SIST EN ISO 11146-2:2021

Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles and beam propagation ratios - Part 2: General astigmatic beams (ISO 11146-2:2021)

This document specifies methods for measuring beam widths (diameter), divergence angles and beam propagation ratios of laser beams. This document is applicable to general astigmatic beams or unknown types of beams. For stigmatic and simple astigmatic beams, ISO 11146‑1 is applicable.
Within this document, the description of laser beams is accomplished by means of the second order moments of the Wigner distribution rather than physical quantities such as beam widths and divergence angles. However, these physical quantities are closely related to the second order moments of the Wigner distribution. In ISO/TR 11146‑3, formulae are given to calculate all relevant physical quantities from the measured second order moments.

Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel und Beugungsmaßzahlen - Teil 2: Allgemein astigmatische Strahlen (ISO 11146-2:2021)

Dieses Dokument legt Verfahren zum Messen der Strahlabmessungen (Strahldurchmesser), Divergenzwinkel und Beugungsmaßzahlen von Laserstrahlen fest. Dieses Dokument ist für allgemein astigmatische Strahlen oder Strahlen unbekannter Art anzuwenden. Bei stigmatischen und einfach astigmatischen Strahlen ist ISO 11146 1 anzuwenden.
In diesem Dokument wird die Beschreibung von Laserstrahlen durch die Momente zweiter Ordnung der Wigner-Verteilung gegenüber der Beschreibung durch physikalische Größen wie Strahlabmessungen und Divergenzwinkel bevorzugt. Diese physikalischen Größen stehen jedoch in engem Zusammenhang mit den Momenten zweiter Ordnung der Wigner-Verteilung. In ISO/TR 11146 3 sind Gleichungen zur Berechnung aller relevanten physikalischen Größen aus den Momenten zweiter Ordnung angegeben.

Lasers et équipements associés aux lasers - Méthodes d'essai des largeurs du faisceau, angles de divergence et facteurs de limite de diffraction - Partie 2: Faisceaux astigmatiques généraux (ISO 11146-2:2021)

Le présent document spécifie les méthodes pour le mesurage des largeurs (diamètres) du faisceau, angles de divergence et  facteurs de limite de diffraction. Le présent document s'applique aux faisceaux astigmatiques généraux ou si le type de faisceau est inconnu. Pour les faisceaux stigmatiques et astigmatiques simples, l'ISO 11146-1 s'applique.
Au sein du présent document, la description des faisceaux laser est réalisée au moyen des moments de second ordre de la distribution de Wigner, plutôt que par des grandeurs physiques telles que les largeurs de faisceau et les angles de divergence. Toutefois, ces grandeurs physiques sont étroitement liées aux moments de second ordre de la distribution de Wigner. Dans l'ISO/TR 11146‑3, des formules sont données pour calculer toutes les grandeurs physiques concernées à partir des moments de second ordre mesurés.

Laserji in laserska oprema - Preskusne metode za širine laserskega žarka, kota divergence in faktorja širjenja žarkov - 2. del: Osnovni astigmatični žarki (ISO 11146-2:2021)

General Information

• Status: Published
• Public Enquiry End Date: 19-Jul-2020
• Publication Date: 22-Aug-2021
• ICS: 31.260 - Optoelectronics. Laser equipment
• Technical Committee: VAZ - Healthcare
• Current Stage: 6060 - National Implementation/Publication (Adopted Project)
• Start Date: 28-Jul-2021
• Due Date: 02-Oct-2021
• Completion Date: 23-Aug-2021
• Ref Project: EN ISO 11146-2:2021 - Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles and beam propagation ratios - Part 2: General astigmatic beams (ISO 11146-2:2021)

Relations

• Replaces: SIST EN ISO 11146-2:2005 - Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles and beam propagation ratios - Part 2: General astigmatic beams (ISO 11146-2:2005)
• Effective Date: 01-Sep-2021

Overview

EN ISO 11146-2:2021 - “Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles and beam propagation ratios - Part 2: General astigmatic beams” - specifies standardized measurement methods for laser beam widths (diameters), divergence angles and beam propagation ratios for general astigmatic beams or beams of unknown type. Adopted by CEN and superseding the 2005 edition, this part uses the second order moments of the Wigner distribution as the basis for beam description, from which common physical quantities (e.g., beam widths, divergence, M²) are derived. The methods are valid within the paraxial approximation.

