1、Designation: E2729 09 (Reapproved 2015)Standard 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, the yea
2、r 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 todeconvolve, at least partially, the spectral bandpass diffe
3、rencesof raw spectral data acquired by abridged spectrophotometry.Such differences are introduced because the spectral passbandmust be of significant bandwidth to allow sufficient energy toreach the detector. On the other hand, the spectral data thatshould be being reported is that of a virtual 1-nm
4、 bandwidthspectrum in order to be useful in the CIE method of tristimulusintegration which involves 1-nm summation.1.2 The standard establishes practices for whether, when,and how a bandpass rectification should be made to anyreflectance or transmittance spectrum acquired by abridgedspectrophotometr
5、y.1.3 It is applicable where the shape of the passband istriangular and the bandwidth is equal to the measurementinterval between passbands. Information is provided in Section7 for users when that condition is not satisfactorily met.1.4 This standard does not purport to address all of thesafety conc
6、erns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E284 Terminology of AppearanceE308 Prac
7、tice for Computing the Colors of Objects by Usingthe CIE System3. Terminology3.1 DefinitionsFor definition of terms used in thispractice, refer to Terminology E284.3.2 Definitions of Terms Specific to This Standard:3.2.1 virtual 1-nm bandwidth spectrum, nspectral datathat have been corrected by nume
8、rical methods so as to matchas closely as possible a spectrum from the same source but witha putative bandwidth of 1 nm.4. Summary of Practice4.1 The practice assumes that the shape of the passband istriangular and that the bandwidth is equal to the measurementinterval between passbands. This condit
9、ion is thought to be metby a majority of commercial instruments in use in spectropho-tometry and spectrocolorimetry. Under those conditions, themethods of Section 6 are to be utilized to rectify the rawreflectance or transmittance data for its bandpass differencesimmediately upon the return of the d
10、ata to the host computerprogram from the acquiring instrument, or before presentationof the data to the user.5. Significance and Use5.1 Failure to make such a rectification introduces differ-ences from the true value of the spectrum of about 0.02 to 0.4E*abunits. All users are required to make a rec
11、tification ofsuch bandpass differences. It is especially incumbent uponwriters of computer programs whose function it is to acquiresuch spectra from instruments to see that a competent rectifi-cation is implemented in the program before any additionalprocessing of the spectrum, or calculations invol
12、ving thespectrum are accomplished, or before the spectrum is madeavailable to a user.5.2 Legacy measuring systems are explicitly exempted fromany requirements for retrofitting of hardware or software andmay continue to utilize previously accepted methods of makingthe bandwidth rectification.6. Metho
13、dology6.1 The First and Last PassbandsIn the first and lastpassband being rectified, no correction is called for. Thecorrected spectral value Rs,should be set equal to themeasured spectral value Rm,.Rs,15 Rm,1(1)Rs,n5 Rm,n1This practice is under the jurisdiction of ASTM Committee E12 on Color andApp
14、earance and is the direct responsibility of Subcommittee E12.04 on Color andAppearance Analysis.Current edition approved April 1, 2015. Published April 2015. Originallyapproved in 2009. Last previous edition approved in 2009 as E2729 09. DOI:10.1520/E2729-09R15.2For referenced ASTM standards, visit
15、the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.
16、 United States1where the subscripts 1 and n refer to the wavelength index ofthe first and last passbands being corrected.6.2 The Second and Next-to-last PassbandsThe secondand next-to-last passbands being rectified are subject to thefollowing correction:Rs,2520.10Rm,111.21Rm,22 0.12Rm,310.01Rm,4(2)R
17、s,n21520.10Rm,n11.21Rm,n212 0.12Rm,n2210.01Rm,n23where the second subscript refers to the wavelength index ofthe bandpass considered.6.3 The Remaining Interior PassbandsThe remaining in-terior passbands are subject to the following five-point rectifi-cation:Rs,i5 0.01Rm,i222 0.12Rm,i2111.22Rm,i2 0.1
18、2Rm,i1110.01Rm,i12(3)where the subscript i is the wavelength index of the passbandbeing corrected and varies over the range of 3 to n2.7. Applicable Bandpass Shapes7.1 The coefficients of the foregoing rectification equationshave been calculated under the assumption that the passbandsare spaced at e
19、qual intervals. The interval is assumed to beequal to the full-width half-height of the passbands. Further,assumption is made that the passbands are triangular in shapeand that the reflectance, or transmittance, functions may becharacterized by a quadratic function in the range of anypassband. These
20、 assumptions are believed to be true for mostinstruments, materials, and measurements known to the Sub-committee with jurisdiction for this practice. Accordingly, theabove correction is among the best practices for making arectification of bandpass differences.7.2 While the underlying theory leading
21、 to the rectificationequations is based on triangular passbands, some relatedbandpass shapes may be adequately rectified by the methods ofthis practice. This is true of Gaussian and Lorentzian functionband shapes, and may be true of instruments with concavediffraction gratings imaged on diode arrays
