Lasers and laser-related equipment - Test methods for laser beam widths, divergence angles and beam propagation ratios - Part 1: Stigmatic and simple astigmatic beams (ISO 11146-1:2021)

This document specifies methods for measuring beam widths (diameter), divergence angles and beam propagation ratios of laser beams. This document is only applicable for stigmatic and simple astigmatic beams. If the type of the beam is unknown, and for general astigmatic beams, ISO 11146‑2 is applicable.

Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel und Beugungsmaßzahlen - Teil 1: Stigmatische und einfach astigmatische Strahlen (ISO 11146-1:2021)

Dieses Dokument legt Verfahren zur Messung von Strahlabmessungen (Strahldurchmesser), Divergenz-winkeln und Beugungsmaßzahlen von Laserstrahlen fest. Dieses Dokument ist nur für stigmatische und einfach astigmatische Strahlen anzuwenden. Wenn die Art des Strahles unbekannt ist und bei allgemein astigmatischen Strahlen, ist ISO 11146 2 anzuwenden.

Lasers et équipements associés aux lasers - Méthodes d'essai des largeurs du faisceau, angles de divergence et facteurs de limite de diffraction - Partie 1: Faisceaux stigmatiques et astigmatiques simples (ISO 11146-1:2021)

Le présent document spécifie les méthodes pour mesurer les largeurs (diamètres) du faisceau, les angles de divergence et les facteurs de limite de diffraction. Le présent document s'applique uniquement aux faisceaux stigmatiques et astigmatiques simples. Si le type de faisceau est inconnu et pour les faisceaux astigmatiques généraux, l'ISO 11146‑2 s'applique.

Laserji in laserska oprema - Preskusne metode za širine laserskega žarka, kota divergence in faktorja širjenja žarkov - 1. del: Stigmatični in enostavni astigmatični žarki (ISO 11146-1:2021)

General Information

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Published
Current Stage
6060 - Definitive text made available (DAV) - Publishing
Due Date
21-Jul-2021
Completion Date
21-Jul-2021

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SLOVENSKI STANDARD
SIST EN ISO 11146-1:2021
01-september-2021
Nadomešča:
SIST EN ISO 11146-1:2005
Laserji in laserska oprema - Preskusne metode za širine laserskega žarka, kota

divergence in faktorja širjenja žarkov - 1. del: Stigmatični in enostavni astigmatični

žarki (ISO 11146-1:2021)

Lasers and laser-related equipment - Test methods for laser beam widths, divergence

angles and beam propagation ratios - Part 1: Stigmatic and simple astigmatic beams

(ISO 11146-1:2021)

Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel

und Beugungsmaßzahlen - Teil 1: Stigmatische und einfach astigmatische Strahlen (ISO

11146-1:2021)

Lasers et équipements associés aux lasers - Méthodes d'essai des largeurs du faisceau,

angles de divergence et facteurs de limite de diffraction - Partie 1: Faisceaux
stigmatiques et astigmatiques simples (ISO 11146-1:2021)
Ta slovenski standard je istoveten z: EN ISO 11146-1:2021
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
SIST EN ISO 11146-1:2021 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST EN ISO 11146-1:2021
---------------------- Page: 2 ----------------------
SIST EN ISO 11146-1:2021
EN ISO 11146-1
EUROPEAN STANDARD
NORME EUROPÉENNE
July 2021
EUROPÄISCHE NORM
ICS 31.260 Supersedes EN ISO 11146-1:2005
English Version
Lasers and laser-related equipment - Test methods for
laser beam widths, divergence angles and beam
propagation ratios - Part 1: Stigmatic and simple
astigmatic beams (ISO 11146-1:2021)

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 1: Faisceaux Beugungsmaßzahlen - Teil 1: Stigmatische und einfach

stigmatiques et astigmatiques simples (ISO 11146- astigmatische Strahlen (ISO 11146-1:2021)

1:2021)
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 11146-1:2021 E

worldwide for CEN national Members.
---------------------- Page: 3 ----------------------
SIST EN ISO 11146-1:2021
EN ISO 11146-1:2021 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

---------------------- Page: 4 ----------------------
SIST EN ISO 11146-1:2021
EN ISO 11146-1:2021 (E)
European foreword

This document (EN ISO 11146-1:2021) 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 11146-1:2005.

