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What Does Your Meter Meter?

Exposure, Calibration and the K Factor
by Gisle Hannemyr

When you read up on light meters an exposure on the Internet, you sometimes stumble over the notion that the light meter of modern cameras is calibrated to a luminance value that is roughly equivalent to the reflectance of 12 % grey. The earliest instance of this myth I've seen is an article by Thom Hogan dated November 2003 titled Meters Don't See 18% Gray. So Thom Hogan probably have the dubious honour of having invented this particular myth.

1. Introduction

On his webpage, Thom Hogan writes: “Light meters are calibrated at the factory using ANSI standards. The standard has always been for a luminance value that is roughly equivalent to the reflectance of 12% gray.” In a postscript to the same article, he adds: “No manufacturer I've talked to knows anything about a K factor, though, and they all speak specifically about the ANSI standard as their criteria for building and testing meters.”

Thom Hogan's opinions is respected by many Nikon shooters. However, he has got the most of that article wrong, including the number 12 %. He refers to unspecified “ANSI standards”, but there is only one ANSI standard for light meter calibration: ANSI/NAPM IT3.302-1994. This standard is a word-for-word reprint of ISO 2720:1974 General Purpose Photographic Exposure Meters (Photoelectric Type) – Guide to Product Specification.

All reflected and incident light meters are calibrated using the criteria set forth in this ISO/ANSI standard. Absolutely no reference to 12 % grey appear in the standard, and it explicitly references the “constant K” – i.e. the “K factor” than Hogan says that nobody knows anything about.

So how is the light meter in Thom Hogan's camera calibrated? Well, Hogan is a Nikon shooter, and Nikon exposure meters are calibrated to yield the same exposure for incident and reflected light if the reflected light meter is used to meter off a perfectly flat, diffuse, and front-lit object with 15.7 % reflectance. Some may (inaccurately) say that Nikon's light meters are calibrated to see a luminance value that is roughly equivalent to the reflectance of 15.7 % grey. Why 15.7 %? Read on to find out.

2. Kodak vs. Ansel Adams

Kodak, who sells grey cards carefully calibrated to reflect 18 % of incoming light, used to include the following instructions in each package:

Meter readings of the grey card should be adjusted as follows: 1) For subjects of normal reflectance increase the indicated exposure by 1/2 stop. 2) For light subjects use the indicated exposure; for very light subjects decrease exposure by 1/2 stop 3) If the subject is dark to very dark increase the indicated exposure by 1 to 1.5 stops.

Unfortunately, many users became confused by these instructions, so Kodak removed them around 1980. However, the instructions are sound, so I'll expand on them here.

Kodak's instructions tell you two things. First: While the Kodak card is calibrated to 18 % reflectance, your meter is probably not. If you photograph a “normal” scene (i.e. middle grey with 18 % reflectance), you should increase exposure by half a stop. Second: The meter's reading off the grey card doesn't give the correct exposure for every scene. If the scene is very light, or very dark, you may need to adjust exposure to subdue the highlights or lift the shadows to fall within the dynamic range of your recording medium (silver halide or silicon).

On the subject of exposure metering, Ansel Adams learnt that exposure meters was calibrated with something called a “K factor”. He was not happy about it. In his landmark book, The Negative, he wrote:

If pressed, the manufacturers of some exposure meters will acknowledge that they depart from standard calibration of their meters by incorporating a “K factor.” This factor is supposed to give a higher percentage of acceptable images under average conditions than a meter calibrated exactly to an 18 percent reflectance. The practical effect of the K factor is that if we make a care­ful reading from a middle-grey surface and expose as indicated, the result will not be exactly a middle grey! […] With nearly all meters, this factor is equivalent to giving a one-third stop increase in exposure. Although the manufacturers may be acting with good intention, I find it far preferable to work with what I consider the true characteristics of the light and films. Intelligent use of the meter eliminates the need for such artificial aids as the “K factor.” (Adams 2002, pp. 42f)

Adams goes on to suggest (ibid. pp. 66f) that the photographer should increase the ISO speed on the light meter with the fraction of EV necessary, to compensate for the K factor. Increasing the ISO speed will of course decrease the exposure, negating what Adams thought was an error introduced by the K factor.

So, from two great authorities on exposure, Kodak and Ansel Adams, we have conflicting advice. Kodak tells you to increase exposure with respect to what your meter tells you for subjects of normal reflectance, Ansel Adams tells you to decrease it.

I believe it is Kodak that has got it right. Towards the end of this essay I'll introduce Jeff Conrad's (2003) conjecture about why Adams got this one wrong.

