On standard aperture values

[Doug Kerr]

This is all fascinating, and is perhaps "my art", but it surely pales in comparison with this:

https://openphotographyforums.com/forums/threads/my-photo-of-the-week.25142/post-219046

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

In a later edit to my post I quoted the passage from ISO 516 that recognizes just that!

Best regards,

Doug

I did read it.

 

[Doug Kerr]

ISO 517 seems to suggest, but does not clearly state, that the apertures should ideally be per the theoretical values, not the list of aperture markings. (There is of course a tolerance provided for.)

Maybe.

Best regards,

Doug

 

[Ted Cousins]

ISO 517 seems to suggest, but does not clearly state, that the apertures should ideally be per the theoretical values, not the list of aperture markings.

Hello, Doug,

How about some extreme theoretical values?! After some playing, I got Libre Calc to do a series starting at 𝑓/0.5 based on the 6th root of 2, voila:

I tried some rounding and failed ...

... I'm beginning to think that there is no published rounding method that matches the de facto photographic standard in one shot.

 

[Doug Kerr]

Hi, Ted,

... I'm beginning to think that there is no published rounding method that matches the de facto photographic standard in one shot.

That seems very likely. Here and there are discussions of rounding procedures but they all seem to "serve several different gods".

As an aside, if the number series you showed is for f-numbers, then they are at 2/3 stop intervals. (From f/1 to f/2 is two stops, since it would be 4x the exposure.)

If they are for exposure times, or the reciprocal of exposure times, then they are at 1/3 stop intervals.

Best regards,

Doug

 

[Ted Cousins]

As an aside, if the number series you showed is for f-numbers, then they are at 2/3 stop intervals. (From f/1 to f/2 is two stops, since it would be 4x the exposure.)

Hi, again,

I wondered about that ... still playing trying to match ISO 517's listed 1/3 stop values

"I'll be baack"

 

[Doug Kerr]

Hi, Ted,

This table shows the theoretical f-number values at intervals of 1/3 stop over a 7-stop range:

The theoretical values are at integer multiples of the 6th root of 2.

The precision of the theoretical values is that to which my MS Excel (very old) works for this calculation. The stop values are to a maximum of 5 significant figures,

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

This table shows the theoretical f-number values at intervals of 1/3 stop over a 7-stop range:

View attachment 14469
The theoretical values are at integer multiples of the 6th root of 2.

The precision of the theoretical values is that to which my MS Excel (very old) works for this calculation. The stop values are to a maximum of 5 significant figures,

Best regards,

Doug

Yes, the 6th root of 2 in Libre Calc also matches ISO 517's 1/3-stop listing ...
... still playing ... main purpose is rounding

 

[Doug Kerr]

Hi, Ted,

It is strange that, so far as I have yet found, there is no ISO standard that gives a preferred list of aperture markings for a nominal spacing of 1/2 or 1/3 stop.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

The only comprehensive lists of aperture value markings I have are the Canon lists, taken from the manual for the Canon EOS 3 camera. I will refer here to the "1/3 stop" list.

Its values seem to be derived by rounding the theoretical value to 2 significant figures, with only one "clinker":

5.656854249 -> 5.6

But the other rounded values in fact are consistent with ISO 517, and the marking 5.6 is on that list. So ISO 517 seems to overtake the rounded value in that one place.

Interesting enough, that value (5.6) is in fact the rounded (to 1 decimal place) value of the theoretical Renard.20 value. But the Renard R''20 value is 5.5!

So go figger!

Best regards,

Doug

 

[Doug Kerr]

I was in error about the "clinkers" in the Canon aperture list.

These values are not the theoretical values rounded to the nearest integer:

1.2, 3.5, 5.6, 22

They are all rounded down from the theoretical values; the others are rounded to the nearest integer.

All values are all consistent with the ISO 517 values (where corresponding ones exist).

Sorry about the error before.

