Fluorite lenses: Corrective capabilities beyond ordinary optical glass

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.

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.

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

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.

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.

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

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.)

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!

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.

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

But English and German should :-)

admittedly

01960s

Since 1136? :p

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

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.

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.

Good explanation (assuming it’s accurate) thank you

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.

I was kind of hoping they would explain why it helps prevent chromatic aberration. Unfortunately their explanation stops short, basically just saying that 'it does' without going into the details of why.

My first guess would be something to do with it having a well suited refractive index, but it is almost equal to that of glass. The best candidate I've found is that the group velocity dispersions are opposite, which seems like it might explain it, if only I knew what it meant.

When a lens is designed, typically an optimiser is used to try to find a combination of lens elements that focuses light of all wavelengths to the same spot across the whole image. If all the same type of glass is used, then it's hard for the optimiser to find a solution that corrects for the chromatic aberration across all the spectrum, because if it adjusts (for instance) something to fix the green aberration then it'll mess up the blue and vice-versa. But if a different type of glass is used such as fluorite, which has a different pattern of chromatic dispersion, then that gives the optimiser an extra degree of freedom, so it is more able to independently control the aberration in the different colours and make a lens that performs well.

Over the past ten years, lenses have gotten unbelievably better. Apsherical elements have done some of the lifting, and glass formulas another, but how much have computational tools changed how lenses are designed?

What are you basing this observation on? I haven't seen any significant improvement in photography or cinema lens performance over many decades. The principles have been understood for 150 years, and using ray-tracing software is standard since the 70s. Cheap lens systems in phones got a lot better, and digital sensors are much more sensitive than film though.

The main reason why lenses have become significantly better over the last 10-20 years (certainly at the consumer level) is mainly because camera sensors have become significantly better over the last 10-20 years, and therefore the lenses have had to be engineered to a higher standard to avoid the lens foibles being quite so obvious in the higher resolution images that are now possible. The engineering principles are largely the same with a few smaller advances, but to accomodate the demanded-for improvements consumer lenses are now bigger, heavier, more expensive, and have more interesting optical designs. It's purely demand-driven, not technology-driven.

Exactly. It can't be ignored that these new lenses are much bigger & heavier and much more expensive as a result. That helps a lot. But it makes them worse if a) you need to carry them a long way for your type of photography b) your photography doesn't actually benefit from or require their advantages.

A lot of these benefits seem more important to the measurement focused hobbyists. But if you don't actually care about shooting at f/1.2-f/1.4 a lot of the time you might want to save the money.

All you have to do is compare a recent 50mm f/1.4 lens such as the Sigma Art or Sony GM to an older design before the advent of computer-aided optimization (eg the Canon EF 50/1.4).

The new designs are very contrasty and sharp wide open, almost across the frame. The older designs need to be stopped down to achieve critical sharpness, and suffer in the corners. Just so much progress in the past 15 years.

Not who you're replying to, but it seems this is a classic case of mistaking not noticing change is evidence of no change.

I've been following this newsletter for a while as I have a passing interest in (photographic/cinematic) lens design.

https://www.pencilofrays.com/

Anecdotally, a lot. Modeling of Aspherical elements has gotten better and it is much easier to make them as well. Mamiya made some of the first APO computer corrected lenses back in 1988 - https://lens-db.com/mamiya-apo-sekor-z-350mm-f56-1988/

It's a bit buried, but this (to me) is the most interesting sentence :

Fluorite lenses are also unique in their extraordinary partial dispersion tendencies: the red to green wavelengths are dispersed with the same tendencies as glass, but the green to blue wavelengths are dispersed more than glass.

It has both low dispersion (less overall aberrations) and a unique shape to the dispersion curve (more control). Glasses typically all have similar dispersion curves. The weird shape of fluorite's dispersion curve gives your optimization function an extra lever to play with.

Does this mean it has an index of refraction that depends on wavelength? How can that be? Is the bond length some multiple of blue (or green/red), where there's some quick "change" in what the photon "sees"?

Glass has this too. it's why achromats and apochromats were developed (using rather clever ideas like pairing two different types of glass, which cancel each other's dispersions.

All the physical explanations I've seen invoke the EM equations and quantum mechanics to explain it (and I don't understand it well enough to translate).

