EN ISO 21254-2:2011

SLOVENSKI STANDARD
01-oktober-2011
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SIST EN ISO 11254-1:2000
SIST EN ISO 11254-2:2002
SIST EN ISO 11254-2:2002/AC:2003
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Lasers and laser-related equipment - Test methods for laser-induced damage threshold -
Part 2: Threshold determination (ISO 21254-2:2011)
Laser und Laseranlagen - Prüfverfahren für die laserinduzierte Zerstörschwelle - Teil 2:
Bestimmung der Zerstörschwelle (ISO 21254-2:2011)
Lasers et équipements associés aux lasers - Méthodes d'essai du seuil
d'endommagement provoqué par laser - Partie 2: Détermination du seuil (ISO 21254-
2:2011)
Ta slovenski standard je istoveten z: EN ISO 21254-2:2011
ICS:
31.260 Optoelektronika, laserska Optoelectronics. Laser
oprema equipment
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 21254-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
July 2011
ICS 31.260 Supersedes EN ISO 11254-1:2000, EN ISO 11254-2:2001
English Version
Lasers and laser-related equipment - Test methods for laser-
induced damage threshold - Part 2: Threshold determination
(ISO 21254-2:2011)
Lasers et équipements associés aux lasers - Méthodes Laser und Laseranlagen - Prüfverfahren für die
d'essai du seuil d'endommagement provoqué par laser -
laserinduzierte Zerstörschwelle - Teil 2: Bestimmung der
Partie 2: Détermination du seuil (ISO 21254-2:2011) Zerstörschwelle (ISO 21254-2:2011)
This European Standard was approved by CEN on 14 July 2011.

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, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2011 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 21254-2:2011: E
worldwide for CEN national Members.

Contents Page
Foreword .3

Foreword
This document (EN ISO 21254-2:2011) 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 2012, and conflicting national standards shall be withdrawn at
the latest by January 2012.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 11254-1:2000, EN ISO 11254-2:2001.
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, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
Endorsement notice
The text of ISO 21254-2:2011 has been approved by CEN as a EN ISO 21254-2:2011 without any
modification.
INTERNATIONAL ISO
STANDARD 21254-2
First edition
2011-07-15
Lasers and laser-related equipment —
Test methods for laser-induced damage
threshold —
Part 2:
Threshold determination
Lasers et équipements associés aux lasers — Méthodes d'essai
du seuil d'endommagement provoqué par laser —
Partie 2: Détermination du seuil

Reference number
ISO 21254-2:2011(E)
©
ISO 2011
ISO 21254-2:2011(E)
©  ISO 2011
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
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Published in Switzerland
ii © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Test methods .1
4.1 General .1
4.2 1-on-1 test method .1
4.3 S-on-1 test method .3
5 Accuracy.7
6 Test report.7
6.1 General .7
6.2 1-on-1 test.8
6.3 S-on-1 test .8
Annex A (informative) Example of a measurement procedure (1-on-1 test).9
Annex B (informative) Example of a test report for a 1-on-1 test.15
Annex C (informative) Example of a measurement procedure (S-on-1 test) .20
Annex D (informative) Example of a test report for an S-on-1 test.24
Annex E (informative) Extrapolation method for S-on-1 tests .31
Annex F (informative) Conversion of damage data into defect densities.33
Bibliography.36

