ISO 6760-1:2025

International
Standard
ISO 6760-1
Second edition
Optics and photonics — Test
2025-07
method for temperature coefficient
of refractive index of optical
glasses —
Part 1:
Minimum deviation method
Optique et photonique — Méthode d'essai pour déterminer le
coefficient de température de l'indice de réfraction des verres
optiques —
Partie 1: Méthode de la déviation minimale
Reference number
© ISO 2025
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Principle . 2
5 Measuring apparatus . 4
5.1 Goniometer .4
5.2 Light source .4
5.3 Detector .4
5.4 Thermal chamber .4
6 Specimen prism . 5
7 Measurement . 5
7.1 Measurement of apex angle . .5
7.2 Measurement of the angle of minimum deviation .5
8 Calculation . 6
8.1 Absolute refractive index .6
8.2 Temperature coefficient of absolute refractive index .8
8.3 Temperature coefficient of relative refractive index .8
9 How to express the temperature coefficient of refractive index . 9
10 Test report . 9
Annex A (informative) Formula for calculating the refractive index of air .10
Annex B (informative) Calculation method for obtaining the relative refractive index of glass
at an arbitrary temperature, air pressure and relative humidity .13
Annex C (normative) Half prism method .15
Annex D (normative) Interpolation formula forΔn/ΔT .20
Annex E (informative) Derivation and verification of Δn /ΔT .21
rel
Bibliography .24

iii
Foreword
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This document was prepared by Technical Committee ISO/TC 172, Optics and photonics, Subcommittee SC 3,
Optical materials and components.
This second edition cancels and replaces the first edition (ISO 6760-1:2024), which has been technically
revised.
The main changes are as follows:
— The status of Annex C and Annex D was changed from “informative” to “normative”.
A list of all parts in the ISO 6760 series can be found on the ISO website.
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
Introduction
Optical glass is widely used in optical devices such as cameras, telescopes, and microscopes, and its refractive
index is measured by the minimum deviation method (see ISO 21395-1) and the V-block refractometer
[4]
method (see ISO 21395-2 ). Here, when designing an optical apparatus that requires high resolution, it
is necessary to consider the temperature change of the refractive index of the optical glass in the usage
environment, however up until now, there is no International Standard. In view of the above situation,
this document proposes a method for measuring the temperature coefficient of refractive index of optical
glass with high accuracy, aiming to help mutual understanding of measured value users and contribute to
efficiency and fairness.
v
International Standard ISO 6760-1:2025(en)
Optics and photonics — Test method for temperature
coefficient of refractive index of optical glasses —
Part 1:
Minimum deviation method
1 Scope
This document specifies the measurement method used for calculating the temperature coefficient of the
refractive index by measuring the refractive index, which changes with the temperature of the optical glass
using the minimum deviation method.
The intended temperature range for the specified measurement method is –40 °C to +80 °C.
The intended wavelength range for the specified measurement method is 365 nm to 1 014 nm.
-6 -1
The intended accuracy for the specified measurement method is 1 × 10 K .
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 21395-1:2020, Optics and photonics — Test method for refractive index of optical glasses — Part 1: Minimum
deviation method
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
temperature coefficient of refractive index
ratio of refractive index change to temperature change at a selected wavelength
[2]
Note 1 to entry: Similar to ISO 9802 .
3.2
temperature coefficient of absolute refractive index
Δn /ΔT
abs
ratio of refractive index change in vacuum to temperature change at a selected wavelength
[2]
[SOURCE: ISO 9802:2022 , 3.4.2.3, modified — The word "absolute" was moved in the term.

3.3
temperature coefficient of relative refractive index
Δn /ΔT
rel
ratio of refractive index change at an air pressure of 1,013 3 × 10 Pa and a relative humidity of 0 % to
temperature change at a selected wavelength
[2] 5
[SOURCE: ISO 9802:2022 , 3.4.2.4, modified — 1,013 3 × 10 Pa and a relative humidity of 0 % were added.]
Note 1 to entry: This definition of Δn /ΔT is for a specific pressure and humidity. Δn /ΔT can be calculated for any
rel rel
other pressure and humidity by understanding the index of air in those conditions.
3.4
thermal chamber
chamber where the temperature of the specimen can be changed and maintained to a preset temperature
4 Principle
As shown in Figure 1, a specimen prism is placed in a thermal chamber. The temperature of the specimen
prism is changed from T to T or from T to T , and the refractive index of the specimen prism is measured
1 2 2 1
(see also Annex A) at the temperatures of T and T respectively, in accordance with the method described in
1 2
ISO 21395-1 to find the temperature coefficient of refractive index. Figure 2 shows the concept of calculating
this temperature coefficient of refractive index.
Alternatively, the measurement principle accordance with Annex C shall be applied.
NOTE 1 In this document the term “light” is used to describe not only optical radiation visible to the human eye but
also radiation in the infrared and ultraviolet spectrum.
NOTE 2 In this document, all temperature symbols are represented by "T". The original symbol for temperature in
ISO 80000-5 is "t" or "ϑ " for temperature in Celsius degrees, and "T" for absolute temperature.

