TITLE: What is the geometric derivation of 2D Fraunhofer aperture diffraction?
QUESTION [0 upvotes]: In this derivation, I can understand the formulas stated for 1D diffraction for both x andy (with the phase difference $\delta= ksin\theta y$) in the far-field limit, but how can we just sum the phases from both the x and y components in such a simple manner?
I would expect a formula like pythagoras would be needed instead of just $\delta = k(sin(\phi) x + sin(\theta)y)$.

REPLY [0 votes]: You would need a more complicated formula if you were doing Fresnel diffraction, but here you are making the Fraunhofer approximation that all rays are parallel.
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