Another ISO 12232 metric of digital camera sensitivity

[Doug Kerr]

ISO 12232:2019, Amendment 1:2020 added a new metric of digital camera sensitivity, the encoding-relative sensitivity (ERS).

This is defined in terms of the photometric exposure required to produce a digital output signal of the value that is said to be equivalent to L*=50 (presumably referring to the L*a*b* color space coordinate) for the encoding system that is in use.

This seems to be, for all practical purposes, equivalent to the ISO SOS, but takes a different approach to referring to the digital output value.

Best regards,

Doug

 

[Doug Kerr]

For comparison, the ISO SOS is defined in terms of the phtometric exposure needed to produce a digital output of 0.461 of "full scale". (That would be about 118 on a 0-255 scale, as for a 8-bit representation) .

It is likely that this presumes the use of digital encoding with gamma=2.2, as in the case for the sRGB color space. But that is not really directly stated.

If that is indeed the case, then that encoded value corresponds to a relative luminance of about 0.182 (0.461^2.2). But that premise not being stated, the definition of the ISO SOS is a bit ambiguous,

In the L*a*b* color space a relative luminance of 0.182 gets an encoded L* value of about 49.7 (50 for all practical purposes).

Best regards,

Doug

 

[Ted Cousins]

For comparison, the ISO SOS is defined in terms of the phtometric exposure needed to produce a digital output of 0.461 of "full scale". (That would be about 118 on a 0-255 scale, as for a 8-bit representation) .

It is likely that this presumes the use of digital encoding with gamma=2.2, as in the case for the sRGB color space. But that is not really directly stated.

If that is indeed the case, then that encoded value corresponds to a relative luminance of about 0.182 (0.461^2.2). But that premise not being stated, the definition of the ISO SOS is a bit ambiguous,

In the L*a*b* color space a relative luminance of 0.182 gets an encoded L* value of about 49.7 (50 for all practical purposes).

Best regards,

Doug

I missed this thread, duh.

FWIW, Lindbloom's CIE calculator gives sRGB = 118.9133 for L*=50 with sRGB gamma.

best.

Ted

 

[Doug Kerr]

Hi, Ted,

FWIW, Lindbloom's CIE calculator gives sRGB = 118.9133 for L*=50 with sRGB gamma.

Yes.

This is thought by some to justify describing sRGB 118 as representing "mid gray".

That is a really nice tool, isn't it.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

Yes.

This is thought by some to justify describing sRGB 118 as representing "mid gray".

That is a really nice tool, isn't it.

Absolutely my favorite - I use it a lot.

As to mid-gray, that's whatever Chuck Norris would have said it is, ho ho.

 

[Doug Kerr]

Hi, Ted,

As to mid-gray, that's whatever Chuck Norris would have said it is, ho ho.

If somebody wants to think that sRGB118-118-118 describes "mid-gray", why not?

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

If somebody wants to think that sRGB118-118-118 describes "mid-gray", why not?

Why not indeed. I once asked on DPR what the range of mid-tones is - which started quite a long controversy ... Zone V got mentioned a lot ...

Ever seen this?

Observe that Kodak's Middle Gray is not "half-way" between their steps 3 & 4 ...

 

[Doug Kerr]

Hi, ted,

Why not indeed. I once asked on DPR what the range of mid-tones is - which started quite a long controversy ... Zone V got mentioned a lot ...

Ever seen this?

No, I think I have not seen that. I'm not even sure what is does!

Column 1 seems to refers to some known step target, or maybe to "step targets in general", since for each stop there is listed a range of reflectance. But also a specific reflectance. So step 2 has a reflectance of 42%, and a reflectance of 30-60%..

Observe that Kodak's middle gray is not "half-way" between their steps 3 & 4 ...

Ah.

Thanks.

Best regards,

Doug

 

[Doug Kerr]

The reality is that if one were to agree that an sRGB representation of 118,118,118 represents "mid gray", that would not establish anything.

Best regards,

Doug

 

[Ted Cousins]

Hi, ted,

No, I think I have not seen that. I'm not even sure what is does!

Column 1 seems to refers to some known step target, or maybe to "step targets in general", since for each stop there is listed a range of reflectance. But also a specific reflectance. So step 2 has a reflectance of 42%, and a reflectance [range] of 30-60%..