22、 with more pixelsthan wavelengths being reported. Those passbands are trap-ezoidal in shape.7.3 If the user has specific knowledge as to departures fromthe above assumptions with respect to his particular measure-ment conditions, he may calculate a set of correction coeffi-cients fitting his own cas
23、e from principles laid down in thepublished literature. Most helpful in this regard will be articlesby Stearns (1,2),3Fairman (3), Oleari (4), Venable (5), Gardner(6), and Ohno (7). Corrections using such coefficients aredeemed to meet the requirements of this practice.8. Precision and Bias8.1 The r
24、ectification has no impact on the precision of anytest method.8.2 In the absence of any rectification, the bias introducedby the bandpass differences is as much as 0.25 in daylightilluminants and about 0.4 in fluorescent illuminants in units ofE*ab. The correction of Section 6 reduces the bias to ab
25、out0.02 for daylight illuminants and to about 0.04 E*abforfluorescent illuminants illuminating typical non-fluorescentsurface colors.9. Keywords9.1 bandpass rectification; spectral deconvolutionAPPENDIX(Nonmandatory Information)X1. BEST PRACTICES FOR THE IMPLEMENTATION OF THE SPECTROPHOTOMETRIC BAND
26、PASS RECTIFICATIONX1.1 Effective with the issuance of the practice, ASTM haschanged the standard method for implementing the bandpassrectification of a measured spectrum from the jurisdiction ofPractice E308 to the jurisdiction of this separate standard. Thisinvolves an implementation model in which
27、 both instrumentand software manufacturers will have to participate, and it willrequire the understanding and cooperation of the user commu-nity. The following is written to assist both instrument manu-facturers and users in selecting the best practices in implement-ing the new bandpass correction s
28、cheme.X1.1.1 To explain the change in brief, the bandpass rectifi-cation was previously most often made at the time of tristimu-lus integration. Under the jurisdiction of this standard therectification has been moved to a separate action prior tointegration. This assures that the spectral data, as w
29、ell as thetristimulus values, have been corrected, and leaves no doubt inthe users mind as to whether or not the spectrum has beenrectified as all spectra will hereafter be rectified.X1.1.2 Bulk Rectification of Legacy FilesIt would be abest practice for manufacturers to provide users a utilityprogr
30、am to which they could submit their standard, batchrecord, history, or color measurement files for processing frombandpass unrectified to bandpass rectified. The utility wouldtake each record in turn, process it, and return it to its rightfulplace in the rectified output file. Processing by such a u
31、tility,with the concomitant flagging of the rectified records, willeliminate, once and for all time, any worry about the status oflegacy files. Each record so upgraded will need to be flagged asdiscussed in X1.1.4 and following to avoid the possibility ofthe records being duplicatively treated at a
32、later date.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.E2729 09 (2015)2X1.1.3 Record by Record Rectification of Legacy FilesAnother option among the best practices, is to process eachrecord brought into software after the implementation date andto re
33、store it to its place in the original file rectified and flaggedas discussed in 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 beenrectified by any means in the database as being a record thathas already been
34、 corrected. Rectifying software may then beprogrammed automatically to avoid redundantly correctingsuch a record. This has the capacity to avoid even human errorshould the user believe a file, or record, has not been previouslyprocessed.X1.1.5 Suggested FlaggingMost spectrophotometric da-tabase syst
35、ems will contain a table which describes thegeometric conditions under which the spectrum has beenmeasured. At the present time these geometric conditions maybe limited to “Specular Included,” “Specular Excluded,” and“0/45” or some other short list of geometries. It would bebeneficial to users if ma
36、nufacturers adopted the practice ofextending this list to items such as “Specular Included BPRectified,” “Specular Excluded BP Rectified,” etc. This can bedone without change in the database definition on the part ofthe manufacturer, and gives the user a target location in thedatabase where he may e
37、xpect to find the bandpass rectificationflag.REFERENCES(1) Stearns, E. I, “Influence of spectrometer slits on tristimuluscalculations,” Color Research and Application, 1981, 6:7884.(2) Stearns, E. I. and Stearns, R. E., “An example of a method forcorrecting radiance data for bandpass error,” Color R
38、esearch andApplication, 1988, 13, pp. 257259.(3) Fairman, H. S., “An improved method for correcting radiance data forbandpass error,” Color Research and Application (in press).(4) Oleari, C., “Spectral-reflectance-factor deconvolution and colorimet-ric calculations by local-power expansion,” Color R
39、esearch andApplication, 2000, 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,” ColorResearch and Application, 1989, 31, pp. 374380.(7) Ohno, Y., “A
40、flexible bandpass correction method for spectrometers,”10th Annual Congress of the International Colour Association, AICColour 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 sta
41、ndard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years an
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44、9,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http:/ 09 (2015)3
