SIST EN ISO 11145:2026

• Abstract:

  This document defines basic terms, symbols and units of measurement for the field of laser technology in order to unify the terminology, and to arrive at clear definitions and reproducible tests of beam parameters and laser-oriented product properties.; NOTE The laser hierarchical vocabulary laid down in this document differs from that given in IEC 60825–1. ISO and IEC have discussed this difference and agree that it reflects the different purposes for which the two standards serve. For more details, see informative Annex A.

• Status: Published
• Public Enquiry End Date: 25-Jun-2025
• Publication Date: 19-Aug-2026
• ICS: 01.040.31 - Electronics (Vocabularies)
• ICS: 31.260 - Optoelectronics. Laser equipment
• Technical Committee: VAZ - Healthcare
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 30-Jul-2026
• Due Date: 04-Oct-2026
• Completion Date: 20-Aug-2026
• Ref Project: EN ISO 11145:2026 - Optics and photonics - Lasers and laser-related equipment - Vocabulary and symbols (ISO 11145:2026)

• Replaces: SIST EN ISO 11145:2019 - Optics and photonics - Lasers and laser-related equipment - Vocabulary and symbols (ISO 11145:2018)
• Effective Date: 01-Sep-2026
• Referred By: SIST EN 4678:2011 - Aerospace series - Weldments and brazements for aerospace structures - Joints of metallic materials by laser beam welding - Quality of weldments
• Effective Date: 29-Jul-2026
• Referred By: SIST EN ISO 3691-4:2023 - Industrial trucks - Safety requirements and verification - Part 4: Driverless industrial trucks and their systems (ISO 3691-4:2023)
• Effective Date: 28-Jan-2026

SIST EN ISO 11145:2026 defines the basic terms, symbols and units used in laser technology. CEN publishes it as the European adoption of ISO 11145:2026, and it is meant for people who need a common laser vocabulary for specifications, measurements, test reports and product descriptions.

The standard is a terminology and symbol reference, not a test-method or safety-classification document. In practice, it helps engineers and laboratories use the same words and symbols when describing beam parameters, laser components and laser-oriented product properties.

What does SIST EN ISO 11145:2026 specify?

SIST EN ISO 11145:2026 specifies the vocabulary for lasers and laser-related equipment, together with the symbols and units used for those terms. Its scope is to unify terminology and support clear definitions and reproducible tests of beam parameters and laser-oriented product properties.

SIST EN ISO 11145:2026 is organized into four clauses plus one informative annex:

• Clause 1 - Scope
• Clause 2 - Normative references
• Clause 3 - Terms and definitions
• Clause 4 - Symbols and units of measurement
• Annex A - Explanation of the difference in terminology between IEC 60825-1 and ISO 11145

Annex	What it covers
Annex A	The terminology difference between IEC 60825-1 and ISO 11145, including the laser hierarchy used in this standard

The document also notes that its laser hierarchical vocabulary differs from IEC 60825-1, and Annex A explains why the two standards use different purposes and therefore different terms.

What are the key requirements of SIST EN ISO 11145:2026?

SIST EN ISO 11145:2026 mainly requires consistent use of defined terms, symbols and units. Because it is a vocabulary standard, the practical requirement is to describe beam properties, pulse properties and laser assemblies with the exact definitions given in Clause 3 and the symbols listed in Clause 4.

Beam position, axis and alignment

SIST EN ISO 11145:2026 defines the beam centroid, beam positional stability, beam axis and misalignment angle. The beam centroid is based on first-order moments, while beam positional stability is expressed as four times the standard deviation of measured movement.

In practice, this tells you how to describe where a beam is, how much it moves, and how far it is tilted from the manufacturer’s mechanical axis. That matters when setting up alignment checks, pointing stability reports, or acceptance criteria for optical systems.

Beam size, shape and distribution

SIST EN ISO 11145:2026 distinguishes between encircled-power terms and second-order-moment terms for beam diameter, beam radius, beam width and beam cross-sectional area. It also defines beam ellipticity, circular irradiance distribution and principal axis.

In practice, this means the measuring method must match the term used. If a report uses encircled-power values, it must identify the percentage included by the subscript u; if it uses second-order moments, it must use the σ-based terms. That avoids comparing numbers that were obtained by different methods.

Beam waist, divergence and propagation

SIST EN ISO 11145:2026 defines beam waist, beam waist location, astigmatic beam waist separation, Rayleigh length, far field, beam divergence angle, beam parameter product, beam propagation ratio and beam propagation factor. It also distinguishes encircled-power and second-order-moment versions of the waist and divergence terms.

