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I have learned that by Using Rayleigh Sommerfeld boundary condition, the inconsistency, which is present in the Fresnel-Kirchhoff Diffraction theory, can be removed. But the Fresnel-Kirchhoff Diffraction theory is valid when the the dimension of the aperture is large compared to the wavelength of the incoming wave. My question is that can we use the Rayleigh- Sommerfeld Diffraction theory for the case, where the dimension of the aperture is alomost or nearly equal to the wavelength? If possible, then would you please give me any reference.

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  • $\begingroup$ Can I recommend that you ask v3 of this question separately in its own thread? It looks rather drastically different, and it's not recommended to edit posts to that extent. I'm doing a rollback to v1 on this post; if someone knows a good answer to that, they can post it here. You should post v3 separately, If people have answers to your question about the proof, those would best be posted on that separate thread. $\endgroup$ – user191954 Sep 29 '18 at 15:58
  • $\begingroup$ Sir, thanks for your suggestion but I am restricted to ask any further question as I have reached already at the limit of asking question. That is why I edited the old post. $\endgroup$ – R. Bhattacharya Sep 29 '18 at 16:19
  • $\begingroup$ Have you deleted any of your own questions recently? Your profile seems to show that you have only a handful of posts overall; I don't think it should be triggering any rate-limiting. Also, could you recognise anything from the section titled "Asking" in the meta post here: meta.stackexchange.com/questions/164899/… ? $\endgroup$ – user191954 Sep 30 '18 at 7:58
  • $\begingroup$ See physics.meta.stackexchange.com/q/10639/50583 and physics.meta.stackexchange.com/q/9698/50583 for details about automatic question restrictions. You have 8 deleted questions which weigh the algorithm rather heavily in your disfavour. $\endgroup$ – ACuriousMind Sep 30 '18 at 9:09
  • $\begingroup$ Okay.. I shall visit the link.. Thanks for making me aware of the fact. $\endgroup$ – R. Bhattacharya Sep 30 '18 at 9:56
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The answer is yes. When the linear dimension of the aperture is almost nearly equal to the wavelength, then using Rayleigh-Sommerfeld diffraction formula one can get the answer. For detail discussion and derivation the following reference is given: 1) E. Marchand & E. Wolf, Consistent formulation of the Rayleigh-Kirchhoff diffraction theory , Journal of Optical society of America, Volume 56, Number 12., December, 1966.

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