Fourrier Transform

A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. This transformation is widely used in imaging because it allows to see signals at regular frequencies.

Siril allows to transform an image in the frequency space thanks to a Fast Fourier Transform algorithm. The result is in the form of two images. The first one, automatically loaded, contains the magnitude (or modulus) of the transform, the second one contains the phase. The location of the two images must be entered in the Direct Transform tab (see illustration below) of the dialog. It is then possible to modify the modulus image by removing frequency peaks corresponding to unwanted signals. It is important not to forget to save the changes.

The Centered option, when checked, centers the origin of the Direct Fourier Transform. If not, the origin is at the top-left corner.

dialog

Direct Transform tab.

To reconstruct the image, click on the Inverse Transform tab and enter the filepath of the modulus and phase images.

dialog

Inverse Transform tab.

Siril command line

fftd modulus phase
Applies a Fast Fourier Transform to the loaded image. modulus and phase given in argument are the names of the saved in FITS files

Siril command line

ffti modulus phase
Retrieves corrected image applying an inverse transformation. The modulus and phase arguments are the input file names, the result will be the new loaded image