Column 1 goes with 0.3 steps of density over a range excluding top, middle and bottom, see also page 6 here:

https://www.kodak.com/content/products-brochures/Film/Basic-Photographic-Sensitometry-Workbook.pdf

 

[Ted Cousins]

Column 1 goes with 0.3 steps of density over a range excluding top, middle and bottom, see also page 6 here:

https://www.kodak.com/content/products-brochures/Film/Basic-Photographic-Sensitometry-Workbook.pdf

Doug,

As I trawl around the web, it seems that there is no standard for step wedge/chart base values ... and, although the inner steps are often 0.3, 0.15 and even 0.1, not even that is always so:

Step 6 comes close to 18% which I seem to recall is 0.744727 density or thereabouts.

This might be of interest - note what reflectance Zone V is not...

 

[Doug Kerr]

Hi, Ted,

All very interesting. Especially interesting are the "zone" step chart specs.

I note that in the "zone" chart the reflectances are seemingly given relative to reflectance at the base "density", not in absolute terms.

Thanks

Best regards,

Doug

 

[Doug Kerr]

Hi, Ted,

In those step chart specs as you show them the columns are not labeled.

But likely Column 2 would have been labeled "density".

Strictly speaking, that term applies to transparent media (such as a test chart on film). We can simplistically describe this as the ratio of the amount of luminous flux passing through the region of interest to the amount of luminous flux incident on the region.

But is it is common to use it, with a rather parallel meaning, to reflective media. That is usually log10 (R).

Best regards,

Doug

 

[Doug Kerr]

The "density" often cited in such things as the specifications for a "reflective step target" is precisely called the reflective density. In the phtometric context, the term density, used without qualification, is ordinarily taken to mean what is precisely called the transmisssive density (as is used in connection with, for example, film).

Best regards,

Doug

 

[Doug Kerr]

The reflective density, Drefl, of a surface is log10 (R), where R is the reflectance of the surface. But keep in mind that R is only defined for a Lambertian surface (a "perfectly diffuse reflecting surface").

Best regards,

Doug

 

[Ted Cousins]

The reflective density, Drefl, of a surface is log10 (R), where R is the reflectance of the surface. But keep in mind that R is only defined for a Lambertian surface (a "perfectly diffuse reflecting surface").

Stouffer also makes transmissive charts, where the column headed "Target" has values of density like their reflective wedges. The column density increments are indicated by the last two digits of the part number, e.g. T1015

Stouffer Industries

Highlighted in error - insignificant ...

Looks like the right-hand column is nominal values similar to electrical supply nominal voltages, i.e. 120, 240, 480, whereas what comes out of a wall socket can vary.

 

[Ted Cousins]

FYI, here's a Kodak reflective step-wedge in 0.1 density steps which are mapped to reflectance and RGB with two values of gamma.

I know the mapping functions.

Note that mid-gray is not 0.744724 density and not 0.180 reflectance and not 118/255 RGB(sRGB) ...

 

[Doug Kerr]

Hi, Ted,

I know the mapping functions.

Looks like straight power functions with the exponent (gamma) as indicated.

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

Looks like straight power functions with the exponent (gamma) as indicated.

Hello Doug,

Yes, density to reflectance R=1/(10^D) ergo 1/(10^0.75)=0.1778

Density to RGB(gamma) = ((1/(10^D))^(1/gamma))*255 ergo ((1/(10^0.75))^(1/2.2))*255=116 (not SRGB gamma).

Other arrangements should give the same result, e.g. using density to reflectance, then reflectance to RGB.

No doubt you could pretty up the equations and/or simplify them ...

best regards,

Ted.

 

[Doug Kerr]

Hi, Ted,

Thanks for demonstrating/confirming that.

Hello Doug,

Yes, density to reflectance R=1/(10^D) ergo 1/(10^0.75)=0.1778

Density to RGB(gamma) = ((1/(10^D))^(1/gamma))*255 ergo ((1/(10^0.75))^(1/2.2))*255=116 (not SRGB gamma).

Other arrangements should give the same result, e.g. using density to reflectance, then reflectance to RGB.

No doubt you could pretty up the equations and/or simplify them ...

I don't think they could be simplified from the versions you show. As to prettying-up the presentation, I think that for this medium what you did is fine.

Best regards,

Doug

 

[Doug Kerr]

Well, why not.

Here is the equation Ted cited presented in something like standard mathematical form:

This is a little "simpler", but I think not as useful to the typical reader:

I use here "RGB" to represent all of the nonlinear variables R, G, and B. (Often, in rigorous work, those are designated R', G', and B' to indicate the nonlinear form of that coordinate. Some authors use R*, G*, and B*, adapting the notation used in connection with the L*a*b* color space.)

