Monday, November 16, 2009

Color Creeks Ray Winey Has Found People Up

Bill Longley, Adjunct Professor, Eastern Michigan University
Retired, Ford Motor Co.

[Who was the first to perform colorant formulation on a digital computer? Bill Longley here makes the case that---at least in the U.S.---it was his mentor, Ray K. Winey. Winey is also known for the metameric specimens he made, which screamed, “Matching under two lights is not enough!” It is hard to make metamers, and also to convince people to avoid mistakes in color science, yet Winey did both. - MHB]


I had the rare good luck after graduating from college in 1958 to work under direction of Ray K. Winey at US Rubber Co (later Uniroyal) in coloring of Naugahyde upholstery material. Ray had majored in chemistry at Notre Dame and spent his career in Mishawaka, Indiana, never wanting to wander very far. When he spotted an interesting conference he would send one of us and then eagerly debrief us upon our return. Ray, now deceased, was a genius with an intriguing grasp of poetry as well as battlefield war strategy. His recall and passion for all aspects of color science was overwhelming to color chemists who came under his direction.

Davidson & Hemmendinger had introduced the COMIC, an analog computer with wavelength/reflectance scope which aided the colorist in developing initial colorant formulations. I persuaded Ray to make the short drive to Chicago to see COMIC at an equipment show. Here we met Henry Hemmendinger, who patiently demonstrated COMIC for the umpteenth time that day. Ray folded his arms and commented, “Very interesting, but I prefer the digital approach.” Henry wanted more discussion, so he called for assistance with the exhibit and then he and Ray moved to a nearby table and launched into an unforgettable session.

Ray summarized his work on digital computer matching in a company report [1] dated 15 August 1962, complete with color standards and resulting swatch matches. The report discusses limitations of analog computing, especially assumption of zero scattering. Rather than requiring the colorist to select pigments for the match, Ray directed the program to consider all possibilities of 3 pigments plus white, and then report the matches with least spectral differences. If dissatisfied with results, he could direct the program to add a fourth pigment. Ray’s report cites Kubelka-Munk and computes relative K and S coefficients, 10 parts TiO2 to one part color pigment. He relates reflection to K/S ratio using the Saunderson surface correction. Computing was slow so he loaded data into the Bendix G20 at close of office hours and collected results the next morning. Contemporaries in the field who have seen a copy of the report have marveled at digitally calculated two-constant theory at that early date. It wasn’t until five years later that D&H offered the COMIC II digital computation unit.

Details and comments on the report are offered by another Winey protégé, Ron Penrod, at www.rpdms.com. Site viewers will also find there an excellent color matching program, workable in four modes with conversions. [Editor’s note: Do any readers know if E. Atherton’s program from the UK (reported in 1961 J. Soc. Dyers Col., and reputed to have run since 1956) had the capabilities described here?]

Ralph Stanziola and Max Saltzman were among many who visited Ray in Mishawaka. He enjoyed showing visitors his “dilemma” samples (two metameric swatches), asking how the visitor would add a correction to the metameric mismatch that was redder than the standard in daylight and greener in tungsten. Told this was impossible, he then presented another swatch containing pigments that flared green to the standard in daylight and red in tungsten. In fact this is how the standard had been made.

Ray had some classic correspondence with Norman Macbeth and Warren Reese concerning Macbeth claims for their industrial light-source unit, that samples matching in D7500 daylight (blue end) and D2300 tungsten (yellow end) would match anywhere. Ray produced numerous samples to disprove the claim. Eventually Macbeth added cool white fluorescent as a third source for matching, also standardizing on D6500 daylight. I like to think that Ray provided the impetus.

I offer these notes here to credit Ray for his pioneering work in color science. I inherited Ray’s “golden” files and sometimes wonder what to do with the intriguing letters and metameric specimens. I have his hand-written note saying he wanted to write a book Color Creeks I Have Found People Up. He never wrote the book, but certainly had enough material for it.


1. D. F. Larimore and R. K. Winey, "Color Matching with the Aid of a Digital Computer," Report No. 62-L3-35, US Rubber Co., Divisional Laboratories, Consumer and Industrial Products Division, Mishawaka, Indiana, 15 August 1962.

