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Diffraction theory is formulated with the time-frequency Fourier Transform of the electric field. Namely, if our field is ##u(\mathbf{r},t)## then diffraction theory expresses integrals using the field ##u(\mathbf{r},\omega)##.

When we consider Fresnel and Fraunhofer diffraction for an incident field which is a plane wave, we say the field ##u(\mathbf{r},\omega)=1## in all space.

But this isn't the FT of a plane wave. There is a delta function missing.

My confusion is mainly that... Articles online consider the incident field (the time FT) as all the terms in ##u(\mathbf{r},t)## except ##e^{-i\omega_o t}##.

I have ignored many equations here, since I don't think it is necessary to type in the relevant integrals. If you think this should be necessary tell me.

Thanks!

When we consider Fresnel and Fraunhofer diffraction for an incident field which is a plane wave, we say the field ##u(\mathbf{r},\omega)=1## in all space.

But this isn't the FT of a plane wave. There is a delta function missing.

My confusion is mainly that... Articles online consider the incident field (the time FT) as all the terms in ##u(\mathbf{r},t)## except ##e^{-i\omega_o t}##.

I have ignored many equations here, since I don't think it is necessary to type in the relevant integrals. If you think this should be necessary tell me.

Thanks!

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