Doug Kerr
Well-known member
The basis ISO speed system rates film speed with a number that is nominally linear with "sensitivity". A film speed stated in that form looks like this: ISO 100. This is often called the "arithmetic" expression of speed.
But in effect the measured speed is rounded to one of a list of "standard" speeds for convenience in use. Those standard speeds are generally separated by 1/3 stop, so that if we move up in the list three steps, we usually find a speed that is exactly twice the speed at which we started.
But every so often, the jump is a little different, one reason being to keep us in "tidy" series' of values.
Thus if we start with ISO 320, then 3 steps higher is IS0 640, but 3 steps further is ISO 1250 (not 1280), and 3 steps further yet is ISO 2500 (not 2560).
Another such hiccup is found in the series 16, 32, 64, 125, 250, 500.
There is a second impact of these occasional hiccups. Because of a relationship to another form of notation I will mention shortly, the real underlying theoretical "pace" of the series is that a movement of 10 steps in the list should produce a speed 10 times higher (this is just like dB measurement in electrical or acoustic engineering!).
And that is not precisely the same as 3 steps being 2 times the speed. (The two "step sizes" only differ by about 0.1%, however). (Remember, in electrical engineering, a 2:1 change in power is about 3.010 dB, but we often say, "3 dB".)
When we take a little hiccup in the steps to join a new "tidy series" (as when we leave 160, 320, 640 to follow 1250, 2500, 5000), we make up some for the discrepancy in step size.
As a result, although over a limited range we might have 3 steps -> 2:1, over a longer range the relationship converges on 10 steps -> 10:1.
For example, from ISO 5 to ISO 160 is 15 steps, or 5 "three-step jumps", which should be an increase of 2^5 times (32 times), and it is.
But from ISO 1 to ISO 100,000 is 50 steps, which should be 5 "decades", and it is.
Very clever!
The logarithmic expression
In the past, there was a second expression of film which was logarithmic with sensitivity. A film speed stated in that form looks like this: ISO 21°. (And in fact, at one time the preferred way to express, for example, a film speed gave both, thus: ISO 100/21°.)
It turns out that consecutive integer values of this (only integer values are permitted) are associated with consecutive speeds in the list of standard speeds.
We see the principle of this series of values described in two ways:
• A change of 3 in the number represents a change of 2 times in the speed.
• A change of 10 in the number represents a change of 10 times in the speed. (We hear this one less often.)
Which is it?
As I said above, these values are associated with standard values of the speed (in "arithmetic" form).
And as we saw above:
• For a modest size run, a change of 3 steps in the list represents a 2:1 change in speed (but there are "hiccups" every so often.
• Over the long haul, a change of 10 steps in the list represents a 10:1 change in speed.
So both of those descriptions are correct, but neither of them gives the whole story.
For theoretical work, we use this relationship between the arithmetic expression of ISO speed (usually designated S) and the logarithmic expression (usually designated S°):
This follows the "long-term run" of the relationship as it applies to the standard ISO speed values, and is in fact the underlying theoretical basis for the series.
Nicely enough, it also works precisely for such important "check points" as:
ISO 1 -> ISO 1°
ISO 100 -> ISO 21°
ISO 400 -> ISO 27°
But it isn't exact for many other points in the list. For example, it isn't exact for:
ISO 400 -> ISO 24°
(For ISO 24°, the theoretical arithmetic speed would be ISO 398.1)
And is isn't all that close for:
ISO 160 -> 23
(For ISO 23°, the theoretical arithmetic speed would be ISO 158.5)
Of course, none of these curiosities are of any practical importance, given the broad rounding that is in play.
But it is important that if we get involved in theoretical work, we remember how it actually works.
For example, if we believe that the "three steps is a 2:1 change" rule is the actual underlying theoretical premise of the series (false), we can go badly wrong as we reach higher parts of the series.
And if we believe that "10 steps is a 10:1 change" is the underlying theoretical premise (true), but don't pay any attention to where it starts (it starts at ISO 1 -> ISO 1°, but it is easy to assume, by parallel with other logarithmic scales, that ISO 1 -> ISO 0°), we can have a tragic gaffe such as the one in ISO 2720 I recently described elsewhere.
Benediction
The bottom line: "Pay attention".
So, do electrical engineers ever think that a 2:1 power change is actually 3 dB (precisely)?
Not I.
Today
Today the S° notation is deprecated, and there is no equivalent of it for ISO speed as defined for digital cameras.
The APEX speed value (Sv)
We do use today a different logarithmic expression of ISO speed, the APEX speed value (Sv).
Like all APEX "values", a change of one unit in this represents a 2:1 change in the actual property being represented.
In modern times the two scales are tied together here:
ISO 100 = Sv 5
At one time, the relationship was slightly different. You need not hear about that - it would just make your head hurt.
There is no series of standard values for Sv, and expression as a decimal fraction is OK where needed.
ISO speed ( or maybe ISO SOS or ISO REI) is recorded in Exif metadata by way of Sv (as a rational number).
At one time the ASA standard for film speed in the US (superseded by the ISO standard) included provision for the use of a logarithmic expression for ASA speed (identical to the APEX Sv, as I have defined it above). The values were called ASA grades and were shown thus: ASA 5°.
On a classic exposure meter
My Miranda Cadius exposure meter (early 1960s, I think) has provision for setting the exposure index in three forms:
• ASA (meaning the ASA speed, essentially identical to the eventual ISO speed).
• DIN (meaning per the the older German system, essentially identical to the eventual ISO speed logarithmic system, S°).
