luminous intensity measurement is solely understood as referred to a specific direction and contained in a w solid angle.
In the same way that a plane angle measured in radians corresponds to a surface, a solid or stereo angle corresponds to a volume measurement and is measured in stereoradians.
The radian is defined as the plane angle within an arc of a circle, equal to the radius of the circle.

The stereoradian is defined as the solid angle which corresponds to a spherical cap whose surface equals the square of the sphere radius

Luminous output of a source of light in one specific direction equals the ratio between the luminous flux contained in whatever solid angle whose axis coincides with the considered direction. Its symbol is I, and its unit of measurement is the candela (cd). The formula which expresses it is the following:

Candela is defined as the luminous intensity of a specific source which emits luminous flux equal to one lumen in a solid angle per stereoradian (sr).

Luminance measurement is conducted by means of a special device called a luminancemetre or nitmeter. It is based on two optical systems, directional and measurement systems, respectively.

The directional system is oriented in such a way that the image coincides with the point to be measured. Once it has been oriented, the light that reaches it is transformed into electric current. Its values are measured in cd/m2.