Expsure metering - a gaffe in the international standard

ISO standard 2720 gives the requirement for "free-standing" photographic exposure meters. It has many curious things, but perhaps the most curious is a serious outright gaffe in the mathematics, leading a a bizarre provision of the specifications.

With regard to reflected light metering, the photographic exposure recommended by the meter is to be in accordance with this, the incident light exposure metering equation:



where t is the exposure time (shutter speed), N is the f-number of the aperture, S is the exposure index (as the ISO speed), L is the measured luminance of the scene, and K is a parameter, the reflected light metering calibration constant. By choosing a value of K, the manufacturer of the meter determines what exposure recommendation he wants the meter to give for any given scene luminance and exposure index.

At the time ISO 2720 was issued, the sensitivity of film could be stated in two ways: one was on the familiar "arithmetic" scale (e.g., ISO 100) and the other was on the "logarithmic" scale (e.g., ISO 21°), which in fact corresponded to the earlier DIN scale.

The two forms are related this way:



This is of course consistent with the well-known relationship between the two scales:

Thus we could substitute that relationship into the first equation and get the reflected light metering equation in a form that uses the logarithmic expression of the exposure index, S° (I won't trouble you by actually doing that, although, if this spoils the story for you, Tom, let me know, and I'll provide it in a supplement to this note.)

Now to the gaffe. ISO 2720 actually provides for two forms of K, one (K1) to be used in the exposure metering equation in terms of the linear form of the exposure index, S, and another (K2) to be used in the exposure metering equation in terms of the logarithmic form of the exposure index, S°. And the standard provides that for any decision made as to the value of K for a particular meter design:

K2 = 1.26 K1​

Now this seems awfully strange. In reality, most exposure meters of the era could allow you to set the exposure index either in terms of the "arithmetic" scale (perhaps to ISO 100) or the "logarithmic" scale (to ISO 21°), typically by bringing the number wanted into one of two little windows. Of course the two scales were linked together by the relationship given above - if one set 100 in the "ISO" window, then 21 would appear in the "ISO° window.

But having set the exposure index (by way of either value), the meter then would exhibit a certain behavior, which is characterized by the value of K. It is absurd to think of this one meter having two different values of K, depending on whether I considered myself to have set the exposure index to ISO 100 or to ISO 21°. The meter had no idea in what form of the exposure index I was working. It was set to ISO 100/ISO 21°.

This bizarre situation resulted in the authors of the standard having based their work on an erroneous understanding of the relationship between the arithmetic and logarithmic scales for the film sensitivity, namely this:

THIS IS WRONG

This then led to a wrong exposure equation in the form that works from S°.

Then, when trying out the two forms of the equation with for example, ISO 100 and ISO 21°, they noticed that the exposure results for any given luminance differed by a factor of about 1.26. (That is 10^(1/10), the result of the lost "-1".)

So to fix that, they provided for different values of K, K1 and K2, for the two "situations"! They plugged it.

There is an exactly parallel situation for the incident light metering equation(s), whose parameter is C.

That's all pretty revolting.

Best regards,

Doug

Doug Kerr said:

ISO standard 2720 gives the requirement for "free-standing" photographic exposure meters. It has many curious things, but perhaps the most curious is a serious outright gaffe in the mathematics, leading a a bizarre provision of the specifications.

With regard to reflected light metering, the photographic exposure recommended by the meter is to be in accordance with this, the incident light exposure metering equation:

Click to expand...

That certainly looks dubious: "reflected light metering" is to be in accordance with "the incident light exposure metering equation".

At the time ISO 2720 was issued, the sensitivity of film could be stated in two ways: one was on the familiar "arithmetic" scale (e.g., ISO 100) and the other was on the "logarithmic" scale (e.g., ISO 21°), which in fact corresponded to the earlier DIN scale.

Click to expand...

Is it possible that an uncorrected error goes right back to "the earlier DIN scale"?

Now this seems awfully strange. In reality, most exposure meters of the era could allow you to set the exposure index either in terms of the "arithmetic" scale (perhaps to ISO 100) or the "logarithmic" scale (to ISO 21°), typically by bringing the number wanted into one of two little windows. Of course the two scales were linked together by the relationship given above - if one set 100 in the "ISO" window, then 21 would appear in the "ISO° window.

Click to expand...

You'd think the little windows could be cut in new positions on the calculator dials to avoid this confusion. Or is this too easy? One wonders if ISO standard 2720 is worth keeping even if it helps sell more exposure meters but at the cost of wrong readings!

You're always the bearer of bad news, Doug, even if it simply shows how ignorant I am.
Revolting is right. Worse than the Neighbours dog shitting on my gerberas.

HJi, Maris,

Maris Rusis said:

That certainly looks dubious: "reflected light metering" is to be in accordance with "the incident light exposure metering equation".

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Oops! Yes, of course I should have said, "the reflected light exposure metering equation".

Is it possible that an uncorrected error goes right back to "the earlier DIN scale"?

Click to expand...

Yes, It may be. I have to look at the historical evolution there.

You'd think the little windows could be cut in new positions on the calculator dials to avoid this confusion. Or is this too easy?

Click to expand...

There is no confusion on the meter calculators. They all have the right relationship between S and S°. The screw up is only in the standard.

One wonders if ISO standard 2720 is worth keeping even if it helps sell more exposure meters but at the cost of wrong readings!

