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Colors

Measuring Light

  • Colorimetry is the science of measuring light and color.
  • Sensations that arise from light energy of different wavelengths
  • Color is a phenomenon of human perception and not a universal property of light
  • The photodetectors in human retina consists of rods and cones
    • Rods : Sensitive to brightness
    • Cones : Sensitive to color

Cone Responses

  • Three types of cones in human retina
    • S-cones : Sensitive to short wavelengths
    • M-cones : Sensitive to medium wavelengths
    • L-cones : Sensitive to long wavelengths
  • Response of a cone is magnitude of electrical signal generated in response to light of a particular wavelength. \(\phi(\lambda)\) is the wavelength density function of the incident light, and \(L(\lambda)\), \(M(\lambda)\), and \(S(\lambda)\) are the response functions of the L, M, and S cones, respectively. The response of the cones can be expressed as:
\[ L = \int_{\lambda} \phi(\lambda) L(\lambda) d\lambda \]
\[ M = \int_{\lambda} \phi(\lambda) M(\lambda) d\lambda \]
\[ S = \int_{\lambda} \phi(\lambda) S(\lambda) d\lambda \]

Colorometric Concepts

  • Luminance : Brightness of a color
  • Chromaticity : Color without brightness
  • Dominant Wavelegth : Single spectral color (hue)
  • Purity : Ratio of pure color to white light (saturation)

Color matching

Photoreceptors act as linear intergrators of light energy. This means it's possible to find two different spectral distributions \(-\phi_1(\lambda)\) and \(-\phi_2(\lambda)\) that produce the same response in the cones. This is the basis of color matching. This is called metamerism.

  • Spectral tri-stimulus values - using monochromatic light sources to match a given color
  • CIE defined three primaries: 435.8 nm(B), 546.1 nm(G) and 700.0 nm(R)
  • A color can be matched by a linear combination of the three primaries
  • Negative values means that wavelength is too saturated to be produced by the primary

It's possible to transform one set of tristimulus values to another

  • CIE defined a standard observer with color matching functions \(X(\lambda)\), \(Y(\lambda)\), and \(Z(\lambda)\)
  • Cannot be realized physically

Color spaces

  • We could define an orthogonal coordinate system with \(X\), \(Y\), and \(Z\) as the axes
  • Color gamut: spacial extent of volume in which colors lie
\[ x = \frac{X}{X+Y+Z} \hspace{1cm} y = \frac{Y}{X+Y+Z} \hspace{1cm} z = \frac{Z}{X+Y+Z} \]
\[ X = \frac{x}{y} Y \hspace{1cm} Z = \frac{1-x-y}{y} Y \]

We usually represent Z in terms of X and Y, and Y is the luminance.

Chromaticity Diagram

Chromaticity Diagram
Chromaticity Diagram
  • All colors visible to the human eye lie within the horseshoe shaped curve
  • The straight line connecting two points on the curve represents all the colors that can be produced by mixing the two colors
  • The edge of the diagram, called the specral locus, represents pure mono-chromatic colors. These are the most saturated colors
  • The least saturated colors are at the center of the diagram, where the white point is located
  • Color gamut: subet of colors that can be produced by a particular device

Other color spaces

Space Description Cons
RGB Additive color model, Based on human perception of color Not perceptually uniform, High correlation between components
HSV Hue, Saturation, Value Hue discontinuity at 0 and 360 degrees, Bad correlation between computed and perceived lightness
CMYK Subtractive color model, used in printing