|
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.
|
