Modeling and calibrating nonlinearity and crosstalk in back focal plane interferometry for three-dimensional position detection

Back focal plane (BFP) interferometry is frequently used to detect the motion of a single laser trapped bead in a photonic force microscope (PFM) system. Whereas this method enables high-speed and high-resolution position measurement, its measurement range is limited by nonlinearity coupled with crosstalk in three-dimensional (3-D) measurement, and validation of its measurement accuracy is not trivial. This Letter presents an automated calibration system in conjunction with a 3-D quadratic model to render rapid and accurate calibration of the laser measurement system. An actively controlled three-axis laser steering system and a high-speed vision-based 3-D particle tracking system are integrated to the PFM system to enable rapid calibration. The 3-D quadratic model is utilized to correct for nonlinearity and crosstalk and, thus, extend the 3-D position detection volume of BFP interferometry. We experimentally demonstrated a 12-fold increase in detection volume when applying the method to track the motion of a 2.0 μm laser trapped polystyrene bead.