SIST EN ISO 11146-1:2005

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 11146-1:2005)

This International Standard specifies methods for measuring beam widths (diameter), divergence angles and beam propagation ratios of laser beams. This Part of the standard shall only be applied for stigmatic and simple astigmatic beams. If the type of the beam is unknown and for general astigmatic beams Part 2 of this standard shall be applied.

Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel und Beugungsmaßzahlen - Teil 1: Stigmatische und einfach astigmatische Strahlen (ISO 11146-1:2005)

Dieser Teil der ISO 11146 legt Verfahren zur Messung von Strahlabmessungen (Strahldurchmesser), Divergenzwinkeln und Beugungsmaßzahlen von Laserstrahlen fest. Dieser Teil der ISO 11146 darf nur für stigmatische und einfach astigmatische Strahlen angewendet werden. Wenn die Art des Strahles unbekannt ist und bei allgemein astigmatischen Strahlen muss ISO 11146-2 angewendet werden.

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 11146-1:2005)

L'ISO 11146-1:2005 spécifie les méthodes pour mesurer les largeurs (diamètres) du faisceau, les angles de divergence et les facteurs de propagation des faisceaux laser.
L'ISO 11146-1:2005 s'applique uniquement aux faisceaux stigmatiques et astigmatiques simples. Si le type de faisceau est inconnu et pour les faisceaux astigmatiques généraux, il convient d'appliquer l'ISO 11146-2.

Laserji in laserska oprema – Preskusne metode za širine laserskega žarka, kota divergence in faktorja širjenja žarkov - 1. del: Stigmatični in enostavni astigmatični žarki (ISO 11146-1:2005)

General Information

• Status: Withdrawn
• Publication Date: 31-May-2005
• Withdrawal Date: 15-Aug-2021
• ICS: 31.260 - Optoelectronics. Laser equipment
• Technical Committee: VAZ - Healthcare
• Current Stage: 9900 - Withdrawal (Adopted Project)
• Start Date: 28-Jul-2021
• Due Date: 20-Aug-2021
• Completion Date: 16-Aug-2021
• Ref Project: EN ISO 11146-1:2005 - 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 11146-1:2005)

Relations

• Replaced By: SIST EN 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)
• Effective Date: 01-Sep-2021
• Replaced By: SIST EN 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)
• Effective Date: 08-Jun-2022
• Replaces: SIST EN ISO 11146:2000 - Laser and laser-related equipment - Test methods for laser beam parameters - Beam widths, divergence angle and beam propagation factor (ISO 11146:1999)
• Effective Date: 12-Sep-2009
• Replaces: SIST EN ISO 11146:2000 - Laser and laser-related equipment - Test methods for laser beam parameters - Beam widths, divergence angle and beam propagation factor (ISO 11146:1999)
• Effective Date: 08-Jun-2022

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 11146-1:2005
01-junij-2005
/DVHUMLLQODVHUVNDRSUHPD±3UHVNXVQHPHWRGH]DãLULQHODVHUVNHJDåDUNDNRWD
GLYHUJHQFHLQIDNWRUMDãLUMHQMDåDUNRYGHO6WLJPDWLþQLLQHQRVWDYQLDVWLJPDWLþQL
åDUNL,62
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 11146-1:2005)
Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel
und Beugungsmaßzahlen - Teil 1: Stigmatische und einfach astigmatische Strahlen (ISO
11146-1:2005)
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 11146-1:2005)
Ta slovenski standard je istoveten z: EN ISO 11146-1:2005
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
SIST EN ISO 11146-1:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 11146-1:2005

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SIST EN ISO 11146-1:2005
EUROPEAN STANDARD
EN ISO 11146-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
January 2005
ICS 31.260
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-
1:2005)
Lasers et équipements associés aux lasers - Méthodes Laser und Laseranlagen - Prüfverfahren für
d'essai des largeurs du faisceau, angles de divergence et Laserstrahlabmessungen, Divergenzwinkel und
facteurs de limite de diffraction - Partie 1: Faisceaux Beugungsmaßzahlen - Teil 1: Stigmatische und einfach
stigmatiques et astigmatiques simples (ISO 11146-1:2005) astigmatische Strahlen (ISO 11146-1:2005)
This European Standard was approved by CEN on 6 October 2004.
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 Central Secretariat 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 Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 11146-1:2005: E
worldwide for CEN national Members.

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SIST EN ISO 11146-1:2005

EN ISO 11146-1:2005 (E)





Foreword


This document (EN ISO 11146-1:2005) has been prepared by Technical Committee ISO/TC 172
"Optics and optical instruments" in collaboration with Technical Committee CEN/TC 123 "Lasers
and laser-related equipment", 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 July 2005, and conflicting national standards
shall be withdrawn at the latest by July 2005.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium,
Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary,
Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.


