ASTM E2729-09(2015)
(Practice)Standard Practice for Rectification of Spectrophotometric Bandpass Differences
Standard Practice for Rectification of Spectrophotometric Bandpass Differences
SIGNIFICANCE AND USE
5.1 Failure to make such a rectification introduces differences from the true value of the spectrum of about 0.02 to 0.4 ΔE*ab units. All users are required to make a rectification of such bandpass differences. It is especially incumbent upon writers of computer programs whose function it is to acquire such spectra from instruments to see that a competent rectification is implemented in the program before any additional processing of the spectrum, or calculations involving the spectrum are accomplished, or before the spectrum is made available to a user.
5.2 Legacy measuring systems are explicitly exempted from any requirements for retrofitting of hardware or software and may continue to utilize previously accepted methods of making the bandwidth rectification.
SCOPE
1.1 This standard outlines the methods that can be used to deconvolve, at least partially, the spectral bandpass differences of raw spectral data acquired by abridged spectrophotometry. Such differences are introduced because the spectral passband must be of significant bandwidth to allow sufficient energy to reach the detector. On the other hand, the spectral data that should be being reported is that of a virtual 1-nm bandwidth spectrum in order to be useful in the CIE method of tristimulus integration which involves 1-nm summation.
1.2 The standard establishes practices for whether, when, and how a bandpass rectification should be made to any reflectance or transmittance spectrum acquired by abridged spectrophotometry.
1.3 It is applicable where the shape of the passband is triangular and the bandwidth is equal to the measurement interval between passbands. Information is provided in Section 7 for users when that condition is not satisfactorily met.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:E2729 −09(Reapproved 2015)
Standard Practice for
Rectification of Spectrophotometric Bandpass Differences
This standard is issued under the fixed designation E2729; 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 3.2 Definitions of Terms Specific to This Standard:
3.2.1 virtual 1-nm bandwidth spectrum, n—spectral data
1.1 This standard outlines the methods that can be used to
that have been corrected by numerical methods so as to match
deconvolve, at least partially, the spectral bandpass differences
ascloselyaspossibleaspectrumfromthesamesourcebutwith
of raw spectral data acquired by abridged spectrophotometry.
a putative bandwidth of 1 nm.
Such differences are introduced because the spectral passband
must be of significant bandwidth to allow sufficient energy to
4. Summary of Practice
reach the detector. On the other hand, the spectral data that
should be being reported is that of a virtual 1-nm bandwidth
4.1 The practice assumes that the shape of the passband is
spectrum in order to be useful in the CIE method of tristimulus
triangular and that the bandwidth is equal to the measurement
integration which involves 1-nm summation.
intervalbetweenpassbands.Thisconditionisthoughttobemet
1.2 The standard establishes practices for whether, when, by a majority of commercial instruments in use in spectropho-
and how a bandpass rectification should be made to any tometry and spectrocolorimetry. Under those conditions, the
reflectance or transmittance spectrum acquired by abridged methods of Section 6 are to be utilized to rectify the raw
spectrophotometry. reflectance or transmittance data for its bandpass differences
immediately upon the return of the data to the host computer
1.3 It is applicable where the shape of the passband is
program from the acquiring instrument, or before presentation
triangular and the bandwidth is equal to the measurement
of the data to the user.
interval between passbands. Information is provided in Section
7 for users when that condition is not satisfactorily met.
5. Significance and Use
1.4 This standard does not purport to address all of the
5.1 Failure to make such a rectification introduces differ-
safety concerns, if any, associated with its use. It is the
ences from the true value of the spectrum of about 0.02 to 0.4
responsibility of the user of this standard to establish appro-
∆E* units. All users are required to make a rectification of
priate safety and health practices and determine the applica-
ab
bility of regulatory limitations prior to use. such bandpass differences. It is especially incumbent upon
writers of computer programs whose function it is to acquire
2. Referenced Documents
such spectra from instruments to see that a competent rectifi-
cation is implemented in the program before any additional
2.1 ASTM Standards:
processing of the spectrum, or calculations involving the
E284 Terminology of Appearance
spectrum are accomplished, or before the spectrum is made
E308 PracticeforComputingtheColorsofObjectsbyUsing
available to a user.
the CIE System
5.2 Legacymeasuringsystemsareexplicitlyexemptedfrom
3. Terminology
any requirements for retrofitting of hardware or software and
3.1 Definitions—For definition of terms used in this
maycontinuetoutilizepreviouslyacceptedmethodsofmaking
practice, refer to Terminology E284.
the bandwidth rectification.
