Wednesday, September 26, 2012

Why does my cyan have the blues?

When I started in the print industry as an apprentice to Gutenberg, I noticed that the folks in the press room called the inks red, yellow, and blue. This confused me. Everything I had read in color theory books said that cyan, magenta, and yellow were the subtractive primaries. These were the primaries that you use to make a wide range of colors with pigments and filters. Pigments and filters work by subtracting certain wavelengths of light. On the other hand, red, green, and blue were the additive primaries, and these were used to make all the colors when you are mixing light, as in a TV or computer monitor.

Polaroid snapshot of me working at my first job
Why were those silly printers using some of the additive and some of the subtractive primaries? Didn’t they realize that this reduced their gamut? That was the theory, anyway[1].
Just a naming issue?
Anyone who knows me, or who loves me[2] can attest to the fact that I am a firm believer that ignorance is the main explanation for every cultural and scientific phenomenon. In this case, my previous blog about counting colors provides a clue as to the sort of ignorance that might explain why magenta is so curiously called red.
The eleven people who read my previous blog learned that there are only eleven basic one-word color names in our active vocabulary. Neither cyan nor magenta made that list[3]. Clearly the folks on press were calling the inks “red” and “blue” because they have no other words to describe the colors.
Cyan ink is blue, and magenta is red
In my normal incisive way, it took me a few years to realize that the pressmen were not quite as ignorant as I thought they were. I guess I spent too much time running for buckets of halftone dots to actually put my head in a bucket of ink. When I finally did put my head in a bucket of ink (as part of a hazing[4] experiment) I could see that cyan ink is blue, and that magenta ink is red when you look at them in a bucket.
Cyan and magenta inks are blue and red in the can
Cyan and magenta inks are cyan and magenta on paper
So, this confusion is obviously beyond my original explanation. Just like when a fellow accidently calls his wife by the name of a former girlfriend, you can bet there is something deeper going on.
Beer’s law revisited
In yet another very popular[5] blog of mine, I provided a charming explanation of Beer’s law. This blog post is a prerequisite for the following exciting discussion.
Let’s just say that we have a perfect magenta ink. A perfect magenta ink will reflect all the red light and all the blue light that hits it. As for the green light, a light shade of magenta might reflect about 10% of the green. A rich shade of magenta will reflect about 1%.
Now we bring in Beer’s law. Let’s say we start with that light magenta and add another layer of the same ink. Beer’s law would predict that the reflectance would multiply. Since perfect magenta reflects 100% of red and blue light, Beer’s law predicts that the double layer of magenta will reflect 100% of the red and blue light. Beer’s law would further predict that the green light would reflect at only 10% X 10%, which is 1%. A double layer of light magenta becomes a rich magenta.
Key point here: for this perfect magenta ink, the hue is still that of magenta. It still reflects most of the red and blue light, and absorbs most of the green light.
Let’s just say that we now switch over to a magenta that is less pure. Let’s just say that for some inexplicable reason, the publishers of Schlock magazine are unwilling to spend $100,000 per gallon for their ink. The bargain ink they decide to use does not reflect quite as much blue light as we would hope; maybe it only reflects 40% of the blue light when we put a thin film down, and maybe 10% of the green light. Let’s say that the red light is still reflected at 100%.[6]
What happens when we double the amount of ink on the paper?  Beer’s law takes over, and we see that blue light is reflected at 40% X 40% = 16%.  Green light? The reflectance goes from 10% down to 1%. Red light stays at 100%. The table below summarizes the Beer’s law estimation.