Endorsement notice

The text of ISO 11146-1:2005 has been approved by CEN as EN ISO 11146-1:2005 without any
modifications.

2

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SIST EN ISO 11146-1:2005

INTERNATIONAL ISO
STANDARD 11146-1
First edition
2005-01-15

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 11146-1:2005(E)
©
ISO 2005

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
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©  ISO 2005
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Published in Switzerland

ii © ISO 2005 – All rights reserved

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(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. 6
5.1 Applicability. 6
5.2 Beam widths and beam diameter . 6
5.3 Beam divergence angles. 6
5.4 Beam propagation ratios. 6
5.5 Combined measurement of beam waist locations, beam widths, beam divergence angles
and beam propagation ratios. 7
6 Measurement arrangement and test equipment. 7
6.1 General. 7
6.2 Preparation. 7
6.3 Control of environment . 7
6.4 Detector system. 7
6.5 Beam-forming optics and optical attenuators . 8
6.6 Focusing system. 8
7 Beam widths and beam diameter measurement. 8
7.1 Test procedure. 8
7.2 Evaluation. 8
8 Measurement of divergence angles . 10
8.1 Test procedure. 10
8.2 Evaluation. 10
9 Combined determination of beam waist locations, beam widths, divergence angles and
beam propagation ratios . 11
10 Test report. 13
Bibliography . 16

© ISO 2005 – All rights reserved iii

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
ISO 11146-1 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 9,
Electro-optical systems.
This first edition of ISO 11146-1, together with ISO/TR 11146-3 cancels and replaces ISO 11146:1999, the
contents of which have been technically revised and augmented.
ISO 11146 consists of the following parts, under the general title Lasers and laser-related equipment — Test
methods for laser beam widths, divergence angles and beam propagation ratios:
 Part 1: Stigmatic and simple astigmatic beams
 Part 2: General astigmatic beams
 Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods
(Technical Report)

iv © ISO 2005 – All rights reserved

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(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 part of ISO 11146 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 part of ISO 11146, 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 part of ISO 11146 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.
The International Organization for Standardization (ISO) draws attention to the fact that it is claimed that
compliance with this document may involve the use of a patent concerning the determination of beam
characteristics by measuring along the beam caustic of the transformed beam produced by a lens as
described in 5.5.
ISO takes no position concerning the evidence, validity and scope of this patent right.
The holder of this patent right (U.S. No. 5,267,012) has assured ISO that he is willing to negotiate licences
under reasonable and non-discriminatory terms and conditions with applicants throughout the world.
In this respect, the statement of the holder of this patent right is registered with the ISO. Information may be
obtained from:
Coherent Inc.
5100 Patrick Henry Drive
Santa Clara, CA 95056-0980
USA
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights other than those identified above. ISO shall not be held responsible for identifying any or all such patent
rights.
© ISO 2005 – All rights reserved v

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SIST EN ISO 11146-1:2005

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SIST EN ISO 11146-1:2005
INTERNATIONAL STANDARD ISO 11146-1:2005(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 part of ISO 11146 specifies methods for measuring beam widths (diameter), divergence angles and
beam propagation ratios of laser beams. This part of ISO 11146 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 should
be applied.
2 Normative references
The following referenced documents are indispensable for the application 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 optical instruments — 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 optical instruments — Lasers and laser-related equipment — Test methods for laser
beam power (energy) density distribution
IEC 61040:1990, 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, IEC 61040 and
the following apply.
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
∞∞
E(,xy,z)xxyd d
∫∫
−∞ −∞
xz() = (1)
∞∞
E(,xy,z)dx dy
∫∫
−∞ −∞
© ISO 2005 – All rights reserved 1

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
and
∞∞
E(,xy,z)y dx dy
∫∫
−∞ −∞
yz() = (2)
∞∞
E(,xy,z)dx dy
∫∫
−∞ −∞
NOTE For practical application, the infinite integration limits are reduced in a specific manner as given in Clause 7.
3.2
second order moments of a power density distribution
22 2
σ,,σσ
x yxy
normalized weighted integrals over the power density distribution, given as
∞∞
2
E(,xy,z)(x −x) dx dy
∫∫
−∞ −∞
22
σ ()zx== (3)
x
∞∞
Ex(,y,z)dx dy
∫∫
−∞ −∞
and
∞∞
2
E(,xy,z)(y −y) dx dy
∫∫
−∞ −∞
22
σ ()zy== (4)
y
∞∞
Ex(,y,z)dx dy
∫∫
−∞ −∞
and
∞∞
E(,xy,z)(x−−x)(yyx)d dy
∫∫
−∞ −∞
2
σ ()zx==y (5)
xy
∞∞
Ex(,y,z)dx dy
∫∫
−∞ −∞
NOTE 1 For practical application, the infinite integration limits are reduced in a specific manner as given in Clause 7.
2
NOTE 2 σ z is a symbolic notation, and not a true square. This quantity can take positive, negative or zero value.
()
xy
NOTE 3 The angular brackets are the operator notations as used in ISO 11146-2 and ISO/TR 11146-3.
3.3
principal axes of a power density distribution
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 The axes of maximum and minimum extent are always perpendicular to each other.
2 © ISO 2005 – All rights reserved

