18% Gray Reflectance and Middle Gray

There is a lot of confusion about the 18% reflectance, gray card, and the gray level that human vision system judges as being midway between black and white, the middle gray. The confusion is due to the attempts to apply the parameter from the chemical photography process into human perception and into the digital image processing.

Where is the middle gray, above both the swatches are exactly the same, only the background is different. Human vision just does not have such a middle gray that can be described by a single percentage value. Film has.

The Kodak Middle Gray

Let us first see what Kodak says about 18% gray. Instructions of the Kodak Q13 Gray Scale (scanned gif of the instructions, 200kB) says: "The background approximates an 18% neutral gray to neutralize flare and adjacency effects" that btw is all that that there is about the 18% gray. The Q13 Gray Scale itself looks like this:

Q-13 Gray Scale, shown on black background. Compensated for viewing with an uncalibrated PC system (in gamma space 2.5).  The steps are 0.1 D (density).

BTW: Kodak Q-13 and Q-14 are otherwise equal except the size, 8" and 14" respectively. They contain two charts, the above Gray Scale and SWOP printed Color Patches that looks like this:

Q-13 Color Control Patches, shown on black background. Compensated for viewing 
with an uncalibrated PC system (in gamma space 2.5). 

Difference Between Chemical and Digital Processing and Human Perception

The Q-13 specification says that the stepping in the gray scale is accurately by 0.1 in density. At a glance we can see that density steps are nowhere near perceptually uniform, perceived steps are huge in the highlights and very small in the shadows. 

Actually The Student Filmmaker's Handbook says:

"The eye easily detects density differences as low as 0.02 in the average highlight density, but can detect density differences only on the order of 0.20 in the average shadow density." (at the the end of this page, fourth-last paragraph)
 
About the A, M and B patches the Q13 specification says: "The patches identified with the designations A, M and B are used in KODAK Three-Aim Point Control methods for reproducing color reflection copy with traditional masking and color separations procedures. A, M and B patches correspond with reflection densities of 0.0, 0.70, and 1.60, respectively, which represent average highlight, middletone, and shadow values in color or black-and-white reflection copy." 

So we have an additional clue about the middletone, the patch M. Now we need to convert the density values of the A, M and B patches into reflectance.

Reflectance in percentage = 100 * (10 ^ - density).

	Density	Reflectance
average highlight	0	100%
average mid tone	0,7	19,95%
average shadow	1,6	2,51%

In other words the M patch (middletone) lives on a range 0 to 1.6 in density that translates to 40:1 in reflectance. And we know that the patch M represent middletone value in color or black-and-white reflection copy where it has 19.95% reflectance, that is about 20%.

Important issue to note is that a middle value in any system depends on the extreme values in a way or an other. The M patch is specified for color or black-and-white reflection copy that have density range from 0 to 1.6 in other words 100/2.51 = 39.8:1 or about 40:1 in reflectance.

The photographic paper can not reflect 100% it is limited to about 90%...95% and the tonal range in a color or black-and-white reflection copy is not linear, the overall transfer function of an image on photographic paper is the product of the transfer curves of the film and that of the paper plus some development induced changes to them. 

The resulting overall transfer function has the form of a slanted S-character. Digital processing allows to correct this slanted s-shape transfer function, an operation that is often referred as "opening up the shadows" that in fact is the same as linearization of the shadows.

To conclude, what appears to be 20% reflectance (M patch in Q13) on the color or black-and-white reflection copy that has the slanted s-shape transfer function and the mere 40:1 viewing range will be quite something else in the digital end product that in addition to the far better linearity has the much higher range of 256:1 in reflectance. That is the same as to say that the absolute black level differs greatly between the two and because of this also the middle gray is different.

In short, trying to to apply the chemical process parameters 1-to-1 into digital photographic imaging will have strong adverse affect to the quality.

What is the Middle Gray for Human Vision System or Perception

Simply there is no single middle gray value for perception, it adapts.

The eye has enormous overall working range, like 1000000000000:1 or more in luminance or in reflectance, this range spans from less than starlight through moonlight up to very bright daylight and to still higher. However we can not see the whole range at the same time. 

Over this huge range the vision has three main mechanisms that affect to the lightness sensitivity:

• rod  vision = scotopic vision = dark adapter vision, rods are only able to detect grays, no colors are seen when the eye is dark adapted. Adaptation to rod vision takes several minutes.
• cone vision = photopic vision = light adapted vision, cones are able to detect colors.
• change of pupil diameter.

Both the scotopic vision and photopic vision are absolutely linear to luminance, sensitivity for luminance is higher in scotopic than in photopic vision. Between them is the mesopic range where both the cone and rod response are active. The pupil diameter changes mainly over the mesopic range.

The lowest luminance levels that CRT monitors can show fall into the upper mesopic range. Therefore a linear step wedge on linearly calibrated (gamma 1.0) system does not appear to be perceptionally completely linear.

However when photographic images are shown on the CRT (instead of a computer generated wedge) the eye will always be adapted into photopic vision.

Hence the mid gray for photographic images is near to 50% gray on linearly calibrated system (RGB level 128). For computer generated graphic, allowing the pupil to change the diameter by 4:1 (two bits) the middle gray is about 42% (RGB level 107), gamma space 1.25 match with this rather well.

The conclusion to make from all this is that photographic images should not be digitally manipulated to have an average 18% luminance. The 18% middle gray belongs to the chemical process and it is a very important parameter there. It gives us a good average with what we can expose the non-linear film in a reproducible way so that the scene range will be properly captured by the film.

Also what the perception judges to be middle-gray depends very strongly on the actual illumination level, if you have the real Q-13 target (or what ever gray step table) view the step table under direct sunlight and evalute the patch that appears to you as the middle gray. Then e.g. go inside to a room that is very weakly illuminated and evaluate the middle gray again.

Accurate CGI Simulation for Kodak Grayscale (Q-13 and Q14)

The below CGI simulation of Kodak Grayscale is accurately calculated from the density values, it is JPEG image saved at least compression there is no error due to jpeg compression to the patches, this was verified patch by patch. The simulation has the nativePC ICC profile embedded so when opening it into Photoshop do allow Photoshop to make the color conversion this way you get it accurately into your working space.

Accurate CGI simulation of Kodak Grayscale chart.