ISO 9050:2003

Glass in building - Determination of light transmittance, solar direct transmittance, total solar energy transmittance, ultraviolet transmittance and related glazing factors

ISO 9050:2003 specifies methods of determining light and energy transmittance of solar radiation for glazing in buildings. These characteristic data can serve as a basis for light, heating and ventilation calculations of rooms and can permit comparison between different types of glazing. ISO 9050:2003 is applicable both to conventional glazing units and to absorbing or reflecting solar-control glazing, used as glazed apertures. The appropriate formulae for single, double and triple glazing are given. Furthermore, the general calculation procedures for units consisting of more than components are established. ISO 9050:2003 is applicable to all transparent materials. One exception is the treatment of the secondary heat transfer factor and the total solar energy factor for those materials that show significant transmittance in the wavelength region of ambient temperature radiation (5 microns to 50 microns), such as certain plastic sheets.

Verre dans la construction — Détermination de la transmission lumineuse, de la transmission solaire directe, de la transmission énergétique solaire totale, de la transmission de l'ultraviolet et des facteurs dérivés des vitrages

General Information

• Status: Published
• Publication Date: 01-Sep-2003
• ICS: 81.040.20 - Glass in building
• Technical Committee: ISO/TC 160/SC 2 - Use considerations
• Drafting Committee: ISO/TC 160/SC 2/WG 2 - Light and energy transmission properties and thermal properties of glazing
• Current Stage: 9092 - International Standard to be revised
• Start Date: 18-Dec-2024
• Completion Date: 13-Dec-2025

Relations

• Consolidated By: ISO 8676:2011 - Hexagon head screws with metric fine pitch thread - Product grades A and B
• Effective Date: 06-Jun-2022
• Revises: ISO 9050:1990 - Glass in building - Determination of light transmittance, solar direct transmittance, total solar energy transmittance and ultraviolet transmittance, and related glazing factors
• Effective Date: 15-Apr-2008

Overview

ISO 9050:2003 - "Glass in building - Determination of light transmittance, solar direct transmittance, total solar energy transmittance, ultraviolet transmittance and related glazing factors" - specifies standardized methods to measure and calculate how glazing transmits and reflects light and solar energy. It applies to conventional and solar‑control glazing, single, double and triple units, and most transparent materials (with noted exceptions for materials that transmit significantly in the 5 µm–50 µm region). Results support daylighting, heating and ventilation calculations and allow comparison between glazing products.

Key topics and technical requirements

• Measured and calculated parameters
  • Spectral transmittance and reflectance (spectral range stated in the standard)
  • Light transmittance (τv) and external/internal light reflectance (ρv,o / ρv,i) using illuminant D65 and photopic V(λ)
  • Solar direct transmittance, total solar energy transmittance (solar factor, g), UV transmittance (τUV)
  • Colour rendering index, CIE damage factor and skin damage factor
• Measurement conditions
  • Quasi‑parallel, near‑normal incidence (beam axis within 10° of surface normal; individual rays within 5°)
  • Use of spectrophotometers and integrating spheres for diffuse samples
  • Calibration and verification of wavelength and photometric linearity using reference materials
  • Recommended measurement accuracy (transmittance/reflectance reproducibility around ±0.01)
• Calculation procedures
  • Formulae for single, double and triple glazing; general methods for units with more components (Annex A)
  • Spectral data of individual components must be used when calculating multiple glazing performance
  • Guidance on handling diffusing, wedged or thick samples to avoid systematic errors

Practical applications and users

ISO 9050:2003 is used by:

• Glass manufacturers and coating suppliers to document performance data and compare products
• Fenestration and façade engineers performing daylighting, thermal and solar gain calculations
• Architects and building services designers specifying glazing for comfort, energy efficiency and solar control
• Testing laboratories and certification bodies producing standardized test reports for product data sheets
• Researchers analysing solar control, UV protection and daylighting impacts

Using ISO 9050 helps ensure consistent, comparable glazing data for energy modeling, compliance, product selection and specification.

