ASTM E903-20

Standard Test Method for Solar Absorptance, Reflectance, and Transmittance of Materials Using Integrating Spheres

SIGNIFICANCE AND USE
5.1 Solar-energy absorptance, reflectance, and transmittance are important in the performance of all solar energy systems ranging from passive building systems to central receiver power systems. This test method provides a means for determining these values under fixed conditions that represent an average that would be encountered during use of a system in the temperate zone.  
5.2 Solar-energy absorptance, reflectance, and transmittance are important for thermal control of spacecraft and the solar power of extraterrestrial systems. This test method also provides a means for determining these values for extraterrestrial conditions.  
5.3 This test method is designed to provide reproducible data appropriate for comparison of results among laboratories or at different times by the same laboratory and for comparison of data obtained on different materials.  
5.4 This test method has been found practical for smooth materials having both specular and diffuse optical properties. Materials that are textured, inhomogeneous, patterned, or corrugated require special consideration.  
5.4.1 Surface roughness may be introduced by physical or chemical processes, such as pressing, rolling, etching, or deposition of films or chemical layers on materials, resulting in textured surfaces.  
5.4.2 The magnitude of surface roughness with respect to the components of the spectrophotometer and attachments (light beam sizes, sphere apertures, sample holder configuration) can significantly affect the accuracy of measurements using this test method.  
5.4.3 Even if the repeatability, or precision of the measurement of textured materials is good, including repeated measurements at various locations within or orientations of the sample, the different characteristics of different spectrophotometers in different laboratories may result in significant differences in measurement results.  
5.4.4 In the context of 5.4.3, the term ‘significant’ means differences exceeding the calibration or m...
SCOPE
1.1 This test method covers the measurement of spectral absorptance, reflectance, and transmittance of materials using spectrophotometers equipped with integrating spheres.  
1.2 Methods of computing solar weighted properties from the measured spectral values are specified.  
1.3 This test method is applicable to materials having both specular and diffuse optical properties.  
1.4 This test method is applicable to material with applied optical coatings with special consideration for the impact on the textures of the material under test.  
1.5 Transmitting sheet materials that are inhomogeneous, textured, patterned, or corrugated require special considerations with respect to the applicability of this test method. Test Method E1084 may be more appropriate to determine the bulk optical properties of textured or inhomogeneous materials.  
1.6 For homogeneous materials this test method is preferred over Test Method E1084.  
1.7 This test method refers to applications using standard reference solar spectral distributions but may be applied using alternative selected spectra as long as the source and details of the solar spectral distribution and weighting are reported.  
1.8 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.9 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.

General Information

• Status: Published
• Publication Date: 30-Sep-2020
• ICS: 77.140.80 - Iron and steel castings
• Technical Committee: E44 - Solar, Geothermal and Other Alternative Energy Sources
• Drafting Committee: E44.20 - Optical Materials for Solar Applications

Relations

• 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 E2554-18 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
• Effective Date: 01-Apr-2018
• Refers: ASTM E2554-18e1 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
• Effective Date: 01-Apr-2018
• Refers: ASTM E772-13 - Standard Terminology of Solar Energy Conversion
• Effective Date: 01-Sep-2013
• Refers: ASTM E2554-13 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
• Effective Date: 01-Apr-2013
• Refers: ASTM E772-11 - Standard Terminology of Solar Energy Conversion
• Effective Date: 01-Sep-2011
• Refers: ASTM E971-11 - Standard Practice for Calculation of Photometric Transmittance and Reflectance of Materials to Solar Radiation
• Effective Date: 15-Aug-2011
• Refers: ASTM E1175-87(2009) - Standard Test Method for Determining Solar or Photopic Reflectance, Transmittance, and Absorptance of Materials Using a Large Diameter Integrating Sphere
• Effective Date: 01-Apr-2009
• Refers: ASTM E1084-86(2009) - Standard Test Method for Solar Transmittance (Terrestrial) of Sheet Materials Using Sunlight
• Effective Date: 01-Apr-2009
• Refers: ASTM E275-08 - Describing and Measuring Performance of Ultraviolet and Visible Spectrophotometers
• Effective Date: 15-Oct-2008
• Refers: ASTM G197-08 - Standard Table for Reference Solar Spectral Distributions: Direct and Diffuse on 20<span class='unicode'>°</span> Tilted and Vertical Surfaces
• Effective Date: 01-Jun-2008
• Refers: ASTM G173-03(2008) - Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37&#176; Tilted Surface
• Effective Date: 01-Jun-2008
• Refers: ASTM E2554-07 - Standard Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method in a Single Laboratory Using a Control Sample Program
• Effective Date: 01-May-2007
• Refers: ASTM E424-71(2007) - Standard Test Methods for Solar Energy Transmittance and Reflectance (Terrestrial) of Sheet Materials
• Effective Date: 01-Mar-2007
• Refers: ASTM E490-00a(2006) - Standard Solar Constant and Zero Air Mass Solar Spectral Irradiance Tables
• Effective Date: 01-Apr-2006

Overview

ASTM E903-20 is a widely recognized standard developed by ASTM International for determining the solar absorptance, reflectance, and transmittance of various materials using integrating sphere spectrophotometers. These optical properties are critical for understanding and optimizing the performance of materials used in solar energy systems, ranging from passive building elements to advanced photovoltaic and extraterrestrial applications. By utilizing standardized methods and calibrations, ASTM E903-20 ensures reproducible and comparable data on how materials interact with the solar spectrum.

Key Topics

• Measurement Techniques:

  • The standard specifies methods for measuring spectral absorptance, reflectance, and transmittance via integrating sphere spectrophotometers.
  • It supports both specular (mirror-like) and diffuse (scattered light) optical properties.
  • Procedures include correction for measurement errors using appropriate reference and working standards.

• Material Compatibility:

  • Applicable to smooth and homogeneous materials, as well as those with optical coatings.
  • Materials that are textured, inhomogeneous, patterned, or corrugated require special considerations to ensure accurate measurements.
  • For certain complex or highly scattering materials, alternate methods like ASTM E1084 may be recommended.

• Solar Weighted Calculations:

  • Provides guidance on calculating solar-weighted optical properties using standard terrestrial or extraterrestrial solar spectral distributions.
  • Offers methods for photovoltaic-specific calculations, accounting for photon energy relevant to the bandgap of absorber materials.

• Reporting Requirements:

  • Detailed identification of tested material, measurement conditions, and calculated solar optical properties must be reported, including estimated accuracy and uncertainty.
  • Instrument information and reference solar spectrum used are to be documented for traceability and comparison.

Applications

• Solar Photovoltaic and Thermal Systems:

  • Selection and characterization of materials for solar panels, collectors, and concentrators.
  • Optimization of solar absorptance and reflectance in energy-efficient building envelopes, such as cool roofs and advanced glazing.

• Spacecraft and Extraterrestrial Systems:

  • Assessment of materials for thermal control in satellites and extraterrestrial solar power systems, considering space-specific spectral distributions.

• Material Development and Quality Control:

  • Comparative analysis of optical performance across product batches and between different laboratories.
  • Benchmarking innovations in optical coatings, films, and textured materials for solar applications.

• Research and Regulatory Compliance:

  • Supporting academic research into material science and renewable energy technologies.
  • Assisting manufacturers and engineers in fulfilling international standards and sustainability requirements.

Related Standards

To maximize measurement reliability and ensure consistency with ASTM E903-20, the following standards are commonly referenced:

• ASTM E275 - Describing and measuring performance of ultraviolet and visible spectrophotometers.
• ASTM E424 - Test methods for solar energy transmittance and reflectance of sheet materials.
• ASTM E490 - Solar constant and spectral irradiance reference data for extraterrestrial applications.
• ASTM E1084 - Alternative for measuring bulk optical properties of textured or inhomogeneous materials.
• ASTM E1175, E971 - Related photometric and outdoor solar measurement methods.
• ASTM G173, G197 - Reference tables for solar spectral irradiance, both direct and diffuse, on various surfaces.
• CIE 38, CIE 44 - International Commission on Illumination guidelines for radiometric and reflection measurements.

Practical Value

Implementing ASTM E903-20 benefits industries and researchers working with solar technologies by:

• Providing standardized, reproducible, and comparable methods for evaluating materials' solar optical performance.
• Facilitating data-driven material selection for maximizing energy efficiency and performance in solar-related systems.
• Supporting compliance with international standards and enhancing the credibility of reported optical data.

Keywords: ASTM E903-20, solar absorptance, solar reflectance, solar transmittance, integrating sphere, spectrophotometer, optical properties, solar energy materials, photovoltaic, building envelopes, material testing standard.

