# Organic and Inorganic Gases by Extractive FTIR Spectrometry (3800)

​ORGANIC AND INORGANIC GASES BY EXTRACTIVE FTIR SPECTROMETRY
FORMULA: Table 1
MW: Table 1
METHOD: 3800, Issue 1 OSHA : NIOSH: ACGIH:
CAS: Table 1
EVALUATION: FULL
3800
RTECS: Table 1 Issue 1: 15 March 2003
PROPERTIES: Table 1
Table 1 Table 1 Table 1
SYNONYMS: See example compounds in Table 1
SAMPLING
MEASUREMENT
SAMPLER:
Portable direct-reading instrument (filter, if required)
FLOW RATE:
~0.1 to ~20 L/min (systemdependent)
TECHNIQUE:
EXTRACTIVE FOURIER TRANSFORM INFRARED (FTIR) SPECTROMETRY
ANALYTE:
See Table 1 (Additional compounds may be identified/quantified according to data quality objectives and QA/QC requirements)
VOL-MIN: -MAX:
Instrument dependent None
PRESSURE:
Extracted gases between 725 and 795 mm Hg absolute
ANALYTICAL FREQUENCIES:
See Table 2 for example compounds
TEMPERATURE:
Extracted gases between 10 and 30 °C
CALIBRATION:
Calibration gas standards
IDENTIFICATION: BLANKS:
Nitrogen gas, or zero air
Infrared spectra interpretation and computerized reference library searches
RANGE:
See Table 2 (dependent on compound and absorption pathlength)
ESTIMATED LOD:
See Table 2 for example values at 10-meter absorption pathlength
PRECISION ( þ r ):
See Appendix E, 2B and 2C
ACCURACY RANGE STUDIED:
See Table 1
BIAS:
See Appendix E
OVERALL PRECISION ( Ö r T ):
See Appendix E
ACCURACY:
See Appendix E
APPLICABILITY: The usefulness of FTIR techniques has been demonstrated in ambient air and combustion gas mixtures [7,8]. With the participation of an experienced analyst (see Appendix A), the method can be used for the characterization of workspace air containing mixtures of volatile organic and inorganic compounds. See Table 1 for examples.
INTERFERENCES: Overlap of infrared absorption features may affect the quantification of each compound. By appropriate use of multivariable least squares analyses, the analyst may be able to obtain accurate compound concentrations for overlapping compounds.
OTHER METHODS: This method is based on portions of EPA Method 320 [1] and its addendum [2] which describe the determination of gaseous compound concentrations by extractive FTIR spectrometry. Several compatible ASTM standards describing infrared techniques and terminology are also available [3-6].
NIOSH Manual of Analytical Methods, Fourth Edition ​ORGANIC AND INORGANIC GASES by FTIR Spectrometry: METHOD 3800, Issue 1, dated 15 March 2003 - Page 2 of 47 REAGENTS:
EQUIPMENT:
1. Nitrogen gas (N 2) or zero air, HP or be tter. 2. Calibration Transfer Standard (CTS) Gas, 2% accuracy or better. The proper concentration depends on both the compound used and the system absorption pathle ngth. F or ethylene in nitrogen, a standard concentration leading to a concentration - absorption pathlength product of 100 to 400 ppm-m is recomm ended. (For example, a standard of 10 ppm to 40 ppm ethylene in nitrogen is recomm ended for a 10 m eter a bso rption cell). 3. Liquid nitrogen* (LN 2) for cooling the infrared detector, if required.
1. FTIR spectrometer system (source, interferometer, sample absorption cell, and dete ctor) con figure d with a bso rption. A minimum instrumental linewidth (MIL) 2 cm -1 or lower is recomm ended. NOT E:A lower or higher MIL may be required or suitable for specific gas matrices. Choose internal abs orption ce ll ma terials to m inim ize surface/analyte interactions. 2. Com puter system with hardware, software, and required reference spectra for acquisition, s torage, and analysis of sam ple spectra. (A data backu p syste m is recom m end ed.) 3. Sam pling pum p, 0.1 to 10 L/m in, with appropriate particulate filters. 4. Non-reactive gas regulators and sam ple tubing. 5. Rota m ete rs or o the r de vices, 20% accuracy, for measuring flow rates of sample and calibration gases. 6. Tem perature measurement and/or control equ ipm ent fo r all sam pling system elem ents and IR absorption cell. NOT E:Temperature control equipment required if ambient temp. <10 °C or >30 °C. 7. Pressure gauge for measuring absolute gas pressure in absorption cell, 5% accuracy at one atm osp here (760 m m Hg) abs olute pressure. 8. For system tests (but not for normal operation): Vacuum pum p and gauge capable of 100 mm Hg abs. pressure; midinfrared attenuating filters (50% and 25% ); impinger.