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 11146-1:2021 has been approved by CEN as EN ISO 11146-1:2021 without any

modification.
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SIST EN ISO 11146-1:2021
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SIST EN ISO 11146-1:2021
INTERNATIONAL ISO
STANDARD 11146-1
Second edition
2021-07
Lasers and laser-related equipment —
Test methods for laser beam
widths, divergence angles and beam
propagation ratios —
Part 1:
Stigmatic and simple 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 1: Faisceaux stigmatiques et astigmatiques simples
Reference number
ISO 11146-1:2021(E)
ISO 2021
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© 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: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
---------------------- Page: 8 ----------------------
SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Coordinate systems ............................................................................................................................................................................................ 7

5 Test principles ......................................................................................................................................................................................................... 7

5.1 Applicability .............................................................................................................................................................................................. 7

5.2 Beam widths and beam diameter ........................................................................................................................................... 7

5.3 Beam divergence angles .................................................................................................................................................................. 8

5.4 Beam propagation ratios ................................................................................................................................................................ 8

5.5 Combined measurement of beam waist locations, beam widths, beam divergence

angles and beam propagation ratios .................................................................................................................................... 8

6 Measurement arrangement and test equipment ................................................................................................................ 8

6.1 General ........................................................................................................................................................................................................... 8

6.2 Preparation ................................................................................................................................................................................................ 8

6.3 Control of environment ................................................................................................................................................................... 9

6.4 Detector system ...................................................................................................................................................................................... 9

6.5 Beam-forming optics and optical attenuators ............................................................................................................. 9

6.6 Focusing system ..................................................................................................................................................................................10

7 Beam widths and beam diameter measurement .............................................................................................................10

7.1 Test procedure ......................................................................................................................................................................................10

7.2 Evaluation .................................................................................................................................................................................................10

8 Measurement of divergence angles ................................................................................................................................................12

8.1 Test procedure ......................................................................................................................................................................................12

8.2 Evaluation .................................................................................................................................................................................................12

9 Combined determination of beam waist locations, beam widths, divergence angles

and beam propagation ratios ...............................................................................................................................................................12

10 Test report ................................................................................................................................................................................................................14

Bibliography .............................................................................................................................................................................................................................17

© ISO 2021 – All rights reserved iii
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(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 11146-1:2005), 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 edition of 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
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
Introduction

The propagation properties of every laser beam can be characterized within the method of second order

moments by ten independent parameters (see ISO/TR 11146-3). However, due to their higher symmetry

most laser beams of practical interest need fewer parameters for a complete description. Most lasers of

practical use emit beams which are stigmatic or simple astigmatic because of their resonator design.

This document describes the measurement methods for stigmatic and simple astigmatic beams while

ISO 11146-2 deals with the measurement procedures for general astigmatic beams. For beams of

unknown type the methods of ISO 11146-2 are applicable. Beam characterization based on the method

of second order moments as described in both parts 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 and describes the procedures for

background subtraction and offset correction.

In this document, the second order moments of the power (energy) density distribution are used for the

determination of beam widths. However, there may be problems experienced in the direct measurement

of these quantities in the beams from some laser sources. In this case, other indirect methods of the

measurement of the 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.
© ISO 2021 – All rights reserved v
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SIST EN ISO 11146-1:2021
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SIST EN ISO 11146-1:2021
INTERNATIONAL STANDARD ISO 11146-1:2021(E)
Lasers and laser-related equipment — Test methods
for laser beam widths, divergence angles and beam
propagation ratios —
Part 1:
Stigmatic and simple 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 only applicable for stigmatic and simple astigmatic

beams. If the type of the beam is unknown, and for general astigmatic beams, ISO 11146-2 is applicable.

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 11146-2, Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles

and beam propagation ratios — Part 2: General astigmatic beams

ISO 13694, Optics and photonics — Lasers and laser-related equipment — Test methods for laser beam

power (energy) density distribution

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 13694, 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 these 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 2021 – All rights reserved 1
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
3.1
first order moments of a power density distribution
xy,

centroid coordinates of the power density distribution of a cross section of a beam given as

∞ ∞
Ex (),,yz xxy dd
∫ ∫
−∞−∞
xz()= (1)
∞ ∞
Ex (),,yz ddxy
∫ ∫
−∞−∞
and
∞ ∞
Ex (),,yz yx ddy
∫ ∫
−∞−∞
yz()= (2)
∞ ∞
Ex (),,yz ddxy
∫ ∫
−∞−∞

Note 1 to entry: The first order moments are used for the definition of beam centroid in ISO 11145.

