Comment by numpad0 | Hacker News Reader

Comment by numpad0 | Hacker News Reader

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I still haven't come across a summary I liked so I'll try:

Refractive index of a material, typically ~1.5, is not a fixed single number for material. Rather it is wavelength dependent, because diffraction is of course quantum interference thing strengthening at new directions and canceling out elsewhere. Wavelength-index plot shows some sort of exponential or asymptotic, monotonically decreasing curve from UV towards IR.

This means any convex lens always has a higher than intended magnification at blue, higher still at green, okay at red, and only technically right at Sodium vapor yellow, creating "aberrated(NOT after Ernst Abbe)" color-shifted image at its focal point.

To counter this, convex and concave lenses built from different chemical compositions that show different rates of decreasing indices are used, such as Schott BK7 and F2, so that extra positive magnification for blue at first convex lens cancels out with extra negative power for blue at following concave lens, and so on. The chain of lenses can be continued to cancel out effects at as many additional wavelengths, as well as side effects and other types of imperfections, as desired.

Significance of Fluorite or CaF2 crystals in this context is, this material shows a completely flat curve on that wavelength-refractive index plot, referred to as "abnormal dispersion". It naturally focuses all colors across visible spectrum to a same point, skipping over a lot of lens and lens canceling out. Challenge is scaling out camera-sized crystals of Calcium and Fluoride with optical clarity is hard, which Canon has been trying for a few decades.

> creating "aberrated(after Ernst Abbe)" color-shifted image at its focal point

This is a clever bit of folk etymology [1], but aberrate is derived from the Latin verb aberro, meaning to wander or stray [2].

[1]: https://en.wikipedia.org/wiki/Folk_etymology

[2]: https://en.wiktionary.org/wiki/aberro#Latin

It would be interesting to know if the term was or wasn't related.

I've been around enough brainstorming sessions to see people come up with sneaky ways to name things after themselves; someone named Abbe deciding to use "aberration" to describe the particular distortion of an image because it sounds like Abbe is totally plausible.

On the other hand, if the term predated Abbe's work and the creation of the Abbe number, it's also possible Abbe decided to work on the problem -- or his mentor assigned him the topic -- because Abbe sounds like aberration.

(It doesn't mean there is a connection, I'm just saying that just because the etymology of the word is independent doesn't mean the use of the word is also.)

Here's an 1825 use of "chromatic aberration" in "An elementary treatise on optics" by Henry Coddington: https://archive.org/details/elementarytreati00codd/page/94/m...

Ernst Abbe was born in 1840, says https://en.wikipedia.org/wiki/Ernst_Abbe . There are many uses of chromatic aberration in archive.org which predate Abbe's research in optics.

The Wikipedia adds "Already a professor in Jena, he was hired by Carl Zeiss to improve the manufacturing process of optical instruments, which back then was largely based on trial and error." which seems like it had nothing to do with his surname.

I've seen clever ways of sneaking loved ones' names into projects as well. I'm a habitual offender.

You might be interested in the series of inventions that led to the modern flush toilet. There are at least two funny names in that history, which may or may not be related to colloquialisms used when discussing toilet matters.

Prince John: Such an unusual name, "Latrine." How did your family come by it?

Latrine: We changed it in the 9th century.

Prince John: You mean you changed it TO "Latrine"?

Latrine: Yeah. Used to be "????house."

FYI. This comes from Robin Hood: Men in Tights” by Mel Brooks.

My favorite example is that the Poynting vector points to the direction of energy flow!

> Challenge is scaling out camera-sized crystals of Calcium and Fluoride with optical clarity is hard, which Canon has been trying for a few decades

Not really an informative summary on that. They’ve been succeeding, not trying, for decades. The problem of growing the crystals was solved in the 60s and this is commonplace now.

Fluorite is also used in Fuji lenses, and Nikon/Sony have their own special glass to deal with the same problems.

