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Colour

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An overview of colour systems, coulour tolerancing and Yellowness index. Along the way something is mentionned about CCT too.

An overview of colour systems, coulour tolerancing and Yellowness index. Along the way something is mentionned about CCT too.


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  • 1. Colour … … is in the eye of the beholder … isn’t it ?
  • 2. Contents
    • What is colour ?
    • CIE-colour systems
      • Tristimulus XYZ, Yxy, xyz, L*a*b*, L*C*h ° , Munsell
    • Measurement geometry
      • Reflectance, reflectance and appearance
      • CIE-geometries, SPIN&SPEX
    • Color difference/tolerancing
      • Delta L*,a*,b*; Delta L*,C*,h ° ; Delta E; CMC, CIE94
    • Yellowness index
      • Whiteness, yellowness, D1925, E313, CCT, mirek
      • Visual evaluation versus figures
  • 3. 10.000.000
    • Ten million! That is the number of different colors that we can distinguish. No wonder we cannot remember colors well enough to identify a particular shade. Nevertheless, in the end, the color must be right.
    • Visual color perception is influenced by different color sensitivities from person to person (mood, age, etc.), varying environments such as lightness and color, as well as the deficiency to communicate and document color and color differences.
    • These shortcomings can only be solved by using color instrumentation with internationally specified color systems. This guarantees objective description of colored objects.
  • 4. What is colour ?
    • Three things are necessary to see color:
      • A light source (illuminant)
      • An object (sample)
      • An observer/processor
    • We as humans see color because our eyes process the interaction of light hitting an object. What if we replace our eyes with an instrument: can it see and record the same color differences that our eyes detect?
  • 5. CIE-color systems (1)
    • In 1931 the CIE standardized color order systems by specifying the light source (or illuminants), the observer and the methodology used to derive values for describing color.
    • The CIE Color Systems utilize three coordinates to locate a color in a color space. These color spaces include:
      • CIE XYZ
      • CIE L*a*b*
      • CIE L*C*h°
    • Let’s take a look how these values are calculated.
  • 6. CIE-color systems (2)
    • Color measurement instruments receive color the same way our eyes do: by gathering and filtering the wavelengths of light reflected from (or transmitted through) an object. The instrument perceives the reflected light wavelengths as numeric values. These values are recorded as points across the visible spectrum and are called spectral data. Spectral data is represented as a spectral curve. This curve is the color’s fingerprint.
    Measured data of a sample
  • 7. CIE-color systems (3)
    • Once we obtain a color’s reflectance curve, we can apply mathematics to map the color onto a color space.
    • To do this, first we take the reflectance curve and multiply the data by a CIE standard illuminant. The illuminant is a graphical representation of the light source under which the samples are viewed. Each light source has a power distribution that affects how we see color. Examples of different illuminants are A : incandescent, D65 : daylight and F2 : fluorescent.
    Measured data of a sample X Spectrum of D65/10 ° -illuminant
  • 8. CIE-color systems (4)
    • We then multiply the result of this calculation by the CIE standard observer. The CIE commissioned work in 1931 and 1964 to derive the concept of a standard observer, which is based on the average human response to wavelengths of light (Figure 3). In short, the standard observer represents how an average person sees color across the visible spectrum.
    CIE 2 ° and 10° standard observers
  • 9. CIE-color systems (5)
    • Once these values are calculated, we convert the data into the tristimulus values of XYZ. These values can now identify a color numerically.
  • 10. CIE-color systems (6)
    • Tristimulus values, unfortunately, have limited use as color specifications because they correlate poorly with visual attributes. While Y relates to value (lightness), X and Z do not correlate to hue and chroma. As a result, when the 1931 CIE standard observer was established, the commission recommended using the chromaticity coordinates xyz. These coordinates are used to form the chromaticity diagram below. The notation Yxy specifies colors by identifying value (Y) and the color as viewed in the chromaticity diagram (x,y).
