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What is Luminance?

the sun

Luminance is the intensity of light coming from a given planar source. This planar source is an area projected in a given direction that is defined by a solid angle, which is the cone created between the lens receiving the light and a source point on the planar light source.

As you read this you are probably looking at a computer display. You are able to see every pixel on the screen because the light from every point is getting to the retina of your eye. You are also able to see all of the pixels on the screen from multiple viewpoints because each pixel has a corresponding cone of light that travels in three dimensional space out toward your eyes. Your eyes have lenses that focus the light from the screen onto a plane on the back of your eye called the retina. The solid angle, in this case, is the angle on the screen that defines the cone of light with end points on the lens of your eye. It is the angle that creates the two dimensional plane projected out towards you and subtended by your eyes. Solid angles are measured in units of steradians.

On an everyday basis, luminance is used to indicate how bright something is. Your computer display, for example, has a certain luminance based on how much light per square meter it is able to throw onto your retina (the actual number is between 50 and 300 candelas per square meter). A luminance photometer is able to determine the luminance of a surface by calculating the luminous flux for a given focal plane created by an onboard lens that intercepts the light from a given source. The light is then refocused onto a measurement plane on the back of the photometer that can take light intensity readings. The sorts of people who are most concerned about luminance are those who work on large indoor lighting projects and manufacturers of computer and television displays.

The luminance of a surface is mathematically represented as the second derivative of luminous flux with respect to the area of the surface and the solid angle. With a given luminous flux function, we are able to determine the luminance of a surface that emits light as:

Lv = d2F / (d.A.dΩ.cos θ)

where Lv is the luminance of the surface (in SI units cd/m2), F is the luminous flux, A is the area of the surface emitting light, θ is the angle between the normal of the surface and the direction the light is coming from, and Ω is the solid angle. Luminous flux has the SI units of candela*steradian. It is a measurement of the perceived power of light, or the rate at which energy is delivered by light from a given light source.

Illuminance, should not be confused with luminance, which is the degree to which a surface is illuminated by some external light source. The sun, for example, has a very high luminance value of 109 cd/m2, but it is likely to have a very low illuminance value because of the very low level of incident light (e.g. from other stars).

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