More on 18% Gray

I’m not quite sure what got me going on 18% gray. I suppose it might have been the association with Ansel Adams, who obviously knew what he was doing, and the notion that 18% and 50% were not equal. I mean, how could they say that 18% gray was the same as 50% gray; where did that come from?

Of course, in Photoshop, one of the built-in options for filling a layer is 50% gray; and there didn’t seem to be anything off the wall about that. Then, I watched Dean Collin’s “On Lighting” DVD; and much of what he had to say about photographic lighting began with the concept of metering off an 18% gray card. He frequently referred to the apparent issue that, if 18% gray was the mid-value of exposure, then 1-stop up was 36%, 2-stops up were 72%, and 3-stops up blew the image. That seemed pretty simple, and yet contradicted the core of Adam’s Zone System, which had 4 or 5 stops up and down from Zone V. How could Adams be so wrong? Or was Dean Collins wrong? Both have exceptional reputations as photographers, so what was I missing?

So, I got to googling around and came across Thom Hogan on Meters Don’t See 18% Gray and that just added even more confusion. After all, if I couldn’t see how 18% matched up with 50%, then all of the other ideas that maybe it was really 12% or 14% or something instead didn’t really clear anything up.

In my mind, there was a fairly simple binary sequence associated with doubling anything, light, apertures, exposures, whatever. It went like this:

1 2 4 8 16 32 64 128 512 1024 and so on, up to 2 to the power 10.

There is certainly nothing obvious about 18% in this sequence. However, if you take the mid-stop values in this sequence, you get

1.4 2.8 5.6 11.3 22.6 45.2 90.5 181 362 724

and at least the initial values will be familiar to any photographer from lens aperture settings.

Now, if you express this sequence as a percentage of the maximum value of 1024, you get

0.14% 0.28% 0.57% 1.1% 2.3% 4.5% 9.1% 18% 36% 72%

Well, isn’t that interesting… There is the exact upper end to the sequence that Dean Collins was talking about, and 18% is there as clear as day. However, it’s in the wrong place since in this sequence it would have to be the middle of Zone VII not Zone V. In short, if cameras worked along the lines of this sequence, you couldn’t help but blow out the highlights on every shot.

So, I finally went to the source and got a copy of Ansel Adams’ The Negative. My humble copy is the 14th paperback edition, printed 2008. On page 33, Adams writes that the “18% reflectance value is mathematically a middle gray on a geometric scale from ‘black’ to ‘white,’ and it is this value that the meter is calibrated to reproduce in the final print….” Well this is just dead wrong.

The geometric mean of two numbers is the square root of their product (you can google this.) So if black is 0 and white is 1, the geometric mean is badly defined [it’s just 0, which gets you nowhere.] So, for Adams claim to make any sense, black can’t be 0. It’s possible to come up with arbitrary values for black and white that will give you a geometric mean of 18%, but minor changes to those values will give very different results.

One can also come up with a way to pick an offset from 0 and 1 that yields 0.18 as the geometric mean. If we set x to be black and (1 – x) to be white, then we want their product to be 0.18^2, so the equation to solve is x (1-x) = 0.18^2. This is a quadratic equation that’s easy to solve and x is 0.033. The result is that if we define black as 3.3% and white as 96.7%, we’ll get a geometric mean at 18%; but that’s extremely arbitrary. Besides, move black to 2% and white to 98% and the geometric mean shifts to 14%, so the arbitrary game isn’t even very stable. The results of this approach aren’t satisfying at all.

On page 55 of my edition of The Negative, Adams introduces a binary scale of subject luminances in exposure units that goes like this:

———————————————————————————————–

Subject Luminances:

Exposure Value 1/2 1 2 4 8 16 32 64 128 256 512
Exposure Zone (0) I II III IV V VI VII VIII IX (X)

Now, other than being offset by a factor of 1/2, this is the same scale that I was using above. Unlike that scale, Zone V is 5 stops down from the maximum of 512, and corresponds on this scale to a value of about 3.1%. He has also associated the straight binary sequence with mid-points on his Zone scale; this contrasts with the approach above of finding the geometric means (the square roots of the scale values.) Certainly, there is no 18% gray value here; and because of the binary sequence, the 50% value of maximum is just 1 stop down from the peak value.

