Wednesday, July 31, 2013

The color of a bunch of dots, Part 4

If you have been wondering for years about TVI bananagrams, you have come to the right blog post. This blog post is the definitive blog post on TVI bananagrams. But if (for some crazy reason) you have not been wondering all your life about TVI bananagrams, then this could still be a watershed moment in your understanding of dot gain and its fuzzy sister, tone value increase.

Cyana bananagram

Dot squish

Pat Noffke and John Seymour presented a paper at TAGA in 2012 entitled A Universal Model for Halftone Reflectance. [1] In the paper, they developed an equation for what they called Dot Area Increase. This is a measure of how much a dot squishes out when it hits the paper. This is similar to what Murray and Davies called dot gain, but there is one novel difference. In both models, dots get bigger when they hit the paper, but in the Noffke-Seymour model, they also get thinner because of the whole law of conservation of ink thing. Because the dots are thinner, the color of the dot is less rich than the solid.

A halftone dot, before and after the steamroller

If there isn't any dot squish for a particular hypothetical printing, then a 30% dot would cover 30% of the area, and the thickness of the dot would be same same as the thickness of the solid ink. This hard dot has no dot area increase. The equation for reflectance in this case is the Murray-Davies equation.

Murray-Davies equation for hard dots

At the other extreme, the dots squish out completely so there is no longer any semblance of the dot structure (think gravure). Perfectly soft dots. Contone - continuous tone. At this extreme, one can use Beer's law to estimate the reflectance of a halftone. You will no doubt recall the equation from my blog on Beer's law
Beer's law equation for continuous tone

I should add here, that the two equations here should be applied on a wavelength by wavelength basis.

I should also 'splain a bit about the "Ain" that is being used as an exponent. Normally in Beer's law, this is where you would put something to do with ink film thickness. So, why did I stick the dot area in that spot? Imagine that you start out with perfect, hard halftone dots that are, I dunno, 30% dot area. Since they are perfect, let's just assume that the ink thickness of the dots is the same as the thickness of the solid.

Now, let's say that these dots get stepped on by an elephant. They are squished out so as to cover the whole area uniformly. How thick is the ink now? If the original dot area is 30%, then the new ink thickness is 30% of that of the solid. So, the exponent of Ain represents the thickness of the fully squished out dots.

Poor defenseless halftone dot, about to become a continuous tone

The dot squish equation

The pure genius of the Noffke-Seymour paper is that they considered what happens in between. In the figure below, the left side shows the starting condition. The halftone dot covers 25% of the area, and has the full thickness of the solid. The right side shows what happens after squishing [3]. The dot now covers 39% of the area, and as a result, is thinner by whatever ratio is necessary to preserve ink volume. I dunno? Maybe the ratio is 25% / 39%? I guess that's about 0.64. [4]

A tale of two halftone dots

Using the halftone dot at the right to illustrate the Noffke-Seymour formula, Beer's law is used to estimate the reflectance of the light blue area covered by ink. A thickness of 0.64 (as compared with the thickness of the solid) is used. Since a wandering photon has a 39% chance of hitting the area covered by ink, this reflectance is multiplied by 39%. This accounts for the light that reflects from the ink. The remaining photons will hit the paper, so (in true Murray-Davies fashion) the reflectance of the paper is multiplied by 61%, and this is added to the first number.

The equation below tells the whole story. "Ain" is the dot area going in. In the example above, this would be 25%.. "Aout" is the final area of coverage after squishing, 39% in the example.
The beautiful Noffke-Seymour equation

Note that at the extreme of no squish, Ain = Aout, the equation simplifies to Murray-Davies. At the other extreme, then Aout = 1, and this equation simplifies to Beer's law. 

In the first big finding, the authors of this paper looked at spectra from a big pile of tone curves, and came to the conclusion that pretty much every printing modality (web offset, stochastic web offset, gravure, newspaper, flexo, and ink jet [5]) all fit conveniently between these two extremes. This is huge. (But that's just my opinion.) Tone value increase for any type of printing can be described in terms of how broadly the dots squish. That's all you need to know.