Key
1 light source
2 collimator
3 incident light
4 goniometer containing the telescope and detector
5 window
6 rotating stage containing the thermal chamber
7 thermal chamber containing the specimen prism
8 specimen prism
9 transmitted light
10 telescope
11 detector
12 thermometer
Figure 1 — Measurement set-up with thermal chamber
nn−
Δn
=
ΔT TT−
Key
X temperature
Y refractive index
T , T temperature of specimen prism
1 2
n refractive index of specimen prism at temperature T
1 1
n refractive index of specimen prism at temperature T
2 2
Figure 2 — Conceptual diagram for calculation of temperature coefficient of refractive index

5 Measuring apparatus
5.1 Goniometer
The goniometer shall be in accordance with ISO 21395-1:2020, 5.2.
5.2 Light source
The light source shall be in accordance with ISO 21395-1:2020, 5.3.
5.3 Detector
The detector shall be in accordance with ISO 21395-1:2020, 5.4.
5.4 Thermal chamber
The thermal chamber shall follow the requirements below. An example of a thermal chamber is shown in
Figure 3. The thermal chamber shall
a) have the ability to change the temperature of the specimen prism between the temperatures to be
measured,
b) have a structure that can maintain the temperature distribution in the specimen within the range of
1,0 K during raising and lowering of the temperature,
c) have a thermometer to measure the temperature of the specimen prism with an accuracy of ±0,2 K or better,
d) have the ability to provide a vacuum with a residual pressure of less than 10 Pa for the purpose of having
a negligible influence of the refractive index of air and of preventing condensation, and
e) have windows made of a parallel plate of quartz glass polished on both sides. The wedge angle between
the parallel polished faces shall not exceed 5 arc sec, the flatness of the parallel polished faces shall be
λ/10 or better.
NOTE Quartz glass is used because it has a high transmittance over a wide wavelength range, a high durability
against temperature changes, and is resistant to breakage.

Key
1 window
2 specimen prism
3 thermometer
4 thermal conductor specimen holder
5 heating and cooling unit
6 three-way valve
7 vacuum gauge
a
Incident light.
b
Outgoing light.
c
Leak inlet.
d
To vacuum pump.
Figure 3 — Example of thermal chamber
6 Specimen prism
The specimen prism shall be in accordance with ISO 21395-1:2020, Clause 6.
7 Measurement
7.1 Measurement of apex angle
The apex angle of the specimen prism shall be measured in accordance with ISO 21395-1:2020, 8.2.
7.2 Measurement of the angle of minimum deviation
The angle of minimum deviation of the specimen prism shall be measured at two or more temperatures in
accordance with ISO 21395-1:2020, 8.3.

The bisector of the apex angle, α, is parallel to the bisector of the angle, β, formed by the opposite two-
surface window of the thermal chamber. (See Figure 4)
The degree of vacuum around the specimen prism shall be less than 10 Pa. The minimum deviation angle
should be measured at a temperature within ±0,5 °C with respect to the target temperature.
NOTE 1 Allowable measurement error is an error in the measurement of the refractive index. When the allowable
-6
measurement error is smaller than 0,5 × 10 , the allowable angle difference between the bisectors of α and β is within
-5
2°; when the allowable measurement error is smaller than 0,5 × 10 , the allowable angle difference between the
bisectors of α and β is within 6°.
NOTE 2 The temperature to be measured is arbitrary. Allow sufficient time for the specimen prism to reach a
uniform temperature throughout. In most cases, the temperatures measured are -40 °C, -20 °C, 0 °C, 20 °C, 40 °C, 60 °C
and 80 °C.
8 Calculation
8.1 Absolute refractive index
The absolute refractive index at each temperature of the specimen prism shall be calculated by Formula (1)
(adaptation of ISO 21395-1:2020, Clause 4):
αδ+ T
()
 