6. Methodology
This practice is under the jurisdiction of ASTM Committee E12 on Color and
Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
6.1 The First and Last Passbands—In the first and last
Appearance Analysis.
passband being rectified, no correction is called for. The
Current edition approved April 1, 2015. Published April 2015. Originally
corrected spectral value R should be set equal to the
approved in 2009. Last previous edition approved in 2009 as E2729 – 09. DOI:
s,λ
10.1520/E2729-09R15.
measured spectral value R .
m,λ
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
R 5 R (1)
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
s,1 m,1
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. R 5 R
s,n m,n
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2729−09 (2015)
wherethesubscripts1andnrefertothewavelengthindexof 7.2 While the underlying theory leading to the rectification
the first and last passbands being corrected. equations is based on triangular passbands, some related
bandpass shapes may be adequately rectified by the methods of
6.2 The Second and Next-to-last Passbands—The second
this practice. This is true of Gaussian and Lorentzian function
and next-to-last passbands being rectified are subject to the
band shapes, and may be true of instruments with concave
following correction:
diffraction gratings imaged on diode arrays with more pixels
R 520.10R 11.21R 2 0.12R 10.01R (2)
s,2 m,1 m,2 m,3 m,4
than wavelengths being reported. Those passbands are trap-
ezoidal in shape.
R 520.10R 11.21R 2 0.12R 10.01R
s,n21 m,n m,n21 m,n22 m,n23
7.3 If the user has specific knowledge as to departures from
where the second subscript refers to the wavelength index of
the above assumptions with respect to his particular measure-
the bandpass considered.
ment conditions, he may calculate a set of correction coeffi-
6.3 The Remaining Interior Passbands—The remaining in-
cients fitting his own case from principles laid down in the
terior passbands are subject to the following five-point rectifi-
published literature. Most helpful in this regard will be articles
cation:
by Stearns (1,2), Fairman (3), Oleari (4),Venable (5), Gardner
(6), and Ohno (7). Corrections using such coefficients are
R 5 0.01R 2 0.12R 11.22R 2 0.12R 10.01R
s,i m,i22 m,i21 m,i m,i11 m,i12
deemed to meet the requirements of this practice.
(3)
8. Precision and Bias
wherethesubscriptiisthewavelengthindexofthepassband
being corrected and varies over the range of 3 to n−2.
8.1 The rectification has no impact on the precision of any
test method.
7. Applicable Bandpass Shapes
8.2 In the absence of any rectification, the bias introduced
7.1 The coefficients of the foregoing rectification equations
by the bandpass differences is as much as 0.25 in daylight
have been calculated under the assumption that the passbands
illuminants and about 0.4 in fluorescent illuminants in units of
are spa
...
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: E2729 − 09 E2729 − 09 (Reapproved 2015)
Standard Practice for
Rectification of Spectrophotometric Bandpass Differences
This standard is issued under the fixed designation E2729; 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 standard outlines the methods that can be used to deconvolve, at least partially, the spectral bandpass differences of
raw spectral data acquired by abridged spectrophotometry. Such differences are introduced because the spectral passband must be
of significant bandwidth to allow sufficient energy to reach the detector. On the other hand, the spectral data that should be being
reported is that of a virtual 1-nm bandwidth spectrum in order to be useful in the CIE method of tristimulus integration which
involves 1-nm summation.
1.2 The standard establishes practices for whether, when, and how a bandpass rectification should be made to any reflectance
or transmittance spectrum acquired by abridged spectrophotometry.
