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Orio
Joined: 24 Feb 2007 Posts: 29545 Location: West Emilia
Expire: 2012-12-04
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Posted: Sun Oct 18, 2009 11:38 pm Post subject: F/Stop scale with intermediate values |
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Orio wrote:
Here's a tentative of F/stop scale with intermediate values of (roughly) thirds of stop.
I calculated empirically and for some values, I used the common intermediate values used in cameras and lenses, which may not be full precise, so if more expert people notices mistakes please point out:
f/1
f/1.1
f/1.3
f/1.4
f/1.6
f/1.8
f/2
f/2.2
f/2.5 (should be f/2.6)
f/2.8
f/3.2
f/3.6
f/4
f/4.5 (should be f/4.4)
f/5
f/5.6
f/6.3 (should be f/6.4)
f/7.1 (should be f/7.2)
f/8
f/9
f/10
f/11 (should be f/11.2)
f/12.6
f/14.2
f/16
f/18
f/20
f/22
f/25.2
f/28.4
f/32
f/36
f/40
f/44
f/50.4
f/56.8
f/64
Note the discrepancy at f/11.2 from the common values on cameras and lenses (f/11)
Other commonly used values in lenses and cameras do not correspond to my calculations (f/2.5 instead of f/2.6, f/4.5 instead of f/4.4, f/6.3 instead of f/6.4 and f/7.1 instead of f/7.2) _________________ Orio, Administrator
T*
NE CEDE MALIS AUDENTIOR ITO
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sichko
Joined: 20 Jun 2008 Posts: 2475 Location: South West UK
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Posted: Mon Oct 19, 2009 7:23 am Post subject: |
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sichko wrote:
Hi Orio - I'm sure that these values are adequate fo all practical purposes.
However there are one or two errors in the last places. The problem comes from rounding errors. So the common multiplier for whole stops is not 1.4 but 1.414 or 1.414213 or 1.414213562 or ... - in other words the square root of two - to as many places after the point as are needed. So 1.4 is an adequate approximation for 1.414....., 2.8 is OK for 2.828.... but the next one in this set is 5.656 wich we might round up to 5.7 rather than 5.6... and eventually 44 becomes 45.3. Of course the % error doesn't increase. The numbers just look worse. Anyway, for those who want them, here's an accurate set given to one decimal place (except for 1, 2, 4 etc which are perfect integers)..
1 2 4 8 16 32 64
1.2 2.2 4.5 9.0 18.0 35.9
1.3 2.5 5.0 10.1 20.2 40.3
1.4 2.8 5.7 11.3 22.6 45.3
1.6 3.2 6.3 12.7 25.4 50.8
1.8 3.6 7.1 14.3 28.5 57.0 _________________ John |
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Arkku
Joined: 28 Feb 2007 Posts: 1416 Location: Helsinki, Finland
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Posted: Mon Oct 19, 2009 5:19 pm Post subject: |
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Arkku wrote:
To get the accurate values one can just use powers of the square root of 2; to increase the aperture by one stop increase the power by 1. So, for example, sqrt(2)^0 = 1, sqrt(2)^1 = 1.41…, sqrt(2)^2 = 2, sqrt(2)^3 = 2.82…, etc. To get the intermediate values, you can use fractional powers, e.g. sqrt(2)^½ = 1.18… (rounded to f/1.2).
The commonly displayed scale of values is rounded in a pretty strange manner, however, e.g. sqrt(2)^5 = 5.656… so f/5.6 would actually round to f/5.7, and sqrt(2)^9 = 22.62… so f/22 would round to f/23. If we accept that one should round down after two significant digits, the fractional values for half- and third-stop intervals become inconsistent with common usage. So, all-in-all, there's no well-defined way how the scale should be rounded. I've written an algorithm to produce scales at the desired intervals using complex rounding rules reasonably consistent with the commonly displayed scale. (The theoretical scale, that is—electronic cameras complicate things further by e.g. substituting values based on that manufacturer's lenses, or the lens currently mounted…)
Anyhow, here are the computer-generated scales (first the "typical" rounded f-stop, then the accurate value from sqrt(2)^AV, rounded to two decimal places).
