For years colorists, mathematicians, physicists and other scientists had sought a practical means of selecting the pigments and quantities of a starting point recipe that hopefully would produce a specific color. The goal was a non-metameric "match" or at least a batch close enough to be easily and quickly adjusted to get the desired results. Anyone with experience in color critical applications, faced with more than a basic palette of color choices, and lacking colorant content information of the standard color knows very well how valuable this automation would be. Let's go back a few years and explore the developmental history of some of the basic tools and concepts needed to get to this epitome of color creation. Hmmm..., maybe if we knew the standard reflectances.
Curve capability in 1929 drawn in 30 seconds! We are now able to measure the percent reflectance at various wavelengths and draw curves for our color of unknown composition. It is beyond the scope of this presentation, but an experienced colorist with an accurate curve can often make good guesses about the pigment or dye content of an unknown color - a rare skill seldom seen today. As my dear friend Ralph Stanziola (who nearly always started his presentations talking about curves) said, "The curve tells you a lot about a color and every color has a curve".
Notice also that the article says the spectro is used to match colors without the human eye playing any part. Pretty optimistic for 1929! All I can say is, "Are we there yet?"
Been there, done that - make sure your sound is on.
I was not alone, no visual standard at all! - Click for more info.
OK, now we have a curve. What can we do with our new found information? 1931 was a pretty good year and a lot of pretty smart people were working to answer this question. They came up with a way to use the curve of a standard, the energy information for a particular light, and some characterization of the human observer to assign three numeric parameters (X, Y & Z) that define the standard's color in a particular light. Click for more detail So everyone was playing with the same size ball, the energy information for several lights were standardized along with the tabulated numbers to be used for the observer. These became the famous 1931 CIE 2 Degree Observer along with the most common, surviving Illuminants A and C. For the first time in color history we are able to assign numeric descriptions to a color as well as calculate the geometric distance between points representing two different colors, Delta E. Colorimetry was born. How we should calculate this delta E, how does it relate to what we see, and what DE is an acceptable match are issues still being debated yet today, over eighty years later!
This is very nice, but what does it have to do with our problem? Well, maybe not a lot since we haven't determined what role the light plays in this whole issue. We'll consider for the moment that two colors with identical curves will be the same color and proceed from there.
According to Kubelka-Munk as simplified for the above case, the percent reflectance at a given wavelength of the light moving up can be calculated as R=1+(K/S)-[(K/S)2+2(K/S)]½. Conversely, if we know the R%, then (K/S)=(1-R)2/2R. We are making some progress now that we can relate the Hardy reflectance curve to these new scattering and absorption parameters, or at least their ratio. We can now fast forward 10 years or so to 1942 when Saunderson published details of a lot of his work and research on this issue.
Saunderson's color matching work was based on calculating colorant mixtures as sum of the products of concentrations times K or S for each colorant as applicable. In other words (the language of mathematicians), Kmix= C1K1+C2K2 +C3K3+...+CnKn and Smix= C1S1+C2S2 +C3S3+...+CnSn. Therefore, (K/S)mix= Kmix/Smix= (1-R)2/2R.
Remember that these summations apply to a single wavelength and may be quite different at any other visible wavelength. It is this selective (by wavelength) absorption and scattering that creates color in the first place.
At this point we still need to determine the K's and S's of our individual pigments. We know that white looks white because of near total scattering of all visible light with very little or no absorption at any wavelength. If we made mixes of our colored pigments with white, measured the reflectances, and did the math we would have a wealth of information from simpler equations, Kmix= CpKp+CwKw & Smix= CpSp+CwSw This might be a good way to start. Saunderson did all this and more and found the accuracy of his results were improved by correcting for the reflection of white light from the top surface and the portion of colored light being reflected repeatedly from both the top and bottom internal surfaces as shown above.
Further simplifying Kubelka-Munk to (K/S)mix= Cp(K/S)p+ Cw(K/S)w by using the (K/S) ratio as a single entity results in the single or one constant version. The earlier equations are known as the two constant method. This single constant application was used to create the analog "computer" shown above. This may have been developed as early as 1958 and was still marketed in 1967 when my employer purchased one of these machines as the color matching tool for a new manufacturing facility opened in 1966.
To operate the COMIC one dialed in standard data on 16 calibrated, multiturn pots, each producing a dot on the cathode ray tube. There was also a set of 16 for the batch, initially set to zero. Each colorant had its own box of 16 trim pots pre-adjusted during calibration to the values representing its K/S numbers (also done by dialing in values and adjusting each pot with a screwdriver while watching the dots move on the tube). One could then plug in up to 5 of these colorant boxes, each controlled by a multiturn pot that acted as a mixture concentration dial as it interacted with its related box. The combination of the boxes additively represented the summation of all the K/S data for their (electronic)mixture. The task was to twist and turn the 5 concentration dials to converge the dots and read the relative concentrations for initial batch. One then prepared the sample, dialed in the 16 batch numbers and if you hadn't moved the standard pots in the meantime and if the colors were the same, the dots would be together (not sure that ever happened). One could then start adjusting the pigment concentration pots to simulate additions and when again satisfied with the dots, read the batch corrections from the concentration dials. There was some provisions for calculating XYZ to aid the adjustment (in cases of metamerism where the dots cannot be converged) as I recall. This machine was definitely not suited for any high volume, precise color operation. I don't recall ever achieving any kind of practical utility from this machine other than a learning experience. In fact, higher management was really reluctant to invest in any more "comedies" to the extent that our company's computer color matching capabilities were pretty much dormant for maybe another 10 years.