Friday, September 25, 2009

C. V. Raman’s Explorations in Color Science

by Michael H. Brill, Datacolor

This year (and hopefully this month) will mark the end of my ten-year chairmanship of CIE TC1-56, during which I found that the laws of color matching are not so simple as Hermann Grassmann thought. Is color science possible without Grassmann’s underpinnings? To find out, I look at a little-known corner of history….

Chandrasekhar Venkata (C. V.) Raman (1888-1970) was always interested in the science of color. Indeed, that interest seemed to motivate his Nobel-Prize-winning work in spectroscopy. A 1921 trip returning to India from England made him marvel at the blue of the ocean, and to posit that blue as arising from molecular scattering of light by water molecules, not just reflection of the blue of the sky (as Lord Rayleigh supposed). By 1928, Raman found that blue light through glycerin had a shift to the green, and that the shift was due to quantum transitions in molecular electron states. Raman spectroscopy was soon born, quantum mechanics and the photon theory of light were vindicated, and the Nobel Prize followed two years later.

In 1959, after a fruitful career in optics, acoustics, and the interaction of light with sound waves, Raman turned his attention exclusively to color, including the colors of plants and minerals and color blindness. He used only a pocket spectroscope, some black-and-white photographic film, and a few functional human visual systems. The color-science period of his life was to last more then ten years, and gave rise to many publications in the annals of the Indian Academy of Sciences in Bangalore. I found one book of this work [1] on a shelf in Datacolor earlier this year, and a Google search revealed this work and a lot more, on individual pdf pages from the Indian Academy of Sciences. Even partial retrieval of the work was painful, but it was worthwhile and timely for me.

Here is a quote from a 1966 work [2]:
“It is a remarkable fact that a person endowed with normal vision is capable of recognizing quite small differences in colour if these are presented to him in an appropriate fashion. For example, the two yellow lines in the spectrum of a mercury lamp, whose wavelengths are respectively 5770 Å and 5790 Å and which are of equal intensity when seen simultaneously through the eye-piece of a spectrometer exhibit an observable difference in colour, the former line appearing of a greenish hue while the latter is a pure yellow. This fact suggested to the author that an arrangement by which the entire continuous spectrum is presented as a series of discrete lines would be a useful device for the study of the spectrum colours and especially for exhibiting the differences in the rate of progression of colour in different parts of the spectrum.
“The idea indicated above can be realized in practice by setting two half-silvered plates of glass in parallel positions before the slit of a wave-length spectrometer and viewing the spectrum of a brilliant source of white light of restricted area normally through the combination. The entire spectrum is then seen as an array of discrete lines or bands in a dark field, their number and spacing being determined by the separation between the plates. By making one of the plates movable with respect to the other, the number of lines or bands seen in the spectrum can be varied within wide limits. […] A channeled spectrum of 100 bands […] was presented.” (p. 269)
“ A remarkable and convincing demonstration that Daltonian vision arises by reason of an abnormal enhancement of the sensation of yellow in relation to other colours in the spectrum…” (p. 270)

This work is experimentally ingenious. I’m especially impressed with Raman’s recognition of (and use of) the subtle property of human vision that enhances the discrimination of colors when they are separated by a dark boundary. But something is missing in the description. There’s no mention of trichromacy, none of the heritage of Newton, Young, Helmholtz, or Hering. That seems to be true of all of Raman’s work. And of course, Grassmann’s laws are also absent from the discussion

How could a 20th century physics Nobelist devote ten years to color research and write copious articles without once referring to the trichromacy of color vision? Perhaps the answer can be found in Raman’s famous 1968 lecture, “Why the sky is blue” [3]. Here, Raman recounts the familiar Rayleigh-scattering story, but adds much more. Why don’t we see the stars during the day? Because the atmosphere of the earth is a veil that hides them by scattering the Sun’s light. Why isn’t the sky blue on a moonlit night (for which the same spectrum acts in an attenuated form)? Well, here Raman isn’t so sure. He says it’s a difficult question why we don’t see colors at night. He never mentions rods and cones, or of the body of literature that culminated in the same year with Yves LeGrand’s second edition of Light, Color, and Vision. And yet Raman espouses a holistic philosophy of science: “Ultimately you find that you have to travel the whole field of science before you get the answer to the question: Why the sky is blue?” Another quote reveals how exploratory he is willing to be: “To get any colour, red, green, or blue, you have to take out the yellow. Yellow is the deadly enemy of colour.” Later, he seems to be getting closer to opponent-color theory: “It is the reduction of the yellow of the spectrum that is to say the predominance of the blue which is responsible for the blue light of the sky.” But here’s the final take-home lesson: “I want you to realize that the spirit of science is not finding short and quick answers. The spirit of science is to delve deeper.” I will guess that Raman was well aware of rods, cones, and trichromatic theory, but felt he had not been able to delve deeper, to add as much to the vision explanation as he had to the simple one-sentence “Rayleigh scattering” answer to “Why is the sky blue?”