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:E903 −20
Standard Test Method for
Solar Absorptance, Reflectance, and Transmittance of
Materials Using Integrating Spheres
This standard is issued under the fixed designation E903; 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 2. Referenced Documents
1.1 This test method covers the measurement of spectral
2.1 ASTM Standards:
absorptance, reflectance, and transmittance of materials using
E275 Practice for Describing and Measuring Performance of
spectrophotometers equipped with integrating spheres.
Ultraviolet and Visible Spectrophotometers
E424 Test Methods for Solar Energy Transmittance and
1.2 Methods of computing solar weighted properties from
Reflectance (Terrestrial) of Sheet Materials
the measured spectral values are specified.
E490 Standard Solar Constant and Zero Air Mass Solar
1.3 This test method is applicable to materials having both
Spectral Irradiance Tables
specular and diffuse optical properties.
E772 Terminology of Solar Energy Conversion
1.4 This test method is applicable to material with applied
E971 Practice for Calculation of Photometric Transmittance
optical coatings with special consideration for the impact on
and Reflectance of Materials to Solar Radiation
the textures of the material under test.
E1084 Test Method for Solar Transmittance (Terrestrial) of
Sheet Materials Using Sunlight
1.5 Transmitting sheet materials that are inhomogeneous,
E1175 Test Method for Determining Solar or Photopic
textured, patterned, or corrugated require special consider-
Reflectance, Transmittance, andAbsorptance of Materials
ations with respect to the applicability of this test method. Test
Using a Large Diameter Integrating Sphere
Method E1084 may be more appropriate to determine the bulk
E2554 Practice for Estimating and Monitoring the Uncer-
optical properties of textured or inhomogeneous materials.
tainty of Test Results of a Test Method Using Control
1.6 For homogeneous materials this test method is preferred
Chart Techniques
over Test Method E1084.
G173 TablesforReferenceSolarSpectralIrradiances:Direct
1.7 This test method refers to applications using standard
Normal and Hemispherical on 37° Tilted Surface
reference solar spectral distributions but may be applied using
G197 Table for Reference Solar Spectral Distributions: Di-
alternative selected spectra as long as the source and details of
rect and Diffuse on 20° Tilted and Vertical Surfaces
the solar spectral distribution and weighting are reported.
2.2 Other Documents:
1.8 This standard does not purport to address all of the
Federal Test Method Standard No. 141, Method 6101
safety concerns, if any, associated with its use. It is the
ASHRAE Standard 74-1988
responsibility of the user of this standard to establish appro-
CIE 38 Radiometric and Photometric Characteristics of Ma-
priate safety, health, and environmental practices and deter-
terials and their Measurement
mine the applicability of regulatory limitations prior to use.
CIE 44 Absolute Methods for Reflection Measurement
1.9 This international standard was developed in accor-
NIST SP 250-48 Spectral Reflectance
dance with internationally recognized principles on standard-
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
mendations issued by the World Trade Organization Technical
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Barriers to Trade (TBT) Committee.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
AvailablefromStandardizationDocuments,OrderDesk,Building4,SectionD,
700 Robbins Ave., Philadelphia, PA 19111-5049, Attn: NPODS.
1 4
This test method is under the jurisdiction of ASTM Committee E44 on Solar, Available from American Society of Heating, Refrigeration, and Air-
Geothermal and OtherAlternative Energy Sources and is the direct responsibility of Conditioning Engineers, Inc., 191 Tullie Circle, NE. Atlanta GA 30329.
Subcommittee E44.20 on Optical Materials for Solar Applications. Available from U.S. National Committee of the CIE (International Commission
Current edition approved Oct. 1, 2020. Published October 2020. Originally on Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond
approved in 1982. Last previous edition approved in 2012 as E903–12. DOI: St., Salem, MA 01970, http://www.cie-usnc.org.
10.1520/E0903-20. Online, Available: https://www.nist.gov/publications/spectral-reflectance
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E903−20
NIST SP 250-69 Regular Spectral Transmittance power systems. This test method provides a means for deter-
mining these values under fixed conditions that represent an
3. Terminology
average that would be encountered during use of a system in
the temperate zone.
3.1 For definitions of terms used in this test method, refer to
Terminology E772.
5.2 Solar-energyabsorptance,reflectance,andtransmittance
are important for thermal control of spacecraft and the solar
3.2 Definitions of Terms Specific to This Standard:
power of extraterrestrial systems. This test method also pro-
3.2.1 integrating sphere, n—an optical device used to either
vides a means for determining these values for extraterrestrial
collect flux reflected or transmitted from a sample into a
conditions.
hemisphere or to provide isotropic irradiation of a sample from
a complete hemisphere. It consists of a cavity that is approxi-
5.3 This test method is designed to provide reproducible
mately spherical in shape with apertures for admitting and
data appropriate for comparison of results among laboratories
detecting flux and usually having additional apertures over
or at different times by the same laboratory and for comparison
which sample and reference specimens are placed.
of data obtained on different materials.
3.2.2 near normal-hemispherical, adj—indicates irradiance
5.4 This test method has been found practical for smooth
to be directional near normal to the specimen surface and the
materials having both specular and diffuse optical properties.
flux leaving the surface or medium is collected over an entire
Materials that are textured, inhomogeneous, patterned, or
hemisphere for detection.
corrugated require special consideration.
3.2.3 photovoltaic solar, adj—referring to an optical prop- 5.4.1 Surface roughness may be introduced by physical or
erty; indicates a weighted average of the spectral property
chemical processes, such as pressing, rolling, etching, or
using the number of photons per second per unit area per unit deposition of films or chemical layers on materials, resulting in
wavelength derived from a standard solar irradiance distribu-
textured surfaces.
tion as the weighting function. 5.4.2 The magnitude of surface roughness with respect to
the components of the spectrophotometer and attachments
3.2.4 smooth, adj—havinganevenandlevelsurface,having
(light beam sizes, sphere apertures, sample holder configura-
no roughness or projections. Free from inequalities or uneven-
tion) can significantly affect the accuracy of measurements
ness of surface.
using this test method.
3.2.5 specular, adj—indicates the flux leaves a surface or
5.4.3 Even if the repeatability, or precision of the measure-
medium at an angle that is numerically equal to the angle of
ment of textured materials is good, including repeated mea-
incidence, lies in the same plane as the incident ray and the
surements at various locations within or orientations of the
perpendicular, but is on the opposite side of the perpendicular
sample, the different characteristics of different spectropho-
to the surface.
tometers in different laboratories may result in significant
3.2.5.1 Discussion—Diffuse has been used in the past to
differences in measurement results.
refer to hemispherical collection (including the specular com-
5.4.4 In the context of 5.4.3, the term ‘significant’ means
ponent). This use is deprecated in favor of the more precise
differences exceeding the calibration or measurement
term hemispherical.
uncertainty, or both, established for the spectrophotometers
3.2.6 textured, adj—the nature of a surface other than
involved, through measurement of or calibration with standard
smooth. Having some degree of unevenness, roughness or
reference materials.
projections.
5.4.5 The caveats of 5.4.3 and 5.4.4 apply as well to
measurement of smooth inhomogeneous or diffusing materials,
4. Summary of Test Method
where incident light may propogate to the edge of the test
4.1 Measurements of spectral near normal-hemispherical
material and be ‘lost’ with respect to the measurement.
transmittance (or reflectance) are made over the spectral range
5.5 This test method describes measurements accomplished
from 300 to 2500 nm with an integrating sphere spectropho-
over wider spectral ranges than the Photopic response of the
tometer.
human eye. Measurements are typically made indoors using
4.2 The solar transmittance, reflectance, or absorptance is
lightsourcesotherthannaturalsunlight,thoughitispossibleto
obtained by calculating a weighted average with a standard or
configure systems using natural sunlight as the illumination
selected solar spectral irradiance as the weighting function by
source, as in Practice E424. Practice E971 describes outdoor
eitherdirectcalculationofsuitableconvolutionintegrals,orthe
methodsusingnaturalsunlightoverthespectralresponserange
weighted (see 8.3.3) or selected (see 8.3.4) ordinate method.
of the human eye.
5.6 Light diffracted by gratings is typically significantly
5. Significance and Use
polarized. For polarizing samples, measurement data will be a
5.1 Solar-energyabsorptance,reflectance,andtransmittance
function of the orientation of the sample. Polarization effects
are important in the performance of all solar energy systems
may be detected by measuring the sample with rotation at
ranging from passive building systems to central receiver
various angles about the normal to the samples.
6. Apparatus
Online, Available: https://www.nist.gov/publications/nist-measurement-
services-regular-spectral-transmittance 6.1 Instrumentation:
E903−20
6.1.1 IntegratingSphereSpectrophotometer—Aspectropho- 6.1.1.4 Some commercial instruments have sample ports
tometer with an integrating sphere attachment capable of equipped with quartz windows. There is a possibility for
measuring the spectral characteristics of the test specimen or multiple reflections to occur between sample and window
material over the solar spectral region from 300 to 2500 nm is surfaces and miss or inadvertently enter the sample port. In
required. Double beam, ratio recording instruments are recom- transmission measurement mode ensure that any light reflected
mended because of their low sensitivity to drift in source from the sample is collected at the sample port. Best practice is
brightness or amplifier gain. Recording spectrophotometers to ensure that the sample does not interact with the optical
with integrating spheres that have been found satisfactory for system of the spectrophotometer.
