Tristimulus values

Editor : Optomon

 From now on, we will have time for detailed analysis and understanding about color because this is fundamental knowledge to develop quantitative measurement systems. For better knowledgeable understanding, I referred to well summarized website of KURABO Electronics Division(クラボウ エレクトロニクス事業部).

Almost everything around us has its own color or colors. Why do leaves look green?
The following three elements are involved when we see and recognize the color of an object:

1. Light
2. Object having color
3. Human sensation

Fig 1. Perception of colors

 Light is one type of electromagnetic wave, which include gamma rays, X-rays, ultraviolet rays, visible infrared rays, and radio waves in the ascending order of their wavelengths. X-rays (which are used for radiography) and radio waves (which are used for TV, radios, and cell- phones) are examples of magnetic waves that we are familiar with. Infrared rays are used for a variety of analyses. Visible rays, as the name implies, are rays that have wavelengths ranging from 380 to 780 nm (nm: one billionth of 1 meter).

Fig 2. Electromagnetic waves vs. visible rays

 As shown in Fig. 2, visible rays have colors specific to each wavelength (colors of light). Light that has continuous energy across the entire range of visible wavelengths, such as sunlight, is called white light.
When the leaf is perceived as green in sunlight, the following process occurs, as shown in Fig. 1 :

1. The white light emitted by the sun reaches the leaf.
2. Part of the white light is absorbed by pigments of the leaf and the other part reflected.
3. The reflected light reaches our eyes and is perceived as a color by our brains.

 In other words, when the leaf has green pigments, the red color, which is the complementary color of green, is absorbed. The color that has been reflected and reaches our eyes is the color of the white light without the red component; i.e., green. In this way, the color of light that reaches our eyes is determined.

Fig 3. Process of generation of reflected light

 Expressing this mechanism scientifically, the energy specific to each wavelength of light from the light source is called the spectral distribution of the light source, and it is represented by the symbol S(λ). The light-reflecting property of an object is called the spectroscopic reflectance factor (or simply the reflectance) and is represented by the symbol R(λ).

 When S(λ)is multiplied by R(λ)for each wavelength, the product represents the reflected light, which is shown using the symbol of S(λ)、R(λ).

Fig 4. Color received by the eye

 The excitations resulting from red, green, and blue stimulation are referred to as three stimulation values, and are represented by the symbols X(λ), Y(λ), and Z(λ). To obtain X, Y, and Z, color-matching functions are required. Color-matching functions are the values that have been experimentally determined to show to what extent the red, green, and blue stimulations are felt for each wavelength of light. The relationship between them is shown in Fig. 5.

Fig 5. Color-matching functions

 The x(λ) function represents the degree to which redness is sensed at each wavelength. The y(λ) and z(λ) functions similarly represent the respective degrees for blueness and greenness at each wavelength. This means that the degree of red, blue, and green stimulation is considered to be the accumulated effect of stimulations between the wavelengths that can be sensed. Once the values for the reflected light that enters the eye and the color-matching functions are found, the X, Y, and Z values for the resulting stimulation intensity can be obtained.

 All of the currently used colorimetric values and color difference values are based on these three stimulation values. Various attempts have been made to match the distribution of colors and the degrees of color differences sensed by the human eye.

 Shown below is the equation for finding the three stimulation values for object colors :

To be continued on May’s issue…