Related Links:
F-stop Pages
| F/stop | 1/3rd stop | 1/2 stops | 2/3rd stop |
| 1 | 1.1 | 1.2 | 1.3 |
| 1.4 | 1.6 | 1.7 | 1.8 |
| 2 | 2.2 | 2.4 | 2.5 |
| 2.8 | 3.2 | 3.4 | 3.5 |
| 4 | 4.5 | 4.8 | 5 |
| 5.6 | 6.3 | 6.7 | |
| 8 | 9.5 | ||
| 11 | 13.5 | ||
| 16 | 19 | ||
| 22 | 27 | ||
| 32 | 38 | ||
| 45 | 54 | ||
| 64 |
Sounds very complicated and not very exact. It is much simpler to multiply
with roots of 2 to calculate the exact values. Fourth root for 1/2 stops,
sixth root for 1/3 stops and so on.
Example: series of 1/2 aperture stops when multiplied with the fourth root
of 2. (rounded values)
1.000 1.189 1.414 1.681 2.000 2.378 2.828 3.363 4.000 4.757 5.657 6.727 8.000 9.514 11.314 13.454 16.000
Greetings AriP.
From Pentax Mailing List;
From: "Bob Blakely" [email protected]
To: [email protected]
Subject: Re: f/calc and The Mathematics of Apertures
Date: Sun, 23 Apr 2000
I have lenses with these markings:
Note that f/3.5 is 1/3 stop faster than f/4
Note that f/4.5 is 1/3 stop slower than f/4
Also f/1.2 is 1/2 stop faster than f/1.4
Actual stop Marked 1.00000 whole 1.12246 1/3 1.1 1.18921 1/2 1.2 1.25992 2/3 1.41421 whole 1.4 1.58740 1/3 1.68179 1/2 1.7 1.78180 2/3 1.8 2.00000 whole 2 2.24492 1/3 2.2 2.37841 1/2 2.4 2.51984 2/3 2.5 2.82843 whole 2.8 3.17480 1/3 3.2 3.36359 1/2 3.56359 2/3 3.5 4.00000 whole 4 4.48985 1/3 4.5 4.75683 1/2 5.03968 2/3 5.65685 whole 5.6 6.34960 1/3 6.3 6.72717 1/2 7.12719 2/3 8.00000 whole 8 8.97970 1/3 9.51366 1/2 10.07937 2/3 11.31371 whole 11 12.69921 1/3 13.45434 1/2 14.25438 2/3 16.00000 whole 16 17.95939 1/3 19.02731 1/2 20.15874 2/3 22.62742 whole 22 25.39842 1/3 26.90869 1/2 28.50876 2/3 32.00000 whole 32
Regards,
Bob...
From Nikon Mailing List:
Date: Mon, 11 Sep 2000
From: Ihor Karpinsky [email protected]
Subject: Re: [NIKON] Shutter speed table
Geert Van de Wiele wrote:
> ... what is the exact shutter speed corresponding to 1/6 stop > less than 1/250 of a second, and how to calculate it correctly?
Difference between two consecutive complete EVs in time scale (for
shutter)
is 2
(shutter speed should be increased (decr.) two times for 1 EV difference).
What I mean:
for example, (1/125) sec +1EV = 1/60 (in shutter speed scale).
And real shutter speeds are in ...1,2,4,8,16,32,64,128,256,512,1024... set
(2^N)
for denominator of a real time in seconds scale.
So, 1/128 of a sec. multiply by 2 (for 1 EV greater) equal 1/64 of a sec.
1 EV diff. equal multiply (divide) by 2 (2^1).
...128(125), 256(250), 512(500), 1024(1000),... shutter speed scale
1/2 EV diff. equal multiply (divide) by 2^(1/2) = square root of 2 = ~
1.4142
...128(125), 181, 256(250), 362, 512(500),... shutter speed scale
1/3 EV diff. equal multiply (divide) by 2^(1/3) = cubic root of 2 = ~ 1.26
...128(125), 161, 203, 256(250), 323, 406, 512(500),... shutter speed
scale
1/6 EV diff. equal multiply (divide) by 2^(1/6) = hex root of 2 = ~ 1.12
...128(125), 161, 203, 256(250), 323, 406, 512(500),... shutter speed
scale
> Anyone > knows the formula? Anyone has a table?