Yeah, according to the article, their first commercial lens with flourite was delivered in 1969.

I thought there was at one time an issue with the fluorite elements in those huge many-kilobuck lenses absorbing moisture from the air and cracking or having other sorts of failures. Canon for a while stayed with fluorite while Nikon worked out ED glass that avoided the problem. I don't know if today's Canon L lenses use fluorite.

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

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

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.

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

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.

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.

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

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.

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

> 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

How about a practical demonstration of optical Fourier transforms?

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

> aberrated(after Ernst Abbe)

Are you saying the word aberration comes from Ernst Abbe's last name? Because it doesn't, it comes from latin. https://www.etymonline.com/word/aberration

My mistakes. I stand corrected.

some of this is correct

'naturally focuses all colors across visible spectrum to a same point' would be no dispersion, not 'abnormal dispersion'. abnormal dispersion (usually called anomalous dispersion) is when the refractive index increases with increasing wavelength, instead of decreasing as in normal dispersion

https://en.wikipedia.org/wiki/Dispersion_(optics)#Material_d...

if you had a material with no dispersion you could just make a lens out of it and avoid chromatic aberration, but since you don't, you need to use the dispersions of different materials to cancel it out in the way you describe

fluorite doesn't have anomalous dispersion in the visible spectrum, it just has low dispersion

canon has evidently successfully been scaling out camera-sized crystals of calcium fluoride since the 01960s. other companies have too actually; https://en.wikipedia.org/wiki/Fluorite says

> In the laboratory, calcium fluoride is commonly used as a window material for both infrared and ultraviolet wavelengths, since it is transparent in these regions (about 0.15 µm to 9 µm) and exhibits an extremely low change in refractive index with wavelength. Furthermore, the material is attacked by few reagents. At wavelengths as short as 157 nm, a common wavelength used for semiconductor stepper manufacture for integrated circuit lithography, the refractive index of calcium fluoride shows some non-linearity at high power densities, which has inhibited its use for this purpose. In the early years of the 21st century, the stepper market for calcium fluoride collapsed, and many large manufacturing facilities have been closed. Canon and other manufacturers have used synthetically grown crystals of calcium fluoride components in lenses to aid apochromatic design, and to reduce light dispersion. This use has largely been superseded by newer glasses and computer-aided design. As an infrared optical material, calcium fluoride is widely available and was sometimes known by the Eastman Kodak trademarked name "Irtran-3", although this designation is obsolete.

sodium, fluorite, calcium, and fluoride are not brand names or other proper nouns and thus should not be capitalized in english as they are in german

> 01960s

Since 1136? :p

(sorry, can't have a pedantic thread without pedantic jokes, it's obligatory)

But English and German should :-)

admittedly

Abbe was amazing. He worked with Zeiss and a couple other glass manufacturers to systematize optics. One of his greatest accomplishments, beyond levelling up glass quality, was developing an actual "theory of optics" which explained optical phenomena in terms of diffraction. He defined diffraction limited imaging, which meant that people were able to resolve details as fine as opticals can possibly allow (this has only recently been surpassed using Nobel-prize-winning technology). Abbe illumination, which is a way to set up your microscope's light paths to get optimal quality.

He is also known for introducing the eight hour workday(!) and all sorts of employee/company innovations.

My friend from grad school shows how to set up abbe illumination and talks/shows a bit about how to set up optical fourier transforms. https://www.youtube.com/watch?v=d8Tqoo0S6gc

If you want to draw a straight line of technology development that led to industrialization and an incredible increase in life quality, it goes right through Abbe (and Newton, Pasteur, Maudsley, and Rutherford). All of these people were absolute giants who saw far past the limitations of their day and continue to inspire new generations of geniuses who can take advantage of the amazing resources we have available today (thorlabs.com is a good example).

Diffraction isn't a quantum effect. Classical waves diffract.

Good explanation (assuming it’s accurate) thank you

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