3Blue1Brown has a nice animated video about this: https://youtu.be/KTzGBJPuJwM?si=ssBPKL8LVhsQ3wNZ

This is, I think, just one of those spots where "all models are wrong, some models are useful" is true. From the wikipedia page on Refractive Index (https://en.wikipedia.org/wiki/Refractive_index):

The refractive index may vary with wavelength. This causes white light to split into constituent colors when refracted. This is called dispersion. This effect can be observed in prisms and rainbows, and as chromatic aberration in lenses.

--- snip ---

For most materials the refractive index changes with wavelength by several percent across the visible spectrum. Nevertheless, refractive indices for materials are commonly reported using a single value for n, typically measured at 633 nm.

So we were all lied to in our introductory optics classes. n isn't a constant for a given material but rather n(lambda) but weakly.

Amazing question! Yup. Refractive index is a function of wavelength. I bet you already knew that on some level, because that's why prisms do their thing. As an extreme example, imagine X-rays: they barely refract at all, they just pass straight through stuff! Also, the change is actually quite smooth.

https://refractiveindex.info/

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

Glass has an index of refraction that depends on wavelength; this is how a prism works. This is also why chromatic aberration exists at all.

It's a consequence of the relationship between absorption and index of refraction in glasses, which follow the Karmers-Kronig relationship [0]. As the wavelength approaches atomic resonance, the index increases or decreases depending on which side of the absorption peak the wavelength is.

0. https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relatio...

Fluorite just has low dispersion and therefore a lens made from it has less chromatic aberration than glass.

the red to green wavelengths are dispersed with the same tendencies as glass, but the green to blue wavelengths are dispersed more than glass.

I admittedly responded without reading the source, so please accept my apologies.

Despite how it is worded the total dispersion of Fluorite is less than glass.

That quote is referring to the ‘extraordinary partial dispersion’ property. They are using this to better correct the aberration than could be done with two pieces of glass alone. This seems to be illustrated in the diagrams well.

Some further stuff to read up on is the Abbe number that describes the refractive index vs wavelength derived from a set of light sources.

https://en.wikipedia.org/wiki/Abbe_number

The higher the Abbe number the lower the dispersion of a material.

Fluorite is ~95

https://refractiveindex.info/?shelf=main&book=CaF2&page=Mali...

Random choice below but glass tends to be ~25 - 80

https://refractiveindex.info/?shelf=glass&book=HOYA-C&page=E...

Fluorite just has low dispersion and therefore a lens made from it has less chromatic aberration than glass.

So why not make the entire lens from fluorite? Because pairing an element with one with different refractive index can lower the overall dispersion.

Typically you'll see compound lenses are made of pairs of elements where one is positive (convex) and the other negative (concave): instead of making one lens with power of, say, +4, the group is made from one that's +5 and one that's -1 of different type of glass so the refractive indexes cancel-out dispersion and other aberrations.

Isn't that covered in the 7th paragraph?

'the red to green wavelengths are dispersed with the same tendencies as glass, but the green to blue wavelengths are dispersed more than glass. Using a convex fluorite lens element alongside a high-dispersion glass concave lens element therefore eliminates residual chromatic aberration'

I thought the reason underlying that is that fluorite is not a glass, technically. It is a crystal. But I’m not a MatSci person so that doesn’t leave me any bit more informed.

It seemed to, the dispersion is different so you can cancel the dispersion from glass (dispersion is the refractive index variation with wavelength).

Chromatic aberration happens because of dispersion --- the fact that the refractive index changes with wavelength. By combining materials with different properties (e.g. low dispersion, or high refractive index), you can cancel out the aberration in lens designs such as achromatic doublets, apochromatic triplets, etc.

In general, materials that are high in refractive index have high dispersion (e.g. crown glass) and materials that have low dispersion also have low refractive index. But ideally we want a material that has high refractive index but low dispersion so that it can both bend light without introducing a lot of chromatic aberration.

Fluorite has extraordinarily low dispersion while having a refractive index that's only slightly lower than glass, making it a good material to be used in conjunction with other materials.

Possibly a poor analogy, but imagine making a particle accelerator with the goal that objects of different mass put into it are accelerated and leave it going the same velocity.

The current state of technology allows that the best we can do is make one that accelerates lighter objects slightly more than heavier objects.

However, we've found a way to make an accelerator using a different design that accelerates heavier objects more than lighter objects. If we pass objects through the first accelerator, then the second, the second accelerator reverses out some of the non-linearity of the first. Unfortunately this second accelerator is very, very expensive to make.

