1. SCI 200 Physical Science Lecture 9 Color Mixing Rob Daniell July 28, 2011

2. revised 2011.07.27SCI200 - Lecture 102 Color Mixing  Gilbert & Haeberli: Physics in the Arts  Chapter 7 Additive color mixing  Chapter 8 Subtractive color mixing  Supplementary materials:  Malacara, Daniel: Color Vision and Colorimetry: Theory and Applications,SPIE Press, Bellingham, 2001  Wikipedia articles on Hue, sRGB, & ITU Recommendation 709 (Rec. 709)

3. revised 2011.07.27SCI200 - Lecture 103 Color Mixing  Trichromacy allows fairly strong hue discrimination  Nevertheless:  The same hue can be produced by different spectral distributions  Response of cones to any particular spectral distribution of light is complex  Is there a (relatively) simple way to describe or specify a particular hue?

4. revised 2011.07.27SCI200 - Lecture 104 Spectral Response of Cones  Two laser pointers (left) at 532 nm and 633 nm give the same hue as a single laser pointer (right) at 570 nm  Note that the authors seem to ignore the 2 pulses in the Type II cone produced by the 633 nm light  Gilbert & Haeberli, Physics in the Arts, pp. 86-87.

5. revised 2011.07.27SCI200 - Lecture 105 Idealized Color Wavelength Ranges  Gilbert & Haeberli, Physics in the Arts, p. 83. 400-500 nm 500-600 nm 600-700 nm

6. revised 2011.07.27SCI200 - Lecture 106 Color Mixing  Additive mixing  Two light sources  Combined by adding the intensity at each wavelength  Subtractive mixing  Filters, paints, dyes  Combined effect is produced by subtracting colors  Also depends on the light source

7. revised 2011.07.27SCI200 - Lecture 107 Additive Color Mixing  (a), (b), & (c): three non- monochromatic light sources  (d), (e), & (f): three two- color mixtures, each producing a third color  (g): spectral yellow  (h): unsaturated yellow produced by combining spectral green and spectral red  (i): the three non-spectral light sources mixed to produce white

8. revised 2011.07.27SCI200 - Lecture 108 Additive Color Mixing  (a): spectral blue + spectral yellow = white  Complementary colors  (b): broad band white  Mixture of many colors  metamers: Two different intensity distributions that appear the same to your eye

9. revised 2011.07.27SCI200 - Lecture 109 Additive Color Mixing Additive color rules: R + G + B = W R + G = Y G + B = C R + B = M Complementary colors: R + C = W G + M = W B + Y = W Can 3 colors be combined to produce any other color? C = Cyan, M = Magenta, Y = Yellow W = White

10. revised 2011.07.27SCI200 - Lecture 1010 Additive Color Mixing Red, Green, & Blue can be combined to produce most colors, but some saturated colors cannot be reproduced. Red, Green, & Blue can be combined to produce more colors than any other choice of primary colors C = Cyan, M = Magenta, Y = Yellow W = White

11. revised 2011.07.27SCI200 - Lecture 1011 Additive Color Mixing  CIE Color Matching experiments in 1922  Illuminated region subtended a visual angle of 2°  Only the viewer’s fovea is illuminated  Matching field produced by 700 nm, 546.1 nm, 435.8 nm  Three spectral lines in mercury vapor

12. revised 2011.07.27SCI200 - Lecture 1012 Additive Color Mixing  Hue, Saturation, and Luminance of the reference field were to be matched as closely as possible.  For some wavelengths (in fact, nearly all wavelengths) of the monochromatic source, a perfect match was impossible.  Except by adding one of the red, green, or blue matching colors to the reference field.

13. revised 2011.07.27SCI200 - Lecture 1013 Additive Color Mixing Suppose you attempt to match spectral cyan (490 nm) using spectral red (650 nm) spectral green (530 nm) spectral blue (460 nm) Spectral cyan produces I: 1 pulse II: 7 pulses III: 2.5 pulses spectral blue + spectral green produce I: 2 + 0 = 2  1 II: 2.5 + 16.5 = 19  9.5 III: 1 + 9 = 10  5

14. revised 2011.07.27SCI200 - Lecture 1014 Additive Color Mixing Spectral cyan: I: 1 pulse II: 7 pulses III: 2.5 pulses 50% blue + 36% green: I: 1 + 0 = 1 II: 1 + 6 = 7 III: 0.5 + 3 = 3.5 Spectral cyan + 33% red: I: 1 + 0 = 1 II: 7 + 0 = 7 III: 2.5 + 1 = 3.5 50% blue + 36% green matches spectral cyan + 33% red

