ISO 13142:2021

INTERNATIONAL ISO
STANDARD 13142
Second edition
2021-06
Optics and photonics — Lasers
and laser-related equipment —
Cavity ring-down method for high-
reflectance and high-transmittance
measurements
Optique et photonique — Lasers et équipement associé aux lasers —
Méthode d'alternance de la cavité pour les mesurages du facteur de
réflexion et du facteur de transmission
Reference number
ISO 13142:2021(E)
©
ISO 2021

---------------------- Page: 1 ----------------------
ISO 13142:2021(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved

---------------------- Page: 2 ----------------------
ISO 13142:2021(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols used and units of measure . 2
5 Test principles . 2
5.1 General . 2
5.2 Decay time of initial cavity and reflectance of cavity mirrors . 2
5.3 Decay time of test cavity and reflectance/transmittance of test sample . 4
5.4 High reflectance/transmittance measurement with an optical feedback CRD technique . 5
6 Preparation of test sample and measurement arrangement . 6
6.1 Test sample . 6
6.2 Laser source . 6
6.3 Ring-down cavity . 7
6.4 Detection unit . 7
6.5 Data acquisition and processing . 7
6.6 Environment . 8
7 Test procedure . 8
7.1 General . 8
7.2 Measurement of decay time of initial cavity . 8
7.3 Calculation of reflectance of cavity mirrors . 9
7.4 Measurement of decay time of test cavity . 9
7.5 Calculation of reflectance/transmittance of test sample . 9
7.6 Assessments of the measurement . 9
8 Main error factors .10
8.1 Influence of the instrumental response time on reflectance/transmittance
measurement .10
8.1.1 General.10
8.1.2 Multi-parameter fitting method .10
8.1.3 Data truncation method .11
8.2 Measurement error of the reflectance of cavity mirrors .11
8.3 Measurement error of the reflectance/transmittance of test sample .12
9 Test report .12
Annex A (informative) Reflectance/transmittance reliability check experiment .14
Annex B (informative) Test report .15
Bibliography .17
© ISO 2021 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO 13142:2021(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on 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 the following
URL: www .iso .org/ iso/ foreword .html.
This document was prepared by ISO/TC 172, Optics and photonics, Subcommittee SC 9, Lasers and
electro-optical systems.
This second edition cancels and replaces the first edition ISO 13142:2015, which has been technically
revised.
The main changes compared to the previous edition are as follows:
— addition of transmittance measurements into the document.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2021 – All rights reserved

---------------------- Page: 4 ----------------------
ISO 13142:2021(E)

Introduction
With the development of film-deposition technology, the performance of optical thin films, especially
the highly reflective (HR) and highly anti-reflective (AR) coatings which are widely used in large
high-power laser systems, interferometric gravitational-wave detectors, laser gyroscopes, and
cavity-enhanced and cavity ring-down spectroscopy applications, has been substantially improved
in recent years. Laser-based optical systems require some optical components with extremely high
reflectance or transmittance characteristic. It is necessary to be able to measure this reflectance
or transmittance characteristic precisely. Up to now, the ISO standardized testing methods for
reflectance/transmittance of optical laser components have the accuracy limit of approximately 0,01 %
(for measurement of absolute reflectance/transmittance), which are not appropriate for measuring
the reflectance /transmittance higher than 99,99 %, or in some cases measurement accuracy better
than 0,01 % is required. The measurement procedures in this document have been optimized to allow
the measurement of high reflectance or transmittance (larger than 99 %, theoretically up to 100 %)
of optical laser components using the cavity ring-down technique which provides reflectance or
transmittance data with high accuracy, high repeatability and reproducibility, and high reliability.
© ISO 2021 – All rights reserved v

---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 13142:2021(E)
Optics and photonics — Lasers and laser-related
equipment — Cavity ring-down method for high-
reflectance and high-transmittance measurements
1 Scope
This document specifies measurement procedures for the precise determination of the high reflectance
or high transmittance (>99 %) of optical laser components.
The methods given in this document are intended to be used for the testing and characterization of high
reflectance of both concave and plane mirrors or high transmittance of plane windows used in laser
systems and laser-based instruments. The reflectance of convex mirrors or transmittance of positive
or negative lenses can also be tested by taking into consideration the radius of curvature of the mirror
surface or the focal length of the lens. This document is complementary to ISO 15368 which specifies
the measurement procedures for the determination of reflectance and transmittance of optical
components with spectrophotometry. ISO 15368 is applicable to the measurements of reflectance and
transmittance in the range from 0 % to 100 % with a typical accuracy of ±0,3 %, and is therefore not
applicable to the precise measurements of reflectance and transmittance higher than 99,9 %.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 11145, Optics and photonics — Lasers and laser-related equipment — Vocabulary and symbols
ISO 14644-1, Cleanrooms and associated controlled environments — Part 1: Classification of air cleanliness
by particle concentration
ISO 80000-7, Quantities and units — Part 7: Light and radiation
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 11145 and ISO 80000-7 and
the following apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
reflectance
ratio of the reflected
radiant or luminous flux to the incident flux in the given conditions
3.2
transmittance
ratio of the transmitted
radiant or luminous flux to the incident flux in the given conditions
© ISO 2021 – All rights reserved 1