Well, Dr. Raman, I am ready to delve deeper now that TC1-56 is at its end. Simple sound bites such as “linearity” and “trichromacy” aren’t going to cut it anymore.

1. “Memoirs of the Raman Research Institute No. 137: Floral Colours and the Physiology of Vision”, by Sir C. V. Raman (Bangalore, 1963); pp. 57-108.

2. C. V. Raman, The New Physiology of Vision, Chapter XXXIX. Daltonian Colour Vision, J. Indian Academy of Sciences, pp. 267-274 (1966). http://www.ias.ac.in/jarch/proca/63/00000280.pdf and subsequent pages (last 3 digits in filename).

3. C. V. Raman, “Why the Sky is Blue,” Lecture Dec. 22, 1968 at Ahmedabad. http://dspace.rri.res.in/bitstream/2289/1509/1/1968%20(Dec.%2022)%20Raman's%20Lecture%20-%20Ahmedabad.pdf

Tuesday, July 21, 2009

Color and Thesauruses

by Nathan R. Moroney, HP Labs

At the recent MCSL 25th Anniversary Symposium, Nathan Moroney showed us a “book with 5000 authors” comprising color names printed in colors that denote their synonyms. The 5000 authors were contributors to his on-line color thesaurus. Here are more details from Nathan ...

Is the color “zaofulvin” synonymous with “orpiment” or “smalt”?
The 1911 edition of Roget’s Thesaurus1, which early-on attempted to cluster color names, has an answer.

As you can see from Table 1, “zaofulvin” and “orpiment” are synonyms.











WhiteNiveous
Canescent
Lactescent
BlackAtramentous
Fulginous
GrayFavillous
Cinereous
BrownCasteneous
Fuscous
RedAnotto
Realgar
Minium
GreenVerdine
Copperas
YellowOrpiment
Zaofulvin
Luteous
PurpleGridelin
Heliotrope
BlueBice
Zaffer
Smalt
OrangeGild
Ocherous

But if a thesaurus is “a resource to group words according to similarity”2 then how are we to judge the similarity of words, and particularly of color names? Kilgarriff2 summarizes the contrasting methods of manual creation (e.g., for Roget’s Thesaurus) with the automatic extraction from corpora or large collections of machine-encoded text. He also emphasizes that, besides grouping words according to similarity, a thesaurus should also indicate how frequently each word is used.

The ISCC-NBS color dictionary3 significantly advanced the grouping of color names by providing about 300 name categories for over 7,500 color names taken from 13 different earlier color dictionaries and vocabularies. This work partitions Munsell color space for the core vocabulary and maps it to the larger collection of earlier color-name collections. This is a hybrid approach that merges multiple manual efforts into a single manual or expert framework.

Modern efforts at thesaurus creation through automatic extraction are making progress, but experiments with nine similarity metrics show4 that much more work is needed. Some of the challenge is to have a large enough collection of text for analysis. However, size alone is not the solution. For instance, the very large Moby Thesaurus5 returns “pineapple” and “pear” as synonyms for “orange”, thereby apparently including the fruit meaning with the color-name meaning.

An alternative approach is the direction construction of a specific color naming corpus using the World Wide Web. For the past eight years, I collected over 35,000 color names from over 5,000 online volunteers. Each volunteer named seven randomly generated colored patches displayed on a white background. The colors were selected from a uniform red, green and blue sampling of what was at the time the “web-safe” palette for lower bit-depth displays. Of these 35,000 color names, many are used repeatedly. Assuming an imposed minimum of three participants to provide a specific color name, the program derives over 600 color names. Using these names as an initial collection, it computes synonyms by finding the closest color names in a corresponding color space. It also finds the color names that are closest to the inverses in hue and lightness as possible color antonyms. Finally, because the data are collected from thousands of participants, the program infers the relative frequency of use. In this way, we created a color thesaurus that is closest to an aggregate or collective clustering of colors across a large number of English speakers.

