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A Note on the Focusing module

 

 

This module provides the functionalities to process Synthetic Aperture Radar (SAR) data, in RAW format, acquired by the following spaceborne sensors: ERS-1/2, JERS-1, ENVISAT ASAR, ALOS PALSAR and Sentinel-1.

 

In the RAW data, the SAR signal energy reflected from one single point is spread along both azimuth and range direction; the purpose of SAR focussing is to collect this dispersed energy into a single pixel. This process, which involves a complex mathematical procedure,  consists of:

 

The focusing process is carried out, by means of an ω-k processor, to obtain Single Look Complex data (SLC) where the signal Intensity is related to the ground electromagnetic reflectivity, while the phase is related to the acquisition geometry and to the ground topography.

 

Note that:

–Single Look Complex data generated with this module are not appropriate to derive absolutely radiometric calibrated values.

–The multitemporal combination (e.g. Persistent Scatterers module, multi-temporal filtering, etc.) of single look, ground range or geocoded SARscape products - coming from original Level 0 (i.e. RAW data) and Level 1 (i.e. SLC or Ground Range data) standard products - cannot be done due to not comparable digital numbers between.  

 

Note that:

–Default setting for selected parameters can be specified in the Preferences panel.

–The SAR Tutorial, which includes basic knowledge on SAR theory and data processing, complements the online help.

 

Technical Note

 

The ω-k processor, first developed by F. Rocca [1], [2], [3], represents the porting to Synthetic Aperture RADAR systems of the wavenumber-domain migration, an algorithm in use in the geophysics community since early 80’s. It was R. Stolt in 78 [4], who derived a close form expression of a frequency domain interpolation scheme, namely ”Stolt Interpolation”, that allows the implementation of quite a simple focusing scheme that exploits a couple of 2D Fast Fourier Transform (FFT). Thanks to the Solt interpolation, a complicated space-varying performed by a simple, cost less, and quite efficient Fourier based, ”Fast Convolution”. The technique accuracy, due to the exactness of the transfer function, and at the same time its simplicity (just some 100 lines of C++ code), make the Stolt Interpolation based ω-k algorithm, one of the best candidates for SAR processing. Stolt migration has been applied for wavelength ranging from tenths of meters in geophysics, down to millimetres. Its capability to process data acquired within aperture from 0 to 89 deg. [5] makes it appealing for Ultra Wide Aperture (UWA) systems [6], [7], whereas its (theoretically) infinite depth of focusing makes it suited for Ultra Wide Band (UWB) systems, [7], [8], [9],[10]. Furthermore, it has been shown that the ω-k algorithm is quite suited to integrate a motion compensation scheme (when the sensor orbit is no longer straight) [11], [12], [13], and to be adapted to bistatic survey [9], [14], [15], [16]. The algorithm is naturally suited to process different kind of SAR acquisitions: from STRIPMAP [1], [17], [18], [19] to SPOTLIGHT [20] [21] and SCANSAR [22],[23]. Compared to the Range-Doppler algorithm, the ω-k is more efficient as it is a full 2D FFT approach (being an FFT based-approach, the gain in efficiency reduces as the impulse response becomes short, like for low resolution SARs), and has not the strong limitation in bandwidth and antenna aperture, as it does not involve approximations. Compared to other wave-number domain algorithms, like the Chirp-Scaling approach, the ω-k attains similar computational complexity, yet being simpler in its formulation (hence, to be implemented) and - at the same time – involving no approximations on antenna aperture and resolution [18]. That is the reason why the processor is preferred for high resolution or high aperture SARs. Compared to other exact wave-number domain algorithm, like the Exact Transfer Function [18], [24]. That is the reason the list of groups that proposed variant of the ω-k algorithm is large including, besides Politecnico di Milano and Politecnico di Bari [1], [2], [3], DLR (Germany) [25], [18], CNR-IREA (Italy) [17], Defence Research Establishment (FOA, Sweden), [8], University of British Columbia (UBC, Canada) [19], State University of New York [9], [26], Georgia Institute of Technology, [7], JRC (Ispra, Italy) [27], University of Illinois at Urbana [6], [5], Research Establishment for Applied Science (FGAN, Germany)[16]), etc.

 

It may occur that azimuth ambiguities, ghosts or similar image artifacts (especially visible in azimuth direction) are reported. These problems are generally more visible where the signal is very low (i.e. over water bodies).

These effect are typically related to variations in the SAR instrument performance, which are quite normal during the satellite life. The configuration of the focusing algorithm, which is designed in a way to obtain the best signal resolution by exploiting - in azimuth - the largest available bandwidth, depends on specific parameters which are different depending on sensor and acquisition mode (they are stored in the "description_files" folder of the SARscape installation directory). The sarmap technical team continuously adapts these parameters upon known antenna performance variations; however, in case of any unexpected image artifact, users are kindly asked to contact us and provide relevant data samples in order to optimize the focusing performance.

