Tolerances for spot colors

There is a little bit of a hole in the most recent version of the ISO spec for flexo printing[1]. I will explain the hole, discuss my analysis, and provide a patch for this hole, but first a bit of background.

There is a family of standards called ISO 12647, which all cover printing. In particular, they provide some target color values, along with acceptance tolerances around those colors. In almost all case, those tolerances are in terms of ΔE, with the newer revisions of the standards shifting from ΔE_ab to ΔE₀₀.

Part 6 of this standard is devoted to standards for flexographic printing. Flexo printing is used on such a wide variety of substrates that it is often not possible to nail a particular color. As a result, tolerances based on a ΔE-type color difference are not possible. One has to be content with getting the correct hue.

ISO 12747-6:2012 states target hue angles for C, M, and Y, and provides a ±6^o tolerance. Spot colors are also given a tolerance in terms of hue angle, but it’s ±8^o. Black, however, does not have a hue angle tolerance. This makes a great deal of sense, since black is neutral. The hue angle is undefined.

Tolerances from ISO 12647-6

But, “black” is not the only black. My Pantone book lists six shades of black. Presumably, the target a* and b* values for these inks are also 0, so the hue angle is undefined. This is the question that led to the realization of the hole in the standard: “how can analysis software decide if the ink name ‘midnight’ or ‘inkwell’ is equivalent to black?”[2]

Worse yet, what if the target for a spot color is not quite exactly neutral, but near neutral? If the chroma[3] of a spot color is small, then a tolerance of 8^o might be impossibly tight. For example, in my Pantone book, the ink “Warm gray 5” has an L*a*b* value of {69.61, 2.58, 1.00}. Let’s say the hue of this ink is rotated by 8° to {69.61, 2.70, 1.63} so as to be at the very edge of acceptance in terms of hue. The color difference is a meager 0.38 ΔE₀₀. Holding a printer to a 8° tolerance is pretty tight.

For highly saturated colors, a tolerance of a specified number of degrees around a target hue is perfectly reasonable. But as a color gets closer to a near neutral, it would be preferable to shift over to a ΔE₀₀ tolerance. At what chroma value do you need to shift between a ΔE₀₀ tolerance to a hue angle tolerance?

First naïve approach

I call this the naïve approach, because I am going to make a mistake. It turns out that the mistake is not huge, and it gives some intuitive understanding, so I will leave it in on this first pass. Watch for the mistake.

The figure below shows two colors r₁ and r₂, in the a*b* plane. Both have a chroma of c, but are separated by 8^o. If r₁ is the target hue, then r₂ is at the edge of the 12647-6 tolerance window.

The arc length between the two colors is fairly trivial to compute. I could use the normal trig stuff, but since the arc is so small, I will just estimate the ΔE (which I a straight-line distance) with the arc length.

Thus, if we assume a tolerance of 1.5 ΔE, the crossover is close to a chroma of 10. Below that point, a hue tolerance is overly restrictive.

Second, not so naïve approach

Did anyone catch the mistake I made? Yes, you in the back? Ahhhh… the old accidentally used ΔE_ab instead of ΔE₀₀ mistake! The formula for ΔE₀₀ is just a tiny bit more complicated than the formula for ΔE_ab.[4]  So, I need a slightly less naïve way to look at this problem.

Suppose I picked a color at random, and then rotated it by 8° - that is to say, shifted the hue by 8° without changing L* or the chroma, C*_ab. What is the color difference (in ΔE₀₀) between the original color and the hue-shifted color? Then let’s say you computed that for a whole big bunch of colors just to see how it all played out. You would expect that, the larger the chroma, the larger the color difference, right?

Well, I just happened to have a large collection of colors (11,488 of them to be exact) just laying around from a blog of mine on counting colors. Below is a plot of the color difference caused by an 8° hue shift as a function of chroma.

Color difference caused by an 8° hue shift

Is this cool?

To answer the rhetorical question, yes, it is cool. But the data is a bit sparse down there in the lower left-hand corner around 1.5 ΔE₀₀ where we are looking for our answer. This is not a surprise, since my color database only includes colors on a grid with spacing of 5.

So, I took a little different approach. For my next plot, I looked at points in color space with a chroma of 10. (This is the estimate we came up with by analyzing ΔE_ab.) These are all shades of gray, essentially, with a moderate amount of a color cast to them. I looked at how much color difference there was for each of them when they shifted in hue by 8°. The plot below shows this color change as a function of original hue angle.

