Wednesday, February 20, 2013

Followup to the spectrophotometric romance

This is a followup to my blog "A spectrophotometric romance". Be forewarned, this post is rated PG, for Print Geek. And it will be only just a little bit silly.

This post is necessary in order to consolidate comments, questions, and answers that have appeared in many different places. To date (Monday, Feb 18) the post has been viewed 753 times. Since there are only 587 certifiable print geeks in the world, this blog post is the Justin Beiber YouTube video of the print geek crowd.

There have been 76 comments in four LinkedIn discussion groups and on the blog. I have had email and phone conversations about the post with nine people, none of whom are in my immediate family. The interested folks include manufacturers of spectrophotometers and reference materials, printers, physicists, color scientists, people in standards groups, and designers.

Netflix called me the other day to complain that my email traffic was starting to bog down streaming video speed in Los Angeles, the greater New York metropolitan area, and one neighborhood in Scranton, PA. So please forgive me if I left out one of your astute comments. 

Can I read a full copy of the TAGA paper?

Sure. Here is a link to the full paper: Evaluation of Reference Materials for Calibration ofSpectrophotometers. The paper was presented at the 2013 TAGA conference in Portland, OR.

Now for the obligatory plug. TAGA is great. I try not to miss the TAGA conference. It is one of the only conferences where you can learn about new technologies in all parts of the printing industry. You will hear from academics and professionals alike, without the sales hype of most conferences. The next TAGA conference will be held in Fort Worth in March 2014. I hope to see you there. If you do, then buy me a beer.

Do you want a second opinion about TAGA?  Here is what Sandy Hubbard had to say about this year’s TAGA conference: TAGA, You’re It!

What is going on in the industry to try to fix the problem of inter-instrument agreement?

Idealliance (in the US) and Fogra (in Europe) have assembled groups of experts from all the graphic arts spectrophotometer manufacturers to work on the issue. I was cautiously optimistic at the start, and am cautiously a bit more optimistic after attending the first meeting. I attended the US meeting. I was impressed that everyone in the room was sincere in their desire to find agreement on how to find agreement. I didn’t hear any finger-pointing or blustering about why one company provided the one true measurement system and everyone else is wrong.

Of course, we spent the first six hours complaining about how spectrophotometer owners use their delicate instruments to hammer in nails and drop ketchup and fired onions into the optics. But we got past that soon enough, and started complaining about cops who give out speeding tickets and about politicians.

The ISO standards group that covers color measurement for the graphics arts (TC130) has also made some recent changes that will eventually improve inter-instrument agreement. See the heading “What is being courageously changed?” below.

Why do the instruments disagree?

Speaking of finger-pointing, why can’t the various spectrophotometer designers just build their instruments the correct way? Then they all would agree, right?

That all makes sense, but the difficulty is that there are many different ways to build a spectrophotometer “correctly”. The different correct ways may not give the same results. You may think that I am just copping out, since I represent an instrument manufacturer, but listen up. I have a parable for you.

Tevye (from Fiddler on the Roof) is in the marketplace talking politics. One person speaks of the great new world that the tsar is bringing. Tevye looks at this man and says, “You’re right”. The second man disagrees, and says that the tsar is bringing ruin to the country. Tevye looks at this man and says, “You’re right”. The third man is beside himself. “Tevye, how can they both be right!?” Tevye ponders a moment, and then says, “You’re also right!” If two instruments disagree, it is totally possible for both of them to be right.

Here is the short list of things that can go cause disagreement.

Fluorescence – Recently, optical brighteners have become ubiquitous. They are added to paper to make the paper appear brighter. The trouble is, the amount of whitening that happens depends on the amount of UV content in the light in the spectro. If two spectros emit different amounts of UV, they will excite the optical brighteners by different amounts, and the spectros will disagree.

I think we should point the finger at the darn paper companies who put the optical brighteners in the paper. Or maybe at the designers who like the paper that is whiter.

White level – Believe it or not, the various standards labs can’t quite agree on what “white” is. If you send a white tile to be measured by several of them, you may see a 1 ΔE of difference in L*. This is a clear case of “you’re right”. I think we should point the finger at the standards labs.

Lateral diffusion – A spectro illuminates a small area of the sample, and collects the light reflected by another small area. One would think that these should be the same size, this would cause a problem. If the sample has some translucence (it’s cloudy), then light will scatter outside the aperture. The smaller the aperture, the bigger the relative effect. Now get this… a few of the BCRA II tiles have bunches of lateral diffusion.

