we assume that the azimuth Time Band Product (TBP is large, we get k w k w ρ az = v s = v s (9 B a k R T D where k w is a correction factor, close to one, that depends on the window superimposed on the target spectrum to meet the design goals on sidelobes etc. The TBP is expressed as follows: T BP = B a T D = B2 a k R In the case here assumed, k R > 23Hz/s, therefore we are in the large TBP case for azimuth bandwidth B a 48 Hz, that would correspond to an azimuth resolution of 14 m. Such resolutions would not be of interest for an interferometric system as the volume decorrelation and the azimuth spectral shift would become consistent [5]. Note that both the conventional and the proposed modes share the dwell time and the TBP. However, while in the former the burst time, T B, is equivalent to T D, as the AAP slicing by the burst actually determines the resolution, in the latter case this parameter is subject to some freedom as resolution is determined by the AAP rate, k ψ, and by combining (6,7 and (9. Furthermore, the antenna sweep rate, k a, is constrained in order to obtain a continuous coverage of the scene. The total bandwidth spanned in the burst duration, should be (at least equal to the one spanned by a target in the inter-burst interval; in practice the target P 4 in Fig. 4.b would be observed by the two bursts, albeit at different Doppler, for the complete dwell time: B T = k a (T B T D k R (T R T B + T D (1 As a very preliminary computation, let us assume that the burst time T B is the same for all the N s subswaths: T R = N s T B, α = 1 + k a k R = 3 as results from (1 and (8. Unlike ScanSAR, where the burst duration is bounded to the dwell time, T B = T D, here we have one more degree of freedom, and interest lies, in principle, in long bursts to get T B T D and reduce the loss due to the edges and the rank. IV. TOPSAR SCAN PATTERN OPTIMIZATION So far, we have assumed the equal distribution of the total observation time into the N s subswaths. However, in TOP- SAR, like in any multi-swath ScanSAR, there is a somewhat weird jumping of the PRF due to constraints coming from the acquisition geometry, that causes ambiguities to affect some subswaths much more than others. In our case, note that the PRF in swath 2 is much higher than in the other (see Tab. III, therefore we expect less ambiguity. The fulfillment of design goals on either the Distributed Target Ambiguity Ratio (DTAR or the Point Target Ambiguity Ratio (PTAR and the Noise Equivalent σ (NEσ are fundamental items for the optimization of the scanning timeline, in both ScanSAR and TOPSAR. In the 1-look, 3 subswath ScanSAR system assumed here, the burst durations {T (1 B, T (2 B, T (3 B } are fully determined by the desired azimuth resolution and the antenna beamwidth, in fact we have T R = T (1 B + T (2 B + T (3 B + T G (12 = T (1 D + T (2 D + T (3 D + T G (13 where T G is a fixed margin that accounts for the switching time between different subswaths.in ScanSAR mode, T R should be equal to the antenna footprint time, but not in TOPSAR (see Fig. 4 where, in principle, we are free to increase the burst length. Note that, as the subswaths are imaged with different PRF (see Tab. V, different ambiguities can be expected if the same portion of the antenna beamwidth is processed. However, we could optimize the values of T B,k ψ for each of the three subswaths, subject to the overall constraint (12, to achieve uniform performance in terms of resolution and ambiguities. The whole process is divided into three phases: 1 determine the part of the antenna beam that will be exploited in focusing; 2 fix the final azimuth resolution and consequently the steering laws; 3 set the global ScanSAR timeline. 1 Since the generic target illumination is equivalent to that of a fixed antenna STRIMAP-SAR, with the same PRF but

5 for a shrinking factor α, as shown in (6, the design of the angular interval [ ϑ /2, ϑ /2] to be exploited for focusing is exactly the same. The choice of ϑ is a trade-off between the desire for good resolution (demanding large angular intervals and the need for strong ambiguities suppression, that requires processing small angular apertures signal ambiguity radians x 1 3 Fig. 5. Subswath 1. The angular interval to be processed in order to have a Distributed Ambiguity rejection of -25 is marked by continuous bars. The dashed vertical bars delimit the angular interval correspondent to the PRF. As an example, Fig. 5 represents the portion of the azimuth beam to be processed to meet