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Will, this gaffe does not cause any "wrong readings". It is just a red herring. Nobody making exposure meters pays attention to the silly second set of values of K and C. (Actually, there is no way they could pay attention to it in making a meter!)

Thanks.

Best regards,

Doug

Hi, Maris,

I don't find anything in the history of the DIN film speed norm coming up on its succession by the ISO standard that would seem to have "aided and abetted" the gaffe in ISO 2720.

I think what likely happened is this.

It was often said of the logarithmic form of the ISO film speed expression that "a 20 degree change in the logarithmic speed corresponds to a 100:1 change in the arithmetic speed."

And that is quite correct, but not the whole story. That does not tell us where the logarithmic progression starts - what value of S corresponds to S° = 0.

A person not really sensitive to basic mathematical concepts might, with no justification whatsoever, jump to the conclusion that the progression starts with S°=0 corresponding to S=1. That would mean that S = 100 would correspond to S°=20. That would mean that the equation relating S and S° would be:



But in fact, the progression starts with S°=0 corresponding to S = 0.794 (although we essentially never hear that number). That would mean that the actual equation relating S and S° is:


And of course under that equation, S° = 1 corresponds to S = 1, and thus S° = 21 corresponds to S = 100, which is the commonly-remembered correct relationship under the ISO standards for film sensitivity.

But who knows. It is hard to know exactly how people screw up.

Best regards,

Doug

Hi, Maris,

I commented before that an exposure meter manufacturer (I'll assume a traditional analog exposure meter with the familiar circular exposure calculator) could not actually implement different values of K "for use with the exposure index in arithmetic and logarithmic forms."

Suppose the index I have in mind is what is formally designated "ISO 100/21°". I can turn the exposure index dial on the meter calculator until "100" shows up in the first little window, or until "21" shows up in the second little window. Both are the exact same setting of the dial - if I set the first window to "100, "21" will appear in the second window.

Having done that (one way or the other), the meter, for a certain measured scene luminance, will issue a certain exposure recommendation - that is, it will exhibit a certain value of K.

Now what would fulfill the silly notion in ISO 2720 was if the meter manufacturer bungled the dial layout so that when "100" was set in the first window, "20" would show up in the second window. But that is of course just plain incorrect under the definition of the two ISO speed measures.

By the way, very few exposure meters actually had two windows for exposure index in terms of the ISO S and S°.

What was common was, before the onset of the ISO measures of film speed, they might have a window for the ASA speed and the DIN speed. Although those were not formally linked, for all practical purposes ASA 100 corresponded to DIN 21 (earlier called DIN 21°). This dual setting basis was of course to accommodate users of American film (whose speed was stated as the ASA value) or European film (whose speed was stated as the DIN value).

When the ISO standard came into use, film would be labeled "ISO 100/21°" But, except for working with meters that had only a "DIN" scale, there was no point in people thinking in terms if the dual numbers. Thus that film became thought of as "ISO 100". and exposure meter manufacturers typically began having only one "little window" on their calculators. Now that the logarithmic scale had become recognized in a truly international standard, it essentially disappeared from use.

Best regards,

Doug

Hi, Tom,

Tom dinning said:

You're always the bearer of bad news, Doug, even if it simply shows how ignorant I am.

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Don't brag. You get no extra points in my book for ignorance, feigned or not.

Best regards,

Doug

Doug Kerr said:

Hi, Maris,

But who knows. It is hard to know exactly how people screw up.

Best regards,

Doug

Click to expand...

It may be an unworthy thought but perhaps the gaffe originates in the ultimate mathematical blunder: that any quantity raised to the zero-th power must produce zero when, of course, any quantity raised to the zero-th power always yields exactly one. Oh, say it aint so!

Hi, Maris,

Maris Rusis said:

It may be an unworthy thought but perhaps the gaffe originates in the ultimate mathematical blunder: that any quantity raised to the zero-th power must produce zero when, of course, any quantity raised to the zero-th power always yields exactly one. Oh, say it aint so!

Click to expand...

Well, all kinds of horrors are possible!

Thanks.

Best regards,

Doug

Hi, Maris,

It seems that the gaffe is not a result of any bona fide mathematical misunderstanding but rather just of algebraic carelessness.

The table in the standard of actual numerical values of S (the "arithmetic" film speed) vs. S° (the "arithmetic" film speed) clearly confirms that the relationship between them is:

[Equation 1]

Of course the relationship is perhaps not apparent by inspection, but requires a little mathematical understanding.

The standard gives ("for use with the arithmetic expression of speed") this rearrangement of the basic reflected light metering equation:

[Equation 2]

Now if we substitute Equation 2 into Equation 1, we should get the exposure equation in that form but for use with the logarithmic form of the film speed, S°:

[Equation 3]

But in fact the standard, at that point, gives this:

WRONG [Equation 4]

This suggests that the person who did that somehow did not know the actual relationship between S° and S. It may be, as I said recently, that, having heard that "a 20 step change in S° represents a 100:1 change in S" *, just assumed that the relationship was:

WRONG [Equation 5]

and substituted that into equation 2 to get equation 4.

Incidentally, when I first published the story of this matter a number of years ago, one of my regular critics provided a fascinating justification for the approach taken in the standard. I did not consider it to have any merit.

Best regards,

Doug