This is how lenses of different refractive indexes are used: one element partially corrects the dispersion produced by earlier elements. Fluorite has the right refractive index to correct aberrations created in long focal length lenses.

I found the article explained exactly why using fluorite helped chromatic aberration. It adds another degree of freedom, due to the partial dispersion.

This article shows a "map" of available glasses, with each glass shown by its refractive index and dispersion constant -- in a particular way. The explanation is that if all you have are glasses on that "glass line," you can make a lens with equal focal length at two wavelengths but not three. You need glasses that are not on the "glass line," and one of them is calcium fluoride. Also, some plastics such as acrylic and polystyrene can be used, but have their own issues such as thermal expansion.

Finding a lens with 2 equal focal lengths is equivalent to a graph of focal length versus wavelength that's roughly a parabola. With 3 equal focal length, the graph looks like a cubic curve.

https://www.opticsforhire.com/blog/apochromatic-lens/

The glasses also have to be economical, able to take a good polish, clear, chemically resistant (to avoid staining), mechanically robust, etc. It's not an easy design problem since the "exotic" glasses with extreme refractive properties also tend to have worse properties overall.

I looked for a simple explanation of why dispersion matters, and this seems helpful:

https://www.targettamers.com/guides/apochromatic-lenses/

in the context of apochromatic lenses: those that are optimized for three different wavelengths of light, not just two, which an achromatic lens does.

In the old days, calculations were done by hand, not that this is a big deal, but the big deal is that some really outstanding lens designs were made this way. Computers make the optimization extremely fast these days, but the calculations rely on the properties of the elements, which also vary in cost, durability and so on. So the computer can’t optimize for a continuous range of refractive indices and dispersions, only discrete real-world ones that the glass makers list, and which are specified (or not) to the program by the designer.

Fluorine also has special properties as a coating.

https://www.digitalcameraworld.com/features/this-is-why-your...

Computers make the optimization extremely fast these days...

A lot of computer design is now aimed at optimising for tolerances in lens elements and mechanical housings to reduce precision necessary when assembling them: they can drop elements into the tube and ship them off with little or no calibration: this is done particularly with kit lenses which are price sensitive.

I did error budgeting for environmental effects on optical systems at Itek. Glad to see so many optics folks here. I wonder who they are, but won't ask. ;-)

I assume that's the same Itek that made lenses for the Corona Spy Satellite program?

That's cool as heck. I am just a photographer, but I collect aerial lenses and own 2 Pacific Optical 18" f/3 lenses in 70mm format, serial numbers 6 and 13. I'll keep my eyes peeled for a surplus Itek 24" f/3.5 though :)

Yes, same one. I find de-classified articles and books now, and share them with former colleagues. All the designs I worked on were meant for space. And I have no idea if any were actually deployed.

As I noted in the “handle” post, k310 is the office number I had at Itek, as well as a nifty sonata by Mozart.

I later worked for Lockheed. More space optics and other cool stuff. I was in the R&D division.

I hope you can make good use of those lenses. I stuck with commercial optics (Nikon and Hasselblad). My optical hacking never exceeded making some adapters with a Unimat SL that I got. Surprise, computers got my attention, and my first “real” computer was an IMSAI that I built.

I read a lot. Kingslake, Smith and so on. A nice book, if you can find it is “Photographic Optics” by Neblette. It goes over all the classic designs, including all the familiar camera lenses from the 70’s and 80’s. Nowadays, computers do all the designing, and you can’t recognize “classic” designs like the tessar, Sonnar and so on, in them. But TBH, I finally got a new 105 macro lens with unrecognizable (to me) design from Nikon to augment the old 55mm macro that I started out with in 1970 or so. A simple double-gauss design.

Did you know what those “P” and “H” and other suffixes meant on Nikon lenses? They are the number of elements, in Optics Latin. H for hex, or 6 elements, P for penta or 5, and so on. The old lenses, without the “AI” aperture index gizmo, fit the new mirrorless body with the FTZ adapter. I gather that they were no-go on the DSLR’s. I skipped the DSLR generation entirely, since I used a Coolpix with 24-1000mm effective focal length for many, many years. Heck, it worked and got me great photos.

That's awesome! Thanks for taking the time to reply.