ISO 21254-2:2011(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.
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.
ISO 21254-2 was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 9,
Electro-optical systems.
This first edition of ISO 21254-2:2011, together with ISO 21254-1:2011, cancels and replaces
ISO 11254-1:2000 and ISO 11254-2:2001, which have been technically revised.
ISO 21254 consists of the following parts, under the general title Lasers and laser-related equipment — Test
methods for laser-induced damage threshold:
⎯ Part 1: Definitions and general principles
⎯ Part 2 : Threshold determination
⎯ Part 3: Assurance of laser power (energy) handling capabilities
⎯ Part 4: Inspection, detection and measurement [Technical Report]
iv © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
Introduction
This part of ISO 21254 specifies test methods for determining single-shot and multiple-shot laser-induced
damage thresholds (LIDTs) of optical components, both coated and uncoated. The aim is to provide methods
which will enable measurement results to be obtained which are consistent and can be rapidly and accurately
compared between different test laboratories.
In the single-shot test, which is referred to as the 1-on-1 test in this International Standard, each unexposed
site on the sample surface is subjected to only one pulse of laser radiation. Repeated laser radiation pulses
can damage optical components, or otherwise cause them to deteriorate, at irradiation levels below those
measured for single-shot damage. Besides reversible effects induced by thermal heating and distortion,
irreversible damage due to ageing, microdamage and the generation or migration of defects is observed. The
degradation of the optical quality is a function of the laser operating parameters and the optical system in
which the component is located. The multiple-shot test, referred to as the S-on-1 test, is based on a protocol
that uses a series of pulses with constant energy density at each unexposed test site.
In addition to an evaluation technique based on the survival curve for 1-on-1 tests, this part of ISO 21254 also
describes two methods for the reduction of raw data obtained from S-on-1 damage tests: one using the
characteristic damage curve and the other an extrapolation technique. The characteristic damage curve
method calls for S-on-1 testing at a large number of sites on the optical surface of the specimen and
generation of a set of three graphs indicating energy density values corresponding to probabilities of damage
of 10 %, 50 % and 90 % for a selected number of pulses. The characteristic damage curve represents the
results of a complete and extended laser-induced damage test, and it is recommended for basic investigations
in newly developed or critical laser optics. The second method of S-on-1 testing, the extrapolation method,
uses a considerably smaller number of test sites. This method generates a distribution diagram of the
damaged and undamaged regions for the behaviour of the damage threshold as a function of the number of
pulses per site. This diagram is of limited reliability but may be employed for the quality control of optical laser
components which have already been qualified by a complete damage test or as part of the preparation for
extended damage testing.
Realistic laser damage tests suitable for industrial applications require a large number of pulses (10 to
10 pulses) and hence involve a disproportionate experimental cost. This part of ISO 21254 therefore also
outlines a procedure for obtaining the S-on-1 threshold by extrapolation of the characteristic damage curve in
order to estimate the real lifetime of an optical component.
NOTE It should be realized that the laser-induced damage threshold of an optical component which is subjected to
repeated pulses of radiation can be affected by a variety of different degradation mechanisms, including contamination,
thermal heating, migration or generation of internal defects, and structural changes. These mechanisms are influenced by
the laser operating parameters, the environment and the component mounting conditions. For these reasons, it is
necessary to record all the parameters and to bear in mind that the damage behaviour might differ in tests carried out in
different operating conditions.
The test procedures described in this part of ISO 21254 are applicable to all combinations of laser
wavelengths and pulse lengths. However, comparison of laser damage threshold data can be misleading
unless the measurements have been carried out at the same wavelength, using the same pulse length and
beam diameter. Definitions and the general principles of laser-induced damage threshold measurements are
given in ISO 21254-1.
INTERNATIONAL STANDARD ISO 21254-2:2011(E)