this purpose are commercially available.
6.1.1.5 In spectrophotometer systems with multiple gratings
and multiple detectors, discontinuities in the spectral data due
NOTE 1—For determining extraterrestrial solar optical properties using
to changes in bandwidth, grating efficiency, or detector sensi-
Standard E490, the spectral region should extend down to 250 nm.
NOTE 2—This test method is used primarily for solar thermal and some tivity may occur at grating and detector switch over points. If
photovoltaic applications that require the full spectral range be covered.
observed, the magnitude and cause of the discontinuity should
There are other applications for which a narrower range is sufficient and
be investigated. Careful calibration over the entire spectral
that could otherwise use the procedures of this test method. For example,
band of interest should account for such discrepancies.
some applications involving photovoltaic cells utilize a narrower spectral
responsive range and some others pertain only to visible light properties
6.2 Standards:
that have an even narrower spectral range. In such cases, the user of the
test method is permitted to use a narrower range. Similarly, a user with an 6.2.1 In general, both reference and working (comparison)
applicationrequiringabroaderspectralrangeispermittedtouseabroader
standards are required.
range. Any deviations from the spectral range of this test method should
be noted in the report.
NOTE 5—Reference standards are the primary standard for the calibra-
tion of instruments and working standards. Reference standards that have
6.1.1.1 The integrating sphere shall be either a wall-
high specular reflectance, high diffuse reflectance, and low diffuse
mounted type such that the specimen may be placed in direct
reflectance were formerly available from the National Institute of Stan-
contact with the rim of an aperture in the sphere wall for
dards and Technology as Standard Reference Materials (SRM). See
transmittance and reflectance measurements or center-mount
NIST Special Publications 250-48 and 250-69. However, the
type (Edwards type) such that the specimen is mounted in the low demand and high cost of these materials has been replaced
center of the sphere for reflectance and absorptance measure- by offers of measurement services from National Metrology
Institutions (NMI) such as NIST. These laboratories offer to
ments.
measure customers samples and report spectral optical proper-
6.1.1.2 The interior of the integrating sphere shall be fin-
ties. These become NIST (or NMI) traceable reference stan-
ished with a stable highly reflecting and diffusing coating.
dards for customers. The customers often include commercial
Sphere coatings having the required properties can be prepared
firms which then produce SRMs and reference standards based
using pressed tetrafluoroethylene polymer powder, or other
on their NMI traceable standards and provide them to their
highly reflective, stable material.
customers along with traceability and uncertainty information.
NOTE 3—For high accuracy (better than 60.01 reflectance units)
These SRMs and reference standards are permitted within the
measurementswithabsolutesphereconfiguration,theratiooftheportarea
context of this standard. Example NMIs include the National
to the sphere wall plus port area should be less than 0.001 (1). In general,
Physical Laboratory (NPL) of the United Kingdom, the Na-
largespheres(>200mm)meettheserequirementsandarepreferredwhile
tional Research Council (NRC) of Canada, the Physical Tech-
small spheres (< 100 mm) can give rise to large errors.
nical Bureau (PTB) of Germany, The National Laboratory of
6.1.1.3 For the evaluation of near normal-hemispherical or
Metrology and Test (LNE-INM) of France, etc.
hemispherical-near-normal reflectance, the direction of the
6.2.1.1 Working standards are used in the daily operation of
incident radiation or the direction of viewing respectively shall
the instrument to provide comparison curves for data reduc-
be between 6 and 12° from the normal to the plane of the
tion. In general, ceramic and vitrified enamel surfaces are
specimen so that the specular component of the reflected
highly durable and desirable. A working standard shall be
energy is not lost through an aperture. Ambient light must be
calibrated by measuring its optical properties relative to the
prevented from entering the sphere by placing a ring of black
properties of the appropriate reference standard using proce-
or white material around the external rim of the specimen ports
dures given in 8.2.
or by covering the entire sphere attachment with a light tight
housing. Black backing or border material may result in
NOTE 6—Even the best standards tend to degrade with continued
significant light absorption or loss, while white backing mate-
handling. They should be handled with care and stored in a clean, safe
rial should be more representative of the sphere interior and
manner. Working standards should be recalibrated periodically and
cleaned, renewed, or replaced if degradation is noticeable.Avoid touching
affect measurement results to a lesser extent. Several accept-
the optical surfaces. Only clean soft cloth gloves should be worn for
able system configurations are illustrated in Appendix X1.
handling the standards. Only lens tissue or sterile cotton is recommended
NOTE 4—The hemispherical near-normal irradiation-viewing mode is for cleaning. This is especially important for reference standards carrying
also allowed under this test method since the Helmholtz reciprocity NIST calibration.
relationshipwhichholdsintheabsenceofpolarizationandmagneticfields
guarantees equivalent results are obtainable.
National Institute of Standards and Technology, Office of Standard Reference
The boldface numbers in parentheses refer to the list of references at the end of Materials, Room B311, Chemistry Bldg.,Washington, DC 20234.Additional details
this standard. covering the appropriate SRMs (2019–2022) are available on request.
E903−20
6.2.2 For transmitting specimens, incident radiation shall be 7.1.3 The most accurate results may be obtained from
used as the standard relative to which the transmitted light is transparent and slightly translucent specimens with two sur-
evaluated. For some applications calibrated transmittance stan- facesthatareessentiallysmooth,orplaneandparallel.Inorder
dards are available. to reduce light scattered out the edges of translucent specimen,
the minimum distance between the edge of the beam and the
6.2.3 For diffuse high-reflectance specimens, a working
edge of the aperture shall be ten times the thickness of the
standard that has high reflectance and is highly diffusing over
specimen. The caveats of 5.4.1 to 5.4.5 should be observed
the range of the solar spectrum is required.
when measuring textured or highly diffusing materials.
NOTE 7—Identified suitable working standards are tablets of pressed
7.1.4 The transmittance of highly scattering translucent
tetrafluoroethylene polymer, BaSO , BaSO -based paints, and white
4 4
samples is not easily measured with an integrating sphere
ceramic tile.
instrument, because a significant portion of the incident flux
6.2.4 For specularly reflecting specimens, a working stan-
will be scattered outside the aperture. For such materials the
dard that is highly specular is required. Identified suitable
standard test method using the sun as a source (Test Methods
working standards are vacuum-deposited thin opaque films of
E1084 or E1175) is preferred. Smith et al. (3) discuss diffuse
metals. All front surface metalized working standards shall be
material transmittance issues (side losses, etc.) and discuss
calibrated frequently with an absolute reflectometer or relative
0.01 (reflectance) accuracy and considerations for beam and
to a standard reference mirror traceable to a national standard-
aperture geometry.
izing laboratory reference before being acceptable in this test
NOTE 11—If such a sample must be measured, the edge losses can be
method. An acceptable working standard for low-specular
greatly reduced by using a circular sample of diameter slightly less than
reflectance is a flat piece of optically polished black glass.
that of the aperture, and coating the edge with silver, using the wet mirror
NIST no longer provides specular reflectance standard refer-
process. Alternatively, small stops can be cemented to the edges of the
ence materials; but will measure user provided mirrors to
sample, so that it can be suspended in the aperture with about half of its
provide traceable calibration data. thickness extending outside the aperture.
7.2 Specimens for Edwards Sphere—The area of the speci-
NOTE 8—Although aluminum is most often used because of its high
reflectance and ease of deposition, it is very unstable and scratches easily. men shall be limited to 0.01 of the surface area of the sphere.
Other metals such as chromium, nickel, and rhodium are much more
NOTE 12—For a 200-mm diameter sphere, the required specimen size
durable. High vacuum (≥ 10 torr) is required for obtaining pure films
would be less than or equal to 20 mm in radius.
with the best optical properties (2).
8. Procedure
6.2.5 For absorber materials, a working standard that has
low reflectance over the range of the solar spectrum is required
8.1 Calibration—Calibrate linearity and wavelength scales
in order to obtain an accurate zero line correction.
of the spectrophotometers as recommended by the manufac-
turerorinaccordancewithPracticeE275.Checkoncalibration
NOTE 9—Black semi-matt porcelain enameled substrates, black
annually.
barbeque, stove, or wrought iron fence paints, and opaque black glass are
suitable working standards. For very low-reflectance materials light traps
8.2 Measurement:
reflecting < 0.005 can be fabricated to calibrate sphere performance.
8.2.1 Correction for 100 % and Zero Line Errors:
NOTE 10—Light traps can be made from a stack of razor blades, a 60°
black cone, or by forming an approximate exponential horn by drawing a
8.2.1.1 Record 100 % and zero line curves at least twice a
glass tube and painting it with high-gloss black paint.
day during testing.
6.2.6 If an absolute sphere is completely free of the flux
NOTE 13—Variations in signal from the two beams are normal, usually
losses referred to in X3.1.2, no working standard is required.A
wavelength dependent, and give rise to nonideal 100 % lines. Similarly,
comparison of the measured reflectance of a primary reference
beam cross talk, light scattering or leaks, and detector noise give rise to a
nonideal zero line. These effects produce errors in the measured ratio of
standardtoitscalibrationvaluewillgiveagoodestimateofthe
the flux reflected by the specimen and the working standard.
error due to flux losses, if any, from a nearly absolute sphere
such as described in Appendix X1, X1.1.2 and X1.1.3.