I think we should point the finger at the print buyers who force us to measure colorbar patches that are 1.5 mm tall. Or the paper companies. You would think they could make each sheet on a paper roll just a millimeter or two longer to make room for decent sized color patches.

By the way, someone wrote a paper about lateral diffusion a long time ago. The guy’s probably in a nursing home in Milwaukee singing Those Were the Days.

Linearity – One would expect that a decent engineer would be able to design a spectro that is linear. Of course, there is a little problem that detectors are nonlinear when they come close to saturation. By the way, that’s where the detector has its best noise immunity.

And there is the little problem that transistors and all that stuff like to be nonlinear down where the signal levels are smallest. Oh, and the issue that it is hard to devise a set of samples to calibrate nonlinearity with. One is left with assembling a series of gray samples with different reflectance values, and having a national standards lab measure them.

Did I mention that the national standards labs are ghastly expensive when you ask them to measure something?  I think I’ll open my own national standards lab. Or just blame the stupid laws of physics.

Black level – Theoretically two spectrophotometers could disagree on the reflectance of a perfectly black object. I think they probably do disagree just a tiny bit, but I don’t have enough data to verify this.

Wavelength shift – Just like two spectros might not agree on what 50% reflectance is, they might disagree on where 500 nm is. Thankfully, we have physical standards, such as mercury-argon lamps, that we can use that will emit at certain precise wavelengths. But… it would be nice if there were a few more emissions lines. Stupid laws of physics, anyway.

Spectral bandpass – Don’t even get me started on this one!

Goniophotometry – This one is a favorite of mine, simply because of all the cool words. Besides “goniophotometry”, there is “indicatrix”, and the acronym “BDRF”.

The basic idea is that the amount of light reflected from a surface depends on the angle that the light hits and upon the angle that it is viewed. In practical terms, a 0/45 spectrophotometer that collects all the light emitted between 40 and 50 degrees might not agree with one that collects all the light emitted between 43 and 47 degrees.

When you see me at TAGA 2014, buy me a beer and we can talk about the birds and the goniophotometers.

By the way, someone once wrote a TAGA paper about the goniophotometry of printing ink. The writing in the paper shows many of the early warning signs for dementia.

So many possible issues! In the words of Rabbi Seymour Goldstein, “Oy vey, mein kapella! This is so meshuga, it gives me such tsuris!”

Also in the words of Rabbi Seymour,

“Grant me the courage to change those things that I can change,
The serenity to accept those that cannot be changed,
The wisdom to know the difference,
And a little duct tape and shoe polish to fill in the gaps.”

What is being courageously changed?

There are a number of things that have changed or are changing to try to improve inter-instrument agreement.

One concrete decision that came out of the Idealliance meeting (in the US) was that we all agreed to trace our “white” back to the same national standards lab. We decided to go with the US-based standards lab NIST. I don’t know if this was discussed at the European meeting, but hopefully we can all decide on a single national lab.

The ISO standards group that works in the graphic arts color measurement arena (TC 130) has recently made some important changes that have already, or will, improve inter-instrument agreement.

Most notable is the “M0 / M1 change”, which addresses the optical brightener issue. Spectrophotometers with the M1 designation will agree in UV content so that optically brightened papers will be measured the same. For more information, have a look at some other wonderfully written articles: “The problem with optical brighteners”, and “New lighting conditions”.

Another change (one that is interesting only to the print uber-geeks) was made to ISO 13655, having to do with wavelength bandwidth. Interested in more information? Buy me a couple of beers and we’ll talk. Buy me a few more beers after that, and we can go sing Don’t Stop Believin’ at a karaoke bar.

These changes to the standards are essential, but they take a while to filter down. The really odd thing is that a change to the standards rarely changes existing equipment, you know? For some reason, I need to send my old spectro in to get it updated, or maybe buy a new one, for gosh sakes.

What serenity is required?

Now it is the print buyer’s turn to get the pointy finger.

There is a rule of thumb in the statistical processing world. The accuracy of an instrument is only allowed to take up 30% of a tolerance window. Thus, if the tolerance window for a certain printed color is 2.0 ΔE, then my instrument must be accurate to within 0.6 ΔE. If you go beyond that, it just makes things worse.

The reality is unfortunately that two instruments of different make and model will likely not agree to within 0.6 ΔE. Setting tolerances closer than that will inevitably just make people want to drink more beer.

