Power Per Unit Solid Angle

The power (flux) per unit solid angle (sometimes called pointance) is the nearest precise terminology to the common term intensity. It expresses the directionality of the radiated energy and is appropriate for the description of point sources. In the case of radiant power, it is expressed in watts per steradian. For visible light it is expressed in lumens per steradian = candela.

If the intensity ( I = dΦ/dω ) of a source is the same in all directions, the source is called isotropic. Otherwise, for a flat radiating surface, known as a lambertian, the intensity falls off as the cosine of the observation angle with respect to the surface normal.

Power Per Unit Area Per Unit Solid Angle

The power per unit area per unit solid angle is sometimes called sterance. In the radiant case it is measured in watts/m² steradian and is also called radiance. In the luminous case it is measured in lumens/m² steradian which is equivalent to candela/m² = nit. This quantity is also called luminance.

Point Source vs Extended Source

For a point source, the emitted light intensity or pointance is the same in all directions, or isotropic. It behaves according to the inverse square law.

A flat surface that reflects or emits equal luminance in every direction from the surface is said to be a lambertian surface. For example, an evenly illuminated flat surface such as a sheet of paper is approximately lambertian in that the luminance that you see from any direction is essentially the same. The intensity or pointance from such a surface in any direction is proportional to the cosine of the reflected angle.

Reflection from a surface can be complicated by surface roughness. For an ideal lambertian surface the reflection will follow the cosine law. The ray showing 50% is at the angle 30° from the surface where cos 60° = 0.5. An interesting aspect of lambertian reflection is that although the luminous intensity will be half as much at that angle, the visual area that your eye sees is also half as much, so the surface appears equally "bright" from that angle.

The Candela

The candela is the foundation unit for the measurement of visible light. It is one of the seven foundation SI units. It's formal definition is:

The candela is abbreviated cd and its standard symbol is I_v. The candela is then used to define the lumen and other quantities used in the measurement of visible light. It is approximately equal to the old unit "candlepower" and is generally taken to be equivalent.

For an isotropic source, the relationship between the candela and lumens is 1 cd = 4π lm and the unit relationships is 1 cd = lm/sr.

Candela per square meter

The candela per square meter (cd/m²) is the derived SI unit of luminance for a surface. It is used to characterize the amount of visible light from a light-emitting surface, such as the light provided by a display device. From Wikipedia "The sRGB spec for monitors targets 80 cd/m². Typically, calibrated monitors should have a brightness of 120 cd/m². Most consumer desktop liquid crystal displays have luminances of 200 to 300 cd/m². High-definition televisions range from 450 to about 1500 cd/m²."

The unit cd/m² is called a nit.