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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 11, NOVEMBER 2014
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Estimation and Compensation of Phase Shifts in SAR Focusing of Spotlight Data Acquired With Discrete Antenna Steering V. Zamparelli, P. S. Agram, and G. Fornaro, Senior Member, IEEE
Abstract—Modern spaceborne synthetic aperture radar sensors are able to operate the spotlight mode to achieve very high resolution images at microwave frequencies. This mode is characterized by antenna steering to increase the illumination interval. The steering is carried out by beam switching on bursts during the data acquisition interval. In addition to an unavoidable spectrum modulation in azimuth, phase shifts can occur from burst to burst. In this letter, we describe the problem and a procedure able to estimate the phase shifts based on the image contrast maximization technique for subsequent compensation at the data focusing stage. Results on real data acquired by the COSMO-SkyMed sensor demonstrate the effectiveness of the proposed solution. Index Terms—Image contrast method, spotlight mode, synthetic aperture radar (SAR) focusing.
I. I NTRODUCTION
S
YNTHETIC aperture radar (SAR) systems can image an area on the ground in different operating modes. The standard one is the stripmap mode, in which the antenna points toward a fixed direction with respect to the flight platform path, i.e., the antenna footprint covers a parallel strip on the imaged surface as the platform moves along the track. In this letter, we focus on an operating mode that allows generating highresolution images, i.e., the spotlight mode. In this mode, the sensor steers the antenna beam in such a way that it restricts the imaged terrain strip along the azimuth direction [1]. Modern SAR sensors are equipped with active antennas formed by transmitting/receiving (TX/RX) modules capable of beam setting on a pulse repetition interval (PRI) basis. In the spotlight mode, the imaging platform steers the antenna to increase the illumination interval of a target, thus synthesizing a virtual antenna much larger than the antennas that can be achieved with the stripmap mode and providing a much finer azimuth resolution [2], [3]. The spotlight mode is hence a practical choice when the objective is to collect fine-resolution data over small scenes. The stripmap mode, on the other hand, is tailored to coarser resolution mapping of large regions.
Manuscript received December 16, 2013; revised February 20, 2014; accepted March 12, 2014. V. Zamparelli and G. Fornaro are with the Institute for Electromagnetic Sensing of the Environment (IREA), National Research Council (CNR), 80124 Napoli, Italy (e-mail: [email protected]; [email protected]). P. S. Agram is with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2014.2313914
A pure spotlight mode, i.e., the staring spotlight mode, is achieved by changing the antenna pointing in such a way that the beam of the antenna always illuminates the same area on the ground [4], enabling us to acquire very high resolution images. For some applications, it is however necessary to achieve a tradeoff between the coverage of stripmap mode and the increased azimuth resolution of the staring spotlight mode through the so-called hybrid (or sliding spotlight) acquisition mode. The main characteristic of this mode is that the radar antenna beam is steered about a point under the ground in a manner that produces a sliding footprint (with respect to the staring case) on the ground. Accordingly, it is possible to generate an image whose azimuth size is larger than that achieved in the spotlight mode with an azimuth resolution intermediate between the stripmap and staring spotlight cases [5], [6]. When the system is operating in the spotlight (staring or sliding) mode, an electronic beam steering of the antenna is adopted. In principle, the antenna beam pointing should be changed continuously on a PRI basis over time. In many cases, such as COSMO-SkyMed (CSK), RADARSAT-2, and TerraSAR-X, the antenna beam steering is carried out on the TX/RX modules on a burst basis. The burst antenna switch impacts the azimuth spectrum and leads to a degradation of the impulse response function. This effect has been clearly detected on modern X-band high-resolution systems [7] and can be mitigated either by reducing the size of the burst, i.e., by increasing the number of antenna steering (switches), or by including prewhitening filters on the received bursts. In addition to the amplitude modulation, the discrete antenna steering process can introduce other effects. Due to possible spurious delays in the phase shifters that implement the radiation pattern, phase offsets can be present on the received data from burst to burst with respect to the expected phase excursion due to the change of the target to sensor distance. Other effects can be related to the atmospheric phase delay variations due to the change of the incidence angle, under which radiation crosses the atmosphere during the illumination interval: This effect can be modeled to a zero order as the phase shifts from burst to burst. In cases of long bursts, the zero-order approximation could not be valid; hence, the proposed approach should be applied with reference to subburst. The presence of phase offsets between bursts results in suboptimally focused images, if not properly accounted for at the data focusing stage. In this letter, we propose an algorithm aimed at the estimation and compensation of phase shifts between bursts in the synthetic
1545-598X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
1922
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 11, NOVEMBER 2014
Fig. 1. Sliding spotlight acquisition geometry.