In one-half stop increments:
Code: |
AV f-stop
0 1 1
1/2 1.2 1.19
1 1.4 1.41
1/2 1.7 1.68
2 2 2
1/2 2.4 2.38
3 2.8 2.83
1/2 3.4 3.36
4 4 4
1/2 4.8 4.76
5 5.6 5.66
1/2 6.7 6.73
6 8 8
1/2 9.5 9.51
7 11 11.31
1/2 13 13.45
8 16 16
1/2 19 19.03
9 22 22.63
1/2 27 26.91
10 32 32
1/2 38 38.05
11 45 45.25
1/2 54 53.82
12 64 64
1/2 76 76.11
13 90 90.51
1/2 107 107.63
14 128 128
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In one-third stop increments:
Code: |
AV f-stop
0 1 1
1/3 1.1 1.12
2/3 1.3 1.26
1 1.4 1.41
1/3 1.6 1.59
2/3 1.8 1.78
2 2 2
1/3 2.2 2.24
2/3 2.5 2.52
3 2.8 2.83
1/3 3.2 3.17
2/3 3.6 3.56
4 4 4
1/3 4.5 4.49
2/3 5 5.04
5 5.6 5.66
1/3 6.3 6.35
2/3 7.1 7.13
6 8 8
1/3 9 8.98
2/3 10 10.08
7 11 11.31
1/3 13 12.70
2/3 14 14.25
8 16 16
1/3 18 17.96
2/3 20 20.16
9 22 22.63
1/3 25 25.40
2/3 28 28.51
10 32 32
1/3 36 35.92
2/3 40 40.32
11 45 45.25
1/3 51 50.80
2/3 57 57.02
12 64 64
1/3 72 71.84
2/3 80 80.63
13 90 90.51
1/3 101 101.59
2/3 114 114.04
14 128 128
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(Edit: The typically displayed scale was probably obtained by taking f/1 and f/1.4 and repeatedly doubling them, i.e. those values ×2 are f/2 and f/2.8, those values ×2 are f/4 and f/5.6, etc. This is a good way to generate the whole f-stops as long as one remembers any two consecutive f-stops; double them to go forwards, halve them to go backwards. But when using powers one must use the square root of two, and not e.g. 1.4, or the integer stops will be off…)
Last edited by Arkku on Mon Oct 19, 2009 11:46 pm; edited 1 time in total |
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hexi
Joined: 01 Jul 2009 Posts: 1631 Location: France
Expire: 2011-11-18
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Posted: Mon Oct 19, 2009 6:45 pm Post subject: |
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hexi wrote:
Uhhh well, its a bit complicated to me and i'm not a math fan... here what i have with the in between stops on the CZJ Sonnar 135mm
wide open : 3.5
then two stop between f5.6
i think its f4 and f5
f7 - f8 - f9 - f11 - f13.5 - f19 - f22
oh sounds strange but when metering light its very good, cause i have precision up to 1/3 light measure given, so hooray for between stops. anyway i take the closest, depending of mood _________________ Happy owner and user of :
SLR's > Contax Aria - RX
DSLR > Canon 5D
Lenses : C/Y Planar 1.4/50 - Distagon 2.8/35 - Planar 1.4/85
http://www.flickr.com/photos/sonnar85 |
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sichko
Joined: 20 Jun 2008 Posts: 2475 Location: South West UK
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Posted: Tue Oct 20, 2009 11:54 am Post subject: |
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sichko wrote:
If you wish to calculate the "number of stops", NOS, between two given aperture values, A & B, the equation is given by...
NOS = [log(A/B)]/log[square root of 2]
So for example, 5.6 & 4 gives us NOS = 0.97. The difference between 0.97 and "1" will be small for many purposes. Rounding up the exact value for the "stop near 5.6" reduces the absolute value of the error - but not by much. So, for 5.7 and 4 we get NOS=1.02.
For 11 & 8 NOS = 0.92 - if a tenth of a stop is important to you this error might be significant. _________________ John |
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Orio
Joined: 24 Feb 2007 Posts: 29545 Location: West Emilia
Expire: 2012-12-04
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Posted: Tue Oct 20, 2009 1:26 pm Post subject: |
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Orio wrote:
With film, 1/10th of a stop is irrelevant. There is no film so sensitive to respond to a change of 1/10th of a stop, except -perhaps- special film that used to be created for army.
With a digital sensors, I think it's more or less the same, except perhaps a computer could scan and find a 1/10th stop exposure difference. A human eye most certainly won't. _________________ Orio, Administrator
T*
NE CEDE MALIS AUDENTIOR ITO
Ferrania film is reborn! http://www.filmferrania.it/
Support the Ornano film chemicals company and help them survive!
http://forum.mflenses.com/ornano-chemical-products-t55525.html |
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Arkku
Joined: 28 Feb 2007 Posts: 1416 Location: Helsinki, Finland
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Posted: Tue Oct 20, 2009 5:05 pm Post subject: |
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Arkku wrote:
sichko wrote: |
So for example, 5.6 & 4 gives us NOS = 0.97. The difference between 0.97 and "1" will be small for many purposes. |
In practice the difference between f/4 and f/5.6 will be as close to 1 as manufacturing tolerances allow, however, since the displayed values are rounded for the user to see but not necessarily for the camera or lens itself…
In any case, a difference less than one third of a stop is generally insignificant for any use, and one must remember that various tolerances make it difficult to reach even this precision in exposure (e.g. ISO ratings are not exact, the aperture may not be perfectly calibrated, camera may be using shutter speeds as powers of two instead of what it displays, lens may have a t-stop different than f-stop due to loss of light in elements, focusing may cause bellows factor that's not accounted for in electronics especially with vintage lenses, etc).
