1、Designation: E2729 09 (Reapproved 2015)E2729 16Standard Practice forRectification of Spectrophotometric Bandpass Differences1This standard is issued under the fixed designation E2729; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision,
2、 the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This standard outlines the methods that can be used to deconvolve, at least partially, the spectral bandp
3、ass differences ofraw spectral data acquired by abridged spectrophotometry. Such differences are introduced because the spectral passband must beof significant bandwidth to allow sufficient energy to reach the detector. On the other hand, the spectral data that should be beingreported is that of a v
4、irtual 1-nm bandwidth spectrum in order to be useful in the CIE method of tristimulus integration whichinvolves 1-nm summation.1.2 The standard establishes practices for whether, when, and how a bandpass rectification should be made to any reflectanceor transmittance spectrum acquired by abridged sp
5、ectrophotometry.1.3 It is applicable where the shape of the passband is triangular and the bandwidth is equal to the measurement interval betweenpassbands. 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 o
6、f the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E284 Terminology of Appea
7、ranceE308 Practice for Computing the Colors of Objects by Using the CIE System3. Terminology3.1 DefinitionsFor 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, nspectral data that have been
8、corrected by numerical methods so as to match asclosely as possible a spectrum from the same source but with a putative bandwidth of 1 nm.4. Summary of Practice4.1 The practice assumes that the shape of the passband is triangular and that the bandwidth is equal to the measurement intervalbetween pas
9、sbands. This condition is thought to be met by a majority of commercial instruments in use in spectrophotometry andspectrocolorimetry. Under those conditions, the methods of Section 6 are to be utilized to rectify the raw reflectance ortransmittance data for its bandpass differences immediately upon
10、 the return of the data to the host computer program from theacquiring instrument, or before presentation of the data to the user.5. Significance and Use5.1 Failure to make such a rectification introduces differences from the true value of the spectrum of about 0.02 to 0.4 E*abunits. All users are r
11、equired to make a rectification of such bandpass differences. It is especially incumbent upon writers ofcomputer programs whose function it is to acquire such spectra from instruments to see that a competent rectification is1 This practice is under the jurisdiction of ASTM Committee E12 on Color and
12、 Appearance and is the direct responsibility of Subcommittee E12.04 on Color andAppearance Analysis.Current edition approved April 1, 2015Aug. 1, 2016. Published April 2015August 2016. Originally approved in 2009. Last previous edition approved in 20092015 asE2729 09. 09 (2015). DOI: 10.1520/E2729-0
13、9R15.10.1520/E2729-16.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard a
14、nd is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only
15、 the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1implemented in the program before any additional processing of the spectrum, or calcula
16、tions involving the spectrum areaccomplished, 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 maycontinue to utilize previously accepted methods of making the bandwidth rectific
17、ation.6. Methodology6.1 The First and Last PassbandsIn the first and last passband being rectified, no correction is called for. The correctedspectral value Rs, should be set equal to the measured spectral value Rm,.Rs,15Rm,1 (1)Rs,n 5Rm,nwhere the subscripts 1 and n refer to the wavelength index of
18、 the first and last passbands being corrected.6.2 The Second and Next-to-last PassbandsThe second and next-to-last passbands being rectified are subject to the followingcorrection:Rs,2520.10Rm,111.21Rm,220.12Rm,310.01Rm,4 (2)Rs,n21520.10Rm,n11.21Rm,n2120.12Rm,n2210.01Rm,n23where the second subscript
19、 refers to the wavelength index of the bandpass considered.6.3 The Remaining Interior PassbandsThe remaining interior passbands are subject to the following five-point rectification:Rs,i 50.01Rm,i2220.12Rm,i2111.22Rm,i 20.12Rm,i1110.01Rm,i12 (3)where the subscript i is the wavelength index of the pa
20、ssband being corrected and varies over the range of 3 to n2.7. Applicable Bandpass Shapes7.1 The coefficients of the foregoing rectification equations have been calculated under the assumption that the passbands arespaced at equal intervals. The interval is assumed to be equal to the full-width half
21、-height of the passbands. Further, assumptionis made that the passbands are triangular in shape and that the reflectance, or transmittance, functions may be characterized by aquadratic function in the range of any passband. These assumptions are believed to be true for most instruments, materials, a
22、ndmeasurements known to the Subcommittee with jurisdiction for this practice. Accordingly, the above correction is among the bestpractices for making a rectification of bandpass differences.7.2 While the underlying theory leading to the rectification equations is based on triangular passbands, some
23、related bandpassshapes 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 beingreported. Those passbands ar
24、e trapezoidal in shape.7.3 If the user has specific knowledge as to departures from the above assumptions with respect to his particular measurementconditions, he may calculate a set of correction coefficients fitting his own case from principles laid down in the publishedliterature. Most helpful in
25、 this regard will be articles by Stearns (1,2),3 Fairman (3), Oleari (4), Venable (5), Gardner (6), and Ohno(7). Corrections using such coefficients are deemed to meet the requirements of this practice.8. Precision and Bias8.1 The rectification has no impact on the precision of any test method.8.2 I
26、n the absence of any rectification, the bias introduced by the bandpass differences is as much as 0.25 in daylight illuminantsand about 0.4 in fluorescent illuminants in units of E*ab. The correction of Section 6 reduces the bias to about 0.02 for daylightilluminants and to about 0.04 E*ab for fluor
27、escent illuminants illuminating typical non-fluorescent surface colors.9. Keywords9.1 bandpass rectification; spectral deconvolution3 The boldface numbers in parentheses refer to a list of references at the end of this standard.E2729 162APPENDIX(Nonmandatory Information)X1. BEST PRACTICES FOR THE IM
28、PLEMENTATION OF THE SPECTROPHOTOMETRIC BANDPASS RECTIFICATIONX1.1 Effective with the issuance of the practice, ASTM has changed the standard method for implementing the bandpassrectification of a measured spectrum from the jurisdiction of Practice E308 to the jurisdiction of this separate standard.