8.2.1.2 For spheres with separate sample and reference
ports, record the 100 % line curves using identical high-
7. Test Specimens reflectance specimens in both ports. The specimens are iden-
tical in reflectance if the recorded curve does not change when
7.1 Specimens for Wall-Mounting Spheres:
the two specimens are interchanged.
7.1.1 The size of test specimens required depends on the
8.2.1.3 For reflectance measurements, record the zero line
dimensions of the integrating sphere. For wall-mounted
with a perfect absorber or light trap in the sample port.
spheres the specimen must be large enough to cover the
aperture of the sphere. There may be no limit on maximum
NOTE 14—The practice of recording the zero line with the sample beam
blocked at the entrance port is discouraged because the effect of scattered
dimension. For textured or patterned samples, either the
light incident on the sphere wall is not included.
specimen shall be large enough to make a number of measure-
ments over different areas, or several specimens representing 8.2.1.4 For transmittance measurements, record the zero
the different areas of the material shall be used.
line with the sample beam blocked, preferably as far in front of
the entrance port as convenient.
7.1.2 Opaque specimens shall have at least one surface that
is essentially planar over an area large enough to cover the 8.2.2 Reflectance of Opaque Specimen—Comparison Type
aperture of the sphere. Sphere:
E903−20
8.2.2.1 Record the spectral 100 % and zero lines as indi- by first obtaining the solar reflectance as in 8.3 and subtracting
cated in 8.2.1. from 1, that is, τ = 0 in the Kirchoff relationship:
s
8.2.2.2 Record the spectral reflectance of specimen over the
α 1τ 1ρ 51 (4)
s s s
range 300 mm to 2500 mm relative to the working standard by
8.2.6.1 For non-opaque samples, either obtain both the solar
placing the specimen on the sample port and the standard on
reflectance and solar transmittance using the described tech-
the reference port. Include the specular component in the
niques and calculate the solar absorptance by using the
reflectance measurement.
Kirchoff relationship, or use an Edwards-type integrating
8.2.2.3 Compute the spectral reflectance, ρ(λ), for the
sphere instrument with the specimen mounted so that the beam
specimen, at wavelength λ using:
that exits through the back of the specimen is free to fall on the
ρ~λ! 5 ~S 2 Z !⁄~100 2 Z !ρ'~λ! (1)
λ λ λ λ
sphere wall. In this case the sum τ(λ)+ ρ(λ) is measured
where: directly. Then use 8.3 and the Kirchoff relationship to deter-
mine the solar absorptance.
S = recorded specimen reading,
λ
Z = zero line reading,
λ
8.3 Computation of Solar Properties—Solar energy trans-
100 = 100 % line reading, and
λ
mittance or reflectance is computed by the weighted ordinate,
ρ'(λ) = calibrated spectral reflectance for the working stan-
50 selected ordinate, 100 selected ordinate, or photovoltaic
dard or reference, all at wavelength λ.
solar method.
NOTE 15—Slightly different procedures may be required for other
8.3.1 Solar Spectral Irradiance Distribution:
sphere designs.
8.3.1.1 For terrestrial applications, Tables G173 or a repre-
8.2.3 Reflectance of Opaque Specimen in an Absolute
G197, or a specially
sentative terrestrial spectrum, such as
Sphere:
selected and specified terrestrial spectrum, may be used.
ρ~λ! 5 ~S 2 Z !⁄~100 2 Z ! (2)
λ λ λ λ
Calculate the optical properties using either the convolution
integral of the selected spectrum and the measured property,
where:
the ordinate method in 8.3.3, or one of the selected ordinate
100 = 100 % correction obtained with the specimen port
λ
methods described in section 8.3.4 and Appendix X2. For
replaced by a sample having a coating and a curva-
extraterrestrial applications, Standard E490 shall be used.
ture identical to the sphere wall. The zero line
8.3.1.2 Calculate the optical properties using either the
correction for an absolute sphere is usually so small
convolution integral of the selected spectrum and the measured
that it can be neglected.
property, the weighted ordinate method of 8.3.3, or one of the
NOTE 16—Slightly different procedures may be required for other
sphere designs. selectedordinatemethodsdescribedin8.3.4andAppendixX2.
8.3.2 Product of Optical Properties—When calculating so-
8.2.4 For reflectance of transparent or translucent materials
lar optical efficiency of a complicated system such as a
or specimens having transmittance greater than 0.001, back the
reflecting concentrator with an absorber in a transparent
specimen by a light trap or black material having a low
envelope,theproductofρ,τ,andαisrequired.Theappropriate
reflectance (< 0.02) over the 300 to 2500-nm spectral range.
procedure is to measure the spectral optical properties of each
For these measurements, the zero line shall be recorded with
component ρ(λ), α(λ), and τ(λ) respectively and form the
the specimen removed but the light trap or backing still in
product η(λ)= ρ(λ)α(λ)τ(λ) before solar weighting. Calculate
place. Obtain the spectral reflectance following 8.2.2.
η as described in 8.3.3 or 8.3.4. Calculation of η from
8.2.5 Transmittance—Cover the specimen and reference s s
individually weighted properties can lead to substantial error,
ports at the rear of the sphere with surfaces having the same
that is, η ≠ρ α τ (4). See also Section 7.2 of (5).
coating and optical properties as the sphere walls when s s s s
8.3.3 Weighted Ordinates—Obtain the solar reflectance ρ
measuring transmittance (Note 17). Record spectral curves
s
by integrating the spectral reflectance over the standard spec-
without specimen in place. Record spectral curves with the
tral irradiance distribution, E , as follows:
specimen over the specimen beam entrance port of the sphere
λ
over the range 300 mm to 2500 mm. Calculate the spectral n n
ρ 5 Σ ρ ~λ ! E ∆λ ⁄ Σ E ∆λ (5)
s S i λi iD S λi iD
transmittance as:
i51 i51
τ λ 5 S 2 Z ⁄ 100 2 Z (3)
~ ! ~ ! ~ !
λ λ λ λ
Solar transmittance τ or absorptance α , is obtained from a
s s
where: similar expression with ρ(λ) replaced by τ(λ)or α(λ) respec-
tively. Here n is the number of wavelengths for which E is
S = signal recorded with the specimen over the entrance λ
λ
known. The ∆λ, are not constant but are given by:
port, i
Z = zero line reading with the specimen beam blocked
λ ∆λ 5 λ 2 λ ⁄ 2 (6)
~ ! ~ !
i i11 i21
with an opaque material, and
For i = 1 and i = n, one assumes a ∆λ equal to the last
100 = line recorded with no specimen over the specimen
λ
interval, that is, ∆λ = λ – λ and ∆λ = ∆λ – ∆λ .
beam entrance port.
l 2 l n n n-1
NOTE 17—The working standards, 6.2.3, could be used with only a 8.3.4 Selected Ordinates:
small error.
8.3.4.1 In the selected ordinate method, the solar irradiance
8.2.6 Absorptance—For opaque samples record the reflec- distribution is divided into n wavelength intervals each con-
tance spectrum as in 8.2.2. The solar absorptance is calculated taining 1/n of the total irradiance. The spectral reflectance or
E903−20
transmittance of the sample is evaluated at the centroid λ of 9.2 Estimatedprecision(repeatability)andestimatedoverall
i
each interval, λ. The solar reflectance is then calculated as accuracy reported as uncertainty due to combined systematic
i
follows: and statistical (precision) errors. The accuracy and precision
n shall be reported in the same units as the optical property itself.
ρ 51⁄n Σ ρ λ (7)
~ !
s i The method by which the uncertainty was established shall be
i51
reported.
8.3.4.2 The wavelengths λ, for the 50 and 100 selected
i
9.3 Identification of the instrument used. Manufacturer’s
ordinates derived from Tables G173 are provided in Appendix
name and model number including specifications, modifica-
X2.
tions and accessories is sufficient for a commercial instrument.
8.3.5 Photovoltaic Solar:
Other instruments must be described in detail including esti-
8.3.5.1 Photovoltaic solar energy conversion is effective
mations of their accuracy.
only over a wavelength range shorter than the photovoltaic
9.4 Solar spectral irradiance and weighting method used for
absorber’s bandgap wavelength λ . Restricting the longest
g
computation of the solar optical property.
wavelength of the weighting function to λ yields an averaged
g
value of an optical property that is more representative of a
10. Precision and Bias
material’s performance in a photovoltaic system than one
10.1 No material specific information is presented about
averaged over a fixed wavelength interval.
either the precision or bias of this test method. The reproduc-
8.3.5.2 In photovoltaic solar energy conversion, the current
ibility and repeatability of this test method are not provided at
generated, and thus electrical power generated, depends on the
this time because an ASTM Interlaboratory Study (ILS) has
number of photons absorbed in the absorber material. The
never been run. While there have been several attempts to run
number of photons in a wavelength interval depends on the
an ILS since 1982 (the year this standard was originally
spectral irradiance in that interval, E , as well as the energy of
λ
approved), due to a repeated lack of laboratories willing to
photons in that interval; The energy of a photon of a given
participate in a measurement-based ILS one has never been
wavelength E , is given by:
ph
conducted
E 5hc⁄λ (8)
ph
10.2 Uncertainties in the solar optical properties determined
where h is Planck’s constant and c is the speed of light. The
by the application of this test method arise from random errors
number of photons per second per unit area in the spectral
associated with signal detection and electronic processing,
interval, N is given by:
errors introduced by the geometry of the integrating sphere
ph,λ
systemandthedistributionofscatteredorreflectedlight,errors
N 5λE ⁄hc (9)
ph,λ λ
inthevaluesforstandardreferencematerials,sourceilluminate
8.3.5.3 In the photovoltaic solar method, obtain the photo-
beam configuration (size, orientation, and dispersion), sample
voltaic solar reflectance ρ (λ ) as follows:
pv g
orientation, positioning and configuration, and how correctly
m
the spectral solar irradiance used in the calculation matches
Σ ρ λ λ E ∆λ
~ !
S i i λi D
that at the actual location of system deployment. The contri-
i51
ρ λ 5 (10)
~ !
pv g m
butionfromeachofthesesourcesisdiscussedinAppendixX3.
Σ λ E ∆λ
S i λi D
i51 Experience has shown that high accuracy is relatively difficult
to achieve and depends strongly on operator skill, experience,
Here m indicates the index ofλ that is the wavelength equal
i
and care, as well as on equipment design and maintenance.
or most nearly equal to λ .
g
Measurement results are required to be reported at a resolution
Photovoltaicsolartransmittanceτ (λ )orphotovoltaicsolar
pv g
of 0.1%, to permit resolution of incremental improvements in
absorptance α (λ ) is obtained from a similar expression with
pv g
