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Optics Lesson 5: Color Optics

Recommended Article : 【Physics】 Physics Index


1. Munsell Color System

2. Ostwald Color System

3. CIE Standard Colorimetric System

4. CIE RGB Color System

5. CIE XYZ Color System

6. CIE Lab* Color System

7. YUV Color System

8. HSV Color System

9. Luv* Color System



1. Munsell Color System

Figure. 1. Munsell Color System

⑴ Overview

① Devised by the American painter Albert H. Munsell in 1905

② Modified by the Optical Society of America’s Colorimetry Committee in 1943 and widely used internationally

⑵ Three elements of color

① Hue: Differentiated color categories

② Chroma: Clarity, purity, and intensity of a color, also referred to as saturation

③ Lightness or brightness: The degree of lightness or darkness of a color

⑶ Color representation

Figure. 2. Color representation in the Munsell Color System [Footnote: 2]

① Based on the primary colors of red, yellow, green, blue, and purple, with additional colors such as orange, lime, turquoise, teal, and violet, totaling 10 colors

② Each color is divided into 10 steps, resulting in 100 colors. The 5th step represents the primary color

③ Significance: Achieving objective scientific representation of color through the three attributes of hue, lightness, and chroma

Limitation 1: Gaps between colors are not strictly defined, especially for blue

Limitation 2: Variation in chroma positions makes color mixing difficult

⑷ Lightness representation

① Assigned values from 0 to 10: 0 represents black, and 10 represents white

② For achromatic colors, “N” is prefixed, followed by an appropriate value

⑸ Chroma representation

① Centered on the achromatic axis, numbered from 0, increasing horizontally with higher saturation



2. Ostwald Color System

⑴ Devised by the German chemist Friedrich W. Ostwald

⑵ Color representation

① All colors are represented using the sum of white amount (W), black amount (B), and pure color amount (C), normalized to 100

② Using yellow, red, blue, and green as primary colors, with orange, violet, magenta, and cyan in between, divided into 24 equidistant complementary colors

③ Advantages: Developed with consideration of color and human physiological aspects

④ Disadvantages: Color names are difficult to understand in the representation. Lack of clear relationships between colors hampers practical use

⑶ Lightness and chroma representation: Not separately represented in the Ostwald color system



3. CIE Standard Colorimetric System

⑴ Established by the Commission Internationale de l’Éclairage (CIE) in 1931

⑵ A scientific color system reflecting both physical light quantities and human perceptual qualities

Advantage 1: Can express source illuminants’ color unlike Munsell or Ostwald systems that are limited to object colors

Advantage 2: Independent of human perception



4. CIE RGB Color System

⑴ Color matching experiments: Conducted actively in the early 20th century using three primary colors

① 1st: RGB primary wavelengths defined as 700.0, 546.1, and 435.8 nm

② 2nd: White screen divided into reference and test surfaces

③ 3rd: Illumination of reference surface with three independent brightness-adjustable primary lights

④ 4th: Illumination of test surface with specific test light wavelength, adjusting reference surface’s primary lights to match brightness

⑤ 5th: Color matching: Standard observer judges if mixed color matches test color

⑥ 6th: Averaging results from multiple observers: Called color-matching functions

⑦ Example 1: Mixing approximately 80 W of R primary light and 0.4 W of G primary light creates the same color as 1 W of orange light at 600 nm

⑧ Example 2: Mixing R primary light, G primary light, and B primary light in ratios 243.9 W:4.697 W:3.505 W produces white

⑵ Tristimulus curves: Defined to satisfy the following

Figure. 3. Tristimulus curves in terms of primary units [Footnote: 3]

① E: Spectrum entering the observer’s eye

② R, G, B: Primary lights

③ Drawback: Contains negative values, leading to inconveniences

RGB to gray

Method 1: gray = (R + G + B) / 3

Method 2: gray = 0.2989 R + 0.5870 G + 0.1140 B



5. CIE XYZ Color System

⑴ Tristimulus curves: Defined as follows

Figure. 4. Tristimulus curves in the CIE XYZ Color System

① S(λ): Spectral radiance based on wavelength λ

② I(λ): Spectral reflectance based on wavelength λ, ranging from 0% to 100%

③ E(λ): Spectrum entering the observer’s eye

④ K: Scaling Factor, ranging from 1 to 100

⑤ Generally, integration is performed for visible wavelengths λ ∈ [380, 780]

⑵ Experimental process

Figure. 5. Experimental process in the CIE XYZ Color System

⑶ CIE Color Coordinates (x, y, z) are normalized versions of X, Y, Z

⑷ Relationship between RGB tristimulus and XYZ tristimulus

① Matrix transformation

② (Comment) The relationship between RGB and XYZ tristimulus seems non-linear; thus, the above formula might not be suitable

③ Instead, refer to the online converter at http://www.easyrgb.com/en/convert.php#inputFORM



6. CIE Lab* Color System

⑴ XYZ → Lab* transformation

⑵ Lab* → XYZ transformation

⑶ (Xn, Yn, Zn) are normalization values for CIE XYZ with respect to standard white, such as (98.072, 100, 118.225)



7. YUV Color System

⑴ RGB to YUV

① Y = 0.299 R + 0.587 G + 0.114 B

② U’ = (B - Y) × 0.565

③ V’ = (R - Y) × 0.713

⑵ YUV to gray

① gray = Y



8. HSV Color System

⑴ HSV to RGB

① When 0 ≤ H < 360, 0 ≤ S ≤ 1, 0 ≤ V ≤ 1,

② C = V × S, X = C × (1 - ( H / 60° ) mod 2 - 1 ), m = V - C

③ R = (R’ + m) × 55, G = (G’ + m) × 255, B = (B’ + m) × 255



9. Luv* Color System



Input : 2020.05.26 09:27

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