This data is formatted as a web-based color thesaurus,6 which has been well received by online users. It has served almost 200,000 color names to date --- although zaofulvin and orpiment are not included.

(1) Peter Mark Roget, Roget's Thesaurus (1911), Project Gutenberg edition, http://www.gutenberg.org/etext/10681, retrieved May 2009.

(2) Adam Kilgarriff, "Thesauruses for Natural Language Processing", Proc. Natural Language Processing and Knowledge Engineering, p. 5-13, (2003)

(3) Kenneth L. Kelly and Deane B. Judd, The ISCC-NBS Method of Designating Colors and a Dictionary of Color Names, National Bureau of Standards Circular 553, (1965).

(4) James R. Curran and Marc Moens, "Improvements in Automatic Thesaurus Extraction", Unsupervised Lexical Aquisition: Proceedings of the Workshop of the ACL Special Interest Group on the Lexicon (SIGLEX), Philadelphia, Association for Computational Linguistics, pp. 59-116, (July 2002).

(5) Moby Thesaurus – online interactive version from dict.org, http://www.dict.org/bin/Dict?Form=Dict3&Database=moby-thes , results retrieved May 2009.

(6) The Online Color Thesaurus - http://www.hpl.hp.com/personal/Nathan_Moroney/color-thesaurus.html.

Tuesday, May 26, 2009

Lessons from Eastman Kodak in the Great Depression

by Michael H. Brill, Datacolor

We know 1931 as the birth-year of the ISCC and of the CIE Standard Observer, but others associate that year with the Great Depression. Color science seems to have matured and thrived during the Depression years, and in particular we can learn many things….

Great wine thrives in a dry season, and great color science has thrived in times of economic downturn. Eastman Kodak thrived twice in this way before most of us were born. The first time was in the 1890s, when the panic was about redeeming securities for gold (of which there was not enough). In Rochester, a backwater with no particular natural resources, Kodak produced its Brownie and Folding Pocket cameras. Photography took off.

Then, in the Great Depression of the 1930s (whose circumstances are more familiar to us), color photography took off. The ingredients were present well in advance: Invention of the subtractive technique by Cros and Ducos du Hauron (1869), and CMY color separations that required three separate shots for one picture (or three beam-split images in register). Rudolf Fischer’s discovery of dye-coupling (1912) was critical, but lay in hibernation until, in 1935, Mannes and Godowsky at Kodak (locally known as “Man and God”) invented three-layer subtractive-color film that enabled a full color photo in a single shot. At that point Kodachrome film was born [1]. There followed in 1937 and 1938 a number of top-notch color-photography articles [e.g., J. A. C. Yule, J. Opt. Soc. Am. 28, 419-426 (1938); D. L. MacAdam, J. Opt. Soc. Am. 28, 466-480 (1938); D. L. MacAdam, J. Opt. Soc. Am. 28, 399-418 (1938); A.C. Hardy and F. L. Wurzburg, J. Opt. Soc Am. 27, 227-240 (1937).]

Credit is of course due to the inventors of Kodachrome and to the authors of these articles, but also credit belongs to the direction of the Kodak laboratories by C. E. K. Mees, author of many books on organization management as well as on photography. Much constructive incubation was happening during the bad years. Together with a keen sense of what is needed to “prime the pump” during such years, Mees had a perspective of science and technology as being in a reciprocal relationship. Martin Scott [2] has said, “Paraphrasing Mees: ‘Science has been good to Photography, and Photography should be good to Science.’ Guided by that motto, he made many special films and emulsions for scientists with no regard for profitability.”

Credit for Kodak’s success accrues to an even higher managerial level. It must not be forgotten that, in 1931, Kodak and 13 other companies fostered what was known as the Rochester plan [3]---a system of unemployment insurance that came some years before Roosevelt’s national plan. Because only 14 companies participated, the plan lasted only a few years, but it managed to cushion the blow to unemployed workers from 1933 to 1935, and Kodak didn’t need it by 1936. (Presumably Kodachrome helped here.) Notable in the implementation of the Rochester plan was a curious confluence of pragmatism and compassion: “Just before implementation of the Rochester Plan, corporate executives at Kodak let plant managers know that they would be held accountable for future unemployment and that it would not reflect favorably upon them if benefit payments were too high.“ [3] Big bonuses were not linked with layoffs...then. Another difference from our recent experiences nationally: Kodak stockpiled inventory and redirected people to increase this inventory during lean times. This is the exact opposite of “just-in-time” delivery, and helped decrease the need for seasonal layoffs (and perhaps longer-term effects as well).

