## 2 GRECOSAR
### Overall description  
Electromagnetic (EM) calculations are performed in GRECOSAR via a graphic-based approach for which a bitmap resident in the RAM memory is generated from the input model. By using a particular illumination point of view fixed by the user-defined Line of Sight (LOS) direction, GRECOSAR renders the model with the PC graphic card and isolates the visible entities (edges and surfaces) from the back-facing ones. Over these entities, EM methods are applied making RCS prediction faster and independent of the input geometry. The main EM methods used by GRECOSAR are:  
* Physical Optics (PO) for perfectly conducting surfaces. * Method of Equivalent Currents (MEC) with [PERSON]'s Physical Theory of Diffraction (PTD) coefficients or [PERSON]'s Incremental Length Diffraction Coefficients (ILDC) for perfectly conducting edges. * Multiple reflection analysis by a Geometrical Optics (GO) + PO ray-tracing algorithm. Bi-static GO is used for all reflections except the last one, for which PO is used. GO divergence factors for curved surfaces are computed approximately. All these methods have shown accurate RCS estimation performance according to several tests done in anechoic chambers and comparison with other codes [11; 12]. In practical terms, they allow to analyze targets of electrical size as large as \(2^{n}\lambda/16\), with a maximum phase error of \(\lambda/8\), where \(n\) is the number of bits in which the distance to the observer is discretized. This means that, with a 24-bit discretization, targets as large as \(10^{6}\lambda\) can be managed with \(\lambda\) being the operating wavelength. For a proper GRECO(r) performance, input models should be modelled with parametric surfaces by using CAD tools. In this work, the CAD package GiD(r) of the International Center of Numerical Methods for Engineering [13] has been adopted. Once defined, target models need from an additional tessellation meshing procedure that discretizes parametric surfaces into small planar facets. Otherwise, the PC's graphic card would not be able to deal with target's geometry. Regarding the simulated scenario, any type of POLInSAR sensor can be defined for any desired imaging geometry. For maritime environments, ship bearing, motions and velocity are managed with a surrounding sea surface, which is updated by a user-defined dynamic pattern [8]. Due to GRECO(r) restrictions, the sea is modeled with small facets'taking the dielectric properties of salt water into account. A complex relative permittivity of \(\epsilon=75-j\cdot 27\) has been selected for a salinity of 35 practical salinity units (psu) and a temperature of \(25^{o}C\)[14; 15]. The vertical coordinate of each facet point within the sea (not the ship) is updated at each synthetic aperture position by a dynamic height profile, which is based on the two-scale model adopted in sea height estimation theory [16; 17]. Such option has been selected as better accommodates to the facet-based structure of input models as directly provides the values of the vertical z coordinate. This does not happen for sea spectrum theory [18; 19] where an intermediate bilinear interpolation step, which can increase processing time according to surface dimensions and discretizing accuracy, is required [8]. However, this option permits to easily introduce accurate wind effects on sea scattering and, for this reason, it will be evaluated to be included in GRECOSAR. By now, wind influence is simply tackled by only managing wind orientation. For sake of simplicity, a simple version of the two-scale approach has been used for which a small scale wave modulates the surface of a large scale one along time \(t\) by (see Fig. 1),  
\[h(x,y,t)=h_{l}\cos\{\kappa_{l}x^{\prime}-\sqrt{g\kappa_{l}}t\}+h_{s}\cos\{ \kappa_{s}x^{\prime}-\sqrt{g\kappa_{s}}t\} \tag{1}\]  
where surface dynamics are fixed by \(\sqrt{g\kappa_{i}}\) with \(g\) being the acceleration of gravity and \(\kappa_{i}=2\pi/\lambda_{i}\) the wavenumber vectors of the larger (\(i=l\)) and smaller (\(i=s\)) scale waves.