On the infamous "18% average scene reflectance" and various ISO standards

[Doug Kerr]

ISO standard 12232-2006 defines various measures of the sensitivity of a digital camera's imaging system. One important measure is the ISO saturation-based speed, Ssat, which ISO 12232 defines thus:

Ssat=78/Hsat

where Hsat is the saturation phtometric exposure of the imaging system.

Shortly after, the standard says:

NOTE Equation (5) provides 1/2 “stop" of headroom (41 % additional headroom) for specular highlights above the
signal level that would be obtained from a theoretical 100 % reflectance object in the scene, so that a theoretical 141 %
reflectance object in the scene would produce a focal plane exposure of Hsat. Therefore, an 18 % reflectance test card in
the scene would produce a focal plane exposure of 128/1 000 Hsat. Thus, the multiplicative constant 78 in Equation (5) is
equal to 10 times 1 000/128, where the value 10 is the constant from Equation (1).

But that result is not enacted by the definition in Equation (5) of this standard, nor otherwise by this standard. To enact that result in a metered shot also requires a certain "calibration" of the exposure meter used to set the camera for the shot, a matter that is not at all covered in ISO 12232.

We might imagine that the author of that passage anticipated that the standard for the calibration of exposure meters would "play along". And in fact, the ANSI standard for exposure meters, ANSI PH3.49-1971, did just that, recommending a value of K of 12.5, which would essentially bring about the situation described in the passage I quoted from ISO 12232.

But well before the time ISO 12232-2006 was issued, ANSI PH3.49 had been superseded by ISO standard 2720-1974.

That standard might have stated a preferred value for the reflective light calibration constant, K. which (in concert with a certain "exposure strategy") would being into place the relationship discussed in ISO 12232. (That value would have been K=12.6 if we assume that the lens transmittance is 100%.)

But in fact ISO 2720 does not prescribe nor even suggest a value of K. And so we cannot infer from ISO 2720 an assumed value of the average scene reflectance nor an assumed exposure strategy.

Thus the infamous 18% is never really stated as "assumed" by any current ISO standard or combination of same, nor is the infamous "1/2 stop headroom" exposure objective.

It is interesting to note that ISO 12232-1998, the first edition of this standard, does not include the passage cited above.

Best regards,

Doug

 

[Doug Kerr]

I have only the first few pages of ISO 12232-2019 (a "free preview"), which superseded ISO 12232-2006, so I can't tell whether that quoted passage has survived or not.

Best regards,

Doug

 

[Ted Cousins]

I have only the first few pages of ISO 12232-2019 (a "free preview"), which superseded ISO 12232-2006, so I can't tell whether that quoted passage has survived or not.

Best regards,

Doug

With a quick look, I too could only find the preview pages. I tried Google AI but it just gave links to posts of yours here!

However, I did note this little jewel which ISO absorbed from CIPA DC-2004:

In CIPA, I had assumed that it was to do with SOS but, in ISO, it is a general-purpose expression. Particularly of note is the constant 0.65 or 65/100 in ISO-speak. As you know it caters for a real lens and is significantly lower than other such.

Since it applies to a reference lens but mounted on any camera with any sensor, it should come as no surprise if image "exposures" can vary for a given focal plane exposure Hm ...

... I wonder what the variance of "Exposure" is ** ...

... what does 2721 say or imply? ...

** I use the term in quotes for those who think that the popular marking of the brightness slider in an editor as "Exposure" is correct; 'cuz it ain't.

 

[Doug Kerr]

Hi, Ted,

Thanks for that.

With a quick look, I too could only find the preview pages. I tried Google AI but it just gave links to posts of yours here!

However, I did note this little jewel which ISO absorbed from CIPA DC-2004:

View attachment 14256

In CIPA, I had assumed that it was to do with SOS but, in ISO, it is a general-purpose expression. Particularly of note is the constant 0.65 or 65/100 in ISO-speak. As you know it caters for a real lens and is significantly lower than other such.

The basic relationship can be derived from fundamental photometrics, and is given by:

where Hi is the photometric exposure on the image plane for some scene element; Ls is the luminance of that scene element; t is the exposure time in seconds; A is the aperture, as an f-number; and T is the transmittance of the lens.

