This paper addresses how to determine a sufficient frame (sampling) rate for an optical motion tracking system using passive reflective markers. When using passive markers for the optical motion tracking, avoiding identity confusion between the markers becomes a problem as the speed of motion increases, necessitating a higher frame rate to avoid a failure of the motion tracking caused by marker confusions and/or dropouts. Initially, one might believe that the Nyquist-Shannon sampling rate estimated from the assumed maximal temporal variation of a motion (i.e. a sampling rate at least twice that of the maximum motion frequency) could be the complete solution to the problem. However, this paper shows that also the spatial distance between the markers should be taken into account in determining the suitable frame rate of an optical motion tracking with passive markers. In this paper, a frame rate criterion for the optical tracking using passive markers is theoretically derived and also experimentally verified using a high-quality optical motion tracking system. Both the theoretical and the experimental results showed that the minimum frame rate is proportional to the ratio between the maximum speed of the motion and the minimum spacing between markers, and may also be predicted precisely if the proportional constant is known in advance. The inverse of the proportional constant is here defined as the tracking efficiency constant and it can be easily determined with some test measurements. Moreover, this newly defined constant can provide a new way of evaluating the tracking algorithm performance of an optical tracking system.
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