## 1 Introduction  
Small gold particles supported on dielectric supports have attracted considerable attention due to their extraordinary properties that are exploited in numerous applications [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. In recent years the main foci of interest have been the optical properties, which are in the visible range and dominated by the excitation of localized surface plasmon polariton resonances, _i.e._, by a collective excitation of the conduction band electrons. For simplicity, we refer to this kind of excitation as plasmon resonance or simply plasmon. In contrary to the correspondent plasma oscillations in bulk material or on a smooth surface, the localized surface plasmon polariton resonances can be excited directly by an incoming electromagnetic wave. Accompanied with the excitation of a plasmon resonance is a greatly enhanced local field in the vicinity of the nanoparticle surface. The optical properties of single spherical particles have been exactly described by [PERSON] [12]. [PERSON] obtained his solution after a multipole expansion of the electromagnetic fields, which yields the extinction cross section of the particles as the sum of absorption and scattering of a series of multipole excitations. For particles much smaller than the wavelength of light, the quasistatic approximation simplifies the general electrodynamic problem into electrostatic [13; 14; 15]. Within this approximation, scattering and higher multipole modes are neglected and the plasmon is solely due to absorption of an electric dipole. The absorption cross section \(\sigma_{abs}\) depends on the photon energy of the incoming electromagnetic wave and on the imaginary part of the polarizability of the nanoparticle:  
\[\sigma_{\rm abs}=k\cdot\texttt{Im}\{\alpha(\omega)\}=4\pi kR^{3}\texttt{Im }\left\{\frac{\varepsilon-\varepsilon_{\rm m}}{\varepsilon+2\varepsilon_{\rm m }}\right\} \tag{1}\]  
In the general case of ellipsoidal metal particles, the polarizability along the axis \(i\) is given by [13; 14; 15; 16]:  
\[\alpha_{i}=V\frac{\varepsilon-\varepsilon_{m}}{\varepsilon_{m}+L_{i}( \varepsilon-1)} \tag{2}\]  
where \(V\) is the particle volume, \(L_{i}\) is the depolarization factor along the \(i\) axis, \(\varepsilon\) and \(\varepsilon_{m}\) are the dielectric constants of the metal and the embedding medium, respectively. A resonance of the polarizability, _i.e._, of the absorption, appears, if the denominator in Equation (2) becomes zero. The resonance condition depends on the depolarization factor \(L_{i}\), which is a function of the particle eccentricity, _i.e._, of its shape. According to Equation (2), for ellipsoidal nanoparticles three plasmon resonances can be excited. Since the plasmon resonance is highly sensitive to the nanoparticle morphology, optical spectroscopy has widely been used as a characterization tool [17; 18; 19; 20; 21; 22]. While the position of the plasmon resonance is sensitive to the particle morphology and environment, its width is usually a superposition of homogeneous and inhomogeneous broadening. The homogeneous broadening is related by the dielectric constant to the electronic properties of the metal and eventually to the surrounding, while inhomogeneous broadening is caused by the width of the size and shape distribution of a nanoparticle ensemble. Although theoretical modeling is widely used to characterize nanoparticle ensembles, the full potential of the optical properties has not been exploited for a long time, due to a lack of adequate modeling, as pointed out in [23]. Since for plenty applications of noble metal nanoparticles the optical and, thus, the morphological parameters are of enormous interest, one would like to determine the size and shape of the nanoparticles as precisely as possible. Different techniques are employed to characterize the particle morphology [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39].