3. Rendering Middle Grey

Let us for the moment assume that your light meter is supposed to meter “middle grey” (whatever that is). What sort of luminance value between 0 (black point) and 255 (white point) is then supposed to be rendered for this tone in a gamma adjusted image file?

histogram
Histogram from shot of a uniform grey card appears to shifted left 0.5 EV of centre.

First a reality check. What do the camera actually do. I used my Sigma SD10 DSLR to photograph a standard, uniform grey card (any neutral and uniform surface will do) in daylight (5500 K). Exposure was spot metered with a Sekonic L-778 meter. The resulting RAW file was processed with “as-shot” settings in ACR to produce a gamma adjusted TIFF.

The resulting histogram is shown to the right. It has a mean value of 105, slightly left of centre. If a middle grey reading is supposed to place the mean in the centre, it is underexposed by around a third of a stop.

But should middle grey be rendered as 127.5 (the mean value between 0 and 255)?

A slightly more sophisticated argument says that 18 % reflectance should be rendered as 117. This number is computed from this formula:

ζ1/γ x 255

where ζ (zeta) is the reflectance and equal to 0.18 (18 %) and γ is the gamma and is equal to 2.2 (which it is supposed to be these days).

Finally, there is the approach taken by Norman Koren in his Equations for zones. Koren thinks that middle grey should be rendered as 126, and he invents a tone mapping function that yield this value. There is nothing magical about Koren's function, he has just picked values that mimics the S-curve many RAW-converters apply to the data when converting into a visual representation. If you think middle grey should be rendered as 126 (or any other value) there is of course nothing to stop you from applying whatever tone curve you fancy to the bits in the RAW file as part of your conversion workflow.

(I plan to redo the exposure test more extensively soon, with several different cameras. I will also be getting both in-camera JPEGs and RAW files, and I will test with the camera's meter as well as external reflective and incident metering. Watch this space for updates.)

4. How Exposure Meters are Really Calibrated

But a value of 105 is lower than both 118 and 127.5. And while the exposure or ISO on my Sigma SD10 may be out of whack, a lot of people report similar results with their cameras. When they perform the exposure test described above, their histograms turn out slightly left of centre.

This led me to trying to find out more about how reflected light metering and the mysterious “K factor” that Adams talks about.

A big light bulb lit up over my head when I found this paper by Jeff Conrad (2003). Reflected light exposure meters, Conrad says, are calibrated with the use of the following equation, which defines the relationship between EV, desired camera exposure settings, and scene luminance:

2EV = N2/t = (L x S)/K

EV is the exposure value, N is aperture expressed as a f-number, t is the shutter time in seconds, L is luminance expressed in candela per square meter, S is ISO speed, and K is the reflective meter calibration constant (the “K factor” Adams gripes about). The standard also mentions C, which is a similar calibration constant, used in the corresponding equation for incident-light meters.

ISO 2720:1974 (ISO 1974) has the following to say about the values for K and C:

The constants K and C shall be chosen by statistical analysis of the results of a large number of tests carried out to determine the acceptability to a large number of observers, of a number of photo­gra­phs, for which the exposure was known, obtained under various conditions of subject manner and over a range of luminance.

The standard also recommends a range for K between 10.6 and 13.4, and a range for C between 240 and 400.

To illustrate how the equation may be used let's assume we meter a scene where the luminance is 3200 candela per square meter. This corresponds to a scene lit by bright sunlight, EV 15, (or 14.64386 to be more accurate), aka. “sunny 16”. So naturally, we want our meter to yield exposure suitable for “sunny 16” conditions, i.e. f/16, 0.01 second, at ISO 100. In the equation, we put EV=14.64386, N=16, t=0.01, L=3200 and S=100. We find that in this case, by setting K=12.5, the equation “computes”. I.e.:

214.64386 = 162/0.01 = (3200x100)/12.5 = 25600.

ISO wants manufacturers to run a large number of similar tests, and at the end pick a figure for K that gives the most acceptable results.

As noted, Ansel Adams didn't like this. He refers to “the true characteristics of the light and films” that is somehow disturbed by the introduction of an “artificial aid” – the K factor. According to Conrad (p. 7) this was due to Adams being familiar with an ameri­can­ised version of the exposure equation, where luminance was expressed in imperial units (i.e. candela per square feet). In this version of the equation the K factor is very close to 1, so it is possible to ignore it and still have the equation compute. However, mathematically, mixing imperial and SI units doesn't make sense, so there is nothing “true” or natural about computing exposure this way.

