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Spectral radiance
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 (W·sr−1·m−2·Hz−1) and that of spectral radiance in wavelength is the watt per steradian per square metre per metre (W·sr−1·m−3)—commonly the watt per steradian per square metre per nanometre (W·sr−1·m−2·nm−1). 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.
The specific (radiative) intensity is a quantity that describes the rate of radiative transfer of energy at P1, a point of space with coordinates x, at time t. It is a scalar-valued function of four variables, customarily written as where:
I (x, t ; r1, ν) is defined to be such that a virtual source area, dA1, containing the point P1 , is an apparent emitter of a small but finite amount of energy dE transported by radiation of frequencies (ν, ν + dν) in a small time duration dt , where and where θ1 is the angle between the line of propagation r and the normal P1N1 to dA1; the effective destination of dE is a finite small area dA2 , containing the point P2 , that defines a finite small solid angle dΩ1 about P1 in the direction of r. The cosine accounts for the projection of the source area dA1 into a plane at right angles to the line of propagation indicated by r.
The use of the differential notation for areas dAi indicates they are very small compared to r2, the square of the magnitude of vector r, and thus the solid angles dΩi are also small.
There is no radiation that is attributed to P1 itself as its source, because P1 is a geometrical point with no magnitude. A finite area is needed to emit a finite amount of light.
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Spectral radiance
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 (W·sr−1·m−2·Hz−1) and that of spectral radiance in wavelength is the watt per steradian per square metre per metre (W·sr−1·m−3)—commonly the watt per steradian per square metre per nanometre (W·sr−1·m−2·nm−1). 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.
The specific (radiative) intensity is a quantity that describes the rate of radiative transfer of energy at P1, a point of space with coordinates x, at time t. It is a scalar-valued function of four variables, customarily written as where:
I (x, t ; r1, ν) is defined to be such that a virtual source area, dA1, containing the point P1 , is an apparent emitter of a small but finite amount of energy dE transported by radiation of frequencies (ν, ν + dν) in a small time duration dt , where and where θ1 is the angle between the line of propagation r and the normal P1N1 to dA1; the effective destination of dE is a finite small area dA2 , containing the point P2 , that defines a finite small solid angle dΩ1 about P1 in the direction of r. The cosine accounts for the projection of the source area dA1 into a plane at right angles to the line of propagation indicated by r.
The use of the differential notation for areas dAi indicates they are very small compared to r2, the square of the magnitude of vector r, and thus the solid angles dΩi are also small.
There is no radiation that is attributed to P1 itself as its source, because P1 is a geometrical point with no magnitude. A finite area is needed to emit a finite amount of light.