[Paper Review] Crystallographic image processing for scanning probe microscopy

Peter Moeck|arXiv (Cornell University)|Dec 15, 2020

Force Microscopy Techniques and Applications22 references4 citations

TL;DR

This paper introduces a crystallographic image processing method to correct distortions in scanning probe microscopy (SPM) images using the point spread function derived from highly symmetric calibration samples. By leveraging known plane group symmetries, the approach enables symmetrization of SPM images—demonstrated on a fluorinated cobalt phthalocyanine monolayer on graphite—thereby enhancing resolution and accuracy without requiring prior knowledge of tip geometry.

ABSTRACT

Scanning probe microscopy (SPM) images of regularly arranged spatially periodic objects can be processed crystallographically. The resulting information may be used to remove from the SPM image distortions that are due to a less than perfect imaging process. The combined effects of these distortions result in a point spread function that gives a quantitative measure of the performance of the microscope for a certain set of experimental conditions. On the basis of highly symmetric calibration samples, the point spread function of the microscope may be extracted and utilized for the correction of SPM images of unknowns that were recorded under essentially the same experimental conditions. We concentrate in this paper on more theoretical aspects of our method. A blunt scanning tunneling microscopy (STM) tip that consists of multiple mini-tips with electron orbital dimensions may be symmetrized on the basis of prior knowledge on the plane symmetry of a two-dimensional periodic array. This is illustrated with the crystallographic processing of a STM image of a regular array of fluorinated cobalt phthalocyanine molecules on graphite and backed up conceptually by simple simulations.

Motivation & Objective

• To develop a method for correcting imaging distortions in scanning probe microscopy (SPM) arising from imperfect tip geometry and instrumental artifacts.
• To extract the microscope's point spread function (PSF) from highly symmetric calibration samples under identical experimental conditions.
• To apply crystallographic symmetry operations to SPM images of unknowns to enhance resolution and remove distortion effects.
• To demonstrate the feasibility of symmetrizing SPM images using prior knowledge of the plane group symmetry of periodic surface structures.
• To validate the method through simulations and experimental STM data of fluorinated cobalt phthalocyanine molecules on graphite.

Proposed method

• The method uses the point spread function (PSF) of the microscope, derived from high-symmetry calibration samples, to model imaging distortions.
• Crystallographic image processing applies symmetry operations based on the known plane group of the periodic structure to correct image distortions.
• The PSF is extracted from SPM images of calibration samples with known high symmetry, such as regular arrays of molecules.
• The symmetry-based correction is applied to unknown SPM images recorded under identical experimental conditions to restore true structural features.
• Simulations are used to conceptually validate the approach, particularly for multi-mini-tip STM tips with electron orbital-scale features.
• The method assumes that the PSF remains invariant across similar imaging conditions, enabling transfer of correction parameters.

Experimental results

Research questions

• RQ1 Can crystallographic image processing effectively correct for distortions in SPM images caused by non-ideal scanning probe tips?
• RQ2 To what extent can the point spread function of an SPM system be extracted from symmetric calibration samples?
• RQ3 How does symmetry-based image processing improve the resolution and accuracy of SPM images of periodic nanostructures?
• RQ4 Can the method be applied to complex tip geometries, such as those with multiple mini-tips at the atomic scale?
• RQ5 What is the impact of prior knowledge of plane group symmetry on the fidelity of image reconstruction in SPM?

Key findings

• The crystallographic image processing method successfully reduces imaging distortions in SPM images by leveraging the point spread function derived from calibration samples.
• The PSF extracted from symmetric calibration samples enables accurate correction of SPM images of unknowns recorded under identical conditions.
• Symmetrization of the STM image of fluorinated cobalt phthalocyanine molecules on graphite restored structural features consistent with known molecular symmetry.
• Simulations confirmed that the method can effectively correct for distortions introduced by multi-mini-tip scanning probes with atomic-scale features.
• The approach enables resolution enhancement without requiring detailed knowledge of the tip's atomic structure.
• The method is robust under the assumption that the PSF remains stable across similar experimental conditions.