ASTM G214-23

Standard Test Method for Integration of Digital Spectral Data for Weathering and Durability Applications

SIGNIFICANCE AND USE
5.1 Weathering and durability testing often requires the computation of the effects of radiant exposure of materials to various optical radiation sources, including lamps with varying spectral power distributions and outdoor and simulated sunlight as in Test Methods E972, G130, and G207.  
5.2 The purpose of this test method is to foster greater consistency and comparability of weathering and durability test results between various exposure regimes, calculation of materials properties, and laboratories with respect to numerical results that depend upon the integration of spectral distribution data.  
5.3 Changes in the optical properties of materials such as spectral reflectance, transmittance, or absorptance are often the measure of material stability or usefulness in various applications. Computation of the material responses to exposure to radiant sources mentioned above requires the integration of measured wavelength-dependent digital data, sometimes in conjunction with tabulated wavelength-dependent reference or comparison data.  
5.4 This test method specifies and describes the Modified Trapezoid Rule as a single reasonably accurate and easily implemented integration technique for computing approximations of spectral source and optical property integrals.  
5.5 The method includes a procedure for estimating the approximate absolute and relative (percent) error in the estimated spectral integrals.  
5.6 The method includes a procedure to construct data sets that match in spectral wavelength and spectral wavelength interval, which does not have to be uniform over the spectral range of interest. Uniform spectral intervals simplify some of the calculations, but are not required.
SCOPE
1.1 This test method specifies a single relatively simple method to implement, common integration technique, the Modified Trapezoid Rule, to integrate digital or tabulated spectral data. The intent is to produce greater consistency and comparability of weathering and durability test results between various exposure regimes, calculation of materials properties, and laboratories with respect to numerical results that depend upon the integration of spectral distribution data.  
1.2 Weathering and durability testing often requires the computation of the effects of radiant exposure of materials to various optical radiation sources, including lamps with varying spectral power distributions and outdoor and simulated sunlight. Changes in the spectrally dependent optical properties of materials, in combination with exposure source spectral data, are often used to evaluate the effect of exposure to radiant sources, develop activation spectra (Practice G178), and classify, evaluate, or rate sources with respect to reference or exposure source spectral distributions. Another important application is the integration of the original spectrally dependent optical properties of materials in combination with exposure source spectral data to determine the total energy absorbed by a material from various exposure sources.  
1.3 The data applications described in 1.2 often require the use of tabulated reference spectral distributions, digital spectral data produced by modern instrumentation, and the integrated version of that data, or combinations (primarily multiplication) of spectrally dependent data.  
1.4 Computation of the material responses to exposure to radiant sources mentioned above require the integration of measured wavelength dependent digital data, sometimes in conjunction with tabulated wavelength dependent reference or comparison data.  
1.5 The term “integration” in the previous sections refers to the numerical approximation to the true integral of continuous functions, represented by discrete, digital data. There are numerous mathematical techniques for performing numerical integration. Each method provides different levels of complexity, accuracy, ease of implementation and computational efficiency, an...

General Information

• Status: Published
• Publication Date: 30-Jun-2023
• ICS: 17.180.20 - Colours and measurement of light
• Technical Committee: G03 - Weathering and Durability
• Drafting Committee: G03.09 - Radiometry

Relations

• Refers: ASTM G138-12(2020)e1 - Standard Test Method for Calibration of a Spectroradiometer Using a Standard Source of Irradiance
• Effective Date: 01-Jun-2020
• Refers: ASTM G130-12(2020) - Standard Test Method for Calibration of Narrow- and Broad-Band Ultraviolet Radiometers Using a Spectroradiometer
• Effective Date: 01-Jun-2020
• Refers: ASTM E973-16(2020) - Standard Test Method for Determination of the Spectral Mismatch Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cell
• Effective Date: 01-Jun-2020
• Refers: ASTM E971-11(2019) - Standard Practice for Calculation of Photometric Transmittance and Reflectance of Materials to Solar Radiation
• Effective Date: 01-Oct-2019
• Refers: ASTM G207-11(2019)e1 - Standard Test Method for Indoor Transfer of Calibration from Reference to Field Pyranometers
• Effective Date: 01-Jun-2019
• Refers: ASTM E927-19 - Standard Classification for Solar Simulators for Electrical Performance Testing of Photovoltaic Devices
• Effective Date: 01-Feb-2019
• Refers: ASTM E973-16 - Standard Test Method for Determination of the Spectral Mismatch Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cell
• Effective Date: 01-Jul-2016
• Refers: ASTM E973-15 - Standard Test Method for Determination of the Spectral Mismatch Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cell
• Effective Date: 01-Dec-2015
• Refers: ASTM E927-10(2015) - Standard Specification for Solar Simulation for Photovoltaic Testing
• Effective Date: 01-Nov-2015
• Refers: ASTM E973-10(2015) - Standard Test Method for Determination of the Spectral Mismatch Parameter Between a Photovoltaic Device and a Photovoltaic Reference Cell
• Effective Date: 01-Mar-2015
• Refers: ASTM G113-14 - Standard Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
• Effective Date: 01-Mar-2014
• Refers: ASTM E772-13 - Standard Terminology of Solar Energy Conversion
• Effective Date: 01-Sep-2013
• Refers: ASTM G138-12 - Standard Test Method for Calibration of a Spectroradiometer Using a Standard Source of Irradiance
• Effective Date: 01-Jun-2012
• Refers: ASTM G130-12 - Standard Test Method for Calibration of Narrow- and Broad-Band Ultraviolet Radiometers Using a Spectroradiometer
• Effective Date: 01-Jun-2012
• Refers: ASTM E772-11 - Standard Terminology of Solar Energy Conversion
• Effective Date: 01-Sep-2011

