In the last post, Part One, we left off with two facts: We depend on a numerical description of color and color difference rather than judging a sample vs. a standard visually; and NCCA began to investigate ΔE_{2000} to determine how well it might work in the coil industry.

Let’s start Part Two with a short discussion on ΔE_{2000}. It is way more than the usual ΔE with a little “2000” as a subscript. (If only it were that easy.) Our current ΔE is a straightforward root-mean-squared calculation, as shown here:

ΔE_{Hunter} = [(L_{2}-L_{1})^{2} + (a_{2}-a_{1})^{2} + (b_{2}-b_{1})^{2}]^{1/2}

This sweet little formula has served us well for 50+ years. In a sense, it is simply measuring the distance between two points in three-dimensional space. It works, *usually*, but we know that we cannot use the standard ΔE when it comes to saturated colors. ΔE_{2000} was created to overcome the deficiencies of ΔE. Color scientists have known for decades that a good approach to color *must* factor in the human response to color, which means we need humans to weigh-in with opinions on sets of panels and the color differences associated with these sets. Our current ΔE does not consider anything other than a machine’s response to color, which, admittedly, is better than nothing—and it’s worked for us for a long time.

As color scientists attempted to create a better system, the first thing they did was to gather a bunch of observers and have them participate in Just Noticeable Difference (JND) color experiments. As the name suggests, the scientists wanted to learn something about that point at which a difference can be detected. A JND experiment can be done for color, smell, taste, etc. In the case for color, the scientists gathered the JND data from visual observations and then wrapped a lot of math around the results to create a color difference system that starts with people and ends with data. That’s what ΔE_{2000} is all about. (At the end of this post you will find the formula to calculate ΔE_{2000}). But to learn if this color difference system would be appropriate for our coil-coating industry, we had to do our own JND experiment. And the first thing we did was to gather panel pairs for which observers would rate the color differences.

But first let me reiterate a point because it is the crux of the issue: A simple RMS ΔE calculation, whether using Hunter or CIE color space, is a mathematical calculation based on a machines response to the color of a standard and a sample. ΔE_{2000}, on the other hand, is a mathematical calculation based on *human* response to color differences. And humans see color differently, so there is nothing simple about a ΔE_{2000} calculation. (You’ll see the calculation at the end of this blog.)

For the NCCA color study, we gathered 323 panels and eventually distilled the number down to 108 panels, or 54 color pairs. A pair of panels, therefore, are two panels, close in color to each other. We collected and stored the spectral data on everything so we could make a proper evaluation of human vs. machine response to color differences. In an effort to test the repeatability of an observer’s observations, 15 sets (pairs) of panels were repeated. In other words, we had 39 unique panel pairs, and of these 39 pairs 15 were selected for repeat observations. If you think this might be a little sneaky, wait…there’s more. Of the 39 unique pairs, 8 of the pairs were *identical*. Yep, we took a panel, cut it in half, taped the halves together, and asked the observers to rate the color difference between the panels.

We took our experiment to METALCON (Las Vegas, 2017), where 28 observers participated in our experiment. That might not seem like a lot, but each observer took about 20-30 minutes to review the entire set of panels. The METALCON show was 15 hours long and spread over three days, and we worked with observers—nonstop—for 13 of those 15 hours.

The NCCA Color Project at METALCON 2017

And what did we learn? Stay tuned for the next blog post, Part Three.

David Cocuzzi

NCCA Technical Director

As promised, here is the calculation for ΔE_{2000}. Good luck! If you look really hard, you will find the usual L, a, and b terms, along with many other terms that I do not profess to completely understand.