I think, you already know the formula.
> Would anyone know the same for aperture stops, also up to 1/6 of a stop
Same story, but note, that amount of light on the film is proportional to
square of aperture diaphragm circle, so base for aperture scale
is square root of 2, not 2.
- --
Best Regards! Ihor Karpinsky.
[Ed. note: Mr. Erwin Puts is a noted Leica lens tester and author of many
photographic articles and resources; his posted note discusses how
accurately our processes really are, and relates to issues of metering to
1/10th f/stop...]
From Leica Mailing List:
Date: Mon, 20 Nov 2000
From: imx [email protected]
Subject: [Leica] Accuracy and reproducibility
Recently there was a discussion about the drop in transmission of light
when using an UV filter. But how accurate can we work in BW photography?
Most products and processes allow for plus/minus 5% margin. Let us add a
few steps.
We start with the exposure meter: 5% deviation from the indicated value
versus the true light level. Often 1/10 of a stop and more..
The shutter speed of the Leica M may deviate by 10 to 15%.
The mechanism of the aperture stop is allowed to deviate by 5% from the
indicated value.
The true filmspeed may deviate by 1/6 of a stop from the nominal value.
The development process itself brings again a deviation of 5% to 10%, As
humans we cannot reproduce the process exactly and time, temperature, mix
of
chemicals, quality of chemicals are all parameters that may deviate by at
least 10%.
Mostly the plus deviations in this chain will cancel out the minus
deviations, but even then we have to assume that one exposure of 1/15 sec
at 1.4 on ISO400 film may deviate from the same exposure on a second film
by at least 25% and in worst case situations, you may be off by 40%, even
if you try to control all parameters and try to be as accurate as you can.
Exposure meter: 5% Shutter 5% - 10% Aperture 5% Filmspeed 5% - 10% Development 5% - 10%.
With a Leica R8 we are lucky as the shutterspeed is more accurately
controlled and the true aperture may be accounted for at the exposure
metering stage. We are also lucky as the exposure meter can use smaller
increments of shutter speed when we are in aperture priority.
But with an M, we have to work in increments of half a stop. This implies
that whatever figures the exposure meter gives, we have to round off to
these half stops. If the meter reads (as example) EV 10.3, we can use only
EV 10 or EV 10.5, as we can select only half stops (apertures 2.8 and 3.4:
again examples). With EV 10 we overexpose by a 1/3 stop and with EV10.5 we
underexpose by 1/5 stop. But given the margins, both exposures might be
right, or both may be off.
I once shot 36 frames at the same speed and aperture of a grey card and
after development, measured the density of each negative. Any variations
between the densities could only be explained by the error margin of the
shutterspeed. There was a measurable and sometimes visible deviation.
The upshot: deviations in a magnitude of 1/4 to 1/3 stop will occur, even
if we control our process as good as we can. It is hardly possible to use
a narrow margin of 1/6 of a stop, and we should settle for 1/4 stop as a
reasonable margin of accuracy.
But: if all deviations add up, we may differ by a full stop compared to
another person. So if someone remarks that he gets fine results with TriX,
pushed to 800, he may in fact be using his tolerance values and another
person with TriX at 400, might get identical results in identical
situations, depending on his margin of tolerance.
Upshot 2: never follow the specifications, given by others, as their set
of system components may deviate significantly from your own. Establish
your own set of specifications and stick with them. If you fail to get
good results with TRiX at 800 (your system), and another one gets good
resuts with TriX at 800 (his system), do not think you are doing something
wrong and do not try to emulate the other's recommendations. Or if you do,
make comparison shots with both sets of specs in ONE situation.
I do all comparison shots with flash light as this is the only way to make
sure that at least one big variable is under control.
Erwin
From ROllei Mailing List:
Date: Wed, 27 Dec 2000
From: Richard Knoppow [email protected]
Subject: Re: [Rollei] Off topic: Rapid Rectilinear
you wrote:
>I have a B&L f4 135mm (approx?) mounted in an EKC ball bearing shutter,
This is actually US 4, equivalent to f/8. US stops are equal to N^2/16
where N is the relative aperture (f/stop).