accuracy. However, it is extremely difficult to achieve absolute
ρ(λ) replaced by τ(λ)or α(λ) respectively.
accuracy in any of the optical properties to better than1%to
2 %, or 10 to 20 times the required reporting resolution.
9. Report
References (6, 7, 8) discuss interlaboratory comparison results,
9.1 The report shall include the following:
on the order of 0.02 units, or 2 approximately 2 %.
9.1.1 Complete identification of the material tested, speci-
11. Keywords
men size and thickness, texture or surface contour if any,
description of optical properties such as diffuse or specularly 11.1 absorptance; diffuse; integrating sphere; reflectance;
reflecting, clear or translucent transmitting, etc. smooth; solar absorptance; solar reflectance; solar transmit-
9.1.2 Solar transmittance, absorptance, or reflectance, or all tance; spectral; spectrophotometer; specular; texture; transmit-
three, determined to the nearest 0.001 unit or 0.1 %. tance
E903−20
APPENDIXES
(Nonmandatory Information)
X1. INTEGRATING SPHERE GEOMETRIES
X1.1 A number of different integrating sphere geometries X1.1.1.1 Spheresofthistypesometimeshavespecularports
have been used over the years to obtain the optical reflectance with plugs that can be removed for measuring the diffuse
and transmittance of materials. Each geometry has advantages reflectance with the specular component excluded.
for specific applications. For a thorough understanding of
X1.1.2 Edwards Sphere—A sphere of the Edwards type
sphere applications and performance, Refs 1, 9, 10, and 11
(Fig. X1.2) with a center-mounted sample allows ratio record-
should be consulted. Presented in X1.1.1 through X1.1.4 are
ing of absolute reflectance (12). This geometry is the only one
the geometries felt to be most applicable for the use of this test
in which the angular dependence of reflectance can be easily
method. Many of the comments on specific applications can be
evaluated. By rotating the sample for normal incidence, the
applied to more than one of the geometries. For a discussion of
entrance port becomes a specular trap and diffuse reflectance
errors, see Section 10 and Refs 1 and 9.
with the specular component excluded can also be measured.
X1.1.1 Four-Port Sphere—Because of its versatility, the Finally, since both reflected and transmitted light is collected
four-port geometry shown in Fig. X1.1 is the most common by the sphere, absorptance of transmitting samples can be
sphere supplied with commercially available spectrophotom- directly measured.
eters. The reference and sample beams may either cross as
X1.1.2.1 The errors that can occur are related primarily to
shown or be parallel. The sphere gives the reflectance factor of
the uniformity and diffuseness of the sphere coating. A
the specimen relative to that of the reference material. Cali-
significant drawback is the small sample size required and the
bration with a reference standard is essential. In the transmit-
necessity of placing it inside the sphere.
tance mode the reference and sample ports are covered with
X1.1.3 Wall-Mount “Absolute”—The sphere shown in Fig.
matched references preferably of the same curvature and
X1.3 has a wall-mounted sample that is baffled from the view
material as the sphere wall. The major problem with most
of the detector (11). The ratio signal obtained with this
commercial spheres of this type is that their size is small,
geometry is nearly absolute. Replacing a segment of the sphere
usually less than 100 mm in diameter, so that the ratio of the
wall with a black cavity that traps all the specularly reflected
total port area to the sphere wall area including the ports is
light permits the measurement of the diffuse component only.
large. This can introduce significant errors in a measurement
The addition of the light trap reduces the sphere’s efficiency
due to flux loss. Large errors can also arise if the angular
and shifts the measurement further away from being absolute.
distribution of the light reflected from the specimen is different
After correction for changes in sphere efficiency (4), the
from that reflected by the standard. In transmittance measure-
specular component can be calculated from the difference in
ments of translucent samples, this effect always occurs since
measurements with and without the light trap.
the standard is the nonscattering open port. Careful baffle
design can substantially reduce errors due to different light X1.1.4 Transmittance Sphere—Fig. X1.4 shows measure-
scattering distribution. ment geometry specifically for determining transmittance at
FIG. X1.1Four-port, Comparison-type Integrating Sphere (Most Common)
E903−20
FIG. X1.2Edwards-type, Absolute Integrating Sphere for Center-Mounted Specimen
FIG. X1.3Absolute Integrating Sphere for Wall-Mounted Specimen (11)
near-normal angles of incidence (4). The sphere has only three or view a very limited segment of the sphere wall that is also
ports including the detector and collects nearly all of the baffled from the sample port. In the latter case, low signal-to-
transmitted flux. For maximum freedom from errors due to noise would require long integration times for the detection
differences in specimen scattering properties, the detector shall circuit. All baffles should have high reflectance and can be
be baffled from viewing the sample and either view all the coated with sphere wall material or they can be specular
remaining wall area with an isotropic 2π solid angle response mirrors.
E903−20
FIG. X1.4Integrating Sphere for Transmittance Measurements (11)
X2. COMPUTATIONAL TECHNIQUE FOR TABULATED SELECTED ORDINATE VALUES
X2.1 Wavelength and equal energy values for the 100 and X2.2 Summary of Weighted Ordinate Calculation Steps
50 selected ordinates are based on an interpolation procedure Using Selected Source Spectrum:
based on wavelength intervals bounding equal integrated
X2.2.1 From the original source spectrum, calculate the
power (energy), E , from the first value (E ) to the last value
T o
integral contribution between each adjacent wavelength ac-
(E ) under the spectral curves.
∞
cording to Eq X2.1.
X2.1.1 The area between two adjacent wavelengths in the
X2.2.2 For each successive wavelength interval, add the
spectralcurvesofTablesG173iscomputedusingthetrapezoid
integral for that interval to that of the previous integral to
rule.Thepower P betweenwavelengthλ andλ iscomputed
i i i+1
produce the cumulative integral to each individual wavelength
from:
accordingtotheequationinX2.1.2.Thecumulativetotalatthe
P 5 0.5~λ 2 λ !~E 1 E ! (X2.1)
final wavelength is the total integrated spectral power, E .
i11 i11 i i i11
T
X2.2.3 Generate a table of m rows for the selected number,
Where E is the power at wavelength λ.
i i
m of weighted ordinates. The first column contains the bin
X2.1.2 Thecumulativepower,P uptoλ isthesumof
c(i+1) i+1
numbers, 1 – m inclusive. For the second column, compute the
i11
all P ≤ P : P 5 Σ p
i i+1 c i 1 1 i F for k = 1.m from Eq X2.2 for each bin k.
~ !
K
X2.2.4 The last column of the table will be the centroid
X2.1.3 For the m(=50or m = 100) selected ordinates, the
wavelength for the band associated with each F computed in
proportion, F ,ofthetotalpower, E ,withineachordinatebin, K
K T
X2.2.3. To find that wavelength, compare the cumulative
K, is given by:
power, Pc, in successive wavelength intervals for the original
i
F 5 E ~2 K 2 1!⁄~2 m! (X2.2)
K T
selected spectrum with the F for the selected bin. There will
K
X2.1.4 For theoretical purposes, the center wavelength for be two wavelengths, λ and λ where Pc ≤ F ≤ Pc at
i i+1 i K (i+1)
each equal power (energy) interval is derived from:
those wavelengths. Use Eq X2.4 to interpolate between λ and
i
λ to obtain the wavelength that matches the F value.
i+1 K
∆F
F 5 F 2 ∆λ (X2.3)
K i11 K
∆λi
X2.3 Tables X2.1-X2.4 display the 100 and 50 selected
where: ordinate data for direct normal spectral irradiance, and the 100
and 50 selected ordinate data for the global hemispherical 37°
F = P /E
i ci T
tilt spectral irradiance, respectively.
∆λ = λ – λ
K i+1 i
F (defined by Eq X2.2) is between the values of F (at λ)
K i i
X2.4 For horizontal surface applications. Tables X2.5 and
and F (at λ ), and ∆λ = λ – λ.
i+1 i+1 i i+1 i
X2.6 display the 50 and 100 selected ordinate data for the
global horizontal spectrum derived from the Tables G173
X2.1.5 The equation for computing the central wavelength
reference spectra, except that the air mass used is AM = 1.0,
for the equal energy intervals, based on the above criteria is:
with the sun vertically overhead, and not AM 1.5. Note the
F E 2 P
~ !
K T ci
integrated total global horizontal at AM 1.0 for the Tables
λ 5λ 1 λ 2 λ (X2.4)
~ !
K i i11 i
~P 2 P !
-2
ci11 ci
G173 conditions is 1100.87 Wm .
NOTE X2.1—The interpolation for the central wavelength of the equal
energy interval is computed using the wavelengths and cumulative
X2.5 Note that the selected ordinate approach may be used
fraction of the total integrated energy bracketing the cumulative energy
for any specified spectral distribution. The Tables G173 refer-
computed from Eq X2.2, from the high resolution spectral Table 2 in
Tables G173. ence spectra in conjunction with the tables below can be used
E903−20
TABLE X2.1 100 Selected Ordinates for G173 Direct Normal Irradiance AM 1.5
NOTE 1—Data given at the midpoint of the equal energy intervals.
kF E -λ λ kF E -λ λ
K o o k K o o k
1 0.005 4.50 338.04 51 0.505 454.57 745.21
2 0.015 13.50 365.63 52 0.515 463.57 753.17
3 0.025 22.50 385.00 53 0.525 472.57 764.51
4 0.035 31.50 401.14 54 0.535 481.57 773.88
5 0.045 40.51 411.34 55 0.545 490.58 782.24
6 0.055 49.51 420.86 56 0.555 499.58 790.83
7 0.065 58.51 430.56 57 0.565 508.58 799.77
8 0.075 67.51 439.68 58 0.575 517.58 808.83
9 0.085 76.51 447.56 59 0.585 526.58 819.13
10 0.095 85.51 454.65 60 0.595 535.58 829.82
11 0.105 94.51 461.58 61 0.605 544.58 839.89
12 0.115 103.52 468.00 62 0.615 553.59 849.61
13 0.125 112.52 475.25 63 0.625 562.59 858.23
14 0.135 121.52 481.84 64 0.635 571.59 869.88
15 0.145 130.52 487.20 65 0.645 580.59 880.07
16 0.155 139.52 495.49 66 0.655 589.59 890.52
17 0.165 148.52 502.20 67 0.665 598.59 903.30
18 0.175 157.52 508.88 68 0.675 607.59 917.32
19 0.185 166.53 515.53 69 0.685 616.60 921.65
20 0.195 175.53 522.56 70 0.695 625.60 961.68
21 0.205 184.53 529.29 71 0.705 634.60 978.10
22 0.215 193.53 535.85 72 0.715 643.60 991.67
23 0.225 202.53 542.56 73 0.725 652.60 1004.62
24 0.235 211.53 549.16 74 0.735 661.60 1005.35
25 0.245 220.53 555.71 75 0.745 670.60 1031.75
26 0.255 229.54 562.43 76 0.755 679.61 1045.92
27 0.265 238.54 569.13 77 0.765 688.61 1060.64
28 0.275 247.54 575.90 78 0.775 697.61 1076.11
29 0.285 256.54 582.62 79 0.785 706.61 1092.34
30 0.295 265.54 589.33 80 0.795 715.61 1112.29
31 0.305 274.54 596.31 81 0.805 724.61 1161.08
32 0.315 283.54 603.15 82 0.815 733.61 1183.50
33 0.325 292.55 609.89 83 0.825 742.61 1205.25
34 0.335 301.55 616.7
...

