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Luminance

Luminance (cd/m2) is the concept for the luminous intensity emitted per unit area of a surface in a specific direction.  It is defined as the luminous intensity of the light emitted or reflected in a given direction from an element of the surface, divided by the area of the element projected in the same direction.

This brings in the concept of apparent or projected area; this is the apparent area of an object from a given viewpoint.  The diagram below shows the various apparent areas for three different viewpoints around a pyramid. Depending on the viewing direction we can see a greater or lesser amount of the surface area. The greater the intensity per unit area and the greater the apparent area that can be seen the higher the luminance will be.

apparentarea

Luminance is a useful concept as it can be regarded as a measurable form of the sensation of brightness.  Thus luminance is a measure to use when assessing peoples reactions to the lit environment.  However the relationship between luminance and brightness is not that straight forward.  The figure below illustrates the point.

apparentbrightness

The two grey squares in the diagram are the same colour and thus under uniform lighting they have the same luminance.  However, the square with the dark surround looks brighter than the square on the left.

Luminous Intensity (Candela)

Luminous Intensity is defined as the luminous flux emitted in a given direction per unit solid angle.

Therefore if the luminous flux is concentrated into a smaller solid angle the intensity will increase. So two different lamps emitting the same luminous flux (lumen) could have completely different luminous intensity distribution. Think of a an omni-directional globe versus a narrow beam spotlight - the spotlight uses a reflector to concentrate/focus the luminous flux into a smaller beam angle and therefore all the light in concentrated in a particular direction over a smaller solid angle resulting in increased luminous intensity.

LuminousIntensity

This brings in the concept of solid angle and more particularly unit solid angle. A unit soild angle is called a Steradian.

The steradian (sr) is the Standard International (SI) unit of solid angular measure. There are 4 pi, or approximately 12.5664, steradians in a complete sphere.

A steradian is defined as conical in shape, as shown in the illustration. Point P represents the center of the sphere. The solid (conical) angle q, representing one steradian, is such that the area A of the subtended portion of the sphere is equal to r2, where r is the radius of the sphere.

SolidAngle