Lasers and laser-related equipment — Test methods
for laser-induced damage threshold —
Part 2:
Threshold determination
WARNING — The extrapolation of damage data can lead to an overestimation of the laser-induced
damage threshold. In the case of toxic materials (e.g. ZnSe, GaAs, CdTe, ThF , chalcogenides, Be,
Cr, Ni), this can lead to serious health hazards. See ISO 21254-1:2011, Annex A, for further comments.
1 Scope
This part of ISO 21254 describes 1-on-1 and S-on-1 tests for the determination of the laser-induced damage
threshold of optical laser components. It is applicable to all types of laser and all operating conditions.
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 photonics — Lasers and laser-related equipment — Vocabulary and symbols
ISO 21254-1:2011, Lasers and laser-related equipment — Test methods for laser-induced damage
threshold — Part 1: Definitions and general principles
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11145 and ISO 21254-1 apply.
4 Test methods
4.1 General
The general principles of laser-induced damage threshold measurements, and the apparatus and sampling
techniques used, are described in ISO 21254-1.
4.2 1-on-1 test method
4.2.1 General
In the 1-on-1 test, each unexposed site on the surface of the sample is exposed to a single laser pulse with
defined beam parameters. From the experimental data, a plot depicting the probability of damage as a
function of the energy density or power density is constructed.
ISO 21254-2:2011(E)
4.2.2 Test parameters
The test equipment shall be characterized by the parameters described in ISO 21254-1:2011, 6.2.6.5.
4.2.3 Procedure
Test sites are positioned in the beam and irradiated by single shots of laser radiation with different energy
densities or power densities. Expose a minimum of ten sites to one preselected pulse energy (or beam power)
and record, for each site, the actual pulse energy (or beam power) measured by the beam diagnostic unit as
well as the state of damage after irradiation (damage or no damage). Repeat this sequence for other pulse
energies or beam powers. The range of pulse energies or beam powers employed shall be sufficiently broad
to include low values which result in no damage at any site and sufficiently high values which induce damage
at each site tested.
4.2.4 Evaluation of measurements
Damage threshold data are obtained by the damage-probability method. To construct a plot of the probability
of damage versus the quantity in terms of which the laser-induced damage threshold is to be expressed, the
probability of damage is determined for each energy-density or power-density increment by calculating the
ratio of the number of damaged sites to the total number of sites tested. Linear extrapolation of the damage-
probability data to zero damage probability yields the threshold value. An example is shown in Figure 1.

Key
X energy, in millijoules
Y damage probability
NOTE The test conditions were as follows: d = 1,44 mm, λ = 10,6 µm, τ = 100 ns, tail 3,5 µs (TEA CO laser),
86,5 H 2
specimens: KBr windows, 50 items, diameter 40 mm.
Figure 1 — Graph for the determination of the damage threshold from experimental data