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: E903 − 12 E903 − 20
Standard Test Method for
Solar Absorptance, Reflectance, and Transmittance of
Materials Using Integrating Spheres
This standard is issued under the fixed designation E903; 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 covers the measurement of spectral absorptance, reflectance, and transmittance of materials using
spectrophotometers equipped with integrating spheres.
1.2 Methods of computing solar weighted properties from the measured spectral values are specified.
1.3 This test method is applicable to materials having both specular and diffuse optical properties.
1.4 This test method is applicable to material with applied optical coatings with special consideration for the impact on the textures
of the material under test.
1.5 Transmitting sheet materials that are inhomogeneous, textured, patterned, or corrugated require special considerations with
respect to the applicability of this test method. Test Method E1084 may be more appropriate to determine the bulk optical
properties of textured or inhomogeneous materials.
1.6 For homogeneous materials this test method is preferred over Test Method E1084.
1.7 This test method refers to applications using standard reference solar spectral distributions but may be applied using alternative
selected spectra as long as the source and details of the solar spectral distribution and weighting are reported.
1.8 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.9 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:
This test method is under the jurisdiction of ASTM Committee E44 on Solar, Geothermal and Other Alternative Energy Sources and is the direct responsibility of
Subcommittee E44.20 on Glass Optical Materials for Solar Applications.
Current edition approved Dec. 1, 2012Oct. 1, 2020. Published December 2012October 2020. Originally approved in 1982. Last previous edition approved in 19962012
as E903–96 which was withdrawn August 2005 and reinstated in December 2012. DOI: 10.1520/E0903-12.–12. DOI: 10.1520/E0903-20.
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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E903 − 20
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
E971 Practice for Calculation of Photometric Transmittance and Reflectance of Materials to Solar Radiation
E1084 Test Method for Solar Transmittance (Terrestrial) of Sheet Materials Using Sunlight
E1175 Test Method for Determining Solar or Photopic Reflectance, Transmittance, and Absorptance of Materials Using a Large
Diameter Integrating Sphere
E2554 Practice for Estimating and Monitoring the Uncertainty of Test Results of a Test Method Using Control Chart Techniques
G173 Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface
G197 Table for Reference Solar Spectral Distributions: Direct and Diffuse on 20° Tilted and Vertical Surfaces
2.2 Other Documents:
Federal Test Method Standard No. 141, Method 6101
ASHRAE Standard 74-1988
CIE 38 Radiometric and Photometric Characteristics of Materials and their Measurement
CIE 44 Absolute Methods for Reflection Measurement
NIST SP 250-48 Spectral Reflectance
NIST SP 250-69 Regular Spectral Transmittance
3. Terminology
3.1 The following definitions are consistent with Terminology For definitions of E772. Additional terms appropriate to this test
method are included in terms used in this test method, refer to Terminology E772.
3.2 Definitions:Definitions of Terms Specific to This Standard:
3.2.1 absorptance, α, n—the ratio of the absorbed radiant flux to the incident radiant flux.
3.2.2 diffuse, adj—indicates that flux propagates in many directions, as opposed to direct beam, which refers to collimated flux.
When referring to reflectance, it is the directional-hemispherical reflectance less the specular reflectance.
3.2.1 integrating sphere, n—an optical device used to either collect flux reflected or transmitted from a sample into a hemisphere
or to provide isotropic irradiation of a sample from a complete hemisphere. It consists of a cavity that is approximately spherical
in shape with apertures for admitting and detecting flux and usually having additional apertures over which sample and reference
specimens are placed.
–2
3.2.4 irradiance, E, n—a radiometric term for the radiant flux that is incident upon a surface (W·m ).
3.2.2 near normal-hemispherical, adj—indicates irradiance to be directional near normal to the specimen surface and the flux
leaving the surface or medium is collected over an entire hemisphere for detection.
3.2.3 photovoltaic solar, adj—referring to an optical property; indicates a weighted average of the spectral property using the
number of photons per second per unit area per unit wavelength derived from a standard solar irradiance distribution as the
weighting function.
3.2.7 radiant flux, Φ, n—a radiometric term for the time rate of flow of energy in the form of electromagnetic energy (watts).
3.2.8 reflectance, ρ, n—the ratio of the reflected radiant flux to the incident radiant flux.
Available from Standardization Documents, Order Desk, Building 4, Section D, 700 Robbins Ave., Philadelphia, PA 19111-5049, Attn: NPODS.
Available from American Society of Heating, Refrigeration, and Air-Conditioning Engineers, Inc., 191 Tullie Circle, NE. Atlanta GA 30329.
Available from U.S. National Committee of the CIE (International Commission on Illumination), C/o Thomas M. Lemons, TLA-Lighting Consultants, Inc., 7 Pond St.,
Salem, MA 01970, http://www.cie-usnc.org.
Available on line at http://www.nist.gov/pml/div685/pub/upload/sp250-48.pdfOnline, Available: https://www.nist.gov/publications/spectral-reflectance
Available on line at http://www.nist.gov/calibrations/upload/SP250-69.pdfOnline, Available: https://www.nist.gov/publications/nist-measurement-services-regular-
spectral-transmittance
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3.2.4 smooth, adj—having an even and level surface, having no roughness or projections. Free from inequalities or unevenness
of surface.
3.2.10 solar, adj—(1) referring to radiometric quantities, indicates that the radiant flux involved has the sun as its source, or has
the relative spectral distribution of solar flux, and (2) referring to an optical property, indicates a weighted average of the spectral
property, with a standard solar spectral irradiance distribution as the weighting function.
3.2.11 spectral, adj—(1) for dimensionless optical properties, indicating that the property was evaluated at a specific wavelength,
λ, within a small wavelength interval, Δλ about λ, symbol wavelength in parentheses as L(350 nm), or as a function of wavelength,
symbol L(λ), and (2) for a radiometric quantity, the concentration of the quantity per unit wavelength (or frequency), indicated by
the subscript lambda, as L = dL/dλ; at a specific wavelength, the wavelength at which the spectral concentration was evaluated
λ
may be indicated by the wavelength in parentheses following the symbol, L (350 nm).
λ
3.2.11.1 Discussion—
The parameters of frequency, ν, wavenumber, κ, or photon energy may be substituted for wavelength, λ, in this definition.
3.2.5 specular, adj—indicates the flux leaves a surface or medium at an angle that is numerically equal to the angle of incidence,
lies in the same plane as the incident ray and the perpendicular, but is on the opposite side of the perpendicular to the surface.
3.2.5.1 Discussion—
Diffuse has been used in the past to refer to hemispherical collection (including the specular component). This use is deprecated
in favor of the more precise term hemispherical.
3.2.6 textured, adj—the nature of a surface other than smooth. Having some degree of unevenness, roughness or projections.
3.2.14 transmittance, τ, n—the ratio of the transmitted radiant flux to the incident radiant flux.
4. Summary of Test Method
4.1 Measurements of spectral near normal-hemispherical transmittance (or reflectance) are made over the spectral range from
approximately 300 to 2500 nm with an integrating sphere spectrophotometer.
4.2 The solar transmittance, reflectance, or absorptance is obtained by calculating a weighted average with a standard or selected
solar spectral irradiance as the weighting function by either direct calculation of suitable convolution integrals, or the weighted (see
8.3.3) or selected (see 8.3.4) ordinate method.
5. Significance and Use
5.1 Solar-energy absorptance, reflectance, and transmittance are important in the performance of all solar energy systems ranging
from passive building systems to central receiver power systems. This test method provides a means for determining these values
under fixed conditions that represent an average that would be encountered during use of a system in the temperate zone.
5.2 Solar-energy absorptance, reflectance, and transmittance are important for thermal control of spacecraft and the solar power
of extraterrestrial systems. This test method also provides a means for determining these values for extraterrestrial conditions.
5.3 This test method is designed to provide reproducible data appropriate for comparison of results among laboratories or at
different times by the same laboratory and for comparison of data obtained on different materials.
5.4 This test method has been found practical for smooth materials having both specular and diffuse optical properties. Materials
that are textured, inhomogeneous, patterned, or corrugated require special consideration.
5.4.1 Surface roughness may be introduced by physical or chemical processes, such as pressing, rolling, etching, or deposition of
films or chemical layers on materials, resulting in textured surfaces.
5.4.2 The magnitude of surface roughness with respect to the components of the spectrophotometer and attachments (light beam
sizes, sphere apertures, sample holder configuration) can significantly affect the accuracy of measurements using this test method.
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5.4.3 Even if the repeatability, or precision of the measurement of textured materials is good, including repeated measurements
at various locations within or orientations of the sample, the different characteristics of different spectrophotometers in different
laboratories may result in significant differences in measurement results.
5.4.4 In the context of 5.4.3, the term ‘significant’ means differences exceeding the calibration or measurement uncertainty, or
both, established for the spectrophotometers involved, through measurement of or calibration with standard reference materials.
5.4.5 The caveats of 5.4.3 and 5.4.4 apply as well to measurement of smooth inhomogeneous or diffusing materials, where incident
light may propogate to the edge of the test material and be ‘lost’ with respect to the measurement.
5.5 This test method describes measurements accomplished over wider spectral ranges than the Photopic response of the human
eye. Measurements are typically made indoors using light sources other than natural sunlight, though it is possible to configure
systems using natural sunlight as the illumination source, as in Practice E424. Practice E971 describes outdoor methods using
natural sunlight over the spectral response range of the human eye.
5.6 Light diffracted by gratings is typically significantly polarized. For polarizing samples, measurement data will be a function
of the orientation of the sample. Polarization effects may be detected by measuring the sample with rotation at various angles about
the normal to the samples.
6. Apparatus
6.1 Instrumentation:
6.1.1 Integrating Sphere Spectrophotometer—A spectrophotometer with an integrating sphere attachment capable of measuring
the spectral characteristics of the test specimen or material over the solar spectral region from approximately 300 to 2500 nm is
required. Double beam, ratio recording instruments are recommended because of their low sensitivity to drift in source brightness
or amplifier gain. Recording spectrophotometers with integrating spheres that have been found satisfactory for this purpose are
commercially available.
NOTE 1—For determining extraterrestrial solar optical properties using Standard E490, the spectral region should extend down to 250 nm.
NOTE 2—This test method is used primarily for solar thermal and some photovoltaic applications that require the full spectral range be covered. There
are other applications for which a narrower range is sufficient and that could otherwise use the procedures of this test method. For example, some
applications involving photovoltaic cells utilize a narrower spectral responsive range and some others pertain only to visible light properties that have
an even narrower spectral range. In such cases, the user of the test method is permitted to use a narrower range. Similarly, a user with an application
requiring a broader spectral range is permitted to use a broader range. Any deviations from the spectral range of this test method should be noted in the
report.
6.1.1.1 The integrating sphere shall be either a wall-mounted type such that the specimen may be placed in direct contact with
the rim of an aperture in the sphere wall for transmittance and reflectance measurements or an Edwards type center-mount type
(Edwards type) such that the specimen is mounted in the center of the sphere for reflectance and absorptance measurements.
NOTE 3—The interior of the integrating sphere shall be finished with a stable highly reflecting and diffusing coating. Sphere coatings having the required
properties can be prepared using pressed tetrafluoroethylene polymer powder, or other highly reflective, stable material.
6.1.1.2 The interior of the integrating sphere shall be finished with a stable highly reflecting and diffusing coating. Sphere coatings
having the required properties can be prepared using pressed tetrafluoroethylene polymer powder, or other highly reflective, stable
material.
NOTE 3—For high accuracy (better than 60.01 reflectance units) measurements with absolute sphere configuration, the ratio of the port area to the sphere
wall plus port area should be less than 0.001 (1). In general, large spheres (> 200 mm) meet these requirements and are preferred while small spheres
(< 100 mm) can give rise to large errors.