I am a young guy - just turned 30 last month - but I exclusively shoot and develop film and have my own mini darkroom. I enjoy the challenge and physicality of it all, plus I already spend enough time around computers and digital tech as a software engineer so it's nice to have some analog pursuits. An IMSAI is a bit before my time, but I have a soft spot for older CPUs like the similar z80 or 6502 from writing emulators.

For 35mm I mostly shoot on Canon FD, so while I recognize some of those classic design names I haven't shot on them. I haven't been able to shoot on the behemoth PO lenses as much as I'd like since they weigh nearly 60 pounds a piece and are a hassle to use, but I've jerry rigged a Graflex Crown Graphic to the back and can do a manual shutter with some ND filter and a quick on/off of the lens cap. They cover 4x5 or more at the distances I use them and are incredible lenses for portraiture.

My next projects are to mount both PO lenses together and put Graflex Speed Graphic 4x5 cameras behind each in order to make a massive binocular camera. I also have a Goerz 47" process lens that's got an image circle of nearly a meter, so my next shoot with that will be a 1:1 self portrait on xray film, since it's the only semi affordable option for such a massive exposure.

Great! You’re having fun. I got a few odd surplus lenses but since I started photography by taking flower and landscape photos, the “optics lab” part never took flight.

Trying to keep things simple here.

Itek made semiconductor lithography stuff way back when right? I did a stint at one of its competitors. I didn't know about the spy satellite stuff. Neat!

I'm not a lens designer, but want to play one on TV.

in the context of apochromatic lenses: those that are optimized for three different wavelengths of light, not just two, which an achromatic lens does.

Achromatic lenses (corrected for blue and green) was acceptable for black and white orthochromatic film and plates which are only sensitive to blue and green. Even with panchromatic b+w film, achromatic lenses are usually satisfactory, but the chromatic aberration becomes visible with colour film. Aprochromatic lenses are corrected for blue, green and red.

Lenses can also be corrected for broader spectrums that include UV and IR: Nikon made such a lens – the UV 105mm f4.5 – for technical/scientific applications.

Zeiss and Hasselblad sold some superachromat lenses as well.

Mamiya did as well, for the RZ67. Or at least, their charts claim they are corrected well into 700nm+: https://ianbfoto.com/downloads/Mamiya%20RZ67/Mamiya%20RZ67%2...

They say no focus adjust is necessary for the APO lenses for IR, B&W, and color film.

Telescopes for astronomy are often corrected well into the infrared regime due to some of the fairly interesting emission lines that can be imaged using an appropriate camera.

The linked article perfectly explains it though no?

Never bother someone who has just came out of a rabbit hole.

I laughed at the fact that you seem so familiar with this state and are sympathetic to it.

Future improvements in simulations and manufacturing will probably enable micromanaging light in 3 dimensions. Ive seen some very strange fractal and composite lenses.

I mean, dispersion matters simply because people generally don't want colored fringing and general haziness in their photos?

There are two types of chromatic aberration (CA), both caused by dispersion.

* Axial: perfect focusing is impossible because different wavelengths focus at different distances. If green light is focused correctly, then red and blue light is out of focus. This affects the entire image and is very difficult to fix in post-processing.

* Transverse: there's no unique image because magnification depends on wavelength. Blue light forms a slightly larger image than green, and green larger than red. This manifests as color fringing, most apparent near the edges and corners of the image, far from the optical axis. This can be alleviated algorithmically, by resizing the red and blue sub-images to match the green one.

Recently I learned that today's lenses don't contain "just glass" as optical elements but often specially designed plastic elements too.

Here's a video by Gordon Laing showing a "Canon lens TEARDOWN! What's INSIDE a new lens?"

https://youtube.com/watch?v=YH5_nVRWHZ0

Some Canon lenses like the EF 17-40mm L use "replica" aspherical elements...

Replica aspherical lens elements are produced by using an aspherical surface mold and ultraviolet-light-hardening resin to form an aspherical surface layer on a spherical glass lens.

Isn’t that a super budget lens? How’s the pixel peeper performance?

I owned the EF 17-40mm/4 years ago and did not like it, other than the affordable price. The corner sharpness was poor. Plus it lacked image stabilization. I was so happy when I upgraded to the EF 16-35mm/4 IS and got a noticeable boost in sharpness, and I could shoot with longer shutter speeds and lower ISO in indoor/night situations.

"L" has a red ring and everything!