aperture image formation. The procedure, which is easily implemented in any processing chain, is based on the burst-toburst focusing of the different looks of the acquisition and uses the contrast maximization method. An experiment carried out on the real data acquired by the CSK constellation in the spotlight mode is included to demonstrate the effectiveness of the estimation/compensation approach.
Fig. 2. Staircase approximation of the aspect angle: ideal continuous (blue) and real bursted (red) beam pointing. A reduction of the number of bursts (10) with respect to the real case (50) corresponding to experimental results of Section III has been used to emphasize the effect of the approximation.
where γ(x) is thescene reflectivity function, λ is the sensor wavelength, R = r2 + (x − x)2 is the sensor-target distance evaluated in the chosen reference system, and w(·) is the antenna illumination pattern. From (2), we obtain the following relation between the aspect angle and the hybrid factor: (1 − A)x = −r tan ϕ(x ).
II. S IGNAL A NALYSIS OF S POTLIGHT DATA W ITH D ISCRETE B EAM S TEERING We start the analysis by considering the sliding spotlight geometry of Fig. 1. The reference system is (x, r), with the x-axis assumed coincident with the (rectilinear) platform flight path (azimuth) and r being the distance coordinate from the flight path. The sensor moves at a constant velocity v along the azimuth direction and acquires the raw data in a generic position x within the trajectory flight portion XI . In the sliding spotlight mode, the antenna is steered during flight along the azimuth direction to an ideal point located under the ground, which is called T in Fig. 1. Hence, the generic target S ≡ (x, r) is illuminated by the antenna beam only if the radar sensor is between the positions xmin and xmax . Each sensor position xi is associated with a different antenna steering angle ϕ(x ), which is, in simple words, the angle under which the antenna acquires the ideal echo of point T . A (positive) parameter takes into account the hybrid imaging mode, which is called the hybrid factor, and is defined as follows: A=
Δr vf = ≤1 v r + Δr
In the ideal spotlight modes, the beam is always pointing around the point on (staring) or under (sliding) the ground. As a consequence, the beam illuminating the scene (staring) or the ideal plane under the ground (sliding) is fixed (see Fig. 1). In the real cases, the beam orientation is changed over bursts of transmitted pulses, i.e., a discretization of the rotation is achieved through a staircase (zero order) approximation of the ideal steering ϕ(x ) (see Fig. 2). The difference between the approximated and ideal aspect angle variations causes the presence of periods of sliding followed by backward jumps of the footprint on the plane, including the steering point. By considering N burst and letting XB = (XI /N ) the following discrete grid: xi = xmin + (i − 1)XB
(4)
we have
h1 (x ) =
N
dx γ(x)e−j
4π λ R(x −x, r)
i=1
(1)
where r + Δr is the minimum sensor-target distance for the steering point (located under the ground), v is the platform velocity, and vf (< v) is the velocity of the antenna footprint on the ground. A = 0 identifies the staring spotlight case, A = 1 is the stripmap case, and 0 < A < 1 is the sliding spotlight mode [6]. We consider, for simplicity, the azimuth component of the SAR system transfer function: The extension to the 2-D case is straightforward, i.e., x −j 4π R(x −x,r) 2 λ w (Ax − x)rect h(x ) = γ(x)e dx XI (2)
(3)
×rect
w2 (x − x − xdi )
x − xi − XB /2 XB
(5)
where xdi = r tan ϕi .
(6)
The situation corresponding to the generic ith element of the sum in (5) is depicted in Fig. 3. III. B URST- TO -B URST P HASE S HIFTS AND E STIMATION P ROCEDURE To account for the existence of a possible phase shift in the azimuth ramp code generation as well as possible phase delays
ZAMPARELLI et al.: ESTIMATION AND COMPENSATION OF PHASE SHIFTS IN SAR FOCUSING
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associated with an adjacent look pair γˆci (x ) = ejδi γˆi (x ) + γˆi+1 (x )ejΔδi x ∈ Ici .