Finally, the bananagram

I have saved the best for last. The other huge finding is shown below, the invention of the bananagram [6]. The bananagram below is an a*b* plot of all possible tone curves for a given cyan ink [7]. The left edge of the banana is the tone curves generated by assuming that the halftone dots are perfectly hard. The right hand side is a similar curve made with the assumption that the dots are perfectly flattened out.

Cyana bananagram

Now, lemme tell you about the rainbow colored lines. The yellow line, as an example, is all possible a*b* values that a 40% cyan halftone dot could take. Starting with a perfectly hard 40% cyan halftone, as you gradually squish it out, you will see it trace out the curve from one side of the banana to the other.

Wow. The position along that line tells you how hard the dots are. If you know the dot hardness (along with the spectra of the solid and the paper, and the original tone value), you can figger out the color of the halftone.

Foreshadowing the next blog post

I need to eventually tie up at least one loose end. I have been throwing dot gain kind of equations around willy-nilly, or perhaps yuley-niely. We have (so far) the following three equations to explain the color of a halftone: Murray-Davies, Yule-Nielsen [2], and Noffke-Seymour.

Murray-Davies (we all know) is a lump of over-cooked turnips when it comes to accurately predicting or measuring color. Yule-Nielsen, seems to be all the rage. Then these young upstarts come along with yet another formula that is gonna save the world! How can this all be reconciled?

Stay tuned for the thrilling conclusion!

[1]  I know these guys. One of them seems to be around whenever I stop at the bar for a beer. I guess he must hang out there a lot. Anyway, these two guys do bunches of seriously good stuff. And they're modest, too. Well, at least one of them is.

[2]  If you have been paying careful attention, you will notice that I have reverted back to the more common spelling the the latter gentleman's name. In a previous blog, I cited the original paper from the TAGA Proceedings, along with a scan of the heading for this paper. In the original published paper, the name is spelled "Neilsen", which is contrary to virtually every citation of the name. I ranted and raved about how 11,400 patent citations use the misspelling "Nielsen". As such, I would imagine that these 11,400 patents are potentially invalid. Gary Field did some excellent detective work, and has convinced me that the TAGA paper is a transcription error. The gentleman's name is Waldo J. Nielsen. Assignees of these patents can breathe easier.

[3] I keep talking about squishing, but this might not always be the case. In a web offset press, where there is a lot of pressure between the plate and the blanket and the paper, then squishing is probably a valid term. But in the case of gravure, where the ink has a very low viscosity, maybe it's not so much squishing as it is just spreading out. In newspaper, where the paper does not have a coating, maybe the significant effect has more to do with the ink being wicked into the paper. All of these I have put under the umbrella term "squishing." Whatever you squish under your umbrella is your own business.

[4] How should I know what the ratio is?  Am I called John the Arithmetic Guy??!?!?

[5] No data was harmed in the filming of this experiment.

[6] I expect to see bananagram T-Shirts available on the internet. There will be bananagram support groups for people who have family members sucked into the cult. I expect this will be a topic in the next state of the union address, with plenty of polarized commentary on Fox News and MSNBC.

[7] In three dimensions, this is a surface, sort of like a fly's wing or a sail. In other words, the possible range of colors of a halftone of a given ink can be described by a three dimensional figure that looks like a fly's wing.

Wednesday, July 17, 2013

Ruminations on beer

The word "beer" has occurred in 14 of my blog posts. Go figger. As all my friends know, I don't even like beer. And I always tell the truth in my blog posts.

Beer is frequently featured in my posts because of Beer's law. I am probably the first person in history to remark on the connection between August Beer's name and the yellow, foamy liquid. And I am certainly the first person to use actual beer to demonstrate Beer's law.


