Optics and photonics - Lasers and laser-related equipment - Test methods for laser beam power (energy) density distribution (ISO 13694:2018)

This document specifies methods by which the measurement of power (energy) density distribution is
made and defines parameters for the characterization of the spatial properties of laser power (energy)
density distribution functions at a given plane.
The methods given in this document are intended to be used for the testing and characterization of
both continuous wave (cw) and pulsed laser beams used in optics and optical instruments.
This document provides definitions of terms and symbols to be used in referring to power density
distribution, as well as requirements for its measurement. For pulsed lasers, the distribution of timeintegrated
power density (i.e. energy density) is the quantity most often measured.

Optik und Photonik - Laser und Laseranlagen - Prüfverfahren für die Leistungs-(Energie-)dichteverteilung von Laserstrahlen (ISO 13694:2018)

Dieses Dokument legt Verfahren zur Messung der Leistungs-[Energie-]dichteverteilung fest und definiert Parameter zur Charakterisierung der räumlichen Eigenschaften von Laserleistungs-[Energie ]dichteverteilungsfunktionen in einer gegebenen Ebene.
Die in diesem Dokument beschriebenen Prüfverfahren sind zur Prüfung und Charakterisierung der Strahlen von Dauerstrichlasern wie auch von Pulslasern in der Optik und optischen Elementen bestimmt

Optique et photonique - Lasers et équipements associés aux lasers - Méthodes d'essai de distribution de la densité de puissance (d'énergie) du faisceau laser (ISO 13694:2018)

Le présent document spécifie des méthodes permettant de procéder au mesurage de la distribution de densité de puissance (d'énergie) et définit les paramètres de caractérisation des propriétés spatiales des fonctions de distribution de densité de puissance (d'énergie) laser dans un plan donné.
Les méthodes d'essai données dans le présent document sont destinées à être utilisées dans le cadre des essais et de la caractérisation des faisceaux laser continus et impulsionnels.
Le présent document donne des définitions de la terminologie et des symboles à utiliser dans le cadre de la distribution de la densité de puissance, ainsi que les spécifications relatives au mesurage de cette distribution. Pour les lasers impulsionnels, la distribution de la densité de puissance intégrée sur le temps (c'est-à-dire la densité d'énergie) représente la grandeur la plus souvent mesurée.

Optika in fotonska tehnologija - Laserji in laserska oprema - Metode za preskušanje gostote porazdelitve moči (energije) žarka (ISO 13694:2018)

Ta dokument določa metode, s katerimi se izvaja merjenje gostote porazdelitve moči (energije) ter parametre za karakterizacijo prostorskih lastnosti funkcij gostote porazdelitve moči (energije) na dani ravnini.
Metode, podane v okviru tega dokumenta, so namenjene preskušanju in karakterizaciji tako trajnih valov (cw) ter tudi pulznih laserskih žarkov, ki se uporabljajo v optiki in optičnih instrumentih.
Ta dokument vsebuje opredelitve izrazov in simbolov, ki se uporabljajo pri sklicevanju na gostoto porazdelitve moči, kot tudi zahteve za njeno merjenje. Pri impulznih laserjih se najpogosteje meri časovno integrirana gostota porazdelitve moči (tj. energijska gostota).

General Information

Status
Published
Public Enquiry End Date
04-Oct-2017
Publication Date
06-Feb-2019
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
15-Jan-2019
Due Date
22-Mar-2019
Completion Date
07-Feb-2019

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SIST EN ISO 13694:2019
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SIST EN ISO 13694:2016
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Optics and photonics - Lasers and laser-related equipment - Test methods for laser

beam power (energy) density distribution (ISO 13694:2018)

Optik und Photonik - Laser und Laseranlagen - Prüfverfahren für die Leistungs-(Energie

-)dichteverteilung von Laserstrahlen (ISO 13694:2018)

Optique et photonique - Lasers et équipements associés aux lasers - Méthodes d'essai

de distribution de la densité de puissance (d'énergie) du faisceau laser (ISO
13694:2018)
Ta slovenski standard je istoveten z: EN ISO 13694:2018
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
SIST EN ISO 13694:2019 en