Related standards

• ISO 9845‑1 (reference solar spectral irradiance)
• ISO 10291 / 10292 / 10293 (thermal transmittance and U‑value methods)
• ISO/CIE 10526, ISO/CIE 10527, CIE 13.3 (colorimetric and illuminant references)
• ISO 15099 (detailed procedures for complex or scattering multiple glazing)

Keywords: ISO 9050:2003, glass in building, light transmittance, solar transmittance, total solar energy transmittance, UV transmittance, glazing factors, spectral transmittance, glazing calculations.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 9050
Second edition
2003-08-15
Glass in building — Determination of
light transmittance, solar direct
transmittance, total solar energy
transmittance, ultraviolet transmittance
and related glazing factors
Verre dans la construction — Détermination de la transmission
lumineuse, de la transmission solaire directe, de la transmission
énergétique solaire totale, de la transmission de l'ultraviolet et des
facteurs dérivés des vitrages
Reference number
©
ISO 2003
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©  ISO 2003
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ii © ISO 2003 — All rights reserved

Contents Page
Foreword. iv
1 Scope. 1
2 Normative references . 1
3 Determination of characteristic parameters. 2
3.1 General. 2
3.2 Performance of optical measurements. 2
3.3 Light transmittance. 3
3.4 Light reflectance . 5
3.5 Total solar energy transmittance (solar factor) .6
3.6 UV-transmittance . 14
3.7 CIE damage factor. 14
3.8 Skin damage factor . 15
3.9 Colour rendering . 15
4 Reference values. 16
5 Test report. 16
Annex A (normative) Calculation procedures . 22
Bibliography . 27

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 9050 was prepared by Technical Committee ISO/TC 160, Glass in building, Subcommittee SC 2, Use
considerations.
This second edition cancels and replaces the first edition (ISO 9050:1990), which has been technically revised.

iv © ISO 2003 — All rights reserved

INTERNATIONAL STANDARD ISO 9050:2003(E)

Glass in building — Determination of light transmittance, solar
direct transmittance, total solar energy transmittance,
ultraviolet transmittance and related glazing factors
1 Scope
This International Standard specifies methods of determining light and energy transmittance of solar radiation
for glazing in buildings. These characteristic data can serve as a basis for light, heating and ventilation
calculations of rooms and can permit comparison between different types of glazing.
This International Standard is applicable both to conventional glazing units and to absorbing or reflecting
solar-control glazing, used as glazed apertures. The appropriate formulae for single, double and triple glazing
are given. Furthermore, the general calculation procedures for units consisting of more than components are
established.
This International Standard is applicable to all transparent materials. One exception is the treatment of the
secondary heat transfer factor and the total solar energy factor for those materials that show significant
transmittance in the wavelength region of ambient temperature radiation (5 µm to 50 µm), such as certain
plastic sheets.
NOTE For multiple glazing including elements with light-scattering properties, the more detailed procedures of
ISO 15099 can be used. For daylighting calculations, procedures can be found in reference [1].
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 9845-1:1992, Solar energy — Reference solar spectral irradiance at the ground at different receiving
conditions — Part 1: Direct normal and hemispherical solar irradiance for air mass 1,5
ISO 10291:1994, Glass in building — Determination of steady-state U values (thermal transmittance) of
multiple glazing — Guarded hot plate method
ISO 10292:1994, Glass in building — Calculation of steady-state U values (thermal transmittance) of multiple
glazing
ISO 10293:1997, Glass in building — Determination of steady-state U values (thermal transmittance) of
multiple glazing — Heat flow meter method
ISO 10526:1999/CIE S005:1998, CIE standard illuminants for colorimetry
ISO/CIE 10527:1991, CIE standard colorimetric observers
CIE 13.3:1995, Technical report — Method of measuring and specifying colour rendering properties of light
source
3 Determination of characteristic parameters
3.1 General
The characteristic parameters are determined for quasi-parallel, almost normal radiation incidence. For the
measurements, the samples shall be irradiated by a beam whose axis is at an angle not exceeding 10° from
the normal to the surface. The angle between the axis and any ray of the illuminating beam shall not exceed
5° (see reference [2]).
The characteristic parameters are as follows:
 the spectral transmittance τ (λ), the spectral external reflectance ρ (λ) and the spectral internal
o
reflectance ρ (λ) in the wavelength range of 300 nm to 2 500 nm;
i
 the light transmittance τ , the external light reflectance ρ and the internal light reflectance ρ for
v v,o v,i
illuminant D65;
 the solar direct transmittance τ and the solar direct reflectance ρ ;
e e
 the total solar energy transmittance (solar factor) g;
 the UV-transmittance τ ;
UV
 the general colour rendering index R .
a
If the value of a given characteristic is required for different glass thicknesses (in the case of uncoated glass)
or for the same coating applied to different glass substrates, it may be obtained by calculation (see Annex A).
If nothing else is stated, the published characteristic parameters shall be determined using the standard
conditions given in 3.3 to 3.7. Other optional conditions given in Clause 4 shall be stated.
When calculating the characteristic parameters of multiple glazing, the spectral data of each glass component
instead of integrated data shall be used.
3.2 Performance of optical measurements
Optical measurements in transmission and reflection require special care and much experimental experience
to achieve an accuracy in transmittance and reflectance of about ± 0,01.
Commercial spectrophotometers (with or without integrating spheres) are affected by various sources of
inaccuracy when used for reflectance and transmittance measurements on flat glass for building.
The wavelength calibration and the photometric linearity of commercial spectrophotometers shall be checked
periodically using reference materials obtained from metrological laboratories.
The wavelength calibration shall be performed by measuring glass plates or solutions which feature relatively
sharp absorption bands at specified wavelengths; the photometric linearity shall be checked using grey filters
with a certified transmittance.
For reflectance measurements, reference materials having a reflection behaviour (i.e. reflectance level and
ratio of diffuse and direct reflectance) similar to the unknown sample shall be selected.
Thick samples (e.g. laminated glass or insulating units) can modify the optical path of the instrument’s beam
as compared to the path in air and therefore the sample beam hits an area of the detector having a different
responsivity.
2 © ISO 2003 — All rights reserved