15. revised 2011.07.27SCI200 - Lecture 1015 Additive Color Mixing 50% blue + 36% green matches spectral cyan + 33% red But spectral cyan + spectral red yields white: So spectral cyan + 33% red is the same as 67% cyan + 33% white That is, unsaturated cyan

16. revised 2011.07.27SCI200 - Lecture 1016 Additive Color Mixing Above: Spectral cyan on left; unsaturated cyan on the right 50% blue + 36% green matches spectral cyan + 33% red But spectral cyan + spectral red yields white: So spectral cyan + 33% red is the same as 67% cyan + 33% white That is, unsaturated cyan

17. revised 2011.07.27SCI200 - Lecture 1017 Additive Color Mixing Combine 460 nm (blue), 530 nm (green), and 650 nm (red) To match the wavelength on the horizontal axis Negative fractions mean you must ‘unsaturate’ the color you are trying to match Standard observer: Based on data from 1931

18. revised 2011.07.27SCI200 - Lecture 1018 Additive Color Mixing Previous figure redrawn so that complementary spectral colors lie opposite each other. Saturated colors lie along the outside Mixtures of two colors are proportional to the distance between them along the line joining them A line from one spectral color through the white point ends at the complementary color White point depends on the precise standard used The hue of the color at F is found by extending a line from white through F to the edge

19. revised 2011.07.27SCI200 - Lecture 1019 Additive Color Mixing International Commission for Illumination (CIE) Did not want to use ‘negative colors’ to match saturated colors Defined ‘imaginary colors’ [X], [Y], and [Z] Not physical colors, but related Defined ‘color matching functions’ x, y, and z Relative amounts of [X], [Y], and [Z] needed to match a given spectral color (wavelength) Results in “tristimulus” values x, y, and z z = 1 - x - y x and y together are called the ‘chromaticity’ of a color

20. revised 2011.07.27SCI200 - Lecture 1020 Additive Color Mixing CIE Chromaticity Diagram: Horseshoe shaped curve represents saturated monochromatic colors 380 nm - 700 nm ‘purples’ (mixtures of blue and red) lie along bottom edge z = 1 - x - y Interior of horseshoe represents unsaturated colors

21. revised 2011.07.27SCI200 - Lecture 1021 Additive Color Mixing CIE Chromaticity Diagram: Specify a color by three values Chromaticity (x and y) Lightness (or Brightness) No representation is perfect None can reproduce the precise color sensitivity of the human eye Individual differences

22. revised 2011.07.27SCI200 - Lecture 1022 Additive Color Mixing RGB example: 3 standard wavelengths: 700 nm (red) 546.1 nm (green) 435.8 nm (blue) These three colors can only reproduce colors in the interior of the triangle

23. revised 2011.07.27SCI200 - Lecture 1023 Additive Color Mixing CIE chromaticity diagram: Three “primary” colors can only produce the colors inside the triangle - the “gamut” of the color set. This triangle corresponds to the three colors used in a typical color monitor.

24. revised 2011.07.27SCI200 - Lecture 1024 Additive Color Mixing Monochromatic complementary pairs 700 nm -- 494 nm 600 nm -- 490 nm 571 nm -- 380 nm No complementary pairs between 494 nm & 571 nm

25. revised 2011.07.27SCI200 - Lecture 1025 Additive Color Mixing Color Triangle (Fig. 7.4) from textbook Doesn’t cover gamut of the human eye Does not conform to the sRGB standard used for color televisions and computer monitors Does come close to maximizing the gamut of representable colors

26. revised 2011.07.27SCI200 - Lecture 1026 Additive Color Mixing Color Triangle inside a chromaticity diagram (Fig. 7.15) It appears that the text uses Red = 700 nm Green = 530 nm Blue = 440 nm Does not conform to the “sRGB” standard for color television and computer monitors

27. revised 2011.07.27SCI200 - Lecture 1027 Additive Color Mixing sRGB standard Based on 1931 CIE chromaticity Red: x = 0.64, y = 0.33 Green: x = 0.30, y = 0.60 Blue: x = 0.15, y = 0.06 White point: x = 0.3127, y = 0.3290  From the diagram, the dominant wavelengths are  Red: 611 nm  Green: 549 nm  Blue: 464 nm From Wikipedia http://en.wikipedia.org/wiki/Rec._709