2 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
In the case of a laser system with a high pulse-to-pulse energy variation, it is permissible to expose the
specimen to arbitrary pulse energies and to sort the data with respect to appropriate energy intervals after the
test.
NOTE 1 Examples of an efficient measurement procedure giving maximum accuracy for a given number of sites are
presented in Annex A and Annex C for the 1-on-1 and the S-on-1 test, respectively.
NOTE 2 The diameter of the test beam at the specimen position can influence the measurement result. Therefore, the
beam diameter has to be kept constant throughout the entire measurement procedure.
4.3 S-on-1 test method
4.3.1 General
To determine the S-on-1 damage threshold, extensions of the set-up and procedure for 1-on-1 test damage
threshold measurement are necessary. However, a measurement facility for S-on-1 tests can be used for
1-on-1 measurements if the online damage-detection system is combined with a Nomarski-type differential
interference contrast microscope. It is recommended that the online damage-detection system have a facility
for cutting off subsequent pulses and for stopping the pulse counter.
4.3.2 Test parameters
The test equipment shall be characterized by the parameters described in ISO 21254-1:2011, 6.2.6.5, and the
following additional parameters:
a) number of pulses per site S;
b) total number of sites per test N .
ts
NOTE For the S-on-1 test, the parameters given in ISO 21254-1:2011, 6.2.6.5 d) to g), refer to the properties of the
typical pulse defined in ISO 21254-1:2011, 6.2.6.4.
4.3.3 Procedure
An unexposed test site is positioned in the beam and irradiated by a series of S pulses, the pulse typical of the
series having an energy Q . If damage is observed by the online damage detection system before the series
tp
of S pulses is completed, stop the irradiation of the site and record the minimum number of pulses N .
min
Repeat this procedure for different energies of the typical pulse. The number of pulses S shall be constant for
the entire test procedure, and it shall be selected such that the S-on-1 test records the specific laser-induced
damage behaviour of the specimen.
4.3.4 Evaluation of measurements
4.3.4.1 General
After inspecting the specimen, the result of the S-on-1 test described above is a file of data points of the type
(Q , N ), where N u S in the case of damage,
tp min min
(Q , S) when no damage is detected
tp
The evaluation of the data obtained (see Figure 2) may be performed using the characteristic damage curve
(see 4.3.4.2) or the extrapolation method (see 4.3.4.3). The method using the characteristic damage curve
allows accurate determination of the laser-induced damage threshold. This accurate technique should be
used for fundamental investigations and for the testing of prototype components. The extrapolation method,
on the other hand, is a practical technique for estimating the S-on-1 threshold for a large number of pulses.
ISO 21254-2:2011(E)
4.3.4.2 Characteristic damage curve
The procedure for determining the S-on-1 damage threshold (see 4.3.3) is carried out and the resulting file of
data points is recorded. For the evaluation to have sufficient significance, a minimum number N of sites
ms
shall be tested for each energy value Q of the typical pulse. This minimum number of sites N can be
tp ms
approximated by the following relationship:
N = 5 × integral value of (1 + log S) (1)
ms 10
The range of typical-pulse energies Q employed shall be sufficiently broad to include points corresponding to
tp
zero probability of damage as well as points corresponding to 100 % probability of damage.
Damage-probability values for a defined number N of pulses and a specified energy Q are calculated on the
basis of the following data-reduction technique.
The energy scale is divided into a series of intervals [Q − ∆Q, Q + ∆Q) covering the energy range accessible
with the experimental set-up. For the calculation of the damage probability for a certain energy Q and for a
selected number N of pulses, data points with Q = [Q − ∆Q, Q + ∆Q) are selected from the file of data points.
tp
Data points with N u N correspond to sites which are damaged, whereas data points with N > N or S W N
min min
correspond to sites not damaged in the energy interval considered. The damage probability for the energy Q is
calculated as the ratio of the number of data points corresponding to damaged sites to the total number of
data points considered in the evaluation.
NOTE 1 The value of ∆Q has to be chosen such that a significant fraction of data points is available for a distinct interval
[Q − ∆Q, Q + ∆Q). The value of ∆Q is kept constant during the evaluation procedure, and it determines the statistical error
of the threshold values. An example of an efficient measurement procedure with suitably selected parameters is given in
Annex C.
This procedure is repeated for other values of the energy Q to generate a data set of damage-probability
values for the selected number N of pulses. The resulting data set represents discrete points on a damage-
probability curve which is plotted versus the energy of the typical pulse. From this curve, the energy values
Q , Q and Q for the corresponding damage-probability values of 10 %, 50 % and 90 % are deduced by
10 50 90
extrapolation.
Linear extrapolation of the damage-probability curve to zero damage probability yields the threshold energy
(see 4.2.4) which shall be converted into units of threshold energy density H or threshold power density E .
th th
Linear extrapolation using the two data points next to the targeted damage probability is sufficient. If a large
number of data points are available, more sophisticated extrapolation methods are permitted. The
extrapolation procedure used shall be stated in the test report.
In Figure 2, data points corresponding to damaged spots are represented by and those corresponding to
undamaged spots are represented by o. The evaluation procedure used for the damage-probability method is
illustrated by the interval [Q − ∆Q, Q + ∆Q) marked on the graph. More than one point can occur for a specific
data pair (Q , S) or (Q , N ) during the test. The number of points for a specific data pair may be indicated
tp tp min
on the graph.
Figure 2 is an illustrative representation of a typical data set obtained in an S-on-1 laser-induced damage
threshold (LIDT) test. Therefore, the pulse energy scale is given in arbitrary units, and no numbers are given
to indicate the presence of identical data points.