A similar source of inaccuracy occurs in case of samples with significant wedge angles which deflect the
transmitted (and reflected) beams. It is recommended to check the reproducibility by repeating the
measurement after rotating the sample.
Additionally, in the case of reflectance measurements, glass sheets cause a lateral shear of the beam
reflected by the second surface, causing reflectance losses (whose extent is particulary evident in the case of
thick and/or wedged samples). This source of inaccuracy shall be taken into account particularly in the case of
reflectance measurements through the uncoated side. In order to quantify and correct systematic errors, it is
recommended to use calibrated reflectance standards with a thickness similar to the unknown sample.
In the case of diffusing samples (or samples with a non-negligible diffusing component or wedged samples),
transmittance and reflectance measurements shall be performed using integrating spheres whose openings
are sufficiently large to collect all the diffusely transmitted or reflected beam. The sphere diameter shall be
adequate and the internal surface adequately coated with a highly diffusing reflectance material, so that the
internal area can provide the necessary multiple reflections. Reference materials with characteristics similar to
the unknown sample as specified above shall be used.
If the transmittance or reflectance curve recorded by the spectrometer exhibits a high level of noise for some
wavelengths, the values to be considered for those wavelengths should be obtained after a smoothing of the
noise.
In this International Standard, these requirements are not all treated in detail. For more information, see
reference [3] which gives comprehensive and detailed information on how to perform optical measurements.
3.3 Light transmittance
The light transmittance τ of glazing shall be calculated using the following formula:
v
780 nm
τλλDV ∆λ
() ()
∑ λ
λ = 380 nm
τ = (1)
v
780 nm
DVλλ∆
()
λ
∑
λ = 380 nm
where
D is the relative spectral distribution of illuminant D65 (see ISO/CIE 10526),
λ
τ (λ) is the spectral transmittance of glazing;
V(λ) is the spectral luminous efficiency for photopic vision defining the standard observer for photometry
(see ISO/CIE 10527);
∆λ is the wavelength interval.
Table 1 indicates the values for D V(λ)∆λ for wavelength intervals of 10 nm. The table has been drawn up in
λ
such a way that ΣD V(λ)∆λ = 1.
λ
In the case of multiple glazing, the spectral transmittance τ (λ) shall be obtained by calculation from the
spectral characteristics of the individual components. Alternatively measurements on non-diffusing multiple
units may be performed using an integrating sphere. This may be achieved after reducing the interspaces
under conditions that allow the collection of the whole transmitted beam (see 3.2).
The calculation of the spectral transmittance τ (λ) shall be performed using methods such as algebraic
manipulation, the embedding technique of reference [4] or by recursion techniques (e.g. according to
reference [5]). Any algorithm that can be shown to yield consistently the correct solution is acceptable.
For the calculation of τ (λ) as well as for the calculation of spectral reflectance (see 3.4), the following symbols
for the spectral transmittance and spectral reflectance of the individual components are used:
τ (λ) is the spectral transmittance of the outer (first) pane;
τ (λ) is the spectral transmittance of the second pane;
τ (λ) is the spectral transmittance of the nth (inner) pane (e.g. for triple glazing n = 3);
n
ρ (λ) is the spectral reflectance of the outer (first) pane measured in the direction of incident radiation;
ρ′ (λ) is the spectral reflectance of the outer (first) pane measured in the opposite direction of incident
radiation;
ρ (λ) is the spectral reflectance of the second pane measured in the direction of incident radiation;
ρ′ (λ) is the spectral reflectance of the second pane measured in the opposite direction of incident
radiation;
ρ (λ) is the spectral reflectance of the nth (inner) pane measured in the direction of incident radiation;
n
ρ′ (λ) is the spectral reflectance of the nth (inner) pane measured in the opposite direction of incident
n
radiation.
For the spectral transmittance τ (λ) as a function of the spectral characteristics of the individual components of
the unit, the following formulae are obtained.
a) For double glazing:
τλ( )τ (λ )
τ λ = (2)
()
1 − ρ′ λρ λ
() ( )
b) For triple glazing:
τλτ λτ λ
() ()
()
12 3
τλ = (3)
()
′′  ′
11−⋅ρ λρ λ−ρ λρ λ−τ λ ρ λ ρ λ
() ( ) () () ( ) ( ) ()
12 2 3 2 1 3
 
