SIST EN ISO 11146-2:2005

SLOVENSKI STANDARD
SIST EN ISO 11146-2:2005
01-junij-2005
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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)
Laser und Laseranlagen - Prüfverfahren für Laserstrahlabmessungen, Divergenzwinkel
und Beugungsmaßzahlen - Teil 2: Allgemein astigmatische Strahlen (ISO 11146-2:2005)
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 11146-2:2005)
Ta slovenski standard je istoveten z: EN ISO 11146-2:2005
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
SIST EN ISO 11146-2:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 11146-2:2005

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SIST EN ISO 11146-2:2005
EUROPEAN STANDARD
EN ISO 11146-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
February 2005
ICS 31.260
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 11146-2:2005)
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 2: Faisceaux Beugungsmaßzahlen - Teil 2: Allgemein astigmatische
astigmatiques généraux (ISO 11146-2:2005) Strahlen (ISO 11146-2:2005)
This European Standard was approved by CEN on 3 February 2005.
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.
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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 11146-2:2005: E
worldwide for CEN national Members.

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SIST EN ISO 11146-2:2005

EN ISO 11146-2:2005 (E)





Foreword


This document (EN ISO 11146-2:2005) 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 August 2005, and conflicting national
standards shall be withdrawn at the latest by August 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 11146-2:2005 has been approved by CEN as EN ISO 11146-2:2005 without any
modifications.

2

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SIST EN ISO 11146-2:2005

INTERNATIONAL ISO
STANDARD 11146-2
First edition
2005-02-15

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 des facteurs de limite de
diffraction —
Partie 2: Faisceaux astigmatiques généraux




Reference number
ISO 11146-2:2005(E)
©
ISO 2005

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SIST EN ISO 11146-2:2005
ISO 11146-2:2005(E)
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©  ISO 2005
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ii © ISO 2005 – All rights reserved

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SIST EN ISO 11146-2:2005
ISO 11146-2:2005(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Coordinate system .5
5 Test principles .5
5.1 General .5
5.2 Spatial second order moments of the Wigner distribution.5
5.3 Second order moments of the Wigner distribution .5
5.4 Derived quantities .5
6 Measurement arrangement and test equipment .6
6.1 General .6
6.2 Preparation.6
6.3 Control of environment.6
6.4 Detector system.6
6.5 Beam-forming optics and optical attenuators.7
7 Measurement of the second order moments .7
7.1 General .7
7.2 Measurement of the second order moments of power density distributions.7
7.3 Measurement of all second order moments of the Wigner distribution.9
8 Determination of effective beam propagation ratio.11
9 Determination of intrinsic astigmatism.11
10 Determination of the twist parameter.12
11 Test report.12
Bibliography.15

© ISO 2005 – All rights reserved iii

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SIST EN ISO 11146-2:2005
ISO 11146-2:2005(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 11146-2 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 9,
Electro-optical systems.
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 11146-2:2005
ISO 11146-2:2005(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.
Part 1 of ISO 11146 describes the measurement methods for stigmatic and simple astigmatic beams while
this part of ISO 11146 deals with the measurement procedures for general astigmatic beams. This part of
ISO 11146 is applicable to beams of unknown type. Beam characterization, based on the method of second
order moments as described in Part 1 and this part of ISO 11146, 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. 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 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 was
investigated and evaluated by an international interlaboratory experiment carried out in 1997. The results of
this interlaboratory testing were taken into consideration in 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 5.3 and 5.4.
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 11146-2:2005

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SIST EN ISO 11146-2:2005
INTERNATIONAL STANDARD ISO 11146-2:2005(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 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 applicable to general astigmatic beams or
unknown types of beams. For stigmatic and simple astigmatic beams, ISO 11146-1 is applicable.
Within this part of ISO 11146, 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 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 11146-1:2005, Lasers and laser-related equipment — Test methods for laser beam widths, divergence
angles and beam propagation ratios — Part 1: Stigmatic and simple astigmatic beams
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 11146-1, IEC 61040
and the following apply.
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” refers to continuous wave sources. It might be
replaced by “energy density distribution” in case of pulsed sources.
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 centred second order moments by
© ISO 2005 – All rights reserved 1

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SIST EN ISO 11146-2:2005
ISO 11146-2:2005(E)
22
dx=+22 y (1)
g
NOTE 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 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 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
∞∞
E(,xy,z)xxyd d
∫∫
−∞ −∞
xz() = (2)
∞∞
E(,xy,z)dx dy
∫∫
−∞ −∞
and
∞∞
E(,xy,z)y dx dy
∫∫
−∞ −∞
yz() = (3)
∞∞
E(,xy,z)dx dy
∫∫
−∞ −∞
where E(x,y,z) is the power density distribution at the specific plane z = constant.
3.6
second order moments of the Wigner distribution
22 2 2
xy,,xy,ΘΘ, ,ΘΘ,xΘ,xΘ,yΘ,yΘ
x yxy x y x y
ten second order moments of the Wigner distribution of the beam at location z
NOTE 1 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 © ISO 2005 – All rights reserved

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SIST EN ISO 11146-2:2005
ISO 11146-2:2005(E)
2 2 2
NOTE 2 In ISO 11146-1, the three spatial second order moments are defined as σ , σ and σ . In this part of
x y xy
ISO 11146 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 Three angular moments 〈Θ 〉, 〈Θ 〉 and 〈Θ Θ 〉 are independent of z. The other seven second order moments
x y x y
are, in general, functions of z.
3.7
spatial second order moments of the Wigner distribution
22
xy,,xy
subset of the second order moments, which can be directly obtained from measured power density distribution
by
∞∞
2
E(,xy,z)(x − x ) dx dy
∫∫
−∞ −∞
2
xz() = (4)
∞∞
Ex(,y,z)dx dy
∫∫
−∞ −∞
∞∞
2
E(,xy,z)(y − y ) dx dy
∫∫
−∞ −∞
2
yz() = (5)
∞∞
Ex(,y,z)dx dy
∫∫
−∞ −∞
and
∞∞
E(,xy,z)(x−−x )(y y )dx dy
∫∫
−∞ −∞
xy ()z = (6)
∞∞
Ex(,y,z)dx dy
∫∫
−∞ −∞
3.8
beam matrix
P
symmetric and positive definite 4×4 matrix containing all ten second order moments of the Wigner distribution
and its elements and given by
2

xxy xΘΘx
xy


2
xy y yΘΘy

xy
P = (7)
2

xyΘΘ Θ ΘΘ
x xx xy


2
xyΘΘ ΘΘ Θ
yy xy y

3.9
effective beam propagation ratio
2
M
eff
invariant quantity related to the focusability of a general astigmatic beam, defined as:
© ISO 2005 – All rights reserved 3

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SIST EN ISO 11146-2:2005
ISO 11146-2:2005(E)
1
4π
2
4

M =
...