Light and Color

Notes of Real-Time Rendering Chapter 8

The transformation of colors that represent scene linear light quantities into final display colors.

Light Quantities

Radiometry(辐射度量学)

Radiometry deals with the measurement of electromagnetic radiation.

Radiometric quantities(辐射度量) exist for measuring various aspects of electromagnetic radiation.

In radiometry, the basic unit is radiant flux(辐射通量), $\phi$. Radiant flux is the flow of radiant energy over time measured in watts($W$).

Irradiance(辐照度) is the density of radiant flux with respect to area, $d\phi/dA$.

Solid angle(立体角), which is a three-dimensional extension of the concept of an angle. An angle can be thought of as a measure of the size of a continuous set of directions in a plane, with a calue in radians equal to the length of the arc this set of directions intersects on a enclosing circle with radius 1. A solid angle measures the size of a continuous set of directions in three-dimensional space, measured in steradians(球面度), which are defineed by the area of the intersection patch on an enclosing sphere with radius 1. Solid angle is represented by the symbol $\omega$.

Radiant intensity(辐射强度), $I$, which is flux density with respect to direction--more precisely, solid angle. It is measured in watts per steradian.

Radiance(辐射率), $L$, is a measure of electromagnetic radiation in a single ray. It is defined as the density of radiant flux with respect to both area and solid angle($d^2\phi/dAd\omega$).

Radiance is what sensors measure, so it is of prime importance for rendering. The purpose of evaluating a shading equation is to compute the radiance along a given ray, from the shaded surface point to the camera.

The radiance in an environment can be thought of as a function of five variables(or six, including wavelength), called the radiance distribution.

An important property of radiance is that it is not affected by distance, ignoring atmospheric effects such as fog.

Most light waves contain a mixture of many different wavelengths. This is typically visualized as a spectral power distribution (SPD)(光谱功率分布), which is a plot showing how the light's energy is distributed across different wavelengths.

Since full SPDs are unwieldy to use for rendering, especially at interactive rates, in practice radiometric quantities are represented as RGB triples.

Photometry(光度测定)

Radiometry deals purely with physical quantities, without taking account of human perception. Photometry weights everything by the sensitivity of the human eye. The results of radiometric computations are converted to photometric units by multiplying by the CIE photometric curve, a bell-shaped curve centered around 555 nm that represents the eye's response to various wavelengths of light.

Each radiometric quantity has an equivalent metric photometric quantity.

Luminance is often used to describe the brightness of flat surfaces.

Radiometric Quantity : Units	Photometric Quantity : Units
radiant flux : watt ($W$)	luminous flux(光通量) : lumen (lm)
irradiance : $W/m^2$	illuminance(光照度) : lux (lx)
radiant intensity : $W/sr$	luminous intensity(发光强度) : candela (cd)
radiance : $W/(m^2sr)$	luminance(亮度) : $cd/m^2 = nit$

Colorimetry(色度)

Colorimetry deals with the relationship between spectral power distribution and perception of color.

In color matching, three colored lights are projected on a white screen so that their colors add together and form a patch. The functions relating each set of matching weights to the test patch wavelengths are called color-matching-function.

The three weighted $r$, $g$, and $b$ lights cannot directly represent all visible colors, as their color-matching functions have negative weights for various wavelengths.