28. revised 2011.07.27SCI200 - Lecture 1028 Additive Color Mixing AdobeRGB standard Based on 1931 CIE chromaticity Red: x = 0.64, y = 0.33 Green: x = 0.21, y = 0.71 Blue: x = 0.15, y = 0.06 White point: x = 0.3127, y = 0.3290  From the diagram, the dominant wavelengths are  Red: 611 nm  Green: 535 nm  Blue: 464 nm  Green point is main difference with sRGB From Wikipedia http://en.wikipedia.org/wiki/Rec._709

29. revised 2011.07.27SCI200 - Lecture 1029 Additive Color Mixing Complementary Colors to the “line of purples” appear to range from c491 nm to c579 nm

30. revised 2011.07.27SCI200 - Lecture 1030 Additive Color Mixing correspondence between wavelength and hue (angle): –complicated

31. revised 2011.07.27SCI200 - Lecture 1031 Additive Color Mixing correspondence between RGB and hue (angle):

32. revised 2011.07.27SCI200 - Lecture 1032 Additive Color Mixing LEDs approximate monochromatic red, green and blue: Red = 645 nm Green = 510 nm Blue = 465 nm

33. revised 2011.07.27SCI200 - Lecture 1033 Additive Color Mixing LEDs approximate monochromatic red, green and blue: Red = 645 nm Green = 510 nm Blue = 465 nm

34. revised 2011.07.27SCI200 - Lecture 1034 Additive Color Mixing Methods  Methods and Techniques  Simple addition  Two or more light sources  Stage lights  Partitive mixing  Separate sources close to each other  Television screens & CRT displays  LCD displays  Rapid succession  Uses persistence of vision

35. revised 2011.07.27SCI200 - Lecture 1035 Subtractive Color Mixing Subtractive color combination: Filters that absorb or block light of certain colors Ink or pigments that reflect only certain colors and absorb the others Primary Subtractive Colors: Cyan, Magenta, Yellow Supplemented by Black in “four color printing” C = Cyan, M = Magenta, Y = Yellow

36. revised 2011.07.27SCI200 - Lecture 1036 Subtractive Color Mixing: Idealized Filters Idealized Red Filter Idealized Green Filter Idealized Blue Filter

37. revised 2011.07.27SCI200 - Lecture 1037 Subtractive Color Mixing: Idealized Filters Idealized Red Filter + Idealized Green Filter = “black” (no transmission)

38. revised 2011.07.27SCI200 - Lecture 1038 Subtractive Color Mixing: Idealized Filters Idealized Cyan Filter (blocks Red) Idealized Magenta Filter (blocks Green) Idealized Yellow Filter (blocks Blue)

39. revised 2011.07.27SCI200 - Lecture 1039 Subtractive Color Mixing: Idealized Filters Idealized Cyan Filter + Idealized Magenta Filter = Blue filter

40. revised 2011.07.27SCI200 - Lecture 1040 Subtractive Color Mixing: Block Diagrams Subtractive Primaries: C = B + G = W - R M = B + R = W - G Y = G + R = W - B -G-R-B

41. revised 2011.07.27SCI200 - Lecture 1041 Subtractive Color Mixing: Block Diagrams Basic Subtractive Rules: C + M = B C + Y = G M + Y = R C + M + Y = Bk (Black) -R -G-G -B -G -B -R -G-G -B

42. revised 2011.07.27SCI200 - Lecture 1042 Subtractive Color Mixing Dyes & Pigments: Chemicals that absorb and/or reflect selective parts of the visible spectrum Ideal dyes & pigments follow the same rules as ideal filters (i.e., subtractive color mixtures) Real filters, dyes, and pigments often behave in complicated and (almost) unpredictable ways.

43. revised 2011.07.27SCI200 - Lecture 1043 Subtractive Color Mixing Real filters, dyes & pigments: Usually smooth “corners” Sometimes complicated structure Rarely achieve trans- missions and reflectances of 100%

44. revised 2011.07.27SCI200 - Lecture 1044 Subtractive Color Mixing Real filters, dyes & pigments: Can produce unexpected results The transmission of two or more filters in series is the product of the transmissions of each individual filter. For example: one filter with 70% transmission combined with another filter with 50% transmission produces a combined transmission of 35% 1 filter 2 identical filters 10 identical filters

45. revised 2011.07.27SCI200 - Lecture 1045 Subtractive Color Mixing Real filters, dyes & pigments: Can produce unexpected results Combining filters or dyes with different transmittance functions can result in startling color shifts. blue dye yellow dye one-to-one mixture

46. revised 2011.07.27SCI200 - Lecture 1046 Subtractive Color Mixing With subtractive colors the perceived color depends on the light source cool white flourescent bulb reflectance of a magenta object resulting intensity distribution, the product of (a) and (b).