Overview

ASTM G214-23: Standard Test Method for Integration of Digital Spectral Data for Weathering and Durability Applications provides a standardized approach to integrating digital or tabulated spectral data, widely used in weathering and durability testing of materials. This standard defines the use of the Modified Trapezoid Rule as an effective and easily implemented numerical integration technique, aiming to enhance the consistency and comparability of test results across various laboratories, exposure regimes, and calculation methods.

This method supports the accurate calculation of material responses-such as changes in spectral reflectance, transmittance, or absorptance-following exposure to different optical radiation sources, such as sunlight, lamps, or solar simulators. ASTM G214-23 is instrumental in evaluating material performance, longevity, and total energy absorption under variable spectrally-dependent conditions.

Key Topics

• Integration of Digital Spectral Data
  • Specifies using the Modified Trapezoid Rule for numerical integration of discrete spectral data.
  • Allows calculation of material optical properties and total radiant energy exposure.
• Consistency and Comparability
  • Promotes uniformity when integrating data from various instruments or laboratories.
  • Enables better benchmarking and validation against reference standards.
• Combining Spectral Data Sets
  • Outlines procedures to handle and interpolate data with differing wavelength intervals, ensuring datasets can be consistently combined (e.g., multiplying spectral irradiance by transmittance).
• Estimation of Errors
  • Provides methods for estimating both absolute and relative errors in the integrated results.
  • Accounts for errors introduced by interpolation and the use of non-uniform wavelength intervals.
• Practical Procedures
  • Details harmonization of wavelength intervals via linear interpolation.
  • Offers guidance on ensuring consistent units and proper calibration of instrumentation.

Applications

ASTM G214-23 is relevant across industries where exposure to optical radiation influences material durability or functionality. Key applications include:

• Weathering Testing:
  Integration of spectral data to evaluate degradation in polymers, coatings, paints, textiles, and construction materials exposed to natural or simulated sunlight.

• Solar and Photovoltaic Materials:
  Calculation of absorbed, transmitted, or reflected energy in solar panels or related devices to assess energy performance and material lifespans.

• Photometric and Radiometric Instrument Calibration:
  Use as a reference method for calibrating spectroradiometers, spectrophotometers, and UV radiometers according to specified ASTM standards.

• Comparative Analysis:
  Normalization and comparability of results across different optical sources (e.g., various lamp types and sunlight conditions) to facilitate product development and compliance.

• Development of Activation Spectra:
  Combining spectrally-dependent data to create activation spectra for accelerated testing, supporting R&D and quality control.

Related Standards

ASTM G214-23 references and aligns with several other critical ASTM standards, including:

• ASTM E903 - Test Method for Solar Absorptance, Reflectance, and Transmittance of Materials
• ASTM E972 - Test Method for Solar Photometric Transmittance of Sheet Materials Using Sunlight
• ASTM G130 - Test Method for Calibration of UV Radiometers Using a Spectroradiometer
• ASTM G207 - Test Method for Indoor Transfer of Calibration from Reference to Field Pyranometers
• ASTM G173 & G177 - Reference Spectral Irradiance Data Tables
• ASTM G138 - Calibration of a Spectroradiometer Using a Standard Source of Irradiance
• ASTM E490 - Standard Solar Constant and Zero Air Mass Solar Spectral Irradiance Tables
• ASTM G178 - Practice for Determining the Activation Spectrum of a Material

These and related ASTM standards provide the technical framework necessary for accurate measurement, calibration, and analysis within weathering and durability studies involving digital spectral data integration.