Of course, part of the credit for Kodak’s success during the 1930s belongs to circumstance. During other economic downturns, Kodak learned how to stockpile inventory, respect research, and reward employee retention. Part of the circumstance was the extreme profitability of photographic film---which has lately become somewhat obsolete.

What can we learn for today from Kodak’s Depression experience? Do our lean inventories and draconian logistics destabilize our corporate survivability? Do AIG-style bonuses de-incentivize economic prudence? Does “just-in-time” research undermine longer-term goals? Maybe we should just leave this alone and paraphrase Freud: Sometimes a roll of film is just a roll of film.

I would like to adopt Martin Scott’s positive note that may inform other answers: “Five hundred years of letterpress; fifty years of lithography; and now, how many years of the new technologies? If I've learned anything, it is not to predict, and especially don't presume to know the rate of change.”

Michael H. Brill

[1] Beaumont Newhall, The History of Photography,” Museum of Modern Art, New York, 1964, p. 193.

[2] Martin L Scott, “Introduction: Images for Science,” Images from Science 2, June 2008, http://www.rit.edu/cias/ritphoto/ifs-2008/about_IFS.html

[3] Richard E. Noll, “Marion B. Folsom and the Rochester Plan of 1931,” Rochester History (Vol. 61, 1999), Ed. Ruth Rosenberg Naparsteck.

Friday, April 10, 2009

Language and color perception

by Terry Regier, University of Chicago and Paul Kay, University of California at Berkeley

[At the 2007 IS&T/SID Color Imaging Conference, Terry Regier gave a keynote address on how color discrimination is influenced by linguistic categories in the right but not in the left visual field. Now he revisits the topic with noted color/language expert Paul Kay. While reading, you might contemplate, how do I try this at home? - MHB ]

Does language affect perception, or not? The yes-or-no framing of this question obscures an interesting possibility. Several recent studies on color suggest that language does indeed affect perception (or at least perceptual discrimination) – but it does so primarily in the right visual field (RVF), and much less if at all in the left visual field (LVF), a pattern suggested by the functional organization of the brain. Thus, half of our perceptual world is viewed through our native language, and half is viewed without a linguistic filter.

This pattern was first shown in a study [1] that probed the discrimination of colors straddling the boundary between green and blue, a boundary present in English but absent in many other languages. The study found evidence for categorical perception of color – faster discrimination of colors from different categories – but only in the RVF, not in the LVF. This lateralization was disrupted by a concurrent task that interfered with verbal processing, but not by a concurrent task of comparable difficulty that interfered only with non-verbal processing – suggesting that the pattern is verbal in origin. Other studies replicated and extended this finding, exploring the cross-cultural and developmental origins of our tendency to view half of our visual world through language, and half of it less so if at all.

If color categories affect perception, at least in half the visual field, where do those categories come from? Why do languages have the color categories they do? An influential universalist view of color naming holds that color categories across languages are organized around the universal focal colors black, white, red, green, yellow, and blue. A recent relativist challenge holds in contrast that there are no such universal foci, and that color categories are defined at their boundaries by largely arbitrary linguistic convention. Both of these views are partly supported and partly challenged by existing data, which show universal tendencies in color naming, coupled with interesting cross-language variation of category boundaries.

This complex picture can be accounted for starting with the observation that perceptual color space is irregular, in the sense that the maximum possible saturation varies unevenly across hue/lightness combinations. One proposal [2] is that color naming reflects optimal or near-optimal partitions of this irregular space. Recently, this idea was formalized and tested against empirical data [3]. A well-formedness measure was defined that captures the extent to which a given categorical partition of color space maximizes perceptual similarity within color categories and minimizes it across categories. Across the 110 languages of the World Color Survey – a database of color naming from non-industrialized societies worldwide – color naming tended to be near-optimal in well-formedness. At the same time, linguistic convention may get some wiggle room: Often, similar but different partitions are roughly equally well-formed, suggesting a middle ground between “nature” and “nurture” in color naming across languages.