For multiple glazing with more than three components, relationships similar to Equations (2) and (3) are found
to calculate τ (λ) of such glazing from the spectral characteristics of the individual components. As these
formulae become very complex, they are not given here.
As an example for calculating τ (λ) according to the procedures of this International Standard, a glazing
composed of five components may be treated as follows:
 first consider the first three components as triple glazing and calculate the spectral characteristics of this
combination;
 next, run the same procedure for the next two components as double glazing;
 then calculate τ (λ) for the five component glazing, considering it as double glazing consisting of the
preceding triple and double glazing.
4 © ISO 2003 — All rights reserved

3.4 Light reflectance
3.4.1 External light reflectance of glazing
The external light reflectance of glazing ρ shall be calculated using the following formula:
v,o
780 nm
ρλλDV ∆λ
() ()
∑ o λ
λ = 380 nm
ρ = (4)
v,o
780 nm
DVλλ∆
()
λ
∑
λ = 380 nm
where ρ (λ) is the spectral external reflectance of glazing, and D , V(λ), ∆λ and the integration procedure are
o λ
as defined in 3.3
For multiple glazing, the calculation of the spectral external reflectance ρ (λ) shall be performed using the
o
same methods as given in 3.3 for the calculation of the spectral transmittance τ (λ).
For the spectral external reflectance ρ (λ) as a function of the spectral characteristics of the individual
o
components of the unit, the following formulae are applied.
a) For double glazing:
τλρ λ
() ( )
ρλ=+ρ λ (5)
() ()
o1
′
1 − ρ λ ρ λ
() ( )
b) For triple glazing:
′
τ λ ρλ 1−+ρλ ρ λ τ λτ λ ρλ
() () ( ) () () () ()
12 2 3 1 2 3

ρλ()=+ρ ()λ (6)
o1
11−⋅ρ′′λρ λ−ρ λρ λ−τ λ ρ′ λ ρ λ
() () ( ) ( ) () () ( )
12 2 3 2 1 3
 
