Radiometry

The development of radiometry has led to a quite systematic and well-defined system of radiometric quantities. Some of the used terms and their precise definitions had to be revised for that purpose. However, older terms and deviating meanings are still widespread not only in older literature, but also because many professionals working primarily with optics and laser technology, for example, but not specifically in radiometry, have not (or not fully) adopted the suggested terms and definitions. The following table also specifies such alternative terms which are used particularly in optics and laser technology:

Quantity	Symbol	Alternative term	Units	Remarks
radiant energy	Qe	optical energy, pulse energy	joule (J)	total radiated energy, e.g. of a light pulse
radiant energy density	we	optical energy density	J/m3	applied e.g. to blackbody radiation
radiant flux	Φe	radiant power, optical power	W = J/s	radiant energy per unit time
spectral flux	Φe,ν or Φe,λ	optical power spectral density	W/Hz or W/nm	radiant flux per unit frequency or wavelength
radiant intensity	Ie,Ω		W/sr	radiant flux per unit solid angle
spectral intensity	Ie,Ω,ν or Ie,Ω,λ		W sr−1 Hz−1 or W sr−1 nm−1	radiant intensity per unit frequency or wavelength
radiance	Le,Ω	brightness (not recommended)	W sr−1 m−2	radiant flux per unit area and unit solid angle
spectral radiance	Le,Ω,ν or Le,Ω,λ		W sr−1 m−2 Hz−1 or W sr−1 m−2 nm−1	radiance per unit frequency or wavelength
irradiance	Ee	flux density	W/m2	received radiant flux on a surface
spectral irradiance	Ee,ν or Ee,λ		W m−2 Hz−1 or W m−2 nm−1	irradiance per unit frequency or wavelength
radiosity	Je		W/m2	radiant flux per unit area, leaving a surface (by emission, reflection or transmission)
spectral radiosity	Je,ν or Je,λ		W m−2 Hz−1 or W m−2 nm−1	radiosity per unit frequency or wavelength
radiant exitance	Me		W/m2	like radiosity, but counting only emitted radiation
spectral exitance	Me,ν or Me,λ		W m−2 Hz−1 or W m−2 nm−1	radiant exitance per unit frequency or wavelength
radiant exposure	He		J/m2	received radiant energy per unit area, equal to the time-integrated irradiance
spectral exposure	He,ν or He,λ		J m−2 Hz−1 or J m−2 nm−1	radiant exposure per unit frequency or wavelength
hemispherical emissivity	ε			radiant exitance relative to that of a blackbody at the same temperature
hemispherical absorptance	A			fraction of absorbed radiant flux on a surface
hemispherical reflectance	R			fraction of reflected radiant flux on a surface
hemispherical transmittance	T			fraction of transmitted radiant flux on a surface
hemispherical attenuation coefficient	μ		m−1	fraction of absorbed or scattered radiant flux per unit length

The subscript “e” of many of those quantities (which is frequently omitted) indicates that they refer to physical energies rather than to visual impressions (“v”) as in photometry. For most radiometric quantities, there is a related photometric quantity, for example radiant flux ↔ luminous flux, radiant intensity ↔ luminous intensity, radiance ↔ luminance, irradiance ↔ illuminance, etc.

Radiometric quantities can be applied not only to visible light, but also to infrared light, ultraviolet light and radiation in other spectral regions.

There is a related field named actinometry, which refers to photon numbers instead of energies. For example, one uses a photon flux in units of m⁻² s¹, where radiometry deals with a radiant flux in units of W/m² = J m⁻² s⁻¹.

Some of those quantities are spectral quantities, referring to some unit frequency or wavelength interval. Their symbols contain “ν” or “λ” in the subscript. By integration of those over all optical frequencies or wavelengths, respectively, one obtains the corresponding integral quantities. For example, the radiant intensity equals the frequency- or wavelength-integrated spectral radiant intensity.

See the article on spectral quantities for more details.

There are also various quantities like I_e,Ω which refer to unit solid angles, and their integration over all solid angles (often only over a hemispherical region, i.e., a total solid angle of 2π) one obtains the corresponding integral quantities. Note that in cases a factor like cos θ is involved in the integrand.

For some of the listed quantities, e.g. for the hemispherical absorptance, the corresponding spectral quantities or angle-resolved quantities are not listed in the table above; they are defined in completely analogous ways.

Various types of instruments can be used for measuring radiometric quantities:

• Optical power meters can be used for measuring a radiant flux, e.g. generated by a laser, and optical energy meters for a radiant energy.
• For highly divergent light, such devices are normally not usable. Here, one may need to use an integrating sphere in conjunction with a suitable detector, e.g. a bolometer or a pyroelectric detector.
• A photodiode can be used for measuring an irradiance, if it is calibrated for the wavelength of some quasi-monochromatic light and its active area is small enough for the required spatial resolution. The irradiance is the radiant flux divided by the active area. For measuring the irradiance over a larger area with high spatial resolution, one may use a kind of image sensor.

Related quantities such as the radiance of a light source are usually calculated from other measured values, e.g. from the irradiance at a location in some distance from the source.

The term radiometer can be understood as referring to any instruments measuring radiometric quantities. However, it is most common for instruments measuring quantities of invisible radiation.

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