Title: photon radiance
Long Title: IUPAC Gold Book - photon radiance
DOI: 10.1351/goldbook.P04639
Status: current
Index: quantity

Definition
Number of photons (quanta of radiation, \(N_{\rm{p}}\)) per time interval (photon flux), \(q_{\rm{p}}\), leaving or passing through a small transparent element of surface in a given direction from the source about the solid angle \(\varOmega\), divided by the solid angle and by the orthogonally projected area of the element in a plane normal to the given beam direction, \(\rm{d}S_{\perp } = \rm{d}S\, cos\,\theta\), with \(\theta\) the angle between the normal to the surface and the direction of the beam. Equivalent definition: Integral taken over the hemisphere visible from the given point, of the expression \(L_{\rm{p}}\, cos\,\theta\,\rm{d}\varOmega\), with \(L_{\rm{p}}\) the photon radiance at the given point in the various directions of the incident beam of solid angle \(\varOmega\) and \(\theta\) the angle between any of these beams and the normal to the surface at the given point.

Notes
1) Mathematical definition: \[L_{\rm{p}} = \frac{\rm{d}^{2}q_{p}}{\rm{d}\varOmega \, \rm{d}S_{\perp }} = \frac{\rm{d}^{2}q_{p}}{\rm{d}\varOmega \, \rm{d}S\, cos\,\theta}\] for a divergent beam propagating in an elementary cone of the solid angle \(\varOmega\) containing the direction \(\theta\). SI unit is \(\rm{m}^{-2}\ \rm{s}^{-1}\ \rm{sr}^{-1}\).
2) For a parallel beam it is the number of photons (quanta of radiation, \(N_{\rm{p}}\)) per time interval (photon flux), \(q_{\rm{p}}\), leaving or passing through a small element of surface in a given direction from the source divided by the orthogonally projected area of the element in a plane normal to the given direction of the beam, \(\theta\). Mathematical definition in this case: \(L_{\rm{p}} = \rm{d}q_{\rm{p}}/\left ( \rm{d}S\, cos\,\theta \right )\) If \(q_{\rm{p}}\) is constant over the surface area considered, \(L_{\rm{p}} = q_{\rm{p}}/\left ( S\, cos\,\theta \right )\), SI unit is \(\rm{m}^{-2}\ \rm{s}^{-1}\).
3) This quantity can be used on a chemical amount basis by dividing \(L_{\rm{p}}\) by the Avogadro constant, the symbol then being \(L_{n\rm{,p}}\), the name 'photon radiance, amount basis'. For a divergent beam SI unit is \(\pu{mol m-2 s-1 sr-1}\); common unit is \(\pu{einstein m-2 s-1 sr-1}\). For a parallel beam SI unit is \(\pu{mol m-2 s-1}\); common unit is \(\pu{einstein m-2 s-1}\).

Related Terms
- Avogadro constant: https://goldbook.iupac.org//terms/view/A00543
- angle: https://goldbook.iupac.org//terms/view/A00346
- chemical amount: https://goldbook.iupac.org//terms/view/C01019
- radiance: https://goldbook.iupac.org//terms/view/R05037
- visible: https://goldbook.iupac.org//terms/view/VT07496

Source
- PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 396 (https://doi.org/10.1351/pac200779030293)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/P04639/html
- json: https://goldbook.iupac.org/terms/view/P04639/json
- xml: https://goldbook.iupac.org/terms/view/P04639/xml

Citation: Citation: 'photon radiance' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.P04639
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Accessed: 2026-06-06T22:37:41+00:00