    • Hue is represented at all points around the peri-meter of the chromaticity diagram. Chroma, or saturation, is represented by a movement from the central white (neutral) area out toward the diagram’s perimeter, where 100% saturation equals pure hue.
  • 11. CIE-color systems (7)
    • The ability for humans to discriminate colors is not uniform in the Yxy color space. MacAdam determined for a number of colors what the minimum difference must be before a certain percentage of people can discriminate this difference under ideal circumstances (photopic lighting, free field of view, no time limit).
    • The center of the ellipses are the reference colors and the boundary is the noticeable difference. Therefore we can say a color difference will not be noticeable in practice if it is confined within the MacAdam ellipses. For reasons of clarity the ellipses are magnified here by a factor of 10 and the diagram shows only a portion of the color points assessed .
  • 12. CIE-color systems (8)
    • To overcome the limitations of chromaticity diagrams like Yxy, the CIE recommended alternate, uniform color scales: CIE 1960 UCS updated in 1976 which is a rescaled chromaticity diagram later even more adapted to CIELUV and CIE 1976 (L*a*b*) or CIELAB, and CIELCH (L*C*h°).
    • The CIELAB and CIELCH color scales are based on the opponent-colors theory of color vision, which says that two colors cannot be both green and red at the same time, nor blue and yellow at the same time. As a result, single values can be used to describe the red/green and the yellow/blue attributes.
  • 13. CIE-color systems (9)
    • CIE UCS (Uniform Chromaticity Scale) Diagram and CIELUV
    • The diagram depicted here is the 1976 version.
    • In 1960 the coordinates were defined as:
    In 1976 this was modified to: and CIELUV coordinates are defined as:
  • 14. CIE-color systems (10)
    • CIELAB (L*a*b*)
    • When a color is expressed in CIELAB, L* defines lightness, a* denotes the red/green value and b* the yellow/blue value. The a* axis runs from left to right. A color measurement movement in the +a direction depicts a shift toward red. Along the b* axis, +b movement represents a shift toward yellow. The center L* axis shows L = 0 (black or total absorption) at the bottom. At the center of this plane is neutral or gray.
  • 15. CIE-color systems (11)
    • To demonstrate how the L*a*b* values represent the specific colors of Flowers A and B, We’ve plotted their values on the CIELAB Color Chart too.
    • The a* and b* values for Flowers A and B intersect at color spaces identified respectively as points A and B. These points specify each flower’s hue (color) and chroma (vividness/dullness).
    • When their L* values (degree of lightness) are added, the final color of each flower is obtained.
  • 16. CIE-color systems (12)
    • CIELCH (L*C*h°)
    • While CIELAB uses Cartesian coordinates to calculate a color in a color space, CIELCH uses polar coordinates. This color expression can be derived from CIELAB. The L* defines lightness, C* specifies chroma and h° denotes hue angle, an angular measurement.
    • The L*C*h° expression offers an advantage over CIELAB in that it’s very easy to relate to the earlier systems based on physical samples, like the Munsell Color Scale shown below.
  • 17. CIE-color systems (13)
    • How to calculate CIELAB and CIELCH ?
    • If the tristimulus values are know, converting to other color spaces is done by straightforward calculations:
      • L* = 116 (Y/Yn) 1/3 – 16
      • a* = 500 [(X/Xn) 1/3 – (Y/Yn) 1/3 ]
      • b* = 200 [(Y/Yn) 1/3 – (Z/Zn) 1/3 ]
      • L* =116 (Y/Yn) 1/3 – 16
      • C* = (a2 + b2) 1/2
      • h° = arctan (b*/a*)
    • Note 1: Xn, Yn, Zn, are values for a reference white for the illumination/observer used, usually the source with Yn = 100.
    • Note 2: if the ratio of X/Xn , Y/Yn or Z/Zn ≤ 0.008856 then terms in the expressions change to : 7.787(Q/Qn) + 4/29 where Q is replaced with X, Y or Z.
    • Now we can calculate color coordinates in different color diagrams and spaces, but we assumed something from the start : that we are able to measure the “colour fingerprint” of an object, but how exactly can we do this ?
