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by Bart Arondson

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Talking about fast lenses, Wikipedia mentions

Nikon TV-Nikkor 35mm f/0.9-Fastest Nikon lens ever made

Why don't, for example, f/0.5 lenses exist?

Is there some special construction that comes into play for an f/0.9 lens?

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Note this is the fastest Nikon lens. Zeiss makes a F/0.7 which was famously used by Stanley Kubrik for candlelit scenes: visual-memory.co.uk/sk/ac/len/page1.htm - Never heard of an F/0.5 though. –  Itai May 16 '11 at 2:44

5 Answers 5

You know, I was going to argue lens mount and then I realized that I have a 200mm f/2.8 and the aperture on that is 71.4mm which is larger than the opening on my camera. So, I the only reason I can think of is cost...

To get the advantages of an aperture wider than the mount diameter, the maker has to be doing some extra work with the rear elements and that will cost. This becomes a cost benefit analysis because they aren't going to expend the effort on a lens that will then cost so much that almost nobody will buy it (happens every now and then, Google the Canon 5200mm lens). They have to ask, what does the extra light really give on any given lens? I think, for the most part, once you're in to the 1:1 ratio of aperture to focal length, the answer is not a lot, or at least not a enough to justify.

As to how they can squeeze the benefit of an aperture larger than the mount, well, I'm not a physicist or a lens maker... I'll leave that to people smarter than I. Mind you, I suspect that there is a limit to how big an opening you can get for a given focal length, regardless, but how to arrive at that, I don't know.

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F/0.7 is a stop brighter than F/1.0. But the cost of that stop would be too much. –  Nick Bedford May 16 '11 at 3:46
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Remember that the physical aperture size as calculated from relative aperture is only as viewed through the front lens element (which tends to magnify the innards a bit.) The true physical size of the aperture is usually not quite that large. It is possible to correct for an aperture larger than the mount with more optics...but thats part of where the added cost of wider apertures comes into play. –  jrista May 16 '11 at 5:21
    
@jrista - Would the correction not be in the rear elements then? –  John Cavan May 16 '11 at 13:58
    
Yes, it usually is. I think they call that exit-pupil correction. –  jrista May 16 '11 at 15:28
    
I think the comment by @jrista here is a crucial part of the overall answer — while it's possible to make the exit and entrance pupils asymmetrical, that's not conventional in lens design and would almost certainly add to the expense. See en.wikipedia.org/wiki/Pupil_magnification –  mattdm May 17 '11 at 17:25

The wider a maximum aperture, the more prevalent optical aberrations will tend to be (given a "simple" lens.) Wide aperture lenses become increasingly difficult to manufacture at reasonable cost, as you have to put more effort into correcting those optical aberrations. Additional lens elements are necessary to mitigate chromatic aberration (which can become quite horrendous at apertures wider than f/2), correct for distortions (to maintain rectilinear behavior and minimize distortion effects), correct for spherical aberration and the focus shifts that result from it (or, leave the spherical aberration in, and correct for focus shift with additional electronic intelligence), etc.

It should also be noted that a larger f/# must maintain the ratio of light allowed with other similar lenses. An f/0.9 lens must allow 1.5 more stops (more than 2x as much light) than an f/1.4 lens, and the physical size of the aperture to achieve that often requires a larger lens barrel diameter. Increasing the barrel diameter requires, at the very least, a larger front element, which can quickly add to the cost of a lens. An f/0.5 lens must allow nearly 3 stops more light through as an f/1.4 lens (a volume of 8x greater light), and requires a physical aperture that has a diameter 2.8 times larger. Note that it is important to remember that the physical aperture size as calculated from relative aperture is only as viewed through the front lens element (which tends to magnify the innards a bit.) The true physical size of the aperture is usually not quite that large, however lenses with particularly large maximum apertures beyond f/1 do generally necessitate a bulky lens barrel. It is possible to correct for an aperture larger than the mount with more optics...but thats part of where the added cost of wider apertures comes into play.

Combined with the necessity of correcting the increasing effects of optical aberrations, faster lenses require larger elements, more glass, in more groups, with more moving groups, to achieve usable quality at wide apertures. That amounts to tremendous cost, requiring prices that are out of range for most photographers. When it comes to a manufacturer like Zeiss, the creation of an f/0.7 lens (the fastest camera lens on earth, as far as I know), it is probably more of a prestige thing than a money maker...the best lens maker on earth had better have the best lenses in all cases, right? ;)

(As it turns out, Zeiss pretty much does, given their superb optics, and between having the fastest 50mm f/0.7 lens, and the longest at and clearest telephoto lens with their Apo Sonnar T* 1700mm f/4 lens...and believe me, a 1700mm f/4 is almost as insane as a 50mm f/0.7...thats a TON of light for such a long focal length!)