Thin layer
Thick layer
From this table, it would seem that the thick layer of magenta is a lot closer to red. The plot below shows the actual spectra of two magenta patches, one at a larger ink film thickness than the other. The plot leads one to the same impression – that a thick layer of magenta is closer to red in hue than a thin layer.
Spectrum of a magenta ink, normal thickness and thick
The tentative conclusion is that magenta turns red when it is thick because it is impure, or more accurately, because there are several different reflectance levels in the spectrum. When Beer’s law kicks in, the areas of the spectrum where the reflectance is “mid-level” (i.e. 40% reflectance) are grossly effected by the ink film thickness.
The plots below are the spectra of cyan and yellow inks. If the previous rule applies, then we would expect that cyan ink will have an appreciable change in hue as it gets thicker. From the plot of cyan ink, we see that the reflectance values between 500 nm and 600 nm are “intermediate”, somewhere between the highest value and the darkest value. This is the green range. As cyan ink gets thicker, we would expect the amount of green light reflected to drop.
Thus, based on Seymour’s rule of ink hue shift, a quick look at the plot below would suggest that thick cyan ink will be blue, just like thick magenta ink will be red. Yellow ink has very little in the way of intermediate values. It basically has either 75% reflectance or 3%. From that, you would guess that yellow ink will not change in hue. Note that a bucket of yellow ink does indeed look yellow.
Plots of cyan and yellow ink
But spectra can be a bit misleading when trying to discern color. I don’t know many people who can look at a spectrum and tell what the color is. So, I offer a little computational experiment to further validate Seymour’s rule of ink hue shift.
First, I will show the results. Then I will explain how I got them. The chart below shows the a*b* values of a set of ten magenta patches with increasing ink film thickness. These values are the ten blue diamonds in the plot. There is clearly a strong hook. The first five are pretty much along a line without much hue shift. The sixth one goes around the bend, and the last four are changing a lot more in hue than they are in chroma.
The magenta hook, real and estimated

For the other views of this data, I have published an addendum to this blog post.
The magenta colored line in the plot is a prediction of what I call the “ink trajectory”. This is the set of all L*a*b* values that an ink will go though as you change the ink film thickness. To compute this estimated trajectory, I started with the spectrum of the sixth patch and that of the paper. (You will note that the magenta line goes right through that point.) I loaded these spectra into a spreadsheet, and used Beer’s law to estimate the spectrum over a range of ink film thickness. You will note that the estimated trajectory comes reasonable close to predicting actual measured values, and definitely predicts the hook.
For those who want more detail, I have a little more description below. This is excerpted from a paper I presented at TAGA in 2008.
This pretty well settles it in my mind. Magenta ink on paper is magenta. Magenta ink in a bucket is red. I have explained this with some simple ciphering with Beer’s law. This led me to define Seymour’s rule of ink hue shift, which allows you to tell (just by looking at a spectrum), whether an ink will have an appreciable hook.
I then showed some really, really impressive results that show that, armed with just the spectrum of your paper and that of your ink on that paper, you can determine the magenta hook. This is clearly a triumph of modern science.
I have come a long way since I was ransacking the printing plant to find those elusive halftone dots!
This is where I admit to some of the lies in the previous section.
First off, Beer’s law is only an approximation. It makes the simplistic assumption that a photon will either pass right through the ink, or get absorbed. It does not make allowances for photons that reflect directly from the surface, or for photons that bounce around a bit in the ink and maybe come out of the ink without ever having visited the paper.
Despite those simplifications is does fairly well. For the standard process inks. I do not have data to see whether it works for Pantone inks. If anyone has a cup of data to spare
One limitation that I glossed over is that it does not do well at predicting the reflectance of a double layer of ink. Us folks in the know like to say that ink is “sub-additive”, which means that Beer’s law does not do well at predicting the reflectance of a double layer of ink. It will, however, give you a spectrum that is attainable, however. Just not at that particular ink film thickness.
Well, that was kind of a lie as well. There are limitations, especially when you get up to the very high densities. You will note that my hook graph fits the data pretty decently, but it would not be nearly so good if I tried to predict the lightest density from the darkest, or the other way around.
There is one more lie, or one more pair of lies actually, but they are subtle. I demonstrated two ways of deciding whether the spectra of magenta showed a hue change. The first way was kind of hand-wavy. “Look at the spectra and see that it looks a lot like red. Ignore the little bump behind the curtain at 450 nm.”
Well, this argument may fly for someone who has not spent thousands of hours looking at spectra. But, if you have devoted a lifetime to deciphering spectra, you would know that sometimes the stuff happening down at the dark end is important. That little bump at 450 nm might just have a big effect on the color.
In this case, it didn’t. Converting to CIELAB demonstrated that the magenta is definitely turning red.
Or did it turn red? This is where the lie gets very subtle. We are trained from childhood to believe that colors with the same CIELAB hue angle are actually the same hue. But I have stubbornly disagreed with this all along. My first grade teacher almost flunked me over this point. I was glad to come upon a paper by Nathan Moroney where he made an off-hand comment that agreed with me.
The issue has to do with the fact that the CIELAB formula performs a nonlinear function on the XYZ values, which are a linear combination of the actual sensors in the eye, but which probably don’t actually exist in the eye or the brain. But that is grist for another blog.