Beer's law is a law about light and color measurement. So, you can imagine my delight when the world finally got serious about measuring the color of beer! The Beertone guide below puts an end to all those arguments in the tavern about whose beer is darker. A simple flip of the deck under properly calibrated lighting can identify the color of each and every beer in the Beertone database.

The legacy of Hugh Beaver

Speaking of bar arguments, Sir Hugh Beaver was also interested in eliminating them. He was on a hunting trip and found himself amidst an argument about whether the golden plover or the grouse was the fastest European bird [1]. He found it devilishly hard to research the question, so he decided to create a book to answer all such questions. What does this have to do with beer? Sir Hugh Beaver was then the director of the Guinness Brewery [2]. Originally, it was just a marketing gimmick. He soon realized that this was a bonafide business in its own right.  

Hugh Beaver of Guinness and Hugh Beaumont of Leave It to Beaver
Two lives inextricably intertwined

Speaking of publications from Guinness, the book of world records was not the first time that the Guinness Brewery became famous for its publications. The so-called "Student's t-test" came out of that little place in 1908 [3]. William Sealy Gosset was researching ways to improve all matters having to do with barley and yeast, and beer production. At the time, he thought his work was of little consequence. Little did he know that his name was to go down in the history of statistics. 

Well, his name didn't quite go down in history, but his pseudonym did. It seems that a previous Guinness employee had spoiled the water. Trade secrets had been published, so Guinness adopted a policy that employees were not allowed to publish anything. Gosset negotiated an agreement with Guinness where they allowed him to publish so long as he published under a pseudonym and did not publish any of their data. The author of this landmark paper in statistics (March 1908 volume of Biometrika) was "Student". 

The amazing world of Guinness bubbles

Speaking of bar arguments and Guinness, to this day, there has been an ongoing argument about the direction of the flow of bubbles in a freshly poured pint. It appears that bubbles travel downward, rather than upward as one might expect. One enterprising group of scientists at Stanford University headed down to the pub with a high speed camera to test this. Optical illusion, or fact? Their conclusion was that the "...bubbles at the center rise up and create a circulation in the glass.  The circulation causes bubbles at the edge of the glass to be pushed downwards."
OMG! The bubbles really do head for the bottom of the glass!

This is not the last word, by any means. The critical research continues. Last year saw the publishing of a paper at Cornell which literally turned the world of fizzy-ology upside down:

"In this paper, we use simulations and experiments to demonstrate that the flow in a glass of stout beer depends on the shape of the glass. If it narrows downwards (as the traditional stout glass, the pint, does), the flow is directed downwards near the wall and upwards in the interior and sinking bubbles will be observed. If the container widens downwards, the flow is opposite to that described above and only rising bubbles will be seen."
Pint and Anti-pint

Just as an aside, I tried this experiment at home. I could not replicate their results. Every time I turned the pint glass upside-down, the bubbles headed downward. Along with the stout.

But the two previous explanations lack the big words to give them the level of pretension that the whole topic deserves. This following paper provides adequate levels of pretension. The lead author is from Limerick, Ireland, so she no doubt is an expert on stout. Here is what she has to say:

"Our theory involves a physically based regularization of the basic equations of the two-phase flow, using interphasic pressure difference and virtual mass terms, together with bulk or eddy viscosity terms."

I offer the following as an alternative for the abstract: [4] 

There were some researchers from Limerick
Who proved bubbles go down - quite a mean trick.
They modeled two-phase flow 
To explain why it's so
With a pressure difference interphasic.

I am guessing that my own name may not go down in history as the author of the first limer-abstract. It's a shame. But I realize that this limerick won't get much airplay because limericks are supposed to be naughty. [5]

To beer or not to beer?

Speaking of "naughty", what about beer and mating rituals? 

