Beyond the blur: using experimentally determined point spread functions to improve scanning Kelvin probe imaging

Scanning Kelvin probe microscopy (SKPM) is a powerful technique for investigating the electrostatic properties of material surfaces, enabling the imaging of variations in work function, topology, surface charge density, or combinations thereof. Regardless of the underlying signal source, SKPM results in a voltage image which is spatially distorted due to the finite size of the probe, long-range electrostatic interactions, mechanical and electrical noise, and the finite response time of the electronics. In order to recover the underlying signal, it is necessary to deconvolve the measurement with an appropriate point spread function (PSF) that accounts the aforementioned distortions, but determining this PSF is difficult. Here we describe how such PSFs can be determined experimentally, and show how they can be used to recover the underlying information of interest. We first consider the physical principles that enable SKPM, and discuss how these affect the system PSF. We then show how one can experimentally measure PSFs by looking at well defined features, and that these compare well to simulated PSFs, provided scans are performed extremely slowly and carefully. Next, we work at realistic scan speeds, and show that the idealised PSFs fail to capture temporal distortions in the scan direction. While simulating PSFs for these situations would be quite challenging, we show that measuring PSFs with similar scan conditions works well. Our approach clarifies the basic principles of and inherent challenges to SKPM measurements, and gives practical methods to improve results