6.1.1.3 For the evaluation of near normal-hemispherical or hemispherical-near-normal reflectance, the direction of the incident
The boldface numbers in parentheses refer to the list of references at the end of this standard.
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radiation or the direction of viewing respectively shall be between 6 and 12° from the normal to the plane of the specimen so that
the specular component of the reflected energy is not lost through an aperture. Ambient light must be prevented from entering the
sphere by placing a ring of black or white material around the external rim of the specimen ports or by covering the entire sphere
attachment with a light tight housing. Black backing or border material may result in significant light absorption or loss, while
white backing material should be more representative of the sphere interior and affect measurement results to a lesser extent.
Several acceptable system configurations are illustrated in Appendix X1.
NOTE 4—The hemispherical near-normal irradiation-viewing mode is also allowed under this test method since the Helmholtz reciprocity relationship
which holds in the absence of polarization and magnetic fields guarantees equivalent results are obtainable.
6.1.1.4 Some commercial instruments have sample ports equipped with quartz windows. There is a possibility for multiple
reflections to occur between sample and window surfaces and miss or inadvertently enter the sample port. In transmission
measurement mode ensure that any light reflected from the sample is collected at the sample port. Best practice is to ensure that
the sample does not interact with the optical system of the spectrophotometer.
6.1.1.5 In spectrophotometer systems with multiple gratings and multiple detectors, discontinuities in the spectral data due to
changes in bandwidth, grating efficiency, or detector sensitivity may occur at grating and detector switch over points. If observed,
the magnitude and cause of the discontinuity should be investigated. Careful calibration over the entire spectral band of interest
should account for such discrepancies.
6.2 Standards:
6.2.1 In general, both reference and working (comparison) standards are required.
NOTE 5—Reference standards are the primary standard for the calibration of instruments and working standards. Reference standards that have high
specular reflectance, high diffuse reflectance, and low diffuse reflectance were formerly available from the National Institute of Standards and Technology
as Standard Reference Materials (SRM). See NIST Special Publications 250-48 and 250-69. However, the low demand and high cost
of these materials has been replaced by offers of measurement services from National Metrology Institutions (NMI) such as NIST.
These laboratories offer to measure customers samples and report spectral optical properties. These become NIST (or NMI)
traceable reference standards for customers. The customers often include commercial firms which then produce SRMs and
reference standards based on their NMI traceable standards and provide them to their customers along with traceability and
uncertainty information. These SRMs and reference standards are permitted within the context of this standard. Example NMIs
include the National Physical Laboratory (NPL) of the United Kingdom, the National Research Council (NRC) of Canada, the
Physical Technical Bureau (PTB) of Germany, The National Laboratory of Metrology and Test (LNE-INM) of France, etc.
NOTE 7—As of 2012, NPL still offers spectral reflectance standard reference materials at: http://www.npl.co.uk/optical-radiation-photonics/optical-
characterisation-of-materials/products-and-services/reflectance-standards
6.2.1.1 Working standards are used in the daily operation of the instrument to provide comparison curves for data reduction. In
general, ceramic and vitrified enamel surfaces are highly durable and desirable. A working standard shall be calibrated by
measuring its optical properties relative to the properties of the appropriate reference standard using procedures given in 8.2.
NOTE 6—Even the best standards tend to degrade with continued handling. They should be handled with care and stored in a clean, safe manner. Working
standards should be recalibrated periodically and cleaned, renewed, or replaced if degradation is noticeable. Avoid touching the optical surfaces. Only
clean soft cloth gloves should be worn for handling the standards. Only lens tissue or sterile cotton is recommended for cleaning. This is especially
important for reference standards carrying NIST calibration.
6.2.2 For transmitting specimens, incident radiation shall be used as the standard relative to which the transmitted light is
evaluated. For some applications calibrated transmittance standards are available.
6.2.3 For diffuse high-reflectance specimens, a working standard that has high reflectance and is highly diffusing over the range
of the solar spectrum is required.
NOTE 7—Identified suitable working standards are tablets of pressed tetrafluoroethylene polymer, BaSO , BaSO -based paints, and white ceramic tile.
4 4
6.2.4 For specularly reflecting specimens, a working standard that is highly specular is required. Identified suitable working
National Institute of Standards and Technology, Office of Standard Reference Materials, Room B311, Chemistry Bldg., Washington, DC 20234. Additional details
covering the appropriate SRMs (2019–2022) are available on request.
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standards are vacuum-deposited thin opaque films of metals. All front surface metalized working standards shall be calibrated
frequently with an absolute reflectometer or relative to a standard reference mirror traceable to a national standardizing laboratory
reference before being acceptable in this test method. An acceptable working standard for low-specular reflectance is a flat piece
of optically polished black glass. NIST no longer provides specular reflectance standard reference materials; but will measure user
provided mirrors to provide traceable calibration data.
NOTE 8—Although aluminum is most often used because of its high reflectance and ease of deposition, it is very unstable and scratches easily. Other
metals such as chromium, nickel, and rhodium are much more durable. High vacuum (≥ 10 torr) is required for obtaining pure films with the best optical
properties (2).
6.2.5 For absorber materials, a working standard that has low reflectance over the range of the solar spectrum is required in order
to obtain an accurate zero line correction.
NOTE 9—Black semi-matt porcelain enameled substrates, black barbeque, stove, or wrought iron fence paints, and opaque black glass are suitable working
standards. For very low-reflectance materials light traps reflecting < 0.005 can be fabricated to calibrate sphere performance.
NOTE 10—Light traps can be made from a stack of razor blades, a 60° black cone, or by forming an approximate exponential horn by drawing a glass
tube and painting it with high-gloss black paint.
6.2.6 If an absolute sphere is completely free of the flux losses referred to in X3.1.2, no working standard is required. A
comparison of the measured reflectance of a primary reference standard to its calibration value will give a good estimate of the
error due to flux losses, if any, from a nearly absolute sphere such as described in Appendix X1, X1.1.2 and X1.1.3.
7. Test Specimens
7.1 Specimens for Wall-Mounting Spheres:
7.1.1 The size of test specimens required depends on the dimensions of the integrating sphere. For wall-mounted spheres the
specimen must be large enough to cover the aperture of the sphere. There may be no limit on maximum dimension. For textured
or patterned samples, either the specimen shall be large enough to make a number of measurements over different areas, or several
specimens representing the different areas of the material shall be used.
7.1.2 Opaque specimens shall have at least one surface that is essentially planar over an area large enough to cover the aperture
of the sphere.
7.1.3 The most accurate results may be obtained from transparent and slightly translucent specimens with two surfaces that are
essentially smooth, or plane and parallel. In order to reduce light scattered out the edges of translucent specimen, the minimum
distance between the edge of the beam and the edge of the aperture shall be ten times the thickness of the specimen. The caveats
of 5.4.1 to 5.4.5 should be observed when measuring textured or highly diffusing materials.
7.1.4 The transmittance of highly scattering translucent samples is not easily measured with an integrating sphere instrument,
because a significant portion of the incident flux will be scattered outside the aperture. For such materials the standard test method
using the sun as a source (Test Methods E1084 or E1175) is preferred. Smith et al. (3) discuss diffuse material transmittance issues
(side losses, etc.) and discuss 0.01 (reflectance) accuracy and considerations for beam and aperture geometry.
NOTE 11—If such a sample must be measured, the edge losses can be greatly reduced by using a circular sample of diameter slightly less than that of
the aperture, and coating the edge with silver, using the wet mirror process. Alternatively, small stops can be cemented to the edges of the sample, so
that it can be suspended in the aperture with about half of its thickness extending outside the aperture.
7.2 Specimens for Edwards Sphere—The area of the specimen shall be limited to 0.01 of the surface area of the sphere.
NOTE 12—For a 200-mm diameter sphere, the required specimen size would be less than or equal to 20 mm in radius.
8. Procedure
8.1 Calibration—Calibrate linearity and wavelength scales of the spectrophotometers as recommended by the manufacturer or in
accordance with Practice E275. Check on calibration annually.
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8.2 Measurement:
8.2.1 Correction for 100 % and Zero Line Errors:
8.2.1.1 Record 100 % and zero line curves at least twice a day during testing.
NOTE 13—Variations in signal from the two beams are normal, usually wavelength dependent, and give rise to nonideal 100 % lines. Similarly, beam cross
talk, light scattering or leaks, and detector noise give rise to a nonideal zero line. These effects produce errors in the measured ratio of the flux reflected
by the specimen and the working standard.
8.2.1.2 For spheres with separate sample and reference ports, record the 100 % line curves using identical high-reflectance
specimens in both ports. The specimens are identical in reflectance if the recorded curve does not change when the two specimens
are interchanged.
8.2.1.3 For reflectance measurements, record the zero line with a perfect absorber or light trap in the sample port.
NOTE 14—The practice of recording the zero line with the sample beam blocked at the entrance port is discouraged because the effect of scattered light
incident on the sphere wall is not included.
8.2.1.4 For transmittance measurements, record the zero line with the sample beam blocked, preferably as far in front of the
entrance port as convenient.
8.2.2 Reflectance of Opaque Specimen—Comparison Type Sphere:
8.2.2.1 Record the spectral 100 % and zero lines as indicated in 8.2.1.
8.2.2.2 Record the spectral reflectance of specimen over the range 300 mm to 2500 mm relative to the working standard by placing
the specimen on the sample port and the standard on the reference port. Include the specular component in the reflectance
measurement.
8.2.2.3 Compute the spectral reflectance, ρ(λ), for the specimen, at wavelength λ using:
ρ~λ! 5 ~S 2 Z !⁄~100 2 Z !ρ'~λ! (1)
λ λ λ λ
where:
S = recorded specimen reading,
λ
Z = zero line reading,
λ
100 = 100 % line reading, and
λ
ρ'(λ) = calibrated spectral reflectance for the working standard or reference, all at wavelength λ.
NOTE 15—Slightly different procedures may be required for other sphere designs.
8.2.3 Reflectance of Opaque Specimen in an Absolute Sphere:
ρ λ 5 S 2 Z ⁄ 100 2 Z (2)
~ ! ~ ! ~ !
λ λ λ λ
where:
100 = 100 % correction obtained with the specimen port replaced by a sample having a coating and a curvature identical to the
λ
sphere wall. The zero line correction for an absolute sphere is usually so small that it can be neglected.
NOTE 16—Slightly different procedures may be required for other sphere designs.
8.2.4 For reflectance of transparent or translucent materials or specimens having transmittance greater than 0.001, back the
specimen by a light trap or black material having a low reflectance (< 0.02) over the 300 to 2500-nm spectral range. For these
measurements, the zero line shall be recorded with the specimen removed but the light trap or backing still in place. Obtain the
spectral reflectance following 8.2.2.
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8.2.5 Transmittance—Cover the specimen and reference ports at the rear of the sphere with surfaces having the same coating and
optical properties as the sphere walls when measuring transmittance (Note 1917). Record spectral curves without specimen in
place. Record spectral curves with the specimen over the specimen beam entrance port of the sphere. sphere over the range 300
mm to 2500 mm. Calculate the spectral transmittance as:
τ~λ! 5 ~S 2 Z !⁄~100 2 Z ! (3)
λ λ λ λ
where:
S = signal recorded with the specimen over the entrance port,
λ
Z = zero line reading with the specimen beam blocked with an opaque material, and
λ
100 = line recorded with no specimen over the specimen beam entrance port.
λ
NOTE 17—The working standards, 6.2.3, could be used with only a small error.
8.2.6 Absorptance—For opaque samples record the reflectance spectrum as in 8.2.2. The solar absorptance is calculated by first
obtaining the solar reflectance as in 8.3 and subtracting from 1, that is, τ = 0 in the Kirchoff relationship:
s
α 1τ 1ρ 5 1 (4)
s s s
8.2.6.1 For non-opaque samples, either obtain both the solar reflectance and solar transmittance using the described techniques and
calculate the solar absorptance by using the Kirchoff relationship, or use an Edwards-type integrating sphere instrument with the
specimen mounted so that the beam that exits through the back of the specimen is free to fall on the sphere wall. In this case the
