Metering, ISO sensitivity, and stuff

We have here many interesting discussions on topics such as optimization of exposure for best noise performance, techniques for enhancing dynamic range, and so forth.

I thought I would take this opportunity to review a few technical matters that seem to pop up in may of these discussions.

"18% gray"

We often hear it said that:

• "exposure meters are calibrated to 18% gray".

This statement doesn't really describe anything definable.

In many case, what the speaker perhaps means is:

1. Automatic exposure systems are calibrated such that (assuming scene-average metering), for a shot taken with automatic exposure control, in the developed image a neutral area whose actual luminance in the scene is the same as the average luminance for the scene will be coded with RGB values that (considering the color space in effect) represent a luminance 18% of that represented by the maximum digital code (RGB=255,255,255). (That would be 117,117,117 for the sRGB color space.)

Three versions of an assumed corollary are:

2a. For a metered shot, in the developed image, a neutral scene area whose luminance is 100/18 times the average luminance will receive a digital code of 255,255,255 (just at saturation).

2b. If for a uniform-luminance neutral scene we take the exposure factors (aperture, shutter speed) chosen by the automatic exposure system, manually set an exposure 100/18 times that, and shoot, the entire image will receive digital code 255,255,255.

2c. If for a uniform-luminance neutral scene we take the exposure factors (aperture, shutter speed) chosen by the automatic exposure system at a certain ISO sensitivity setting, manually set those factors, change to an ISO sensitivity 100/18 that used during the metering, and shoot, the entire image will receive digital code 255,255,255.

Exposure meter calibration

Let's start with item (1). Whether or not a particular camera does that depends on two distinct factors:

• The "calibration" of the automatic exposure control system.

• The approach used in the camera for assessment of the ISO sensitivity for any given "ISO" setting.

The reason these interact is that the calibration of the exposure control system is defined in terms an equation one of whose parameters is the EI (exposure index) setting "fed" to the metering system, where we can look at EI as "what we tell the exposure meter the ISO sensitivity of the film or digital sensor is".

Of course, for an internal exposure control system, the value of ISO sensitivity we choose for camera operation is automatically fed to the exposure control system as the EI.

So perhaps, if we want to make a "general" statement (with respect to digital cameras), we might want to mean:

• If the calibration of the automatic exposure control system is in accordance with the applicable international standard, ISO 2721, and

• The assessment of the ISO sensitivity of the digital sensor system is in accordance with the applicable international standard, ISO 12232.

then we can expect a certain result.

ISO sensitivity

But ISO 12232 specifies four ways to assess the ISO sensitivity of a digital camera. All are, incidentally, predicated on behavior as observed in the developed image, and so do us no good if we are thinking in terms of the raw output.

2a. The ISO Speed (saturation), based on the photometric exposure required to cause saturation of the sensor chain (as revealed in the RGB values in the developed image).

2b. The ISO speed (noise), based on noise performance at low photometric exposures. It is only cited when it leads to a "more conservative" rating than 2a.

3. The ISO Standard Output Sensitivity (SOS). This is essentially defined just like 2a, except it is 0.707 times as large.

4. The ISO Recommended Exposure Index (REI). This is chosen by the camera manufacturer, the intent being that it is the value that (set as the EI into the metering system) produces a "good exposure in a lot of cases".

Implications

So, if

• the automatic exposure control system of the camera is calibrated per ISO 2720, and

• the ISO sensitivities of the camera are defined as the ISO Speed (saturation) (2a above)

then we can expect this:

• for a metered shot (scene-wide average metering), the average photometric exposure on the sensor is 12.5% of the saturation photometric exposure

Now, if

• the automatic exposure control system of the camera is calibrated per ISO 2720, and

• the ISO sensitivities are defined as the ISO SOS (3 above)

then we can expect this:

• for a metered shot (scene-wide average metering), the average photometric exposure on the sensor is 18% of the saturation photometric exposure.

So, for a camera of this latter type, if we take a metered shot of a neutral uniform-luminance test scene, will the RGB values of the developed image, interpreted under the applicable color space, represent 18% of full scale (which would, incidentally, be about RGB 117,117,117)? Not usually. How can this be?

Because the camera, in "developing" the sensor data, almost always applies some "tonal scale mapping", which disrupts that handy relationship.

Note that is we think in terms of the "traditional" ISO Speed (2a), we can expect the critical ratio to be 12.5%, not 18% (although defined in a different way than is usually thought of). Where does the value 18% come from?

Because the ISO standard definition of the calibration of automatic exposure control systems is predicated on a scene element having the same luminance as the scene average receiving a photometric exposure of 18% of a value 1/2 stop below saturation.

One way to describe the original object of that is:

• For a scene with an average reflectance of 18% (arbitrarily considered a "standard test scene"), a metered exposure would result in a scene element with a reflectance of 100% (a simplistic "lightest possible object') receiving a photometric exposure 1/2 stop below saturation.

That is, the scheme, for the arbitrary "standard test scene", allows "1/2 stop of headroom" to guard against overexposure of a potential 100% reflectance object in the scene.

And that's where the love affair with the magickal number, 18%,. comes from.


Aren't you glad you asked!

In recent years, Canon has stated the ISO sensitivities of their EOS cameras (probably others as well) in terms of the ISO REI, the "Recommended Exposure Index". That means that they are not committing that this number is determined in any objective fashion. Rather, it is what they recommend using as the Exposure Index for metering (a concept that really only is useful to the user in the case of metering with an external exposure meter).

Recall that the result of a metered exposure comes from the interaction between:

• The "calibration" of the automatic exposure system.

and

• The basis for assessment of the ISO sensitivity of the camera.

Numerous tests comparing the behavior of the Canon EOS exposure metering system itself (that is, in terms of exposure recommendation for a certain scene luminance and EI setting) with respected external exposure meters suggest that these metering systems themselves are generally consistent in their calibration with the pertinent international standard (ISO 2721).

If we stipulate to that, we can then, from the camera's exposure results, determine with fair accuracy the actual premise of the assessment of ISO sensitivity. That process suggests that, notwithstanding Canon's "coy" (some might say, "CYA") adoption of the "REI" presentation of ISO sensitivity ("hey - all bets are off - try it, you'll like it"), the numbers actually closely follow the ISO "SOS" basis.

Some simple tests of my Canon EOS 40D are consistent with that. In particular, a metered exposure of a uniform-luminance test object yields, in the JPEG output image, RGB triples at or close to 118, 118, 118 (implying, under the sRGB color space, a luminance 18% of the luminance implied at full scale, 255,255,255).

To drive the photometric exposure to just below saturation (254, 254, 254) required:

• for the same ISO sensitivity, an increase over the metered exposure of about 3-1/3 stops (10 times).

• for the same exposure, an increase in ISO sensitivity of 10 times (3-1/3 stops).

Again, we might have thought that this ratio would be about 5.6 times (2.5 stops) (100/18); the discrepancy, as discussed in the note above, presumably comes from the intrusion of tone mapping in the image processing (and the exact degree presumably would depend on such camera settings as contrast).

(My tests were done with all image processing settings at zero and AWB in effect.)

Best regards,

Doug

Just as an aside, fans of the number 18% who are eager for some rationale for considering that reflectance or relative luminance (which is properly called 82% gray) to be "middle gray" should be comforted to note that in the L*a*b* color model, that value has an L* (lightness) value of very nearly 50 (on a 100-point scale).

Best regards,

Doug