(11)
For each (adjacent) looks pair, the domain over which the image contrast analysis is carried out is provided by the intersection of the azimuth samples corresponding to the two looks. The domain of interest for the generic ith look is centered on the output azimuth (slow) time toi given by [11] toi = ti − fdi /α
Fig. 3.
Effect of discrete aspect change across two adjacent bursts.
due to atmospheric phase propagation during the acquisition interval, we introduce the presence of phase offsets from burst to burst, i.e., h1 (x ) =
N
h1i (x ) ejδi
(7)
(12)
where ti = (xi /v) is the azimuth time of the ith burst, fdi = 2v sin ϕi /λ is the average Doppler frequency of the ith look, and α = 2v 2 /(λr) is the Doppler rate. The sequential implementation of the ICM procedure over all adjacent looks provides the measurements of all the variations of the relative phase offsets (Δδi ). Finally, the phase offsets for each beam are estimated by combining the phase offsets between adjacent pairs as follows: δi =
i−1
Δδj
δ1 = 0
(13)
j=1
i=1
where δi is the phase offset corresponding to burst i that we aim to estimate and compensate. The independent focusing of the raw data (hi ) corresponding to each burst i following known approaches [3], [6], [8], [9] produces the focused image look γˆi (x ). The correct focused image can be then generated as a coherent sum of properly phase compensated looks, i.e.,
γˆ (x ) =
N
γˆi (x ) e−jδi .
(8)
i=1
Neglecting the phase offsets δi between the looks corresponding to various bursts would hence result in suboptimally focused images. Phase offsets between adjacent bursts can be estimated via the use of the image contrast maximization (ICM) technique [10], which maximizes the image contrast during the combination of looks, i.e., the normalized effective power of the image intensity, and gives a measure of the image focusing. The ICM phase calibration of looks is based on the concept that, in a focused image, each scatterer provides a strong peak of the intensity; hence, the contrast is improved. On the contrary, in a defocused image, the intensity levels are concentrated around the mean value, and the contrast is low [10]. More specifically, by letting Δδi = δi+1 − δi ,
i = 1, . . . , N − 1
(9)
and E[·] be the spatial mean function, it is possible to perform a “look by look” analysis, to evaluate the image contrast for every couple of adjacent focused looks, by maximizing the image contrast as follows: E [|ˆ γci | − E (|ˆ γci |)]2 (10) IC = E (|ˆ γci |)
and are applied to each look in (8) to mitigate their effects on the final image. Alternatively, the ICM procedure can be applied to azimuth looks of a range portion of the data, and the estimated shifts can be compensated at the raw data level before the application of focusing procedures able to process in one shot the data corresponding to all the integration interval [3], [6]. IV. R ESULTS To validate the analysis addressed earlier, we now present some results performed on real data. We used CSK [12] data provided within the framework of the CSK AO Project 2103, relevant to the city of Matera (South Italy) during 2009. The image, covering an area of approximately 7 km × 7 km, is composed of 22 134 range records (azimuth length), and the system adopts the use of 50 bursts, each one of 434 azimuth samples. The relevant system parameters are a chirp bandwidth of 342 MHz, an azimuth resolution of 0.80 m, and a central frequency of 9.6 GHz. The ICM procedure has been applied to all the 49 adjacent looks. In Fig. 4, three (out of the 50 looks) looks, corresponding to the 20th, 25th, and 30th looks, are shown to highlight the presence of common areas for the implementation of the image contrast procedure. Fig. 5 shows the phase offset values estimated between each of the 49 look couples (pairs of adjacent bursts), whereas Fig. 6 represents the estimated phase shift behavior after integration. In Fig. 7, we show the focused image relevant to the whole area of interest; azimuth is horizontal, and range is vertical. Furthermore, in Fig. 8, a zoom in on an industrial area is shown to perceive the focusing capabilities of the proposed approach and the impressive quality of CSK data. To demonstrate the improvement associated with the compensation of the phase shifts, we show in Fig. 9 the images obtained without (top) and
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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 11, NOVEMBER 2014
Fig. 6. Phase shifts of the looks after integration of the phase-shift differences shown in Fig. 5.