SPECIAL PRECAUTIONS: This m eth od req uires the use of com pressed gases and/o r cryogenic liquids and/or toxic chemicals. These m aterials are dangerous and should be handled only by experienced personnel and according to relevant safety standards. This method does not address all of the safety conc erns ass ociated w ith its use . It is the res pon sibility of the user to establish app ropriate safety and hea lth prac tices and to determ ine the app licability of regulatory limitations.
NOTE: Please refer to the Appendices for explanation s of the term inology used in this docum ent (Appendix A) and several FTIR system tests which m ust be com pleted before any tes ting is perform ed (Appendix B). Appendices C, D, and E provide (respectively) a general description of FT IR spectrom etry, considerations for preparing reference libraries, and examples of calculations req uired for performance of this method.
NIOSH Manual of Analytical Methods, Fourth Edition ​ORGANIC AND INORGANIC GASES by FTIR Spectrometry: METHOD 3800, Issue 1, dated 15 March 2003 - Page 3 of 47 PRE-TEST PROCED URES: The following procedures (Steps 1 and 2) may be performed only by an experienced “analyst” (see Append ix A ). 1.
Verify that the FTIR system has been tested for wavenumber reproducibility, minimum instrumental linewidth (MIL), absorption pathlength, system resp onse tim e, residual squared area (RSA ), and detector linearity as desc ribed in App end ix B. If the system is new and/or has been recently assembled and/or has been recently serviced, perform and document results of the tests described in Appendix B before proceeding. 2. Prepare a test plan. The plan must include the following: a. The proposed system configuration, including the absorption pathlength and integration time for sample spectra. b. The data quality objectives, ana lytical region s, and expected Limit of Detection (LOD) values for each ana lyte. See Ta ble 2 a nd A ppe ndix E for exa m ple values and calculations. c. The names of all “operators” and “analysts” to be involved in the test. Analysts must be experienced in all aspects of the test procedures listed below, and may perform any or all of the test procedures. Ope rators m ust be expe rienced in the perform ance of Steps 3 through 13 listed below, and may perform only those portions of the test procedures. d. Verification that the system configuration, existing RS A values, and related LO D values are consistent with the test’s d ata quality objectives . (See App end ix E, Section 3.)
The follow ing p roce dures (Ste ps 3 throu gh 13) m ay be perfo rmed by a n experienced operator or analyst. 3. Activate the FTIR system according to the m anu fac turer ’s instruction s. A llow suffic ient tim e for the infrared source, the infrared detector, and (if required) the temperature control systems to stabilize. 4. Verify that the computer system is programm ed to store interferogram s; if the available data storage cap acity is insufficient for storage of all interferogram s, store single beam spectra instead. Verify adequacy and performance of the (recomm ended) data backup system. 5. Bypassing the sampling system, flow N 2 or zero air directly into the infrared absorption cell until a sta ble infrared response and moisture levels are reached. Record a background spectrum using an integration time equal to or greater than that planned for subsequent sample spectra. 6. Use the entire FTIR system (including all sampling components) to record an absorbance spectrum of a sam ple stream of N 2 or zero air. Use the integration time planned for subsequent sample spectra. Verify that the sam ple flow rate m eets or ex cee ds that specified in the syste m res ponse tim e documentation. Examine the resulting “system zero” (SZ) spectrum and verify the absence of contaminants in the sampling system and infrared absorption cell. If contaminants are detected, clean or replace the appropriate sampling system com ponents and/or infrared absorption cell and record a new SZ spe ctrum . If contam inants ca nno t be eliminated , the tes t resu lts and LOD values may require revision during the qua lity control proce dure s (see S teps 14 throug h 17 ).
CALIBRATION: 7. Using the entire sampling system, acquire two or more pre-test CTS spectra and use them to calculate the system absorption pathlength LS (see Appendix B, Section 1). Use the integration time planned for sub seq uen t sam ple sp ectra . Verify tha t L S is within 5% of the value quote d in the tes t plan. Verify that the sam ple tem pera ture a nd p ressure are within 10 to 30 °C and 725 to 795 m m Hg, resp ective ly. 8. W hen possible, perform the following system checks before sampling. If necessary, they may be delayed until performance of the (post-testing) quality control procedures (see Steps 14 through 17). If performed after sampling, the results of these procedures may require revision of the test results and LODs. a. LOD Check. Using one of the SZ spectra, calculate the RSA values (see Appendix B, Section 2) and LOD values (see Ap pendix E, Sec tion 2) in the analytical regions pertaining to the test analytes. Verify that the system pathlength, current RSA values, and current LODs are c ons istent w ith the test’s da ta quality objectives (see App endix E, Section 3).
