This is another research tool to obtain important results in the study of the Shroud. In mathematics it is a very important image processing tool to reach results in particular interest domains no other way reachable with the tools used in the spatial domain so far.

It works transforming an image from the spatial to the frequency domain that, to simplify, can be considered as a set of coefficients associated to the image brightness variation rapidity. Next to the details, like the area between the forehead and the eyebrows, brightness levels change sharply and, therefore, frequencies are high; on the other hand, in an area without interruption there are no variations and frequencies are consequently very low.

However, an image transformed this way contains the same eidetic information of the early image: only the way the information is represented distinguishes the two domains.

The Fourier transform allows to verify the Shroud image is not a painting since, otherwise, there would be preferential directions caused by the artist’s strokes. The values resulting from the Fourier transform can be represented as images. Fig. 19 represents the face transform and shows there are no preferential directions whose aspect would be that of little thickenings in the shape of bright stains.

The Fourier transform can also be applied to selectively cancel some information from the image if its contribution to the frequency spectrum is evident. For example, if you want to divide the image from its support, the herringbone pattern cloth, you act on those frequencies evidently corresponding to the tissue weave. In fig. 20 you can see a detail of the right orbital area and the transformed equivalent.

By observing the spectrum the weave contribution is obvious: the little nebulas. By filtring the spectrum, that is by cancelling the frequency contributions caused by the weave and calculating the antitransformed image, that is the image resulting from the modified spectrum, one obtains the contribution due to the image and the weave as subtraction.
Fig. 21 shows the two separated images.