Today, the world of microelectronics, metrology plays a very important role in controlling the manufacture of semiconductors. An optical characterization technique based on the analysis of the diffraction of light by an object, scatterometry, is a very advantageous technic. Indeed, this control technique is nondestructive and can be measured with great precision the dimensions of periodic patterns or isolated. The miniaturization of electronic components requires imperatively needs accurate numerical computation. Among the numerical methods for calculating electromagnetic scattering from networks, the method most commonly used is the Fourier Modal Method (FMM). The problems inherent to this method, as the Gibbs phenomenon, are all the more undesirable it decreases the size of transistors. More generally, the MMF is ineffective for the characterization of structures very isolated or very dense and can not even function at all. The objective of this thesis is to overcome the limitations of the FMM. We remain within the modal methods but we are exploring new ways of using different bases of development that do not have the disadvantages of Fourier bases. First, we introduced the B-spline functions which are the first step towards the multi-resolution analysis with wavelet splines. We formulated the problem of diffraction by a 1D network as an eigenvalue problem that we solved numerically using the Galerkin method. We studied in detail the importance of the discretization with respect to permittivity discontinuities of the function. Then we introduced the wavelet analysis and multiple levels of detail for the diffraction problem. This thesis contains a varied range of numerical examples concerning dielectric and metallic networks. We have carefully compared the convergence of our methods with other methods, especially with the FMM. We have shown that multiresolution analysis can handle cases where the DMF fails.
