Is metamerism a big issue in print? (Part 2)

This is part 2 in a series of blog posts that recap my presentation on metamerism at Color 20. If you were actually looking for the first part, the part where I set up the characters and give the back story, then you should go to the first part.

Ahhh... so you decided to tough this blog post out? Well, good on ya, mate!

Today's post is about the intersection of expanded gamut, spot color replacement, and metamerism. I suspect that this might result in another standing-room-only blog post.

Is metamerism a big deal when you are doing spot color replacement?

Expanded gamut

In kindergarten, I was taught the lie that red, yellow, and blue were the primary colors. I will never forgive my kindergarten teacher for that. That really messed me up when I found out that the real primaries for ink were cyan, magenta, and yellow. There is a big long story about that, but for now, I will just pass the explanation along to Stephen Westland and Stephen Westland and David Briggs and David Briggs. Good articles, all of them.

And then I got even more confused when people kept talking about black ink. Why do you need black ink, if you can get all the color with just CMY? (I mean, I thought the whole idea of primaries is to give you all possible colors?) Well, there are many reasons for using black, but one of them is that you can't get all the colors with just CMY. One notable color that you can't get is black.

And guess what? Even with CMY and K, you can't get all the colors. If you want more colors, you need to add more primaries. Expanded gamut printing uses color beyond CMYK, typically orange, green, and violet, to get more of the entire range of visible colors.

(Interesting fact: Generally we would call this CMYKOGV printing, but that's a really silly order for the letters. Maybe it should be CVMOYGK?)

Spot color replacement

I know that some of you are thinking that spot color replacement is what you do to get your Dalmatian ready for St. Pat's Day. Nope. Good guess though. (To get your Dalmatian ready for St. Pat's Day, I would recommend giving him a long reddish-brown, silky coat.)

My dog Spot is not looking excited about the St. Patty's Day festivities

Historically, there has been a distinction made between process colors and spot colors. Process colors are CMYK and are used in packaging for image content. Each pixel of the printed image gets some build of those four inks. Spot colors are specialty inks that are mixed to the desired color and are printed in, well, certain spots of the printed package. The spot color inks don't usually get overprinted with other inks, and are generally not used in imagery.

This is not an endorsement. They do go well with a wasabi mustard, though.

The package above uses (maybe) a total of eight inks -- cyan, magenta, yellow, and black for the image and spot colors of dark blue, light blue, black, and green. (And there is probably a white to cover the metallic (mylar) surface. White is not referred to as a spot color, but rather a flood coat. I think this is an egregious abuse of the English language.) Each of these inks gets its own print unit.

The next print run will likely require a different set of spot colors. This leads to an expense, since the old spot color inks needs to be cleaned out between print runs. There would be an economic advantage to printing those spot color with an equivalent combination of process color inks. But if we augment those process inks with a few extra colors of inks, typically orange or red, green, and violet or blue, then nearly all spot colors can be emulated with this augmented set of inks. No need to clean up after each print run!

So, there is an economic advantage, but it comes with a hidden cost: metamerism. If one package printed with CMYK+spots should land on the shelf next to one printed with CMYKOGV, then the best we can hope for is a metameric match. Perhaps there is an excellent match under D50, but can you find a store that has good D50 lighting?

That leads us to the question of the day....

Is the degree of metamerism enough to worry about?

Disclaimer #1: I suspect that many of the people who have implemented spot color replacement have gone through the exercise of evaluating the degree of metamerism for the spot colors that are important to them. I don't intend to minimize this or necessarily replace this worthwhile test. My goal here is to help set expectations in general.

Disclaimer #2: If you are bringing a new design into production, metamerism probably isn't an issue for you, beyond perhaps needing to explain to the brand owner why the color of the package didn't match the Pantone book in the designer's living room. If you are switching production of an existing pretzel pouch to spot color replacement, and expect a short period of co-mingling on the store shelves, I leave it to you to decide on the importance of the transition period and weigh the cost of that against savings.

Those who read the previous blog will recall this image of a set of metameric sextuplets, all of which are perfect matches to my version of Pantone 147C under D50/2.