---------------------- Page: 6 ----------------------
ISO 13142:2021(E)

4 Symbols used and units of measure
Table 1 — Symbols used and units of measure
Symbol Term Unit
c speed of light in measurement environment m/s
c speed of light in vacuum m/s
0
h(t) impulse response of the ring-down cavity
h (t) Instrumental response function
0
L length of the initial cavity m
0
L length of the test cavity m
ΔL measurement error of the initial cavity length m
0
ΔL measurement error of the test cavity length m
n refractive index of air in measurement environment
R average reflectance of the concave cavity mirrors, equals square root of R ×R
1 2
R reflectance of the test sample
s
T transmittance of the test sample
s
R , R reflectance of two concave cavity mirrors
1 2
R reflectance of the planar cavity mirror
3
τ instrumental response time s
inst
t time s
u(t) negative-step function
the overall optical loss coefficient (absorption plus scattering) of the gases inside the cavity
−1
α m
at the laser wavelength
n refractive index of the transmissive test sample substrate
s
d thickness of the transmissive test sample or central thickness of a lens to be tested m
δ(t) delta function
θ angle of incidence of the test sample rad
ρ radius of curvature of concave surface of the cavity mirror m
τ decay time of the initial cavity s
0
τ decay time of the test cavity s
Δτ measurement error of the decay time of the initial cavity s
0
Δτ measurement error of the decay time of the test cavity s
5 Test principles
5.1 General
The conventional reflectance/transmittance measurement techniques (spectrophotometry and laser
ratiometry) are based on measuring the relative changes of light power reflected/transmitted by the
test sample. The measurement accuracy is limited by the power fluctuations of the light sources. The
cavity ring-down (CRD) technique, on the other hand, is based on the measurement of the decay rate
of laser power trapped in a ring-down cavity consisting of at least two highly reflective mirrors. It is
therefore totally immune to the power fluctuations of the light sources. The CRD technique can achieve
a measurement accuracy that far exceeds the limit set by the power fluctuations of the light sources.
5.2 Decay time of initial cavity and reflectance of cavity mirrors
When a laser beam is coupled into the ring-down cavity, it will gradually leak out of the cavity as a
small fraction of the light is transmitted through the cavity mirrors at each reflection. The temporal
2 © ISO 2021 – All rights reserved

---------------------- Page: 7 ----------------------
ISO 13142:2021(E)

behaviour of the cavity output signal immediately after the laser pulse (in the pulsed case, as shown
in Figure 1) or immediately after the laser power is switched off [in the continuous wave (cw) case, as
shown in Figure 2, or at the falling edge of a square-wave modulated power] can be expressed as an
exponentially decay function of time according to the following decay route given in Formula (1):
 
−t
It()∝I exp (1)
 
0
τ
 0 
Where I is the initial light intensity of the cavity output signal, τ can be expressed as given in
0 0
Formula (2):
L
0
τ = (2)
0
cLα −ln RR
()
01 2
With Formula (3):
c
0
c= (3)
n
For the case where at test laser wavelength the absorptance and scattering loss of gases inside the
ring-down cavity are negligible, the empty cavity ring-down time, τ , is only dependent upon the cavity
0
length and the reflectance of the cavity mirrors and Formula (2) reduces to Formula (4):
−L
0
τ = (4)
0
cRln R
12
By experimentally measuring the decay time, τ , the average reflectance of the cavity mirrors can be
0
calculated as Formula (5):
−L
 
0
RR==R exp (5)
 
12
cτ
 
0
Key
1 laser 6 input cavity mirror, concave high reflectance mirror
2 mode matching optics 7 output cavity mirror, concave high reflectance
mirror
3 initial cavity 8 polarizer
4 focusing lens 9 control and data-processing unit
5 photo-detector
Figure 1 — Schematic of optical arrangement for pulsed-CRD technique for high reflectance
measurement
© ISO 2021 – All rights reserved 3

---------------------- Page: 8 ----------------------
ISO 13142:2021(E)