If we assume T to be 0.833 (could well be), this becomes:

Since it applies to a reference lens but mounted on any camera with any sensor, it should come as no surprise if image "exposures" can vary for a given focal plane exposure Hm ...

Well, that equation is photometrically general (to the focal plane), and does not in any way depend on what kind of sensor, or any such. (Recall what it tells is "phtometric exposure", and you are right, "exposure" (not otherwise qualified) can mean many things.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

Thanks for that.

The basic relationship can be derived from fundamental photometrics, and is given by:
View attachment 14257
where Hi is the photometric exposure on the image plane for some scene element; Ls is the luminance of that scene element; t is the exposure time in seconds; A is the aperture, as an f-number; and T is the transmittance of the lens.

If we assume T to be 0.833 (could well be), this becomes:
View attachment 14258

Thank for the fundamental formula, Doug! since 0.65 is not equal tp pi/4 (0.785398 to six dp's) they snuck in something else, whatever.

[edit] "snucked" explained in my next post[/edit]

best,

Ted.

 

[Ted Cousins]

View attachment 14257
where Hi is the photometric exposure on the image plane for some scene element; Ls is the luminance of that scene element; t is the exposure time in seconds; A is the aperture, as an f-number; and T is the transmittance of the lens.

If we assume T to be 0.833 (could well be), this becomes:
View attachment 14258

Indeed it could:

[/ATTACH]

I must read specs more fully - your answer was there all the time!

 

[Doug Kerr]

Hi, Ted,

[edit] "snucked" explained in my next post[/edit]

Indeed, that verb has an irregular simple past tense!

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

... I wonder what the variance of "Exposure" is ** ...

That of course depends on just what you are asking about.

Perhaps the question is, "What is the variance of the photometric exposure across the mage in a given shot?"

That of course depends on the distribution of luminance across the scene. I'm sure there have been a lot of studies seeking to characterize that for scenes "often encountered" in practical photography.

Or perhaps the question is, "What is the variance of the average photometric exposure over successive shots with the same camera, or across different cameras?"

If all the shots were metered, and for each the value of K was the same, and for each the lens transmittance, T, was the same, then we should expect negligible variation in the average phtometric exposure.

Best regards,

Doug

 

[Ted Cousins]

That of course depends on just what you are asking about.

Can't find where I said that and I have forgotten the context, sorry.

Perhaps the question is, "What is the variance of the photometric exposure across the mage in a given shot?"

No

That of course depends on the distribution of luminance across the scene. I'm sure there have been a lot of studies seeking to characterize that for scenes "often encountered" in practical photography.

Or perhaps the question is, "What is the variance of the average photometric exposure over successive shots with the same camera, or across different cameras?"

If all the shots were metered, and for each the value of [edit]L[/edit] was the same, and for each the lens transmittance, T, was the same, then we should expect negligible variation in the average [photometric] exposure.

No. Photometric exposure perhaps i.e. Hm - but I am talking about the 'developed' result, e.g. an sRGB JPEG.

My point I think is that, for the same focal plane Hm, different cameras will produce different RGB conversions because the sensor and the converter properties vary from unit to unit.

Remember that Hm applies to the focal plane, not to the sensor, et subs

All the best,

Ted,

 

[Doug Kerr]

Hi, Ted,

Remember that Hm applies to the focal plane, not to the sensor, . . .

But we assume that what is at the focal plane is(for a digital camera) the sensor, so I think there is no distinction there. The main reason "focal plane" is said is to embrace both film and digital cameras (which is the situation for ISO 2720 and 2721).

Recall also that Hm is a certain photometric exposure, defined as existing under certain conditions, not "phtometric exposure" as a generalized phenomenon (H).

Indeed for the same photometric exposure on the sensor different cameras will produce different RGB values in the "developed" image. Not the least of the reasons is that this depends on the value of S for the camera. But I know what you are saying.

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

Keep in mind that in ISO 12232, the ISO SOS is defined based on a the phtometric exposure ("on the focal plane") that results in a certain result in the output signal (which seemingly is assumed to be in some RGB form).