I have been reading a delightful blog by Christian Rudder. He has the enviable position of being allowed free access to the scads of data from the dating site "OkCupid". They have a database with zillions of questions, answered by zillions of people, and he has been doing correlations to find answers to these questions that correlate with each other. For example, one would expect that if someone identified themselves as being into Harleys and Metallica, it's likely that they would also be into My Little Pony. 

But Christian wasn't really looking for My Little Pony fans, he was looking for something more practical. I am guessing that he knew something that I discovered the hard way--the Heisenberg Uncertainty Principle of First Dates: The mere act of asking a woman if she will go all the way on a first date will effect whether she will. Generally speaking, the effect is negative.

So, Christian wanted to know what "safe" question you could ask on a first date to get some indication as to whether you might get lucky. He had the answers to the question "would you consider sleeping with someone on the first date". And he had answers to a zillion other questions. Here is the astounding revelation in his blog post about safe questions for a first date. "Among all our casual topics, whether someone likes the taste of beer is the single best predictor of if he or she has sex on the first date."

Ask her if she likes beer!

Speaking of dating and beer, let's talk about beer goggles. Do "the girls all git purdier at closin' time", as the song says? Amanda Ellison, senior lecturer in the Department of Psychology at Durham University and author of the book "Getting your head around the brain" would like to dispel the rumor of beer goggles. Here is what she has to say about the effect of alcohol:

The area of the brain that makes us want to mate keeps functioning, no matter how much we drink, meaning that people can still assess how visually-appealing others are. ...alcohol switches off the rational and decision making areas of the brain while leaving the areas to do with sexual desire relatively intact, and so this explains beer goggles. 

Before and after that third pint of Guinness

We don't rate people as getting more attractive when we have a few under the belt. We just get better at making bad decisions. And mind you... those decisions often find us getting into trouble with the law. Beer's law.


[1] Apparently the question about whether the African or the European swallow was faster is uncontested, since the bridge keeper at the Bridge of Death is the sole decider of Truth.

[2] This epiphanic moment that marked the nascence of the Guninness Book of World Records was on my birthday, November 10. Beaver was born in Johannesburg in 1890. I visited Johannesburg 120 years later. I once had a copy of the Guinness Book, and I once had a Guinness beer. To the best of my knowledge, neither Hugh nor myself have ever robbed a bank. The coincidences are endless.

[3] Student's t test is not (as you would expect) an annual competition sponsored by some school between Lipton, and Bigelow, and Celestial Seasons. It is a method in statistics that is used to test the validity of experimental results. Suppose I want to find out if having a couple of beers for breakfast will improve the appearance of my hair. I run a number of trials, on some days I have my normal breakfast of two beers, and on other days I abstain. For each day, I count the number of compliments I get on my hair. At the end of the experiment, if I get more compliments on beer days, it might be because the beer really does make my hair look better, or it could just be at random. For example, maybe on beer days, I just happened to get served more often by that cute young gal at Starbucks who has a crush on me. Student's t test is a way of gauging the likelihood that the experimental results might just be random chance.

[4] I am following my normal practice of poking fun at things that are too difficult for me to understand. Its a defense mechanism.

[5] (From the Wikipedia entry on limericks) Gershon Legman, who compiled the largest and most scholarly anthology, held that the true limerick as a folk form is always obscene, and cites similar opinions by Arnold Bennett and George Bernard Shaw,[5] describing the clean limerick as a "periodic fad and object of magazine contests, rarely rising above mediocrity." From a folkloric point of view, the form is essentially transgressive; violation of taboo is part of its function.

Wednesday, July 10, 2013

"Is my green the same as yours?", revisited

Last May, I wrote an insightful and compelling blog post about whether we all see colors the same way. In my normal clever way, I called it "Is your green the same as my green?" Just a few days ago, I was given a bunch of really cool data that allows me to take another look at this question.


First, I need to tell you about Dr. Sophie Wuerger's recent paper, entitled "Colour Constancy Across the Life Span: Evidence for Compensatory Mechanisms". It is obvious that this is a scholarly paper because she spells "color" with a "u".
This technical paper is clearly above my head

Spoiler alert: I am about to give away the ending to her paper. If you don't want me to spoil a great story, then stop reading my blog. Go read her paper. Now.