Note 2 to entry: For practical application, the infinite integration limits are reduced in a specific manner as given

in Clause 7. The limitation of the integration area here differs from the integration area given in ISO 11145.

3.2
second order moments of a power density distribution
22 2
σσ,, σ
xy xy
normalized weighted integrals over the power density distribution, given as:
∞ ∞
Ex,,yz xx− zx ddy
() ()
 
−∞ −∞
σ zx== (3)
∞ ∞
Ex,,yz dxxyd
−∞ −∞
and
∞ ∞
Ex,,yz yy− zx ddy
() ()
 
−∞ −∞
σ zy== (4)
∞ ∞
Ex,,yz dxxyd
−∞ −∞
and
∞ ∞
Ex,,yz xx− zy  − yz ddxy
() () ()
   
−∞ −∞
σ zx==y (5)
∞ ∞
Ex,,yz ddxy
∫ ∫∫
−∞ −∞

Note 1 to entry: For practical application, the infinite integration limits are reduced in a specific manner as given

in Clause 7.

Note 2 to entry: σ z is a symbolic notation, and not a true square. This quantity can take positive, negative

or zero value.

Note 3 to entry: The angular brackets are the operator notations as used in ISO 11146-2 and ISO/TR 11146-3.

2 © ISO 2021 – All rights reserved
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
3.3
principal axes
x’, y’

axes of the maximum and minimum beam extent based on the second

order moments of the power density distribution in a cross section of the beam

Figure 1 — Beam profile with the laboratory and principle axes coordinate systems

Note 1 to entry: The axes of maximum and minimum extent are always perpendicular to each other.

Note 2 to entry: Unless otherwise stated, in this document x’ is the principal axis which is closer to the x-axis

of the laboratory coordinate system, and y’ is the principal axis which is closer to the y-axis of the laboratory

coordinate system.

Note 3 to entry: If the principal axes make the angle π/4 with the x- and y-axes of the laboratory coordinate

system, then the x’-axis is by convention the direction of maximum extent.
Note 4 to entry: See Figure 1.
3.4
azimuthal orientation

azimuthal angle between the x-axis of the laboratory system and the

principal axis x’
© ISO 2021 – All rights reserved 3
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
3.5
beam widths
d (z ), d (z )
σx’ 0x’ σy’ 0y’

extent of a power density distribution in a cross-section of the beam at an axial location z along the

principal axes x’ and y’, respectively, based on the second order moments of the power density

distribution

Note 1 to entry: This definition differs from that given in ISO 11145:2018, 3.5.2, where the beam widths are

defined only in the laboratory system, whereas for the purposes of this document the beam widths are defined in

the principal axes (3.3) system of the beam.

Note 2 to entry: Formulae for calculation of the beam widths from the three second order moments are given in

7.2.
3.6
beam ellipticity
ε(z)

parameter for quantifying the circularity or squareness of a power (energy) density distribution at an

axial location z
 
min dz() , dz()
σσxy''
 
ε ()z =
 
max dz , dz
() ()
σσxy''
 
Note 1 to entry: It follows that 01<ε z ≤ .

Note 2 to entry: If ε(z) ≥ 0,87, elliptical distributions can be regarded as circular.

Note 3 to entry: In case of a rectangular distribution, ellipticity is often referred to as “aspect ratio”.

Note 4 to entry: In contrast to the definition given here, in literature the term “ellipticity” is sometimes related to

dz()
σ y

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

dz()
in ISO 11145 and ISO 13694.
3.7
circular power density distribution
power density distribution having an ellipticity greater than or equal to 0,87
[SOURCE: ISO 11145:2018, 3.6.4]
3.8
beam diameter
d (z)

extent of a circular power density distribution in a cross section of the beam at an axial location z,

based on the second order moments

Note 1 to entry: Formulae for calculation of the beam diameter from the second order moments are given in 7.2.