Fig. 4. Three looks of the CSK data generated from three different bursts.
Fig. 7.
Focused image on the whole area.
Fig. 8.
Zoom in on an industrial area.
Fig. 5. Phase shifts between adjacent looks.
with (bottom) the application of the proposed procedure. By comparing the images, it is possible to appreciate the mitigation of sidelobes in azimuth in the image obtained by applying the ICM-based phase-shift compensation (lower image). Fig. 10 shows the azimuth profile of the amplitude response of the strong scatterer indicated by the arrow in Fig. 9: From this figure, the improvement in terms of sidelobe reduction (see the arrows) is evident. In order to assess the nature of the phase shifts, we also estimated the phase variation corresponding to the propagation through the atmosphere via the model used in [13]. The analysis demonstrated that the phase variation
induced by the atmosphere for our test data set is limited to values below 5◦ , which is significantly smaller than the offsets shown in Fig. 6.
ZAMPARELLI et al.: ESTIMATION AND COMPENSATION OF PHASE SHIFTS IN SAR FOCUSING
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on real data. The procedure allows us to compensate for the presence of phase shifts due to spurious phase delays occurring in the synthesis of the different beams in a spotlight acquisition, which can be either associated to the antenna switch mechanism or to (unknown and unmodeled) the atmosphere of phase delay variation in very high resolution systems characterized by large excursion of the aspect angles. Once estimated, for instance on a range subportion of the image, the phase offsets can be directly applied, at a prefocusing phase calibration stage, to the raw data bursts. It is also worth to note that, should the phase offsets be systematic for the sensor, they could be estimated only once for each specific antenna switching and corrected on the raw data prior to the application of the classical efficient SAR focusing algorithms, such as for instance the one in [6]. ACKNOWLEDGMENT The authors would like to thank the Italian Space Agency for providing, under the AO 2103 “Advanced Focusing of COSMO-SkyMed Data,” the real data used in this letter. R EFERENCES
Fig. 9. Effect of the phase offset compensation: (top) image without the compensation shows higher levels of sidelobes with respect to (bottom) the one obtained compensating the phase shifts.
Fig. 10. Azimuth profile of the amplitude of the central strong scatterer in Fig. 9 indicated by the arrow (black dashed line) before and (red continuous line) after correcting the phase offsets.
V. C ONCLUSION This letter has addressed the problem of estimating and compensating possible intraburst phase shifts in spotlight data focusing. A method for the estimation of the phase offsets based on the ICM technique has been proposed and tested
[1] G. Franceschetti and R. Lanari, Synthetic Aperture Radar Processing. Boca Raton, FL, USA: CRC Press, 1999. [2] W. G. Carrara, R. S. Goodman, and R. M. Majewski, Spotlight Synthetic Aperture Radar Signal Processing Algorithms. Norwood, MA, USA: Artech House, 1995. [3] R. Lanari, M. Tesauro, E. Sansosti, and G. Fornaro, “Spotlight SAR data focusing based on a two-step processing approach,” IEEE Trans. Geosci. Remote Sens., vol. 39, no. 9, pp. 1993–2004, Sep. 2001. [4] J. Mittermayer, S. Wollstadt, P. Prats-Iraola, and R. Scheiber, “The TerraSAR-X staring spotlight mode concept,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 6, pp. 3695–3706, Jun. 2014. [5] P. Belcher and C. J. Backer, “High resolution processing of hybrid stripmap/spotlight mode SAR,” Proc. Inst. Elect. Eng.—Radar Sonar Navig., vol. 143, no. 6, pp. 366–374, Dec. 1996. [6] R. Lanari, S. Zoffoli, E. Sansosti, G. Fornaro, and F. Serafino, “New approach for hybrid stripmap/spot light SAR data focusing,” Proc. Inst. Elect. Eng.