In practice, these definitions support beam-quality statements and propagation calculations. The document notes that only second-order-moment-based beam widths and divergence angles allow calculation of beam propagation in the way intended here, so users need to record which method was used before comparing results.

Coherence and polarization

SIST EN ISO 11145:2026 defines coherence, temporal coherence, spatial coherence, coherence length, coherence time, polarization, circular polarization, elliptical polarization, linear polarization, partial polarization, random polarization and degree of linear polarization.

In practice, these terms let users describe the phase relationship and field orientation of laser radiation in a controlled way. That matters when specifying sources for interferometry, fiber coupling, imaging, or any application where polarization state affects performance.

Radiant power, energy and pulse timing

SIST EN ISO 11145:2026 defines irradiance, fluence, continuous wave radiant power, radiant pulse energy, radiant pulse power, radiant average power and peak radiant power. It also defines pulse duration, FWHM pulse duration and pulse repetition rate.

In practice, this gives a common language for both continuous wave and pulsed lasers. Users can state whether a value is power or energy, whether it is average or peak, and how pulse width and repetition rate were determined.

Laser hierarchy, device types and efficiency

SIST EN ISO 11145:2026 defines laser, continuous wave laser, pulsed laser, laser radiation, laser beam, laser device, laser assembly, laser unit, lifetime, laser efficiency, quantum efficiency and device efficiency.

In practice, these terms are important when describing how much of a system is included in a product specification. Annex A shows the intended hierarchy - laser, laser device, laser assembly and laser unit - and explains how that hierarchy differs from the IEC 60825-1 vocabulary.

What terms does SIST EN ISO 11145:2026 define?

SIST EN ISO 11145:2026 defines the terms that users need to describe laser beams and laser equipment consistently. A few of the key terms are:

• Continuous wave [cw] laser - a laser that emits continuously for periods of time greater than or equal to 0,25 s.
• FWHM pulse duration - the full width at half maximum of a pulse, measured between the half-peak points on the leading and trailing edges.
• Relative intensity noise [RIN] - the normalized measure of radiant power fluctuations versus frequency.
• Beam propagation ratio (M) - a measure of how far the beam parameter product is from that of a perfect Gaussian beam.
• Beam propagation factor (K) - the reciprocal of the beam propagation ratio, with K = 1/M.
• Beam ellipticity - the parameter used to quantify how circular or square an irradiance or fluence distribution is.
• Laser unit - one or more laser assemblies together with handling units, measurement systems and control systems.

Who uses SIST EN ISO 11145:2026?

SIST EN ISO 11145:2026 is used by laser and photonics engineers, optical designers, test laboratories, manufacturers, and quality or procurement teams that work with laser specifications. It is especially useful when a product needs a shared description of beam size, divergence, polarization, pulse behavior or system hierarchy.

It also supports users who need to compare measurements across companies or documents. Annex A is particularly relevant for manufacturers and integrators who work at different levels of assembly and need to understand the difference between ISO and IEC terminology.

What changed in SIST EN ISO 11145:2026 from the previous edition?

SIST EN ISO 11145:2026 supersedes EN ISO 11145:2018 and is identified as the sixth edition. The foreword states that it has been technically revised.

The stated changes are:

• “power density” was replaced by “irradiance”
• “energy density” was replaced by “fluence”
• the word “radiant” was added to clarify power and energy terms
• “encircled-power” was added to several terms
• the term and definition for “principal axis” were added

Which standards are used with SIST EN ISO 11145:2026?

SIST EN ISO 11145:2026 has no normative references. The document still points readers to related standards that support beam measurement and laser safety work:

• ISO 11146 (all parts) - test methods for laser beam widths, divergence angles and beam propagation ratios
• ISO/TR 11146-3 - the moving slit method for measuring beam width
• ISO 11670 - test methods for beam positional stability
• ISO 13694 - test methods for laser beam irradiance (fluence) distribution
• IEC 60825-1 - laser safety vocabulary and classification, which Annex A discusses in relation to ISO 11145 terminology

What does the SIST EN ISO 11145:2026 document contain?

SIST EN ISO 11145:2026 contains 20 defined terms in Clause 3, covering beam geometry, beam quality, coherence, polarization, radiant power and energy, pulse timing, optical resonators, modes, spectral bandwidth, relative intensity noise, laser types and efficiency. Clause 4 provides a consolidated table of symbols and units for those terms.