Anyone have a spare cup of wisdom?

Wisdom… I wish I was smart enough to know what to say about this.

Hopefully my TAGA paper has contributed to the collective wisdom. My message was to know when a courageous attempt to make two instruments agree should have been tempered with a bit of serenity.

Duct tape and shoe polish

Another discussion item in the US inter-instrument agreement consortium was the development of a test strip with a selection of colored patches that could be measured by different instruments. After measurement, something could be done with the readings.

We discussed several options about what could be done:

1) The measurements taken with a single instrument could be compared over time to verify that the instrument has not changed,

2) One instrument could be compared with another to see if they measure substantially the same,

3) An instrument could be compared with measurements from a national standards lab (or perhaps a secondary lab) to assess the accuracy of the spectrophotometer, or

4) The set of samples could be used to standardize one instrument to another -- that is to provide a way of converting one instrument so as to match another.

The four potential goals are successively more complicated and expensive. In particular, obtaining measurements from a national standards lab would cost thousands of dollars, so it is not cost effective for most users. The fourth option may require a color scientist/math guy, so might only be an option for the spectrophotometer companies that can afford to hire color scientist/math guys.


I am not done playing with duct tape. I am in the process of cogitating on colligation. The ancient Greek, Ptolemy developed a set of equations that could be used to predict the positions of the planets at any time. The equations were based on a lot of wrong assumptions like the Earth is in the center, and all the rest of the celestial bodies move in circles that revolved around circles. The model worked, at least to an extent.

A millennium or so later, Copernicus decided that the Sun belonged at the center. (I hope everyone celebrated his birthday yesterday?) Then Kepler came along and decided that ellipses made the whole thing simpler, and then Newton provided the big colligation. The inverse square law of gravity was the grand unifying theory that explained the whole enchilada.

My goal is to colligate. I have gone through the Ptolemaic thing in my TAGA paper, and shown that things go subtly awry when you have the wrong starting assumptions. I have done the Keplerian thing and did regression with (what might be) the right assumptions. It’s time to roll up the sleeves and do the Newtonian thing.

I plan to collect a bunch of spectros, enough to represent the range of physical differences that we see out in the field. I plan to collect a bunch of sample sets. I have the ones that I used for the TAGA paper, but I will gather more. Some new samples are already on a plane, headed to my office.

Then I plan to systematically go through specifically designed sample sets to try to ascertain what differences exist between the real world instruments. For example, I will measure a set of white and gray samples with varying levels of gloss to see if there is a goniophotometric difference – a difference in gloss rejection. I will measure a series of white to gray samples to ascertain whether the typical instruments in the field differ in their view of linearity.

And so on.

I am not sure where the colligation will lead. It could be that it will show that courage will be required, and there will be another round of “gosh darn it, we need to tighten up specs on something or other”. Or it could be that more duct tape is in order, and a simple standardization, carefully applied, can make an appreciable improvement.

I am still cogitating on this inter-instrument colligation. I welcome any suggestions or offers of help. At least, up to the point where I spend 23 hours and 56 minutes a day responding to emails. 

Monday, February 18, 2013

John the Math Guy breaks out of the blog, Jan 2013

I have been hiding in my blog for a while, and decided it would be a good idea to get out to see more of the internet. Here are some of the tracks I have left elsewhere.

Labels and Labeling magazine

Adrian Tippets (a good friend who I have never actually met in person) read my blog post called "Layman's Guide to ISO Standards". He liked it so much that he hooked me up with the wonderful folks at Labels and Labeling magazine. One thing led to another, and "ISO comes to in-line color" was born. Here is the summary:

Achieving ISO compliance with an in-line spectrophotometer is a more difficult project than first appears. John Seymour, color expert at QuadTech, lays out the issues.

Munsell blog

I had an interesting interchange of blogs with Jeff Yurek. Jeff writes an entertaining blog with the uber-cool name "dot color". (I wish I could think of names like that.)

The interchange started with "Why does my cyan have the blues?" Jeff Yurek (a close, close friend who I never met) read this post and was obviously totally blown away my the incredible writing style and the vast knowledge that I evinced with my post. Or maybe he was just desperate for a blog post topic? Either way, he summarized my post in his blog post "How does ink thickness change the appearance of printed color?". 

