Design methods for six-degree-of-freedom displacement measurement systems using cooperative targets

Six-degree-of-freedom displacement measurement systems generally employ various kinds of cooperative targets, and calculate displacement from the coordinate values of reflective rays. To improve the performance of measurement systems, a new design methodology is required, which considers the relationship between each axial output and the coordinate values, Jacobian matrix. Several performance indices are derived from Jacobian matrix and the design parameter values are determined through the optimization process. In a design example, the improvement of performance is verified by evaluating resolution, accuracy and crosstalk. The newly designed measurement system shows a maximum error of ± 0.5 μm for translation and ± 2 arcsec for rotation.