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
3.4
orientation of a power density distribution
ϕ
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 From this definition it follows that −<πϕ4 < π 4 for ϕ ≠ π 4 ; if ϕ=±π 4 , ϕ 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,
σx σy
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 centered
second order moments of the power density distribution
NOTE 1 If the principal axes make the angle π/4 with the x- and y-axes of the laboratory coordinate system, then d is
σx
by convention the larger beam width.
NOTE 2 This definition differs from that given in ISO 11145:2001, subclause 3.5.2, where the beam widths are defined
only in the laboratory system, whereas for the purposes of this part of ISO 11146 the beam widths are defined in the
principal axes system.
3.6
ellipticity of a power density distribution
ε
ratio between the minimum and maximum beam widths
3.7
circular power density distribution
power density distribution having an ellipticity greater than 0,87
3.8
beam diameter
d
σ
extent of a circular power density distribution, based on the second order moments
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 azimuth angle shows a constant orientation under free propagation,
and which retains its original orientation after passing through a cylindrical optical element whose cylindrical
axis is parallel to one of the principal axes of the beam
NOTE 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 This part of ISO 11146 deals only with stigmatic and simple astigmatic beams. Refer to ISO 11146-2 for
general astigmatic beams.
© ISO 2005 – All rights reserved 3

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
3.12
beam waist locations
z , , zz

00xy 0
positions from z = 0 reference plane where the beam widths or the beam diameter reach their minimum values
along the axis of propagation
See Figure 1.
NOTE 1 In the case of general astigmatic beams, which are outside the scope of this part of the standard, this
definition does not apply.
NOTE 2 For simple astigmatic beams the waist locations z and z corresponding to the principal axes, may or
0x 0y
may not coincide.
3.13
beam waist widths
dd,
σx00σy
beam widths at the beam waist locations of a simple astigmatic beam
NOTE d is the beam width d at location zd, is the beam width d at location z .
σx0 σx 00x σy σy 0y
3.14
beam waist diameter
d
σ0
beam diameter at the beam waist location of a stigmatic beam

Figure 1 — Beam propagation parameters of a simple astigmatic beam
4 © ISO 2005 – All rights reserved

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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
3.15
beam divergence angles
ΘΘ, , Θ
σx σy σ
measure for the increase of the beam widths or beam diameter with increasing distance from the beam waist
locations, given by
dz()
σx
Θ = lim (6)
σx
()zz−→∞ z − z
0x 0x
and
dz()
σ y
Θ = lim (7)
σy
()zz−→∞ z − z
0y 0y
for simple astigmatic beams and
dz()
σ
Θ = lim (8)
σ
()zz−→∞ z − z
0 0
for stigmatic beams
NOTE 1 The beam divergence is expressed as a full angle.
NOTE 2 This definition differs from that given in ISO 11145:2001, subclause 3.18.2, where the beam divergence
angles are defined only in the laboratory system, whereas for the purposes of this part of ISO 11146 the beam divergence
angles are defined in the principal axes system.
3.16 beam propagation ratios
NOTE 1 The term “beam propagation ratio” replaces “times-diffraction-limit factor” which was used in ISO 11146:1999.
NOTE 2 Beam propagation ratios, as defined in 3.16.1 and 3.16.2, 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.
3.16.1
beam propagation ratios
2
2
and
M 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
2
π d Θ
σx0 σx
M =  (9)
x
λ 4
d Θ
2
π
σyy0 σ
M =  (10)
y
λ 4
3.16.2
beam propagation ratio
2
M
〈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
00
π d Θ
2 σ 0 σ
=  (11)
M
λ 4
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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
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.
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(),d (z) , the ellipticity, ε, and, if appropriate, the beam diameter, dz() , are to be
σσxy σ
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 rear principal plane
σxf σyf
of the focusing element. The corresponding divergence angles Θ and Θ are determined using the
σx σy
relationships
d
σxf
Θ = (12)
σx
f
and
d
σ yf
Θ = (13)
σ y
f
For stigmatic beams, the beam diameter d is measured and the divergence angle Θ is determined by
σf σ
using
d
σ f
Θ = (14)
σ
f
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 the
x y
beam waist widths dd, or the waist diameter d and the related beam divergence angles Θ , Θ
σx00σy σ0 σx σy
or Θ .
σ
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SIST EN ISO 11146-1:2005
ISO 11146-1:2005(E)
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.
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 gases or vapours that can absorb the laser radiation and cause thermal distorti
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