3.9
stigmatism

property of a beam having circular power density distributions in any plane under free propagation

and showing power density distributions after propagation through a cylindrical lens all having the

same azimuthal orientation (3.4) as that lens
4 © ISO 2021 – All rights reserved
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
3.10
simple astigmatism

property of a non-stigmatic beam whose azimuthal orientation (3.4) is constant under free propagation,

and which retains its original azimuthal orientation (3.4) after passing through a cylindrical optical

element whose cylindrical axis is parallel to one of the principal axes (3.3) of the beam

Note 1 to entry: The principal axes (3.3) of a power density distribution corresponding to a beam with simple

astigmatism (3.10) are called the principal axes (3.3) of that beam.
3.11
general astigmatism
property of a beam which is neither stigmatic nor simple astigmatic

Note 1 to entry: This document deals only with stigmatic and simple astigmatic beams. See ISO 11146-2 for

general astigmatic beams.
3.12
beam waist locations
zz,, z
00xy 0

location where the beam widths (3.5) or the beam

diameters (3.8) reach their minimum values along the beam axis
Note 1 to entry: See Figure 2.
Figure 2 — Beam propagation parameters of a simple astigmatic beam

Note 2 to entry: In the case of general astigmatic beams, which are outside the scope of this document, this

definition does not apply, see ISO 11146-2.

Note 3 to entry: For simple astigmatic beams the waist locations z and z corresponding to the principal

′ ′
0x 0y
axes (3.3), may or may not coincide.
© ISO 2021 – All rights reserved 5
---------------------- Page: 17 ----------------------
SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)

Note 4 to entry: For simple astigmatic beams, the beam widths are used; for stigmatic beams the beam diameters

are used.
3.13
beam waist widths
d , d
σσx'00y'

beam width d (z ) and d (z ), respectively, at the corresponding beam

σx’ 0x’ σy’ 0y’
waist locations z or z , respectively
0x’ 0y’
3.14
beam waist diameter
σ 0

diameter d (z ) of the beam at the location of the beam waist z

σ 0 0
3.15
beam divergence angles
ΘΘ,, Θ
σσxy′′ σ

measure for the increase of the beam widths (3.5) or beam diameter (3.8) with increasing distance from

the beam waist locations (3.12), given by
dz()
Θ = lim (6)
zz−
()zz−→∞
0x′ 0x′
and
dz()
σ y′
Θ = lim (7)
σ y
()zz−→∞ zz−
0y 0y′
for simple astigmatic beams and
dz()
Θ = lim (8)
()zz−→∞ zz−
0 0
for stigmatic beams
Note 1 to entry: The beam divergence is expressed as a full angle.

Note 2 to entry: This definition differs from that given in ISO 11145:2018, 3.8.2, where the beam divergence

angles are defined only in the laboratory system, whereas for the purposes of this document the beam divergence

angles are defined in the principal axes (3.3) system.
3.16
Rayleigh length
z , z , z
R Rx’ Ry’

distance in the direction of propagation from the

respective beam waist for which the beam diameter (3.8) or the beam width (3.5) are equal to √2 times

their respective values at the beam waist
Note 1 to entry: For the Gaussian fundamental mode:
 
z =
 
4 λ
 
σ 0
Note 2 to entry: Generally, the formula z = is valid.
[SOURCE: ISO 11145: 2018, 3.9.1]
6 © ISO 2021 – All rights reserved
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SIST EN ISO 11146-1:2021
ISO 11146-1:2021(E)
3.17
beam propagation ratios

Note 1 to entry: The term “beam propagation ratio” replaces “times-diffraction-limit factor” which was used in

ISO 11146:1999.

Note 2 to entry: Beam propagation ratios, as defined in 3.17.1 and 3.17.2, are propagation invariants for stigmatic

and simple astigmatic beams, only as long as the optics involved do not change the stigmatic or the simple

astigmatic character of the beam.
3.17.1
beam propagation ratios
2 2
M and M
x′ y′

〈simple astigmatic beams〉 ratios of the beam parameter product along the principal axes (3.3) of the

beam of interest to the beam parameter product of a diffraction-limited, perfect Gaussian beam of the

same wavelength λ
π d Θ
σσxx0
M = (9)
λ 4
d Θ
π σσyy′′0
M = (10)
λ 4
3.17.2
beam propagation ratio

〈stigmatic beams〉 ratio of the beam parameter product of the beam of interest to the beam parameter

product of a diffraction-limited, perfect Gaussian beam (TEM ) of the same wavelength, λ

d Θ
2 σσ0
M = (11)
λ 4
4 Coordinate systems

The x-, y- and z-axes define the orthogonal space directions in the laboratory axes system and shall be

specified by the user. The z-axis shall coincide approximately with the direction of the beam. The x- and

y-axes are transverse axes, usually horizontal and vertical, respectively. The origin of the z-axis is in a

referenc
...