—Radar Sonar Navig., vol. 148, no. 6, pp. 363–372, Dec. 2001. [7] J. Mittermayer et al., “TerraSAR-X system performance characterization and verification,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 2, pp. 660–676, Feb. 2010. [8] V. Zamparelli, G. Fornaro, R. Lanari, S. Perna, and D. Reale, “Processing of sliding spotlight SAR data in presence of squint,” in Proc. IEEE IGARSS, Munich, Germany, Jul. 2012, pp. 2137–2140. [9] P. Prats-Iraola et al., “On the processing of very high resolution spaceborne SAR data,” IEEE Trans. Geosci. Remote Sens., vol. 52, no. 10, Oct. 2014, to be published. [10] M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” Proc. Inst. Elect. Eng.—Radar Sonar Navig., vol. 152, no. 4, pp. 253–262, Aug. 2005. [11] M. Eineder, N. Adam, R. Bamler, N. Yague-Martinez, and H. Breit, “Spaceborne spotlight SAR interferometry with TerraSAR-X,” IEEE Trans. Geosci. Remote Sens., vol. 47, no. 5, pp. 1524–1535, May 2009. [12] F. Covello, F. Battazza, A. Coletta, G. Manoni, and G. Valentini, “COSMO-SkyMed mission status: Three out of four satellites in orbit,” in Proc. IGARSS, Cape Town, South Africa, Jul. 12–17, 2009, pp. II-773–II-776. [13] P. Prats-Irola et al., “High precision SAR focusing of TERRASAR-X experimental staring spotlight data,” in Proc. IEEE IGARSS, Munich, Germany, Jul. 2012, pp. 3576–3579.
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Estimation and Compensation of Phase Shifts in SAR Focusing of Spotlight Data Acquired With Discrete Antenna Steering V. Zamparelli, P. S. Agram, and G. Fornaro, Senior Member, IEEE
Abstract—Modern spaceborne synthetic aperture radar sensors are able to operate the spotlight mode to achieve very high resolution images at microwave frequencies. This mode is characterized by antenna steering to increase the illumination interval. The steering is carried out by beam switching on bursts during the data acquisition interval. In addition to an unavoidable spectrum modulation in azimuth, phase shifts can occur from burst to burst. In this letter, we describe the problem and a procedure able to estimate the phase shifts based on the image contrast maximization technique for subsequent compensation at the data focusing stage. Results on real data acquired by the COSMO-SkyMed sensor demonstrate the effectiveness of the proposed solution. Index Terms—Image contrast method, spotlight mode, synthetic aperture radar (SAR) focusing.
I. I NTRODUCTION
S
YNTHETIC aperture radar (SAR) systems can image an area on the ground in different operating modes. The standard one is the stripmap mode, in which the antenna points toward a fixed direction with respect to the flight platform path, i.e., the antenna footprint covers a parallel strip on the imaged surface as the platform moves along the track. In this letter, we focus on an operating mode that allows generating highresolution images, i.e., the spotlight mode. In this mode, the sensor steers the antenna beam in such a way that it restricts the imaged terrain strip along the azimuth direction [1]. Modern SAR sensors are equipped with active antennas formed by transmitting/receiving (TX/RX) modules capable of beam setting on a pulse repetition interval (PRI) basis. In the spotlight mode, the imaging platform steers the antenna to increase the illumination interval of a target, thus synthesizing a virtual antenna much larger than the antennas that can be achieved with the stripmap mode and providing a much finer azimuth resolution [2], [3]. The spotlight mode is hence a practical choice when the objective is to collect fine-resolution data over small scenes. The stripmap mode, on the other hand, is tailored to coarser resolution mapping of large regions.
