Limiting factor for Aperture

[KeithB]

After my link to the 50mm/1.0 review, I got to thinking, is there a limiting factor to aperture size? Does the camera format matter? I know it would be difficult to control imperfections/aberrations, but would a f/0.5 lens be possible?

[Bob Atkins]

I think the fastest possible lens in air is 0.5. This corresponds to a numerical aperture of 1 (in air). There are well known examples of f0,95 (Noctilux) and there were 10 Zeiss 50mm  f0.7 lenses made, 6 for NASA for NASA and 3 for Stanley Kubrick who used it when shooting Barry Lyndon (scenes shot by real candlelight) and one kept by Zeiss. The Russians claimed at f0.5 mirror lens, but it only had a circle of coverage of about 3mm, smaller than a digicam sensor. Not sure anyone has actually seen one though.

So the fastest practical camera lens ever made is f0.7. You may see smaller numbers but they are either a joke or take into account the effect of an attached image intensifier and the actual geometric f number is larger than 0.7 (probably larger than 1.0).

A number of very fast telescope mirror cameras have been built for wide field astrophotography. There are f0.75 Schmidt type astrographs, but they couldn't be used on a camera because the focal plane plane is strongly curved (and you'd have to mount the camera in the middle of the lens!).

Superfast microscope objectives are oil immersion, i.e. the space between the lens and subject is filled with oil (which has a higher refractive index than air). They can have a numerical aperture greater than 1, and so an effective f-stop of less than 0.5. You can get them with an NA of 1.4 and an effective f-stop of 0.36.

I think you can similarly get a fast lens by not using any air between the lens and the film. Not exactly very practical for photography!

I suppose that an underwater lens, with the first lens element (not a filter or plane window) directly exposed to the water, could be made faster than f0.5. With a refractive index of 1.33 for water it should be theoretically possible to make an f0.375 underwater lens.

If you want to get technical, Numerical Aperture (NA) = U*sin(a) where U is the refractive index between the lens and subject and a is the half-angle subtended by the lens at the sample. Since the maximum value of the sine function is 1, the maximum numerical aperture approximates to the refractive index of the medium between the lens and the sample. The f-stop approximates to 1/(2*NA) or a maximum of 0.5 for air (refractive index=1).

BTW, You can ignore the Carl Zeiss Super-Q-Gigantar 40mm f/0.33 as it was a joke. They made one for publicity out of scrap parts and a condeser lens, but it was incapable of forming an image on film so the "speed" was simply made up. It looked very impressive.

[KeithB]

Thanks.

I assume the T stop at some point wipes out any gains below a certain F/stop anyway.

[Bob Atkins]

I'd guess that would be a factor. Really fast lenses need a lot of glass, especially if they are well corrected (lots of elements). The absorption of that much glass may well become a factor, though with modern glasses and coatings it should be a small factor. Even if 50 % of the light was lost in the lens it would only make the T-stop of an F/0.5 lens T/0.7.