Turn about is fair play, right? I was desperate for a blog post topic and I decided to co-opt ideas from his blog. I came across a post of his about the Seeing red: can color change your spending habits?. I decided to play off this post by doing extensive research into universality of opinions of color gurus on the psychological effect of the color red. I spent nearly a whole hour on the research that went into the post "Red is the color of..."

Jeff and I played ping-pong for a while. He did a post called  "Shopping for a tablet this holiday season? Don’t forget to look at color performance". Many reviews of the various tablets look at display resolution (pixels per inch). He looked at the color gamut of the displays - how many colors can the display produce.

I followed up with Does my dog appreciate my KindleFire display? in which I either looked at a) tablet apps for testing colorblindness, or b) color-blindness in dogs, or c) the gamuts of various tablet devices, or d) my superior color vision over my wife. I'm not sure what the post was really about, but I got many comments on it, so I followed up with Follow up on colorblindness testing.

Well, Munsell makes stuff for testing colorblindness, so this got the attention of Noni Cavalerie, who is the social media-savvy social media person for Munsell. In particular, she handles the Munsell color blog. Noni, of course, is one of my oldest and dearest friends that I have never met. She couldn;t take it anymore, so she asked me to guest blog. Naturally, I took a subject near and dear to my heart - why I am superior to my dog:  Evolution Trichromacy.

In case you are wondering about this vast superiority I have over my dog, it's because he is colorblind, and I have an opposable thumb. If you want to know why evolution favored primates with trichromatic vision (three types of color receptors), you'll have to read the dog blog.  

FlexoGlobal magazine

I posted a blog called Where are my CIELAB knobs?. My dearest friend Laura Hatch, of FlexoGlobal magazine (a friend who I actually did meet once) liked the blog and asked to repost it. I modified it a little (meaning, I took out the silly stuff), and she made it a Where are my CIELAB knobs?.

Wednesday, February 13, 2013

The function of the heart

There is some holiday coming up. Can't quite think of what it is... I'll have to ask my wife. She knows these things. I hope it's not my anniversary, cuz she would get upset with me if I forgot that. I am pretty sure that our anniversary is in December or March or something, so I think I'm in the clear.


The half-wing function

Let's start with a polynomial equation, we'll call it p(x). I will define it as the sum of three polynomials:

The first of these polynomials, p1(x), is linear in x. I'll have it going from k1 at x = 0, down to 0 at x=pi .

The second polynomial, p2(x), will be 0 at both ends and a second degree parabola in between. In this way, no matter how big I scale it (by using my handy k2 parameter, it won't affect the value of p(x) at the ends. Whenever I get a chance to do this with a polynomial, I go for it.  

I have one more polynomial, we'll make this one a cubic parabola. This one will get nailed down at the ends (x = 0 and x=pi), and will also be zero halfway in between.

I can pick values for the three parameters to give me any cubic polynomial that goes through (0, k1) and (pi, 0). How cool is that? Just for kicks, I chose k1 = 2.0, k2 = 0.3, and k3 = 0.6. The plot below shows the very agreeable cubic polynomial that is generated this way.

The half-wing function

I could have just played with the standard (canonical) form of the cubic parabola, but that gets confusing. with this formulation, k1 allows me to adjust the starting height, k2 allows me to adjust the amount of torsional wiggle, that is, how much the left half bows down and the right half bows the other way. Finally, the k3 parameter allows me to adjust the midpoint up and down.

I did a little work with this idea of expressing polynomials differently a while ago. One particularly cool thing is that this leads to a way to do regression that always goes through some fixed points.

The full-wing function

I like that function, but I would like to see the other half of the wing. I can use the absolute value function to flip this function over. Now the variable along the abscissa is z. I use z to get x, and then plug x into the equation for p. Back when I was teaching algebra, I would say that the absolute value function is like a tavern. Whether you are negative or positive going in, you will always be positive coming out.

The flipping function

This flipping over function gives me a wonderful plot of a pair of sea gull wings, symbolizing peace, since sea gulls are very peaceful animals and never hurt another living thing. Or maybe the plot looks like a champagne glass. That kinda reminds me of some holiday, but I can't quite place it.

The full-wing plot

Going polar

Sea gulls sometimes go to the North Pole. Or maybe that's penguins. I dunno. Some bird flies up to there. Anyway, that whole polar thing gets me thinking about (what else) polar coordinates. The full-wing plot already goes from 0 to 2pi. Maybe I should plot it in polar coordinates? Here is how I get from one to the other.