1.3 It is applicable where the shape of the passband is triangular and the bandwidth is equal to the measurement interval between
passbands. Information is provided in Section 7 for users when that condition is not satisfactorily met.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
E284 Terminology of Appearance
E308 Practice for Computing the Colors of Objects by Using the CIE System
3. Terminology
3.1 Definitions—For definition of terms used in this practice, refer to Terminology E284.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 virtual 1-nm bandwidth spectrum, n—spectral data that have been corrected by numerical methods so as to match as
closely as possible a spectrum from the same source but with a putative bandwidth of 1 nm.
4. Summary of Practice
4.1 The practice assumes that the shape of the passband is triangular and that the bandwidth is equal to the measurement interval
between passbands. This condition is thought to be met by a majority of commercial instruments in use in spectrophotometry and
spectrocolorimetry. Under those conditions, the methods of Section 6 are to be utilized to rectify the raw reflectance or
transmittance data for its bandpass differences immediately upon the return of the data to the host computer program from the
acquiring instrument, or before presentation of the data to the user.
5. Significance and Use
5.1 Failure to make such a rectification introduces differences from the true value of the spectrum of about 0.02 to 0.4 ΔE*
ab
units. All users are required to make a rectification of such bandpass differences. It is especially incumbent upon writers of
computer programs whose function it is to acquire such spectra from instruments to see that a competent rectification is
This practice is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.04 on Color and
Appearance Analysis.
Current edition approved Dec. 1, 2009April 1, 2015. Published January 2010April 2015. Originally approved in 2009. Last previous edition approved in 2009 as E2729
– 09. DOI: 10.1520/E2729-09.10.1520/E2729-09R15.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’sstandard’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
E2729 − 09 (2015)
implemented in the program before any additional processing of the spectrum, or calculations involving the spectrum are
accomplished, or before the spectrum is made available to a user.
5.2 Legacy measuring systems are explicitly exempted from any requirements for retrofitting of hardware or software and may
continue to utilize previously accepted methods of making the bandwidth rectification.
6. Methodology
6.1 The First and Last Passbands—In the first and last passband being rectified, no correction is called for. The corrected
spectral value R should be set equal to the measured spectral value R .
s,λ m,λ
R 5 R (1)
s,1 m,1
R 5 R
s,n m,n
where the subscripts 1 and n refer to the wavelength index of the first and last passbands being corrected.
6.2 The Second and Next-to-last Passbands—The second and next-to-last passbands being rectified are subject to the following
correction:
R 520.10R 11.21R 2 0.12R 10.01R (2)
s,2 m,1 m,2 m,3 m,4
R 520.10R 11.21R 2 0.12R 10.01R
s,n21 m,n m,n21 m,n22 m,n23
where the second subscript refers to the wavelength index of the bandpass considered.
6.3 The Remaining Interior Passbands—The remaining interior passbands are subject to the following five-point rectification:
R 5 0.01R 2 0.12R 11.22R 2 0.12R 10.01R (3)
s,i m,i22 m,i21 m,i m,i11 m,i12
where the subscript i is the wavelength index of the passband being corrected and varies over the range of 3 to n−2.
7. Applicable Bandpass Shapes
7.1 The coefficients of the foregoing rectification equations have been calculated under the assumption that the passbands are
spaced at equal intervals. The interval is assumed to be equal to the full-width half-height of the passbands. Further, assumption
is made that the passbands are triangular in shape and that the reflectance, or transmittance, functions may be characterized by a
quadratic function in the range of any passband. These assumptions are believed to be true for most instruments, materials, and
measurements known to the Subcommittee with jurisdiction for this practice. Accordingly, the above correction is among the best
practices for making a rectification of bandpass differences.
7.2 While the underlying theory leading to the rectification equations is based on triangular passbands, some related bandpass
shapes may be adequately rectified by the methods of this practice. This is true of Gaussian and Lorentzian function band shapes,
and may be true of instruments with concave diffraction gratings imaged on diode arrays with more pixels than wavelengths being
reported. Those passbands are trapezoidal in shape.
7.3 If the user has specific knowledge as to departure
...
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