Best regards,

Doug

 

[Doug Kerr]

The following table is mainly intended to analyze the "Canon EOS 3" series of aperture markings:

The entries shaded pink show where the Canon value is not the theoretical value rounded to the nearest 0.1.

The entries shaded in light green show values of those different series that exactly match the value in the Canon series.

Best regards,

Doug

 

[Doug Kerr]

In the Canon list of aperture marking values, every one is either the theoretical value rounded nearest (the usual meaning of rounding) or rounded down.

I have not yet discerned the rule (if any) by which one or the other rounding is used.

Later.

Best regards,

Doug

 

[Doug Kerr]

It looks as if perhaps the smaller Canon value are the theoretical values rounded to 1 decimal place but with the dividing line (above which the higher value is taken) not being the usual 0.05 but rather more like 0.07.

I will set up a spreadsheet that helps me to look into that. Just now the puppies and I have to have lunch.

Best regards,

Doug

 

[Ted Cousins]

Hi Doug,

Perhaps ISO 517 is only addressing lens actual value markings:

This International Standard pertains to apertures and related properties of photographic lenses affecting the illuminance at the centre of the image.

aperture stop
physical stop that limits the cross-section of the light beam that can pass through the lens to reach the centre of the on-axis image

So that could be why they don't shows lists of intermediate markings per se?

Even though they say ...

Each standard f-number, or “whole stop”, division of scale markings may be divided into two or three
subdivisions in 1/2 or 1/3 steps of a stop calculated, for 1/2 subdivision, in a geometric series with first term 0,5 and factor 4th root of 2 and for 1/3 subdivision in a geometric series with first term 0,5 and factor 6th root of 2 .

... I don't think they mean markings with values, although one might think so at first.
Most if not all of my lenses with aperture rings only have full-stop values marked even when they have intermediate detents, usually half-stops.

From which, we could infer that ISO 517 does not apply to digital cameras!

 

[Ted Cousins]

Out of interest, here are what values appear on my Sigma SD10 LCD in the mounted lens range minimum 𝑓/2.8 to lens max 𝑓/22, camera does 1/3 stops.

I speculate that there is a string array in the firmware for these indications because the control dial is not marked. I wonder: if I change the camera language to German, do the decimal points change to commas? - that would be seriously cool !

My calculated list does not start with the exact value 2.8 because it is extracted from the series that starts with 𝑓/0.5. The obvious "errors" (e.g. line 7) from calculated values tell us that the SD10 displayed values are picked out of the air from old lens markings and are not compliant with any known calculated preferred-value sequence.

 

[Doug Kerr]

Hi, Ted,

Hi Doug,

Perhaps ISO 517 is only addressing lens actual value markings

Yes, we have to distinguish between "marks" and "labels" (although I myself have not been consistently scrupulous about that). The Sekonic L-398A has marks at whole and third stop values, and labels at whole stop values.

:
So that could be why they don't shows lists of intermediate markings per se?

Even though they say ...

... I don't think they mean markings with values, although one might think so at first.
Most if not all of my lenses with aperture rings only have full-stop values marked even when they have intermediate detents, usually half-stops.

Good points.

From which, we could infer that ISO 517 does not apply to digital cameras!

I think what you mean is cameras with digital display of settings, not really digital cameras.

I think its intended scope is universal, but certainly no thought was given to cameras with digital displays.

All good points

Best regards,

Doug

 

[Doug Kerr]

I have looked into what happens if we round the theoretical values to (in the early part of the of the table) to 0.1 (and in the later part, 1) but have the "slice point" (above which we choose the next higher value) a value other than the conventional 0.5 (normalized). (This is an admittedly-artificial exercise.)

If we make that value 0.65, then most of the theoretical values thus rounded match the Canon list. but later on (for the Canon f-numbers 29, 81, and 91, this maneuver fails. (The theoretical values for those are only a little bit over halfway to the next integer value.) For these, the Canon value is the theoretical value rounded in the usual way (which most if the Canon values are).

