A Little Theory Management abcde Color Color Introduction If you are not just interested in the practical side of Color Manage- ment but also wish to know more about the theories behind color reproduction, then this booklet will provide you with some background information. It will explain to you in a concise, yet detailed manner the various aspects concerning color reproduc- tion, i.e. the principles of color and what goes on physically, additive color mixing, the different color spaces and color space transforma- tion in its mathematical context. Even if you never advance beyond this introduction in the booklet, you can still work perfectly well with your Color Management system. However, if you find that the theory which this system is based on is something which attracts to you, you should not just put this booklet aside. Have fun reading this booklet! Color as a physical variable Color as a sensory perception The physical aspect of color is Man’s color vision consists of the represented by light of different analysis, evaluation and encoding of spectral composition. If you record a information which the eye receives spectrogram of the color radiation from such color stimuli. Only after by means of a spectrophotometer subsequent processing of the stimuli you get the color stimulus function does this information become a as a result of this measurement.This color sensation. In this context, the function shows how the radiant eye can be regarded as a reproduc- energy of the light from a color sam- tion system. The retina analyzes the ple is distributed over the entire visi- light reflected from the objects into ble spectrum varying according to three spectral components – namely its wavelength. Radiant Energy red, green and blue.The information UV Blue Green Red Infrared this provides is, according to the Wavelength very latest research results, encoded Additive color mixing into one element of information If we employ additive color defining the brightness and two mixing to mix red and green light defining the chroma. This will be (e.g. by projecting red- and green- examined later in greater detail. filtered light from two slide projec- Color impression: Blue First of all, however, additive tors) we get yellow: color mixing will be described. The highest value of the color sti- mulus function provides information Green Yellow Red on the hue. In the following diagram, a blue hue is suggested: Radiant Energy UV Blue Green Red Infrared Wavelength We can represent this mixing pro- cess in colorimetric terms by means of a small diagram: GreenYellow Red The steeper the rise and fall of the Red curve in the proximity of the maxi- Laser light Red and green are two primary mum value, the purer (more chro- colors. Yellow, on the other hand, is matic) the color. One example of an a mixed color. In our diagram, the extremely pure color is laser light. mixed color – consisting of equal This depicts the color stimulus func- components of the primary colors – tion of a spectral line: Radiant Energy UV Blue Green Red Infrared lies at the exact center of the Wavelength connecting lines. By stopping down the lens in one of the projectors (and thus changing the intensity of one primary color) it is possible to influ- ence the hue of the mixed color. A reduction in green while main- Color spaces taining the intensity of red, for When observing a color, there are Colors of different chroma retain example, will produce orange: three characteristics important to their original hue since the relation- us: ship between the color values of red and green has not changed. In the ● the hue color triangle, they move along the ● the chroma straight connecting line for example ● the brightness (or luminance) from the yellow color locus towards Green Orange Red The term ”hue” refers to the blue: basic color of an object such as green or red.When we look at some- Green Yellow Red thing, it is the first criterium we use to discriminate colors. Achromatic The color locus for the mixed The term ”chroma” describes the Yellow color now moves along the straight purity of colors. If blue is gradually connecting line towards the primary added to a yellow which has been color red.The original hue of the yel- mixed from red and green this gives low has thus changed in the direc- rise to yellow steps of decreasing tion of orange: purity. These are then less chroma- tic: Green Orange Red The diagram now assumes the form of a color triangle: In order to mix a color like cyan, Green Yellow Red Blue a third primary color (blue) is need- ed since mixing the primary colors Increasing the amount of the red and green cannot produce cyan. White third primary color until all three Three primary colors are all that is primary colors are present in equal needed to mix most colors: components will give white. The chroma level is then equal to zero. Cyan Magenta The achromatic point lies in the middle of the color triangle: Blue Magenta Green Yellow Red Blue Cyan White Red This color triangle shows mixed Yellow Achromatic colors cyan, magenta and yellow in Green Point the middle of the straight connecting lines between the primary colors red, green and blue. According to the law of additive color mixing, changes in hue – seen in colorimetric terms – thus mean the movement of color loci along the sides of the color triangle. Blue All other colors which can be pro- The triangle drawn between the Green duced by additive mixing of the coordinates is the chromaticity tri- B = 0,4 three primary colors red, green and angle. A color locus in the color blue lie in the area enclosed by this space is defined by three color vec- Color: Yellowy- color triangle.The further away they tors which represent the compo- Green are from the center of the triangle nents of the primary colors. These G = 1,1 the higher their chroma. A mixed components are known as color Yellow color has a high chroma level if it values. A color, for example, which Cyan Chromaticity: Yellowy- has only a small amount of its third consists of 0.6 red, 1.1 green and Green component or indeed none at all. A 0.4 blue, would be something like a Black maximum of chroma is found in all yellowy-green which is not very colors mixed from only two primary chromatic: R = 0,6 colors. Red If all three color components of a Magenta combination consisting of three pri- In the color triangle we were able Blue mary colors are reduced simulta- to define both hue and chroma. The The point of intersection of the neously while retaining their mixing colors are thus expressed in terms of resulting vector represents the chro- ratio, the hue remains unchanged. their chromaticity and form a chro- maticity ”yellowy-green”, the end The color decreases in brightness, maticity triangle. All colors in the point of the vector being the color however. If the components of all chromaticity triangle are defined by yellowy-green with the inclusion of three primary colors are reduced to their hue and chroma only and not its brightness value. zero, the resulting color will be by their brightness.There can be any black. Like white, black has a amount of brightness in the chroma- chroma level of zero. ticity triangle. In order to integrate brightness into our diagram we need to turn the two-dimensional chroma- ticity triangle into a spatial body known as a color space. The color Green space is a three-dimensional coordi- nate system with coordinates for red, green and blue: Yellow The further the color loci of the primary colors from the origin, the Cyan Green greater the volume of the cuboid color gamut which is formed and White thus the higher the quality of any Chromaticity Color color reproduction system which is Triangle Gamut based on it. All colors lying inside the color Yellow Red gamut can be reproduced by a Cyan White reproduction system which is based Blue Magenta on these primary colors (for exam- Black ple a color monitor). Colors outside the color space cannot be repro- duced.The primary colors of a color Red space are determined essentially by Magenta the equipment which generates Blue them. The CIE color system This is only meaningful, however, The creation of a global color if appropriate standardization is standard which embraces the most performed at the same time which important color gamuts and allows allows the lost value (Z) to be read colors to be communicated is of from the new two-dimensional great importance for the develop- model. This standardization is a- ment of a color reproduction chieved by introducing the chromati- system. city coordinates x, y and z. The following are defined: The CIE color system is such a standard. x = X / (X + Y + Z) In the standard color triangle, the y = Y / (X + Y + Z) right-angled chromaticity triangle This CIE color standard is based z = Z / (X + Y + Z) drawn between zero, x = 1 and y =1 on the imaginary primary colors represents the boundaries of this where: XYZ which cannot be realized physi- reference system. Chromaticities cally.They have been generated on a x + y+ z = 1 cannot lie outside the triangle. The purely theoretical basis and are thus closed curve section represents the The value z of any desired color independent of device-dependent position of the spectral colors: color gamuts such as RGB or can be obtained by subtracting the CMYK.These virtual primary colors chromaticity coordinates x and y y have, however, been selected so that from 1: 1,0 Spectral color all colors which can be perceived by 1 - x -y = z gamut the human eye lie within this color space.