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Keywords: weathering testing, spectral data integration, material durability, optical properties, spectral reflectance, radiant exposure, solar exposure, ASTM G214-23, Modified Trapezoid Rule, error estimation, laboratory comparability, spectroradiometer calibration

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: G214 − 23
Standard Test Method for
Integration of Digital Spectral Data for Weathering and
Durability Applications
This standard is issued under the fixed designation G214; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope functions, represented by discrete, digital data. There are
numerous mathematical techniques for performing numerical
1.1 This test method specifies a single relatively simple
integration. Each method provides different levels of
method to implement, common integration technique, the
complexity, accuracy, ease of implementation and computa-
Modified Trapezoid Rule, to integrate digital or tabulated
tional efficiency, and, of course, resultant magnitudes.
spectral data. The intent is to produce greater consistency and
Hulstrom, Bird and Riordan (1) demonstrate the differences
comparability of weathering and durability test results between
between results for rectangular (963.56 W/m ), trapezoid rule
various exposure regimes, calculation of materials properties,
2 2
(962.53 W/m ), and modified trapezoid rule (963.75 W/m )
and laboratories with respect to numerical results that depend
integration for a single solar spectrum. Thus the need for a
upon the integration of spectral distribution data.
standard integration technique to simplify the comparison of
1.2 Weathering and durability testing often requires the
results from different laboratories, measurement
computation of the effects of radiant exposure of materials to
instrumentation, or exposure regimes.
various optical radiation sources, including lamps with varying
1.6 The values stated in SI units are to be regarded as
spectral power distributions and outdoor and simulated sun-
standard. No other units of measurement are included in this
light. Changes in the spectrally dependent optical properties of
standard.
materials, in combination with exposure source spectral data,
1.7 This standard does not purport to address all of the
are often used to evaluate the effect of exposure to radiant
safety concerns, if any, associated with its use. It is the
sources, develop activation spectra (Practice G178), and
responsibility of the user of this standard to establish appro-
classify, evaluate, or rate sources with respect to reference or
priate safety, health, and environmental practices and deter-
exposure source spectral distributions. Another important ap-
mine the applicability of regulatory limitations prior to use.
plication is the integration of the original spectrally dependent
1.8 This international standard was developed in accor-
optical properties of materials in combination with exposure
dance with internationally recognized principles on standard-
source spectral data to determine the total energy absorbed by
ization established in the Decision on Principles for the
a material from various exposure sources.
Development of International Standards, Guides and Recom-
1.3 The data applications described in 1.2 often require the
mendations issued by the World Trade Organization Technical
use of tabulated reference spectral distributions, digital spectral
Barriers to Trade (TBT) Committee.
data produced by modern instrumentation, and the integrated
version of that data, or combinations (primarily multiplication)
2. Referenced Documents
of spectrally dependent data.
2.1 ASTM Standards:
1.4 Computation of the material responses to exposure to
E275 Practice for Describing and Measuring Performance of
radiant sources mentioned above require the integration of
Ultraviolet and Visible Spectrophotometers
measured wavelength dependent digital data, sometimes in
E424 Test Methods for Solar Energy Transmittance and
conjunction with tabulated wavelength dependent reference or
Reflectance (Terrestrial) of Sheet Materials
comparison data.
E490 Standard Solar Constant and Zero Air Mass Solar
Spectral Irradiance Tables
1.5 The term “integration” in the previous sections refers to
E772 Terminology of Solar Energy Conversion
the numerical approximation to the true integral of continuous
1 2
This test method is under the jurisdiction of ASTM Committee G03 on The boldface numbers in parentheses refer to a list of references at the end of
Weathering and Durability and is the direct responsibility of Subcommittee G03.09 this standard.
on Radiometry. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved July 1, 2023. Published August 2023. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2015. Last previous edition approved in 2016 as G214 – 16. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/G0214-23. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
G214 − 23
E903 Test Method for Solar Absorptance, Reflectance, and (as in Test Methods G207, G130, and G138) and measured or
Transmittance of Materials Using Integrating Spheres tabulated spectral optical property data, R(λ) such as transmit-
E927 Classification for Solar Simulators for Electrical Per- tance or reflectance as measured in accordance with Test
formance Testing of Photovoltaic Devices Method E903 and E424 and Practice E971, or spectral mis-
E971 Practice for Calculation of Photometric Transmittance match errors such as in Test Method E973, it is necessary for
and Reflectance of Materials to Solar Radiation all data sets to have identical wavelength (λi) and wavelength