And ISO 12232 speaks only of the focal plane, even though its scope is only digital still cameras. I imagine this is some sort of academic inertia!

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

A complication that I basically ignore is that we are usually interested in a color camera, whereas the photometric equations in the various standards apply to a monochrome camera.

Various of the standards indeed address this in some places but not others.

Best regards,

Doug

 

[Doug Kerr]

Imagine that we have a "color" camera, but it has a "monochrome" mode and we have it in that mode. When we take its "JPEG" output, for each pixel R=G=B. We assume that the values of B,, G, and B are on a 8-bit basis, with a range of 0-255 (decimal).

We now wish to determine its ISO SOS (in that monochrome mode). That is defined in terms of the photometric exposure on the focal plane (thus on the sensor) such that in the digital output R=G=B=118 (decimal).

Best regards,

Doug

 

[Doug Kerr]

The source of that value (118) is seemingly this:

• Assumed is an exposure objective that a scene element with a reflectance of 100% (considered the "brightest possible" element) will receive a phtometric exposure on the focal plane (sensor) equal to the saturation exposure ( Hsat).

• The average scene reflectance is assumed to be 18.2%,

• Thus the average phtometric exposure on the sensor will be 0.182 Hsat.

• We assume that the encoded output for a phtometric exposure of Hsat will be "full scale"; in an 8-bit context, that would be 255 (decimal). (But the standard seems to use 256.)

• We assume that the encoding follows an inverse gamma function with gamma=2.2.

• Thus the theoretical encoded value for the average phtometric exposure will be:
0.182^(1/2.2)•256=118

Best regards,

Doug

 

[Ted Cousins]

The source of that value (118) is seemingly this:

• Assumed is an exposure objective that a scene element with a reflectance of 100% (considered the "brightest possible" element) will receive a phtometric exposure on the focal plane (sensor) equal to the saturation exposure ( Hsat).

• The average scene reflectance is assumed to be 18.2%,

• Thus the average phtometric exposure on the sensor will be 0.182 Hsat.

• We assume that the encoded output for a phtometric exposure of Hsat will be "full scale"; in an 8-bit context, that would be 255 (decimal). (But the standard seems to use 256.)

CIPA states 255 for 8-bit, not 256.
"MAX is the normalization coefficient（＝maximum digital output level: 255 for 8-bit system）γ{ }, γ -1{ } denote sRGB gamma characteristics and the inverse transformation (linearization) characteristics defined by IEC61966-2-1.
ISO states "where OMAX is the maximum output value of the digital system. For 8-bit systems, the reference level shall be 118." In the world of binary arithmetic, 8-bits can not have a decimal value of 256.

• We assume that the encoding follows an inverse gamma function with gamma=2.2.

I believe that the inverse function is that of sRGB gamma, as specified above by CIPA, not 2.2.
Working backwards via sRGB gamma, 118/255 gives Y = 0.181164, not 0.182. see http://www.brucelindbloom.com/

AI sez Plugging the 18% standard middle-gray reflectance (Y = 0.18) directly into this exact sRGB formula yields:\(N=1.055\times (0.18)^{\frac{1}{2.4}}-0.055\)\(N\approx \mathbf{0.461356}\)When rounded to three decimal places for the ISO standard definition, this evaluates precisely to 0.461. In an 8-bit digital system, this corresponds to a digital value of 117.555 i.e. 118 (out of 255).

• Thus the theoretical encoded value for the average phtometric exposure will be:
0.182^(1/2.2)•256=118

So, sorry Doug, but 0.182, 1/2.2, 256 are all incorrect, IMHO.

best rgds,

Ted.

 

[Doug Kerr]

Hi, Ted,

So, sorry Doug, but 0.182, 2.2, 256 are all incorrect.

Thanks for your diligent and careful work on all this.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

Thanks for your diligent and careful work on all this.

Best regards,

Doug

You're welcome Doug and please pardon my pedantry ...

 

[Doug Kerr]

Hi, Redm

You're welcome Doug and please pardon my pedantry ...

It is very welcome.

Best regards,

Doug