 

References

 

[1] Fabio Rocca. Synthetic aperture radar: "A new application for wave equation  techniques". SEP-56:167--189, 1987.

[2] Claudio Prati, Fabio Rocca, Andrea Monti Guarnieri, and Elvio Damonti: "Seismic migration for SAR focussing: Interferometrical  applications".  28(4):627--640, July 1990.

[3] Ciro Cafforio, Claudio Prati, and Fabio Rocca: "Data focusing using seismic migration techniques". 27(2):199--207, March 1991.

[4] R Stolt: "Migration by Fourier transform". 43:23--48, 1978.

[5] N Cadalli and D C Munson Jr.: "A simulation study of the  w -k SAR algorithm for the highly  squinted case with application to runway imaging". Proc. ICIP-2000, IEEE International Conference, volume 1,  pages 693--696, 2000.

[6] H Choi amd D C Munson Jr.: "On the optimality and exactness of wavenumber-domain SAR data  processing". Proc. ICIP-94, IEEE International Conference, volume 1,  pages 456--460, 1994.

[7] M C Cobb and J H McClellan: "Omega-k quadtree UWB SAR focusing". Proc. 2001 RADAR Conference, volume 1, pages 311--314, 2001.

[8] Hans Hellsten and Lars E Andersson: "An inverse method for the processing of synthetic aperture radar data". 3:111--124, 1987.

[9] Mehrdad Soumekh: "A system model and inversion for synthetic aperture radar".  1(1):64--76, January 1992.

[10] Mehrdad Soumekh: "Reconnaissance with ultra wideband UHF synthetic aperture radar". Pages 21--60, July 1995.

[11] J R Berryhill: "Wave equation datuming". 44(8):1329--1344, August 1979.

[12] G Fornaro: "Trajectory deviations in airborne SAR: analysis and compensation". 35(3):997--1008, July 1999.

[13] A Reigber, A Potsis, E Alivizatos, and A Moreira: "Wavenumber domain SAR focusing with integrated motion compensation". International Geoscience and Remote Sensing Symposium, Toulouse, France, 21--25 July 2003, pages cdrom, 3 pages, 2003.

[14] S Deregowski and F Rocca: "Geometrical optics and wave theory of constant offset sections in layered media". 29:374--406, 1981.

[15] Davide D'Aria, Andrea Monti Guarnieri, and Fabio Rocca: "Focusing bistatic synthetic aperture radar using dip move out". 42(7):1362--1376, 2004.

[16] J H G Ender: "A step to bistatic SAR processing". EUSAR'04, Ulm, Germany, 2004.

[17] G Franceschetti and G Schirinzi: "A SAR processor based on two dimensional FFT codes".  26:356--366, 1990.

[18] Richard Bamler: "A comparison of range-Doppler and wave-number domain SAR focusing algorithms".  30(4):706--713, July 1992.

[19] I G Cumming, Y L Neo, and F H Wong: "Interpretations of the omega-k alogrithm and comparisions with other  algorithms". International Geoscience and Remote Sensing Symposium,  Toulouse, France, 21--25 July 2003, pages cdrom, 3 pages, 2003.

[20] C Prati, A. Monti Guarnieri, and F. Rocca: "SAR focusing with the w-k technique". International Geoscience and Remote Sensing Symposium, Espoo,  Finland, 3--6 June 1991, pages 631--634, 1991.

[21] Walter G Carrara, Ron S Goodman, and Ronald M Majewski. Artech House, Boston, 1995.

[22] Andrea Monti Guarnieri and Claudio Prati:  "ScanSAR focussing and interferometry".  34(4):1029--1038, July 1996.

[23] Richard Bamler: "Adapting precision standard SAR processors to ScanSAR". International Geoscience and Remote Sensing Symposium,  Florence, Italy, 10--14 July 1995, volume 3, pages 2051--2053, 1995.

[24] C Y Chang, M Y Jin, and J C Curlander: "SAR processing based on the exact two-dimensional transfer function". International Geoscience and Remote Sensing Symposium,  Houston, Texas, USA, May 26--29 1992, pages 355--359, 1992.

[25] Andreas Reigber and Rolf Scheiber: "Airborne differential SAR interferometry: First results at  L-band".  41(6):1516--1520, June 2003.

[26] Mehrdad Soumekh: "Wide bandwidth continuous wave monostatic/bistatic synthetic aperture  radar imaging". International Conference on Image Processing, 4--7 October  1998, volume 3, pages 361--365, 1998.

[27] J M Lopez-Sanchez and J Fortuny-Guasch: "3-d radar imaging using range migration techniques". 48(5):728--737,  2000.