a design goal of -25 for DTAR for subswath 1, with parameters set according to Tab. III. Once ϑ is set, the dwell-time is T D = ϑ R /v s and the resolution achievable by the equivalent STRIPMAP-SAR is easily computed as: ρ az,st RIP v s k R T D = λ 2ϑ (14 2 Now fix the desired azimuth resolution ρ az. Obviously the value cannot be small at will: this is left for later discussion. The actual TOPSAR resolution is just the equivalent STRIPMAP-SAR scaled by α (the n apex stands for the n th subswath: λ (1 + R(n k(n λ ρ az = α (n 2ϑ (n = v s ψ 2ϑ (n (15 hence, since we want equal resolution on all the subswaths, we obtain: ( k (n ψ = 2ρ az ϑ (n v s 1 (16 λ R (n 3 In order to get the global ScanSAR timeline we force the total track swept with the good part of the beam to be the same as the length spanned by the platform in the cycle-time T R = T (1 B + T (2 B + T (3 B. This condition is equivalent to the one in (1 and is written: ( k (n ψ (n T B ϑ(n R (n + v s T (n B = v st R (17 leading to a linear system of three equations in the unknowns T (1 B, T (2 B, T (3 B. Basically, the lower ρ az, the longer the bursts, in order to mitigate the waste of the double visit of the points between the bursts (like point P 4 in Fig. 4. Another factor ignored here for preferring longer bursts is the presence of rank. Is there a limit to the azimuth resolution obtainable? Of course. Starting from three STRIPMAP SAR with equal resolution the optimal TOPSAR cannot do better than spend one third of the time on each subswath, and the resolution is three times worse. For the three subswath TOPSAR, there is the following bound on the resolution ρ az : ρ (i az,st RIP ρ az > ρ (1 az,st RIP + ρ(2 az,st RIP + ρ(3 az,st RIP (18 being the resolution of an equivalent STRIPMAP SAR looking in the i-th swath. Thus, the TOPSAR resolution cannot be better than the sum of the STRIPMAP-SAR resolutions on individual subswaths. TABLE III TOPSAR TIMELINE FOR AN AZIMUTH RESOLUTION OF 2 M. Swath IS1 IS2 IS3 ϑ (rad Echoes per burst Rank T B (s k ψ (rad/s Azimuth resolution (m DTAR ( The bound (18 is approached by increasing the burst length, though many assumptions cease to hold for very long bursts. In the case discussed here, the bound would be about 17 m; Fig. 6 shows that a 2 meter resolution is achievable with a quite reasonable cycle-time of 3 seconds. The TOPSAR configuration characteristics are summarized in Tab. IV Fig. 6. azimuth resolution [m] cycle time [s] Achievable resolution as a function of the cycle time for a TOPSAR. V. COMPARISON WITH TRADITIONAL SCANSAR In order to show the merits of TOPSAR we compare its performance with a traditional ScanSAR system with the same 2 m resolution (see Tab. V. For a ScanSAR the DTAR is a function of the along-track position and Fig. 7 shows, for subswath 1, the variations

6 TABLE IV SCANSAR TIMELINE FOR AN AZIMUTH RESOLUTION OF 2 M. Swath IS1 IS2 IS3 PRF (Hz Echoes Rank T B (s Azimuth resolution (m angle, ψ. Any mismatch, ψ, would introduce a shift in the azimuth spectra that would lead to a Asynchronous Scanning Decorrelation, and to a loss in the interferogram azimuth resolution. Although the decorrelation can be removed to some extent in the interferometric processing (see [5], the interferogram resolution loss could not be recovered, hence we have to impose some practical limits. A squint error δψ translates into a Doppler shift of subswath 1 subswath 2 subswath m Fig. 7. DTAR versus along-track position, for the ScanSAR mode. In TOPSAR mode a uniform DTAR of -25 is achieved on the three subswaths. exceeding 15, opposite to the TOPSAR case where, by design, we do better than -25 all over the swath. Another advantage of TOPSAR is the almost uniform NEσ along the track. Fig. 8 shows the difference between TOPSAR NEσ and ScanSAR NEσ. For targets near the burst center TOPSAR performs worse, but it performs better for targets at the margins of the imaged region. If the design is driven by the worst case, than TOPSAR allows for a gain of about 3. f shift = δψ 2v λ The Doppler bandwidth focused for each target is 34Hz (v/ρ az and if we tolerate a maximum relative shift of 1/1 (a 1% resolution loss, the limit imposed on δψ is about.8 o. A further limitation, not clearly assessed in the practice so far, would come out from interferometric phase discontinuities measured at the bursts boundaries, due to a possible dependence of the targets phase centers with the view angles. Finally, we observe that the azimuth-varying Doppler spectrum spanned in TOPSAR