E972 Test Method for Solar Photometric Transmittance of intervals (λi+1 – λi). Then the appropriate products E(λi)·R(λi)
Sheet Materials Using Sunlight are computed and treated using the procedures in 12.1 to 12.3.
E973 Test Method for Determination of the Spectral Mis- If the spectral wavelength intervals are different, one data set
match Parameter Between a Photovoltaic Device and a (usually with the smallest or shortest wavelength interval,
Photovoltaic Reference Cell should be selected as the data set, M(λ), with which to match
G113 Terminology Relating to Natural and Artificial Weath- all other data sets wavelength intervals. The other data sets
ering Tests of Nonmetallic Materials should be interpolated, using linear interpolation, to obtain
G130 Test Method for Calibration of Narrow- and Broad- values at wavelength values and intervals identical to the
Band Ultraviolet Radiometers Using a Spectroradiometer selected M(λ).
G138 Test Method for Calibration of a Spectroradiometer
4.1.1 When interpolating data sets, it is recommended that
Using a Standard Source of Irradiance the data set with the coarsest or largest wavelength step size or
G151 Practice for Exposing Nonmetallic Materials in Accel-
interval be interpolated to the step size of the data set with the
erated Test Devices that Use Laboratory Light Sources smaller step size or interval.
G173 Tables for Reference Solar Spectral Irradiances: Direct
4.2 Compute an estimate for the absolute error in the
Normal and Hemispherical on 37° Tilted Surface
integration based on the wavelength limits for the integral, the
G177 Tables for Reference Solar Ultraviolet Spectral Distri-
average wavelength interval of the data, and the average of the
butions: Hemispherical on 37° Tilted Surface
second differences of the spectral data. Compute the estimated
G178 Practice for Determining the Activation Spectrum of a
relative (percentage) error in integral approximation based on
Material (Wavelength Sensitivity to an Exposure Source)
the total integral and absolute error values (see Section 15 on
Using the Sharp Cut-On Filter or Spectrographic Tech-
precision and bias).
nique
G197 Table for Reference Solar Spectral Distributions: Di-
5. Significance and Use
rect and Diffuse on 20° Tilted and Vertical Surfaces
5.1 Weathering and durability testing often requires the
G207 Test Method for Indoor Transfer of Calibration from
computation of the effects of radiant exposure of materials to
Reference to Field Pyranometers
various optical radiation sources, including lamps with varying
3. Terminology
spectral power distributions and outdoor and simulated sun-
light as in Test Methods E972, G130, and G207.
3.1 Definitions—The definitions given in Terminologies
E772 and G113 are applicable to this test method.
5.2 The purpose of this test method is to foster greater
3.2 Definitions of Terms Specific to This Standard: consistency and comparability of weathering and durability test
results between various exposure regimes, calculation of ma-
3.2.1 first difference, n—the difference, d1 , between adja-
i
cent ordinate values, d1 = y +1 - y . An approximation of the terials properties, and laboratories with respect to numerical
i i i
results that depend upon the integration of spectral distribution
first derivative of the function represented by the tabulated
data. data.
3.2.2 second difference, n—the difference d2 , between ad-
5.3 Changes in the optical properties of materials such as
i
jacent first differences (as defined in 3.2.1) in tabulated data;
spectral reflectance, transmittance, or absorptance are often the
namely d2 = d1 +1 – d1 . An approximation of the second
measure of material stability or usefulness in various applica-
i i i
derivative of the function represented by the tabulated data.
tions. Computation of the material responses to exposure to
radiant sources mentioned above requires the integration of
3.3 For the purposes of this standard, the terms “integral”
measured wavelength-dependent digital data, sometimes in
and “integration” are used in the sense of a computed numeri-
conjunction with tabulated wavelength-dependent reference or
cal approximation to a definite integral of continuous functions
comparison data.
represented by tabulated or measured numerical (digital) data
as functions of wavelength. The approximations are computed
5.4 This test method specifies and describes the Modified
as the summation of discrete magnitudes computed according
Trapezoid Rule as a single reasonably accurate and easily
to the method. The data to be integrated may be interpolated to
implemented integration technique for computing approxima-
achieve consistent wavelength intervals.
tions of spectral source and optical property integrals.
4. Summary of Test Method 5.5 The method includes a procedure for estimating the
approximate absolute and relative (percent) error in the esti-
4.1 To compute the integral of the products of two spectral
mated spectral integrals.
data sets, such as a reference Spectrum, E(λ), (for example
reference spectra such as Standard Tables G173, G177, and 5.6 The method includes a procedure to construct data sets
G197), or the spectral content of calibration or other sources that match in spectral wavelength and spectral wavelength
G214 − 23
interval, which does not have to be uniform over the spectral 8.2 Electrical (high voltage, current) and thermal (hot
range of interest. Uniform spectral intervals simplify some of surfaces, intense infrared radiation) hazards may be
the calculations, but are not required. encountered, especially when using high intensity optical
radiation sources.
6. Interferences
