Hybrid Numerical-Experimental Holographic Interferometry for Investigation of Nonlinearities in MEMS Dynamics

Holographic interferometry is a powerful experimental technique for analysis of structural vibrations, especially if the amplitudes of those vibrations are in the range of micrometers (Caponero et al. (2000); Fagan et al. (1972); Fein (1997); Ganesan et al. (2000); Rastogi (2000); Vest (1979)). Recent advancements in optical measurement technology and development of hybrid numerical-experimental techniques require application of computational algorithms not only for post-processing applications like interpretation of experimental patterns of fringes, but embedding real time algorithms into the measurement process itself (Ragulskis & Saunoriene (2007)). Computation and plotting of patterns of time average holographic fringes in virtual numerical environments involves such tasks as modelling of the optical measurement setup, geometrical and physical characteristics of the investigated structure and the dynamic response of the analysed system (Ragulskis et al. (2003)). Calculation of intensity of illumination at any point on the hologram plane requires computation of definite integrals over the exposure time. If the analysed structures perform harmonic oscillations that do not impose any complications – there exist even analytical relationships between the intensity of illumination, amplitude of oscillation, laser wavelength, etc. But if the oscillations of the investigated structures are non-harmonic (what is commonwhen structures are non-linear) and the formation of patterns of fringes is implemented in the real time mode, the calculation of definite integrals becomes rather problematic. One of the objects of this study is to propose an order adaptive algorithm which could be effectively applicable for calculation of definite integrals in different real time holography applications. Another goal of this study is to show that holographic interferometry, being a non-destructive whole field technique capable of registering micro oscillations of micro electromechanical systems (MEMS) components, cannot be exploited in a straightforward manner (Ostasevicius et al. (2005)). There exist numerous numerical methods and techniques for interpretation of patterns of fringes in the registered holograms of different oscillating objects and surfaces. Unfortunately, sometimes straightforward application of these motion reconstruction Minvydas Ragulskis1, Arvydas Palevicius2 and Loreta Saunoriene3 1,3Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-222, 51638 Kaunas 2International Studies Center, Kaunas University of Technology, A. Mickeviciaus 37, 44244 Kaunas Lithuania Hybrid Numerical-Experimental Holographic Interferometry for Investigation of Nonlinearities in MEMS Dynamics 15