Correction for piezoelectric creep in scanning probe microscopy images using polynomial mapping

We describe a method for using polynomial mapping to correct scanning probe microscope images for distortion due to piezoelectric creep. Because such distortion varies from image to image, this method can be used when the actual locations of some features within an image are known absolutely, or in a series of images in which the actual locations of some features are known not to vary. While the general case of polynomial mapping of degree N requires the determination of 2(N+1)² matrix elements by regression, we find that by understanding the mechanism by which piezoelectric creep distorts scanning probe microscope images, we can fix most of these coefficients at 0 or 1 a priori, leaving only 2(N+1) coefficients to be determined by regression. We describe our implementation of this strategy using the Interactive Data Language (IDL) programming language, and demonstrate our technique on a series of atomic force microscopy (AFM) images of diblock copolymer microdomains. Using our simplified scheme, we are able to reduce the effects of distortion in an AFM image from 5% of the scan width to a single pixel, using only five reference points.