Bandwidth enhancement of a shear-force-controlled distance regulation in near-field microscopy

The distance between sample and probe in a scanning near-field optical microscope is regulated via tracing the shear-force on the tip which is glued to a tuning fork piezo. A lock-in technique is used. We demonstrate that the bandwidth of the control loop is increased if not only amplitude or phase, but a favorable combination of both is used as feedback signal. The enhancement of bandwidth is connected with a reduction of signal-to-noise ratio. The optimum combination of both, bandwidth and signal-to-noise ratio, can be adjusted purely electronically to the specific needs of an experiment. A theoretical model is developed that discloses the relation between the mechanical and electrical properties of the combination of tuning fork and fiber tip. The frequency response of the shear-force detection system is calculated with a numerical simulation based on this model. Experimental frequency response curves are well fitted by these simulations. Our results are especially important for low-temperature scanning microscopy, where the bandwidth enhancement is essential for obtaining a reasonable scanning speed.