  • 18. CIE measurement geometry (1)
    • Measurement geometry ?
    • The optical geometry of the instrument is important because it influences the results. In some instruments an integrating sphere is used that enables the sample to be illuminated diffusely (from all angles equally) and the reflected light to be collected at an angle roughly perpendicular to the surface of the sample.
    • Alternatively, other instruments illuminate the sample at a certain angle and collect light at another angle.
    • It is extremely difficult to correlate measurements taken between instruments if the optical geometry is not identical.
    • For most surfaces the reflectance changes with the angle of illumination and observation.
  • 19. CIE measurement geometry (2)
    • Which geometry will be best suited for your measurement depends on the type of object and the information you want to get/compare.
  • 20. CIE measurement geometry (3)
    • The four CIE standard geometries are:
    • diffuse illumination and light collection at the normal, D/0;
    • normal illumination and diffuse light collection, 0/D;
    • illumination at 45 degrees and light collection at the normal, 45/0;
    • normal illumination and light collection at 45 degrees, 0/45.
  • 21. CIE measurement geometry (4)
    • As will be obvious from the previous slides, the specular (surface) reflection can seriously influence the measurement results. Therefore integrating sphere instruments offer the option to include (SPIN) or exclude (SPEX) the specular component by using a 8 °/D geometry in combination with a “port”.
    • In the “spin“ mode the total reflected light is measured:
      • Diffuse reflection (color) + direct reflection (gloss)
      • Color is measured “independent” of the sample’s gloss or surface texture.
    • In the “spex“ mode, a gloss trap is used to capture the directly reflected light (gloss). This configuration simulates the 45/0 geometry. In case of medium to low gloss samples, deviations will occur between the 45/0 and the sphere spex configuration as the gloss trap does not completely exclude the specular component.
  • 22. Color difference/tolerancing (1)
    • We now know only measurements taken under the same conditions can be compared. Therefore, it is necessary to note the following information in a color measurement report:
      • Color instrument (geometry)
      • Illuminant / observer
      • Color system
      • Sample preparation
    • We also know how to calculate and convert from one colour space to another
    • But how will we interpret these results: when will we approve or reject ? For this we need to correlate the visual appearance to the figures we can generate and determine the maximum allowable difference between a standard and the sample.
  • 23. Color difference/tolerancing (2)
    • Delta CIELAB and CIELCH
    • CIELAB and CIELCH are used to compare the colors of two objects.
    • The expressions for these color differences are ΔL*, Δa*, Δb* or DL*, Da*, Db*, and ΔL*, ΔC*, Δh*, or DL*, DC*, Dh* ( Δ or D symbolizes“delta,” which indicates difference).
    • Given ΔL*, Δa*, Δb*, the total difference or distance on the CIELAB diagram can be stated as a single value, known as ΔE*.
  • 24. Color difference/tolerancing (3)
    • Let’s compare the color of Flower A to Flower C, pictured below.
    • Separately, each would be classified as a yellow rose. But what is their relationship when set side by side? How do the colors differ? Using the equation for ΔL* Δa* Δb*, the color difference between Flower A and Flower C can be found.
    The total color difference can be expressed as ΔE*=13.71 On the a* axis, a reading of –6.10 indicates greener or less red. On the b* axis, a reading of –5.25 indicates bluer or less yellow. On the L* plane, the measurement difference of +11.10 shows that Flower C is lighter than Flower A.
  • 25. Color difference/tolerancing (4)
    • If the same two flowers were compared using CIELCH, the color differences would be expressed as:
      • ΔL* = +11.10
      • ΔC* = –5.88
      • ΔH* = 5.49
    • The ΔC* value of –5.88 indicates that Flower C is less chromatic, or less saturated. The ΔH* value of 5.49 indicates that Flower C is greener in hue than Flower A.
    • The L* and ΔL* values are identical for CIELCH and CIELAB.