[1] Yogi Berra said “In theory there is no difference between theory and practice. In practice there is.”
[2] I am still baffled as to why there are so few people who both know me and love me. Why is there no intersection between these two sets?
[3] Both words came into our language relatively late. Magenta became a word shortly are 1859, and cyan became a word in 1879. You wouldn’t expect them to become common words that quickly, would you? After all, look how long it took “internet”, “email”, and “perifarbe”  to become common words.
[4] “Hazing” of course is some sort of print defect for gravure printing. Nothing to do at all with the old guys picking on the newbie.
[5] Popular? So far, seven people have read the Beer’s law blog post. Well, I should clarify. Seven people stumbled upon the blog post. It is perhaps optimistic of me to expect that all seven of them took the time to actually read the blog rather than just look at the really cool pictures.
[6] Standard process magenta ink is not all that perfect, and there is a ”magenta” ink that is a bit closer to perfect: I am exaggerating just a tiny bit about the price of the alternative. I have not checked the price of Pantone Rhodamine just lately, but I think I can hook you up with a guy who can get you a gallon for something less than $80K a gallon. Unless of course, you are looking for ink jet ink.


  1. I assure you, John, that not only have I looked at the really cool pictures, but I have also read each of your blog posts (and have recommended them to friends). I can't say that I understand all of them, but I enjoy reading them. Takes me back to our days back in the skunkworks.

  2. Thank you, Steve! I appreciate the kind words, and I am glad that people find a bit of entertainment in the blog.

    I miss those days, also. But I suspect the memory of them is more fun than they actually were.

    BTW - I don't understand everything I write, either.

  3. Great post, John.

    Speaking of ink in the can, I was having some difficulty with Pantone 190. I eventually solved them, however, when I switched to Pantone 190. My ink rep assured me that, unlike the 190, the 290 was guaranteed to not turn pink in the can.

  4. John, the phenomenon of which you write here is not limited to printing ink and has been given the name "dye dichroism". Think about yor younger days preparing Easter eggs. The vegtable dyes in the cups look to be the wrong colors, as you have described, "pink" looks red, "yellow" looks red, "blue" looks indigo or navy, and "green" looks ... hmm ... What color does green become? Try your spectral test and seeifbyou can predict that one !


  5. Danny - Do you happen to have the spectrum of a green Easter egg? It's all in the name of science. Good connection, Danny.

  6. Dr. Vigg - I think there might be a typo in your numbers. You went from 190 to 190?? And then changed to 290 - which is a different color altogether.

  7. Congratulations with this fine blog. Do you think a thicker layer of ink will also cause a higher lightfastness? This would imply that processes based on thin ink layers (Benny Landa, HUV - inks) are more vulnerable to UV-radiation than classic offset ink.

    Fons Put

  8. Thank you, Fons.

    Let me start with a few caveats. First, "Flies walk on the ceiling." This is the mantra that I cite when I catch myself pontificating about stuff where I have no direct knowledge. This idea was explained in my first blog post:

    Second caveat, I have no data to support any of the opinions I am about to share. "In God we trust, all others must provide data." (Deming)

    With that said, here are my learned opinions.

    The amount of UV light (which breaks down pigments) that hits a given square centimeter of surface is the same, so I would expect the lightfastness of the ink to not change with ink film thickness.

    The amount of pigment breakdown depends upon the amount of UV light that is absorbed by the pigment. The more absorption, the more breakdown. If the color (spectra) of the inks are somewhat the same, I would expect that the absorbance would be similar. One would expect that HUV inks must have a similar color.

    On the other hand, the critical part is the absorbance in the UV, and not the "color". I have seen some spectral curves of inks in the 300 nm to 400 nm range, and I know enough to know that the absorbance is weird... it can't be inferred from the spectra in the visible range.