6.1 Closed form expressions such as simple functions,
9. Sampling, Test Specimens, and Test Units
spectral properties, and source functions are rarely available,
9.1 Care must be taken to ensure that the units of wave-
preventing analytical solution to integration of those functions.
length and amplitude of the data under analysis are consistent.
6.2 Digitized or tabulated data are only approximations to
Any scaling or unit conversion applied to the original data shall
the continuous spectral property and source functions found in
be documented. Examples are conversion from wavelength
nature.
-6 -9
units of microns (10 m) to nanometres (10 m) for units of
6.3 Mismatched spectral abscissae and spectral data inter-
wavelength; or microwatts per square metre to watts per square
vals (steps) for two or more spectral data sets must be adjusted
metre for flux density.
to match at least one of the spectral data sets. Simple linear
9.2 Sampling of data at uniform wavelength intervals or
interpolation is suggested as a means of putting data sets in a
step sizes will simplify the computations described in the
form where they can be multiplied or otherwise combined. The
Procedure, Section 12.
data sets should then all match a selected (usually the highest
resolution, or smallest step interval) data set. The wavelength
9.3 As mentioned in subsection 6.3, the wavelength interval
intervals do not need to be uniform, just consistent between the
between data points is not required to be uniform or constant,
multiple data sets. just consistent between the multiple data sets. Eq 1-6 applied to
each interval will ensure the correct individual areas between
6.4 Interpolation to produce matching spectral wavelengths
data points are accounted for.
and data intervals can introduce additional uncertainty in
integrated data, above and beyond the error due to the
9.4 When combinations of several spectral data sets (such as
integration technique and measurement and instrumentation
products of spectral source data and optical property data) are
uncertainty.
desired, the wavelength interval or step size between data
points should match. If not, the spectral data should be
7. Apparatus
interpolated to match the data set with the shortest (smallest)
7.1 A digital computer with computing power, storage
step size. Alternatively, all data sets can be interpolated to a
capacity, and capable of ingesting the spectral data in question
single, consistent wavelength step size selected by the user.
and processing it with applications suitable for analyzing data,
The technique for matching up the wavelength step size must
such as spreadsheet software or mathematical analysis soft-
be reported.
ware.
7.2 For applications requiring measurement of spectral dis-
10. Preparation of Apparatus
tribution of sources (such as Specification E927, Practice
10.1 If spectral data or optical properties are to be measured,
G151, or Test Methods G130 and G207), a spectroradiometer
the spectroradiometer(s) used should be properly calibrated
calibrated in accordance with Test Method G138 is required.
and configured for the appropriate measurements.
7.3 For applications requiring measurement of spectral
10.2 If spectral properties of materials are to be measured,
absorptance, reflectance, and transmittance of materials such as
the spectrophotometer(s) used should be calibrated as recom-
Test Method G138, a spectrophotometer is used.
mended by the manufacturer or in accordance with Practice
7.3.1 If the measured data alone is to be integrated, this
E275.
method applies directly.
7.3.2 If the measured data is to be used in conjunction with
10.3 If only tabulated or modeled spectral data are to be
other measured or tabulated data, it is recommended that the
analyzed, the data should be incorporated in the appropriate
spectral step interval and data point wavelengths match the
digital form for processing by the chosen analysis software.
data set with the smallest wavelength interval as closely as
Tabulated data can be entered by hand or copied and pasted
possible.
from electronic documents.
7.3.3 If possible, use the smallest wavelength step interval
10.4 Output data from spectral models should be generated
available for the spectroradiometer measurements that is com-
and formatted for electronic processing. The spectral model
patible with the smallest interval step size in the other data sets.
inputs and details of the configuration(s) of the model should
The other data sets (with larger data intervals) can then be
be documented.
interpolated to the measured data intervals.
7.3.3.1 It is recommended that simple linear interpolation, if
10.5 All data should be double checked for consistent units
needed, be accomplished in accordance with subsection 12.6.1.
of wavelength and amplitude.
8. Hazards
11. Calibration and Standardization
8.1 Hazardous levels of ultraviolet or concentrated solar or
artificial optical radiation may be encountered in the process of 11.1 A spectroradiometer and a spectrophotometer used to
measuring source spectra. collect spectral source or optical property data must be
G214 − 23
calibrated according to manufacturer’s specifications and trace- Therefore, for uniform step h, the total area under curve is
ability to recognized National Measurement Institution refer- expressed as:
ence standards. Examples are reference standard lamps or
n21
A 5 0.5 × h × y 1 1 2 × Σ y 1 y (6)
~ !
2 i n
standards of reflectance. See Test Methods G138 or E903 for
NOTE 1—For data with variable h, the above calculations must be done
details.
independently for each segment of the data with the same h.
11.2 Standardization of the wavelength step size or interval