• °ASA (meaning the ASA grade system, essentially the same as the APEX Sv).
Best regards,
Doug
But in effect the measured speed is rounded to one of a list of "standard" speeds for convenience in use. Those standard speeds are generally separated by 1/3 stop, so that if we move up in the list three steps, we usually find a speed that is exactly twice the speed at which we started.
But every so often, the jump is a little different, one reason being to keep us in "tidy" series' of values.
Thus if we start with ISO 320, then 3 steps higher is IS0 640, but 3 steps further is ISO 1250 (not 1280), and 3 steps further yet is ISO 2500 (not 2560).
Another such hiccup is found in the series 16, 32, 64, 125, 250, 500.
There is a second impact of these occasional hiccups. Because of a relationship to another form of notation I will mention shortly, the real underlying theoretical "pace" of the series is that a movement of 10 steps in the list should produce a speed 10 times higher (this is just like dB measurement in electrical or acoustic engineering!).
And that is not precisely the same as 3 steps being 2 times the speed. (The two "step sizes" only differ by about 0.1%, however). (Remember, in electrical engineering, a 2:1 change in power is about 3.010 dB, but we often say, "3 dB".)
When we take a little hiccup in the steps to join a new "tidy series" (as when we leave 160, 320, 640 to follow 1250, 2500, 5000), we make up some for the discrepancy in step size.
As a result, although over a limited range we might have 3 steps -> 2:1, over a longer range the relationship converges on 10 steps -> 10:1.
For example, from ISO 5 to ISO 160 is 15 steps, or 5 "three-step jumps", which should be an increase of 2^5 times (32 times), and it is.
But from ISO 1 to ISO 100,000 is 50 steps, which should be 5 "decades", and it is.
Very clever!
The logarithmic expression
In the past, there was a second expression of film which was logarithmic with sensitivity. A film speed stated in that form looks like this: ISO 21°. (And in fact, at one time the preferred way to express, for example, a film speed gave both, thus: ISO 100/21°.)
It turns out that consecutive integer values of this (only integer values are permitted) are associated with consecutive speeds in the list of standard speeds.
We see the principle of this series of values described in two ways:
• A change of 3 in the number represents a change of 2 times in the speed.
• A change of 10 in the number represents a change of 10 times in the speed. (We hear this one less often.)
Which is it?
As I said above, these values are associated with standard values of the speed (in "arithmetic" form).
And as we saw above:
• For a modest size run, a change of 3 steps in the list represents a 2:1 change in speed (but there are "hiccups" every so often.
• Over the long haul, a change of 10 steps in the list represents a 10:1 change in speed.
So both of those descriptions are correct, but neither of them gives the whole story.
For theoretical work, we use this relationship between the arithmetic expression of ISO speed (usually designated S) and the logarithmic expression (usually designated S°):
S = 10^((S°-1)/10)
This follows the "long-term run" of the relationship as it applies to the standard ISO speed values, and is in fact the underlying theoretical basis for the series.
Nicely enough, it also works precisely for such important "check points" as:
ISO 1 -> ISO 1°
ISO 100 -> ISO 21°
ISO 400 -> ISO 27°
But it isn't exact for many other points in the list. For example, it isn't exact for:
ISO 400 -> ISO 24°
(For ISO 24°, the theoretical arithmetic speed would be ISO 398.1)
And is isn't all that close for:
ISO 160 -> 23
(For ISO 23°, the theoretical arithmetic speed would be ISO 158.5)
Of course, none of these curiosities are of any practical importance, given the broad rounding that is in play.
But it is important that if we get involved in theoretical work, we remember how it actually works.
For example, if we believe that the "three steps is a 2:1 change" rule is the actual underlying theoretical premise of the series (false), we can go badly wrong as we reach higher parts of the series.
And if we believe that "10 steps is a 10:1 change" is the underlying theoretical premise (true), but don't pay any attention to where it starts (it starts at ISO 1 -> ISO 1°, but it is easy to assume, by parallel with other logarithmic scales, that ISO 1 -> ISO 0°), we can have a tragic gaffe such as the one in ISO 2720 I recently described elsewhere.
Benediction
The bottom line: "Pay attention".
So, do electrical engineers ever think that a 2:1 power change is actually 3 dB (precisely)?
Not I.
Today
Today the S° notation is deprecated, and there is no equivalent of it for ISO speed as defined for digital cameras.
The APEX speed value (Sv)
We do use today a different logarithmic expression of ISO speed, the APEX speed value (Sv).
Like all APEX "values", a change of one unit in this represents a 2:1 change in the actual property being represented.
In modern times the two scales are tied together here:
ISO 100 = Sv 5
At one time, the relationship was slightly different. You need not hear about that - it would just make your head hurt.
There is no series of standard values for Sv, and expression as a decimal fraction is OK where needed.
ISO speed ( or maybe ISO SOS or ISO REI) is recorded in Exif metadata by way of Sv (as a rational number).
At one time the ASA standard for film speed in the US (superseded by the ISO standard) included provision for the use of a logarithmic expression for ASA speed (identical to the APEX Sv, as I have defined it above). The values were called ASA grades and were shown thus: ASA 5°.
On a classic exposure meter
My Miranda Cadius exposure meter (early 1960s, I think) has provision for setting the exposure index in three forms:
• ASA (meaning the ASA speed, essentially identical to the eventual ISO speed).
• DIN (meaning per the the older German system, essentially identical to the eventual ISO speed logarithmic system, S°).
• °ASA (meaning the ASA grade system, essentially the same as the APEX Sv).
Best regards,
Doug