Method of Calibration for a Large Cathetometer System

A method of calibration has been devised for a pair of mutually orthogonal two-axis cathetometers that, when used together, yield measurements of three-dimensional positions of objects mounted on an optical bench. Each cathetometer has a horizontal travel of 1.8 m and a vertical travel of 1.2 m. The cathetometers are required to measure X, Y, and Z coordinates (see figure) to within plus or minus 0.005 in. (plus or minus 0.127 mm). Each cathetometer consists of an alignment telescope on a platform mounted on a two-dimensional translation stage. The knowledge required for calibration of each cathetometer is (1) the two-dimensional position of the cathetometer platform as a function of the electronic readouts of position encoders on the translation stage and (2) the amount of any angular misalignment (roll, pitch, and/or yaw) of the cathetometer platform as a function of the two-dimensional coordinates or the position-encoder readouts. By use of three equations derived from the applicable trigonometric relationships, the calibrated X, Y, and Z coordinates can be computed from the raw encoder readouts.