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In radiometry, radiant exposure or fluence is the radiant energy ''received'' by a ''surface'' per unit area, or equivalently the irradiance of a ''surface,'' integrated over time of irradiation, and spectral exposure is the radiant exposure 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 ...
or
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 is taken as a function of frequency or of wavelength. 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. E ...
of radiant exposure is the
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...
per square metre (), while that of spectral exposure in frequency is the joule per square metre 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 one he ...
() and that of spectral exposure in wavelength is the joule per square metre per metre ()—commonly the joule per square metre per nanometre ().

# Mathematical definitions

## Radiant exposure

Radiant exposure of a ''surface'', denoted ''H''e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as $H_\mathrm = \frac = \int_0^T E_\mathrm(t)\, \mathrmt,$ 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; *''Q''e is the radiant energy; *''A'' is the area; *''T'' is the duration of irradiation; *''E''e is the irradiance.

## Spectral exposure

Spectral exposure in frequency of a ''surface'', denoted ''H''e,''ν'', is defined as $H_ = \frac,$ where ''ν'' is the frequency. Spectral exposure in wavelength of a ''surface'', denoted ''H''e,''λ'', is defined as $H_ = \frac,$ where ''λ'' is the wavelength.

# See also

*
Exposure (photography) In photography, exposure is the amount of light per unit area (the image plane's illuminance times the exposure time) reaching a frame of photographic film or the surface of an electronic image sensor, as determined by shutter speed, lens F-n ...
* Radiant energy * Irradiance

# References

{{Authority control Physical quantities Radiometry