Again, frustrated understanding….

In what follows page 55 in Adams’ book, he makes much of various meters to establish reference exposure values for negatives. On page 66, he introduces an “Exposure Formula” for turning meter readings into physical values for subject luminances. The formula uses the notion of a “key stop” that is defined as the square root of the (then) ASA speed of the film being used, or at least, set into the meter. For example, for an ISO 200 setting then, the “key stop” would be f/14. For a properly calibrated metering system at the key stop and aiming to set exposure for an 18% gray luminance on Zone V, the Exposure Formula is that the correct shutter speed is the reciprocal of the luminance in candles per square foot. For example, this would suggest that if I set my Nikon D80 for ISO 200, put it into aperture priority with f/14, used spot metering, and pointed it at any subject at all with available light, then 1 over the recommended shutter speed should tell me the luminance of that subject in candles per square foot.

Well, is that true? It seems to be a testable hypothesis. On this simple topic, there are a ton of external references. Here are a few for you to stumble through like I did. First a few Wikipedia articles: Film Speed, Exposure Meter, Gray Card, and the Oren-Nayar diffuse model. This sequence of articles are getting at the concept of how physical stuff (that we might want to take a picture of) reflects light. The basic idea being that a surface can’t reflect more light than what’s hitting it (that would violate conservation of energy, don’t you see?) These reflections can be either diffuse, like a matte, or specular, like a mirror. Most stuff that we’ll take pictures of is closer to a diffuse reflector. So, by definition, a perfect 18% gray card is one that is a diffuse reflector that sends back exactly 18% of the incident light energy that falls on it all across the visible spectrum.

We get a little closer to our answer by checking into what Adams’ units, candles per square foot, meant. Now, the candle as a measure of luminous intensity, has been replaced by the candela. The two are more or less equal. Notably, the candela implies a certain power (1/683 Watts) being radiated into a certain solid angle (1 steradian) at a certain frequency of light (540•10**12 Hertz) which just happens to be in the center of the sensitivity of the human eye to visible light. In other words, the unit that Adams was using is not just about any old light, it’s about light that the human eye can see.

After all, that shouldn’t be too surprising, we’re supposed to be making photographs that look something like what people would have seen if they were standing where the camera was. In fact, the candela is a unit of luminous intensity, which is itself a measure of the power of light in a certain direction weighted by a luminosity function that represents the sensitivity of human vision.

So I was led, inevitably, in tracking down the meaning of 18% gray, to consider human vision and how science has come to model it. Now, I was close to the answer; and the real and simple relationship between 18% gray and 50% gray. In reading about luminosity functions, I found that human vision has two components, photopic and scotopic. Photopic vision occurs under normal light, and is associated with color perception due to the cones in the retina. Scotopic vision occurs under low light, and is due to the response of the rods in the retina. More particularly, I learned that the standard photopic luminosity function used to define the candela is taken from the CIE 1931 color space standard.

Well, at last, here comes our answer. The International Commission on Illumination (CIE, ‘cos the original name is in French), did a landmark piece of work in 1931 to define a mathematical model for human color vision. The result is variously called the CIE 1931 XYZ color space or the CIE 1931 color space. It was based on prior research into human color vision, which had discovered that the cones of the retina had response at short, medium, and long wavelengths of light. These response curves were close to, but not exactly equivalent to, blue, green and red, respectively. As a result, and to avoid confusion, they were simply labelled X, Y, and Z, where X is roughly red, Y is roughly green, and Z is roughly blue. You can see the curves yourself on the referenced Wikipedia page.

