World Library  
Flag as Inappropriate
Email this Article


Article Id: WHEBN0006711908
Reproduction Date:

Title: Fluence  
Author: World Heritage Encyclopedia
Language: English
Subject: Joule, Flux, Sievert, Ionizing radiation, Irradiance, Laser hair removal, List of Renault engines
Publisher: World Heritage Encyclopedia


This article is about the concept of fluence in physics. For the car, see Renault Fluence.

In physics, fluence is the flux (either particle or radiative flux) integrated over time. For particles, it is defined as the total number of particles that intersect a unit area in a specific time interval of interest, and has units of m–2 (number of particles per meter squared). Fluence can also be used to describe the energy delivered per unit area, in which case it has units of J/m2. It is considered one of the fundamental units in dosimetry.

In light based medicine and dentistry, fluence, which may be more properly referred to as radiant exposure, is a measurement of energy over area. The area is usually the spot size of the light device.

It has two equivalent definitions:

1. Suppose N particles pass through an area A. The particle fluence for the area A is defined as:

\Phi = \frac{N}{A}.

In the limit of infinitesimal area, this is:

\Phi = \frac{{\rm d} N}{{\rm d} A}.

2. Imagine an infinitesimal volume dV with particles passing through it. The particle fluence can be defined as

\Phi = \frac{\sum {\rm d \ell} }{{\rm d} V},

where \sum {\rm d \ell} is the sum of all the path lengths of the particles that traverse the volume. These definitions are equivalent as can be seen by multiplying the first definition by {\rm d} x/{\rm d} x where dx is the typical path length of a particle in the volume. The numerator ({\rm d}N {\rm d} x) then gives the total path length traced out by the dN particles in the volume ({\rm d}N {\rm d}x \simeq \sum {\rm d \ell}) while the denominator ({\rm d} A {\rm d} x) gives the volume dV.


  • ICRU 33: Radiation Quantities and Units, April, 1980. (

SI radiometry units

Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Radiant energy Qe[nb 2] joule J M⋅L2⋅T−2 energy
Radiant flux Φe[nb 2] watt W M⋅L2⋅T−3 radiant energy per unit time, also called radiant power.
Spectral power Φ[nb 2][nb 3] watt per metre W⋅m−1 M⋅L⋅T−3 radiant power per wavelength.
Radiant intensity Ie watt per steradian W⋅sr−1 M⋅L2⋅T−3 power per unit solid angle.
Spectral intensity I[nb 3] watt per steradian per metre W⋅sr−1⋅m−1 M⋅L⋅T−3 radiant intensity per wavelength.
Radiance Le watt per steradian per square metre W⋅sr−1m−2 M⋅T−3 power per unit solid angle per unit projected source area.

confusingly called "intensity" in some other fields of study.

Spectral radiance L[nb 3]
L[nb 4]
watt per steradian per metre3

watt per steradian per square
metre per hertz

commonly measured in W⋅sr−1⋅m−2⋅nm−1 with surface area and either wavelength or frequency.

Irradiance Ee[nb 2] watt per square metre W⋅m−2 M⋅T−3 power incident on a surface, also called radiant flux density.

sometimes confusingly called "intensity" as well.

Spectral irradiance E[nb 3]
E[nb 4]
watt per metre3
watt per square metre per hertz
commonly measured in W⋅m−2nm−1
or 10−22W⋅m−2⋅Hz−1, known as solar flux unit.[nb 5]

Radiant exitance /
Radiant emittance
Me[nb 2] watt per square metre W⋅m−2 M⋅T−3 power emitted from a surface.
Spectral radiant exitance /
Spectral radiant emittance
M[nb 3]
M[nb 4]
watt per metre3

watt per square
metre per hertz

power emitted from a surface per unit wavelength or frequency.

Radiosity Je watt per square metre W⋅m−2 M⋅T−3 emitted plus reflected power leaving a surface.
Spectral radiosity J[nb 3] watt per metre3 W⋅m−3 M⋅L−1⋅T−3 emitted plus reflected power leaving a surface per unit wavelength
Radiant exposure He joule per square metre J⋅m−2 M⋅T−2 also referred to as fluence
Radiant energy density ωe joule per metre3 J⋅m−3 M⋅L−1⋅T−2
See also: SI · Radiometry · Photometry
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.