In this paper, we present a new method for detecting in-plane displacements in microelectromechanical systems (MEMS) with an unprecedented sub-ångström accuracy. We use a curve-fitting method that is commonly employed in spectroscopy to find peak positions in a spectrum. We fit a function to the intensity profile of the image of a silicon beam that was captured with a CCD camera on an optical microscope. The position resolution depends on the amount of pixel noise and on how the moving feature is spread across the detector pixels. The resolution is usually limited by photon shot noise, which can be controlled and lowered in several ways. To demonstrate the technique we measure the adhesion snap-off of two silicon surfaces. We assess the accuracy of the technique using two different silicon MEMS devices and an experimental ultrananocrystalline diamond device. The lowest position noise that we report is obtained by summing 1,577 image lines and is as low as 60 pm root mean square.