US f/ 1 4 2 5.6 4 8 8 11 16 16 32 22 64 32 128 45
The Uniform System was proposed around 1890 and used until the 1930's
for some lenses.
----
Richard Knoppow
Los Angeles,Ca.
[email protected]
From: "Q.G. de Bakker" [email protected]
Newsgroups: rec.photo.technique.misc
Date: Fri, 16 Feb 2001
Subject: Re: Ever need decimal values for 1/3 stops?
Michael K. Davis wrote:
> Here are the decimal values for "whole" stops and the 1/3 stops in > between: > > 1.0 > [snip] And here's how to calculate a series of fractional stops using any denominator you want: (2^(1/(s * 2)))^n * D s = denominator (2 for 1/2 stop steps, 3 for 1/3 stop steps, etc.) n = number of step D = f/stop for instance: series in 1/5 stop steps starting at f/2.8 (2^(1/(5 * 2)))^1 * 2.8 = 3.0 (2^(1/(5 * 2)))^2 * 2.8 = 3.2 (2^(1/(5 * 2)))^3 * 2.8 = 3.4 (2^(1/(5 * 2)))^4 * 2.8 = 3.7 (2^(1/(5 * 2)))^5 * 2.8 = 4.0 or, series in 1/7 stop steps starting at f/5.6 (2^(1/(7 * 2)))^1 * 5.6 = 5.9 (2^(1/(7 * 2)))^2 * 5.6 = 6.2 (2^(1/(7 * 2)))^3 * 5.6 = 6.6 (2^(1/(7 * 2)))^4 * 5.6 = 6.9 (2^(1/(7 * 2)))^5 * 5.6 = 7.2 (2^(1/(7 * 2)))^6 * 5.6 = 7.6 (2^(1/(7 * 2)))^7 * 5.6 = 8.0 or, 1/6.4 stop added to f/11 (2^(1/(6.4 * 2)))^1 * 11 = 11.9
Etc.
Remember that the normal f/stop scale uses rounded values. They should be
multiples of sqr(2), so 5.6 really is 5.6568..., or 4 * sqr(2), etc.
[Ed note: Mr. Bob Shell is a noted glamour photographers, photo
instructor, author of photo related books and articles, and former editor
of Shutterbug, as well as a noted past repairperson...]
From Russian Camera Mailing List;
Date: Thu, 31 May 2001
From: Bob Shell [email protected]
Subject: Re: f22 on Jupiter-3
> Remember that the glass will cause distortion, so any measurement should be > done with the glass element removed.
No, that is completely wrong. The f-stop is the apparent diameter of the
opening as seen through the front of the lens, not the actual physical
diameter. To measure it properly you need a special device found in
optical labs and test facilities.
Bob Shell
From Nikon MF Mailing List;
Date: Sat, 04 Aug 2001
From: "John Owlett" [email protected]
Subject: Re: Whole F Stops
Scott Perkins wrote:
> All my lens uniformly have 22, 16, 11, 8, & 5.6 as aperature > options but then some have below that 4, 3.6, 3.5, 2.8, 2.0, > 1.8, 1.4 > > I believe some of these are partial stops. > > Would someone please confirm which are the perfect whole stops > equal to one whole click faster or slower shutter speed where > one stop smaller aperature and one stop slower shutter speed > should not affect the meter needle ?
Hi Scott,
The conventional sequence of f/stop numbers -- the perfect whole
stops equal to one whole click faster or slower -- is
0.7 -- 1 -- 1.4 -- 2 -- 2.8 -- 4 -- 5.6 -- 8 -- 11 -- 16 -- 22 -- ...
... -- 32 -- 45 -- 64 -- 90 -- 128
The theory behind this (which we could happily explain if you like
... it's just that there has be some length limit, even on Dr Owl
postings) is that each number is the previous number multiplied by
the square root of two (1.4142...). But the conventional numbers are
close enough for any practical photographic need.
Up until the 1930s, many lenses from France and Germany used a
slightly different sequence of f/stop numbers, each one third of
a stop *smaller* than the conventional sequence:
... -- 4.5 -- 6.3 -- 9 -- 12.5 -- 18 -- 25 -- 36 -- 50 -- ...
In the UK this sequence became known "continental" f/stop numbers.
There are also f/stop numbers often used from the sequence which is
one third of a stop *larger* than the conventional sequence:
... -- 1.8 -- 2.5 -- 3.5 -- ...