Manuscript received December 16, 2013; revised February 20, 2014; accepted March 12, 2014. V. Zamparelli and G. Fornaro are with the Institute for Electromagnetic Sensing of the Environment (IREA), National Research Council (CNR), 80124 Napoli, Italy (e-mail: [email protected]; [email protected]). P. S. Agram is with the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2014.2313914
A pure spotlight mode, i.e., the staring spotlight mode, is achieved by changing the antenna pointing in such a way that the beam of the antenna always illuminates the same area on the ground [4], enabling us to acquire very high resolution images. For some applications, it is however necessary to achieve a tradeoff between the coverage of stripmap mode and the increased azimuth resolution of the staring spotlight mode through the so-called hybrid (or sliding spotlight) acquisition mode. The main characteristic of this mode is that the radar antenna beam is steered about a point under the ground in a manner that produces a sliding footprint (with respect to the staring case) on the ground. Accordingly, it is possible to generate an image whose azimuth size is larger than that achieved in the spotlight mode with an azimuth resolution intermediate between the stripmap and staring spotlight cases [5], [6]. When the system is operating in the spotlight (staring or sliding) mode, an electronic beam steering of the antenna is adopted. In principle, the antenna beam pointing should be changed continuously on a PRI basis over time. In many cases, such as COSMO-SkyMed (CSK), RADARSAT-2, and TerraSAR-X, the antenna beam steering is carried out on the TX/RX modules on a burst basis. The burst antenna switch impacts the azimuth spectrum and leads to a degradation of the impulse response function. This effect has been clearly detected on modern X-band high-resolution systems [7] and can be mitigated either by reducing the size of the burst, i.e., by increasing the number of antenna steering (switches), or by including prewhitening filters on the received bursts. In addition to the amplitude modulation, the discrete antenna steering process can introduce other effects. Due to possible spurious delays in the phase shifters that implement the radiation pattern, phase offsets can be present on the received data from burst to burst with respect to the expected phase excursion due to the change of the target to sensor distance. Other effects can be related to the atmospheric phase delay variations due to the change of the incidence angle, under which radiation crosses the atmosphere during the illumination interval: This effect can be modeled to a zero order as the phase shifts from burst to burst. In cases of long bursts, the zero-order approximation could not be valid; hence, the proposed approach should be applied with reference to subburst. The presence of phase offsets between bursts results in suboptimally focused images, if not properly accounted for at the data focusing stage. In this letter, we propose an algorithm aimed at the estimation and compensation of phase shifts between bursts in the synthetic
1545-598X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
1922
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 11, NOVEMBER 2014
Fig. 1. Sliding spotlight acquisition geometry.
aperture image formation. The procedure, which is easily implemented in any processing chain, is based on the burst-toburst focusing of the different looks of the acquisition and uses the contrast maximization method. An experiment carried out on the real data acquired by the CSK constellation in the spotlight mode is included to demonstrate the effectiveness of the estimation/compensation approach.
Fig. 2. Staircase approximation of the aspect angle: ideal continuous (blue) and real bursted (red) beam pointing. A reduction of the number of bursts (10) with respect to the real case (50) corresponding to experimental results of Section III has been used to emphasize the effect of the approximation.
where γ(x) is thescene reflectivity function, λ is the sensor wavelength, R = r2 + (x − x)2 is the sensor-target distance evaluated in the chosen reference system, and w(·) is the antenna illumination pattern. From (2), we obtain the following relation between the aspect angle and the hybrid factor: (1 − A)x = −r tan ϕ(x ).
II. S IGNAL A NALYSIS OF S POTLIGHT DATA W ITH D ISCRETE B EAM S TEERING We start the analysis by considering the sliding spotlight geometry of Fig. 1. The reference system is (x, r), with the x-axis assumed coincident with the (rectilinear) platform flight path (azimuth) and r being the distance coordinate from the flight path. The sensor moves at a constant velocity v along the azimuth direction and acquires the raw data in a generic position x within the trajectory flight portion XI . In the sliding spotlight mode, the antenna is steered during flight along the azimuth direction to an ideal point located under the ground, which is called T in Fig. 1. Hence, the generic target S ≡ (x, r) is illuminated by the antenna beam only if the radar sensor is between the positions xmin and xmax . Each sensor position xi is associated with a different antenna steering angle ϕ(x ), which is, in simple words, the angle under which the antenna acquires the ideal echo of point T . A (positive) parameter takes into account the hybrid imaging mode, which is called the hybrid factor, and is defined as follows: A=
Δr vf = ≤1 v r + Δr
In the ideal spotlight modes, the beam is always pointing around the point on (staring) or under (sliding) the ground. As a consequence, the beam illuminating the scene (staring) or the ideal plane under the ground (sliding) is fixed (see Fig. 1). In the real cases, the beam orientation is changed over bursts of transmitted pulses, i.e., a discretization of the rotation is achieved through a staircase (zero order) approximation of the ideal steering ϕ(x ) (see Fig. 2). The difference between the approximated and ideal aspect angle variations causes the presence of periods of sliding followed by backward jumps of the footprint on the plane, including the steering point. By considering N burst and letting XB = (XI /N ) the following discrete grid: xi = xmin + (i − 1)XB
(4)
we have
h1 (x ) =
N
dx γ(x)e−j
4π λ R(x −x, r)
i=1
(1)
where r + Δr is the minimum sensor-target distance for the steering point (located under the ground), v is the platform velocity, and vf (< v) is the velocity of the antenna footprint on the ground. A = 0 identifies the staring spotlight case, A = 1 is the stripmap case, and 0 < A < 1 is the sliding spotlight mode [6]. We consider, for simplicity, the azimuth component of the SAR system transfer function: The extension to the 2-D case is straightforward, i.e., x −j 4π R(x −x,r) 2 λ w (Ax − x)rect h(x ) = γ(x)e dx XI (2)
(3)
×rect
w2 (x − x − xdi )
x − xi − XB /2 XB
(5)
where xdi = r tan ϕi .