It is well known that our vision changes as we age. For example, I used to enjoy lite beer. Today? I prefer to curl up with a darker beer. This is obviously due to the fact that the lenses in my eyes have slowly yellowed as I have aged [1]. For those of you are ardent fans of my blog, you already knew about the yellowing of the lens. I talked about that as one of the reasons that I may not see colors quite the same as someone who is still young enough to enjoy lite beer.

Well, Dr. W. completely spoiled that for me! Although the actual stimulus provided to the brain changes with each page of the calendar, Sophie's research shows that the brain corrects for the yellow sunglasses that we don in our old age.

So, in my last informative blog post on the subject, I concluded that the way we see color depends on how old we are. And then here comes along some research -- and research by a person who spells color with a u -- that says that somehow our perception of hue does not change that much as the lens yellows. I quote from the actual paper:

"Our main finding is that colour appearance mechanisms are to large extent unaffected by the known age-related changes in the optical media (yellowing of the lens) whereas the ability to discriminate between small colour differences is compromised with an increase in age."

Wow. Color me flummoxed. A yellowish shade of flummox.

Sophie's Choice
Here is the gist of her experiment. She sat 185 people (aged 18 to 75) in front of a computer monitor and displayed for them a selection of splendid colors [2]. The task before the experimental subjects was to select the color that was either the purest red, green, blue, or yellow in color. For example, a range of colors that were all kinda red in hue would be displayed. All of the colors would have roughly the same brightness and saturation, but would differ in hue. The simple question was phrased like this: "which of the colors has neither a yellowish or bluish shade?"

This test was performed with four color groups: red, green, yellow, and blue. (Yes, Billie, I can see your hand going up. You recognize those colors. I'll get to that later, ok?)  For each of the color groups (hues), there were nine different colors that were investigated.

In a previous blog post about organizing crayons, I introduced a fabulous diagram that helps even the mere novice understand color space. Each of the pages in this diagram represents a different hue. I have shown red, green, and blue, but there are of course a whole bunch of them. Maybe a hundred? Maybe a few hundred?
A fabulous diagram that helps even the mere novice understand color space

Let's just take a look at one of those pages (see blow). This page has all the colors that have a hue of red. Note that I have put nine "X" marks on this page. Those marks show roughly the nine "colors" (combinations of saturation and lightness) that were investigated.

Confused yet?  Let me summarize. There were four hues investigated (red, green, blue, and yellow). For each of these four hues, there were nine different investigations. Ok, so that makes investigations of 36 different colors.

Now, for each of 36 investigations, each of the guinea pigs [3] was asked to select from a zillion and a half different hues to find the one that most exemplified the trustworthy and faithful hue that we have come to know as "red". That was Sophie's Choice.

Here I have another view of the points in color space that were involved in this test. Here, we are looking at color space from above, so that the horizontal axis is the reddishness to greenishness, and the vertical axis is the yellowishness to bluishness. (Yes, Billie, those same four colors came up yet again. Hang on. I'll get to them. Yes, I know that something odd is going on.)
Really cool propeller-gram from the really cool experiment

Now I need to say one more thing about the diagram above. The points in the diagram are not "all the available choices". They are the colors that the experimental subjects actually chose as being red, green, blue, or yellow in hue.

Wow. You know... these results are pretty darn far flung. I'm not liking that. It kinda makes me think that we can't even agree on what red is! No wonder my gorgeous wife and I have trouble agreeing on color names as I reported in my post about spectrophotometric agreement!