47. revised 2011.07.27SCI200 - Lecture 1047 Subtractive Color Mixing With subtractive colors the perceived color depends on the light source (example 2) a gray object a brown object In sunlight, the two objects at right have very different colors. Under an incandescent bulb, which emits much less blue light, the objects have very similar colors.

48. revised 2011.07.27SCI200 - Lecture 1048 Subtractive Color Mixing Different light sources have different intensity distributions: Incandescent light bulb Deluxe Warm White Fluorescent bulb High Pressure Sodium Lamp

49. revised 2011.07.27SCI200 - Lecture 1049 Subtractive Color Mixing Gamut of subtractive primaries: Gamut of color TV or computer monitor: Gamut of color slides:

50. revised 2011.07.27SCI200 - Lecture 1050 Subtractive Color Mixing Printing inks: color is due to a combination of reflection and transmission:

51. revised 2011.07.27SCI200 - Lecture 1051 Homework Discussion Translation between Textbook color triangle and 8 bit RGB Hue, especially “purples”

52. revised 2011.07.27SCI200 - Lecture 1052 Homework Discussion  Translation between Textbook color triangle and 8 bit RGB  8 bit RGB is the color representation system used on most computer monitors and other LCD graphic displays  1 byte = 8 bits: 010110011 2 = 179 10  Smallest number = 0 10  Largest number = 2 8 – 1 = 255  Each pixel is represented by 3 bytes  1 each for red (R), green (G), and blue (B)

53. revised 2011.07.27SCI200 - Lecture 1053 Homework Discussion Translation between color triangle and 8 bit RGB r, g are “given” b = 1 – r – g Example: The point indicated r = 0.55, g = 0.2, b = 1 - 0.55 - 0.2 = 0.25 Problem: Find the equivalent RGB representation

54. revised 2011.07.27SCI200 - Lecture 1054 Homework Discussion Translation between color triangle and 8 bit RGB Point: r = 0.55, g = 0.2, b = 1 - 0.55 - 0.2 = 0.25 1 st Step: Identify brightest component r = 0.55  R = 255 2 nd Step: Calculate the other two components: G = (g/r) × 255 = (0.2/0.55) × 255 = 93 B = (b/r) × 255 = (0.25/0.55) x 255 = 116 8 bit representation: R = 255 G = 93 B = 116

55. revised 2011.07.27SCI200 - Lecture 1055 Homework Discussion Translation between color triangle and 8 bit RGB Practice Problem #1: Locate this point on your color triangle r = 0.15, g = 0.25, b = 1 – r – g = ___________ 1 st Step: Identify brightest component 2 nd Step: Calculate the other two components: 8 bit representation: R = ____ G = ____ B = ____

56. revised 2011.07.27SCI200 - Lecture 1056 Homework Discussion Translation between color triangle and 8 bit RGB Practice Problem #2: Determinre r, g, b from the indicated point: r = _______, g = _______, b = 1 – r – g = ___________ 1 st Step: Identify brightest component 2 nd Step: Calculate the other two components: 8 bit representation: R = ____ G = ____ B = ____

57. revised 2011.07.27SCI200 - Lecture 1057 Homework Discussion Hue Color: r = 0.35, g = 0.55 b = 0.1 Dominant wavelength = 575 nm RGB: R = 162 G = 255 B = 46 G > R > B

58. revised 2011.07.27SCI200 - Lecture 1058 Homework Discussion Hue Color: r = 0.35, g = 0.55, b = 0.1 RGB: R = 162 G = 255 B = 46 Lab: L = luminance a = red vs. green b = blue vs. yellow

59. revised 2011.07.27SCI200 - Lecture 1059 Homework Discussion Hue Color: r = 0.40, g = 0.15, b = 0.45 Dominant wavelength = c545 nm

60. revised 2011.07.27SCI200 - Lecture 1060 Homework Assignment Read Chapters 7 & 8 Homework Packet 10 –Due August 4 Lab on Thursday, July 28 (today) –Color Addition

61. revised 2011.07.27SCI200 - Lecture 1061 Upcoming Labs Lab 7: Color Addition –July 28 Lab 8: Color Subtraction –August 4 Reminder: Last Exam –August 11