(6)
The situation corresponding to the generic ith element of the sum in (5) is depicted in Fig. 3. III. B URST- TO -B URST P HASE S HIFTS AND E STIMATION P ROCEDURE To account for the existence of a possible phase shift in the azimuth ramp code generation as well as possible phase delays
ZAMPARELLI et al.: ESTIMATION AND COMPENSATION OF PHASE SHIFTS IN SAR FOCUSING
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associated with an adjacent look pair γˆci (x ) = ejδi γˆi (x ) + γˆi+1 (x )ejΔδi x ∈ Ici .
(11)
For each (adjacent) looks pair, the domain over which the image contrast analysis is carried out is provided by the intersection of the azimuth samples corresponding to the two looks. The domain of interest for the generic ith look is centered on the output azimuth (slow) time toi given by [11] toi = ti − fdi /α
Fig. 3.
Effect of discrete aspect change across two adjacent bursts.
due to atmospheric phase propagation during the acquisition interval, we introduce the presence of phase offsets from burst to burst, i.e., h1 (x ) =
N
h1i (x ) ejδi
(7)
(12)
where ti = (xi /v) is the azimuth time of the ith burst, fdi = 2v sin ϕi /λ is the average Doppler frequency of the ith look, and α = 2v 2 /(λr) is the Doppler rate. The sequential implementation of the ICM procedure over all adjacent looks provides the measurements of all the variations of the relative phase offsets (Δδi ). Finally, the phase offsets for each beam are estimated by combining the phase offsets between adjacent pairs as follows: δi =
i−1
Δδj
δ1 = 0
(13)
j=1
i=1
where δi is the phase offset corresponding to burst i that we aim to estimate and compensate. The independent focusing of the raw data (hi ) corresponding to each burst i following known approaches [3], [6], [8], [9] produces the focused image look γˆi (x ). The correct focused image can be then generated as a coherent sum of properly phase compensated looks, i.e.,
γˆ (x ) =
N
γˆi (x ) e−jδi .