The bright folks at the CIE figured out that human vision could be separated into two distinct aspects, the perception of brightness and the perception of color, which they called chromaticity. Since the eye is most sensitive to the green part of the spectrum, they decided to use the Y curve as the basis for their measure of brightness. Then, they could refer any given color to a notion of what “white” was. For this they defined three derived values from X, Y, and Z as follows:

 x=X/(X+Y+Z)  y = Y/(X + Y + Z) and  z=Z/(X+Y+Z)=1-x-y .

So, you can go back and forth between x, y, and Y since X = x•Y/y and Z = (1-x-y)•Y/y. The result is a derived color space, the CIE xyY color space. The notion of a color space is used almost everywhere to represent the range of colors that various computer presentation devices such as monitors, printers, and so on, can manage. You can see a graphical representation of this color space here. Note that ‘white’ occurs near the middle of the space where x = y = 1/3.

From the CIE XYZ and xyY color spaces, many other models were derived, such as CIE RGB and CIE L*a*b*. The concept of an RGB color space is much more convenient for practical equipment, such as cameras, monitors, and printers since it is more natural to generate color by combining red, green, and blue than by coming up with X, Y, and Z responsive materials. Of course, there are many practical RGB color spaces, such as sRGB, Adobe RGB, ProPhoto RGB, and so on. To complete the full definition of an RGB space also requires definition of a white point and a tone curve, or gamma correction curve.

This takes us to the CIE L*a*b* color space, often called CIELAB. In this model, L* is a specific measure of brightness, while a* and b* represent color. L* can range from 0 to 100.

 L^*=116f\left(Y\left/Y_n\right.\right) - 16  a^*=500 \left( f\left(X\left/X_n\right.\right) - f\left(Y\left/Y_n\right.\right)\right) , and  b^*=200 \left(f\left(Y\left/Y_n\right.\right) - f\left(Z\left/Z_n\right.\right) \right) .

where X_n, Y_n, and Z_n are the X, Y, and Z values of the white point; that is, the reference illumination.

The function f(t) in the equations is given by

f(t)= \sqrt[3]{t} if t > (6/29)^3 or f(t) = (1/3) (29/6)^2 t + (4/29), otherwise.

Well, here it is, 18% gray and 50% gray. Don’t you see? No… It’s the brightness parameter, L*, as a function of Y, the peak response function of the eye, normalized to scene illumination, Yn.

When Y/Yn = 0.184, then L* = 50!!!

There you go, the relationship between an object that reflects 18% of the incident light and the perception of its brightness as 50% is given within the CIE model of human perception. As such, it is not a claim about any inherent property of light, or scenes, or black relative to white. Rather, it is a claim about the way human perception responds to the illumination of a scene. As such, using 18% as a reference point for photography is part of a calibration strategy to make an image in a print or on a monitor look like the original scene that it is meant to represent to the human observer. I don’t know about, say canine vision, or that of the aliens from Tralfamador; but my guess is that neither dogs nor Tralfamadorians would perceive an Ansel Adams print as a match for the scene it represented since it would not be calibrated for their eyes.

Put another way, Adams’ Zone System and the use of an 18% gray reference point was part of a tonal management workflow from camera to negative to print. This also suggests that, so long as the underlying research behind the CIE color space is accurate about human perception, then a reflectance of 18% gray just is the correct reference point for the perceived tonal mid-point in a photographic image. It is not 12%, for example, which corresponds to a 41% L* value.

As I’ve written in my first blog here, there is a reason that the equivalent of a 12% value is used in many DSLRs. The standard behind this is CIPA-004 on the sensitivity of digital cameras. It is also described in detail by Douglas Kerr at his web page on Measures of the Sensitivity of Digital Cameras. As a hint, I discover that the sensitivity of my Nikon D80 is not really specified in terms of ISO speed at all, but rather a Recommended Exposure Index or REI, which is made to look like an ISO speed rating. As a consequence, Adams’ Exposure Formula is not quite accurate for my D80; and I expect that it would not be quite right for a lot of other DSLRs.

