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The scientist's signal processing toolbox for realtime frequency domain characterization of given systems, in particular ones made by state of the art nanooptical engineering, is incomplete. Nowadays the standard method for the spectral decomposition of time varying signals still uses a computational technique, that is older than 40 years. There exists a vast amount of literature on the challenge of workaround modifications and on refinement proposals to overcome the experimental bottlenecks of the Fast Fourier Transformation in realtime applications. This is a true motivation to rethink the analysis strategy. The thesis demonstrates unequivocally that a powerful alternative to the Fast Fourier Transformation can be provided by adaptive filtering, which is much more flexible, less computational demanding and also faster in realtime spectrum analysis than the prior standard. The train of thoughts on the new method and the experimental results on adaptation dynamics are published here for the first time. We denote the tool as the Adaptive Spectrum Analysis Filter (ASA). The digital signal processing algorithm is evaluated in an atomic force microscope. The custom made instrument is designed to characterize nano resonances of piezomechanical actuators. The modes are sensed by means of a cantilever probe utilizing the well known beam deflection principle that turns the oscillations into a measurable analog voltage. The innovative realtime application of adaptive spectrum analysis decomposes the system response time resolved into the Fourier components and thus determines the complex mechanical transfer function of the actuators. The thesis reports on single line analysis as well as broadband spectral characterization experiments. The degree of complexity – defined here as the logarithmic ratio of system to structure size – is a most relevant and rapidly growing technology parameter. Typical values are on the order of 5 to 6. The study of such systems is a big challenge with respect to the instrument design. Said atomic force microscope is part of a nanocartographer that integrates micro and nano mechanical components by an innovative design to measure the system properties spatially resolved. The resolution limit of 10 nm on a navigation range of 10 cm equals a complexity degree of 7 and is demonstrated by coordinate based imaging of artificial opal films and large scale optical gratings. The nanocartographer plays the role of a nanooptical model system that is featured to qualify the new method of realtime spectrum analysis and to quantify the adaptation properties of the proposed algorithm. The nonlinear analysis techniques involved are rooted in adaptive Kalman filtering. The presented experiments and simulations give proof that a realtime implementation of the strategy on a digital signal processor (DSP) is clearly advantageous as compared to the customary Fast Fourier Transformation. Having up to a 10-fold less numerical effort the adaptive approach allows for a local refinement of the spectral resolution in the frequency domain, where the numerics can be tailored to the observation task in order to obtain a further reduced effort. In case of single frequency analysis the response time constant decreases by a factor of 10. In the course of this project new possibilities of interdisciplinary applications showed up. To give an example : the method has been successfully ported from nanooptics to electrical engineering. Grid harmonics in a public power network have been spectrally decomposed. Moreover compensation mechanisms utilizing solar grid inverters were realized to achieve an effective damping of the harmonics. The application is patented and published under WO 2009/056158 A1. |
