In article , Gareth Knight <gknight@xxxxxxxxxxxxxxxxxxx> wrote
>Hi,
>
>If f8, is really f7.7, this makes quite a difference to me. I have a
>nice Sekonic light meter, which returns its readings in whole f stops
>plus a decimal increment. For instance, it might display 1/125 and
>f8.7. If I'm using slide film, which has such a small margin of error
>anyway, I would like to know that, in this instance I can safely set
>the lens to f8 (since it is actually f7.7) rather than round up to
>f11. In this case, rounding up to f11 might have produced
>underexposure outside the slide film latitude.
>
>Could someone produce a true f-stop table ?
>
Start from f/0.5 and increase in steps of the square root of two. This
assumes a circular aperture for the lens, so the area of the aperture is
proportional to the square root of the aperture diameter. Since most
irises are only an approximation to a circle, small errors are normally
tolerated. The numerical error is NOT at f/8, which is exactly 2^3, but
at f/11 which should really be f/11.31 to maintain the correct ratio
relative to the stops above and below it. This is no more significant
than the error in the standard shutter speed stop sequence going from
1/8th to 1/15th of a second, and is well within the tolerance of any
film.
Real stops (x2 per step) Standard Stops Error
0.5 0.5 0
0.707 0.7 +2%
1 1 0
1.414 1.4 +2%
2 2 0
2.828 2.8 +2%
4 4 0
5.657 5.6 +2%
8 8 0
11.31 11 +5.5%
16 16 0
22.63 22 +5.8%
32 32 0
45.25 45 +1%
64 64 0
Remember, f/# = n1/(n2 x 2 x sin(t)) where t is half the angle subtended
by the aperture at the focal length, f, and nx is the refractive index
of the medium on either side of the optic. This takes account of
Llambert's Law, which defines the amount of light absorbed or emitted by
a surface as a function of the incident angle. For smallish apertures
(f/# greater than ~1.4) the angles of incidence are small and so f/#
approximates to 1/2tan(t) which simplifies to f/D where D is the
diameter of the aperture. Most photographic manuals 'define' f/# to be
f/D because the approximation is so close to the exact value over the
range of apertures encountered in normal photography. The difference is
really only significant for low f/#'s used in technical and scientific
work. A consequence of this is the minimum f/# that can theoretically
be achieved is f/0.5, but this needs an infinitely large aperture, and
is therefore impractical. The fastest practical lens I have seen was a
50mm f/0.6, a huge beast from Rank-Taylor-Hobson, made from germanium
and used in an old thermal imaging system based on pyrovidicon
technology.
Incidentally, it is because f/0.5 is the theoretical minimum f/# that we
start the progression there and have the standard numbers we do.
You can get microscope objectives which are quoted as faster than 0.5,
but these are intended to be immersed in high index oil between the
subject and the lens, which reduces the working f/# by the refractive
index.
You can sometimes find normal lenses marked as faster than f/0.5 as
well, but some experimentation with a TTL meter will show you that they
are not as fast as they claim to be - the figure is based on extending
the photographic approximation of f/D into the low f/# region where it
is no longer accurate.
All of this ignores the transmission of the glass that the lens is made
from - that's why they used to have T-numbers, which took this into
account as well. The more glass the lens is made from, the bigger the
discrepancy between f/# and T/# - at all apertures.
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)
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