General method for determining the sensor readings of motion measurement systems by using skew-ray tracing method

High-accuracy laser-based optoelectronic motion- and position-measuring systems typically utilize light rays that travel from one optical boundary surface to another to perform motion and/or position measurements. It is not a simple task to accurately determine the equations of these sensor readings in terms of positional/angular motions. This problem is addressed in this paper by application of the analytic skew-ray tracing methodology as computed by the finite-difference methodology. An illustrative example of a motion-measurement system and comparison of the position-sensing detector (PSD) readings are given to validate the proposed methodology. It is shown that the proposed methodology can provide accurate expressions of PSD readings. It is also shown that the performance of a corner-cube retro-reflector is better than a cat's eye retro-reflector in positional/angular motion measurement systems.