The clause notes point users toward specific measurement approaches such as the variable aperture method, the moving slit method and second-order-moment-based definitions. Annex A adds an explanatory figure and text on the laser hierarchy used in this standard, while the bibliography lists related beam measurement and safety standards.

SLOVENSKI STANDARD
01-september-2026
Nadomešča:
SIST EN ISO 11145:2019
Optika in fotonska tehnologija - Laserji in z laserji povezana oprema - Slovar in
simboli (ISO 11145:2026)
Optics and photonics - Lasers and laser-related equipment - Vocabulary and symbols
(ISO 11145:2026)
Optik und Photonik - Laser und Laseranlagen - Begriffe und Formelzeichen (ISO
11145:2026)
Optique et photonique - Lasers et équipements associés aux lasers - Vocabulaire et
symboles (ISO 11145:2026)
Ta slovenski standard je istoveten z: EN ISO 11145:2026
ICS:
01.040.31 Elektronika (Slovarji) Electronics (Vocabularies)
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 11145
EUROPEAN STANDARD
NORME EUROPÉENNE
July 2026
EUROPÄISCHE NORM
ICS 01.040.31; 31.260 Supersedes EN ISO 11145:2018
English Version
Optics and photonics - Lasers and laser-related equipment
- Vocabulary and symbols (ISO 11145:2026)
Optique et photonique - Lasers et équipements Optik und Photonik - Laser und Laseranlagen - Begriffe
associés aux lasers - Vocabulaire et symboles (ISO und Formelzeichen (ISO 11145:2026)
11145:2026)
This European Standard was approved by CEN on 12 July 2026.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2026 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 11145:2026 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 11145:2026) has been prepared by Technical Committee ISO/TC 172 "Optics
and photonics" in collaboration with Technical Committee CEN/TC 123 “Lasers and photonics” the
secretariat of which is held by DIN.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by January 2027, and conflicting national standards shall
be withdrawn at the latest by January 2027.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 11145:2018.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 11145:2026 has been approved by CEN as EN ISO 11145:2026 without any modification.

International
Standard
ISO 11145
Sixth edition
Optics and photonics — Lasers
2026-07
and laser-related equipment —
Vocabulary and symbols
Optique et photonique — Lasers et équipements associés aux
lasers — Vocabulaire et symboles
Reference number
ISO 11145:2026(en) © ISO 2026
ISO 11145:2026(en)
© ISO 2026
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
ISO 11145:2026(en)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Beam position .2
3.2 Beam axis .2
3.3 Beam diameter .3
3.4 Beam radius .3
3.5 Beam width . . .4
3.6 Beam cross-sectional area .4
3.7 Beam waist . .5
3.8 Divergence .7
3.9 Rayleigh length .7
3.10 Beam parameter product .8
3.11 Coherence .8
3.12 Polarization .9
3.13 Radiant power and energy .10
3.14 Pulse duration and repetition rate .11
3.15 Optical resonator .11
3.16 Mode. 12
3.17 Spectral bandwidth . 12
3.18 Relative intensity noise . . . 12
3.19 Laser . 12
3.20 Efficiency . 13
4 Symbols and units of measurement . 14
Annex A (informative) Explanation of the difference in terminology between IEC 60825-1 and
ISO 11145 . 16
Bibliography .18
Alphabetical index . 19