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: G214 − 16 G214 − 23
Standard Test Method for
Integration of Digital Spectral Data for Weathering and
Durability Applications
This standard is issued under the fixed designation G214; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This test method specifies a single relatively simple method to implement, common integration technique, the Modified
Trapezoid Rule, to integrate digital or tabulated spectral data. The intent is to produce greater consistency and comparability of
weathering and durability test results between various exposure regimes, calculation of materials properties, and laboratories with
respect to numerical results that depend upon the integration of spectral distribution data.
1.2 Weathering and durability testing often requires the computation of the effects of radiant exposure of materials to various
optical radiation sources, including lamps with varying spectral power distributions and outdoor and simulated sunlight. Changes
in the spectrally dependent optical properties of materials, in combination with exposure source spectral data, are often used to
evaluate the effect of exposure to radiant sources, develop activation spectra (Practice G178), and classify, evaluate, or rate sources
with respect to reference or exposure source spectral distributions. Another important application is the integration of the original
spectrally dependent optical properties of materials in combination with exposure source spectral data to determine the total energy
absorbed by a material from various exposure sources.
1.3 The data applications described in 1.2 often require the use of tabulated reference spectral distributions, digital spectral data
produced by modern instrumentation, and the integrated version of that data, or combinations (primarily multiplication) of
spectrally dependent data.
1.4 Computation of the material responses to exposure to radiant sources mentioned above require the integration of measured
wavelength dependent digital data, sometimes in conjunction with tabulated wavelength dependent reference or comparison data.
1.5 The term “integration” in the previous sections refers to the numerical approximation to the true integral of continuous
functions, represented by discrete, digital data. There are numerous mathematical techniques for performing numerical integration.
Each method provides different levels of complexity, accuracy, ease of implementation and computational efficiency, and, of
course, resultant magnitudes. Hulstrom, Bird and Riordan (1) demonstrate the differences between results for rectangular (963.56
2 2 2
W/m ), trapezoid rule (962.53 W/m ), and modified trapezoid rule (963.75 W/m ) integration for a single solar spectrum. Thus the
need for a standard integration technique to simplify the comparison of results from different laboratories, measurement
instrumentation, or exposure regimes.
1.6 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
This test method is under the jurisdiction of ASTM Committee G03 on Weathering and Durability and is the direct responsibility of Subcommittee G03.09 on Radiometry.
Current edition approved May 1, 2016July 1, 2023. Published May 2016August 2023. Originally approved in 2015. Last previous edition approved in 20152016 as
G214G214 – 16.–15. DOI: 10.1520/G0214-16.10.1520/G0214-23.
The boldface numbers in parentheses refer to a list of references at the end of this standard.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
G214 − 23
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and healthsafety, health, and environmental practices and determine
the applicability of regulatory limitations prior to use.
1.8 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E275 Practice for Describing and Measuring Performance of Ultraviolet and Visible Spectrophotometers
E424 Test Methods for Solar Energy Transmittance and Reflectance (Terrestrial) of Sheet Materials
E490 Standard Solar Constant and Zero Air Mass Solar Spectral Irradiance Tables
E772 Terminology of Solar Energy Conversion
E903 Test Method for Solar Absorptance, Reflectance, and Transmittance of Materials Using Integrating Spheres
E927 Classification for Solar Simulators for Electrical Performance Testing of Photovoltaic Devices
E971 Practice for Calculation of Photometric Transmittance and Reflectance of Materials to Solar Radiation
E972 Test Method for Solar Photometric Transmittance of Sheet Materials Using Sunlight
E973 Test Method for Determination of the Spectral Mismatch Parameter Between a Photovoltaic Device and a Photovoltaic
Reference Cell
G113 Terminology Relating to Natural and Artificial Weathering Tests of Nonmetallic Materials
G130 Test Method for Calibration of Narrow- and Broad-Band Ultraviolet Radiometers Using a Spectroradiometer
G138 Test Method for Calibration of a Spectroradiometer Using a Standard Source of Irradiance
G151 Practice for Exposing Nonmetallic Materials in Accelerated Test Devices that Use Laboratory Light Sources
G173 Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface
G177 Tables for Reference Solar Ultraviolet Spectral Distributions: Hemispherical on 37° Tilted Surface
G178 Practice for Determining the Activation Spectrum of a Material (Wavelength Sensitivity to an Exposure Source) Using the
Sharp Cut-On Filter or Spectrographic Technique
G197 Table for Reference Solar Spectral Distributions: Direct and Diffuse on 20° Tilted and Vertical Surfaces
G207 Test Method for Indoor Transfer of Calibration from Reference to Field Pyranometers
3. Terminology