Not a budget lens, but it was extremely good value for money at the time and had excellent image quality for an ultra-wide zoom. Later lenses were better...

If you like teardowns, I will plug the Lens Rentals blog @ https://www.lensrentals.com/blog which features teardowns such as https://www.lensrentals.com/blog/2021/01/the-secret-of-the-b...

Too bad Roger Cicala stopped writing.

My mother was a geologist. She had a piece of fluorite that was clear, and she would put it over things, and it would double them (you'd see two of everything).

It has some interesting optical characteristics.

If I remember, the stone was soft, and sensitive to shock and temperature changes. Probably makes it challenging to work with.

Pretty sure that was calcite - famous for double refraction.

https://sciencedemonstrations.fas.harvard.edu/presentations/...

You are correct. I misremembered.

Flourite was ... very fluorescent.

as it turns out, pure fluorite has no fluorescence, even though fluorescence is named for fluorite

Well, it has been a long time (like, 40 years), but I’m pretty sure I remember it being strongly fluorescent. It might have been impurities, though.

yeah, that's normal, which is why it's called fluorescence. pure natural minerals are very rare

And here I thought they meant Eyes Glasses .... Darn.

I also thought they meant eyeglasses. I used glasses for a few years and never cared much for chromatic aberration, but once I started to use contacts, going back to glasses makes it very noticeable, specially on the periphery of the lens. Lenses on glasses need to be very high quality to approach the image quality of contacts in terms of distortion.

Last year I got a new prescription and the optometrist convinced me to switch to higher refractive index lenses, because they are thin, light, don't have a subtle yellow hue like CR-39, don't distort the facial features and so on. I agreed and couldn't wear them at all due to insane chromatic aberration. After a few complaints they relented and replaced the lenses with CR-39 and I have been happy ever since.

Do you mean "High Index" lenses? ... I have strong prescriptions of -9.x and -11.x and I have had 1.66 index lenses. I've always noted to doctors light sources move around or float around alot with the lenses. I haven't necessarily noticed a difference with contacts (but I did see sharper with hard contacts) but my eyes cannot tolerate hard or soft lenses.

I have tried even higher index lenses, but anything above 1.66 and the distortions and optical aberrations get too annoying ...

Yes, high refractive index lenses. -9 and -11 sound like actually good reasons to recommend them, at these levels of myopia lower index glasses should be noticeably heavier.

What I couldn't tolerate was specifically chromatic aberration. Every letter in this text box would have a yellow and blue fringe if my head was turned even slightly. And this would happen with every high-contrast border, like someone's t-shirt, a white car or a house against the sky.

Fluorite lenses are incredible, but not a critical win until you get to high mag or up against the speed limits of your system. When it really becomes apparent is when coupled with VR stabilization, which can get you 4+ EV stops of speed. When the subject is that crisp, the chromatic aberration is significant, or, with fluorite, not. Interestingly, modern photography suites offer both correction of effects of lenses (e.g vignetting and pincushion) and chromatic aberration in silicon. Compared to where I started with a circa 1989 Nikkor 70-210 f/4 and film, the pictures I can take today are incredible. The real problem, for me, is editing down to a digestible number of eye-poppingly good shots. I imagine kids these days are thoroughly unimpressed, but I'm humbled by the incredible amount of engineering that has gone into photography.

... modern photography suites offer both correction of effects of lenses (e.g vignetting and pincushion) and chromatic aberration...

Yeah. I haven't worried about chromatic aberration in lenses for about 15 years now. It's trivial to automatically correct in post processing, as long as you shoot RAW.

As am I. Starting with film in a similar era and moving along with every 1 or 2 major generational shift in CMOS since then, I’m delighted to be at a point today where my output is bottlenecked by the actual 55000mbps M2 SSD in my MacBookPro for whizzing through hundreds of GB of stills for every shoot to distill down to about 10 best ones.

The fluorite lenses also allow them to shrink the lens design and make it easier to carry around. They do this by reducing the # of elements required. It's why you mostly see them in big long focal length lenses since that's where the size & weight gets really obnoxious.

I wasn't aware that Canon used flourite elements. You learn something new every day. Nice. Their telephoto lenses also use holographic elements, and I attended a talk (1990 ish) where one of their lens designers spoke about a clever scheme using diffraction order pairs (n and n + 1) to compensate each other. This allowed them to use diffractive dispersion in addition to glass (and now I know flourite) for color correction without introducing stray light (ghosts) due to unwanted diffraction orders, which are nearly impossible to get rid of. These lenses are works of art.