Personally I have my DSLR set to work at one-half stop intervals for less turning of the dial and to better match the aperture ring on manual focus lenses (I've never seen a vintage lens with one-third clicks in the aperture ring, although obviously some lenses have a stepless aperture). |
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estudleon
Joined: 15 May 2008 Posts: 3754 Location: Argentina
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Posted: Wed Apr 21, 2010 10:55 am Post subject: |
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estudleon wrote:
I think that the paerture numbers are a compromise, and the blades positions are a bit different in each lens. You can see that reading the differents shutter speeds in the cams when metering using differents lenses and the "same" nominal aperture.
For example the S-M-C 1,4 nominal aperture is a T number 1,47 or so.
Rino. _________________ Konica 2,8/100
CZJ: 4/20, 2,4/35, 1,8/50 aus jena, 3,5/135MC, Pentacon 1,8/50
Pentax S-M-C-1,4/50
Helios 44-3
Mamiya 2,8/135
Misc. : jupiter 9
Stuff used:
A) SRL
Alpa 10 D - kern macro Switar 1,9/50 -black, Kilffit apochromat 2/100.
Asahi pentax spotmatic super takumar 1,4/50
Contaflex super B tessar 2,8/50 Pro-tessar 115
Leica R3 electronic summicron 2/50 elmarit 2,8/35
Konica Autoreflex 3 (2 black and chrome one), TC, T4. 2,8/24, 3,5/28 not MC and MC, 1,8/40, 1,4/50, 1,7/50 MC and not MC, 1,8/85, 3,2/135, 3,5/135, 4/200
Minolta XG9 2,8/35, 2/45, 3,5/135
Nikkormat FTn 1,4/50, 2,8/135
Fujica ST 801, 605, 705n. 3,5/19, 1,4/50, 1,8/55, 4/85, 3,5/135.
Praktica MTL 5 and a lot of M42 lenses.
Voigtlander. Bessamatic m, bessamatix de luxe, bessamatic cs, ultramatic and ultramatic cs.
Skoparex 3,5/35, skopagon 2/40, skopar 2,8/50, skopar X 2,8/50, super lanthar (out of catalogue) 2,8/50, dinarex 3,4/90, dinarex 4,8/100, super dinarex 4/135, super dinarex 4/200, zoomar 2,8/36-83, portrait lens 0, 1 and 2. Curtagon 4/28 and 2,8/35
Canon AV1, 1,8/50
Rolleiflex SL35 and SL35 E. 2,8/35 angulon, 2,8/35 distagon, 1,4/55 rolleinar, 1,8/50 planar, 4/135 tessar, 2,8/135 rolleinar, x2 rollei, M42 to rollei adap.
Etc.
RF
Yashica Minister III
Voightlander Vito, vitomatic I, Vito C, etc.
Leica M. M2, M3 (d.s.) and M4. Schenider 3,4/21, 2/35 summaron 2,8/35 (with eyes). Summicron 2/35 (8 elements with eyes), 2/35 chrome, 2/35 black, 1,4/35 pre asph and aspheric - old -, 2/40 summicron, 2,8/50 elmar, 2/50 7 elements, 2/50 DR, 2/50 - minolta version, 1,4/50 summilux 1966 version, 1,4/75 summilux, 2/90 large version, 2/90 reduced version of 1987, 2,8/90 elmarit large version, 4/135 elmar. |
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Arkku
Joined: 28 Feb 2007 Posts: 1416 Location: Helsinki, Finland
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Posted: Mon Apr 26, 2010 3:57 am Post subject: |
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Arkku wrote:
estudleon wrote: |
I think that the paerture numbers are a compromise, and the blades positions are a bit different in each lens. You can see that reading the differents shutter speeds in the cams when metering using differents lenses and the "same" nominal aperture.
For example the S-M-C 1,4 nominal aperture is a T number 1,47 or so.
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The f-number and t-number serve quite a different purpose, e.g. an f/2.8 lens with the transmission of t/4 would still have the depth of field and other properties of an f/2.8 lens, but require 1 stop more exposure as though an ND filter was used. As such, t-number depends on the transmission of light—inaccuracies in the construction of the lens (e.g. aperture not stopping down to the exact value), as well as manufacturers lying about the true maximum aperture, truly affect f-number (not the t-number). It is just the markings that are inaccurate in that case.