iii
ISO 11145:2026(en)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 9,
Laser and electro-optical systems, in collaboration with the European Committee for Standardization (CEN)
Technical Committee CEN/TC 123, Lasers and photonics, in accordance with the Agreement on technical
cooperation between ISO and CEN (Vienna Agreement)
This sixth edition cancels and replaces the fifth edition (ISO 11145:2018), which has been technically
revised.
The main changes are as follows:
— the term “power density” was replaced by “irradiance” and “energy density” was replaced by “fluence”.
— the word “radiant” was added to clarify terms for power and energy.
— “encircled-power” was added to terms 3.3.1, 3.4.1, 3.5.1, 3.6.1, 3.7.4, 3.7.6, 3.7.8 and 3.8.1.
— term and definition 3.5.3 “principal axis” was newly added.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
International Standard ISO 11145:2026(en)
Optics and photonics — Lasers and laser-related equipment
— Vocabulary and symbols
1 Scope
This document defines basic terms, symbols and units of measurement for the field of laser technology in
order to unify the terminology, and to arrive at clear definitions and reproducible tests of beam parameters
and laser-oriented product properties.
NOTE The laser hierarchical vocabulary laid down in this document differs from that given in IEC 60825–1.
ISO and IEC have discussed this difference and agree that it reflects the different purposes for which the two standards
serve. For more details, see informative Annex A.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
NOTE 1 The spatial distribution of the irradiance (fluence) in a cross section of a laser beam does not always have
circular symmetry. In this document, all terms related to these spatial distributions are split into those for beam cross
sections with circular distributions and those for beam cross sections with non-circular distributions. A circular
beam is characterized by its radius, w, or diameter, d. For a non-circular beam, the beam widths, d and d , for two
x y
orthogonal directions are given.
NOTE 2 The spatial distributions of laser beams do not have sharp edges. Therefore, the radiant power (energy)
values to which the spatial terms refer are defined. Depending on the application, different cut-off values can be
chosen (for example 1/e, 1/e , 1/10 of the peak value).
NOTE 3 This document uses the subscript u to denote a percentage. For example, the percentage of the total beam
power (energy) included in the value of a given parameter. When stating quantities marked by an index “u”, “u” is
replaced by the specific number, e.g. A for u = 90 %.
NOTE 4 The beam width d (see 3.5.1) and the beam diameter d (see 3.3.1) can differ for the same value of u (d ≠
ux u ux
d ).
u
NOTE 5 In contrast to quantities defined by setting a cut-off value [“encircled radiant power (energy)”], the beam
widths and derived beam properties can also be defined based on the second-order moments of the irradiance
(fluence) distribution function (see 3.5.2). Only beam propagation ratios (see 3.10.2) that are calculated from beam
widths and divergence angles derived from the second-order moments of the irradiance (fluence) distribution function
allow calculation of beam propagation. In this document, quantities based on the second-order moment are marked by
a subscript “σ”.
NOTE 6 A list of symbols is given in Clause 4.

ISO 11145:2026(en)
3.1 Beam position
3.1.1
beam centroid
xz , yz
 
coordinates of the first-order moments of a radiant power (energy) distribution of a beam at location z
xE xy,,zxddy


xz 

Ex,,yz ddxy


yE xy,,zxddy


yz 

Ex,,yz ddxy


where the integration shall be performed over an area such that at least 99 % of the beam power (energy) is
captured
Note 1 to entry: The irradiance, E, is replaced by the fluence, H, for pulsed lasers.
Note 2 to entry: ”Centre of gravity”, “beam position” and the term “beam centroid” are equivalent, formerly the term
was called “beam position”.
Note 3 to entry: These quantities are defined in the beam axis system x,y,z, in which z is the direction of propagation
of the beam.
3.1.2
beam positional stability
Δx(z'), Δy(z')
four times the standard deviation of the measured beam positional movement at plane z′
N 2
 

xz xz
 
  i 
i1

xz 4

N1
N 2
 
yz yz
 

 i 
i1

yz 4

N1
   
where xz and yz are the beam centroids in the z′ plane, xz and yz are the arithmetic means of
   
the beam centroids in the z′ plane, and N is the number of measurements
Note 1 to entry: The term "beam positional stability" is sometimes referred to as “spatial fluctuation widths”, as in
ISO 11670.
3.2 Beam axis
3.2.1
beam axis
straight line connecting the centroids defined by the first-order spatial moments of the cross-sectional
irradiance (fluence) distribution function at successive locations in the direction of propagation (z) of the
beam in a homogeneous medium
3.2.2
misalignment angle
Δϑ
deviation angle of the beam axis from the mechanical axis defined by the manufacturer

ISO 11145:2026(en)
3.3 Beam diameter
3.3.1
encircled-power beam diameter
d (z)
u
diameter of a circular aperture in a plane perpendicular to the beam
axis that contains u % of the total beam power (energy)
Note 1 to entry: For clarity, the term “beam diameter” is always used in combination with the symbol and its
appropriate subscript: d or d .
u σ
Note 2 to entry: To measure encircled radiant power, using the “variable aperture method”, see ISO 11146-series.
3.3.2
beam diameter
d (z)
σ
diameter defined by using the second-
order moment of the irradiance (fluence) distribution function
dz  22 z
 

where the second-order moment of the irradiance distribution function E(x, y, z) of the beam at location z is
given by:
xx zy  yz  Ex,,yz ddxy
  