29、Thisinvolves an implementation model in which both instrument and software manufacturers will have to participate, and it will requirethe understanding and cooperation of the user community. The following is written to assist both instrument manufacturers andusers in selecting the best practices in
30、implementing the new bandpass correction scheme.X1.1.1 To explain the change in brief, the bandpass rectification was previously most often made at the time of tristimulusintegration. Under the jurisdiction of this standard the rectification has been moved to a separate action prior to integration.
31、Thisassures that the spectral data, as well as the tristimulus values, have been corrected, and leaves no doubt in the users mind as towhether or not the spectrum has been rectified as all spectra will hereafter be rectified.X1.1.2 Bulk Rectification of Legacy FilesIt would be a best practice for ma
32、nufacturers to provide users a utility program towhich they could submit their standard, batch record, history, or color measurement files for processing from bandpass unrectifiedto bandpass rectified. The utility would take each record in turn, process it, and return it to its rightful place in the
33、 rectified outputfile. Processing by such a utility, with the concomitant flagging of the rectified records, will eliminate, once and for all time, anyworry about the status of legacy files. Each record so upgraded will need to be flagged as discussed in X1.1.4 and following toavoid the possibility
34、of the records being duplicatively treated at a later date.X1.1.3 Record by Record Rectification of Legacy FilesAnother option among the best practices, is to process each recordbrought into software after the implementation date and to restore it to its place in the original file rectified and flag
35、ged as discussedin the following sections.X1.1.4 Flagging of Records that are RectifiedIn any case, it is best practice to flag any record that has previously been rectifiedby any means in the database as being a record that has already been corrected. Rectifying software may then be programmedautom
36、atically to avoid redundantly correcting such a record. This has the capacity to avoid even human error should the userbelieve a file, or record, has not been previously processed.X1.1.5 Suggested FlaggingMost spectrophotometric database systems will contain a table which describes the geometriccond
37、itions under which the spectrum has been measured. At the present time these geometric conditions may be limited to“Specular Included,” “Specular Excluded,” and “0/45” or some other short list of geometries. It would be beneficial to users ifmanufacturers adopted the practice of extending this list
38、to items such as “Specular Included BP Rectified,” “Specular ExcludedBP Rectified,” etc. This can be done without change in the database definition on the part of the manufacturer, and gives the usera target location in the database where he may expect to find the bandpass rectification flag.REFEREN
39、CES(1) Stearns, E. I, “Influence of spectrometer slits on tristimulus calculations,” Color Research and Application, 1981, 6:7884.(2) Stearns, E. I. and Stearns, R. E., “An example of a method for correcting radiance data for bandpass error,” Color Research and Application, 1988,13, pp. 257259.(3) F
40、airman, H. S., “An improved method for correcting radiance data for bandpass error,” Color Research and Application, 2010(in, 35press)., pp.328333.(4) Oleari, C., “Spectral-reflectance-factor deconvolution and colorimetric calculations by local-power expansion,” Color Research and Application,2000,
41、25, pp. 176185.(5) Venable, W. H., “Accurate tristimulus values from spectral data,” Color Research and Application, 1989, 14, pp. 260267.(6) Gardner, J. L. “Bandwidth correction for LED chromaticity,” Color Research and Application, 1989, 31, pp. 374380.E2729 163(7) Ohno, Y., “A flexible bandpass c
42、orrection method for spectrometers,” 10th Annual Congress of the International Colour Association, AIC Colour 05(2005).ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressl
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