Best regards,

Doug

 

[Ted Cousins]

Good job, Doug!

I find proper math-representation beyond my ken.

Bad enough trying to find sub- and super-scripts in Windows 'charmap'.

best,

Ted.

 

[Doug Kerr]

Hi, Ted,

The tool I mostly use (and used in this case) is the equation editor included in my (quite old) MS Word. It is a very nice WYSIWYG equation editor.

To use that here, I compose the equation in MS Word on a dummy document and then take a screen grab of it and emplace it in a post as a picture.

I have other equation editors but (to me) they are a bit more clumsy to use.

There are a number of conventions for representing mathematical equations via HTML, but I have never really gotten aboard with any of those (and I have no idea whether the OPF platform would deal well with them).

Best regards,

Doug

 

[Ted Cousins]

Hi, Ted,

The tool I mostly use (and used in this case) is the equation editor included in my (quite old) MS Word. It is a very nice WYSIWYG equation editor.

Thanks Doug,

I use OpenOffice not Word, so I'll take a look at that and also poke around with AI ...

Apache OpenOffice Writer does have an Equation Editor - not terribly easy GUI ...

Looked again at Windows charmap ... found these UniCode characters after selecting various fonts

· º ÷ Θ Φ ƒ Σ μ ₁ ₀ ₂ ≈ ≤ ≠ ≥ √ ≡ ∞ ꜛ ϖ ± ² ⁿ ³ ⁺ ⁻ ⁽⁾

from which e.g. t/N²≈K/(L·S)

Or Ev=log₂(N²/t)

best,

Ted

 

[Doug Kerr]

Hi, Ted,

A nice free-standing equation editor, with a nice WYSIWYG interface much like the equation editor in my MD Word, is Math Editor.

But its current "circumstance" is a bit odd - I suspect it is an orphan.

It can still be acquired from various sites.

But when I try to go to its Help facility, my anti-virus software blocks the access, reporting that the site is black-listed.

It has no provision for emitting a composed equation in, for example, HTML. It only provides for capturing a picture of the equation (as PNG, JPG, GIF etc.) And there are some peculiarities involved there.

Here is an old favorite:

Best regards,

Doug

 

[Ted Cousins]

Hello Doug, thanks for the tip.

I now intend to stick with UniCode symbology as opposed to copying and pasting equation images. Have found several ways to insert Unicode symbols into editors like on this site. Have also found that not all targets are equal!

On this site, the posted greek pi looks OK but on DPRevived it looks like a bra:

Some UniCode math symbols

Started by xpatUSA on July 19, 2026 in the Technical Discussions category. 2 replies, last one from July 19, 2026.

dprevived.com

Solution was to find another 'pi' in a different font in Windows 11's CharMap.

such fun ...

Ted

 

[Doug Kerr]

One of the wrinkles with Math Editor is that when it exports a picture of an equation in most formats it is on a "transparent" background. (I don't know how it does that in a JPEG file.) Different receiving applications deal with that in different ways, none of them really very nice).

So when I have composed an equation in Math Editor, I snag a picture of it with my screen capture facility, and if I want a file of the picture, save it from that in the format needed. It ends up with a white background (just as I saw it on-screen).

Best regards,

Doug

 

[Ted Cousins]

One of the wrinkles with Math Editor is that when it exports a picture of an equation in most formats it is on a "transparent" background. (I don't know how it does that in a JPEG file.) Different receiving applications deal with that in different ways, none of them really very nice).

So when I have composed an equation in Math Editor, I snag a picture of it with my screen capture facility, and if I want a file of the picture, save it from that in the format needed. It ends up with a white background (just as I saw it on-screen).

Yes, my Avatar GIF which is a shield with a transparent background shows with a rectangular black background on some sites. Not here it seems ...

 

[Doug Kerr]

My email client app (Thunderbird) allows one, in a message to be sent in HTML, to include equations. They must however be entered in the LaTex code.

Here is an example as rendered in my Thunderbird email composition window:

This is the LaTex code for that:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

The LaTex syntax is generally very logical (although I currently have no fluency in it).

Best regards,

Doug

 

[Ted Cousins]

My email client app (Thunderbird) allows one, in a message to be sent in HTML, to include equations. They must however be entered in the LaTex code.

Here is an example as rendered in my Thunderbird email composition window:

View attachment 14274
This is the LaTex code for that:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Interesting and looks familiar ... when I copy AI text that has pretty formulae into NotePad that's what comes out for the formulae.

best,

Ted.