It seems likely that the Canon list was generally based on rounding ("to nearest") the theoretical values, but with a few departures (where the Canon value is that obtained by "rounding down" the theoretical value). These may have been chosen for various reasons (including "historical continuity" at Canon).

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

I think what we are seeing here is the result (in various arenas) of pragmatic work to bring about the peaceful consistence of these things:

• The theoretical series of aperture f-numbers at 1/3 stop intervals.

• The notion of "tidy" numbers. (Especially before the widespread awareness of binary numbers that came about with the emergence of personal computers, "128" would have seemed less "tidy" than "125"; "1.41" would have seemed "less tidy" than "1.4".)

• The traditional photographer's mantra that three steps should be exactly one stop.

Now how the people involved in the various decisions argued this to various conclusions, I have no real idea.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

I think what we are seeing here is the result (in various arenas) of pragmatic work to bring about the peaceful consistence of these things:

• The theoretical series of aperture f-numbers at 1/3 stop intervals.

• The notion of "tidy" numbers. (Especially before the widespread awareness of binary numbers that came about with the emergence of personal computers, "128" would have seemed less "tidy" than "125"; "1.41" would have seemed "less tidy" than "1.4".)

• The traditional photographer's mantra that three steps should be exactly one stop.

Now how the people involved in the various decisions argued this to various conclusions, I have no real idea.

Best regards,

Doug

Going back a bit (1899):

𝑓/LOL,

Ted

 

[Doug Kerr]

The attached Excel spreadsheet file is here attached with the PDF filetype extension so the OPF software will allow if to be attached. It should be renamed with filetype extension XLS.

It analyzes the "Canon" list of 1/3 stop aperture values to show where the "6 steps = 2x" and "20 steps = 10x" ratios (that's how those work for f-numbers) exist precisely and don't quite exist precisely.

The area just to the right of the lists of values show the 6 different patterns of separation by 6 steps. The ratios are shown for each combination, and are highlighted in red when they do not have the ideal value of 2. The next area is similar, but for the 20 different 20-step interval patterns, where the ideal ratio is 10.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

Going back a bit (1899):

Amazing!

Note that none of those schemes labeled f/4 as "4".

"When all else fails, call it what it is."
-Old Scottish telephone engineer
(Hint: not Alexander Graham Bell.)

Thanks.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

Amazing!

Note that none of those schemes labeled f/4 as "4".

FYI, the source:

F-number - Wikipedia

en.wikipedia.org

best,

Ted.

 

[Doug Kerr]

Hi, Ted,

FYI, the source:

F-number - Wikipedia

en.wikipedia.org

Thanks.

Yes, I had seen that.

Best regards,

Doug

 

[Ted Cousins]

It analyzes the "Canon" list of 1/3 stop aperture values to show where the "6 steps = 2x" and "20 steps = 10x" ratios (that's how those work for f-numbers) exist precisely and don't quite exist precisely.

The area just to the right of the lists of values show the 6 different patterns of separation by 6 steps. The ratios are shown for each combination, and are highlighted in red when they do not have the ideal value of 2. The next area is similar, but for the 20 different 20-step interval patterns, where the ideal ratio is 10.

Doug, is the column headed "series Theor." based on the 6th root of 2, or is it based on the 20th root of 10?

I'm guessing the 6th root of 2 because the 6th root of 2 raised to the power of 20 is not exactly 10, only close.

best,

Ted.

 

[Doug Kerr]

Hi, Ted,

Doug, is the column headed "series Theor." based on the 6th root of 2, or is it based on the 20th root of 10? Those two numbers are different on my Casio ...

6th root of 2.

That is because it is based on f-numbers that increase by exactly one stop for every 3 steps (thus a factor of 2 for every 6 steps).

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,


6th root of 2.

That is because it is based on f-numbers that increase by exactly one stop for every 3 steps (thus a factor of 2 for every 6 steps).

Thanks. So one would not expect a factor of exactly 10 for every 20 steps in that theoretical column. (about 10.08 according to my Casio).

best,

Ted.