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

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SIST EN ISO 13694:2019
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SIST EN ISO 13694:2019
EN ISO 13694
EUROPEAN STANDARD
NORME EUROPÉENNE
December 2018
EUROPÄISCHE NORM
ICS 31.260 Supersedes EN ISO 13694:2015
English Version
Optics and photonics - Lasers and laser-related equipment
- Test methods for laser beam power (energy) density
distribution (ISO 13694:2018)

Optique et photonique - Lasers et équipements Optik und Photonik - Laser und Laseranlagen -

associés aux lasers - Méthodes d'essai de distribution Prüfverfahren für die Leistungs-(Energie-

de la densité de puissance (d'énergie) du faisceau laser )dichteverteilung von Laserstrahlen (ISO 13694:2018)

(ISO 13694:2018)
This European Standard was approved by CEN on 23 September 2018.

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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,

Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, 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

© 2018 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13694:2018 E

worldwide for CEN national Members.
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SIST EN ISO 13694:2019
EN ISO 13694:2018 (E)
Contents Page

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

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SIST EN ISO 13694:2019
EN ISO 13694:2018 (E)
European foreword

This document (EN ISO 13694:2018) 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 June 2019, and conflicting national standards shall be

withdrawn at the latest by June 2019.

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 13694:2015.

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, Former Yugoslav Republic of Macedonia,

France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,

Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,

Turkey and the United Kingdom.
Endorsement notice

The text of ISO 13694:2018 has been approved by CEN as EN ISO 13694:2018 without any modification.

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SIST EN ISO 13694:2019
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SIST EN ISO 13694:2019
INTERNATIONAL ISO
STANDARD 13694
Third edition
2018-11
Optics and photonics — Lasers and
laser-related equipment — Test
methods for laser beam power
(energy) density distribution
Optique et photonique — Lasers et équipements associés aux
lasers — Méthodes d'essai de distribution de la densité de puissance
(d'énergie) du faisceau laser
Reference number
ISO 13694:2018(E)
ISO 2018
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SIST EN ISO 13694:2019
ISO 13694:2018(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2018

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
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2018 – All rights reserved
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SIST EN ISO 13694:2019
ISO 13694:2018(E)
Contents Page

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

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

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

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

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

3.1 Measured quantities ........................................................................................................................................................................... 1

3.2 Characterizing parameters ........................................................................................................................................................... 3

4 Coordinate system .............................................................................................................................................................................................. 7

5 Characterizing parameters derived from the measured spatial distribution ......................................7

6 Test principle ........................................................................................................................................................................................................... 7

7 Measurement arrangement and test equipment ................................................................................................................ 8

7.1 General ........................................................................................................................................................................................................... 8

7.2 Preparation ................................................................................................................................................................................................ 8

7.3 Control of environment ................................................................................................................................................................... 8

7.4 Detector system ...................................................................................................................................................................................... 8

7.5 Beam-forming optics, optical attenuators, and beam splitters ..................................................................... 9

8 Test procedure ........................................................................................................................................................................................................ 9

8.1 Equipment preparation ................................................................................................................................................................... 9

8.2 Detector calibration procedure .............................................................................................................................................10

8.2.1 Spatial calibration ........................................................................................................................................................10

8.2.2 Power (energy) calibration ..................................................................................................................................10

8.3 Data recording and noise correction ................................................................................................................................10

8.3.1 General...................................................................................................................................................................................10

8.3.2 Correction by background-map subtraction ........................................................................................11

8.3.3 Correction by average background subtraction.................................................................................11

9 Evaluation .................................................................................................................................................................................................................12

10 Test report ................................................................................................................................................................................................................12

Annex A (informative) Test report .......................................................................................................................................................................13

Bibliography .............................................................................................................................................................................................................................16

© ISO 2018 – All rights reserved iii
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SIST EN ISO 13694:2019
ISO 13694:2018(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 third edition cancels and replaces the second edition (ISO 13694:2015), which has been technically

revised. The main changes compared to the previous edition are as follows:

a) the definition of beam ellipticity has been harmonized with ISO 11145 and ISO 11146-1;

b) the term “second linear moments” has been replaced by “second moments”;
c) the term “field of view” has been replaced by “aperture”;

d) Clause 9 was rewritten; the paragraphs on clip-levels were corrected to reflect that they are no

longer intended for noise cancelation;

e) the entries “Fitted distribution type”, “Roughness of fit R”, and “Goodness of fit G” have been

removed from the Test Report;
f) the term “aspect ratio” has been removed from the test report.

