13 March 2012 Reconstruction of dynamical perturbations in optical systems by opto-mechanical simulation methods
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High-performance objectives pose very strict limitations on errors present in the system. External mechanical influences can induce structural vibrations in such a system, leading to small deviations of the position and tilt of the optical components inside the objective from the undisturbed system. This can have an impact on the imaging performance, causing blurred images or broadened structures in lithography processes. A concept to detect the motion of the components of an optical system is presented and demonstrated on a simulated system. The method is based on a combination of optical simulation together with mechanical simulation and inverse problem theory. On the optical side raytracing is used for the generation of wavefront data of the system in its current state. A Shack-Hartmann sensor is implemented as a model to gather this data. The sensor can capture wavefront data with high repetition rates to resolve the periodic motion of the vibrating parts. The mechanical side of the system is simulated using multibody dynamics. The system is modeled as a set of rigid bodies (lenses, mounts, barrel), represented by rigid masses connected by springs that represent the coupling between the individual parts. External excitations cause the objective to vibrate. The vibration can be characterized by the eigenmodes and eigenfrequencies of the system. Every state of the movement during the vibration can be expressed as a linear combination of the eigenmodes. The reconstruction of the system geometry from the wavefront data is an inverse problem. Therefore, Tikhonov regularization is used in the process in order to achieve more accurate reconstruction results. This method relies on a certain amount of a-priori information on the system. The mechanical properties of the system are a great source of such information. It is taken into account by performing the calculation in the coordinate system spanned by the eigenmodes of the objective and using information on the spectrum of frequencies present in the current vibration as a-priori data. The position of the individual lenses as a function of time is then calculated from several frames of the wavefront data and extrapolated to future timesteps. Information on the system gathered with this method can be useful for applying and controlling countermeasures against the vibrations during use of the objective or for designing new systems that are less influenced by vibrations.
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H. Gilbergs, N. Wengert, K. Frenner, P. Eberhard, W. Osten, "Reconstruction of dynamical perturbations in optical systems by opto-mechanical simulation methods", Proc. SPIE 8326, Optical Microlithography XXV, 83262N (13 March 2012); doi: 10.1117/12.916615; https://doi.org/10.1117/12.916615

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