This takes me back to the question I raised above, would my D80, set in aperture priority for the key stop corresponding to its ISO setting, meter out a shutter speed that is the reciprocal of the subject luminance in candles per square foot? I believe that the answer is ‘no’. More on that in my next blog entry.

But the upshot of all of this is that, in my belief, almost no image taken with a DSLR will yield a proper print without post-processing to adjust the exposure back to a 50% middle gray. This would certainly be true for my D80.

5 Comments

  1. Joan Gastó

    Hi Allan,

    It is an amazing article, a must see for all filmmakers and photographers. Congratulations and thanks for all the information!

    I might have missed some concepts tough since english is not my first language, so i would like to make a question/example.

    If we were working with a video camera and we would like to set a light meter (with cine functions) to match the camera´s values and to TRUST in its readings, would it be right to use a 18% “mid gray” card and change the aperture until the gray represents 50% in the camera´s spot meter or in a vectorscope? So then we could read the card with the light meter and change the ISO until we have the same aperture value and be sure that we would be reading with the same sensitivity both in c
    amera and light meter?
    Thanks for your time

    Regards from Barcelona
    Joan

  2. Sorry it’s taken me a while to post this response. With upcoming blog posts, you’ll see that I’ve been rather busy lately.

    In any case, here is the core idea. For an accurate exposure and, arguably, representation of a scene photographically, you would like a minimum set of fixed reference values of light from the scene to correspond to a similar set of fixed reference exposures on your film or sensor or whatever your shooting with. For most work, this minimum set is a black point, a neutral point and a white point. In the present case, considering 18% gray, we’re talking about just the neutral point.

    From some of the other posts in this blog and their references, you’ll note that this 18% reference luminance was chosen originally because it meant something in the context of human visual perception, and had nothing much to do with cameras or film as such. Of course, it’s then only natural to attempt to take a value from the scene that the human eye would more or less universally have recognized as a middle and neutral gray and attempt to create a photographic representation, a print say, in which the reflectance of a middle gray in the original scene was matched by the same middle gray for the corresponding region in the print.

    There is a story that Ansel Adams was personally responsible for achieving this kind of “color management” as we might now call it with Kodak and their film and paper back in his day.

    For a variety of reasons, the mapping of a middle gray in a scene to an 18% reference value on a digital SLR sensor has been superseded by other considerations. Since digital sensors are less forgiving than film at the highlights of a scene, it is now typical for camera manufacturers to contrive a reference exposure for middle gray that is closer to 12% or 14% of the nominal 100% value on an sensor pixel. [Keep in mind that there really isn’t a physical sensor pixel as such. Red, green and blue values are calculated for any given “pixel position” by combining a set of physical sensor values from adjacent positions under the sensor light filter. But I am off topic.]

    Also, many real gray card products are not actually at 50%. For example, the Opteka OPT-DGC 3 card set has a gray card that yields Lab values of L* 63.8, a* -1.6, and b* -0.4 with a standard D50 (5000K) light source. This gives RGB values of 162, 162, 160; not 128, 128, 128. In the era of digital photography, this generation of gray card is designed to be used for color correction and not exposure. So the idea here with the Opteka card, and others like the Lastolite Expobalance is to get a reference set of neutral values at 3 points along the tone curve, none of them exactly at black, white or gray. In the case of the Opteka, the black card is at RGB (16, 16, 15) and white is at (220, 224, 223) for a D50 illuminant. Now, I tend to set my black point at RGB (7,7,7) and my white point at (247, 247, 247) as far as Photoshop or other post processing software is concerned. So, a little caution is necessary in using some of these gray cards.

    So, back to your question. You would first have to know what the specifications for your gray card were. Not all of them are designed to deliver a 50% reference under standard light conditions. Second, you’d have to know the specifications for your camera’s sensor. Not all of them are designed to map 50% neutral illuminance to 18% exposure; in fact, most of them are not.