For multiple glazing with more than three components, relationships similar to Equations (5) and (6) are found
to calculate ρ (λ) of such glazing from the spectral characteristics of the individual components. As these
o
formulae become very complex, they are not given here.
As an example for calculating ρ (λ), a glazing composed of five components may be treated in the same way
o
as described in 3.3.
3.4.2 Internal light reflectance of glazing
The internal light reflectance of glazing ρ shall be calculated using the following formula:
v,i
780 nm
ρλλDV ∆λ
() ()
∑ i λ
λ = 380 nm
ρ = (7)
v,i
780 nm
DVλλ∆
()
λ
∑
λ = 380 nm
where ρ (λ) is the spectral internal reflectance of glazing, and D V(λ), ∆λ and the integration procedure are
i λ,
as defined in 3.3.
For multiple glazing, the calculation of the spectral internal reflectance ρ (λ) shall be performed using the
i
same methods as given in 3.3 for the calculation of the spectral transmittance τ (λ).
For the spectral internal reflectance ρ (λ) as a function of the spectral characteristics of the individual
i
components of the unit, the following formulae are applied.
a) For double glazing:
′
τλ()ρ ()λ
ρλ=+ρ′ λ (8)
() ( )
i2
1 − ρ′ λ ρ λ
() ()
b) For triple glazing:
′′ ′
τ λ ρλ 1−+ρλ ρ λ τ λτ λ ρ λ
() () () () () () ( )
32 2 1 3 2 1

ρλ=+ρ′ λ
() ( )
i3 (9)
11−⋅ρ λρ′′λ−ρ λ ρ λ−τ λρ λρ′ λ
() ( ) ( ) ( ) () () ()
32 2 1 2 3 1
 
For multiple glazing with more than three components, relationships similar to Equations (8) and (9) are found
to calculate ρ (λ) of such glazing from the spectral characteristics of the individual components. As these
i
formulae are very complex, they are not given here.
As an example for calculating ρ (λ), a glazing composed of five components may be treated in the same way
i
as described in 3.3.
3.5 Total solar energy transmittance (solar factor)
3.5.1 General
The total solar energy transmittance g is the sum of the solar direct transmittance τ and the secondary heat
e
transfer factor q towards the inside (see 3.5.3 and 3.5.6), the latter resulting from heat transfer by convection
i
and longwave IR-radiation of that part of the incident solar radiation which has been absorbed by the glazing:
g=+τ q (10)
ei
3.5.2 Division of incident solar radiation flux
The incident solar radiant flux per unit area φ is divided into the following three parts (see Figure 1):
e
 the transmitted part τ φ ;
e e
 the reflected part ρ φ ;
e e
 the absorbed part α φ ;
e e
where
τ is the solar direct transmittance (see 3.5.3);
e
ρ is the solar direct reflectance (see 3.5.4);
e
α is the solar direct absorptance (see 3.5.5).
e
6 © ISO 2003 — All rights reserved

