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Can somebody explain the physical meaning of the last exponential term, $e^{j2\pi f_xx+j\pi f_yy}$, in the Rayleigh-Sommerfeld Formula?

Please correct me if I'm wrong, but I understand that $\epsilon(f_x,f_y,0)$ (which is the fourier transform) indicates the individual spatial frequencies and the second term indicates the frequency propagating a distance of $z_i$. What then does the third multiplicative term indicate?

Source: http://optics.sgu.ru/~ulianov/Students/Books/Applied_Optics/Keigo%20Iizuka%20Elements%20of%20Photonics.%20Vol%201.pdf

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That term is just the Fourier transform kernel, as stated in the book itself, this just gives you the inverse Fourier transform so that you obtain the field in spatial coordinates rather than frequencies. If you want a more geometrical understanding of the Fourier transformation, consider the following video https://www.youtube.com/watch?v=spUNpyF58BY, it has a very pedagogical approach.

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  • $\begingroup$ Are you saying the integral itself is the inverse fourier transform? I thought that it was merely an integral to sum up all the frequency terms $\endgroup$ – Goldname May 15 '18 at 15:38
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    $\begingroup$ Exactly, the integral itself IS the inverse fourier transform. $\endgroup$ – ohneVal May 15 '18 at 15:48

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