radiometry Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which ch ...

, radiant intensity is the

radiant flux In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spe ...

emitted, reflected, transmitted or received, per unit

solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The poi ...

, and spectral intensity is the radiant intensity per unit

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...

, depending on whether the

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...

is taken as a function of frequency or of wavelength. These are ''directional'' quantities. The

SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

of radiant intensity is the

watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James ...

per

steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radian ...

(), while that of spectral intensity in frequency is the watt per steradian per

hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that o ...

() and that of spectral intensity in wavelength is the watt per steradian per metre ()—commonly the watt per steradian per nanometre (). Radiant intensity is distinct from

irradiance In radiometry, irradiance is the radiant flux ''received'' by a ''surface'' per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used ...

and radiant exitance, which are often called '' intensity'' in branches of

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...

other than radiometry. In

radio-frequency engineering Radio-frequency (RF) engineering is a subset of electronic engineering involving the application of transmission line, waveguide, antenna and electromagnetic field principles to the design and application of devices that produce or use sign ...

, radiant intensity is sometimes called radiation intensity.

Mathematical definitions

Radiant intensity

Radiant intensity, denoted ''I''_e,Ω ("e" for "energetic", to avoid confusion with photometric quantities, and "Ω" to indicate this is a ''directional'' quantity), is defined as :

I_ = \frac,

where *∂ is the

partial derivative In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Pa ...

symbol; *Φ_e is the

emitted, reflected, transmitted or received; *''Ω'' is the

. In general, ''I''_e,Ω is a function of viewing angle ''θ'' and potentially azimuth angle. For the special case of a

Lambertian surface Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view. More technically, the su ...

, ''I''_e,Ω follows the

Lambert's cosine law In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle ''θ'' between the directi ...

''I''_e,Ω = ''I''₀ cos ''θ''. When calculating the radiant intensity emitted by a source, ''Ω'' refers to the solid angle into which the light is emitted. When calculating radiance received by a detector, ''Ω'' refers to the solid angle subtended by the source as viewed from that detector.

Spectral intensity

Spectral intensity in frequency, denoted ''I''_e,Ω,ν, is defined as :

I_ = \frac,

where ''ν'' is the frequency. Spectral intensity in wavelength, denoted ''I''_e,Ω,λ, is defined as :

I_ = \frac,

where ''λ'' is the wavelength.

Radio-frequency engineering

Radiant intensity is used to characterize the emission of radiation by an

antenna Antenna ( antennas or antennae) may refer to: Science and engineering * Antenna (radio), also known as an aerial, a transducer designed to transmit or receive electromagnetic (e.g., TV or radio) waves * Antennae Galaxies, the name of two collid ...

: :

I_ = E_\mathrm(r) \, r^2,

where *''E''_e is the

of the antenna; *''r'' is the distance from the antenna. Unlike power density, radiant intensity does not depend on distance: because radiant intensity is defined as the power through a solid angle, the decreasing power density over distance due to the

inverse-square law In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be unders ...

is offset by the increase in area with distance.

SI radiometry units

References

External links

Radiation: Activity and Intensity
NDE/NDT Resource Center {{Authority control Physical quantities Radiometry