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 2018 – All rights reserved
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SIST EN ISO 13694:2019
ISO 13694:2018(E)
Introduction

Many applications of lasers involve using the near-field as well as the far-field power (energy) density

distribution of the beam. The power (energy) density distribution of a laser beam is characterized by the

spatial distribution of irradiant power (energy) density with lateral displacement in a particular plane

perpendicular to the direction of propagation. In general, the power (energy) density distribution of the

beam changes along the direction of propagation. Depending on the power (energy), size, wavelength,

polarization, and coherence of the beam, different methods of measurement are applicable in different

situations. Five methods are commonly used: camera arrays (1D and 2D), apertures, pinholes, slits, and

knife edges.

According to ISO 11145, it is possible to use two different definitions for describing and measuring the

laser beam diameter. One definition is based on the measurement of the encircled power (energy); the

other is based on determining the spatial moments of the power (energy) density distribution of the

laser beam.

The use of spatial moments is necessary for calculating the beam propagation factor, K, and the

beam propagation ratio, M , from measurements of the beam widths at different distances along the

propagation axis. ISO 11146-1 describes this measurement procedure. For other applications, other

definitions for the beam diameter can be used. For some quantities used in this document the first

definition (encircled power (energy)) is more appropriate and easier to use.
© ISO 2018 – All rights reserved v
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SIST EN ISO 13694:2019
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SIST EN ISO 13694:2019
INTERNATIONAL STANDARD ISO 13694:2018(E)
Optics and photonics — Lasers and laser-related
equipment — Test methods for laser beam power (energy)
density distribution
1 Scope

This document specifies methods by which the measurement of power (energy) density distribution is

made and defines parameters for the characterization of the spatial properties of laser power (energy)

density distribution functions at a given plane.

The methods given in this document are intended to be used for the testing and characterization of

both continuous wave (cw) and pulsed laser beams used in optics and optical instruments.

This document provides definitions of terms and symbols to be used in referring to power density

distribution, as well as requirements for its measurement. For pulsed lasers, the distribution of time-

integrated power density (i.e. energy density) is the quantity most often measured.

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 — Laser and laser-related equipment — Vocabulary and symbols

ISO 11146-1, Lasers and laser-related equipment — Test methods for laser beam widths, divergence angles

and beam propagation ratios — Part 1: Stigmatic and simple astigmatic beams

ISO 11554, Optics and photonics — Lasers and laser-related equipment — Test methods for laser beam

power, energy and temporal characteristics

IEC 61040, 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 and IEC 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 http: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
3.1 Measured quantities
3.1.1
power density distribution
E(x, y, z)

set of all power densities at location z of a certain cw beam with non-negative values for all transverse

coordinates (x, y)
© ISO 2018 – All rights reserved 1
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SIST EN ISO 13694:2019
ISO 13694:2018(E)
3.1.1.1
power density
E(x , y , z)
P P

portion of the beam power at location z which impinges on the area δA at the location P(x , y ) divided

P P
by the area δA in the limit δA → 0
[SOURCE: ISO 11145:2018, 3.13.6, modified —Notes to entry omitted.]
3.1.2
energy density distribution
H(x, y, z)

set of all energy densities at location z of a certain pulsed beam with non-negative values for all

transverse coordinates (x, y)
Hx,,yz = Ex,,yz dt
() ()
3.1.2.1
energy density
H(x , y , z)
P P

portion of the beam energy (time-integrated power) at location z which impinges

on the area δA at the location P(x , y ) divided by the area δA in the limit δA → 0

P P
Hx ,,yz = Ex ,,yz dt
() ()
PP PP

[SOURCE: ISO 11145:2018, 3.13.4, modified — Notes to entry omitted and Formula added.]

