Glass Refractive Index Measuring System (GRIM) - refractive index in glass
F-number lens
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? ;)
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Aperture f numbercanon
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...
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Working f-number
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f-stop photography
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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:
The PSM-5 and PSM-10 microscopes are part of a complete range of portable equipment and consumables for materialographic, non-destructive preparation and inspection. These tools are supplemented by a wide range of replication products.
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 battery-powered LED light provides an excellent view of the subject for inspection and does not require a separate external power supply.
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 :-)
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.
F-number calculator
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).
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.
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.
Aperture f numberphotography
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.
F-stop vsaperture
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...
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.
f-number formula
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.
With its CMOS sensor, the 3 megapixels digital camera for PSM microscopes is aimed at professionals with high demands in terms of image quality, dynamic and sensitivity. Dedicated to optical microscopy, it is used in the metallography laboratory or on site. The digital camera for PSM microscopes is a good compromise between speed and resolution. Its sensor delivers a resolution of 3.2 megapixels. Its high definition digital sensor provides sharp images with low noise, and fast live image for easy focusing. In combination with Perfect Image Lite software, microscope objectives are easily calibrated, and a scale bar can be automatically merged in the captured image. All cameras parameters can be saved and recalled for maximal ease of use and reproducible images. Measurements on the live or captured images are available, such as length, area, angle and alike. Advanced versions of the software are available for more demanding applications such as grain sizing, cast iron analysis and alike.
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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.
Part of the Struers non-destructive portable preparation and inspection range, the PSM-5 and PSM-10 microscopes are easy to transport. The aluminum transport case can contain all that is necessary to perform an inspection, including microscopes, a camera option, and a microscope adapter.
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.
(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!)
A wide range of accessories means that the hand-held PSM-5 and PSM-10 microscopes can be used for a wide variety of inspection types.