How things can go wrong

As I wander through various standards and specifications, I regularly encounter examples of how things can go terribly wrong if people - even so-called experts - don't pay attention.

One amazing gaffe is found in the ISO standard for free-standing exposure meters (ISO 2720).

Two ways of expressing ISO speed

By way of a brief introduction, I note that the ISO standard for film speed provides for two ways of expressing that quantity. One is the familiar "ISO 100" form, which basically grew from the American standard (we may call that the "linear" form, since it is proportional to "sensitivity").

Another is a "logarithmic" form, for example ISO 21° The degree mark is the cue that this is the logarithmic form, which basically grew from the German (DIN) convention. One unit of change in this measure is a certain ratio of change in the sensitivity. It works a lot like the decibel scale used for power in sound engineering: a change of 10 units means 10 times the speed.

But the reference point is not ISO 1 (as one might guess) but rather about ISO 0.794. The reason has to do with harmonizing the underlying American and German systems. Thus ISO 20° would be 10^2 (100) times the reference value (which is ISO 0.794); that is, ISO 20° theoretically corresponds to ISO 79.37. (In reality, tidy rounded values are specified.)

But we most often see the equivalence expressed as: ISO 21° corresponds to ISO 100.

This means that
where S is the ISO speed in "linear" form and S° is the ISO speed in "logarithmic" form.

In ISO 2720

In the ISO standard for free-standing exposure meters, the "metering equations" for reflected light and incident light metering have a parameter, called the "metering calibration constant". This can be chosen by the meter manufacturer, over a modest permitted range, to provide the metering "strategy" the manufacturer thinks will be "best" for the users of his meter. This constant for the reflected light metering equation is called "K", and for the incident light metering equation "C".

When I first studied this, I was surprised to find that in the standard, there were two versions of "K" and "C". One was said to be applicable when the ISO speed was expressed in "linear" form, and the other for when it was expressed in "logarithmic" form. The two forms of either one of the constants were defined as having, for any choice by the manufacturer, a ratio of 1.26.

How could this be so? The equations should be precisely equivalent.

It took a bit of pondering, but I finally realized what had happened. The authors of the standard, knowing that a the step change in S° meant a 10 times change in S, just assumed that:


and cast the versions of their equations that worked with S° on that basis.

But of course the "S" and "S°" forms of the equations didn't give the same results (in fact by a factor 10^(1/10), or about 1.26.

So to fix that, they established two different values of the calibration constants (C1 and C2, and K1 and K2), defined as having the ratio 1.26.

Aargh!


The gaffe spreads

As a result of people trying to embrace this gaffe if it kills them, we in some work find this assumption:


which of course works for S° = 21 -> S = 100, the case we most often check.

Not a problem anymore

Fortunately, the "logarithmic" expression of film speed is now deprecated, and no corresponding form is provided for the ISO speed of digital sensor systems. So we will probably never encounter this gaffe.

By the way, I have somewhere, buried in long past correspondence, a response to my original note about this gaffe, giving an amazing justification for what the ISO-2720 authors did, and pointing out that thus I was misguided in my critique.

But in fact, they were just not paying attention, and screwed up.

Best regards,

Doug

To give more specific information about the gaffe in ISO 2720:

Recall that the precise definition of the relationship between the "linear" (often called "arithmetic") expression of ISO film speed (S) and the "logarithmic" expression of ISO film speed (S°) is:


The basic reflected light exposure equation in ISO 2720, in terms of S, is:

where t is the exposure time (shutter speed), A is the aperture (as an f-number), K is the reflected light metering calibration constant, L is the measured scene luminance, and S is the ISO film speed on the linear, or "arithmetic", basis.

To get that same exposure equation in terms of S°, we substitute equation [1] into equation [2] and get:


where S° is the ISO film speed on the logarithmic basis.

But the authors of ISO 2720 erroneously used this as the reflected light exposure equation in terms of S°:


They evidently assumed that the relationship between S and S° is:


The exposure result of equation [4] is smaller than the proper result (from equation 3) by a factor of precisely:

which is about 0.79 (or 1/1.26).

In order to "plug" this error, ISO 2720 defines the two forms of the exposure equation as:


and


where K2 is defined as 10^(1/10)•K, or approximately 1.26•K1.

The value of the plug is derived from the need to make the results of the two equations consistent, and is in fact specifically derived from the fact that the speed stated as ISO 21° is the same as the speed stated as ISO 100.

Of course, at that point one should have perhaps noted that this equivalence (ISO 21° -> ISO 100) is not consistent with:


Precisely the same thing happened with respect to the incident light metering equation, resulting in the two forms of it using two different values of the incident light metering calibration constant, C1 and C2.

Of course, one bizarre effect of this gaffe is that the recommended range of K, for example, comes in two forms.

• If the designer of the meter is working with the speed expressed in arithmetic form, then K1 is involved, and the recommended range of K1 is 10.6 to 13.4.

• If the designer is working with the speed expressed in arithmetic form, then K2 is involved, and the recommended range of K2 is 13.3 to 16.9.

Of course, these result in the same range of "calibrations" of the resulting exposure equation.

Best regards,

Doug

Well, one of the worse mistakes was the Hubble telescope which ended up with less then planned for eyesight when a lens was added with the wrong threads, (- Metric v. Whitworth, if I remember correctly)!

Asher