    • The meaning for the appearance of a certain delta is summarised below:
      • ΔL* = difference in lightness/darkness value + = lighter – = darker
      • Δa* = difference on red/green axis + = redder – = greener
      • Δb* = difference on yellow/blue axis + = yellower – = bluer
      • ΔC* = difference in chroma + = brighter – = duller
      • ΔH* = difference in hue
      • ΔE* = total color difference value
  • 26. Color difference/tolerancing (5)
  • 27. Color difference/tolerancing (6)
    • Poor color memory, eye fatigue, color blindness and viewing conditions can all affect the human eye’s ability to distinguish color differences. In addition to those limitations, the eye does not detect differences in hue (red, yellow, green, blue, etc.), chroma (saturation) or lightness equally. In fact, the average observer will see hue differences first, chroma differences second and lightness differences last. As an approximation it is generally accepted that 1 value step = 2 chroma steps = 3 hue steps.
    • In practice, visual acceptability is best represented by an ellipsoid.
    • As a result, our tolerance for an acceptable color match consists of a three-dimensional boundary with varying limits for lightness, hue and chroma, and must agree with visual assessment. CIELAB and CIELCH can be used to create those boundaries. Additional tolerancing formulas, known as CMC and CIE94, produce ellipsoidal tolerances.
  • 28. Color difference/tolerancing (7)
    • CIELAB Tolerancing
    • When tolerancing with CIELAB, you must choose a difference limit for ΔL* (lightness), Δa* (red/green), and Δb* (yellow/blue). These limits create a rectangular tolerance box around the standard.
    • When comparing this tolerance box with the visually accepted ellipsoid, some problems emerge. A box-shaped tolerance around the ellipsoid can give good numbers for unacceptable color. If the tolerance box is made small enough to fit within the ellipsoid, it is possible to get bad numbers for visually acceptable color.
  • 29. Color difference/tolerancing (8)
    • CIELCH Tolerancing
    • CIELCH users must choose a difference limit for ΔL* (lightness), ΔC* (chroma) and ΔH* (hue). This creates a wedge-shaped box around the standard. Since CIELCH is a polar-coordinate system, the tolerance box can be rotated in orientation to the hue angle.
    • When this tolerance is compared with the ellipsoid, we can see that it more closely matches human perception. This reduces the amount of disagreement between the observer and the instrumental values.
  • 30. Color difference/tolerancing (9)
    • CMC Tolerancing
    • CMC is not a color space but rather a tolerancing system. CMC tolerancing is based on CIELCH and provides better agreement between visual assessment and measured color difference. CMC tolerancing was developed by the Colour Measurement Committee of the Society of Dyers and Colourists in Great Britain and became public domain in 1988.
    • The CMC calculation mathematically defines an ellipsoid around the standard color with semi-axis corresponding to hue, chroma and lightness. The ellipsoid represents the volume of acceptable color and automatically varies in size and shape depending on the position of the color in color space.
  • 31. Color difference/tolerancing (10)
    • CMC Tolerancing (cont’d)
    • The figure to the right shows the variation of the ellipsoids throughout color space. The ellipsoids in the orange area of color space are longer and narrower than the broader and rounder ones in the green area. The size and shape of the ellipsoids also change as the color varies in chroma and/or lightness
    • Since the eye will generally accept larger differences in lightness (l) than in chroma (c), a default ratio for (l:c) is 2:1. A 2:1 ratio will allow twice as much difference in lightness as in chroma. The CMC equation allows this ratio to be adjusted to achieve better agreement with visual assessment.
  • 32. Color difference/tolerancing (11)
    • CIE94 Tolerancing
    • In 1994 the CIE released a new tolerance method called CIE94. Like CMC, the CIE94 tolerancing method also produces an ellipsoid. The user has control of the lightness (kL) to chroma (Kc) ratio, as well as a commercial factor (cf). These settings affect the size and shape of the ellipsoid in a manner similar to how the l:c and cf settings affect CMC.
    • However, while CMC is targeted for use in the textile industry, CIE94 is targeted for use in the paint and coatings industry. You should consider the type of surface being measured when choosing between these two tolerances.