Now it's just a matter of plugging it all into Excel. I entered all this stuff into a spreadsheet. I let z go from 0 to 2pi in kinda small steps. I computed x by using the flipping function. I computed p(x), with the values of the k parameters. And these all went into computing a sequence of (x, y) values. Just for grins, I decided to plot them.

Now that I have the blog written, I need to go find out what day I was supposed to be remembering!

I christen this function the Madeloid, in honor of my wife, the Gypsy Songstress, the Shopping Maven, the love of my life.

Would you like a copy of the spreadsheet that created this? Send me an email at

Thursday, February 7, 2013

A spectrophotometric romance

This is a romantic love story. The usual... boy spectrophotometer meets girl spectrophotometer. Sparks fly, and naturally, they fall in love. I haven't cast the parts yet, but I am thinking Jennifer Aniston could play the female lead. My wife might like to see Antonio Banderas as the male spectro.

But like all romantic comedies, there has to be a conflict. In this movie, they start to disagree.
This part of the movie is quite familiar to me. As a guy, I see this disagreement with my little spectrophilia on a daily basis. Is the blouse on that cute young lady teal, aquamarine, cyan, or turquoise? No matter what I say, I know there will be an argument. As a mathematician, I can readily calculate that my odds of winning the argument are no better than 0 in n, where n is a really big number. I mean, really big. Like so close to infinite that you can taste it. 

But as a color scientist with an ego the size of the planet Jupiter, it's hard for me to just let this go. I should know my colors, right?!?!?!??

So I can relate, as can any male, married, applied mathematician color scientists. I think this covers just about everyone who reads this blog.

One would think that they would agree. They are in love, of course. There are these expectations. IFRA published a report [1] on this expectation:

Inter-instrument agreement is usually indicated by a colour difference value between two instruments or between a master instrument and the average of a group of production instruments. Although various ways are used to describe this colour difference, a common value is the average or mean value for a series of twelve British Ceramic Research Association (BCRA) Ceramic Colour Standards Series II (CCS II) ceramic tiles. A value of 0.3 ΔEab is acceptable. 

How much do our hapless lovers disagree? I did a little research. I went digging for technical papers and reports where others had brought spectros together to see how much they agreed - to assess inter-instrument agreement.

Number of Instruments
Samples Measured
Nussbaum [2]
BCRA Tiles
NIST Standard
8 of 9 >2.0 ΔEab
Radencic [3]

Two each from four different manufacturers
Lab-Ref card
Median of all instruments
All >1.0 ΔEab,
Max. 10 ΔEab
Wyble and Rich [4]
BCRA tiles and ink
Paired comparison
Avg. 0.73 ΔEab to 1.68 ΔEab
ICC [5]
Three units of the same model
Gravure printing
Identical model
Avg. 0.47 ΔEab,
Max. 1.01 ΔEab
Dolezalek [6]

46 patches
5 stocks
Paired comparison
50% >1  ΔEab,
20% >2 ΔEab
Hagen [9]

Field study of in-use instruments
13 patches
GretagMacBeth NetProfiler card
Avg. 1.56  ΔEab,
Max. 3.77  ΔEab
X-Rite [10]
One of each of their models
46 patches
9 substrates
Paired comparisons
0.27  ΔEab to
1.08  ΔEab

Looking at the far right column of this chart, it is clear that there are virtually no spectrophotometers that are acceptable by the criteria set forth by IFRA. (Understatement alert) There appears to be something of a disconnect between the expectation of inter-instrument agreement and the actual disagreement that will be seen.

What to do?

I turn to a couple of my friends, Danny Rich [9] and Harold Van Aken [10]. (I was honored to be present last night when Danny received some prestigious award or other for lifetime commitment to blah blah influence on the industry blah blah blah best screen adaptation of a spectrophotometric calibration method.... whatever. The award was prestigious anyway. Tears, laughter, speeches. I am not jealous, by the way. Not trying to put him down. Honest. No, I mean really. [11])

The idea put forth by these two really smart guys is that at least some of the discrepancies between spectrophotometers are due to understandable and predictable phenomena. If the understandable phenomena can be quantified, then they can be corrected.

