irradiance (at a point of a surface), $E$

Radiant power, $P$ , of all wavelengths incident from all upward directions on a small element of surface containing the point under consideration divided by the area of the element. SI unit is $W m −2$ .

Notes:

Mathematical definition: $E = d P d S$ . If the radiant power is constant over the surface area considered, $E = P S$ .
Alternative definition: Integral, taken over the hemisphere visible from the given point, of the expression $L cos ⁡ θ d Ω$ , where $L$ is the radiance at the given point in the various directions of the incident elementary beams of solid angle $Ω$ and $θ$ is the angle between any of the beams and the normal to the surface at the given point.
$E = ∫ 2 π L cos ⁡ θ ⁢ d Ω$
This term refers to a beam not scattered or reflected by the target or its surroundings. For a beam incident from all directions, fluence rate ( $E o$ ) is an equivalent term.
$E = ∫ λ E λ ⁢ d λ$ where $E λ$ is the spectral irradiance at wavelength $λ$ .

Source:

PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 357

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IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.

Last update: 2014-02-24; version: 2.3.3.

DOI of this term: https://doi.org/10.1351/goldbook.I03254.

Original PDF version: http://www.iupac.org/goldbook/I03254.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.

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