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- Resumen es exacto "This work proposes and discusses new optical metrology techniques based on digital signal and image processing that are used in the analysis of materials, microfabrication processes and the functionality of microsystems. Given that microsystems are typically manufactured by using the same techniques as in semiconductor devices industry, the proposed optical techniques are applicable to such _eld of engineering. The proposed methods applied on microsystems with rugosity in the wavelentgh scale were designed by considering the well known properties of speckle _elds. Particularly, a set of methods were evaluated in their performance to determine out-of-plane micro and nanodisplacements in samples subject to deformations. We extended the exact nonlinear reconstruction technique developed for digital holography to improve the phase recovery issue in interferometric methods, that use carrier modulation. It is shown that the analysis of the ridge of the complex wavelet coe_cients corresponding to a nonlinear transformation of the analyzed interferogram can be closely related to the optical phase of the sample minimizing the inuence of the background intensity. We introduce an algorithm for direct phase estimation from a single noisy interferometric pattern by means of implicit smoothing spline (ISS). A simpli_ed method for object phase recovering is also implemented in temporal speckle pattern interferometry by means of a numerical complex modulation and a posterior isolation of the spatiotemporal evolution of the object phase. We use a bivariate empirical mode decomposition framework that avoids the application of the Hilbert transform to analyse amplitude and frequency modulated signals. This Thesis concludes with the design, implementation and comparison of three real-time methods for object phase recovering in temporal speckle pattern interferometry by means of bivariate empirical mode and intrinsic time-scale decompositions. The study of dynamic events linked with the design and development of microsystems is favored by this new real-time processing. The proposed real-time methods avoid the application of the Hilbert transform and improve the accuracy of the measurement by triangulation _ltering of undermodulated pixels. The proposed approaches are compared with state of the art techniques in terms of performance and noise robustness, and the advantages and limitations associated to each method are also discussed. The performance is evaluated by comparing the accuracy of the recovered phase and the computation time by means of numerical simulations. Experimental data obtained from common and simultaneous pi/2 phase-shifting heterodyne interferometry were used to ful_ll the analysis of these new methods in their"
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