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 2021
© ISO 2021
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ii © ISO 2021 – All rights reserved

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
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
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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).
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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

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.
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
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
h(t) impulse response of the ring-down cavity
h (t) Instrumental response function
L length of the initial cavity m
L length of the test cavity m
ΔL measurement error of the initial cavity length m
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
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
τ decay time of the test cavity s
Δτ measurement error of the decay time of the initial cavity s
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

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)
 
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
τ = (2)
cLα −ln RR
()
01 2
With Formula (3):
c
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
length and the reflectance of the cavity mirrors and Formula (2) reduces to Formula (4):
−L
τ = (4)
cRln R
By experimentally measuring the decay time, τ , the average reflectance of the cavity mirrors can be
calculated as Formula (5):
−L
 
RR==R exp (5)
 
cτ
 
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
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
R =−exp (8)
 
s
cττc
 
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

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)
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.
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
...