The fragility of fluorite was one a reason why Nikon gear was chosen for the International Space Station iirc.

Plus that little red marquee looks rad against the infinite universe.

Their fluorite lenses in Takahashi telescopes are a hit among amateur astronomers.

I don't understand why chromatic abberation isn't simply fixed in software.

Knowing that your red, green, and blue images will have slightly different focus points and sizes seems pretty easy to fix.

For a stationary scene, you simply take 3 separate photos - one focussed for each colour, and then rescaled to match each others sizes.

For moving scenes, the math is more complex, but you should still be able to fix most of the issues.

The only real issue is light that is "yellow" - ie. halfway in wavelength between different colours. The only perfect fix for that is to have each pixel be a spectrometer. Even that seems possible by using variable-bandgap sensors.

You can't create information that wasn't in the captured image. CA reduces spatial resolution.

All of the current RAW image processing software have features to reduce chromatic aberration. Many of them have databases of lenses that match the EXIF data of the lens you used to take the photo to help automatically adjust the image the right amount.

I have a FD 300/2.8 S.S.C. Fluorite lens, introduced in 1975. It's a FANTASTIC lens, sharp corner to corner wide open at f/2.8, and excellent for astrophotography. It's able to capture details of the Orion nebula, horsehead nebula, and the spiral arms of the Andromeda galaxy in a single shot. It's also excellent for outdoor portraits and creams backgrounds, though you'll need to use a phone call on speakerphone to talk to your subject.

The list price back then was 420000 JPY which is $5364 in today's dollars. I got it for $400, used.

Back then prices of FD mount lenses dropped dramatically because nobody wanted them: the flange distance was too short to be adapted to any DSLR. I ended up taking apart the entire back part and machining a conversion mount to make it usable on DSLR. (An adapter ring won't work, since it adds thickness.)

Unfortunately with the advent of mirrorless cameras, FD lenses are once again usable with simple adapter rings, and their used market prices have gone back up. However they're still excellent, excellent value for $ in comparison to modern autofocusing equivalents in optics; the lens I have costs ~$600-$1000 on eBay now whereas a new Sony 300/2.8 GM costs $6000. For anyone looking for a fast, large aperture telephoto lens I'd highly recommend looking into FD lenses that have fluorite elements, as long as you don't mind manual focus.

I used to have a FD 500mm f/4.5 which is nice but not as well corrected as modern glass. I got it for $750 which, too, is a bargain.

as long as you don't mind manual focus

Given that the primary use case of large aperture telephoto lenses is sports and wildlife, fast autofocus is a killer feature. Moreover, modern computer optimization has managed to vastly lighten the weight and improve the weight distribution of the lens, not to mention impeccable image quality, which is why for many the $6000 is more than justified.

For astrophotography manual focus is preferable.

For wildlife, manual focus is actually not that hard with some practice, as long as it's not birds.

For sports, yeah, it's difficult.

Curious - is this really expensive to make? Why is chromatic aberration even a thing now if we've had this technology since 1969?

Because it's not really something that matters for the vast majority of consumer photography equipment.

https://istarscopeclub.proboards.com/thread/247/twisting-fac...

^Some 2012 forum post claiming the material cost $2000/kg, although their wording is ambiguous on whether this was the price for the raw material or the finished lens. But based on the manufacturing process described in the source link of this post, it would appear to be a much more cumbersome and complex process than manufacturing regular glass lenses. Fluorite lens are also more fragile which may impact yield %.

Fluorite (CaF2) lenses and windows are also used for infrared applications as they transmit much better than glass.

Maybe I’ll get thinner than 1.75 lenses some day for my crazy high prescription.

Super UD and UD have been some of the gold standards in lenses for a long time. Fluorite plays a huge part in it.

Fun further reading: https://www.canon-europe.com/pro/infobank/fluorite-aspherica...

Don't have much to add, but this article was so pleasing to read. Those diagrams with the light dispersion really tickled me - is that spectrum real or is it a render?

Fluorite is an obsolete term in the optical engineering community. The term used today is simply “calcium fluoride.” Calcium fluoride windows are used extensively as the expendable windows of the 308nm XeCl laser, which anneals every thin film display made.