And even some f/stop numbers from half-stop sequence:
... -- 1.2 -- 1.7 -- ...
As Rick says, modern Nikkor lenses have click stops marked with the
conventional f/stop numbers, except for the maximum aperture. The
maximum aperture usually comes from one of the traditional sequences.
Two final points about f/stop sequences. Apertures with large f/stop
numbers are often unsharp; apertures with small f/stop numbers are
difficult to make.
The problem with large f/stop numbers is that diffraction sets in
with tiny apertures. Diffraction is a fundamental part of the nature
of light ... and is usually explained by pretending that light is a
wave ... by someone who knows more physics than I.
The practical upshot of diffraction is that, in 35mm photography, you
shouldn't normally use apertures smaller than f/22. (Some purists
would limit us to f/16, but I find I often need f/22 to get the
foreground sharp.) With some close-ups, the only way to get any
depth-of-field at all is to use f/32 and risk the diffraction.
(Large-format users often use much smaller apertures (Ansel Adams and
large-format friends once called themselves "f/64") but I don't
understand why they don't have an awful battle with diffraction.)
The problem with small f/stop numbers -- "fast" lenses with wide
apertures -- is that the lens designer has to make compromises with
sharpness in the quest for speed. An f/1.4 lens is usually less
sharp at f/2.8 than an f/2.8 lens of the same focal length.
I'm told that the theoretical maximum aperture for a lens made with
spherical surfaces is 0.7. Nobody gets close to that, and the Noct
Nikkor 58mm f/1.2 achieves its status as King of the 1.2 Lenses by
using a (frighteningly expensive) precision-ground *aspherical* front
element.
I can think of only four 35mm lenses wider than the Noct. The Nikkor
5cm f/1.1 for the rangefinder cameras is probably a collectors-only
item nowadays; likewise the Canon 5cm f/0.95 rangefinder lens. Canon
has a 50mm f/1 in its list for the EOS SLRs, but probably the most
lusted-after lens of the four is the Leica 50mm f/1 Noctilux-M
rangefinder lens. It matches the hand-held available-darkness style
of the Leica rangefinder, and "Noctilust" seems to be a recognized
disease among Leicaphiles.
Hmmm. I'm beginning to ramble. I'll stop.
Later,
Owl
John Owlett, Southampton, UK
Date: Thu, 19 Jul 2001
From: [email protected] (Richard Knoppow)
Newsgroups: rec.photo.equipment.large-format
Subject: Re: Determining Smaller Apertures
"Peter De Smidt" [email protected] wrote:
>My 203 ektar has aperture settings down to F32, and I'd like to have F45 and >F64 available. The iris does close down significantly past F32, and so I >think that it is only a matter of making the appropriate marks for the >aperture indicator. In looking over previous posts on similar topics, it >seems that the thing to do is set the aperture to F32. Measure the iris >opening. Multiply that by .707. Close down to the indicated dimension and >make a mark on the aperture setting scale. Repeat the last 3 steps to mark >F64. Is this procedure the right way to go about the task at hand?
The Kodak lens handbook indicates the iris should close down to
f/45. My Kodak Anastigmat version has f/45 marked but the iris closes
down further.
d The f/stop is a linear ratio of the diameter of the hole to the
focal length. A stop is defined as the iris opening which will admit
either twice or half as much light as the adjacent stop. So, the ratio
is 1.414 or 0.707 depending on which way you are going. Since you know
you want f/45 and f/64 you don't have to calculate this. Just measure
the size of the larger stops and devide them. Half f/32 is f/64, half
f/22 is f/45 (since the stops are actually rounded off.
You can measure the physical size of the stop directly or measure
its projected image. For an uncalibrated lens the second method gives
the effective stop, which takes into account the magnification of the
pupils, but in this case, its just a possibly more convenient way to
measure the stop diameter than physical measurement.
To measure the effective stop put a pin hole source right at the
focal plane of the lens and a translucent screen over the front of the
lens. The projected image of the stop is what you measure. The
distance from the front of the lens to the screen is not critical
since the light coming from the lens is collimated.
At f/64 you will begin to get noticable diffraction blurring.
---
Richard Knoppow
Los Angeles, Ca.
[email protected]