mode would prevent any opportunity of making mixed interferometric applications combined with other IM or ScanSAR acquistions. VII. FOCUSING A TOPSAR acquisition shares similarities with both a SPOT-SAR and a ScanSAR systems. Similarly to a SPOT acquisition, the input data span a bandwidth that is quite larger than the PRF, so folding occurs in the frequency domain. If we assume the total bandwidth spanned by the data to be B T k a T B (see Fig. 4 ad section III, then folding occurs M s times in the azimuth frequency where B T M s P RF = k at B P RF Note that folding increases with the burst length, that eventually can be very long, as discussed in section IV. Fig subswath 1 subswath 2 subswath m NEσ T OP S /NEσ SCAN vs. along-track position. VI. INTERFEROMETRIC REQUIREMENTS The performances achievable by an interferometric TOP- SAR system, like any ScanSAR system, depend upon the capability to observe the same target by the same squint Moreover, as happens for a ScanSAR acquisition, TOPSAR data are acquired in bursts, where each burst has a time duration much shorter than the output image, but is sampled at a finer rate, so the information in terms of time-bandwidth product is conserved. The ratio between input and output data time extent is a factor T R T B N s for both ScanSAR and TOPSAR, as result from (13 and (12. The simplest TOPSAR processor could be designed just by adapting an existing, phase preserving STRIPMAP processor. One has to unfold the input data in the frequency domain, by upsampling M s times the range compressed burst, and then zero-pad in time domain to extend the duration of the burst to an extent T R = N s T B. The upsampled, zeropadded data will span a rectangular TFD support of extent [N s T B, M s P RF ], where terms in square brackets identifies [time, frequency]. Such data can be focused by any available STRIPMAP processor and then subsampled by a factor M s N s with no loss of information, due to the coarse resolution. In

7 fact, the M s N s times subsampling will cause focused data to span a TFD support of size [N s T B, P RF/N s ], with the same area of the input. Clearly, such approach will be highly inefficient, and a much skillful scheme can be designed that avoids the double unfolding of the data in frequency and time domain. Such scheme could be a combination o a ScanSAR and a SPOT processors. A ScanSAR processor usually performs the bulk focusing first, applied to the acquired burst sampled at the PRF, and then uses a proper post-processing to provide the required output, N s times subsampled [5], [8], [9]. Reversely, in the SPOT case (or likewise in the Hybrid mode, the range compressed data are first properly pre-processed and then focused by a full resolution processor [1]. The implementation proposed here will thus include both a SPOT-like preprocessing and a ScanSAR-like post-processing, besides the usual full resolution processor. An interesting alternative, lies in processing the data in small blocks, so that each block can be assumed as a conventional ScanSAR burst, and then putting them all together: this approach is straightforward and discussed in the literature, see [11], [12] for reference. A. Unfolding and Resampling Let we first refer to ScanSAR processing that assumes as input the range focused burst, like the one shown in Fig. 4.a. The burst TFD support has size [T B, P RF ], however the bandwidth of each single target is B a = P RF/N s and targets are acquired over a time span N S T B, so that the output TFD support should have size [N s T B, P RF/N s ]. The task of a skillful processor is to do focusing, time domain extension and subsampling in an efficient way. Different algorithms, achieving comparable quality and much better efficiency have been proposed in the literature [5], [8], [9]. The trick consists in focusing the input, time-domain folded data, by means of a time-folded reference, that leads naturally to a wavenumber domain kernel. The unfolding and subsampling is then accomplished by means of post-processing using a proper frequency selective resampling scheme, shown in Fig. 9. Like the input, also the focused data are folded in the time domain, as Fig. 9.a shows, however the N s targets that contribute to the same time are separable in the frequency domain. This is done by a processing that we will define in this paper as Unfolding and Resampling, a possible implementation is described in [5], and has been adopted in the standard ESA processor, PF-ASAR, for complex, phase-preserving