We eventually had such success with our first DEC PDP based ACS (later Datacolor) system that we progressed to multi-user systems with remote work stations and we really entered the computer color matching age with units in several factories. These later evolved to networked IBM PC systems in the 80's and the rest is history. I'm getting a little ahead of myself here. As it turns out, our company may have really missed the "boat" so to speak, years earlier!
Davidson and Hemmendinger, acquired by Kohlmorgen in the mid-60's, developed a digital computer based color matching system known as the COMIC II in 1967 that was presented to the world at the 1968 NPE show in Chicago. The COMIC II has been traditionally accepted to be the first electronic digital computer based color matching system and its development would naturally be assumed to have included the first true electronic, digitally derived color match. Maybe not! Following are the first two pages of an eighteen page report issued on August 15, 1962 by Ray K. Winey. Pay particular attention to the recommendations #1!
My research indicated the Bendix G-20 to have been introduced in 1961 as the 32K words of 32 bit core memory, transistorized version of the G-15 with single and double precision floating point number as well as integer capability. It was a mainframe type computer produced until 1963 when Bendix sold computer division to Control Data Corporation.
The report details the methods and procedures used to evaluate color matching capability. Two different methods were used for determining K's and S's of the primary pigments, various concentrations and fixed at 10% pigment with white. There were also two methods for making the Kubelka-Munk implementation, 2 constant with and without Saunderson correction. These were combined to produce three methods called Calc 1 - various pigment letdowns, no Saunderson correction; Calc 2 - 10% letdown based on white + pigment, no Saunderson correction; Calc 3 - the previous 10% letdowns with Saunderson correction.
Reflectance data was computed at 17 points, 380 to 700 millimicrons (pre-Système International d'Unités nanometers) spaced at 20 mµ steps. The method for evaluating the quality of the curve match was the computation of the sum of the squares of deviations between the calculated and actual reflectances. A wise selection since no "one number fits all colors", visually related method for calculating DE existed at the time. (Still being debated today.) DE and even visual evaluation are really not necessary since a workable matching system with properly calibrated colorants, given a field of pigment choices including those in the unknown, should always very closely replicate its curve. That being said, those familiar with these issues will understand that even seemingly insignificant curve deviations can have an unexpected effect on both the DE and visual results.
On with the report. After pigment calibration (K's & S's), a sample was made from a test recipe containing three colored pigments plus white, referred to as yellow tan whose reflectance readings were measured. (On a Hardy/GE as described above.) Computer calculated reflectances were generated by the three methods and judged by RDEV2 described above. Calc 1 was not so good, Calc 2 best with Calc 3 not far behind. I calculated DECMC1 for these tables and found 2.31, 1.05, & 0.94. Not a mistake, the DE values were reversed from the RDEV2. Next was the best generated recipe from a field of 27 choices using Calc 1. This batch was made and measured showing table of actual R%'s. Apparently it must have been evaluated only visually since no RDEV2 was shown. My calculated DE was 2.62, not far from the 2.31 predicted by the evaluation trials. Next was a best of group of 8 Calc 2 recipe that was mixed, measured and tabulated. The results from this sample are shown next.
WOW!!! Two more computer matches were made for yellow tan, best of 64 using Calc 2 and Calc 3. These batches were not mixed but my DECMC1 calculations using the computer curves were 1.07 & 0.92. This entire procedure, including the method evaluations, was repeated for another color named red tan. As before the best of 8 Calc 2 was mixed and measured. Following are the deltas for that color.
This report contains standard and batch colorant formulations for an additional 16 colors along with actual color chips for visual comparison. There was no reflectance or RDEV2 data for any of these colors since it was of little value relative to the quality of the color match. My copy of the report shows only color copies of the real samples. Visually, none of the sample pairs exhibit anything out of line for color. It is doubtful that anyone can come forward with any prior efforts that approach the accuracy of this work. A cold start formulation first shot within this range is not the norm even with today's technology. What was Ray seeking anyway? A practical method he could use everyday in his job of producing accurate, non-metameric, close tolerance color matches. I would like to see evidence that any other such system existed at the time!
Nearly 10 years later Ray was still "hanging them on the horns of a dilemma", one of his favorite methods of ending a debate. Although the product now incorporated a fluorescent source, they still didn't understand the metamerism problems facing a colorist devoid of spectral information. Consider the following letter:
The paper, Color Matching--Macbeth-Reese, referenced in Ray's letter follows. It seems that a fluorescent third source was added after 40 years and although in its infancy is working well. That being said, the problem colors where it would be needed are few and far between and are seldom encountered! As seen by Ray's margin notes, the words few and seldom need clarification! The enclosed article mentioned in support of Ray's statement was from ACTA CHROMATICA, Volume 1, Number 1, October, 1962, entitled Metameric Object Colors by Gunter Wyszecki. It is not shown in this presentation but states that metamers are colors with same XYZ's that are not similar spectrally. It follows that changing the function used to calculate the tristimulus values (via illuminant change) will result in computing different XYZ's that are not equal.
The evidence presented here is pretty conclusive that Ray's undaunted quest in this matter resulted in reluctant acceptance by Macbeth that a third light source of a fluorescent nature was needed. He was undoubtedly the primary mover that all color examination lights include a fluorescent source today. In 1995, while searching the web, I came upon the Macbeth web site where they repeated the same erroneous statements regarding the two source examination. I emailed a copy of Ray's letter to them but never received any response. Unlike Ray, I didn't follow up or pursue the issue any further and that's the end of my story.