Characterisation of Coherent Scatterers in Urban Areas by Means of Angular Diversity Rafael Zandona Schneider, Konstantinos P. Papathanassiou, Irena Hajnsek and Alberto Moreira Microwaves and Radar Institute German Aerospace Center PO BOX 1116, 82230, Wessling, Germany Email: Rafael.Zschneider@dlr.de Abstract— The detection of scatterers with pointwise response in SAR images of urban areas using the so-called Coherent Scatterers (CSs) technique was in previous works introduced [1], [2]. In this paper, the potential to exploit sub-aperture images from wide azimuth angular apertures (as it is the case for air- borne systems) to estimate CSs backscattering radiation patterns is addressed. The backscattering radiation pattern is modeled assuming a simple canonical class of scatterers. The model is then inverted using the estimated radiation patterns of individual CSs and their geometrical parameters are evaluated and related to CSs polarimetric properties. Two experiments using dihedral corner reflectors with differentt azimuth orientation and Line of Sight (LOS) rotation angles were performed, in order to verify the agreement with the theory. The data used are at L-band from the airborne E-SAR system of the German Aerospace Center (DLR) and the testsite is the Munich city in Germany. I. I NTRODUCTION The Coherent Scatterers (CSs) technique to detect scatterers with point-like behaviour in SAR images of urban areas was introduced in [1], [2]. Polarimetric and interferometric characterisation of CSs has been discussed, as well as the potential of physical and geometrical information extraction, as the estimation of the scatterers Line Of Sight (LOS) rotation angle and CSs dielectric properties. In [3] the backscattering radiation pattern in the azimuth direction of the so-called Permanent Scatterers (PSs) was estimated using ERS-2 image series and taking advantage of its loss of the on-board gyroscopes. This allowed to acquire images of the same scene with different azimuth aspect angles. A backscattering pattern model for canonical PSs was used to invert PSs geometrical parameters. In this work, azimuth backscattering radiation patterns of CSs are estimated using multi-look images from wide azimuth bandwidth systems. The backscattering radiation patterns are modeled as in [3] and the model parameters are inverted. Their relationship to the scatterer’s type estimated through polarimetry is investigated. Finally, two experiments using dihedral corner reflectors were performed, in order to verify the agreement with the theory. II. CSS BACKSCATTERING RADIATION PATTERN MODEL Each scatterer in a radar-scatterer interaction reirradiates the incident electromagnetic energy, in a given frequency, according to its geometry and dielectric properties, among another factors. The backscattered energy varies in space array θ θ R 0 L δ(i) δ (i) sin θ E (- n-1 2 ) = a (- n-1 2 ) e j 4π λ ( R 0 - L 2 sin θ ) E (0) = a (0) e j 4π λ R 0 E (i) = a (i) e j 4π λ ( R 0 +δ (i) sin θ ) E ( n-1 2 ) = a ( n-1 2 ) e j 4π λ ( R 0 + L 2 sin θ ) ET = + n-1 2  i=- n-1 2 a(i)e j 4π λ (R0+δ(i) sin θ) L 2 sin θ Fig. 1. Geometry of the backscattering of EM waves by a linear array of elements. forming a pattern that is characteristic for each scatterer. In the case of a finite linear array of elements, for which the electromagnetic wavelength is much smaller than the array size but bigger than the individual elements (for a continuous object the elements are infinitesimal), the situation is that of Fig. 1. The total backscattered field E T received far away from the scatterer (far field approximation) is the coherent sum of all individual fields E (i) backscattered from each element (Fig. 1). Assuming a continuous object of length L constituted of infinitesimal elements that return constant amplitudes of values A/L, the coherent sum of the individual fields becomes E T =  + L 2 - L 2 A L e j 4π λ R0 e j 4π λ δ sin θ dδ (1) leading to E T = Ae j 4π λ R0 sinc  2L λ sin θ  , where sinc(x)= sin(πx) πx (2) In order to allow a possible orientation θ S of the scatterer in relation to the radar, and assuming that θ is small, (2) can be approximated by E T = Ae j 4π λ R0 sinc  2L λ (θ - θ S )  (3) Certain CSs can be considered as such canonical objects and their backscattering radiation pattern can be modelled by