4 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
Key
X number of pulses
Y pulse energy, in millijoules
1 undamaged
2 damaged
Figure 2 — Data points resulting from damage testing
To generate the characteristic damage curve, the algorithm described above is repeated for selected numbers
N of pulses to determine the corresponding energy values Q , Q , and Q . These values are converted into
10 50 90
the units in which the damage threshold is expressed and plotted versus the number of pulses. The numbers
of pulses shall be selected in a way that at least five data points are located in the significant region of the
characteristic damage curve. Log-log coordinates are recommended for this plot to make it possible to carry
out a linear extrapolation of the characteristic damage curve for large numbers of pulses (see Figure 3).
NOTE 2 Log-log coordinates might not be appropriate for an extrapolation of the characteristic damage curve for
extremely large numbers of pulses. In many cases, the characteristic damage curve converges to a finite energy density,
and the shape of this convergence might give information on the laser-induced ageing mechanisms involved (see
Annex E).
4.3.4.3 Extrapolation method
A distribution diagram of damaged and undamaged regions can be generated on the basis of a test with a
reduced number of data points. In the extrapolation method, S-on-1 test procedures are performed covering a
range of numbers of pulses per test site that is appropriate for determining, by extrapolation, the S-on-1
damage threshold for a defined large number of pulses. A slightly modified test procedure (see 4.3.3) is
performed for a selected set of data points. In this method, the number of pulses S is varied during the test
procedure, and it shall be selected such that a significant number of sites are irradiated with the selected
number of pulses S. The irradiation of an individual test site is stopped after the defined number of pulses has
been reached or damage has been detected. The result of this irradiation protocol is a set of data points (Q ,
tp
S, state of damage) represented by the energy of the typical pulse, the selected number of pulses, and the
state of damage, respectively. For specimens which show self-quenching damage mechanisms, the
extrapolation method can also be used in damage-testing facilities without an online damage detection system.
In this case, each site is subjected to the selected number of pulses independently of the state of damage.
ISO 21254-2:2011(E)
Key
X number of pulses
Y energy density, in joules per square centimetre
1 90 % LIDT
2 50 % LIDT
3 10 % LIDT
NOTE The test conditions were as follows: τ = 130 fs, d = 87 µm, λ = 780 nm, f = 1 kHz, specimen: HR mirror
eff T,eff p
(Ta O /SiO ) for 780 nm.
2 5 2
Figure 3 — Characteristic damage curve
For each data point, the energy value Q is converted into the unit of energy density or power density and
tp
plotted as a graph presenting this value versus the number of pulses. By separating the data points with
respect to the state of damage, the damaged and undamaged regions are indicated by the graph. This
distribution diagram (see Figure 4) makes it possible to give an approximate estimation of the threshold
energy density for large numbers of pulses.
NOTE Compared to the method using the characteristic damage curve, the extrapolation method is based on a
considerably smaller number of S-on-1 test procedures, and it can be performed on one specimen. Although the reliability
of the extrapolation method is limited, it might be sufficient for quality control of a production process already certified by a
complete damage-probability test or as part of the preparation for extended damage testing. The distribution diagram
resulting from the extrapolation method can be interpreted as a rough estimation of the characteristic damage curve (see
Figure 4), and it can also be deduced from the data file of the characteristic damage curve.
A particular data point (Q , S) with no damage can be considered to be an indication that no damage is likely
tp x
to occur for lower pulse numbers S for the energy value Q . As a consequence, symbols indicating no
tp,x
damage can be plotted in the distribution diagram for all other selected values of S which are lower than the
pulse number S . A particular data point (Q , N ) with damage can be considered to be an indication that
x tp min x
6 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
damage is likely to occur for all higher pulse numbers S for the energy value Q . As a consequence, symbols
tp,x
indicating damage can be plotted in the distribution diagram for all other selected values of S which are higher
than the pulse number N . Technical considerations or the statistical damage behaviour of the specimen
min,x
might restrict the lowest number of N which is detectable in a measurement facility. As indicated in Figure 4,
min
a separation line can be drawn to indicate the energy/pulse regime with no damage of the specimen.