Key topics and technical requirements

• Second order moments (Wigner distribution): Primary descriptive quantities used to characterize beam propagation and geometry.
• Derived physical quantities: Beam diameter, divergence angle and effective beam propagation ratio (M²) are obtained from these moments; calculation guidance is provided in ISO/TR 11146-3.
• Measurement procedures: Requirements for measurement arrangement, detector systems, beam-forming optics, optical attenuators, background subtraction and offset correction.
• Practical measurement steps: Determination of all relevant second order moments across cross-sections, integration range considerations, and procedures to obtain effective M², intrinsic astigmatism and the twist parameter.
• Environmental and equipment control: Guidance on preparation and control of measurement environment and detector calibration (including power/energy detectors).
• Alternative methods (correlation): ISO/TR 11146-3 documents how variable aperture, moving knife-edge and moving slit methods relate to the second-moment approach.
• Reporting: Required test-report content to ensure traceability and reproducibility of beam characterization.

Applications and practical value

• Beam quality assessment: Standardized determination of beam propagation ratio (M²) and divergence for R&D and production verification.
• Laser product specifications: Defining and verifying manufacturer claims for beam width, divergence and beam quality.
• Optical system design & alignment: Accurate characterization of astigmatic or unknown beams for lens selection, focusing, and imaging systems.
• Metrology and certification: Test labs and quality assurance functions use the standard for consistent, comparable measurements.
• Safety & regulatory compliance: Supporting documentation for laser classification and safe system integration.

Who uses this standard

• Laser manufacturers and optical component suppliers
• Photonics R&D teams and system integrators
• Calibration and testing laboratories (metrology labs)
• Quality assurance, compliance and certification bodies
• Academic and industrial researchers working with complex/astigmatic beams

Related standards

• ISO 11146-1 - Stigmatic and simple astigmatic beams
• ISO/TR 11146-3 - Formulas and guidance to calculate physical beam parameters from second order moments
• ISO 11145 - Vocabulary and symbols for lasers and photonics
• EN 61040 - Power and energy measuring detectors for laser radiation

Keywords: EN ISO 11146-2:2021, laser beam widths, divergence angles, beam propagation ratio, general astigmatic beams, Wigner distribution, second order moments, beam characterization, M² measurement.

Standards Content (Sample)

SLOVENSKI STANDARD
01-september-2021
Nadomešča:
SIST EN ISO 11146-2:2005
Laserji in laserska oprema - Preskusne metode za širine laserskega žarka, kota
divergence in faktorja širjenja žarkov - 2. del: Osnovni astigmatični žarki (ISO
11146-2:2021)
Lasers and laser-related equipment - Test methods for laser beam widths, divergence
angles and beam propagation ratios - Part 2: General astigmatic beams (ISO 11146-
2:2021)
Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel
und Beugungsmaßzahlen - Teil 2: Allgemein astigmatische Strahlen (ISO 11146-2:2021)
Lasers et équipements associés aux lasers - Méthodes d'essai des largeurs du faisceau,
angles de divergence et facteurs de limite de diffraction - Partie 2: Faisceaux
astigmatiques généraux (ISO 11146-2:2021)
Ta slovenski standard je istoveten z: EN ISO 11146-2:2021
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 11146-2
EUROPEAN STANDARD
NORME EUROPÉENNE
July 2021
EUROPÄISCHE NORM
ICS 31.260 Supersedes EN ISO 11146-2:2005
English Version
Lasers and laser-related equipment - Test methods for
laser beam widths, divergence angles and beam
propagation ratios - Part 2: General astigmatic beams (ISO
11146-2:2021)
Lasers et équipements associés aux lasers - Méthodes Laser und Laseranlagen - Prüfverfahren für
d'essai des largeurs du faisceau, angles de divergence Laserstrahlabmessungen, Divergenzwinkel und
et facteurs de limite de diffraction - Partie 2: Faisceaux Beugungsmaßzahlen - Teil 2: Allgemein astigmatische
astigmatiques généraux (ISO 11146-2:2021) Strahlen (ISO 11146-2:2021)
This European Standard was approved by CEN on 4 July 2021.

