Four-beam laser interferometry for three-dimensional microscopic coordinate measurement.
We propose a new method for calibrating the three-dimensional (3-D) behavior of a scanning stage. Four laser interferometers are used to determine the position of the corner point of a corner mirror attached to the stage. We calculated the 3-D coordinate of the corner point by using only the length information given by the four laser interferometers; thus a method is realized that is traceable from the practical definition of length and that facilitates the optical alignment that is necessary for the interferometers. We calibrated a commercial 3-D stage by the proposed method with a coordinate accuracy of 20-30 nm.
Large free form measurement using slit beam
In heavy industry, 3D surface measurement of large-scale hull pieces is needed for fabrication and assembly. Until now, there is not such an efficient method as a standard ruler on 3D profile measurement of large-scale curvature plates. We suggest an efficient method of 3D profile measurement to obtain the xyz-coordinates of curvature plates. The measurement system comprises a few slit beam lines and performs profile measurement by projecting structured light source on the object surface.
Mean field model of a game for power
Abstract Our aim is to model a game for power (equivalent to total energy) as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods allow to identify a set of stationary states, i.e. fixed points of the model dynamics. The positions of the unstable fixed points give an insight on the basins of attraction of the stable fixed points. The results are interpreted in terms of modeling of coercive power.