In the delivery room, with D50 lighting, these appeared to be identical sextuplets

The spectra look quite different, but when it comes down to it, is there a large metameric difference?

The following table is stolen from my Color 20 presentation. It shows the CIEDE2000 color difference between Pantone 147C and the emulated version under D65/10. This should give an appreciation for the magnitude of metamerism. The spectra look a lot different, but they still match under one illuminant, and are not a bad match under another.

Not so bad? John shrugs his shoulders. I would be cautious about trying to read much into this table. There are many combinations of CMYKOGV that could yield a given color. The software that I wrote to create the matches did not put a whole lot of thought into which one of those combinations to use. I don't claim that it yielded builds similar to any commercial spot color replacement software, Mileage may vary. This package sold by weight, not volume. Contents may have settled during shipping. Blah blah blah.

Here is another set of metameric sextuplets from my database. In this one, for whatever reason, the spectra are all a reasonably good match. We see some larger disparities around 400 nm, but these are less significant to the eye.

And another set that appear to vary about as much as the first one.

Here are the color differences.

What to make of this table? Once again John shrugs. There are bigger numbers and smaller numbers. The intent here is not to focus on one specific case, but rather to look at the data in aggregate. The database has plenty of aggregate to offer, with 3,604 metameric spectra. Here is the big picture.

I love cumulative probability density functions of color difference data

How to interpret this? John shrugs his shoulders and makes woogly eyes. I have blogged before about this sort of Cumulative Probability Density Function plot, and again here. I show below one very reasonable way to look at this data. The plot can be used to determine the percentage of color differences that are below a certain point.

I arbitrarily set 2.0 ΔE₀₀ as a tolerance. This is a typical tolerance for print under D50/2. From that alone, it seems like a reasonable starting point. But, one may argue that this is a secondary requirement in the eyes of the print buyer. (I want it to match under D50/2, and could you also make sure the match isn't horrible under D65/10?) So maybe this is too wide?

Arguing the other side, there are two contributors that we want to consider. The first is the normal process variation, for which we may set a tolerance of 2.0 ΔE₀₀. The second contributor is the color difference due to metamerism. These two contributors combine in the final analysis. If we allow for 2.0 ΔE₀₀tolerance of normal process variation under D50/2, and we allow for a 2.0 ΔE₀₀ color relative change due to metamerism, then we could see something like 4.0 ΔE₀₀ color change when they happen together.

Now for the math stuff. They two sources of variation could cancel each other out. IT could be that by fluke, the sample is 2.0 ΔE₀₀ off from the target under D50/2, but matches perfectly under D65/10. Generally speaking us folks in the stats world use "sum in quadrature" to describe how tolerances stack up on each other. A 2.0 DE00 variation and a 2.0 ΔE₀₀ variation (statistically speaking) add up to sqrt ((2.0)^2 + (2.0)^2) = about 2.8 ΔE₀₀.

So, is this a big issue for spot color replacement?

Based on this analysis, I can say this: 

If you replace a traditional spot color with another set of pigments,

and you get a perfect match under D50/2,

then you have an 8 in 9 chance of having an acceptable match under D65/10.

I make the assumption here that the normal process variation is less than 2.0 ΔE₀₀, and that a 3.0 ΔE₀₀ variation under D65/10 is considered acceptable. In the next blog post in this series, I will look at other illuminants. 

Tolerance for metameric index

I had a question from Rachel after my previous post regarding reasonable tolerances for the metameric index. I pause to define metameric index in this context. The graph and table I show above fit one definition of metameric index: the color difference that you see between two perfect metamers under one illuminant when you view under a second illuminant.

From my graph, I can say that 2.0 ΔE₀₀ is a reasonable tolerance for metameric index for D65/10. Eight of nine times you can hit that. If you pay a bit of attention to metamerism when you decide on how to render an EG color, you can do better, In the next blog post in this series, I will look at other illuminants. Hint: the change from D50/2 to D65/10 is not huge...

I hope that this leads to some good argument among the folks who like to argue about standards.