The color difference caused by an 8° change in hue, as a function of hue angle

We see that the amount of color change oscillates between 1 and 2 ΔE₀₀, so the average must be somewhere around 1.5 ΔE₀₀. The true average is 1.45 ΔE₀₀. Going back to Table 4 from ISO 12647-6, this is really close to the variation tolerance for spot colors.

For an ink with a target chroma of 10, a tolerance of 8° is roughly equivalent to a tolerance of 1.5 ΔE₀₀.[5] Based on that, I have a simple recommendation for spot colors: If the target chroma is less than 10, then the appropriate tolerance is 1.5 ΔE₀₀. For target chroma of 10 or greater, then the hue angle tolerance of 8° should be used.

Just in case someone wants to repeat this analysis for angles other than 8° or color differences other than 1.5 ΔE₀₀, I provide the useful nomograph below. The t-shirt version should be out just in time for Christmas.

Nomograph for determining the crossover chroma
for various combinations of color difference tolerance and hue tolerance

The red line on the nomograph shows the determination of the crossover chroma between tolerances of 1.5 ΔE₀₀ and 8° of hue. The graph shows a crossover at C* = 10.5. Just between friends, let’s call it 10.

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[1] I am not blaming any of the diligent folks on TC 130 who reviewed this document. I was one of them!

[2] Thanks to Bruce Bachmann and Mike Sisco for this realization.

[3] I am using the word “chroma” to mean C*_ab, which is defined as 

[4] Well, to be fair, the formula for ΔE₀₀ is just a tiny bit more complicated than the formula to get a balanced budget.

[5] One caveat: I have made the assumption that the only change in color is in hue angle.

The color of a bunch of dots, part 3

In this series of blogs on tone value increase, we have been considering two parallel questions: How to predict the color of a halftone, and what to measure about a halftone in order to do process control. In part 3 of the series - the one you are reading right now - I want to consider the process control issue.

For those who can't take the time to read my entire long blog post today (maybe because they have to tend to their sick chameleon?) I will give a spoiler. The Murray-Davies equation, which we use today to compute TVI, has some issues when we try to extend it past CMYK inks printed on a web offset press with standard (AM) screening measured with a densitometer.

TVI depends on wavelength

The graph below might be a bit of a shocker. Then again, maybe not? I guess it depends. The graph is simple enough. I took the spectra of a solid cyan, a 50% cyan, and a solid. I used the Murray-Davies equation that we all know and love to compute the TVI. Rather than using the red channel of a densitometer, I did the computation separately at each wavelength.

Will the real TVI please stand up?

Maybe it's a shocker that the TVI at 630 nm is a healthy 15.7%, and at 500 nm, it's an anemic 2.6%? I think this very clearly shows that TVI is not a direct measure of the dot size. How could the dots be so much bigger if you look at them through a blue green filter instead of a red filter? It's almost like the tone ramp (0%, 10%, 20%, ... 100%) changes in hue... [1]

This is just an oddity, though, right?  It is like the kitten born with two faces, only this kitten is a halftone patch with two different TVI values. Or rather, a halftone with a whole bunch of different TVI values. Still, so long as you make sure that you have the correct setting on your densitometer, you won't have to worry about all the other faces. And process control will work, right?

But, sometimes you don't have density information, particularly in color management. It seems that a lot of data sets have been collected with only colorimetric data; no spectra and no density data. [2] How can you compute density without the spectral data? Can you compute TVI from the XYZ values?

According to ISO 10128, Appendix A, you can compute magenta and black TVI from the Y value and yellow TVI from the Z. To compute the cyan TVI, you need to do a bit more math, but it's not that bad.  There is a formula. Another brilliant researcher presented a paper at TAGA (2008), where he offered up a more complicated formula that works even more better. Brilliant as this researcher is, he stole this formula from another brilliant guy, Steve Viggiano.

So... this is basically just a confusion, right? There isn't really anything here to upset anyone's sense of inner tranquility, right? Keep reading.

TVI does not uniquely define the color of a halftone

Speaking of standards, the ISO standards for print (the ISO 12647 series) defines colorimetric aim points for the four solids and overprints of those solids. But for halftones?  It specifies TVI aim points. This would lead one to believe that, once you get the solid correct, all you need to do is make sure that you TVI is correct. Then you will have the correct color, right? [3]

And if the TVI is not correct, the standard gives you the impression that it is easily corrected in prepress by applying a plate curve. If your 50% has a TVI of 66%, and it should be a 68%, then all you need do is add 2% in a plate curve, right?

