Mathematics of Light

Introduction

Up to the seventeenth century, most theories attributed color to some sort of modification of light that was thought to occur when light interacted with matter. Light, in its purest form (such as sunlight) was thought to be colorless. However, progress in understanding color was made by Isaac Newton when in 1666 he was able to show that normal white light already contained all the colors of the spectrum, which could be separated using a prism. He also concluded from his experiments that objects have color because they selectively reflect certain colors of the spectrum while absorbing light of other colors.

Light is the small part of the electromagnetic spectrum that can affect the human sense of sight. The visible part of the spectrum (for us) ranges from 400 nm (blue) to 700 nm (red). Each wavelength value within the visible band corresponds to a distinct colour.

Parameters of light that are of interest to us:

Wavelength - the length of one light-wave cycle

Frequency - the number of wavelengths per second

Three attributes are used to specify a color: hue, saturation and brightness. These describe only the perception of light, not its physical properties.

1. Hue - a feature of monochromatic light that varies with wavelength and used to denote the various regions of the spectrum (in other words, the basic color from the spectrum).

2. Saturation - how much a color differs from white (ie vivid pure color versus pastel color)

3. Brightness - the perceived intensity of light

Spectral Power Distribution

Monochromatic light is light that has only one wavelength, and thus cannot be further divided into different components using a prism. But most light sources are not monochromatic ...

... middle of paper ...

...d (B) of wavelength 435.8nm.

This means that given an RGB color (C) = L1(R) + L2(G) + L3 (B), its coordinates in the XYZ system are:

X = 2.7689*L1 + 0.38159*L2 + 18.801*L3

Y = L1 + L2 + L3

Z = 0 + 0.012307*L2 + 93.066*L3

This particular transformation was chosen so that the XYZ system would have several convenient properties. One is that there are no negative tristimulus values, which reduces the possibility of error. Another is that the color triangle enclose the spectrum locus as closely as possible.

Works Consulted

Williamson, Samuel J. and Herman Z. Cummins. Light and Color in Nature and Art. 1983. John Wiley and Sons.

Overheim, R. Daniel and David L. Wagner. Light and Color. 1982. John Wiley and Sons.

Bouma, Dr. P. J. Physical Aspects of Colour. 1971. MacMillan.

Wright, W. D. The Measurement of Colour. 1969. Adam Hilger.