Art Classes with Marc Surrency
If we create a positive from this negative, we get a record of everything not red - or a record of the mixture of blue and green light (cyan). For a printing press this would be the cyan printing plate.
In this manner we can use the negative to provide information about the each additive primary's corresponding complement (the subtractive primary). Remember for printing, we need to know the location of the subtractive primaries, cyan, yellow, and magenta. For example, the negative created from the red filtered light contains all of the information about the red light, but a positive made from this negative contains all of the information about it's complement - cyan.
So here's the theory in action. We photograph the wheel using red, green, and blue filters separately creating separation negative for each additive primary color. Each additive primary color (RGB) negative provides the positive for the corresponding subtractive primary (CYM). Positives are made from each negative. For lithographic printing these positives would be the printing plates. A black printing plate would be added to increase contrast (all three additive primaries combined only give gray). The subtractive colors are recombined to give a color image.
These color wheels are the foundations for color photographic reproduction as well as video and computer screens. they are extremely important scientifically and explain some of the problems encountered in mixing paints. However, these color wheels may not be intuitive and sometimes prove cumbersome to use for painting. But more on this later.
2.1 Color Matching
One of the main needs for the ability to describe color is color matching. This is this is the main reason why artist, textile manufactures, painters and other professions and trades where so interested and driven to standardize color descriptions in the first place. It remains today as one of the most popular use of the various color description systems. People still need to match paint manufactured today to paint manufactured a year ago, or printing inks for accurate color reproductions, or dyes for clothing; the list is endless. The first type of standardization of color was performed by creating a set of reference colors and matching the desired color to a reference color. The reference color, in turn, was used as a guide in creating the desired color. The next step in standardization came by arranging the colors in a systematic manner; by hue (blue, green, red, etc.), saturation or chroma (paleness or vividness), and value (lightness, darkness). Any two of the three components can be represented two-dimensionally, but for all three values to be represented simultaneously, three dimensions are required; the introduction of the color solids.
2.1a Color Solids
Most color solids are formed by creating a circle out of the visual spectrum by connecting the ends of the spectrum (blue and red) together, which becomes an equator of hues. Sir Issac Newton was the first to create this solid representation which so many artist think of as the color wheel. The third axis is created by a line passing through the polar axis, and represents brightness ranging from black through tones of grey to white (value). As colors shift radially from the center of the solid toward the edge, they become more saturated (chroma). The most well known and used solids were created by Ostwald and Munsell.
2.1b Ostwald’s Solid
Ostwald's solid is arranged as double cone and is based on 24 hues arranged around the circumference. Each hue is combined in fixed proportions with each of 8 equally spaced neutral values ranging from black to white. Ostwald’s solid, therefore, is based on pigment ratios creating the saturation steps.(Billmeyer, pp.26-28; Rossotti, pp.144-150)
Ostwald’s' Solid and X-section
2.1c Munsell’s Solid
Munsell's solid is arranged so that increasing saturation is created by a series of visually equal steps and contains nine neutral colors. The number of steps to maximum saturated depends on the value and hue, which results in an unsymmetrical solid often called a color tree.(Billmeyer, pp.30-35,52; Rossoti, pp.144-148)
Munsell's solid, pole view and x section
Both Ostwald and Munsell's systems rely on the observer matching a color to a reference color, which is still a subjective measurement. Although the color is matched to a reference color, which has been defined by its chroma, value and hue, the observer and light source, still have not been defined. Since the reference and the color are being lit by the same source and observer, isn't the source and observer parts of the equation canceled out? The answer is yes and no. Since the observer and the source are the same for the matched color sample and reference sample, the difference can be ignored, but they still must be defined. Metamerism is a perfect example why the source and observer are always critical to color matching and definition.
2.2 Tristimulus Colorimetry
2.2a Maxwell’s System
A system that addresses the observer and source, as well as, value, chroma, and hue, in defining a color is based on Tristimulus Colorimetry. In 1855, Maxwell found that most colors either emitted or reflected could be matched by mixing three primary colored light sources. The matching took place in a darkened room, where he projected equally-balanced white light to the object he was trying to match. Three lights (red, green, and blue) with rheostats, were to control their intensity, were arranged so that their beams would be superimposed onto a neutral screen. Colors where matched by adjusting the intensities or amounts of light projected onto the screen. He found that he could match most of the colors in hue, but not saturation. His system for describing color as a combination of three light sources was the foundations for the system widely used today. (Rossotti, pp.153-157)
Maxwell Color Triangle
Mathematically the coordinates are determined as follows: the color reflected by an object (C) or (λ) is composed of a mixture of varying intensities of red (R), blue (B) and green (G) light. (R),(G), and (B) are the intensity or amount of primary colors. The distribution coefficients for those primary colors are derived by expressing the light intensity as a fraction of the total luminescence.
C(λ) = R(R)+G(G)+B(B),
where R,G,B, are the amounts of colors present and (R)+(B)+(C) = 1.