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An f/0.9 lens should allow in more than twice as much light than an f/1.4, and an f/0.5 would be 3 stops faster than f/1.4. –  Evan Krall May 17 '11 at 4:35
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@Evan (continuing your thought) ... letting in 8 times more light and requiring a diameter 1.4/0.5 = 2.8 times greater (much more than "nearly twice"). In short, any f/0.5 lens has to collect light across a disk twice as wide as its focal length and still manage to focus it in a plane with reasonable sharpness. –  whuber May 17 '11 at 5:41
    
@jr Thanks for the clarification. I didn't catch that you were talking about area and not f/number. In fact, your message still refers to "an f/0.5 lens" and "an f/1.4 lens," so you might want to recheck that you are using the f/ notation consistently with your intended meaning. –  whuber May 17 '11 at 14:06
    
@jr Then I'm woefully confused. Please correct my misunderstanding of either (or both) of these crucial points. (1) The "f/" notation is conventional. It only means the ratio of the entrance diameter to the focal length, never anything else. (2) The area of a shape is proportional to the square of its diameter. These are the basis of @Evan's analysis and of my continuation, but I can't reconcile them with your analysis. –  whuber May 17 '11 at 16:38
    
On the most recent edit — f/0.9 to f/1.4 is about 1⅓ stops, right? So that's 2^1⅓ times the light, or about 2.5×. And (as Evan says) f/0.5 to f/1.4 is a full three stops, or 8× the light. This is nitpicking and doesn't alter your point in any way. :) –  mattdm May 17 '11 at 17:05

Lenses faster than f/1.0 exist but the prices skyrocket once you get below 1.0 as you're close to the limit of how far glass can actually bend incoming light! Tolerances become very tight and manufacture is expensive. The limit is around f/0.5 for glass (which has a refractive index of 1.5) to go faster you'd need to use a more exotic material such as quartz or sapphire, pushing the cost even further. I once read a thread online where someone calculated you could.make an f/0.25 lens but it would have to be built entirely out of diamond...

You'd have to have a very good reason to go faster, "to take better pictures indoors without flash" doesn't quite do it. It has to be something like "I'm going to walk on the surface of the moon for the very first time"...

The fastest lens I've ever heard of was f/0.55, almost two stops faster than Canon's legendary f/1.0! They are used for lithographic etching of silicon wafers and the aperture is required to avoid diffraction limiting the resolution. The same effect that causes soft images with DSLRs at f/16 starts to occur at wider and wider apertures as you try to extract more detail.

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"the aperture is required to avoid diffraction" Not quite. Diffraction cannot be avoided, ever, but the size of a focal spot from a faster lens is smaller. The focal spot is the result of diffraction from the exit pupil of the lens, and has a size of 2.44 * wavelength * f-number. –  Colin K May 16 '11 at 15:46
    
Yeah I meant diffraction problems. I'll clarify. –  Matt Grum May 16 '11 at 15:52
    
+1 Fascinating. I was wondering whether there were geometric limits to the f/stop and figured that somewhere around f/0.7 or so would be the limit for singlet (simple) lenses using ordinary glasses. However, it occurred to me that one conceivably could get extremely low f/stops with compound lenses, such as retrotelephoto lenses, or possibly even fiber optics, so I would hesitate to claim that f/0.5 or even f/0.25 is an ultimate limit: people are clever about breaking such apparent barriers! –  whuber May 17 '11 at 20:51
    
Perhaps this is the thread you got that info from? answers.google.com/answers/threadview?id=241629 It provides some equations and puts some extreme values in to guess at maximum f-numbers. –  drfrogsplat May 18 '11 at 3:07

Others have already mentioned cost, and they're right.

Another that's probably more meaningful for most practical purposes is that your depth of field would nearly evaporate into none at all. Just for example, consider a shot with a 50 mm lens from around 3 feet away -- a more or less typical head/shoulders type of shot. At f/1.0, your DoF is already down to 3/4ths of an inch. At f/0.5, it would be approximately 3/8ths of an inch -- if, for example, you focused on somebody's eye lashes, the eye itself would be noticeably blurred (or vice versa).

I guess if your primary ambition is to shoot pictures of stamps under glass at night, the minimal DoF wouldn't be a problem -- but for most subjects, using it well would be challenging.

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There is a Zeiss Lens called "Carl Zeiss Super-Q-Gigantar 0.33/40mm" Yes it got a max aperture of f/0.33 and therefore is the fastest lens ever made.

At the moment it is on auction at Westlicht-Auction. Since I am not sure if I am allowed to link to such a page here is the description:

Carl Zeiss Super-Q-Gigantar 0.33/40mm (c. 1960) This is the world's fastest lens ever made, for Contarex Bullseye. Unique lens made by Carl Zeiss for Public Relation purposes - ex Barringer Collection.

I am not really sure if this monster ever produced pictures, because there are simply no samples around. Everybody seemed to make pictures OF the lens, but not with it :-)

Picture of the Super-Q-Gigantar

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HA! Just love the name...'Gigantar' just exudes a special feeling just hearing it! –  jrista May 17 '11 at 23:19
    
It has to be said though that the lens was not a working one, but rather a mockup as an answer to the fixation on larger and larger apertures during the 1960s. The lens designation "40 mm" was entirely arbitrary set by the designer and had nothing to do ith the optics inside it. petapixel.com/2013/08/06/… –  Hugo Aug 20 at 6:54

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