Key
X number of pulses
Y energy density, in joules per square centimetre
1 undamaged sites
2 damaged sites
NOTE The test conditions were as follows: τ = 130 fs, d = 87 µm, λ = 780 nm, f = 1 kHz, specimen: HR mirror
eff T,eff p
(TiO /SiO ) for 780 nm.
2 2
Figure 4 — Distribution diagram showing damaged and undamaged regions
5 Accuracy
Prepare the calibration error budget outlined in ISO 21254-1 to determine the overall accuracy of the
measurement facility. Variations in the pulse repetition rate, total energy or beam power, spatial profile and
temporal profile shall be included in the error budget.
6 Test report
6.1 General
For the purpose of documenting and presenting the measurement data, the test report shall include the
information specified in ISO 21254-1:2011, Clause 8, items a) to c), and the results for the type of test which
was performed.
ISO 21254-2:2011(E)
6.2 1-on-1 test
Information on the test result:
a) a Nomarski micrograph of a typical damaged test site, choosing a pulse energy or beam power in the
damage-probability range between 20 % and 80 %;
b) a graph of the type shown in Figure 1;
c) the result of the test, given as H or E or F ;
th th
th
d) the total number of sites used for the test, N .
ts
It is recommended that a test report containing the test specifications and the test results be written and
supplied to the customer. An example of such a test report is given in Annex B.
6.3 S-on-1 test
Information on the test result:
a) at least one Nomarski micrograph of a typical damaged test site, choosing a pulse energy in the
damage-probability range between 20 % and 80 % for each number of pulses per site;
b) a graph of the kind shown in Figure 3 with data points joined by lines for S-on-1 damage-probability data
or a graph of the kind shown in Figure 4.
In the event of changes in the damage mechanisms with the number of pulses, include a brief statement on
the damage behaviour observed.
If possible, the supplier or the laboratory shall supply to the customer a test report containing the test
specifications and the test results. An example of such a test report is given in Annex D.
8 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
Annex A
(informative)
Example of a measurement procedure (1-on-1 test)
A.1 General
This annex describes an example of a measurement procedure for a 1-on-1 test. The basic structure of the
procedure consists of three steps.
In the first (initialization) step, the fundamental parameters of the test are calculated or defined. The
initialization may also include a binary search routine for an estimation of the actual damage threshold and for
a determination of the energy density intervals for testing. In the initialization procedure, the fundamental test
parameters are specified on the basis of the intended application and information available from former tests
on specimens of similar design and materials.
In the second step, the specimen is interrogated and the data collected.
In the final step, the data collected are analysed and an estimate of the damage threshold and its uncertainty
are calculated.
A.2 Initialization of the measurement procedure
A.2.1 Total number of test sites, N
ts
From the area A of the specimen available for the damage test, the beam diameter d and the separation
opt T,eff
of the test sites in terms of the laser beam diameter d , the total number N of test sites can be determined.
sep ts
If a rectangular array of test sites is assumed, the total number of sites is given by:
4A
opt
N = (A.1)
ts
()dd
sep T,eff
In the case of an arrangement of the test sites in a hexagonal close-packed (HCP) structure, a factor of 2/ 3
has to be introduced in Equation (A.1):
8A
opt
N = (A.2)
ts
3(dd )
sep T,eff
In this HCP arrangement, all next-neighbour test sites are d ⋅d apart. As minimum conditions for the
sep T,eff
damage frequency method, the value of N should exceed 75 and d should range between 1,25 and 5 for a
ts sep
beam with a Gaussian spatial distribution.
A.2.2 Number of fluence steps, n , probability resolution, P , number of damage sites,
steps res
n
sites
Figure A.1 is used to determine the values of the probability resolution, P , and the number of sites to be
res
damaged per fluence level, n , for a given value of N . For a given value of N , the range of possible
sites ts ts
values of P and n can be seen by following the contour for the value of N from left to right. For a
res sites ts
sufficiently large value of N , there is a large number of possible values for P and n , allowing great
ts res sites
flexibility in the design of the test. For smaller values of N , the choice of design is more limited.
ts
ISO 21254-2:2011(E)
If there is a history or suspicion of a tail of low probability, then the tester should opt for the smallest
acceptable value of P . This will ensure, to the greatest extent possible, that a low-probability tail of this kind
res
is seen by the interrogation protocol. If there is no history of, or concern over, a low-probability tail, then the
preferred choice would be for n to have the largest possible value. The choice of a large value for n
sites sites
leads to the most accurate determination of the damage probability allowed in a particular area available for
the test [see Equations (A.5) and (A.6)].
After the selection of P , Figure A.2 is used to determine the number of fluence levels, or fluence steps, used
res
in the test, n . The value of n is read directly off the curve in Figure A.2.
steps steps
EXAMPLE Selection of n and P
sites res
Consider a test with 200 sites. The n contour for 200 allows values of n from 1 to 5 and corresponding values of
sites sites
P from approximately 0,06 to 0,15. If there is concern over a low-probability tail, then the lower values of P , which
res res
allow more fluence levels to be interrogated, are recommended. If this concern is not present, then a higher value for P
res
is the preferred choice, because it will give higher accuracy in measuring of the damage probability.