SLOVENSKI STANDARD
oSIST prEN ISO 11146-1:2020
01-julij-2020
Laserji in laserska oprema - Preskusne metode za širine laserskega žarka, kota

divergence in faktorja širjenja žarkov - 1. del: Stigmatični in enostavni astigmatični

žarki (ISO/DIS 11146-1:2020)

Lasers and laser-related equipment - Test methods for laser beam widths, divergence

angles and beam propagation ratios - Part 1: Stigmatic and simple astigmatic beams

(ISO/DIS 11146-1:2020)

Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel

und Beugungsmaßzahlen - Teil 1: Stigmatische und einfach astigmatische Strahlen
(ISO/DIS 11146-1:2020)

Lasers et équipements associés aux lasers - Méthodes d'essai des largeurs du faisceau,

angles de divergence et facteurs de limite de diffraction - Partie 1: Faisceaux
stigmatiques et astigmatiques simples (ISO/DIS 11146-1:2020)
Ta slovenski standard je istoveten z: prEN ISO 11146-1
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
oSIST prEN ISO 11146-1:2020 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN ISO 11146-1:2020
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oSIST prEN ISO 11146-1:2020
DRAFT INTERNATIONAL STANDARD
ISO/DIS 11146-1
ISO/TC 172/SC 9 Secretariat: DIN
Voting begins on: Voting terminates on:
2020-04-28 2020-07-21
Lasers and laser-related equipment — Test methods
for laser beam widths, divergence angles and beam
propagation ratios —
Part 1:
Stigmatic and simple 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 1: Faisceaux stigmatiques et astigmatiques simples
ICS: 31.260
IMPORTANT — Please use this updated version dated 2020-02-27, and
discard any previous versions of this DIS. Formulae have been corrected
and the ballot dates have been changed.
THIS DOCUMENT IS A DRAFT CIRCULATED
This document is circulated as received from the committee secretariat.
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THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
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ISO/DIS 11146-1:2020(E)
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TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
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PROVIDE SUPPORTING DOCUMENTATION. ISO 2020
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oSIST prEN ISO 11146-1:2020
ISO/DIS 11146-1:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

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oSIST prEN ISO 11146-1:2020
ISO/DIS 11146-1:2020(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Coordinate systems ............................................................................................................................................................................................ 6

5 Test principles ......................................................................................................................................................................................................... 7

5.1 Applicability .............................................................................................................................................................................................. 7

5.2 Beam widths and beam diameter ........................................................................................................................................... 7

5.3 Beam divergence angles .................................................................................................................................................................. 7

5.4 Beam propagation ratios ................................................................................................................................................................ 7

5.5 Combined measurement of beam waist locations, beam widths, beam divergence

angles and beam propagation ratios .................................................................................................................................... 7

6 Measurement arrangement and test equipment ................................................................................................................ 8

6.1 General ........................................................................................................................................................................................................... 8

6.2 Preparation ................................................................................................................................................................................................ 8

6.3 Control of environment ................................................................................................................................................................... 8

6.4 Detector system ...................................................................................................................................................................................... 8

6.5 Beam-forming optics and optical attenuators ............................................................................................................. 9

6.6 Focusing system ..................................................................................................................................................................................... 9

7 Beam widths and beam diameter measurement ................................................................................................................ 9

7.1 Test procedure ......................................................................................................................................................................................... 9

7.2 Evaluation .................................................................................................................................................................................................... 9

8 Measurement of divergence angles ................................................................................................................................................11

8.1 Test procedure ......................................................................................................................................................................................11

8.2 Evaluation .................................................................................................................................................................................................11

9 Combined determination of beam waist locations, beam widths, divergence angles

and beam propagation ratios ...............................................................................................................................................................11

10 Test report ................................................................................................................................................................................................................14

Bibliography .............................................................................................................................................................................................................................17

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oSIST prEN ISO 11146-1:2020
ISO/DIS 11146-1:2020(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.

This second edition cancels and replaces the first edition (ISO 11146-1:2005), 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.
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 2020 – All rights reserved
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oSIST prEN ISO 11146-1:2020
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Introduction

The propagation properties of every laser beam can be characterized within the method of second order

moments by ten independent parameters (see ISO/TR 11146-3). However, due to their higher symmetry

most laser beams of practical interest need fewer parameters for a complete description. Most lasers of

practical use emit beams which are stigmatic or simple astigmatic because of their resonator design.