    • If the surface is textured or irregular, CMC may be the best fit. If the surface is smooth and regular, CIE94 may be the best choice.
  • 33. Color difference/tolerancing (12)
    • Visual Assessment vs. Instrumental
    • Though no color tolerancing system is perfect, the CMC and CIE94 equations best represent color differences as our eyes see them.
    • Choosing the Right Tolerance
    • When deciding which color difference calculation to use, consider the following five rules (Billmeyer 1970 and 1979):
    • Select a single method of calculation and use it consistently.
    • Always specify exactly how the calculations are made.
    • Never attempt to convert between color differences calculated by different equations through the use of average factors.
    • Use calculated color differences only as a first approximation in setting tolerances, until they can be confirmed by visual judgments.
    • Always remember that nobody accepts or rejects color because of numbers — it is the way it looks that counts.
  • 34. Yellowness Index (1)
    • The American Standards Test Methods (ASTM) has defined whiteness and yellowness indices.
    • The E313 whiteness index is used for measuring near-white, opaque materials such as paper, paint and plastic. In fact, this index can be used for any material whose color appears white.
    • The ASTM’s E313 yellowness index is used to determine the degree to which a sample’s color shifts away from an ideal white (also used for transparent plastics).
    • The D1925 yellowness index was used for measuring (opaque) plastics but is withdrawn and shouldn’t be used anymore. Also, because of the limited digits used, the calculated YI for clear air of the tristimulus values of a 2° observer with C illuminant would be YI = 0,303.
    • Calculation of the Yellowness Index is done by the equation:
  • 35. Yellowness Index (2)
    • The constants in the equation are defined differently depending on the ASTM standard and/or illuminant/observer used as follows and are only defined for C or D65 illuminants which are close to the CIE white point:
    • Absolute YI is a measure for the distance from the CIE white point (if both X and Z are 0 then YI is also 0). A positive YI means a yellowish appearance and a negative YI appears blueish.
    • Delta-YI is simply the difference between two Yellowness Indices.
    1.1498 1.3013 ASTM E 313, D 65 /10° 1.0781 1.2871 ASTM E 313, C/10 ° 1.1335 1.2985 ASTM E 313, D 65 / 2 ° 1.0592 1.2769 ASTM E 313, C/2 ° 1.06 1.28 ASTM D 1925, always 2 ° Cz Cx
  • 36. Yellowness Index (3)
    • Now we now the theory, we will try to answer the following questions:
      • What values of YI and ΔYI are visible?
      • What values of YI and ΔYI are acceptable?
      • What will be the resulting YI and ΔYI if more layers of transparent material are stacked together?
    • First we need to realise that YI is zooming in around the CIE-white point and should only be used for “nearly white” or “nearly colourless” samples. To be able to judge visibility of a given YI, we need to know how we arrived at this YI so that we can calculate corresponding CIE color space coordinates.
    • It seems logical to use the same maximum limits from the blackbody locus as for CCT (correlated colour temperature), so let’s take a look at CCT.
  • 37. Yellowness Index (4)
    • For some purposes, it is convenient for a light source to quote its colour temperature (measured in Kelvins).
    • As long as the light being measured closely approximates a blackbody source, the results are quite accurate. Hence, the locus is particularly useful in the classification of ‘whites’.
  • 38. Yellowness Index (5)
    • CCT is calculated by determining the isotemperature line on which the colour of the light source is positioned. Isotemperature lines are straight lines for which all colours on the line appear visually equal. Δuv is used to specify the deviation from the blackbody locus. The maximum deviation for Δuv is set at ± 0,02.
    • CCT is not suitable for measuring light sources which have narrow-band spectral emittance curves that do not approximate any blackbody curve (for example, many LED).
    • Colour temperature is strictly applicable to light sources which may be precisely matched by a full radiator. The concept is extended to include sources which give light that can be closely - but not exactly – matched by a full radiator. The expression Correlated Colour Temperature (CCT) is used to describe the light from such sources. This is the temperature at which a full radiator produces a light that most nearly matches the light from the given source.
