# In Fourier Optics, does the distance between a lens and a diffraction apparatus have an impact on the shape of fringes?

In our optics lectures we were given the following explanation as to how to deal with a lens as a fourier element:

We are told that to find the intensity function of the diffracted light, we first proceed as if there were no lens, and then scale the argument of said function as described above. My question is, why does the shape not depend on the distance between the lens and the apparature? Surely, the diffracted rays get more spread out the furhter they get, so why does this analysis not include that?

• The rays of each color (wavelength) are assumed to form parallel bundles downstream from the grating, so enter the lens as if from infinity. That is the same regardless of distance between the grating and the lens. That is, until the bundles spread so far that they won't hit the lens. Mar 25, 2021 at 14:56
• Ah I see, thanks for the clarification! Mar 25, 2021 at 15:57