Fraunhofer Diffraction Explained

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In this video, I describe the process of Fraunhofer diffraction (also known as far-field diffraction) in terms of the Fourier Transform and Fourier Optics. I go over the assumptions that underlie Fraunhoffer diffraction (both the paraxial approximation and the small-aperture approximation), and give the mathematical form that it takes.

This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.

Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.

[victorkislovsky]

This is a really great video. If I am not mistaken, starting from 10:24, there should be a factor 1/2 in the power of exp outside of the diffraction integral.

[zacharythatcher]

It took me rewatching several times to figure out why the aperture equation comes out of nowhere at the end, so here is the explanation. The aperture equation is assumed to be a decimal representation of the percentage of light that can go through. 1 being 100% and .5 being 50%, as an example. It essentially represents the density (intensity) of point sources at the plane of diffraction, because it is a proportional multiplier on the point source at the infinitely small point in the integral.

[sungbeom]

I had several challenges but the comments below totally helped. You got great subscribers :)

[Deniz-lexp]

Great video, my professor really left me hanging because he didn't bother to explain how he came up with the fourier part. Thanks for helping

[sanjaythorat]

@Jordan Edmunds, This is really a nice video, but there seems to be something missing after @10:24 and @12:54. Can you please correct it? I think it's too important to be missed. I will be grateful if you could correct it.

[codynelson]

Great videos Jordan. However, I think you should consider updating this one specifically for better continuity. Being the first video in the playlist, I wasn’t looking forward to any of the others. However, I was pleased when they were not choppy. Updating this one will entice people to continue the playlist. As you can see the views here are an entire order of magnitude greater than the rest.

[chriscen]

Thank you for providing us this impressive and high-quality video.

[ANJA-mjto]

Brilliant application of Fourier theory to Fraunhofer diffaction problem and interference phenomena genereally. As you simplify Fraunhofer diffaction we can assume all apertures bounding the transparent part of the surface as rectangulat and of lenght unity propendicular to the plane of the diagram.

[onizhang]

Thanks for your videos! Your drawings + explanations are super helpful

[adrianoseresi]

When I see j being used as the imaginary unit I get visibly ill. But thanks for the video.

[Hubieee]

Thanks alot for the video. Sadly there are some gaps in between that leave out probably simple stuff but in the end after 1 or 2 minutes are skipped it just makes the overall very good video a little fishy. I assume for the last part kx you too the paraxial approximation where the sin(theta) = kx / k and tan(theta) = xs / d, and sin ~ tan so kx/k ~ xs/d so kx = k*xs/d.

[optiondrone]

Excellent work on explaining Jordan, keep up the good work

[gokulkrishnan]

Great video, thanks. But after 12:23, you have directly included g(x) in the equation. If you can explain that how you included g(x) it would be helpful. Thanks

[adlib]

Lost me in the first few secs but had to watch the whole thing anyway😂. Happy to see that those integrals i had to learn in school seem to have some use somewhere👍🏻😱😂😂😂

[alexandermuller]

Interesting. I never thought about that. The intensity distribution of the double slit experiment I did in school is nothing but the Fourier transform of the sources. This is somehow equivalent to the far field of a dipol antenna. We approximate the distance and the phase of the greens function with frauenhofer, and the resulting integral is also a Fourier transform in space.

[Diana-herl]

It feels like the fragment on 10:25 - 10:40 is falling from the general story line. Can you explain the connection in this sudden jump between trigonometrical derivation of kx, Fresnel integral and further assumption you've made afterwards. I really struggle to see the connection.

[yogitshankar]

The portion where you explain why is it called Fourier optics has been edited out from the video

[bendaknee]

Great video, my only suggestion would be to try and be a bit more organized? It's still comprehendible nonetheless.

[grandaurore]

comparing 12:52 and 12:55, why the sign of factory change?

[TheSakr]

What would be the analytical calculations (via aperture function) for double slit diffraction?