Not so fast, boopie.

The graph below is an a*b* plot (a plot looking at color space from above) of cyan, magenta, and yellow tone ramps, along with various other combinations. The blue lines represent the color of tone scales of conventional screening. The red lines represent stochastic screening. It is apparent that certain single color tone scales (cyan and magenta) have a hue shift of several deltaE between the two types of screening.

Comparison of conventional and stochastic screening [4]

When a plate curve is applied, the color is moved along the appropriate curve in color space. (I call this curve the trajectory.) A plate curve cannot make your halftone jump from one trajectory to another. Maybe everyone knows this already, but it bears saying. You cannot use a plate curve to match color between conventional and stochastic screening.

If other forms of printing were to be included, the hue shift in the midtones would be more dramatic. Gravure and ink let printing are still farther from the graph above of conventional printing. To put this another way, hitting the correct TVI does not guarantee the correct color if there is a difference in printing modality. The solids might be spot on and the TVI might be absolutely correct, but the actual color of the 50% tone will not be correct.

TVI of spot colors

What happens if I want to compute the TVI of a spot color (Pantone or PMS)? I just have to pick the right density filter, right? Short answer: For a minority of inks, let's say a quarter of them, this actually works well. But, TVI really sucks at quantifying some spot colors. For others, it's better - somewhere around "lousy".  These are harsh words, but I have data to back them up.

I looked at a set of tone ramps of 394 spot colors. I computed the TVI for each of the tones using the Murray-Davies formula at the wavelength where the spectrum of the solid had the lowest reflectance. Then I sat back and watched the fireworks. Of the 394 inks, almost all of them (353) had a TVI (at 50%) of greater than what we would call "typical", 18%. A total of 70 of the inks had astronomical TVI values of over 35%. Most press operators I know would call that an extreme case of plugging. But it wasn't  plugging at all. The TVI was horribly large, but the color of the halftone looked just fine. Plenty of contrast in the shadows.

The graph below is the spectra of the tone scale of one of the inks that had a TVI of about 35%. Note that, around 600 nm where the reflectance is the very least, the solid, 90%, 80%, and 70% have nearly identical reflectance values. Anywhere in the red part of the spectrum, this looks like an ink with severe plugging.

The spectra of a tone scale of one blue spot color

But have a look at what happens at 450 nm. In the blue part of the spectrum, there is a very clear separation between the shadow tones. In this region, all appears to be right with the world. Despite what TVI tells us, there is contrast in the shadows. [5]

Conclusions

The use of TVI as a process control device has been proven to work for CMYK inks on a web offset press using conventional screening. But...

a) TVI is dependent on the wavelength chosen. If you are dealing with CMYK inks and conventional screening and web offset printing, then so long as you are careful about selecting the correct filter on the densitometer, this isn't a problem. The only time a problem pops up is when TVI is computed from colorimetric data. 

b) When we switch from conventional web offset printing to something else, particularly when there is a difference in the crispness of the dot, having the same color for the solids and the same value for the TVI does not guarantee that the color of the tones will be the same. 

c) When you look at inks other than CMYK, the TVI value sometimes is a useful parameter for process control, but it often is completely misleading.

In the next installment of this series on TVI, I will explain a slightly different equation than the Murray-Davies equation and the Yule-Neilsen equation. In the final installment, I will look at some practical solutions to the issue of process control for halftones of spot colors.

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[1] This isn't just a cyan thing. The same issue can be seen with magenta ink, and to a lesser degree, with black and yellow.

[2] Congress is acting swiftly to ban the disposal of unwanted spectral data, or at least trying to act swiftly. Right now, it is stuck in the quagmire of partisanship with Democrats tying the bill to efforts to save the rain-forests in southeast Kansas, and Republicans demanding that magenta density be removed since the word "magenta" does not appear in the Bible.

[3] Astute readers will note the proliferation of the word "right" added to the end of  a sentence for emphasis.   Some readers might assume that this is a technique used to draw attention to things we might assume but which are not correct, right?

[4] The image is from a presentation by Dr. Bestmann to the ISO technical committee 130 in September of 2011.

[5] This is a drastically shortened version of an article that appeared in IDEAlliance Bulletin magazine, spring of 2012 issue: Measuring TVI of a spot color. If you are interested in obtaining your own subscription to this magazine, have a look at the IDEAlliance website.