3.1.3
power
P(z)
rate of energy transfer in a continuous wave (cw) beam at location z
Pz = Ex,,yz ddxy
() ()
3.1.4
pulse energy
Q(z)
energy in one pulse measured at location z
Qz = Hx,,yz ddxy
() ()

[SOURCE: ISO 11145:2018, term 3.13.3 modified — Included "Measured at location z" and formula Q(z)]

3.1.5
maximum power (energy) density
E (z) [H (z)]
max max

maximum of the spatial power (energy) density distribution function E (x, y, z) [H (x, y, z)] at location z

3.1.6
location of the maximum
(x , y , z)
max max
location of E (z) or H (z) in the xy plane at location z
max max

Note 1 to entry: (x , y , z) cannot be uniquely defined when measuring with detectors having a high spatial

max max
resolution and a relatively small dynamic range.
2 © ISO 2018 – All rights reserved
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SIST EN ISO 13694:2019
ISO 13694:2018(E)
3.1.7
clip-level power (energy) density
E (z) [H (z)]
ηCL ηCL
fraction η of the maximum power (energy) density (3.1.5) at location z
Ez =ηEz
() ()
ηCL max
Hz =ηHz
() ()
ηCL max
0 ≤ η < 1

Note 1 to entry: When no confusion is possible, the explicit dependence on z is dropped in the text description

using some quantities, but not in the definitions or in the Formulae involving the quantities.

3.2 Characterizing parameters
3.2.1
clip-level power (energy)
P (z) [Q (z)]
η η

integral of the power (energy) distribution at location z, evaluated by summing only over locations (x,y)

for which E (x, y, z) > E (z) [H (x, y, z) > H (z)]
ηCL ηCL
3.2.2
fractional power (energy)
f (z)

fraction of the clip-level power (energy) (3.2.1) for a given η to the total power (energy) in the distribution

at location z
fz = for cw-beams
fz = for pulsed beams
0 ≤ f (z) ≤ 1
3.2.3
beam centroid
xz , yz
() ()

coordinates of the first-order moments of a power(energy) distribution of a beam at location z

xE⋅ xy,,zx⋅ddy
xz =
Ex,,yz ⋅ddxy
yE⋅ xy,,zx⋅ddy
yz =
Ex,,yz ⋅ddxy

where the integration shall be performed over an area such that at least 99 % of the beam power

(energy) is captured

Note 1 to entry: The power density E is replaced by the energy density H for pulsed lasers.

Note 2 to entry: For a more detailed definition, see ISO 11145 and ISO 11146-1.
© ISO 2018 – All rights reserved 3
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SIST EN ISO 13694:2019
ISO 13694:2018(E)
3.2.4
beam widths
d (z), d (z)
σx σy

widths d (z) and d (z) of the beam in the respective x and y directions at z, equal to four times the

σx σy

square root of the second moments of the power (energy) density distribution about the centroid

Note 1 to entry: For a more detailed definition, see ISO 11145 and ISO 11146-1.

Note 2 to entry: The provisions of ISO 11146-1 apply to definitions and measurements of:

a) second moment beam widths d and d ;
σx σy

b) beam widths d and d in terms of the smallest centred slit width that transmits u % of the total power

x,u y,u
(energy) density (usually u = 86,5);

c) scanning narrow slit measurements of beam widths d and d in terms of the separation between positions

x,s y,s

where the transmitted power density (3.1.1.1) is reduced to 0,135 E , where E is the peak power (energy)

p p
density;

d) measurements of beam widths d and d in terms of the separation between 0,84 P and 0,16 P obscuration

x,k y,k

positions of a movable knife-edge, where P is the maximum, unobstructed power (energy) recorded by the

large area detector behind the knife-edge plane;

e) correlation factors which relate these different definitions and methods for measuring beam widths.

3.2.5
beam ellipticity
ε (z)

parameter for quantifying the circularity or squareness of a power (energy) 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 d ≥ d

σx σy

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: Technically identical to ISO 11146-1 and ISO 11145.

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

σ y

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

in ISO 11146-1 and ISO 11145.
3.2.6
beam cross-sectional area
A (z)

area of a beam with circular

cross-section
 π 2
Ad= ⋅ ()z
σσ 
 
or elliptical cross-section
 
Ad= ⋅ zd⋅ z
() ()
σσxyσ
 
 
4 © ISO 2018 – All rights reserved
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SIST EN ISO 13694:2019
ISO 13694:2018(E)

Note 1 to entry: For clarity, the term “beam cross-sectional area” is always used in combination with the symbol

and its appropriate subscript: A or A .
u σ
[SOURCE: ISO 11145:2018, 3.6.2]
3.2.7
clip-level irradiation area

irradiation area at location z for which the power (energy) density exceeds the clip-level power (energy)

density (3.1.7)