sum τ(λ) + ρ(λ) is measured directly. Then use 8.3 and the Kirchoff relationship to determine the solar absorptance.
8.3 Computation of Solar Properties—Solar energy transmittance or reflectance is computed by the weighted ordinate, 50 selected
ordinate, 100 selected ordinate, or photovoltaic solar method.
8.3.1 Solar Spectral Irradiance Distribution:
8.3.1.1 For terrestrial applications, Tables G173 or a representative terrestrial spectrum, such as G197, or a specially selected and
specified terrestrial spectrum, may be used. Calculate the optical properties using either the convolution integral of the selected
spectrum and the measured property, the ordinate method in 8.3.3, or one of the selected ordinate methods described in section
8.3.4 and Appendix X2. For extraterrestrial applications, Standard E490 shall be used.
8.3.1.2 Calculate the optical properties using either the convolution integral of the selected spectrum and the measured property,
the weighted ordinate method of 8.3.3, or one of the selected ordinate methods described in 8.3.4 and Appendix X2.
8.3.2 Product of Optical Properties—When calculating solar optical efficiency of a complicated system such as a reflecting
concentrator with an absorber in a transparent envelope, the product of ρ, τ, and α is required. The appropriate procedure is to
measure the spectral optical properties of each component ρ(λ), α(λ), and τ(λ) respectively and form the product η(λ) = ρ(λ)α(λ)τ(λ)
before solar weighting. Calculate η as described in 8.3.3 or 8.3.4. Calculation of η from individually weighted properties can lead
s s
to substantial error, that is, η ≠ ρ α τ (4). See also Section 7.2 of (5).
s s s s
8.3.3 Weighted Ordinates—Obtain the solar reflectance ρ by integrating the spectral reflectance over the standard spectral
s
irradiance distribution, E , as follows:
λ
n n
ρ 5 Σ ρ ~λ ! E Δλ ⁄ Σ E Δλ (5)
S D S D
s i λi i λi i
i51 i51
Solar transmittance τ or absorptance α , is obtained from a similar expression with ρ(λ) replaced by τ(λ) or α(λ) respectively.
s s
Here n is the number of wavelengths for which E is known. The Δλ , are not constant but are given by:
λ i
Δλ 5 λ 2 λ ⁄ 2 (6)
~ !~ !
i i11 i21
For i = 1 and i = n, one assumes a Δλ equal to the last interval, that is, Δλ = λ – λ and Δλ = Δλ – Δλ .
l 2 l n n n-1
8.3.4 Selected Ordinates:
8.3.4.1 In the selected ordinate method, the solar irradiance distribution is divided into n wavelength intervals each containing 1/n
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of the total irradiance. The spectral reflectance or transmittance of the sample is evaluated at the centroid λ of each interval, λ .
i i
The solar reflectance is then calculated as follows:
n
ρ 5 1⁄n Σ ρ~λ ! (7)
s i
i51
8.3.4.2 The wavelengths λ , for the 50 and 100 selected ordinates derived from Tables G173 are provided in Appendix X2.
i
8.3.5 Photovoltaic Solar:
8.3.5.1 Photovoltaic solar energy conversion is effective only over a wavelength range shorter than the photovoltaic absorber’s
bandgap wavelength λ . Restricting the longest wavelength of the weighting function to λ yields an averaged value of an optical
g g
property that is more representative of a material’s performance in a photovoltaic system than one averaged over a fixed
wavelength interval.
8.3.5.2 In photovoltaic solar energy conversion, the current generated, and thus electrical power generated, depends on the number
of photons absorbed in the absorber material. The number of photons in a wavelength interval depends on the spectral irradiance
in that interval, E , as well as the energy of photons in that interval; The energy of a photon of a given wavelength E , is given
λ ph
by:
E 5 hc⁄λ (8)
ph
where h is Planck’s constant and c is the speed of light. The number of photons per second per unit area in the spectral interval,
N is given by:
ph,λ
N 5 λE ⁄hc (9)
ph,λ λ
8.3.5.3 In the photovoltaic solar method, obtain the photovoltaic solar reflectance ρ (λ ) as follows:
pv g
m
Σ ρ ~λ ! λ E Δ λ
S i i λi D
i51
ρ ~λ ! 5 (10)
pv g m
Σ λ E Δ λ
S D
i λi
i51
Here m indicates the index of λ that is the wavelength equal or most nearly equal to λ .
i g
Photovoltaic solar transmittance τ (λ ) or photovoltaic solar absorptance α (λ ) is obtained from a similar expression with ρ(λ)
pv g pv g
replaced by τ(λ) or α(λ) respectively.
9. Report
9.1 The report shall include the following:
9.1.1 Complete identification of the material tested, specimen size and thickness, texture or surface contour if any, description of
optical properties such as diffuse or specularly reflecting, clear or translucent transmitting, etc.
9.1.2 Solar transmittance, absorptance, or reflectance, or all three, determined to the nearest 0.001 unit or 0.1 %.
9.2 Estimated precision (repeatability) and estimated overall accuracy reported as uncertainty due to combined systematic and
statistical (precision) errors. The accuracy and precision shall be reported in the same units as the optical property itself. The
method by which the uncertainty was established shall be reported.
9.3 Identification of the instrument used. Manufacturer’s name and model number including specifications, modifications and
accessories is sufficient for a commercial instrument. Other instruments must be described in detail including estimations of their
accuracy.
9.4 Solar spectral irradiance and weighting method used for computation of the solar optical property.
10. Precision and Bias
10.1 No material specific information is presented about either the precision or bias of this test method. The reproducibility and
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repeatability of this test method are not provided at this time because an ASTM Interlaboratory Study (ILS) has never been run.
While there have been several attempts to run an ILS since 1982 (the year this standard was originally approved), due to a repeated
lack of laboratories willing to participate in a measurement-based ILS one has never been conducted
10.2 Uncertainties in the solar optical properties determined by the application of this test method arise from random errors
associated with signal detection and electronic processing, errors introduced by the geometry of the integrating sphere system and
the distribution of scattered or reflected light, errors in the values for standard reference materials, source illuminate beam
configuration (size, orientation, and dispersion), sample orientation, positioning and configuration, and how correctly the spectral
solar irradiance used in the calculation matches that at the actual location of system deployment. The contribution from each of
these sources is discussed in Appendix X3. Experience has shown that high accuracy is relatively difficult to achieve and depends
strongly on operator skill, experience, and care, as well as on equipment design and maintenance. Measurement results are required
to be reported at a resolution of 0.1%, to permit resolution of incremental improvements in accuracy. However, it is extremely
difficult to achieve absolute accuracy in any of the optical properties to better than 1 % to 2 %, or 10 to 20 times the required
reporting resolution. References (6, 7, 8) discuss interlaboratory comparison results, on the order of 0.02 units, or 2 approximately
2 %.
11. Keywords
11.1 absorptance; diffuse; integrating sphere; reflectance; smooth; solar absorptance; solar reflectance; solar transmittance;
spectral; spectrophotometer; specular; texture; transmittance
APPENDIXES
(Nonmandatory Information)
X1. INTEGRATING SPHERE GEOMETRIES
X1.1 A number of different integrating sphere geometries have been used over the years to obtain the optical reflectance and
transmittance of materials. Each geometry has advantages for specific applications. For a thorough understanding of sphere
applications and performance, Refs 1,9,10, and 11 should be consulted. Presented in X1.1.1 through X1.1.4 are the geometries felt
to be most applicable for the use of this test method. Many of the comments on specific applications can be applied to more than
one of the geometries. For a discussion of errors, see Section 10 and Refs 1 and 9.
X1.1.1 Four-Port Sphere—Because of its versatility, the four-port geometry shown in Fig. X1.1 is the most common sphere
supplied with commercially available spectrophotometers. The reference and sample beams may either cross as shown or be
parallel. The sphere gives the reflectance factor of the specimen relative to that of the reference material. Calibration with a
FIG. X1.1 Four-port, Comparison-type Integrating Sphere (Most Common)
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reference standard is essential. In the transmittance mode the reference and sample ports are covered with matched references
preferably of the same curvature and material as the sphere wall. The major problem with most commercial spheres of this type
is that their size is small, usually less than 100 mm in diameter, so that the ratio of the total port area to the sphere wall area
including the ports is large. This can introduce significant errors in a measurement due to flux loss. Large errors can also arise if
the angular distribution of the light reflected from the specimen is different from that reflected by the standard. In transmittance
measurements of translucent samples, this effect always occurs since the standard is the nonscattering open port. Careful baffle
design can substantially reduce errors due to different light scattering distribution.
X1.1.1.1 Spheres of this type sometimes have specular ports with plugs that can be removed for measuring the diffuse reflectance
with the specular component excluded.
X1.1.2 Edwards Sphere—A sphere of the Edwards type (Fig. X1.2) with a center-mounted sample allows ratio recording of
absolute reflectance (12). This geometry is the only one in which the angular dependence of reflectance can be easily evaluated.
By rotating the sample for normal incidence, the entrance port becomes a specular trap and diffuse reflectance with the specular
component excluded can also be measured. Finally, since both reflected and transmitted light is collected by the sphere,
absorptance of transmitting samples can be directly measured.
X1.1.2.1 The errors that can occur are related primarily to the uniformity and diffuseness of the sphere coating. A significant
drawback is the small sample size required and the necessity of placing it inside the sphere.
X1.1.3 Wall-Mount “Absolute”—The sphere shown in Fig. X1.3 has a wall-mounted sample that is baffled from the view of the
detector (11). The ratio signal obtained with this geometry is nearly absolute. Replacing a segment of the sphere wall with a black
cavity that traps all the specularly reflected light permits the measurement of the diffuse component only. The addition of the light
trap reduces the sphere’s efficiency and shifts the measurement further away from being absolute. After correction for changes in
sphere efficiency (4), the specular component can be calculated from the difference in measurements with and without the light
trap.
X1.1.4 Transmittance Sphere—Fig. X1.4 shows measurement geometry specifically for determining transmittance at near-normal
angles of incidence (4). The sphere has only three ports including the detector and collects nearly all of the transmitted flux. For
maximum freedom from errors due to differences in specimen scattering properties, the detector shall be baffled from viewing the
sample and either view all the remaining wall area with an isotropic 2π solid angle response or view a very limited segment of
the sphere wall that is also baffled from the sample port. In the latter case, low signal-to-noise would require long integration times
for the detection circuit. All baffles should have high reflectance and can be coated with sphere wall material or they can be specular
FIG. X1.2 Edwards-type, Absolute Integrating Sphere for Center-Mounted Specimen
E903 − 20
FIG. X1.3 Absolute Integrating Sphere for Wall-Mounted Specimen (11)
FIG. X1.4 Integrating Sphere for Transmittance Measurements (11)
mirrors.
X2. COMPUTATIONAL TECHNIQUE FOR TABULATED SELECTED ORDINATE VALUES
X2.1 Wavelength and equal energy values for the 100 and 50 selected ordinates are based on an interpolation procedure based on
wavelength intervals bounding equal integrated power (energy), E , from the first value (E ) to the last value (E ) under the
T o ∞
spectral curves.
X2.1.1 The area between two adjacent wavelengths in the spectral curves of Tables G173 is computed using the trapezoid rule.
The power P between wavelength λ and λ is computed from:
i i i+1
P 5 0.5 λ 2 λ E 1 E (X2.1)
~ !~ !
i11 i11 i i i11
Where E is the power at wavelength λ .
i i
E903 − 20
i11
X2.1.2 The cumulative power, P up to λ is the sum of all P ≤ P : P 5 Σ p
c(i+1) i+1 i i+1 c i 1 1 i
~ !
X2.1.3 For the m( = 50 or m = 100) selected ordinates, the proportion, F , of the total power, E , within each ordinate bin, K, is
K T
given by:
F 5 E 2 K 2 1 ⁄ 2 m (X2.2)
~ !~ !
K T
X2.1.4 For theoretical purposes, the center wavelength for each equal power (energy) interval is derived from:
ΔF
F 5 F 2 Δλ (X2.3)
K i11 K
Δλi
where:
F = P /E
i ci T
Δλ = λ – λ
K i+1 i
F (defined by Eq X2.2) is between the values of F (at λ ) and F (at λ ), and Δλ = λ – λ .
K i i i+1 i+1 i i+1 i
X2.1.5 The equation for computing the central wavelength for the equal energy intervals, based on the above criteria is:
~F E 2 P !
K T ci
λ 5 λ 1 λ 2 λ (X2.4)
~ !
K i i11 i
P 2 P
~ !
ci11 ci
NOTE X2.1—The interpolation for the central wavelength of the equal energy interval is computed using the wavelengths and cumulative fraction of the
total integrated energy bracketing the cumulative energy computed from Eq X2.2, from the high resolution spectral Table 2 in Tables G173.
X2.2 Summary of Weighted Ordinate Calculation Steps Using Selected Source Spectrum:
X2.2.1 From the original source spectrum, calculate the integral contribution between each adjacent wavelength according to Eq
X2.1.
X2.2.2 For each successive wavelength interval, add the integral for that interval to that of the previous integral to produce the
cumulative integral to each individual wavelength according to the eq
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