Improving Calibration of an Optical Beam Deflection System

Position measurement methods based on optical beam deflection (OBD) require sensing of the displacement of a cantilever's tip. When the cantilever is scanned over a surface, the tip is deflected due to the tip-to-sample interaction forces. The laser beam reflected from the top surface of the cantilever shifts its position on a quadrant photodiode (QPD). Considering only the rotation at the cantilever's tip approximates the relation between the tip's displacement and the movement of the laser spot on the QPD. To consider the effects due to the translation and rotation at the cantilever's tip, the movement of the laser spot on the QPD is divided into the translational and the rotational components; a parameter is defined as the ratio of the translational and rotational components. This ratio determines whether the translational component is negligible (or not) for different lengths of the cantilever and other geometrical parameters such as inclination of the incident laser beam, inclination of the QPD, and tip to QPD distance, etc. For the same displacement, the ratio is low in microcantilevers, whereas it is high for macro-scale cantilevers. Hence, for the macro-scale cantilever-based applications, such as surface roughness measurement, detecting corrosion in pipes, etc, the translational component cannot be ignored. If the topographic variations are high and the OBD's parameters are not optimized, even for microcantilevers, the translational component needs to be considered (along with the rotational component). In this paper, we improve calibration both analytically and experimentally of a macro-scale OBD setup, where the cantilever tip's displacement is related with the normalized voltage signal from the QPD,. We also discuss the selection of optimum parameters of the incident laser beam that reduce the error in calibration caused by neglecting the cantilever's translation.