Design and implementation of high-bandwidth, high-resolution imaging in atomic force microscopy

Video-rate imaging with subnanometer resolution without compromising on the scan range has been a long-awaited goal in Atomic Force Microscopy (AFM). The past decade saw significant advances in hardware used in atomic force microscopes, which further enable the feasibility of high-speed Atomic Force Microscopy. Control design in AFMs plays a vital role in realizing the achievable limits of the device hardware. Almost all AFMs in use today use Proportional-Integral-Derivative(PID) control designs, which can be majorly improved upon for performance and robustness. We address the problem of AFM control design through a systems approach to design model-based control laws that can give major improvements in the performance and robustness of AFM imaging. First, we propose a cascaded control design approach to tapping mode imaging, which is the most common mode of AFM imaging. The proposed approach utilizes the vertical positioning sensor in addition to the cantilever deflection sensor in the feedback loop. The control design problem is broken down into that of an inner control loop and an outer control loop. We show that by appropriate control design, unwanted effects arising out of model uncertainties and nonlinearities of the vertical positioning system are eliminated. Experimental implementation of the proposed control design shows improved imaging quality at up to 30% higher speeds. Secondly, we address a fundamental limitation in tapping mode imaging by proposing a novel transform-based imaging mode to achieve an order of magnitude improvement in AFM imaging bandwidth. We introduce a real-time transform that effects a frequency shift of a given signal. We combine model-based reference generation along with the real-time transform. The proposed method is shown to have linear dynamical characteristics, making it conducive for model-based control designs, thus paving the way for achieving superior performance and robustness in imaging