This document describes the measurement methods for stigmatic and simple astigmatic beams while

Part 2 deals with the measurement procedures for general astigmatic beams. For beams of unknown

type the methods of Part 2 shall be applied. Beam characterization based on the method of second order

moments as described in both parts 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 an informative Technical Report and describes the

procedures for background subtraction and offset correction.

In this document, the second order moments of the power (energy) density distribution are used for the

determination of beam widths. However, there may be problems experienced in the direct measurement

of these quantities in the beams from some laser sources. In this case, other indirect methods of the

measurement of the 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.

The problem of the dependence of the measuring result on the truncation limits of the integration area

has been investigated and evaluated by an international round robin experiment carried out in 1997.

The results of this round robin testing were taken into consideration during the preparation of this

document.
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oSIST prEN ISO 11146-1:2020
DRAFT INTERNATIONAL STANDARD ISO/DIS 11146-1:2020(E)
Lasers and laser-related equipment — Test methods
for laser beam widths, divergence angles and beam
propagation ratios —
Part 1:
Stigmatic and simple 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 only applicable for stigmatic and simple astigmatic

beams. If the type of the beam is unknown, and for general astigmatic beams, ISO 11146-2 is applicable.

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 11146-2, Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles

and beam propagation ratios — Part 2: General astigmatic beams

ISO 13694, Optics and photonics — Lasers and laser-related equipment — Test methods for laser beam

power (energy) density distribution

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 13694,

EN 61040:1992 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 http:// www .electropedia .org/

NOTE The x-, y- and z-axes in these 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.

3.1
first order moments of a power density distribution
xy,

centroid coordinates of the power density distribution of a cross section of a beam given as

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oSIST prEN ISO 11146-1:2020
ISO/DIS 11146-1:2020(E)
∞ ∞
Ex(, yz,)xxydd
∫ ∫
−∞−∞
xz()= (1)
∞ ∞
Ex(, yz,)ddxy
∫ ∫
−∞−∞
and
∞ ∞
Ex(, yz,) yxddy
∫ ∫
−∞−∞
yz()= (2)
∞ ∞
Ex(, yz,)ddxy
∫ ∫
−∞−∞

Note 1 to entry: The first order moments are used for the definition of beam centroid in ISO 11145.

Note 2 to entry: For practical application, the infinite integration limits are reduced in a specific manner as given

in Clause 7. The limitation of the integration area here differs from the integration area given in ISO 11145

3.2
second order moments of a power density distribution
22 2
σσ,,σ
xy xy
normalized weighted integrals over the power density distribution, given as
∞ ∞
Ex(),,yz ()xx− ddxy
−∞ −∞
σ ()zx== (3)
∞ ∞
Ex(),,yz ddxy
−∞ −∞
and
∞ ∞
Ex,,yz yy− ddxy
()()
−∞ −∞
σ zy== (4)
∞ ∞
Ex,,yz ddxy
−∞ −∞
and
∞ ∞
Ex(),,yz ()xx− ()yy− ddxy
−∞ −∞
σ ()zx==y (5)
∞ ∞
Ex(),,yz dxxyd
−∞ −∞

Note 1 to entry: For practical application, the infinite integration limits are reduced in a specific manner as given

in Clause 7.

Note 2 to entry: σ ()z is a symbolic notation, and not a true square. This quantity can take positive, negative

or zero value.

Note 3 to entry: The angular brackets are the operator notations as used in ISO 11146-2 and ISO/TR 11146-3.

3.3
principal axes

axes of the maximum and minimum beam extent based on the centered

second order moments of the power density distribution in a cross section of the beam

Note 1 to entry: The axes of maximum and minimum extent are always perpendicular to each other.

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3.4
azimuthal orientation

azimuthal angle between the x-axis of the laboratory system and that of

the principal axis of the power density distribution which is closer to the x-axis

Note 1 to entry: From this definition it follows that −<πϕ44<≠πϕ for πϕ/;44if =±πϕ/, is defined as the

angle between the x-axis and the major principal axis (axis of maximum extent) of the power density distribution.

3.5
beam widths
dd,
σσxy

extent of a power density distribution in a cross section of the beam at an axial location z along that

principal axis which is closer to the x- or y-axis of the laboratory coordinate system, respectively, based

on the three centered second order moments of the power density distribution

Note 1 to entry: If the principal axes make the angle π/4 with the x- and y-axes of the laboratory coordinate

system, then d is by convention the larger beam width.