Neither of these findings – that language affects color perception primarily in the right visual field, or that color naming is near-optimal – is anticipated by the traditional universalist-versus-relativist debate over language and perception. Instead, these findings suggest novel perspectives on the relation of language and perception.


[1] A. Gilbert et al. (2006). Whorf hypothesis is supported in the right visual field but not the left. PNAS 103, 489-494.
[2] K. Jameson & R. D’Andrade (1997). “It’s not really red, green, yellow and blue: an inquiry into perceptual color space,” in Color Categories in Thought and Language, C. L. Hardin and L. Maffi (eds.), Cambridge University Press, 295-319.
[3] T. Regier et al. (2007). Color naming reflects optimal partitions of color space. PNAS 104, 1436-1441.

Friday, February 13, 2009

Feynman’s Paint-Mixing Problem


Physics Nobel Laureate Richard Feynman not only played bongo drums in nightclubs, but also wrote two chapters on color and vision in his Lectures on Physics. And that’s not all: There’s also…

Feynman’s Paint-Mixing Problem

Richard Feynman tells an interesting story [1] about revealing a painter's trick in mixing red and white paint to get yellow. Here's how it goes:

Feynman: "I don't know how you get yellow without using yellow."
Painter: "Well, if you mix red and white, you'll get yellow."
Feynman: "Are you sure you don't mean pink?"
Painter: "No, you'll get yellow."
Feynman: "It must be some kind of chemical change. Were you using some special pigments that make a chemical change?"
Painter: "No. Any old pigments will work."

So Feynman got a can of red and a can of white paint, and the painter began to mix them. It kept looking pink to Feynman. But then:

Painter: "I used to have a little tube of yellow here, to sharpen it up a bit---then this'll be yellow."
Feynman: "Oh! Of course! You add yellow, and you can get yellow, but you couldn't do it without the yellow."

Touché. Feynman wins.

But did he really? I remember looking at a white wall through a vial of yellow food-coloring liquid, and seeing it as red. That’s because the transmission spectrum goes from very low at the short-wavelength (blue) end of the spectrum to nearly 1 at the long-wavelength (red) end of the spectrum. As one piles on more layers of the same fluid, the transmission spectrum multiplies by itself wavelength-by-wavelength (an action known as Beer’s law, which by coincidence also happens when you look through beer). Therefore, at the wavelength where one ply of the liquid transmits half the incident energy, two ply of the liquid transmits only 1/4 of the energy. On the other hand, at wavelengths where one ply transmits all the energy, two ply will transmit all the energy as well. For a transmission coefficient that increases monotonically in wavelength (such as most yellows), the transmitted-light spectrum becomes biased toward longer wavelengths (i.e., is redder) when the layer is thicker.

So there’s at least one way red and white can will mix to give yellow: a clear diluting vehicle for the white and a red Beer's-law ink that transmits enough light at medium wavelengths so it yellows up when you see through less of it. Of course, you must have a reflecting background---let's make it matte white. As a numerical example, suppose a unit optical thickness of the red ink has transmittance zero for wavelengths below 540 nm, t for wavelengths between 540 and 640 nm, and 1 for wavelengths above 640 nm. The light reflected from the background through a unit thickness of ink can then be represented as the triplet (0, t2, 1). That triplet will change to (0, t2x, 1) when the optical thickness is changed to x. A deep red ink will have, say, t2 = 0.1, whereupon ten-fold dilution of the ink (x = 0.1) will produce t2x = 0.7943. The layer will therefore be substantially yellow.

You can also do this exercise (at least theoretically) with opaque red and white paints that obey Kubelka-Munk mixture algebra. [2]. I’ll elaborate about that in a future publication.

It seems, then, that the painter could have made a yellow by mixing particular red and white paints, contrary to Feynman’s intuition. But it certainly couldn’t be expected for all reds and whites as asserted by the painter. For example, drinkers of red wine (instead of beer) won’t see the yellowing effect---diluted red wine looks pink, not yellowish. Why should wine obey Feynman’s intuition where beer does not? The subject is worth much experimentation. Care to join me?

[1] R. P. Feynman and R. Leighton, Surely You're Joking, Mr. Feynman (Norton, New York, 1997), pp. 82-83.
[2] G. Wyszecki and W. S. Stiles, Color Science, (2nd Ed., Wiley, New York, 1982), p. 785.

Michael H. Brill, Datacolor