As for f-numbers being a compromise; that's certainly true. It would be more sensible for most users to have a linear scale of AV-numbers (aperture value), e.g. AV 0 would be f/0, AV 1 would be f/1.414…, AV 2 = f/2, etc. This would make it much simpler to see the relationship between the values: ±1 AV equals one stop of difference, and no rounding problems with every other full stop in the common scale being an irrational number.
There are some calculations that require the use of f-numbers, however, but of course converting from AV to f-number would simply be a matter of taking that power of the square root of 2. But the f-notation is too entrenched to ever change in common use, I think. |
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kds315*
Joined: 12 Mar 2008 Posts: 16631 Location: Weinheim, Germany
Expire: 2021-03-09
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Posted: Mon Apr 26, 2010 3:30 pm Post subject: |
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kds315* wrote:
f-stops are simple geometric figures while t-stops are true light transmission values at a given aperture setting (also taking into account coating lossesn, glass transmission losses etc.). It has nothing to do with lying etc. (why would you say that?). T-stops is the standard used in the movie industry, which allows to exchange lenses and still have correct exposure.
These AV values you propose are available on certain macro lenses for decades, nothing new. Zeiss Luminars or Nikon Macro Nikkors for instance use these scales, where Nikon choose 1-2-3... and Zeiss the "Stolzesche Blendenzahlen": 1-2-4-8-16...)
_________________ Klaus - Admin
"S'il vient a point, me souviendra" [Thomas Bohier (1460-1523)]
http://www.macrolenses.de for macro and special lens info
http://www.pbase.com/kds315/uv_photos for UV Images and lens/filter info
https://www.flickr.com/photos/kds315/albums my albums using various lenses
http://photographyoftheinvisibleworld.blogspot.com/ my UV BLOG
http://www.travelmeetsfood.com/blog Food + Travel BLOG
https://galeriafotografia.com Architecture + Drone photography
Currently most FAV lens(es):
X80QF f3.2/80mm
Hypergon f11/26mm
ELCAN UV f5.6/52mm
Zeiss UV-Planar f4/60mm
Zeiss UV-Planar f2/62mm
Lomo Уфар-12 f2.5/41mm
Lomo Зуфар-2 f4.0/350mm
Lomo ZIKAR-1A f1.2/100mm
Nikon UV Nikkor f4.5/105mm
Zeiss UV-Sonnar f4.3/105mm
CERCO UV-VIS-NIR f1.8/45mm
CERCO UV-VIS-NIR f4.1/94mm
CERCO UV-VIS-NIR f2.8/100mm
Steinheil Quarzobjektiv f1.8/50mm
Pentax Quartz Takumar f3.5/85mm
Carl Zeiss Jena UV-Objektiv f4/60mm
NYE OPTICAL Lyman-Alpha II f1.1/90mm
NYE OPTICAL Lyman-Alpha I f2.8/200mm
COASTAL OPTICS f4/60mm UV-VIS-IR Apo
COASTAL OPTICS f4.5/105mm UV-Micro-Apo
Pentax Ultra-Achromatic Takumar f4.5/85mm
Pentax Ultra-Achromatic Takumar f5.6/300mm
Rodenstock UV-Rodagon f5.6/60mm + 105mm + 150mm
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Arkku
Joined: 28 Feb 2007 Posts: 1416 Location: Helsinki, Finland
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Posted: Mon Apr 26, 2010 6:26 pm Post subject: |
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Arkku wrote:
kds315* wrote: |
f-stops are simple geometric figures while t-stops are true light transmission values at a given aperture setting (also taking into account coating lossesn, glass transmission losses etc.). |
Yes, this what I said.
kds315* wrote: |
It has nothing to do with lying etc. (why would you say that?). |
I only meant that if a manufacturer were to lie about the true f-number of the lens (e.g. by rounding to the more marketable number), then it would not affect the t-number. I didn't say that t-numbers have anything to do with lying; rather I said that they don't. =)
kds315* wrote: |
These AV values you propose are available on certain macro lenses for decades, nothing new. |
Yes, I've seen some old lenses with such markings although I think the values were not strictly AV-numbers, i.e. the powers of the square root of two to make the corresponding f-number, but rather offset so that the maximum aperture of the lens in question has the number 1. (Which actually makes the numbers incomparable to other lenses without external knowledge…)
I'm not pitching it as anything new, but rather just lamenting the fact that we are “stuck” with the f-number system in common use. |
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no-X
Joined: 19 Jul 2008 Posts: 2495 Location: Budejky, Czech Republic
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Posted: Mon Apr 26, 2010 8:33 pm Post subject: |
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no-X wrote:
btw. here is table of old aperture value formats:
a) standard system (currently used values are on the left, older scale is on the right)
b) Stolze's system
c) system of Royal Phot. Soc.
d) old Zeiss's system
e) system of Paris congress 1900
I think the list isn't complete, e.g. Kodak used its own values:
_________________ (almost) complete list of Helios lenses |
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