STM image of self-assembled Didodecyl-benzene molecules and its Fast Fourier Transform. A unit cell has been calculated from the peak positions in the FFT image marked by the user using the Peak Marker tool.
Manual Peak Measurement
The manual peak measurement tool measures peaks in the Fourier image with sub pixel accuracy, so that unit cells or noise sources can be accurately determined. Both the Fourier domain coordinates and the corresponding spatial wavelengths are reported. For raster scanned images, such as SPM images, where the scan time is known, the corresponding frequencies in Hz are reported.
Besides the manual analysis tool the module provides fully automatic detection of unit cells and the period of parallel lines with high accuracy.
Interactive tools
Interactive tools for masking the Fourier spectrum and calculating the inverse Fourier image make it easy to suppress specific wavelengths, such as periodic noise. Low-pass, high-pass, band-pass, and band-reject filters with interactive adjustments are also available. The degree of filtering can even be adjusted as the resulting inverse Fourier image may be a weighted sum of the original image and the filtered inverse image.
Filters for later use
Masks and filters can be set up and saved for later use, for example with Batch Processing (requires the Batch Processing & Reporting module).
The Educational Toolbox
In addition to being a strong analytical tool, the Extended Fourier Analysis module can bring new understanding to the relation between the spatial and the Fourier domain and serve as an educational toolbox, as several types of window functions are available for improving the Fourier transform.
STM image of a gold Au(111) surface on top of a mica substrate with the unit cell calculated using the Peak Marker tool highlighted
Fourier image of the gold Au(111) surface with the Peak Marker tool snapped to two peaks
Filled states STM image of a Si(111) 7x7 surface and the corresponding Fourier Transform and the automatically calculated unit cell (Data: Omicron Nanotechnology).
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