Fourier Analysis - Quantify patterns & frequencies
The Extended Fourier Analysis module offers the most advanced set of tools on the market for quantifying repetitive patterns (e.g. atomic lattices) and periodic noise, and for filtering images in the frequency domain.
The Extended Fourier Analysis module is one of the most advanced modules in SPIP™, and offers the experienced user unique flexible tools for analyzing and modifying the FFT (Fast Fourier Transform) spectra of images.
At the same time everyday users have easy to use tools for detecting unit cells and for suppressing periodic noise.
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 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.