Figure A.1 — Contour plot of N
ts
10 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
Figure A.2 — Plot of P versus n
res steps
A.2.3 Top and bottom energy density levels, H and H
top bottom
The top and bottom energy density levels, H and H , can be estimated from historical data available
top bottom
from previous damage tests on comparable specimens. The value of H corresponds to an energy density
top
value with approximately 60 % damage probability. The value of H is near, but above, the estimated
bottom
threshold. If historical data are not available, the values of H and H can be determined by a binary
top bottom
search routine, which is performed on the actual test area. A minimum number of 15 test sites should be used
for this binary search routine. For large test areas with N >150, it is permissible to employ one-tenth of the
ts
total number of sites, N , for this initial binary search.
ts
A.2.4 Resolution of energy density, δH
The energy density resolution is defined by the equation:
HH−
top bottom
δ H = (A.3)
n
steps
where n has been determined as described in A.2.2.
steps
A.3 Test routine
The algorithm for the irradiation sequence of the specimen is illustrated in Figure A.3. The initial energy
density level H is H . After interrogation of the first site, the state of damage is detected and recorded. The
1 top
d nd
variables n and n are counting variables for the number of sites damaged and not damaged, respectively,
i i
at the selected energy density level H . Irradiation of the sample at the ith level continues until at least 12 sites
i
d nd
have been interrogated and nn= or nP= 3/ without observation of a single damage site. When
i sites i res
the irradiation is complete at the ith level and n sites have been damaged, the energy density level is
sites
ISO 21254-2:2011(E)
decreased by δH. If 3/P shots at H are taken without observation of a single damage site, the energy
res
i
density level for the next value of i is increased by 0,5δH and by δH for each level thereafter. This procedure is
repeated until the whole test area has been used.