(8)
i=1
Neglecting the phase offsets δi between the looks corresponding to various bursts would hence result in suboptimally focused images. Phase offsets between adjacent bursts can be estimated via the use of the image contrast maximization (ICM) technique [10], which maximizes the image contrast during the combination of looks, i.e., the normalized effective power of the image intensity, and gives a measure of the image focusing. The ICM phase calibration of looks is based on the concept that, in a focused image, each scatterer provides a strong peak of the intensity; hence, the contrast is improved. On the contrary, in a defocused image, the intensity levels are concentrated around the mean value, and the contrast is low [10]. More specifically, by letting Δδi = δi+1 − δi ,
i = 1, . . . , N − 1
(9)
and E[·] be the spatial mean function, it is possible to perform a “look by look” analysis, to evaluate the image contrast for every couple of adjacent focused looks, by maximizing the image contrast as follows: E [|ˆ γci | − E (|ˆ γci |)]2 (10) IC = E (|ˆ γci |)
and are applied to each look in (8) to mitigate their effects on the final image. Alternatively, the ICM procedure can be applied to azimuth looks of a range portion of the data, and the estimated shifts can be compensated at the raw data level before the application of focusing procedures able to process in one shot the data corresponding to all the integration interval [3], [6]. IV. R ESULTS To validate the analysis addressed earlier, we now present some results performed on real data. We used CSK [12] data provided within the framework of the CSK AO Project 2103, relevant to the city of Matera (South Italy) during 2009. The image, covering an area of approximately 7 km × 7 km, is composed of 22 134 range records (azimuth length), and the system adopts the use of 50 bursts, each one of 434 azimuth samples. The relevant system parameters are a chirp bandwidth of 342 MHz, an azimuth resolution of 0.80 m, and a central frequency of 9.6 GHz. The ICM procedure has been applied to all the 49 adjacent looks. In Fig. 4, three (out of the 50 looks) looks, corresponding to the 20th, 25th, and 30th looks, are shown to highlight the presence of common areas for the implementation of the image contrast procedure. Fig. 5 shows the phase offset values estimated between each of the 49 look couples (pairs of adjacent bursts), whereas Fig. 6 represents the estimated phase shift behavior after integration. In Fig. 7, we show the focused image relevant to the whole area of interest; azimuth is horizontal, and range is vertical. Furthermore, in Fig. 8, a zoom in on an industrial area is shown to perceive the focusing capabilities of the proposed approach and the impressive quality of CSK data. To demonstrate the improvement associated with the compensation of the phase shifts, we show in Fig. 9 the images obtained without (top) and
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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 11, NO. 11, NOVEMBER 2014
Fig. 6. Phase shifts of the looks after integration of the phase-shift differences shown in Fig. 5.
Fig. 4. Three looks of the CSK data generated from three different bursts.
Fig. 7.
Focused image on the whole area.
Fig. 8.
Zoom in on an industrial area.
Fig. 5. Phase shifts between adjacent looks.
with (bottom) the application of the proposed procedure. By comparing the images, it is possible to appreciate the mitigation of sidelobes in azimuth in the image obtained by applying the ICM-based phase-shift compensation (lower image). Fig. 10 shows the azimuth profile of the amplitude response of the strong scatterer indicated by the arrow in Fig. 9: From this figure, the improvement in terms of sidelobe reduction (see the arrows) is evident. In order to assess the nature of the phase shifts, we also estimated the phase variation corresponding to the propagation through the atmosphere via the model used in [13]. The analysis demonstrated that the phase variation
induced by the atmosphere for our test data set is limited to values below 5◦ , which is significantly smaller than the offsets shown in Fig. 6.
ZAMPARELLI et al.: ESTIMATION AND COMPENSATION OF PHASE SHIFTS IN SAR FOCUSING
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on real data. The procedure allows us to compensate for the presence of phase shifts due to spurious phase delays occurring in the synthesis of the different beams in a spotlight acquisition, which can be either associated to the antenna switch mechanism or to (unknown and unmodeled) the atmosphere of phase delay variation in very high resolution systems characterized by large excursion of the aspect angles. Once estimated, for instance on a range subportion of the image, the phase offsets can be directly applied, at a prefocusing phase calibration stage, to the raw data bursts. It is also worth to note that, should the phase offsets be systematic for the sensor, they could be estimated only once for each specific antenna switching and corrected on the raw data prior to the application of the classical efficient SAR focusing algorithms, such as for instance the one in [6]. ACKNOWLEDGMENT The authors would like to thank the Italian Space Agency for providing, under the AO 2103 “Advanced Focusing of COSMO-SkyMed Data,” the real data used in this letter. R EFERENCES
Fig. 9. Effect of the phase offset compensation: (top) image without the compensation shows higher levels of sidelobes with respect to (bottom) the one obtained compensating the phase shifts.
Fig. 10. Azimuth profile of the amplitude of the central strong scatterer in Fig. 9 indicated by the arrow (black dashed line) before and (red continuous line) after correcting the phase offsets.
V. C ONCLUSION This letter has addressed the problem of estimating and compensating possible intraburst phase shifts in spotlight data focusing. A method for the estimation of the phase offsets based on the ICM technique has been proposed and tested
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