But wait just a gol durned minute
The really cool propeller-gram showing the really cool results from a really cool experiment is also a really cool example of a misleading graph. I will zoom in on just one of the red investigations, the one with the highest saturation.
Looking at just one of the investigations

Each of the red dots represents an answer that at least one person (out of the 185) selected. In some cases - the cases where the dots are most far-flung - there was exactly one person so audacious as to say that this represents a true red hue. In the dots that are closer to the center of the line, there are literally zillions of people who chose that answer. The graph does a really lousy job of differentiating the popularity of the various answers [4].

The graph below is a less distorted way of looking at the same data. This is a histogram, showing that there is a pretty tight clustering. The labels are hard to read unless you double click on the image, but about half of the subjects selected a hue angle between 16 and 18 degrees. I am going to call that pretty darn tight, and make the declaration that we all can agree on at least the hue for "red".
Histogram of hue angle for one of the red investigations

What do red, green, yellow, and green mean?
And now for the big moment. Finally. A definition of these four hues!
Note: The uncertainty column was determined by computing the standard deviation of the hue angles, and dividing this by the square root of the number of observations. This is an estimate of how close the average is to the "real" value.

Note: The table above is just the averages for one investigation of each of the four hues. I have not yet looked at all nine. Also, Sophie has provided me with gobs more data. This is only the "dark adapted" data.

Something odd is going on with my Hering
Billie, now to your question. First you noticed that the four hues that Dr. Wuerger chose were red, green, yellow and blue, and that these are the colors of the four chromatic directions in CIELAB space. Very good, Billie. You have been paying attention.

This whole idea of the names for the four directions goes back to a fellow by the name of Ewald Hering. He came up with the idea that we perceive color based on three sets of opponents. Colors are either reddish or greenish. Colors are either yellowish or bluish. Colors are either light or dark. Any color can be defined by where it rates in each of those three attributes.

Noted color scientist Ewald Hering, and noted food of color scientists

Now Billie, you had another question? Yes... you looked at the graph labelled "really cool propeller-gram from a really cool experiment" and started thinking about Hering's theory? What really cool thing did you notice about the graph? OH?

Green is not diametrically opposed to red. To be precise, they are not 180 degrees apart, but about 143.  And blue and yellow are not either. Yellow and blue are about 120 degrees apart.

Hering was wrong? Heresy. Pure blasphemy. I should clarify... The theory is correct qualitatively. But to be quantitatively correct, you need to adjust the meaning of the words. "Pure red" and a certain shade of bluish green (maybe cyan?) are opponents. And "pure yellow" and a certain shade of reddish blue(maybe violet?) are opponents.

This is work in progress. I have just started analyzing the data that Dr. Wuerger has graciously shared with me. But let me tell you one thing... If I ever invent a color space of my own, red is going to lie right on the horizontal axis, and not some silly 16 degrees off.  And I am going to try to get yellow right on the vertical axis. And I am going to try to resolve the issue of what the true opponents of these colors are.

Oh... and my new space is going to be perceptually linear, gosh darn it. None of those ugly deltaE 2000 equations. And I will call the axes JMG.

-John the Math Guy

[1] My predilection for the darker and more full bodied beers is well known. This is often cited in the technical journals as further proof of the yellowing of the lens. There has also been considerable speculation about whether this penchant for dark and full bodied extends from beer to my taste in women. I decline to comment on this controversy. I think it's just silly.

[2] Think of that. 185 people. In front of one computer monitor. She must have the most awesome huge big screen TV in her neighborhood! I know where I am going to watch the next Academy Awards... Wait... they weren't all in front of the monitor at the same time? Oh.  Ok, so I am still open to invitations to watch the Academy Awards.

[3] I have been assured that no animals were harmed in the filming of this experiment.

[4] This was meant as a didactic warning about interpreting scatter plots when the number of points is way big. Basically, the more data points, the larger the impression of the variation. Some day I will do blog post about that cuz I have something cool to show off. It involves using singular value decomposition to compute the square root of a co-variance matrix, so you know that you will need to check back to read that post!

Wednesday, July 3, 2013

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]

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.

[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.