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**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.

**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)2 demonstrate the differences between results for rectangular (963.56 W/m^{2}), trapezoid rule (962.53 W/m^{2}), and modified trapezoid rule (963.75 W/m^{2}) 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.

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 health practices and determine the applicability of regulatory limitations prior to use.*

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**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 Specification for Solar Simulation for Photovoltaic Testing

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

**ICS Code**

ICS Number Code 17.180.20 (Colours and measurement of light)

**UNSPSC Code**

UNSPSC Code

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**DOI:** 10.1520/G0214-16

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**Citation Format**

ASTM G214-16, Standard Test Method for Integration of Digital Spectral Data for Weathering and Durability Applications, ASTM International, West Conshohocken, PA, 2016, www.astm.org

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