Key
1 laser 6 input cavity mirror, concave high reflectance mirror
2 mode matching optics 7 output cavity mirror, concave high reflectance
mirror
3 initial cavity 8 polarizer
4 focusing lens 9 control and data-processing unit
5 photo-detector 10 optical switch
Figure 2 — Schematic of optical arrangement for cw-CRD technique for high reflectance
measurement
5.3 Decay time of test cavity and reflectance/transmittance of test sample
If a reflective/transmissive planar test sample or a lens is to be measured, a test ring-down cavity is
formed by inserting this reflective/transmissive test sample or lens into the initial cavity as shown in
Figure 3 (for reflective sample) or Figure 4 (for transmissive sample or lens). The incident angle of the
laser beam on the test sample follows the required incident angle of the test sample. In case of a lens,
the laser beam should propagate through the centre of the lens. In this case, the decay time of the test
cavity can be expressed as Formula (6):
−L
τ = (6)
cRln ⋅ RR
()
s1 2
for the reflective sample, and as Formula (7):
−+Ln −1 d
 () 
 s 
τ = (7)
cTln ⋅ RR
()
s1 2
for the transmissive sample or lens. Therefore, from Formulae (4) and (6), the reflectance, R , of the
s
reflective test sample can be calculated as Formula (8):
L
 
L
0
R =−exp (8)
 
s
cττc
 
0
And, combining Formulae (4) and (7), the transmittance, T , of the transmissive test sample or lens can
s
be calculated as Formula (9):
L Ln+−1 d
 () 
0 s
T =−exp (9)
 
s
cττc
 0 
4 © ISO 2021 – All rights reserved

---------------------- Page: 9 ----------------------
ISO 13142:2021(E)

Key
6 input cavity mirror, concave high reflectance mirror 11 reflective test sample
7 output cavity mirror, concave high reflectance mirror 12 angle of incidence of test sample
Figure 3 — Schematic of optical arrangement of test cavity for reflectance measurement
Key
6 input cavity mirror, concave high reflectance mirror 11 transmissive test sample or lens
7 output cavity mirror, concave high reflectance mirror 12 angle of incidence of test sample
Figure 4 — Schematic of optical arrangement of test cavity for transmittance measurement
NOTE Reflectances of HR mirrors with 0° angle of incidence (AOI) are normally measured at AOI of 3° to
8°, which is considered sufficient. However, if required, the reflectance measurement at 0° AOI is possible. This
can be done by pairing the test mirror and two cavity mirrors separately (that is, separate pairs of two cavity
mirrors, of one cavity mirror and the test mirror, and of another cavity mirror and the test mirror) to form three
stable straight cavities and measure three decay times for the three combinations, separately. From the three
measured decay times the reflectance of the test mirror, as well as the reflectances of the two cavity mirrors can
be determined via Formula (4), respectively.
5.4 High reflectance/transmittance measurement with an optical feedback CRD
technique
In the cw-CRD case, an optical feedback CRD (OF-CRD) scheme employing a semiconductor laser as the
light source (shown in Figure 5) can be used for the reflectance/transmittance measurement with an
improved signal-to-noise ratio in the CRD signals. In OF-CRD scheme, the initial cavity consists of three
cavity mirrors – two concave mirrors and one planar mirror. The beam from the semiconductor laser is
coaxially coupled into the ring-down cavity through the high-reflectance planar cavity mirror. The
optical feedback (back-reflection of the laser beam) from the ring-down cavity is retro-reflected into
the oscillator cavity of the semiconductor laser. Due to the self-mixing effect of the semiconductor laser,
the spectral linewidth of the laser is significantly reduced by the frequency selected optical feedback,
resulting in significant enhancement of the coupling efficiency of the laser power into the ring-down
cavity and therefore a large increase of the CRD amplitude. When the laser power is modulated by a
square wave signal, the cavity decay signal can be obtained at the falling edge of the square wave signal.
The test principle is the same as that presented in 5.2 and 5.3. The item RR in Formulae (2) to (7)
12
should be substituted by RR ⋅R in OF-CRD scheme.
12 3
The following two measurements are necessary to determine the reflectance/transmittance of the test
sample:
a) τ and L are measured with the initial cavity;
0 0
b) τ and L are measured with the test cavity.
© ISO 2021 – All rights reserved 5

---------------------- Page: 10 ----------------------
ISO 13142:2021(E)

For transmittance measurement, the thickness and refractive index of the test sample substate are
required. In case of a lens as the test sample, the thickness is the central thickness of the lens.
Key
1 semiconductor laser 8 polarizer
2 mode matching optics 9 control and data-processing unit
3 initial cavity with three mirrors 10 test sample
4 focusing lens 11 angle of incidence of the test sample
5 photo-detector 12 input cavity mirror, plane high reflectance mirror
6 cavity mirror, concave high reflectance mirror 13 test cavity with four mirrors, for reflectance
measurement
7 output cavity mirror, concave high reflectance mirror 14 test cavity for transmittance measurement
Figure 5 — Schematic of optical arrangement for OF-CRD technique for high reflectance/
transmittance measurements
6 Preparation of test sample and measurement arrangement
6.1 Test sample
Storage, cleaning and preparation of the test samples shall be carried out in accordance with the
instructions of the manufacturer on the test samples for normal use.
6.2 Laser source
Wavelength of the laser source, angle of incidence and state of polarization shall correspond to those
specified by the manufacturer for the use of the test sample. The state of polarization (p or s) of the
laser beam shall be selected by the polarizer. If the value ranges are accepted for these three quantities,
6 © ISO 2021 – All rights reserved