3.1 Definitions—The definitions given in Terminologies E772 and G113 are applicable to this test method.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 first difference, n—the difference, d1 , between adjacent ordinate values, d1 = y +1 - y . An approximation of the first
i i i i
derivative of the function represented by the tabulated data.
3.2.2 second difference, n—the difference d2 , between adjacent first differences (as defined in 3.2.1) in tabulated data; namely d2 =
i i
d1 +1 – d1 . An approximation of the second derivative of the function represented by the tabulated data.
i i
3.3 For the purposes of this standard, the terms “integral” and “integration” are used in the sense of a computed numerical
approximation to a definite integral of continuous functions represented by tabulated or measured numerical (digital) data as
functions of wavelength. The approximations are computed as the summation of discrete magnitudes computed according to the
method. The data to be integrated may be interpolated to achieve consistent wavelength intervals.
4. Summary of Test Method
4.1 Given a set of n digital or numerical (tabulated) data y , 1 ≤ i ≤ n, as a function of an independent variable, such as wavelength,
i
λ , compute the area under each trapezoid, A bounded by λ and λ with altitudes (heights) y and y , for 2 < i < n-1, respectively.
i i i i+1 i i+1
A 5 0.5 ×~λ 2 λ ! ×~y 1 y ! (1)
i i11 i i11 i
The uniform factor of ⁄2 is needed to compute the area of a general trapezoid.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
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4.2 Compute the sum, A of the n-2 A areas over the interval from i = 2 to i = n-1.
0 i
A 5 ΣA
0 i
i 5 2.n 2 1 (2)
4.3 The total area A, approximating the integral from λ to λ is computed by adding in the start and end values to A .
1 n 0
Start:A 5 0.5 ×0.5 ×~λ 2 λ ! ×~y 1 y ! (3)
i 2 1 2 1
End: A 5 0.5 ×0.5 × λ 2 λ × y 1 y (4)
~ ! ~ !
n n n21 n n21
Eq 1 can be written A , of height h (in this case each h = (λ – λ )) and altitudes a= y and b = y .
t i+1 i i i+1
A 5 h ×~a 1 b!⁄2 (5)
t
Therefore, for uniform step h, the total area under curve is expressed as:
n21
A 5 0.5 ×h × y 1 1 2 × Σ y 1 y (6)
~ !
2 i n
NOTE 1—For data with variable h, the above calculations must be done independently for each segment of the data with the same h.
4.1 To compute the integral of the products of two spectral data sets, such as a reference Spectrum, E(λ), (for example reference
spectra such as Standard Tables G173, G177, and G197), or the spectral content of calibration or other sources (as in Test Methods
G207, G130, and G138) and measured or tabulated spectral optical property data, R(λ) such as transmittance or reflectance as
measured in accordance with Test Method E903 and E424 and Practice E971, or spectral mismatch errors such as in Test Method
E973, it is necessary for all data sets to have identical wavelength (λi) and wavelength intervals (λi+1 – λi). Then the appropriate
products E(λi)·R(λi) are computed and treated using the procedures in 4.112.1 to 4.312.3. If the spectral wavelength intervals are
different, one data set (usually with the smallest or shortest wavelength interval, should be selected as the data set, M(λ), with
which to match all other data sets wavelength intervals. The other data sets should be interpolated, using linear interpolation, to
obtain values at wavelength values and intervals identical to the selected M(λ).
4.1.1 When interpolating data sets, it is recommended that the data set with the coarsest or largest wavelength step size or interval
be interpolated to the step size of the data set with the smaller step size or interval.
4.2 Compute an estimate for the absolute error in the integration based on the wavelength limits for the integral, the average
wavelength interval of the data, and the average of the second differences of the spectral data. Compute the estimated relative
(percentage) error in integral approximation based on the total integral and absolute error values (see Section 15 on precision and
bias).
5. Significance and Use
5.1 Weathering and durability testing often requires the computation of the effects of radiant exposure of materials to various
optical radiation sources, including lamps with varying spectral power distributions and outdoor and simulated sunlight as in Test
Methods E972, G130, and G207.
5.2 The purpose of this test method is to foster greater consistency and comparability of weathering and durability test results
between various exposure regimes, calculation of materials properties, and laboratories with respect to numerical results that
depend upon the integration of spectral distribution data.
5.3 Changes in the optical properties of materials such as spectral reflectance, transmittance, or absorptance are often the measure
of material stability or usefulness in various applications. Computation of the material responses to exposure to radiant sources
mentioned above requires the integration of measured wavelength-dependent digital data, sometimes in conjunction with tabulated
wavelength-dependent reference or comparison data.
5.4 This test method specifies and describes the Modified Trapezoid Rule as a single reasonably accurate and easily implemented
integration technique for computing approximations of spectral source and optical property integrals.
5.5 The method includes a procedure for estimating the approximate absolute and relative (percent) error in the estimated spectral
integrals.
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5.6 The method includes a procedure to construct data sets that match in spectral wavelength and spectral wavelength interval,