Note 2 to entry: This definition differs from that given in ISO 11145:2018, 3.5.2, where the beam widths are

defined only in the laboratory system, whereas for the purposes of this document the beam widths are defined in

the principal axes system of the beam.

Note 3 to entry: Equations for calculation of the beam widths from the three centered second order moments are

given in Clause 7.2.
3.6
beam ellipticity
ε(z)

parameter for quantifying the circularity or squareness of a power (energy) density distribution at z

σ y
ε()z =

where the direction of x is chosen to be along the major axis of the distribution, such that dd≥

σσxy

Note 1 to entry: If ε ≥ 0,87, elliptical distributions can be regarded as circular.

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()
σ y

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

dz()
in ISO 11145 and ISO 13694.
3.7
circular power density distribution
power density distribution having an ellipticity greater than or equal to 0,87
[SOURCE: ISO 11145:2018, 3.6.4]
3.8
beam diameter

extent of a circular power density distribution, based on the second order moments

Note 1 to entry: Equations for calculation of the beam diameter from the centered second order moments are

given in Clause 7.2.
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3.9
stigmatism

property of a beam having circular power density distributions in any plane under free propagation

and showing power density distributions after propagation through a cylindrical lens all having the

same or azimuthal orientation as that lens
3.10
simple astigmatism

property of a non-stigmatic beam whose azimuthal orientation is constant under free propagation,

and which retains its original azimuthal orientation after passing through a cylindrical optical element

whose cylindrical axis is parallel to one of the principal axes of the beam

Note 1 to entry: The principal axes of a power density distribution corresponding to a beam with simple

astigmatism are called the principal axes of that beam.
3.11
general astigmatism
property of a beam which is neither stigmatic nor simple astigmatic

Note 1 to entry: This document deals only with stigmatic and simple astigmatic beams. Refer to ISO 11146-2 for

general astigmatic beams.
3.12
beam waist locations
zz,, z
00xy 0

location where the beam widths or the beam diameters reach their minimum values along the beam axis

Note 1 to entry: See Figure 1.

Note 2 to entry: In the case of general astigmatic beams, which are outside the scope of this part of the standard,

this definition does not apply.

Note 3 to entry: For simple astigmatic beams the waist locations z and z corresponding to the principal

0x 0y
axes, may or may not coincide.
3.13
beam waist widths
dd,
σσxy00

beam width d or d at the location of the beam waist in the x or y (principal) direction, respectively

σx σy

Note 1 to entry: d is the beam width d at location zd, is the beam width d at location z .

σx0 σx 00xyσ σ y 0y
3.14
beam waist diameter
σ 0
diameter d of the beam at the location of the beam waist
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Figure 1 — Beam propagation parameters of a simple astigmatic beam
3.15
beam divergence angles
ΘΘ,, Θ
σσxy σ

measure for the increase of the beam widths or beam diameter with increasing distance from the beam

waist locations, given by
dz()
Θ = lim (6)
zz−
()zz−→∞
0x 0x
and
dz()
σ y
Θ = lim (7)
σ y
()zz−→∞ zz−
0y 0y
for simple astigmatic beams and
dz()
Θ = lim (8)
()zz−→∞ zz−
for stigmatic beams
Note 1 to entry: The beam divergence is expressed as a full angle.

Note 2 to entry: This definition differs from that given in ISO 11145:2018, subclause 3.8.2, where the beam

divergence angles are defined only in the laboratory system, whereas for the purposes of this document the

beam divergence angles are defined in the principal axes system.
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ISO/DIS 11146-1:2020(E)
3.16
Rayleigh length
z , z , z
R Rx Ry

distance from the beam waist in the direction of propagation for which the beam diameter and beam

width are equal to √2 times their respective values at the beam waist
Note 1 to entry: For the Gaussian fundamental mode:
  σ0
z =
 
4  λ
Note 2 to entry: Generally, the formula z = is valid.
[SOURCE: ISO 11145: 2018, 3.9.1]
3.17 Beam propagation ratios

Note 1 to entry The term “beam propagation ratio” replaces “times-diffraction-limit factor” which was used in

ISO 11146:1999.