Wide- Swath product of ENVISAT. Summarized here are its main steps: (1 time domain mosaicking of the data shown in Fig. 9.a, (2 a deramping step, that converts the time-varying spectrum in Fig. 9.b to a low-pass one. The deramping reference is: c 1 ( = exp ( jπk R (R 2 (19 where ZD is the zero-doppler time, and k R (R is the Doppler rate computed at range R as in (3, (3 a low-pass filtering and downsampling, accomplished simultaneously by means of a multirate filter bank [14], (4 a reramping of the data, that just reverses the deramping, with a reference conjugate to (19, to be evaluated in correspondence on the output sampling grid. Alternative implementations of the same task, comparable in both efficiency and quality, are discussed in literature [8], [9]. B. Optimized focusing Let now come to the efficient TOPSAR focusing. We remind that we have to face here with a double folding, both in times and in frequency. The frequency domain folding is shown in Fig. 1.a: we have to unfold this data in order to process at the correct sampling frequency, M s P RF, and, simultaneously to fold it in the time domain to get a support of extent [M s P RF, T B /N s ]. This is done with the very same Unfolding and Resampling step discussed in section VII-A, but applied in the frequency domain, and corresponds to the preprocessor fully discussed in the paper [1]. f a Time domain unfolding Resampling (frequency domain folding PRF N s /PRF 1/PRF T N D s T D (a (b (c Fig. 9. Exemplification of the Unfolding and Resampling steps in the TFD for ScanSAR processing. Fig. 1. Slow TFD support for TOPSAR data: (a input, range compressed data (folded and unfolded; (b same data, after spectral expansion and time domain folding, and (c the support of the focused data folded in the frequency domain. The required processing are detailed in the TOPSAR schematic block diagram of Fig. 11. After SPOT-like pre-

8 RGC data Zero Padding Frequency domain unfolding & resampling See: Fig. 1 (b Wave-number domain focusing (Range, Doppler domain Zero padded data Azimuth FFT Mosaiking (N PRF T az h lp (t N PRF Hi-res ω-k focusing (N PRF PRF 1 2 φ( f = exp a jπ fa ka Dechirping Low-pass filtering & subsampling 1 2 φ( f = exp a jπ fa ka Rechirping 12.a where the amplitude is shown in log-scale to highlight the ambiguities. Note that the single target is well focused, with an azimuth resolution consistent with the design goal of Tab. III, and ambiguities are at very low level: 38 for the PTAR (as can be measured directly form the plot, while the DTAR, measured to be about 25, is consistent with the design goals. In Fig 12.b a data-set with three targets of equal amplitude and located at different azimuth has been simulated and focused. The result shown in the lower plot, is well worth noting for the invariant focused IRF and thus the absence of scalloping. Time domain unfolding & resampling See: Fig. 1 (c Fig. 11. Focused data (Range, azimuth domain Mosaiking (N prf T az h lp (t N PRF Focused data Optimized processor for TOPSAR data 2 φ( = exp( jπk Dechirping Low-pass filtering & subsampling 2 φ( = exp( jπk Rechirping processing, data are arranged in the TFD support shown in Fig. 1.b, where they can be efficiently focused by a wavenumber domain processor. Finally, we need the Unfolding and Resampling adopted for ScanSAR, to get data in the output TFD shown in Fig. 1.c. Some cares has to be taken in computing the dechirping rate in the time domain, the term k t in Fig. 11. We have to account for the stretch of the time axis between the raw data and the focused data. Let us refer to the target that appears at azimuth time r in the raw data, in Fig. 1.b, whose zero-doppler time is labelled as ZD. The instantaneous frequency of the target is: f a = k a r = k R ( ZD r Eventually we get the following expression r = k R k a + k R ZD We can now relate the instantaneous frequency to the zero- Doppler location: f a = k a r = k ak R ZD = k t ZD k t = k ak R k a + k R k a + k R thus we get the expression on the rate k t for the time domain deramping and re-ramping steps in the optimized focusing in Fig. 11. C. Results from simulations The optimized TOPSAR processor has been implemented and tested by simulating the reference mission discussed in section III. We focused on the second subswath, somewhat more critical than the first, as it experiences the highest antenna sweep that results from the optimization shown in section IV. The focused IRF of a single point target is shown in Fig t t PTAR Slow - time [samples] (a Slow - time [s] (b Fig. 12. Optimized processing of simulated TOPSAR data. (a Amplitude image, in log scale, of a single target (in the center: the artifacts due to ambiguities are quite visible 1 footprint apart, and reduced of -4, as appears from the plots below. (b Amplitude image, in log, scale, of three targets at different azimuth (and their ambiguous returns with the same RADAR cross-section. The shapes of these targets, plotted below, do not suffer of scalloping or any other time-varying distortion as in conventional ScanSARs. VIII. ACKNOWLEDGMENTS The authors wish to thank Dr. E. Attema and Prof. F. Rocca for proposing this theme of research and for suggesting the equalizing of system behavior for all the imaged targets (E.A., Dr. Ing D. D Aria at ARESYS for the design, development and testing of the optimized processor and the European Space Agency for partial sponsoring of the work. IX. CONCLUSIONS A novel burst mode SAR acquisition has been introduced. Similarly to ScanSAR, it trades resolution for range coverage, allowing for frequent revisit times. Differently from ScanSAR, the resolution loss is achieved by shrinking the antenna footprint, rather than slicing it. The system behaves like an equivalent STRIPMAP SAR with a longer antenna. TOPSAR images are not affected by azimuth-varying artifacts, like scalloping, and have remarkably lower ambiguities than ScanSARs (up to 7, paving the way for the design of a

9 SAR system where the antenna length is fully decoupled from the azimuth resolution. Moreover the burst length provides a further degree of freedom, that has been optimized to equalize the ambiguity suppression over the subswaths. These features make TOP-SAR the preferred candidate (assuming that antenna steering technology is available for high resolution, large swaths applications, whereas ScanSAR would still be much more useful for those applications where coarse geometric resolution, but high radiometric accuracy, is needed. The quality of the TOPSAR IRF has been checked by performing point-target simulations, and by using an ad-hoc designed, optimized TOPSAR processor. REFERENCES [1] R. K. Moore, J. P. Claassen, and Y. H. Lin, Scanning spaceborne Synthetic Aperture Radar with integrated radiometer, IEEE Transactions on Aerospace and Electronic Systems, vol. 17, no. 3, pp , [2] A. Currie and M. A. Brown, Wide-swath SAR, IEE Proceedings F, vol. 139, no. 2, pp , [3] P. Rosen, S. Hensley, I. R. Joughin, F. K. Li, S. Madsen, E. Rodríguez, and R. Goldstein, Synthetic aperture radar interferometry, Proceedings of the IEEE, vol. 88, no. 3, pp , Mar. 2. [4] M. C. Cobb and J. H. McClellan, Developments in repeat pass interferometric radar for earth and planetary sciences, in RADAR Conference, proc. IEEE, Aprile, 24, vol. 1, 24, pp [5] A. M. Guarnieri and C. Prati, ScanSAR focussing and interferometry, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 4, pp , July [6] M. Y. Jin, Optimal Doppler centroid estimation for a SAR data from a quasi-homogenous source, IEEE Transactions on Geoscience and Remote Sensing, vol. 24, pp , Mar [7] A. M. Guarnieri, ScanSAR interferometric monitoring using the PS technique, in ERS/ENVISAT Symposium, Gothenburg, Sweden, Oct October 2, Mar. 21, p. 7. [8] A. Moreira, J. Mittermayer, and R. Schreiber, Extended chirp scaling algorithm for air and spaceborne SAR data processing in stripmap and ScanSAR imaging modes, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 5, pp , [9] R. Lanari, S. Hensley, and P. A. Rosen, Chirp z-transform based SPECAN approach for phase preserving ScanSAR image generation, IEE Proceedings Radar Sonar Navigation, vol. 145, no. 5, pp , [1] C. Prati, A. M. Guarnieri, and F. Rocca, SPOT mode SAR focusing with the ω k technique, in International Geoscience and Remote Sensing Symposium, Espoo, Finland, 3 6 June 1991, 1991, pp [11] I. G. Cumming, A comparison of phase preserving algorithms for burstmode SAR data processing, in International Geoscience and Remote Sensing Symposium, Singapore, 3 8 Aug 1997, vol. 2, 1997, pp [12] A. Moreira, J. Mittermayer, and O. Loffeld, Spotlight SAR data processing using the frequency scaling algorithm, IEEE Transactions on Geoscience and Remote Sensing, vol. 37, no. 5, pp , [13] R. Bamler and M. Eineder, ScanSAR processing using standard high precision SAR algorithms, IEEE Transactions on Geoscience and Remote Sensing, vol. 34, no. 1, pp , [14] N. J. Fliege, Multirate digital signal processing. New York: John Wiley & Sons, Ltd, 1994.