# Fourier shifting theorem in diffraction

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1. Mar 3, 2015

### blue_leaf77

Suppose one has a simple aperture in one dimension across x direction (1D aperture). Illuminated by plane wave, this aperture will produce certain diffraction pattern which, at sufficiently large distance, is just the aperture's Fourier transform, and we place a detector to measure it. Now this aperture is translated along x direction by let's say $a$, so that the center is now located at $a$. According to Fourier shifting theorem, the diffraction pattern of this translated aperture will still be located at its previous position (before translation), with only minor difference that the spatial phase is tilted at some angle. But intuitively this is not true, if the aperture is translated so is the diffraction pattern. So how does it turn out counterintuitive like this? I hope somebody can solve this.

2. Mar 3, 2015

### blue_leaf77

Ah never mind, I solved it already.