A K factor equal to 1.0 with luminance given in imperial units is equal to a K factor equal to 10.76 with luminance given in SI units. If Adams had his initial Weston exposure meter calibrated to K = 10.76, and later acquired a Pentax spot meter calibrated to K = 14, the latter would indicate about 1/3 stop more exposure, which is probably what Adams complains about when he brings up the K factor in The Negative.

You can look up the K and C calibration constants by reading the technical specifications for a particular light meters (usually at the back of the manual), or by consulting manufac­turers specification sheets.

If we know the K and C calibration constants used by a particular manufacturer, we can also compute the implicit reflectance in percent ζ. We do this using the following equation (from Conrad 2003, p. 8):

ζ = π x (K / C)

where π is mathematical constant pi, K is the reflected light calibration constant and C is the incident light calibration constant.

At least three separate values for K are used: 11.37 (Gossen), 12.5 (Sekonic, Canon, Nikon) and 14 (Pentax and Minolta). Note that the last value is outside the ISO-recommended range. A typical value for C for a flat, perfectly diffuse front-lit receptor is 250. If we set C=250 and K=12.5, ζ becomes 15.7 %. This suggests that Sekonic, Canon and Nikon exposure meters are calibrated to yield the same exposure for incident and reflected light, if the reflected light meter is used to meter off a perfectly flat, diffuse, and front-lit object with 15.7 % reflectance. However, a piece of cardboard is only an approximation to such an object, so thinking that think this means that meters are “calibrated” to meter off a 15.7 % grey card, as some imply, is taking this a bit to far. Nevertheless, if we compute K as a function of ζ=18 % and C=250, we find that K=14.32 is the value that “matches” 18 % reflectance.

The table below shows computed values for ζ as a function of different values for K and C. The column EV1 shows the approximate compensation you need to add in order to render a “perfect” 18 % reflectance grey card as middle grey, assuming C = 250. The column EV2 shows the approximate compensation you need to subtract in order to match the exposure Ansel Adams prescribes for Zone V by adjusting for your meter's K factor.

K\CC=250C=320C=340EV1EV2Brand
K=10.7613.5 %10.6 %9.9 %+0.330Weston?
K=11.3714.3 %11.2 %10.5 %+0.26-0.05Gossen
K=12.5015.7 %12.3 %11.5 %+0.15-0.14Sekonic, Canon, Nikon
K=14.0017.6 %13.7 %12.9 %+0.02-0.23Pentax, Minolta
K=14.3218.0 %14.1 %13.2 %0-0.25-

The additional values for C are for a hemispherical receptor, as used by incident light meters. Common values for C are 320 (Minolta) and 340 (Sekonic).

5. Conclusion

This leaves the question: What sort of EV should you use to place Zone V (aka. “middle grey”)? There is at least three possible answers: 1) The exact EV reported by your meter (this is probably what your meter's manual tells you to use); 2) the EV reported by your meter plus the computed value in the EV1 column to compensate for your meter not being calibrated for 18 % grey; or 3) the EV reported by your meter minus the computed value in column EV2 to follow up on Adams' recommendation.

After looking at the numbers above, I think that it isn't really necessary to make exposure adjustments when reading off a 18 % grey card. All the amounts are minute, and probably within reading error and the meter's tolerance. I see not point in adjusting these, and simply rely on the EV reported by the meter.

Adams, Ansel (2002): The Negative (reprint of final edition from 1981); Little Brown and Company; Bulfinch.

ANSI (1994) ANSI/NAPM IT3.302-1994. American National Standard for General-Purpose Photographic Exposure Meters (Photoelectric Type) – Guide to Product Specification; American National Standards Institute.

Conrad, Jeff (2003): Exposure Metering: Relating Subject Lighting to Film Exposure (pdf)

ISO (1974): ISO 2720:1974. General Purpose Photographic Exposure Meters (Photoelectric Type) – Guide to Product Specification; International Organisation for Standardisation.

ISO (2006): ISO 12232:2006: Photography – Digital still cameras – Determination of exposure index, ISO speed ratings, standard output sensitivity, and recommended exposure index; International Organization for Standardization.

Wikipedia (undated): Light Meter.

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2 responses:

avatar
Consider vignetting

I wonder if you considered the lens vignetting in Paragraph 3. When measuring by spot or center-weight TTL and fairly open lens there is the chance that the lens vignetting causes the histogram to shift into darker tones. Because the edges of the image are darker depending on the lens.

But it is only suggestion that needs to be considered.

Let me know by email.

avatar
Nikon D600 metering 18% grey card

Doing your test (metering the gray card) I found out that my histogram showed the "middle gray" to the right of the 128 value, not to the left as many report.

Any ideas why? this would give reason to Ansel Adams to underexpose half a stop.....

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