Centering a beam of light to the axis of rotation of a planar object

We detail an experimentally simple approach for centering a beam of light to the axis of a rotating surface. This technique can be understood as a rotating analog to knife-edge profilometry, a common experimental technique wherein the intensity (or power) of various masked portions of a beam is used to ascertain the transverse intensity profile of the beam. Instead of collecting the light transmitted through a mask, we give the surface a variable reflectivity (such as with a strip of retro-reflective tape) and sample the light scattered from the surface as it rotates. We co-align the transverse position (not the tilt) of the axis of rotation and the beam centroid by minimizing the modulation amplitude of this scattered light. In a controlled experiment, we compare the centroid found using this approach to the centroid found using the canonical knife-edge approach in two directions. We find our results to be accurate to within the uncertainty of the benchmark measurement, +/- 0.03 mm (+/- 2.9% of the beam waist). Using simulations that mimic the experiments, we estimate that the uncertainty of the technique is much smaller than that of the benchmark measurement, +/- 0.01 mm (+/- 1% of the beam waist), limited here by the size of the components used in these experiments. We expect this centering technique to find applications in experimental and industrial fabrication and processing settings where alignment involving rotating surfaces is critical.