A constant-frequency feedback loop for non-contact frequency-modulated atomic force microscopy via root locus: Implemented on a single-board field-programmable gate array device.

Non-contact, frequency modulated atomic force microscopy is often operated in the constant-frequency mode to obtain a height map of the sample's surface. Once linearized, the dynamics of the constant-frequency closed-loop system are reduced to a single transfer function. By modifying the bandwidth of this transfer function, a tradeoff is achieved between image noise and imaging speed. In this article, a new constant-frequency feedback loop is developed, utilizing the self-excitation technique for resonating the cantilever. Along with the proposed controller, it will be shown with the root locus that one needs to vary a single parameter, the loop gain, to modify the closed-loop bandwidth. The result is a robust, low-order, real-poled, feedback loop that is very easy to tune. The methodology is validated experimentally on a single-board field-programmable gate array device.