Optimized detection of normal vibration modes of atomic force microscope cantilevers with the optical beam deflection method

Recently, higher-order normal vibration modes of atomic force microscope cantilevers were utilized for functional imaging applications. Here, we present a detailed theoretical investigation of the sensitivities with which these modes are detected using the optical beam deflection method. The detection sensitivities depend strongly on the size and position of the focused optical spot. Optimization of the sensitivities is performed for the individual (transverse) normal modes. For the case that multiple normal modes need to be detected simultaneously, a universal sensitivity function is constructed. This function generates accurate values for the detection sensitivity as a function of spot diameter and mode number. Finally, different optimization strategies for the simultaneous detection of multiple normal modes are presented.