C(λ) = R(R)+G(G)+B(B) and C(λ) = R(R)+G(G)+B(B)
1.0(λ) = R(R)/C+G(G)/C+B(B)/C and C= R+G+B
1.0(λ) =)+G(G)/( R+G+B)+B(B)/( R+G+B)
1.0(λ) = r(R)+g(G)+b(B)
r= R/(R+G+B), g=G/(R+G+B), and b=B/(R+G+B)
2.2b CIE Colorimetry
In 1931, the Commission International de l’Eclairage (CIE) adopted the use of tristimulus colorimetry. They recreated Maxwell’s work with defined light source E, defined tristimulus sources (R=700nm, G=546.1nm, B=435.8nm) and created a standard observer. They matched the colors of the spectrum by varying the intensities of the tristimulus colors and recorded the results, creating a chromaticity diagram. They observed the same problems that Maxwell encountered. While they could match all colors in hue, they were not able to match some in saturation. The blue-greens could only be matched by maximizing the saturation of the blue and green lights, then desaturating the object color by adding red light to the neutral light illuminating it, until it matched the blue-green tristimulus lights in hue and saturation.
Now our equation for Chromaticity Coordinates becomes
C(C) = R(R)+G(G)+B(B) for violet and orange to red hues and C(C) +R(R) = G(G) +B(B) or C(C) = -R(R)+G(G)+R(R) for blue-green hues. This also introduces negative values for some of the coordinates. The shaded area of the chromaticity diagram in the following figure, corresponds to hues and saturation’s possible by mixing three primary light sources. The unshaded area of the “horseshoe” corresponds to those hues and saturation’s requiring the desaturation of blue-green by the addition of red.(Walls, p. 342)
The tristimulus values (rλ ,gλ ,bλ ), also known as the distribution coefficients for the tristimulus sources can also be represented in by their spectral curves.
The CIE chose to get rid of the negative coordinate system by a mathematical transform and the adoption of new reference stimuli (X,Y,Z) that lie outside of the spectral locus with a new set of spectral distribution coefficients (xλ ,yλ, zλ ). The purpose of the new reference stimuli , which exist without luminosity and are often referred to as imaginary, was to define references which when mixed together could create all of the hues and saturation.(Rossotti, pp.154-157)
The New Reference Stimuli (X, Y, Z)
Overlaid on the RGB Chromaticity Diagram
The Standard Observer Distribution Coefficients
(the tristimulus power distributions)
The new chromaticity coordinates which express hue and saturation in positive numbers are obtained by taking the ratios of X, Y, and Z present in the object.(Walls, p.348)
x= X/(X+Y+Z) y= Y/(X+Y+Z) z= Z/(X+Y+Z)
Since x+y+z=1, only two of the chromaticity coordinates are needed to completely describe the chroma and saturation; the CIE chose x and y.
Now a chromaticity diagram describing all possible colors in positive numbers is possible. The result was the Horseshoe shaped CIE Chromaticity Diagram.
The CIE Chromaticity Diagram (1931)
The horseshoe curve represents all real visible spectral colors and is called the spectrum locus. The straight line connecting the ends of the spectrum locus (between 420nm and 700nm) creates the purple hues not seen in the spectrum.
E represents equal balanced white light and is created from equal parts of all three colors and exists at coordinates (0.33,0.33). The curve connecting A,B, and C is the locus of the black body sources. A, B, and C are the standard light sources; A is a tungsten filament light operating at 2858K, B is A through a liquid filter to simulate noon light, and C is A through a liquid filter to simulate overcast daylight. One clarification should be made for the CIE diagram, Source refers to real physical light sources whose power distribution can be experimentally determined; Illuminant is a light defined by a power distribution, which may or may not be able to be created by a source. Actual daylight is an example of an illuminant which can not be created by a source.
(note: In the following text, the bars above x-bar, y-bar, and z-bar may not be properly aligned with the text. My apologies)
Now that we have the chromaticity diagram, we can define an objects color by CIE chromaticity coordinates and find its location on the diagram. There are two ways we can accomplish this. One way is to measure the matching color with three light sources. The first step is defining which standard illuminant to use to illuminate the object whose spectral reflection distribution is (R). Once the illuminant (P) has been decided on, the object is illuminated, and its spectral reflection (PxR) is matched using RGB tristimulus color values. The resulting match equals the measurement (P) x (R) x (rλ ,gλ ,bλ ), These are then transformed to spectral distribution coefficients (xλ ,yλ, zλ ) and produce measurements corresponding to (P) x (R) (xλ ,yλ, zλ ). Since, (P) x (R) x (xλ ,yλ, zλ) = X,Y,Z, and x = X/(X+Y+Z), y =Y/(X+Y+Z), we are obtain the tristimulus coordinates x and y and plot the point on the graph. The second way to determine the Chromaticity coordinates is by recording the spectral response of the reflected light from the object and superimposing it onto the standard observer spectra then finding then performing integration on the results. A spectral Representation of this appears as follows:
(note: In the follwoing text the bars above x-bar, y-bar, and z-bar may not be properly alligned with the text. My appologies)
(adapted from Billmeyer, p.46)
© 2006 Marc J. Surrency. Artist scans, images, and web design are protected by copyright. Physical or electronic reproduction in whole or part is unlawful without written permission of the artist.