Key
1 outer pane
2 second inner pane
3 unit incident radiant flux
ρ = 0,38; q = 0,17
e e
τ = 0,41; q = 0,04; therefore g = 0,45
e i
Figure 1 — Division of the incident radiant flux for a double glazing unit
The relationship between the three characteristics is
τρ++α= 1 (11)
ee e
The absorbed part α φ is subsequently divided into two parts q φ and q φ , which are energy transferred to
e e i e e e
the inside and outside respectively:
α =+qq (12)
ei e
where
q is the secondary heat transfer factor of the glazing towards the inside;
i
q is the secondary heat transfer factor of the glazing towards the outside.
e
3.5.3 Solar direct transmittance
The solar direct transmittance τ of glazing shall be calculated using the following formula:
e
2500nm
τλλS ∆
()
λ
∑
λ = 300 nm
τ = (13)
e
2500nm
S ∆λ
∑ λ
λ = 300 nm
where
S is the relative spectral distribution of the solar radiation;
λ
τ (λ) is the spectral transmittance of the glazing;
∆λ and the integration procedure are the same as in 3.3 except that the data points shall be chosen at
the wavelengths given in Table 2.
The relative spectral distribution, S , used to calculate the solar direct transmittance τ , is derived from the
λ e
global solar irradiance given in ISO 9845-1:1992, Table 1, column 5. The corresponding values S ∆λ are given
λ
in Table 2. This table is drawn up in such a way that Σ S ∆λ = 1.
λ
In the case of multiple glazing, the spectral transmittance τ (λ) is calculated in accordance with 3.3.
NOTE Contrary to real situations, it is always assumed, for simplification, that the solar radiation strikes the glazing
as a beam and almost at normal incidence. In the case of oblique incidence of radiation, the solar direct transmittance of
glazing and the total solar energy transmittance are both somewhat reduced. The solar control effect becomes greater in
the case of oblique incidence of radiation.
3.5.4 Solar direct reflectance
The solar direct reflectance ρ of the glazing shall be calculated using the following formula:
e
2 500 nm
ρλλS ∆
()
∑ o λ
λ = 300 nm
ρ = (14)
e
2500nm
S ∆λ
λ
∑
λ = 300 nm
where
S is the relative spectral distribution of the solar radiation (see 3.5.3);
λ
ρ (λ) is the spectral external reflectance of the glazing;
o
∆λ and the integration procedure are the same as in 3.3 except that the data points shall be chosen
at the wavelengths given in Table 2.
In the case of multiple glazing, the spectral external reflectance ρ (λ) is calculated in accordance with 3.4.1.
o
3.5.5 Solar direct absorptance
The solar direct absorptance α shall be calculated from Equation (11).
e
3.5.6 Secondary heat transfer factor towards the inside
3.5.6.1 Boundary conditions
For the calculation of the secondary heat transfer factor towards the inside, q , the heat transfer coefficients of
i
the glazing towards the outside, h , and towards the inside, h , are needed. These values mainly depend on
e i
the position of the glazing, wind velocity, inside and outside temperatures and, furthermore, on the
temperature of the two external glazing surfaces.
8 © ISO 2003 — All rights reserved

As the purpose of this International Standard is to provide basic information on the performance of glazing, the
following conventional conditions have been stated for simplicity:
 position of the glazing: vertical;
 outside surface: wind velocity approximately 4 m/s; corrected emissivity 0,837;
 inside surface: natural convection; emissivity optional;
 air spaces are unventilated.
Under these conventional, average conditions, standard values for h and h are obtained:
e i
h = 23 W/(m ·K)
e
4,4ε

i
h=+3,6 W/(m⋅K)
i

0,837

where ε is the corrected emissivity of the inside surface [for soda lime glass, ε = 0,837 and h = 8 W/(m ⋅K)].
i i i
The corrected emissivity is defined and measured according to ISO 10292.
If other boundary conditions are used to meet special requirements they shall be stated in the test report.
Values for ε lower than 0,837 (due to surface coatings with higher reflectance in the far infrared) should only
i
to be taken into account if condensation on the coated surface can be excluded.
3.5.6.2 Single glazing
The secondary heat transfer factor towards the inside, q, of single glazing shall be calculated using the
i
following formula:
h
i
q = α (15)
ie
hh+
ei
where
α is the solar direct absorptance in accordance with 3.5.2;
e
h , h are the heat transfer coefficients towards the outside and inside, respectively, in accordance with
e i
3.5.6.1.
3.5.6.3 Double glazing
The secondary heat transfer factor towards the inside, q, of double glazing shall be calculated using the
i
following formula:
αα+ α
e1 e2 e2
+

h Λ
e
q = (16)
i

11 1
++

hh Λ
ie
where
α is the solar direct absorptance of the outer (first) pane within the double glazing;
e1
α is the solar direct absorptance of the second pane within the double glazing;
e2
Λ is the thermal conductance between the outer surface and the innermost surface of the double
glazing (see Figure 2), in watts per square metre kelvin (W/m ⋅K);
h , h are the heat transfer coefficients towards the outside and the inside respectively in accordance
e i
with 3.5.6.1.
Key
1 pane 1
2 pane 2
3 outside
4 inside
Figure 2 — Illustration of the meaning of thermal conductance Λ
Characteristics α and α are calculated as follows:
e1 e2
2500nm
′
αλτ λ ρ λ
( ) () ()

11 2
αλλ+∆S
()
1 λ
∑
1 −ρλ′ ρ λ
() ( )

...