   

 z 

Ex,,yz dxddy


where the first-order moments give the coordinates of the beam centroid xz , yz 
 
 
Note 1 to entry: For clarity, the term “beam diameter” is always used in combination with the symbol and its
appropriate subscript: d or d
u σ.
3.4 Beam radius
3.4.1
encircled-power beam radius
w (z)
u
radius of a circular aperture in a plane perpendicular to the beam axis
which contains u % of the total beam power (energy)
Note 1 to entry: For clarity, the term “beam radius” is always used in combination with the symbol and its appropriate
subscript: w or w .
u σ
Note 2 to entry: The beam radius is half the beam diameter d (z).
u
3.4.2
beam radius
w (z)
σ
radius defined by using the second-
order moment of the irradiance (fluence) distribution function
wz  2 z
 

Note 1 to entry: For clarity, the term “beam radius” is always used in combination with the symbol and its appropriate
subscript: w or w .
u σ
Note 2 to entry: The beam radius is half the beam diameter d (z).
σ
ISO 11145:2026(en)
3.5 Beam width
3.5.1
encircled-power beam width
d (z), d (z)
ux uy
width of the smallest slit aligned with the X or Y transverse axes
of the irradiance (fluence) distribution function, transmitting u % of the total beam power (energy) along X
or Y
Note 1 to entry: For circular Gaussian beams, d and d both equal d .
95,4x 95,4y 86,5
Note 2 to entry: For clarity, the term “beam width” is always used in combination with the symbol and its appropriate
subscripts: d , d or d , d .
σx σy ux uy
Note 3 to entry: To measure beam width, using the “moving slit method”, see ISO/TR 11146-3.
3.5.2
beam width
d (z), d (z)
σx σy
width defined by using the second-
order moment of the irradiance (fluence) distribution function along X or Y
dz  4 z
 
xx
dz  4 z
 
 yy
where the second-order moments of the irradiance distribution function E(x, y, z) of the beam at location z
are given by:
xx zE  xy,,zxddy
 
 

 z 

x
Ex,,yz ddxy


yy zE xy,,zxddy
 

 z 

y
Ex,,yz ddxy


where the first-order moments give the coordinates of the beam centroid xz , yz 
 
 
Note 1 to entry: For clarity, the term “beam width” is always used in combination with the symbol and its appropriate
subscripts: d , d or d , d .
σx σy ux uy
Note 2 to entry: To measure beam width, using second-order moments, see ISO 11146-1.
3.5.3
principal axis
axis of the maximum or minimum beam extent
based on the second-order moments of the irradiance distribution function in a cross section of the beam
3.6 Beam cross-sectional area
3.6.1
encircled-power beam cross-sectional area
A (z)
u
smallest completely filled area containing u % of the total beam power
(energy)
Note 1 to entry: For clarity, the term “beam cross-sectional area” is always used in combination with the symbol and
its appropriate subscript: A or A .
u σ
ISO 11145:2026(en)
3.6.2
beam cross-sectional area
A (z)
σ
area of a beam with circular cross-
section
  2
Ad  z

 

 
or elliptical cross-section
 
Ad  zd z
 
 
xy
 
Note 1 to entry: For clarity, the term “beam cross-sectional area” is always used in combination with the symbol and
its appropriate subscript: A or A .
u σ
3.6.3
beam ellipticity
ε(z)
parameter for quantifying the circularity or squareness of an irradiance (fluence) distribution at z
 
min dz ,dz
 
xy
 
 z 

 
max dz ,dz
 
xy
 
Note 1 to entry: It follows that 0 < ε(z) ≤ 1.
Note 2 to entry: In case of a rectangular distribution, ellipticity is often referred to as “aspect ratio”.
Note 3 to entry: In contrast to the definition given here, in literature the term “ellipticity” is sometimes related to
dz

 y
1 . The definition given here has been chosen to be in concordance with the same definition of ellipticity in
dz

x
ISO 11146-1 and ISO 13694.
3.6.4
circular irradiance distribution
irradiance distribution having a beam ellipticity ε(z) greater than or equal to 0,87 at z
3.7 Beam waist
3.7.1
beam waist
portion of a beam where the beam diameter or beam width has a local minimum
3.7.2
beam waist location
z , z , z
0x 0y 0
location where the beam widths or the beam diameters reach their minimum values along the beam axis
Note 1 to entry: A particular beam can have multiple beam waist locations.
Note 2 to entry: The method used to determine beam waist location must be specified when it is not based on the
second-order moment of irradiance (fluence) distribution function. Only a method based on second-order moments
can uniquely define the beam waist location.

ISO 11145:2026(en)
3.7.3
astigmatic beam waist separation
Δz
a
axial distance between the beam waist locations in the orthogonal principal planes of
...