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The center is the average brightness and the other two dots next to it stand for the spatial frequency of the object (two dots meaning ofcourse that there is one spatial frequency).

How can a lens do this? It certainly doesn't take a sheet of paper and start doing calculations to transform the light into the bright spots.

I found an explanation of this in a video of Youtube channel 'Applied Sciences'. In the video 'intro to Fourier optics' he states that the Fourier transform of the lens is actually the focussing of diffraction.

The transparant sheet acts like a grating and causes diffraction. The lens simply focusses this diffraction, which results in the Fourier transform. Meaning that diffraction and Fourier transforms are simply two sides of the same coin. One is a mathematical description, while the other is a 'physical' explanation (physics = applied maths but you know what I mean here).

But my question is this:

If the Fourier transformation as carried out by a lens is simply the focussing of the diffraction, then why don't we see more dots? Diffraction has many bright spots: the zeroth order (the one that is unchanged as if there was no sheet), the first order, but also the second order, the third, the fourth etcetera. Yet only the first and zeroth order of diffraction shows up.

So why don't we see those higher orders?