[riperoni]

Yeah thank you, that summary is better than the article.

The definition of refracitve index in the article is also just wrong, since it is simply not an angle. It can be calculated from incidence and refraction angles of the light beam - very different. See https://en.m.wikipedia.org/wiki/Snell%27s_law

To add to your answer, the refractive index is not just wavelength dependent, but can also be depending on the polarization of light, leading to birefringence: https://en.m.wikipedia.org/wiki/Birefringence

[Balgair]

For HNers and CompSci people, optics is a notoriously difficult field and much more frustrating.

If you break up the Nobel Prizes a bit differently, then the filed of Optics becomes the most dominant. So very many breakthroughs in science are because of some new optics method. Mostly in the bio/chem fields, it's about gaining a new form of 'contrast' (very broadly defined).

People have spent decades trying to align some little crystal just the right way. Or they did it in their living room with cardboard in a weekend. It's a frustrating field.

One fun thing to remember about lenses are that they aren't really light bending thingys, but more accurately a lens is a Fourier transformer. Of a sort. Again, optics s frustrating.

One fun thing for the more matrix-ly minded are Mueller Matrices. Most modern optics SW is based on this calculus, though it goes a lot further nowadays. Also, most developments in optics are all about the little exceptions that Mueller matrices have.

Still, a good little thing to read about, if interested: https://en.wikipedia.org/wiki/Mueller_calculus

[kridsdale1]

I have been way in to Nikon and Canon lenses as well as DSP for like 20 years now, and have a degree in EE and did a ton of quantum, and I never had the insight that a lens is a physical EM Fourier transformer.

Cheers for that.

[tempay]

Does anyone have an explanation of this insight? In principle I have all the pre-requisite understanding but I’m struggling to connect it.

[kridsdale1]

I suppose my interpretation of his message is that if you think of a “ray of light” that is not a mono frequency laser as an “input signal”, a convex lens will smear it out in to its constituent component frequencies. From that perspective you can analyze the original signal (aka color) with a geometrically/spatially separated spectrum of values.

It was a single spatial point of ray intersection with your sensor or eye. You’d need color filters/retinal cells to pick apart the frequencies in the complex waveform.

After rainbow separation, the components are spread across multiple sensors giving you a frequency domain view.

[plasmatorch]

Aside from cranking the math, here's how I think about it: in the far field of a small aperture, the electric field has spherical phase (think expanding circles), and the field distribution is the Fourier transform of the aperture. A lens is an element that adds spherical phase - a plane wave passing through a convex lens now has a spherical phase distribution. So the lens focal point is now the tiny aperture in that system, and since the math works out the same no matter which way the light is going (reciprocity), the focal point is the FT of the field at the input of the lens.

Goodman is great, Hecht and Zajac covers more fun with optics at an intro level.

[sirpilade]

Yes the explanation is diffraction. As light passes through a lens, diffraction acts in similar way as a light through a small pinhole. Incidentally, pinholes and apertures are low pass filters.

Some more info here

Miles V. Klein, Thomas E. Furtak - Optics 2nd ed, Wiley

Joseph W. Goodman - Introduction to Fourier optics, W.H. Freeman

[Balgair]

Upping a cousin comment.

https://www.youtube.com/watch?v=Y9FZ4igNxNA

Adding that, again, optics is a difficult and frustrating field. Don't worry that you're struggling to connect it. It took me a few years in an optics lab working hands on with light every day to really come around.

[aj7]

“A lens creates the spatial Fourier transform from the front focal plane to the rear focal plane.”

[Micanthus]

> a lens is a Fourier transformer. Of a sort.

Can you expand on that? Or have some reading for that?

I guess it makes sense, light is a wave and anything even vaguely to do with waves seems to end up with Fourier transforms, but still I'm curious about the details

[infogulch]

How about a practical demonstration of optical Fourier transforms?

https://www.youtube.com/watch?v=Y9FZ4igNxNA