For the accuracy enhancement of precision machines, the systematic errors are evaluated and compensated using calibration. Among the several calibration methods, the method using reference artifact gives most precise and reliable calibration result. However, the reference artifact must be calibrated four to ten times higher than the accuracy of machines to be calibrated. Because of this requirement, it is very hard to prepare appropriate reference artifact for the precision machines, and the measuring system with nanometer precision, it is impossible to prepare the reference artifact. The self-calibration is very promising mathematical tools for machine calibration in the case of no reference artifact existence
In this thesis, the self-calibration algorithm for precision machines with Cartesian coordinate system is proposed. The calibration process is mathematically modeled as a distortion function. The requirement for self-calibration algorithm is investigated. It shows that the congruency of measuring results and the single comparison orbit of all measuring results gives sufficient condition for the self-calibration. The minimum number of measurement for self-calibration in 1-, 2-, and 3-dimensitional problems are 2, 3, and 4 for each. The self-calibration algorithm for 1-, 2-, and 3-dimensional cases are individually formulated and simulated. The simulation results show that the systematic error can be perfectly separated from the measurement result if no random noise consideration. For the effect of random measurement noise, the guide to the expression of uncertainty in measurement from International Standardization Organization is faithfully followed. The uncertainty analysis reveals that the random measurements noise amplified in the final self-calibration result and the amplification ration is determined from the number of fiducial marks in the artifact. The self-calibration algorithm is experimentally verified.