In radiometry, spectral radiance or specific intensity is the radiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of spectral radiance in frequency is the watt per steradian per square metre per hertz () and that of spectral radiance in wavelength is the watt per steradian per square metre per metre ()—commonly the watt per steradian per square metre per nanometre (). The microflick is also used to measure spectral radiance in some fields.
Spectral radiance gives a full radiometric description of the field of classical electromagnetic radiation of any kind, including thermal radiation and light. It is conceptually distinct from the descriptions in explicit terms of Maxwellian electromagnetic fields or of photon distribution. It refers to material physics as distinct from psychophysics.
For the concept of specific intensity, the line of propagation of radiation lies in a semi-transparent medium which varies continuously in its optical properties. The concept refers to an area, projected from the element of source area into a plane at right angles to the line of propagation, and to an element of solid angle subtended by the detector at the element of source area.
The term brightness is also sometimes used for this concept. The SI system states that the word brightness should not be so used, but should instead refer only to psychophysics.
Definition
The specific (radiative) intensity is a quantity that describes the rate of radiative transfer of energy at , a point of space with coordinates , at time . It is a scalar-valued function of four variables, customarily written as
where: denotes frequency. denotes a unit vector, with the direction and sense of the geometrical vector in the line of propagation from the effective source point , to a detection point .
is defined to be such that a virtual source area, , containing the point , is an apparent emitter of a small but finite amount of energy transported by radiation of frequencies in a small time duration , where , and where is the angle between the line of propagation and the normal to ; the effective destination of is a finite small area , containing the point , that defines a finite small solid angle about in the direction of . The cosine accounts for the projection of the source area into a plane at right angles to the line of propagation indicated by .
The use of the differential notation for areas indicates they are very small compared to , the square of the magnitude of vector , and thus the solid angles are also small.
There is no radiation that is attributed to itself as its source, because is a geometrical point with no magnitude. A finite area is needed to emit a finite amount of light.
Invariance
For propagation of light in a vacuum, the definition of specific (radiative) intensity implicitly allows for the inverse square law of radiative propagation. The concept of specific (radiative) intensity of a source at the point presumes that the destination detector at the point has optical devices (telescopic lenses and so forth) that can resolve the details of the source area . Then the specific radiative intensity of the source is independent of the distance from source to detector; it is a property of the source alone. This is because it is defined per unit solid angle, the definition of which refers to the area of the detecting surface.
This may be understood by looking at the diagram. The factor has the effect of converting the effective emitting area into a virtual projected area at right angles to the vector from source to detector. The solid angle also has the effect of converting the detecting area into a virtual projected area at right angles to the vector , so that . Substituting this for in the above expression for the collected energy , one finds : when the emitting and detecting areas and angles and , and , are held constant, the collected energy is inversely proportional to the square of the distance between them, with invariant .
This may be expressed also by the statement that is invariant with respect to the length of ; that is to say, provided the optical devices have adequate resolution, and that the transmitting medium is perfectly transparent, as for example a vacuum, then the specific intensity of the source is unaffected by the length of the ray .
For the propagation of light in a transparent medium with a non-unit non-uniform refractive index, the invariant quantity along a ray is the specific intensity divided by the square of the absolute refractive index.