Color

What Determines the Colors We See

Light - The Electromagnetic Signal

It is the spectral composition, the energy spectral distribution \(L(\lambda)\) of the light that is the signal the eye receives for the brain to process. Sometimes \(L(\lambda)\) may be referred to as the color, but this is to be distinguished from the actual color we perceive from this light.

Newton's experiments and contributions (1704):

• Decomposition of white light by a prism into many spectral lights, and reconstruction of a white light from the spectral lights by a second prism; A spectral light can not be further decomposed.
• A spinning round plate with sections painted in different colors would look white;
• Realization that perception of color is caused by the spectral composition of the light.

Color Matching and Trichromatic Theory

This theory emerged over the eighteenth century which basically states that any color \(L(\lambda)\) can be reproduced by mixing appropriate amounts of three primary colors with energy distributions \(P_j(\lambda),\;\;(j=1,2,3)\) provided the wavelengths are far enough apart. For example, red, green, and blue. As we will see later, ``far enough apart'' means mathematically the spectral energy distributions of the three colors are linearly independent.

The Color Matching Experiment

The goal of an additive color matching experiment is to superimpose appropriate amounts of the three primaries \(P_j\;\;\;(j=1,2,3)\) so that the resulting color \(L'\) is perceived the same as a given color \(L\). This can be actually carried out by three projectors that project the three primary colors with adjustable intensities on a screen.

This process is symbolically represented by

$ [L]\equiv [L'] = A_1(L) [P_1] + A_2(L) [P_2] + A_3(L) [ P_3]$

This is not a mathematical equation in the normal sense, as the symbols used here have special meanings:
Anything inside a pair of brackets (e.g., \([L]\) or \([P_j]\)) is a color (an arbitrarily given color or a primary color) of certain energy spectral distribution;
\(A_j(L)\) is a scaler coefficients representing the amount of a primary color \(P_j\) needed to match the given color \(L\);
The symbol \(+\) represents the actual mixing of the colors by projecting them on the same screen.
The symbol \(\equiv\) means the color on the left-hand side is equivalent to that on the right-hand side in the sense that they are perceived by the human eye as the same color. (But this does not mean that the two energy distributions are necessarily the same, as discussed later.)
As we are usually concerned with the proportions of the color mixing but not the absolute intensities, the color matching process can be normalized by using a reference white color \(W\). The amount of primary \(P_j\) needed to match \(W\), represented by \(A_j(W)\), is used to normalize the intensity \(A_j(L)\) for matching \(L\):

$ T_j(L)=\frac{A_j(L)}{A_j(W)};;;;(j=1,2,3) $

The \(T_j(L)\)'s are called the tristimulus values.

Photoreceptors and Perception of

Sensitivity functions

There are two types of photoreceptor cells called rods and cones.

• Rods are very sensitive to light and can respond to just a few photons.
• Cones need significantly brighter light.

There are three types of cone cells (called the S type, M type, and L type) with different sensitivities, responding to short, medium, and long wavelengths. Color vision is the result of these three types of cone cells.

The physical intensity measurements of the electromagnetic energy distribution is related to the perceptual brightness and color by the scotopic (dim light mediated by the rods) and the photopic (bright light mediated by the cones) sensitivity or luminosity functions \(S(\lambda)\). Specifically, the magnitude of the response of a photoreceptor (the firing rate) is determined by how much light is, or more specifically, how many photons are, absorbed by the photopigment of the photoreceptors. The more light a receptor catches, the stronger its response will be, and the more sensitive the receptor becomes. This property of the photoreceptors can be represented by its photon capture rate (number of photons absorbed per unit time), or its sensitivity, denoted by \(S(\lambda)\) as a function of wavelength \(\lambda\). The sensitivity functions of the three types of cone cells can be denoted by \(S_i(\lambda)\;\;\;(i=1,2,3)\) which peak approximately at 560 nm, 530 nm and 430 nm respectively, as shown.

Absorption of light in the cones of the human retina.