Fluorite lenses: Corrective capabilities beyond ordinary optical glass
global.canon
global.canon
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.
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
This is a clever bit of folk etymology [1], but aberrate is derived from the Latin verb aberro, meaning to wander or stray [2].
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.)
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.
Latrine: We changed it in the 9th century.
Prince John: You mean you changed it TO "Latrine"?
Latrine: Yeah. Used to be "????house."
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.
'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
Since 1136? :p
(sorry, can't have a pedantic thread without pedantic jokes, it's obligatory)
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
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
Cheers for that.
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.
Some more info here
Miles V. Klein, Thomas E. Furtak - Optics 2nd ed, Wiley
Joseph W. Goodman - Introduction to Fourier optics, W.H. Freeman
Goodman is great, Hecht and Zajac covers more fun with optics at an intro level.
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.
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
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.
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).
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...
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.
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.
They say no focus adjust is necessary for the APO lenses for IR, B&W, and color film.
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.
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 :)
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.
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.
Trying to keep things simple here.
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.
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.
> 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 wildlife, manual focus is actually not that hard with some practice, as long as it's not birds.
For sports, yeah, it's difficult.
Here's a video by Gordon Laing showing a "Canon lens TEARDOWN! What's INSIDE a new lens?"
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.
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.
I've been following this newsletter for a while as I have a passing interest in (photographic/cinematic) lens design.
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.
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.
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...
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.
'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'
> 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.
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).
> 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.
0. https://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relatio...
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.
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.
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.
Fun further reading: https://www.canon-europe.com/pro/infobank/fluorite-aspherica...
I have tried even higher index lenses, but anything above 1.66 and the distortions and optical aberrations get too annoying ...
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.
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.
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.
https://sciencedemonstrations.fas.harvard.edu/presentations/...
Flourite was ... very fluorescent.
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 %.