  • 39. Yellowness Index (6)
    • Equal color differences on the planckian locus are more nearly expressed by equal steps of reciprocal color temperature (RTk) than by color temperature (Tk) itself. The usual unit is the reciprocal megakelvin (MK -1 ), so that the reciprocal color temperature RTk = 10 6 /Tk.
    • A difference of 1 reciprocal megakelvin (also named “mirek” from “micro-reciprocal-kelvin”) indicates approximately the same color difference above 1800K, yet it corresponds to a temperature difference that varies from approximately 4K at 2000K to 100K at 10.000K
    • CCT can be calculated from
    • CIE x,y with (a.o.) the formula:
  • 40. Yellowness Index (7)
    • Now let’s do some calculations:
      • The CIE white point x=0,33333 and y=0,33333 corresponds to a CCT of 5454K and a YI of 0
      • Most fluorescent lampcolours (2700K to 4000K) are evaluated yellowish by the YI(D65-10 ° ) formulae:
        • 2700K => X~0,46; Y~0,41; Z~0,13 => YI(D65-10 ° ) ~ 110
        • 3000K => X~0,435; Y~0,40; Z~0,165 => YI(D65-10 ° ) ~ 94
        • 3500K => X~0,405; Y~0,39; Z~0,205 => YI(D65-10 ° ) ~ 75
        • 4000K => X~0,38; Y~0,375; Z~0,245 => YI(D65-10 ° ) ~ 26
        • 5454K => X~0,333; Y~0,333; Z~0,333 => YI(D65-10 ° ) ~ 0
        • 6500K => X~0,31475; Y~0,31475; Z~0,3705 => YI(D65-10 ° ) ~ -5,2
      • MacAdam 1931 x , y color matching ellipses on the Planckian locus from 3000 to 80000 K have a mean semimajor axis of 0.0029294 (standard deviation 2.2424x10 -4 ) and a mean semiminor axis of 9.3694x10 -4 (standard deviation 1.6345x10 -4 )
  • 41. Yellowness Index (8)
    • And some more calculations:
      • At 3500K, a delta x,y of each 0,0015 (~ the MacAdam treshold) gives a delta Tk of 20K (3480K) and a delta YI(D65-10 ° ) of about 1 (meaning a delta YI of 1 can be detected if a person has indefinite time to study two samples with this delta YI of 1) and that e.g. also corresponds to a delta b (L*a*b*-space) of 0,7
      • There is some consent in industry that a delta YI of 8 is “acceptable”; this corresponds roughly to a delta Tk of 100 between 3000K and 4000K, but it will be clear from the previous that when judged side-by-side, a clear difference will be noticeable
  • 42. Yellowness Index (9)
    • Maybe even more informational are some samples (under fluo 830 light) :
    YI 0,7 b 0,6 YI 1,7 b 1,6 YI 2,5 b 1,7 YI 3,7 b 2,4 YI 4,9 b 3,3 YI 9,0 b 5,9 YI 14,0 b 9,5 YI 16,9 b 11,4 YI 26,7 b 18,9
  • 43. Yellowness Index (10)
    • The same samples using camera flashlight:
    YI 0,7 b 0,6 YI 1,7 b 1,6 YI 2,5 b 1,7 YI 3,7 b 2,4 YI 4,9 b 3,3 YI 9,0 b 5,9 YI 14,0 b 9,5 YI 16,9 b 11,4 YI 26,7 b 18,9
  • 44. Conclusions
    • Specifying, measuring, evaluating and controlling colour requires a lot of knowledge and good communication about used methods, standards and practices.
    • In the end the only “truth” is the visual evaluation by “the customer”, everything else is just a framework to enable objective assessment of a specimen when the customer is not available to judge.
    • A final picture of inside of integrating sphere to show only flat samples can be measured accurately (no good spex measurement possible here)
  • 45. Thanks for your attention …