NIOSH Manual of Analytical Methods, Fourth Edition ​ORGANIC AND INORGANIC GASES by FTIR Spectrometry: METHOD 3800, Issue 1, dated 15 March 2003 - Page 4 of 47 b. W avenumber Reproducibility Check. Record a preliminary workspace air sample spectrum and perform the calculations described in Appendix B, Section 3.
SAMPLING: 9. Using the integration time specified in the test plan, obtain samples and record infrared spectra of the desired ambient gases using the entire sampling system. The sampling location may be changed as desired. For tests of duration greater than 2 hours, or if the FTIR system is moved during sampling, monitor the system ’s single-beam resp ons e level. If changes greater than 5% in non-absorbing regions of the single beam spectrum occur, suspend sampling and record a new background spectrum (see Step 5). Sample spectra must be acquired at each sampling location for a time period no less than the system respon se tim e (se e the system test docu m enta tion). 10. Repeat Step 6; acquire at least one post-test SZ spectrum of N 2 or zero air; confirm the absence of sampling system contaminates. 11. Reco rd at least one post-test CTS spectrum (see Step 7); confirm that the system configuration and the system absorption pathlength (to within 5%) m atch those of the test plan. 12. (Optional) Acquire a pos t-test backgroun d spectrum (see Step 5).
SAMPLE ANALYSIS: 13. Using the analytical regions specified in the test plan, employ an appropriate mathematical analysis (see Ap pendix E) to determ ine preliminary analyte concen trations and their 3F uncertainties from the sam ple spe ctra, re ference spe ctra, a bso rption pathlength, and ga s pre ssu re. NOTE: Reference spectra for all ana lytes m ust m eet or exc eed the Q A/Q C re quirem ents of Appendix D. The reference library must include at least one wavenumber standard spectrum and at least one calibration transfer standard ( CTS) spectrum. The sample absorption due to any analyte may not exceed the m axim um concentration -path length pro duct represente d in the reference library for that compound.
QUALITY CONTRO L: Th e follow ing pro cedu res (Steps 14 throu gh 18 ) may b e perform ed on ly by an exp erienced analyst. 14. Using one of the SZ spectra, calculate the RSA and LOD values (see Appendix E) in the analytical regions pertaining to the test analytes. Verify that the system pathlength, current RSA values, and current LODs are consistent with the test’s data quality objectives. Using a suitable workspa ce air spectrum , perform the W avenumber Reproducibility and Resolution tests described in Appendix B, Sections 3 and 4. If either the W avenumber Reproducibility or Resolution results fail to meet the sp ec ifications, corrective actions are nece ssary (see Step 17 ). 15. Perform qualitative and/or quan titative analyses of the pre- and post-test SZ sp ectra and co nfirm the absence of s am pling syste m conta m inants . If contam inants are found which possess significant absorbance in any analytica l reg ion, co rrective actio ns m ay be necessary (see Step 1 7). Perform qualitative and/or quantitative analyses of the pre- and post-test CTS spectra and confirm that the system absorption pathlength is within 5% of the value quoted in the test plan. 16. Verify that the re ference spe ctra a nd re sults m eet the da ta quality objec tives of the test plan (see Ap pendix D). If they do not, corrective actions may be nece ssa ry (see Step 17). Examine the results of the quantitative sample analysis (Step 13) and verify som e su bse t of them (includ ing tho se w ith rela tively high and relatively low con centrations) m anually to ensure proper operation of analytical program. (Techniques for generating spectra representing the analytes at the concentration indicated by the analysis - “scaled spectra,” as defined in Appendix A— are described in Appendix E. The analyst sh ould gen erate such spectra and compare them , eith er visually or m ath em atic ally, to the indicated sam ple spe ctra.) 17. Corrective actions: If the results of Steps 14 through 16 indicate that the data quality objectives of the test plan have not been achieved, the analyst may perform one or m ore of the following actions: S Averaging of se quential sam ple spectra to reduce the res idual noise area (RSA ). S Inclusion of contaminant reference spectra in the mathem atical analysis.
NIOSH Manual of Analytical Methods, Fourth Edition ​ORGANIC AND INORGANIC GASES by FTIR Spectrometry: METHOD 3800, Issue 1, dated 15 March 2003 - Page 5 of 47
S S S
Development of more accurate analyte or interferant reference spectra. Inclusion of reference spectra for additional compounds in the mathem atical analysis. Exclusion from the m athem atical analysis of analyte and/or interferant com pounds which are clearly absent in the samples. S De-resolution or w avenum ber ad jus tm ent of the reference spectral library to match that of the sam ple spectra (or vice versa). S Revision of the origina l data qua lity objectives (tho se inc luded in the test plan) to levels supported by the test data. NOTE: After performing any such corrective actions, the analyst must repeat Steps 13 through 16 and re-evaluate the LOD value for each analyte compound.