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, Turkey 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
© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 11146-2:2021 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 11146-2:2021) 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 2022, and conflicting national standards shall
be withdrawn at the latest by January 2022.
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 11146-2:2005.
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 websites.
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, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 11146-2:2021 has been approved by CEN as EN ISO 11146-2:2021 without any
modification.
INTERNATIONAL ISO
STANDARD 11146-2
Second edition
2021-07
Lasers and laser-related equipment —
Test methods for laser beam
widths, divergence angles and beam
propagation ratios —
Part 2:
General astigmatic beams
Lasers et équipements associés aux lasers — Méthodes d'essai des
largeurs du faisceau, angles de divergence et facteurs de limite de
diffraction —
Partie 2: Faisceaux astigmatiques généraux
Reference number
ISO 11146-2:2021(E)
©
ISO 2021
ISO 11146-2:2021(E)
© ISO 2021
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 2021 – All rights reserved

ISO 11146-2:2021(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Coordinate system . 6
5 Test principles . 6
5.1 General . 6
5.2 Spatial second order moments of the Wigner distribution . 6
5.3 Second order moments of the Wigner distribution . 6
5.4 Derived quantities . 6
6 Measurement arrangement and test equipment . 6
6.1 General . 6
6.2 Preparation . 6
6.3 Control of environment . 7
6.4 Detector system . 7
6.5 Beam-forming optics and optical attenuators . 8
7 Measurement of the second order moments . 8
7.1 General . 8
7.2 Measurement of the second order moments of power density distributions . 8
7.3 Measurement of all second order moments of the Wigner distribution .10
8 Determination of effective beam propagation ratio .12
9 Determination of intrinsic astigmatism.12
10 Determination of the twist parameter .13
11 Test report .13
Bibliography .16
ISO 11146-2:2021(E)
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 documents 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).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
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 second edition cancels and replaces the first edition (ISO 11146-2:2005), which has been
technically revised. The main changes compared to the previous edition are as follows:
— The terms and definitions were harmonized with the new ISO 11145.
— The "principal axes" were defined more thoroughly and named as x' and y'. Quantities related to the
principal axes coordinate system refer to this definition and use x' and y' in their indices.
— The requirements for the integration range for the determination of the second order moments
have been relaxed.
A list of all parts in the ISO 11146 series can be found on the ISO website.
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 © ISO 2021 – All rights reserved

