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We present a straightforward method for measuring in-plane linear displacements of microelectromechanical systems (MEMS) with a subnanometer resolution. The technique is based on Fourier transform analysis of a video recorded with a Charge-Coupled Device (CCD) camera attached to an optical microscope and can be used to characterize any device featuring periodic patterns along the direction of motion. Using a digital microscope mounted on a vibration isolation table, a subpixel resolution better than 1/100 pixel could be achieved, enabling quasi-static measurements with a resolution of 0.5 nm.