Space-frequency analysis of pseudo-periodic patterns for subpixel position control

This paper reports on visual position measurement based on space-frequency analysis of a pseudo-periodic pattern. This approach can be seen as a two-dimensional extension of the Vernier principle as used in the Vernier caliper. The pseudoperiodic pattern fixed on the target is seen as a secondary scale that is compared to the reference scale formed by the image pixel frame. By performing space-frequency analysis and phase computations, the center of the pseudo-periodic pattern is retrieved with a subpixel accuracy and the in-plane orientation is determined as well. Several configurations allow different kinds of measurement. A single camera vision system leads to in-plane pose estimation. Stroboscopic illumination can be used to quantify vibration amplitudes down to the nanometer range. A two camera setup can be used for displacement measurements along the three spatial directions while the choice of an interference objective, sensitive to out-of-plane direction, can complement the measurement to address the six degrees of freedom. An extended pseudo-periodic pattern was also designed to locate any field of observation within a wide dimension surface.