Here is where the BCRA tiles show up in the movie. I am sure everyone has been expecting this. Who says romantic comedies are predictable. If I have any say in the casting for this movie, I would have George Clooney play the part of the BCRA tiles. He would play a therapist, and would try to help are two hapless spectros to reconcile.
George "BCRA" Clooney does all the usual psychotherapeutic stuff, and there appears to be some agreement on the difference between beige and taupe. But, alas, the improved relations falter and once again the couple are disagreeing, in some cases louder than before. This is a totally unexpected turn of events in a romantic comedy, right?

The table below shows what happens when the BCRA tiles are brought in. Before standardization on the BCRA tiles (this is a fancy word for what us plebeians call calibration) we see median agreement of 0.35 ΔE, 0.66 ΔE, etc. on the four different test sets. 90th percentiles are in parentheses below. After standardization, we see that the 90th percentile agreement of the two instruments is much better than before - on the BCRA tiles, going from 1.84 down to 0.95 ΔE. 

But the other sets of samples? Not much improvement at all. The paint samples that were measured (the Behr samples) actually got much worse in the 90th percentile. Much worse,

Test set

Regression set
Pantone primaries
Pantone ramps
Behr ramps
Before standardization

So. George Clooney, favored because he is the analytical psychotherapist, and because he is just a darn sexy guy, has failed. Now we get the unexpected twist that is to be expected in all romantic comedies. Enter Owen Wilson, dufus extraordinaire.
Owen plays "Behr". He plays a dufus ne'er do well. In his normal inept way, he proves himself to be fully ept. in getting the pitiable instruments together. The tie in to the serious side of this blog is set of paint samples. I walked into a Home Depot. Please don't let them know, but I was just pretending to be buying paint. I looked at the Behr paint samples and selected a set based on being cute. (Get this... I selected Owen "Behr" Wilson because he is cute.)
The 24 colors in the Behr paint samples

The table below (bottom row) shows the results from using the Behr paint samples to standardize the instruments. Note that the worst case examples are all more better, and most are way more better.

Test set

Regression set
Pantone primaries
Pantone ramps
Behr ramps
Before standardization
Behr ramps

So, thanks to the help of Owen "Behr" Wilson, they lived happily ever after.

Scientific conclusions

Ok, now for something completely different. This is the serious part.

First, before Home Depot has a run on samples of the pretty color set, let me say that the set I chose was not scientifically chosen. In a totally uncharacteristic way, I actually told the truth about just picking out the samples based on being pretty. The set was nowhere near perfect. I am sure it could be optimized to make it smaller and more better. I am guessing this might happen.

Second, note that the improvement in inter-instrument agreement is not fabulous. I am guessing that better agreement might not be possible. Sorry.

Third, this experiment is a practical example of a point I made in a previous blog. Regression can go bad if you try to push it too far.

This blog post is derived from my paper, "Evaluation of Reference Materials for Standardization of Spectrophotometers", presented earlier this week at the Portland TAGA conference.

[1] Williams, Andy, “Inter-instrument agreement in colour and density measurement”, IFRA special report, May 2007

[2] Nussbaum, Peter, Jon Y. Hardeber, and Fritz Albregtsen, “Regression based characterization of color measurement instruments in printing application”, SPIE Color Imaging XVI, 2011

[3] Radencic, Greg, Eric Neumann, and Dr. Mark Bohan, “Spectrophotometer inter-instrument agreement on the color measured from reference and printed samples”, TAGA 2008

[4] Wyble, D. and D. C. Rich, “Evaluation of methods for verifying the performance of color-measuring instruments.  Part 2: Inter-instrument reproducibility”, Color Research and Application, 32, (3), 176-194

[5] ICC “Precision and Bias of Spectrocolorimeters”, ICC white paper 22

[6] Dolezalek, Fred, “Interinstrument agreement improvement”, Spectrocolorimeters, TC130, 2005

[7] Hagen, Eddy, “VIGC study on spectrophotometers reveals: instrument accuracy can be a nightmare”, Oct 10, 2008,

[8] X-Rite, “The new X-Rite standard for graphic arts (XRGA)”, CGATS N 1163

[9] Rich, Danny, “Graphic technology — Improving the inter-instrument agreement of spectrocolorimeters”, CGATS white paper, January 2004

[10] Van Aken, Harold, and Ronald Anderson, “Method for maintaining uniformity among color measuring instruments”, US patent 6,043,894

[11] All kidding aside, Danny is a great guy and has been a mentor to me. I am proud to be able to call him a friend. Here is an announcement of Danny being awarded the Robert F. Reed Technology Medal.