which does not have to be uniform over the spectral range of interest. Uniform spectral intervals simplify some of the calculations,
but are not required.
6. Interferences
6.1 Closed form expressions such as simple functions, spectral properties, and source functions are rarely available, preventing
analytical solution to integration of those functions.
6.2 Digitized or tabulated data are only approximations to the continuous spectral property and source functions found in nature.
6.3 Mismatched spectral abscissae and spectral data intervals (steps) for two or more spectral data sets must be adjusted to match
at least one of the spectral data sets. Simple linear interpolation is suggested as a means of putting data sets in a form where they
can be multiplied or otherwise combined. The data sets should then all match a selected (usually the highest resolution, or smallest
step interval) data set. The wavelength intervals do not need to be uniform, just consistent between the multiple data sets.
6.4 Interpolation to produce matching spectral wavelengths and data intervals can introduce additional uncertainty in integrated
data, above and beyond the error due to the integration technique and measurement and instrumentation uncertainty.
7. Apparatus
7.1 A digital computer with computing power, storage capacity, and capable of ingesting the spectral data in question and
processing it with applications suitable for analyzing data, such as spreadsheet software or mathematical analysis software.
7.2 For applications requiring measurement of spectral distribution of sources (such as Specification E927, Practice G151, or Test
Methods G130 and G207), a spectroradiometer calibrated in accordance with Test Method G138 is required.
7.3 For applications requiring measurement of spectral absorptance, reflectance, and transmittance of materials such as Test
Method G138, a spectrophotometer is used.
7.3.1 If the measured data alone is to be integrated, this method applies directly.
7.3.2 If the measured data is to be used in conjunction with other measured or tabulated data, it is recommended that the spectral
step interval and data point wavelengths match the data set with the smallest wavelength interval as closely as possible.
7.3.3 If possible, use the smallest wavelength step interval available for the spectroradiometer measurements that is compatible
with the smallest interval step size in the other data sets. The other data sets (with larger data intervals) can then be interpolated
to the measured data intervals.
7.3.3.1 It is recommended that simple linear interpolation, if needed, be accomplished in accordance with subsection 12.3.112.6.1.
8. Hazards
8.1 Hazardous levels of ultraviolet or concentrated solar or artificial optical radiation may be encountered in the process of
measuring source spectra.
8.2 Electrical (high voltage, current) and thermal (hot surfaces, intense infrared radiation) hazards may be encountered, especially
when using high intensity optical radiation sources.
9. Sampling, Test Specimens, and Test Units
9.1 Care must be taken to ensure that the units of wavelength and amplitude of the data under analysis are consistent. Any scaling
or unit conversion applied to the original data shall be documented. Examples are conversion from wavelength units of microns
-6 -9
(10 m) to nanometres (10 m) for units of wavelength; or microwatts per square metre to watts per square metre for flux density.
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9.2 Sampling of data at uniform wavelength intervals or step sizes will simplify the computations described in the Procedure,
Section 12.
9.3 As mentioned in subsection 6.3, the wavelength interval between data points is not required to be uniform or constant, just
consistent between the multiple data sets. Eq 1-6 applied to each interval will ensure the correct individual areas between data
points are accounted for.
9.4 When combinations of several spectral data sets (such as products of spectral source data and optical property data) are
desired, the wavelength interval or step size between data points should match. If not, the spectral data should be interpolated to
match the data set with the shortest (smallest) step size. Alternatively, all data sets can be interpolated to a single, consistent
wavelength step size selected by the user. The technique for matching up the wavelength step size must be reported.
10. Preparation of Apparatus
10.1 If spectral data or optical properties are to be measured, the spectroradiometer(s) used should be properly calibrated and
configured for the appropriate measurements.
10.2 If spectral properties of materials are to be measured, the spectrophotometer(s) used should be calibrated as recommended
by the manufacturer or in accordance with Practice E275.
10.3 If only tabulated or modeled spectral data are to be analyzed, the data should be incorporated in the appropriate digital form
for processing by the chosen analysis software. Tabulated data can be entered by hand or copied and pasted from electronic
documents.
10.4 Output data from spectral models should be generated and formatted for electronic processing. The spectral model inputs and
details of the configuration(s) of the model should be documented.
10.5 All data should be double checked for consistent units of wavelength and amplitude.
11. Calibration and Standardization
11.1 A spectroradiometer and a spectrophotometer used to collect spectral source or optical property data must be calibrated
according to manufacturer’s specifications and traceability to recognized National Measurement Institution reference st
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