---------------------- Page: 11 ----------------------
ISO 13142:2021(E)

any combination of the wavelength, angle of incidence and state of polarization may be chosen within
these ranges.
Transverse mode matching between the laser beam mode and the mode of the ring-down cavity is
important and absolutely required in CRD techniques, especially in the pulsed-CRD systems. Mode
matching optics (i.e., beam shaping lenses) are helpful to improve the beam quality of the laser and,
further, to reduce the impact of mismatching on the CRD measurements. The impact of mode beating
effect on the CRD measurements can be avoided by applying a single-mode (TEM mode) excitation in
00
the cavity. In this case a single exponentially decay signal could be obtained.
In the pulsed-CRD system, the interval between two adjacent pulses shall be much larger than the
cavity decay time. It is recommended that the duration of the laser pulse be shorter than the cavity
round trip time (2L/c).
In the cw-CRD system, the laser power can be switched off by an optical switch. If a semiconductor
laser which is modulated by square wave is employed, the laser is switched off at the falling edge of
the square wave, so that the optical switch can be eliminated. The modulation frequency has to be
experimentally optimized to maximize the CRD amplitude at the falling edge of the square wave.
6.3 Ring-down cavity
Both initial and test cavities are optically stable cavities, which are defined by 02<<ρ L , 02<<ρ L .
0
The reflectance of a convex mirror can also be measured if the test cavity consisting of cavity mirrors
and the convex test mirror is optically stable. Similarly, the transmittance of a lens can also be measured
if the test cavity consisting of cavity mirrors and the test lens is optically stable. In this case, the focal
length of the test lens should be within a certain range which is determined by the stable cavity
condition for the test cavity.
It is recommended to use cavity mirrors with reflectance higher than 99,9 %. Cavity mirrors with
higher reflectance are preferable as the reflectance/transmittance measurement accuracy improves
with the increasing reflectance of the cavity mirrors. It is important to use cavity mirrors with higher
reflectance when measuring high reflectance of test mirrors. When the reflectance of the test mirror
is expected to be higher than 99,99 %, it is recommended to use cavity mirrors with reflectance
also higher than 99,99 %. In some cases a set of cavity mirrors with different reflectances should be
prepared for measurements of test mirrors with reflectances in a wide range. In all cases reflectance
(R , R and R ) of each cavity mirror shall not be lower than 99,5 %.
1 2 3
6.4 Detection unit
The detection unit consists of a focusing lens, a photo-detector, both appropriate for the laser
wavelength at which the measurement is to be performed, and an oscilloscope or a fast data-acquisition
card.
To ensure that the laser power exiting the output cavity mirror is fully collected, the numerical aperture
(NA) of the focusing lens and the active area of the photo-detector shall be optimized carefully. The
focusing lens shall be coated with an anti-reflective coating at the laser wavelength.
A fast-speed photo-detector with a rise time much shorter than the decay time of the cavity should
be used, so that the impact of the instrumental response time on the reflectance measurement can be
neglected. In the case of a photo-detector with a rise time comparable to the decay time of the cavity,
the influence of the rise time on the reflectance measurement has to be eliminated via data processing,
see 8.1.
6.5 Data acquisition and processing
A certain number of ring-down signals are acquired by an oscilloscope or a data-acquisition card and
averaged to determine the decay time of the initial cavity and of the test cavity. The number of acquired
ring-down measurements should be sufficient to provide an acceptable signal-to-noise ratio. The
number of ring-down signals shall be documented.
© ISO 2021 – All rights reserved 7

---------------------- Page: 12 ----------------------
ISO 13142:2021(E)

6.6 Environment
The environment of the testing place shall consist of dust-free filtered air with 40 % to 60 % relative
humidity. The residual dust shall be reduced in accordance with the clean-room Class 7 as specified
in ISO 14644-1. To minimize the impact of the environmental fluctuations on the test results, it is
recommended that the overall length of the test cavity is kept the same as that of the initial cavity.
7 Test procedure
7.1 General
One of the pulsed-CRD method, the cw-CRD method or the cw OF-CRD method shall be chosen to
measure the reflectance/transmittance. The decay time of both the initial cavity and the test
...