Fourier Transform Imaging Diagram
In optics, the function of converging lens is the same as Fourier Transformation.
So from the above diagram, we can see the principle of the Fourier transform imaging.
The input light forms an object by passing through Object Plane, and then the light goes through the first converging lens L1, in other words, getting a Fourier transformation. After that, the different orders of spatial frequency will be separated along the Focal Plane, at which we can setup some spatial frequency filters to process the images of the object. The filtered light will pass through the second converging lens, in other words, getting a anti-Fourier transformation. After this transformation, we can get the desired image on Image Plane.
If the image is small but not too small, we can put a CCD camera there to help us to see the fine structure.
This system is usually called "4f system".