Illustrated Fourier Transforms

You will find in the following pages some illustrations on usefull notions in crystallography (Fourier Transforms, resolution, convolution ...), using digital photographs. Mathematical developements can be found in the 'Traitement du Signal' lecture. (E. Chabrière & E. Aubert)

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Table of Content :

Digital images, Fourier Transformation

Back to the Chinese Musician: physical meaning of the Fourier Coefficients

Resolution : a first simple example

More details about the Fourier Coefficients

Back to resolution

Moduli and phases of the Fourier Coefficients

Strioscopy (zero-order filtering), bright field / dark field

Relationship between shape of an object / shape of the Fourier Transform

From a slit to a lattice

1D & 2D lattices

2D convolution

Interpretation of a low resolution image using the convolution theorem

Illustrations and examples of the use of the Fourier Transform

        Open the bird's cage...

        Zooming an image using a Fourier Transform

        Naive approach for inserting a signature in a digital image

        Ab-initio phasing by Charge Flipping