In my diffraction notes, this integral comes up on the page about Babinet's principle:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int ^{y=\infty}_{y=-\infty} \int ^{x=\infty}_{x=-\infty} exp(-i(px+qy)) dx dy = \delta (p,q)[/itex]

I'm not sure how this integral is derived as carrying out the integration and putting in the limits seems to give infinity, is it something to do with the completeness relation?

A screenshot of the slide is attached

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# Integrating exp(-i(px+qy)) dxdy over all space

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