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.
New algorithms for motion error detection of numerical control machine tool by laser tracking measurement on the basis of GPS principle.
As a three-dimensional measuring instrument, the laser tracker is widely used in industrial measurement. To avoid the influence of angle measurement error on the overall measurement accuracy, the multi-station and time-sharing measurement with a laser tracker is introduced on the basis of the global positioning system (GPS) principle in this paper. For the proposed method, how to accurately determine the coordinates of each measuring point by using a large amount of measured data is a critical issue. Taking detecting motion error of a numerical control machine tool, for example, the corresponding measurement algorithms are investigated thoroughly. By establishing the mathematical model of detecting motion error of a machine tool with this method, the analytical algorithm concerning on base station calibration and measuring point determination is deduced without selecting the initial iterative value in calculation. However, when the motion area of the machine tool is in a 2D plane, the coefficient matrix of base station calibration is singular, which generates a distortion result. In order to overcome the limitation of the original algorithm, an improved analytical algorithm is also derived. Meanwhile, the calibration accuracy of the base station with the improved algorithm is compared with that with the original analytical algorithm and some iterative algorithms, such as the Gauss-Newton algorithm and Levenberg-Marquardt algorithm. The experiment further verifies the feasibility and effectiveness of the improved algorithm. In addition, the different motion areas of the machine tool have certain influence on the calibration accuracy of the base station, and the corresponding influence of measurement error on the calibration result of the base station depending on the condition number of coefficient matrix are analyzed.
A New Optical Interferometer for Absolute Measurement of Linear Displacement in the Subnanometer Range
A new optical interferometer system for the absolute determination of lattice constant of a crystal is designed and constructed. It can measure linear displacement accurately within the range of 94% of a period of the interference fringes with long term fluctuation of 50 pm for 14 hours and short term fluctuation of 30 pm. Its high visibility, compact and simple structure will allow various applications to precision measurement of dimension in both scientific and industrial fields.