Note 1 to entry: To allow for distributions of all forms, for example hollow “donut” types, the clip-level irradiation

area is not defined in terms of the beam widths (3.2.4) d or d .
σx σy
Note 2 to entry: See clip-level power (energy) density (3.1.7).
3.2.8
clip-level average power (energy) density
E (z), [H (z)]
ηave ηave

spatially averaged power (energy) density of the distribution at location z, defined as the weighted mean

Ez()= for cw-beams
ηave
Hz = for pulsed beams
ηave
Note 1 to entry: E (z) and E (z) (see 3.1.7) refer to different parameters.
ηave ηCL
3.2.9
flatness factor
F (z)

ratio of the clip-level average power (energy) density to the maximum power (energy) density of the

distribution at location z
ηave
Fz = for cw-beams
max
ηave
Fz = for pulsed beams
max
0 < F ≤ 1

Note 1 to entry: For a power (energy) density distribution having a perfectly flat top F = 1.

3.2.10
beam uniformity
U (z)

normalized root mean square (rms) deviation of power (energy) density distribution from its clip-level

average value at location z
 
Uz = Ex,,yz −Ez ddxy for cw-beams
() () ()
η ηave
 
ηave Az
 
Uz = Hx,,yz −Hz ddxy for pulsed beams
() () ()
η ηave
∫∫ 
ηave ()
© ISO 2018 – All rights reserved 5
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SIST EN ISO 13694:2019
ISO 13694:2018(E)

Note 1 to entry: U = 0 indicates a completely uniform distribution having a profile with a flat top and vertical

edges, U is expressed as either a fraction or a percentage.

Note 2 to entry: By using integration over the beam area between set clip-level limits, this definition allows for

arbitrarily shaped beam footprints to be quantified in terms of their uniformity. Hence uniformity measurements

can be made for different fractions of the total beam power (energy) without specifically defining a windowing

aperture or referring to the shape or size of the distribution. Thus using the formulae in 3.2.2 and 3.2.10,

statements such as: “Using a setting η = 0,3, 85 % of the beam power (energy) was found to have a uniformity of

±4,5 % r.m.s. from its mean value at z” can be made without reference to the distribution shape, size, etc.

3.2.11
plateau uniformity
U (z)
quantitative measure for the homogeneity of nearly flat-top profiles
FWHM
Uz = for cw-beams
max
FWHM
Uz = for pulsed beams
max

where ΔE [ΔH ] is the full-width at half-maximum (FWHM) of the peak near E [H ] of

FWHM FWHM max max

the power (energy) density histogram N(E ) [N(H )], i.e. the number of (x, y) locations at which a given

i i
power (energy) density E [H ] is recorded
i i

Note 1 to entry: 0< U (z) < 1; U (z) → 0 as distributions become more flat-topped.

p p
3.2.12
edge steepness
s (z)
η,ε
i i

normalized difference between clip-level irradiation areas (3.2.7) Az and Az with clip-level

() ()
η ε

power (energy) density (3.1.7) values above η E (z) [η H (z)] and above ε E (z) [ε H (z)]

max max max max
respectively
Az −Az
() ()
sz =
ηε,
01≤<ηε <
01 ηε,

Note 1 to entry: s (z) → 0 as the edges of the distribution become more vertical.

η,ε

Note 2 to entry: η is typically set to 10 %, ε to 90 % of the maximum power (energy) density.

Note 3 to entry: Parameters E , E , P , A , F , and U , are illustrated in Figure 1 for a uniform power density

max ηave η η η
distribution (3.1.1) in one dimension.
6 © ISO 2018 – All rights reserved
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SIST EN ISO 13694:2019
ISO 13694:2018(E)

Figure 1 — Illustration for a uniform power density distribution E(x) in one dimension

4 Coordinate system

The x, y, z Cartesian axes define the orthogonal space directions in the beam axes system. The x and

y axes are transverse to the beam and define the transverse plane. The beam propagates along the

z axis. The origin of the z axis is in a reference xy plane defined by the laser manufacturer, e.g. the front

of the laser enclosure. For elliptical beams, the principal axes of the distribution coincide with the x and

y axes, respectively. In cases for which the principal axes of the distribution are rotated with respect to

the laboratory coordinate system, the provisions of ISO 11146-1 describing
...

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