minv, ac
sin
 
 
nT()= (1)
abs
α
 
sin
 
 
where
n (T) is the absolute refractive index of specimen prism at temperature T;
abs
α is the apex angle of the specimen prism;
δ (T) is the minimum deviation angle at temperature T;
min,vac
T is the temperature (°C) of the specimen prism during the measurement (°C).
NOTE In ISO 21395-1 the measurements are performed in air, therefore the refractive index n obtained is the
relative refractive index. In this document, the measurements are performed in vacuum, and therefore the result
obtained by Formula (1) is the absolute refractive index.
Figure 4 shows a schematic drawing of the light path through the thermal chamber windows and the
specimen prism. The internal and external environments are air and vacuum respectively. As a consequence,
light transmitted through a parallel window at non-normal incidence will be deflected.
Consequently the minimum angle of deflection in vacuum δ shall be calculated using the correction
min,vac
Formula (2) to the observed angle of minimum deflection in air δ .
min,air
Key
1 light beam
2 air condition
3 vacuum condition
4 window
5 specimen prism
6 bisector of the specimen prism apex angle
7 bisector of angle formed by the opposite two-surface window of thermal chamber
α apex angle
β angle formed by the opposite two-surface window of thermal chamber
δ δ , apparent minimum deviation angle in air
1 min,air
δ δ , minimum deviation angle in vacuum
2 min,vac
Figure 4 — Schematic drawing of light path through, input window, prism and output window
The angle of minimum deflection in vacuum δ shall be calculated from the observed angle of minimum
min,vac
deflection in air δmin,air using Formula (2):
δ
  β 
min,air
δ =×2 arcsin n ×−sin +β (2)
min,vaca ir  
  
where
n Is the refractive index of air;
air
δ is the minimum deviation angle in vacuum;
min,vac
δ is the apparent minimum deviation angle in air;
min,air
β is the angle formed by the opposite two-surface window of the thermal chamber.

8.2 Temperature coefficient of absolute refractive index
The temperature coefficient of the absolute refractive index between the temperatures of specimen prism
T and T shall be calculated by Formula (3):
1 2
Δn nTnT()− ()
absabs 21abs
= (3)
ΔT TT−
where
-1
Δn is the temperature coefficient (K ) of absolute refractive index of the specimen prism;
abs
ΔT
n (T ), n (T ) is the absolute refractive index of the specimen prism at temperature T , T ;
abs 1 abs 2 1 2
T , T are the temperatures of the specimen prism (°C).
1 2
Alternatively, the temperature coefficient of the absolute refractive index shall be calculated using
Formula (D.3) in Annex D.
NOTE T , T and T -T (ΔT) are arbitrary. In most cases T and T are the temperatures at 6 points shown in 7.2,
1 2 2 1 1 2
and ΔT is 20 K.
8.3 Temperature coefficient of relative refractive index
The temperature coefficient of the relative refractive index of the specimen prism between the temperatures
T and T shall be calculated by Formula (4).
1 2
For the calculation of the temperature coefficient of the relative refractive index of the specimen, the
temperature coefficient of the refractive index of air at a pressure of 1,013 25 × 10 Pa a relative humidity of
0 % and the individual temperatures T and T should be used.
1 2
Temperature coefficients of relative refractive index for a number of well-known spectral wavelength lines
are shown in Table 1. For additional wavelengths, the temperature coefficient of relative refractive index can
be calculated using the refractive index of air, obtained by Formula (A.1).
NOTE 1 Formula (4) is an approximation. The derivation and a proof that the approximation is of negligible
influence is given in Annex E.
NOTE 2 The calculation method for determining the relative refractive index of glass at any given temperature,
pressure, and relative humidity is shown in Annex B.
Δn Δn nT +nT Δn
() ()
relabs absa12bs air
=− × (4)
ΔT ΔT 2 ΔT
where
Δn
rel
-1
is the temperature coefficient (K ) of relative refractive index of the specimen prism;
ΔT
Δn
abs
-1
is the temperature coefficient (K ) of absolute refractive index of the specimen prism;
ΔT
Δn
air
-1
is the temperature coefficient (K ) of refractive index of air.
ΔT
Table 1 — Temperature coefficient of refractive index of air (air pressure 1,013 25 × 10 Pa, relative
humidity 0 %)
-6
Δn /ΔT(10 /K)
air
in the temperature range of
Wavelength
Spectral line
nm
–40 °C to –20 °C to 0 °C to 20 °C to 40 °C to 60 °C to
20 °C 0 °C 20 °C 40 °C 60 °C 80 °C
i 365,01 –1,40 –1,19 –1,03 –0,90 –0,79 –0,70
h 404,66 –1,38 –1,18 –1,02 –0,89 –0,78 –0,69
g 435,83 –1,38 –1,17 –1,01 –0,89 –0,78 –0,
...