ISO 11146-2:2021(E)
Introduction
The propagation properties of laser beams can be characterized by ten independent parameters when
applying the method of second order moments (see ISO/TR 11146-3). Most laser beams need few
parameters for a complete description due to their higher symmetry. Lasers emit beams which are
stigmatic or simple astigmatic due to their resonator design.
ISO 11146-1 describes the measurement methods for stigmatic and simple astigmatic beams while
this document deals with the measurement procedures for general astigmatic beams. This document
is applicable to beams of unknown type. Beam characterization, based on the method of second
order moments as described in ISO 11146-1 and this document, is only valid within the paraxial
approximation.
The theoretical description of beam characterization and propagation as well as the classification of
laser beams is given in ISO/TR 11146-3, which is a Technical Report. The procedures for background
subtraction and offset correction are also given in ISO/TR 11146-3.
In ISO 11146, the second order moments of the power (energy) density distribution function are used
for the determination of beam widths. If problems are experienced in the direct measurements of these
quantities, other indirect methods of measurement of second order moments may be used as long as
comparable results are achievable.
In ISO/TR 11146-3, three alternative methods for beam width measurement and their correlation with
the method used in this document are described. These methods are:
— variable aperture method;
— moving knife-edge method;
— moving slit method.
INTERNATIONAL STANDARD ISO 11146-2:2021(E)
Lasers and laser-related equipment — Test methods
for laser beam widths, divergence angles and beam
propagation ratios —
Part 2:
General astigmatic beams
1 Scope
This document specifies methods for measuring beam widths (diameter), divergence angles and beam
propagation ratios of laser beams. This document is applicable to general astigmatic beams or unknown
types of beams. For stigmatic and simple astigmatic beams, ISO 11146-1 is applicable.
Within this document, the description of laser beams is accomplished by means of the second order
moments of the Wigner distribution rather than physical quantities such as beam widths and divergence
angles. However, these physical quantities are closely related to the second order moments of the
Wigner distribution. In ISO/TR 11146-3, formulae are given to calculate all relevant physical quantities
from the measured second order moments.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 11145, Optics and photonics — Lasers and laser-related equipment — Vocabulary and symbols
ISO 11146-1, Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles
and beam propagation ratios — Part 1: Stigmatic and simple astigmatic beams
EN 61040:1992, Power and energy measuring detectors, instruments and equipment for laser radiation
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11145, ISO 11146-1, EN 61040
and the following apply.
ISO and IEC maintain terminological 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 The x−, y− and z-axes in the following definitions refer to the laboratory system (as described in
Clause 4). Here and throughout this document the term “power density distribution E(x,y,z)” refers to continuous
wave sources. It might be replaced by “energy density distribution H(x,y,z)” in case of pulsed sources.
ISO 11146-2:2021(E)
3.1
generalized beam diameter
d
g
measure of the extent of the power density distribution of a beam in a cross-section at an axial location
z, derived from the second order moments by
dx=+22 y (1)
g
Note 1 to entry: This definition is similar to the beam diameter defined in ISO 11145 or ISO 11146-1. But in this
context the definition is not restricted to circular power density distributions.
3.2
generalized beam waist location
z
0,g
position where the generalized beam diameter (3.1) reaches its minimum value along the axis of
propagation
3.3
generalized Rayleigh length
z
R,g
distance along the beam axis from the generalized beam waist where the generalized beam diameter is
a factor of 2 larger than the generalized beam waist diameter
3.4
Wigner distribution
phase space distribution representing a laser beam in a transverse plane at location z
Note 1 to entry: The Wigner distribution is a function of two spatial and two angular coordinates, giving the
amount of beam power propagating through the point (x,y) in the direction (Θ , Θ ).
x y
3.5
spatial first order moments of the Wigner distribution
xy,
subset of the first order moments, which can be directly obtained from measured power density
distribution by
∞ ∞
Ε ()xy,, z xxy d d
∫ ∫
−∞−∞
xz() = (2)
∞ ∞
Ε ()xy,, zx d dy
∫ ∫
−∞−∞
and
∞ ∞
Ε ()xy,, zy dxy d
∫ ∫
−∞−∞
yz() = (3)
∞ ∞
Ε ()xy,, zx d dy
∫ ∫
−∞−∞
where E(x,y,z) is the power density distribution at the specific plane z = constant
2 © ISO 2021 – All rights reserved

ISO 11146-2:2021(E)
3.6
second order moments of the Wigner distribution
2 22 2
xy,,,,xy ΘΘ,, ΘΘ ,,xxΘΘ yyΘΘ,
xy xy xy xy
ten second order moments of the Wigner distribution (3.4) of the beam at location z
Note 1 to entry: The ten second order moments contain information on the following physical beam properties:
beam size and orientation, divergence angles and their orientation, radii of curvature of the phase paraboloid
and their orientation and the twist parameter. Details on these relations are given in ISO/TR 11146-3.
2 2 2
Note 2 to entry: In ISO 11146-1, the three spatial second order moments are defined as σ , σ and σ . In this
x y xy
document and ISO/TR 11146-3, the angular brackets are used to emphasize the coordinates of the moments. This
22 22 2
means that σ = x , σ = y and σ = xy .
x y xy
2 2
Note 3 to entry: Three angular moments 〈Θ 〉, 〈Θ 〉 and 〈Θ Θ 〉 are independent of z. The other seven second
x y x y
order moments are, in general, functions of z.
3.7
spatial second order moments of the Wigner distribution
xy,, xy
subset of the second order moments, which can be directly obtained from measured power density
distribution by
∞ ∞
Ε ()xy,, zx d()− xx dy
∫ ∫
−∞−∞
xz () = (4)
∞ ∞
Ε ()xy,, zxd dy
∫ ∫
−−∞−∞
∞ ∞
Ε ()xy,, zy d()− yx dy
∫ ∫
−∞−∞
yz () = (5)
∞ ∞
Ε ()xy,, zxd dy
∫ ∫
−−∞−∞
and
∞ ∞
Ε ()xy,, zx()−−xy()yxd dy
∫ ∫
−∞−∞
xy ()z = (6)
∞ ∞
Ε ()xy,, zxd dy
∫ ∫
−∞−∞∞
3.8
beam matrix
P
symmetric and positive definite 4×4 matrix containing all ten second order moments of the Wigner
distribution (3.6) and its elements
...