Three-axis correction of distortion due to positional drift in scanning probe microscopy

Two common sources of distortion in scanning probe microscopy are piezo creep and thermal drift, the latter caused by slow thermal expansions of materials in the sample and microscope due to small changes in temperature over the course of a scan. We present a technique for correcting distortion due to thermal drift along all three spatial axes, along with simultaneous correction of z-axis piezo creep. Our method works by comparing each scanned topographical image to a second, partial scan, taken immediately afterwards, on which the fast and slow scan axes have been reversed. We model the positional distortion as a low-order polynomial function in three dimensions, searching for the set of correctional coefficients that minimizes the root-mean-square difference between the two scans. We demonstrate in a variety of real-world and simulated tests that this technique can routinely reduce distortion from these effects by over 90%, often to a precision of better than a single pixel.