    With digital, you tend to want to expose for the highlights, that is, to ensure that no pixels have any blown channels, red, green or blue. Much camera technology goes into metering scenes across much or all of the entire field on the sensor to get this right. You would then use something like the Opteka or Lastolite products to ensure neutral tone values all across the scene illumination. Post processing s/w like Photoshop and Capture NX is very good at bending curves to achieve tonal neutrality given black, gray, and white points.

    With these caveats though, if you wanted to calibrate your camera for a neutral reference in the scene, you could take a reference card like the Opteka, work out how many stops off 50% it was (1/3 EV), find out what the exposure reference for your camera was (12%, 14% or whatever), work out how many stops off 18% that was (about 0.5 EV). With this compensation factors you could achieve the exposure calibration that you’re describing. The objective test of your exposure calibration should show up in post processing the images that you captured when you meter them in your s/w during editing. For this to come out, you’d also have to consider the color space you’re editing in, I assume PAL for a Barcelona location and video work. Check the PAL specification to see where it puts neutral gray. You might consider this in your work.

    Although it is more focussed on printing, this is also interesting in this context.

    I hope this helps.

  3. great post, thanks for sharing

  4. Ansel Adams wasn’t “wrong,” he also was not using a computer or dSLR, he was working with film.

    You mentioned starting with 18% and doubling (a stop up) or halving (a stop down), which does not seem unreasonable as we are dealing with light which is linear, BUT… not actually the relevant way to look at it.

    Film, sRGB, The human eye are all NOT linear. “18%” was discovered to be the middle grey between black and white as judged by test subjects in controlled laboratory experiments.

    And ALSO, an “18% grey card” is referring to its “Lambertian reflectance” (also called diffuse reflectance). This is not at all the same as an emissive light source, or a specular reflection. (A perfect/ideal Lambertian surface reflects equally in all directions — that is, no matter what angle you view it from, it does not change in intensity. In other words, it is diffuse, flat, not shiny in any way.)

    18% is ALSO the geometric mean between a maximum lambertian reflector such as white snow (about 95%) and a minimum (black soot, around 3.5%). sqrt(95 * 3.5) = 18.23

    In CIEXYZ, Luminance Y of 18.4 equals LIELUV L* of 50, or exactly in the middle of human perception. (Y of CIEXYZ is linear LIGHT, and L* of CIELUV is Perceptually Uniform based on human vision experiments).

    One other thing – if the LIGHT hitting the Lambertian surface is at an angle, then Lambert’s cosine law will affect the luminance. If the light is at a 45 degree angle that will result in an 18% grey card having an APPARENT reflection of about 12.7% (cosine 45 degrees is .707 times 18).

    On your computer, where that 18% should be depends on the transfer curve (gamma) of your colorspace. In sRGB it is 119 119 119 (#777),

    Back to Ansel and film and Kodak: various laboratory AIM density checks are intended to get the negative density in the middle of the total exposure range. These AIM cards have been around 14% to 18% depending on the specific application.

    TLDR:

    A) 18% is HUMAN PERCEPTION of middle grey between a black and a white diffuse surface.

    B) In FILM it is also about where you’d normally want the midpoint of film density.

    C) On the computer in web standard colorspace (sRGB) it’s 119 119 119 (#777).

    D) Some digital cameras internal meter seem to be set about 12.5% — this corresponds with the 45 degree light reflectance off an 18% grey card. Coincidence? We’d need to ask a Nikon engineer I think to know if that’s what they intended…

  5. I agree with just about everything that you’re saying here. I will say that I think that the middle gray on sRGB and most computer monitors is not at 18%; but rather, somewhat less. I’d also agree that typical DSLRs from Nikon and Canon are also calibrated for a mid-gray that’s somewhat low as well; I think to provide more overhead against blowing out pixels.

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