Figure A.3 — Flow chart for test
12 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
A.4 Evaluation of the test results
The final step of the algorithm consists of an evaluation of the data stored during the test routine, as discussed
below. For the determination of the damage threshold and the uncertainty in the result of the test, linear
extrapolation of the measured damage probabilities is performed. For each energy density level H, the
i
observed damage probability P is calculated from the equation:
i
d
n
i
P = (A.4)
i
dnd
nn+
ii
dnd d
where nn+ is the total number of sites exposed to achieve n damaged sites.
ii i
The uncertainty for each point i in the data set is estimated using Equation (A.5) or Equation A.6):
nd
n
2 d
i
σε=+ when 0n > (A.5)
i f
dd nd
nn +n
ii()i
2 d
σε= when 0n = (A.6)
i f
where ε is the fractional uncertainty in the measured energy density.
f
The slope m and intercept b of the weighted linear fit to the measured damage-probability curve are calculated
using Equations (A.7) and (A.8) and Equation (A.9), respectively:
⎡⎤
⎛⎞⎛ ⎞⎛⎞⎛⎞
11 PH H P
ii i i
⎢⎥⎜⎟⎜ ⎟⎜⎟⎜⎟
m=− (A.7)
∑∑ ∑∑
22 2 2
⎜⎟⎜ ⎟⎜⎟⎜⎟
∆
⎢⎥
σσ σ σ
iiii iii i
⎣⎦⎝⎠⎝ ⎠⎝⎠⎝⎠
where
⎛⎞⎛ ⎞⎛⎞
HH
ii
∆=−⎜⎟⎜ ⎟⎜⎟ (A.8)
∑∑ ∑
22 2
⎜⎟⎜ ⎟⎜⎟
σσ σ
⎝⎠iiii⎝ ⎠⎝⎠ii
and
⎡⎤
⎛ ⎞⎛⎞⎛⎞⎛ ⎞
1 HP H PH
ii i ii
⎢⎥⎜ ⎟⎜⎟⎜⎟⎜ ⎟
b=− (A.9)
∑∑ ∑ ∑
22 2 2
⎜ ⎟⎜⎟⎜⎟⎜ ⎟
∆
⎢⎥
σσ σ σ
⎝iiii⎠⎝⎠⎝⎠ii⎝ii⎠
⎣⎦
The damage threshold is determined by the expression:
b
H =− (A.10)
th
m
The calculated threshold should be both positive and less than or equal to the lowest observed energy density
causing damage. If the value of H is not positive, the reported threshold should be given as the lowest
th
observed energy density causing damage. Further, if any additional test sites are available, a binary search
for the threshold should be conducted, with highest energy density in this search being the lowest energy
density corresponding to damage observed when making the measurement.

ISO 21254-2:2011(E)
The uncertainty in the threshold is determined using Equations (A.11) and (A.12) and Equation (A.13):
22 22
σσ=+bmσ (A.11)
th mb
m
where
1 H
i
σ = (A.12)
b
∑
∆
σ
i
and
σ = (A.13)
m ∑
∆
σ
i
The lower limit of the estimated threshold H − σ should be positive and less than or equal to the lowest
th th
observed energy density causing damage. If either of these conditions is not fulfilled for the lower limit, then it
should be replaced by 0.
14 © ISO 2011 – All rights reserved

ISO 21254-2:2011(E)
Annex B
(informative)
Example of a test report for a 1-on-1 test
Measurement of laser-induced damage threshold by a 1-on-1 test in accordance
with ISO 21254-2
Test institute
Name of institute:
Tester/date: dd/mm/yyyy
Specimen
Type of specimen: Original part, HR at 1 064 nm on BK7 glass
Manufacturer:
Storage, cleaning: No special requirements
Specification: Highly reflective mirror, R > 99,5 % at 1 064 nm, 0 rad angle of incidence, standard
coating for normal use
Part identification number:
Date of production: Coating run #1187 of dd/mm/yyyy
Test specification
Pulsed Nd:YAG laser consisting of an electro-optically Q-switched oscillator and an optically isolated amplifier
stage. Single transversal and longitudinal mode operation. Focusing by a biconvex lens with a beam
f-number of 300.
Laser parameters
Wavelength: 1 064 nm
Angle of incidence: 0 rad
Polarization state: linear
Minimum time between shots: 5 s
Effective beam diameter in target plane: 0,34 mm
Pulse duration: 12 ns
Effective pulse duration: 12,7 ns
Y
ISO 21254-2:2011(E)
Key
X time, in nanoseconds
Y power, in arbitrary units
Figure B.1 — Temporal profile
Z
Key
X length scale, in micrometres
Y length scale, in micrometres
Z power, in arbitrary units
Figure B.2 — Spatial profile
16 © ISO 2011 – All rights reserved

X
---------------------- Pa
...