Cartoon of the Fourier slice theorem

This animation shows the reconstruction of a tomogram via the Fourier slice theorem (rather than the filtered back-projection method). For each rotation angle, the transmission profile of a slice is Fourier-transformed and then plotted at its respective rotation angle in Fourier space. The inverse FT of the completed set through 180 degrees yields the original tomogram slice. For details of the tricks of the trade, look at the comments in the code.

I have drawn heavily for the mathematical guts of this program from the code found at https://stackoverflow.com/questions/61260808/implementing-a-filtered-backprojection-algorithm-using-the-central-slice-theorem. I saw no reason to completely reinvent the Fourier wheel… Acknowledgements for this go to 2fly2try, Chris Luengo, and Person.Woman.Man.Camera.TV (LOL).

The phantom was taken from the public domain wikipedia source https://commons.wikimedia.org/wiki/Scrollable_computed_tomography_images_of_a_normal_brain_(case_2).