Note 2 to entry Beam propagation ratios, as defined in 3.17.1 and 3.17.2, are propagation invariants for stigmatic

and simple astigmatic beams, only as long as the optics involved do not change the stigmatic or the simple

astigmatic character of the beam.
3.17.1
beam propagation ratios
2 2
M and M
x y

〈simple astigmatic beams〉 ratios of the beam parameter product along the principal axes of the beam

of interest to the beam parameter product of a diffraction-limited, perfect Gaussian beam of the same

wavelength λ
d Θ
σσxx0
M = (9)
λ 4
d Θ
π σσyy0
M = (10)
λ 4
3.17.2
beam propagation ratio

〈stigmatic beams〉 ratio of the beam parameter product of the beam of interest to the beam parameter

product of a diffraction-limited, perfect Gaussian beam (TEM ) of the same wavelength λ

d Θ
σσ0
M = (11)
λ 4
4 Coordinate systems

The x-, y- and z-axes define the orthogonal space directions in the laboratory axes system and shall be

specified by the user. The z-axis shall coincide approximately with the direction of the beam. The x- and

y-axes are transverse axes, usually horizontal and vertical, respectively. The origin of the z-axis is in a

reference x-y plane defined by the manufacturer, e.g. the front of the laser enclosure.

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5 Test principles
5.1 Applicability

The following test principles are only valid for stigmatic and simple astigmatic beams. For general

astigmatic beams ISO 11146-2 shall be applied.
5.2 Beam widths and beam diameter

For the determination of beam widths or diameter at location z , the power density distribution of the

laser beam shall be measured in the x-y plane at this location z . Suitable background correction shall

be applied to the measured data if necessary (refer to ISO/TR 11146-3). From the measured power

density distribution the first order and centered second order moments are calculated. From the

centered second order moments the beam widths, dz(),(dz), the ellipticity, ε , and, if appropriate,

σσxy
the beam diameter, dz(), are to be determined.
5.3 Beam divergence angles

The determination of the divergence angles follows from measurements of the beam widths or the

beam diameter in the focal plane of a focusing element.

First, the laser beam shall be transformed by an aberration-free focusing element. For a simple

astigmatic beam, the beam widths d and d are measured one focal length, f , away from the

σxf σ yf

rear principal plane of the focusing element. The corresponding divergence angles Θ and Θ are

σx σy
determined using the relationships
σxf
Θ = (12)
and
σ yf
Θ = (13)
σ y

For stigmatic beams, the beam diameter d is measured and the divergence angle Θ is determined

σ f σ
by using
σ f
Θ = (14)
5.4 Beam propagation ratios
2 2 2

For the determination of the beam propagation ratios M , M or M , it is necessary to determine

x y

the beam waist widths dd, or the waist diameter d and the related beam divergence

σσxy00 σ 0
angles ΘΘ, or Θ .
σσxy σ
5.5 Combined measurement of beam waist locations, beam widths, beam divergence
angles and beam propagation ratios

The beam widths data along the propagation axis shall be fitted to a hyperbola as discussed in Clause 9.

The beam waist locations, beam waist widths, beam divergence angles and beam propagation ratios

are derived from the fit parameters.
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6 Measurement arrangement and test equipment
6.1 General

The test is based on the measurement of the cross-sectional power density distribution at a number of

axial locations along the beam propagation axis.
6.2 Preparation

The optical axis of the measuring system should be coaxial with the laser beam to be measured. Suitable

optical alignment devices are available for this purpose (e.g. aligning lasers or steering mirrors).

The aperture of the optical system should accommodate the entire cross-section of the laser beam.

Losses by clipping shall be smaller than 1 % of the total beam power or energy. In order to test this,

apertures of different widths can be introduced into the beam path in front of each optical component.

The aperture which reduces the output signal by 5 % should have a diameter less than 0,8 times the

aperture of the optical component.

The attenuators or beam-forming optics should be mounted such that the optical axis runs through

the geometrical centres. Care shall be taken to avoid systematic errors. Reflections, interference

effects, external ambient light, thermal radiation or air draughts are all potential sources of increased

uncertainty.
6.3 Control of environment

Suitable measures such as mechanical and acoustical isolation of the test set-up, shielding from

extraneous radiation, temperature stabilization of the laboratory, choice of low-noise amplifiers shall

be taken to ensure that the contribution to the total probable uncertainty of the parameters to be

measured is low.

Care should be taken to ensure that the atmospheric environment in high-power laser beam paths does

not contain gase
...

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