    On the other hand, I know nothing about the UV absorption of HUV inks, so I really shouldn't comment.

    On the other hand, I understand that HUV inks dry by using a UV band that is tuned to something in the ink - which I read to mean there is something in the ink that readily absorbs UV. This could lead to pigment breakdown, if the pigments are what is doing the absorbing. Or, it could lead to solvent evaporation, if the solvent is doing the absorbing.

    On the other hand, the ink below the surface is (to some extent) hidden by light scattered in the ink above. This suggests to me that a thicker ink might be somewhat more lightfast, at least to the extent that light is scattered in the ink.

    On the other hand, traditional ink films of ~1 micron are already pretty darn thin and (at least for traditional CMY inks) they are designed to be as transparent as possible, so this might not be a big effect.

    On the other hand, some pigments are more lightfast than others. I overheard someone in an elevator say that they thought they heard someone in a subway say that one popular yellow pigment is much more lightfast than the other popular one.

    I am certain that my comments have made the answer very clear! a) John has a lot of hands, b) John is ignorant of a lot of stuff, and b) it is a complicated issue and depends on which effect is predominant.

  9. Thanks John,

    I think we can certainly conclude that the absorption is (one of) the key factors in lightfastness: cyan ink is less vulnerable than magenta. A small research with yellow ink showed me that the thicker layer is a bit more lightfast, this would explain the light scattering issue. Further I expect some testing of UV and HUV-inks on lightfastness in the near future, hope to see some results there.



  10. Very interesting. It great because it is putting figures to effects I am seeing and reading most weeks. One thing, what about the issue of ink transparency in relation to CMYK overprint colours? Any thing re this and the facts in the blog?

    Paul Sherfield

  11. Thank you, Paul, for the kind words and the idea for a blog. I'm still composting the idea in my head... What level would you like to see:

    a) (Entry level) A blog post about red, green, and blue light, the difference between additive and subtractive primaries, and why paint differs from ink.

    b) (Moderate level) Journeys on a Photon Wing... following the path of a photon when it encounters ink.

    c) (Advanced) The whole Kubelka Munk schtick, with the climax showing what a little bit of turbidity does to your printing gamut.

  12. How about a piece on ink density in litho (offset printing)?! Why simply increasing the density might not necessarily increase the image quality. (And yes, that leaves us with the fact that the ink layer in offset, especially for cmy, is quite thin, semi transparent).

  13. That's a good idea Paul. You got me thinking...

  14. Hi John! Your blog has been very educational for me... Learning about how to control color in the pressroom is so much more complicated than I would have guessed. Thanks for making the learning process a lot more fun.

    I've been trying to adapt the Beer-Lambert law so that I can make these types of ink predictions, and I think I'm getting close. But I'm having trouble integrating the reflectance or spectrum of the paper. Right now I'm using the ink's RGB values as an approximation to its spectrum.... I have to divide by 255, make the prediction, then multiply by 255 to see what color I end up with. Do you happen to know if there's a way to replace the 255 with something that has more to do with how "white" the paper actually is? Thanks!

  15. RGB is problematic since there are so many different interpretations. The RGB from every camera is going to have a different spectral response. Often a gamma will be applied right to the data, which means that the numbers are not linear with reflectance, which is what you need. And there are a variety of numbers to put into the gamma curve.

    RGB will display different on every monitor, since the spectral output is different depending on the type of monitor and the way it's set up. It introduces it's own nonlinearity.

    Then there are standards... sRGB is at least well defined. And monitors can be calibrated quite well. Then you have rendering intent...

    And then there are standards for predicting how an ink will look. Those are in L*a*b*, which can be converted back to sRGB. There are a large number of characterization sets that make those translations...

    So... you have asked a very simple question with a very complicated answer. Probably not what you wanted and maybe not what you need? I dunno what's "good enough" in your case.

    Now for the quick answer. If you have an RGB value for paper, use that. Does this go to a display or something?

    You have an RGB value for cyan ink... where did that come from? Can you get paper the same way?

    If you want to explore this further, I will need a little more context. Send me an email if you like, explaining a bit deeper what you do.