REPORTING: 18. Reporting requirements include the analyte and interferant concentrations, the concentration uncertainties, the FTIR spectrometer configuration, the sampling locations and conditions, the source(s) of the reference spectra, the CTS spectral analysis results, the results of QA/QC procedures, and certificates of analysis for all standard ga ses . Any va riations of the test procedu res and origina l data qua lity objectives from those included in the test plan should also be documented and reported. (Several of the term s us ed h ere a re de fined in Appen dix A and described in the following Ap pen dices. In particular, see T able D1 for a d esc ription of the F TIR spe ctrom eter c onfiguration pa ram eters .)
EVALUATION OF METHOD: Fie ld evaluations of extractive FTIR methods have been performed for many compounds (see, for example, Referen ces 7 an d 8) accord ing to EPA M ethod 301 (R eference 9).
REFERENCES: [1] U.S. EPA (proposed); Method 320 - Measurement of vapor phase organic and inorganic emissions by extractive FTIR spectroscopy; Federal Register V63 No.56, pp.14219-14228 (March 24 1998); also available (on Ma y 19 19 99) a t http://ww w.ep a.go v/ttn/oarpg/t3 /fr_notices /, file frprop .pdf. [2] U.S. EPA (propo sed ); Addendum to Method 320 - Protocol for the use of FTIR spectrometry for the analysis of gaseous emissions from stationary sources; Federal Register V63 No.56, pp.14229-14237 (March 24 1998); also ava ilable (o n M ay 19 1999) at http://www .ep a.g ov/ttn/oa rpg/t3 /fr_ notice s/, file frprop.pdf. [3] ASTM Designation D 6348. Standard test method for determination of gaseous compounds by extractive direct interface fo urier tra nsform infrare d (FTIR ) spe ctros cop y. [4] ASTM Designation D 1356. Standard terminology related to sampling and analysis of atmospheres. [5] ASTM Designation E 168. Practice for general techniques of infrared quantitative analysis. [6] ASTM Designation E 1252. Practice for general techniques for obtaining infrared spectra for qualitative analysis. [7] EPA – Fourier Transform Infrared (FTIR) method validation at a coal-fired boiler, available (on May 19 1999) at http ://www .ep a.g ov/ttnem c01/ftir/reports, file r03.htm l. [8] W .K. Reagen et al., Environmental Science and Technology 33, pp. 1752-1759 (1999). [9] EPA – Validation Protoc ol, M eth od 301, available (o n M ay 19, 1999) through link s provided in the docum ent http://ww w.e pa.go v/ttn /em c/p rom gate.h tm l. [10] EPA FTIR Library of Hazardous Air Pollutants, available (on May 19 1999) at http://www.ep a.go v/ttnem c01 /ftir/data/e ntrop y/. This library contains m ultiple quantitative spectra for approxim ate ly 100 com pou nds with 0.25 cm -1 resolution (bo xca r apo dization). The us er m ust c alculate spectra for the des ired M IL and apod ization fro m the interfero m etric data provide d at the site http://www.epa.gov/ttnemc01/ftir/data/igram/ (see Re ference 2, Ap pendix K). Som e of these spe ctra were recorded at elevated gas te m peratures and m ay not be suita ble for quantitative workspace air ana lyses.
NIOSH Manual of Analytical Methods, Fourth Edition ​[11]NIST Standard Reference Database #79. This library may be purchased through links provided at the website http://www.gases.nist.gov/spectral.htm; it contains quantitative spectra of 24 different compounds for several MILs and several apodization functions.
[12] NIOSH Pocket Guide to Chemical Hazards, US Department of Health and Human Services–Centers and Prevention for Disease Control, June 1997.
[13] 1998 TLV’s and BEI’s Threshold Limit Values for Chemical Substances and Physical Agents, American Conference of Governmental Industrial Hygienists.
[14] CRC Handbook of Chemistry and Physics 75th Edition, CRC Press, 1994.
[15] Griffiths PR and de Haseth JA, Fourier transform infrared spectroscopy, John Wiley and Sons (New York), 1986.
[16] Hamilton WC, Statistics in physical science, Ronald Press Company, New York, 1964, Chapter 4.
[17] "Traceability protocol for establishing true concentrations of gases used for calibration and audits of continuous emissions monitors (Protocol Number 1)," June 1978, Quality Assurance Handbook for Air Pollution Measurement Systems, Volume III, Stationary Source Specific Methods, EPA-600/4-77-027b, August 1977.
[18] Plummer GM and Reagen WK, "An examination of a least squares fit FTIR spectral analysis method," Annual Meeting of the Air and Waste Management Association, Nashville, Tennessee, June 1996; Paper No. 96.WA65.03.
METHOD WRITTEN BY:
Grant M. Plummer, Ph.D. (Rho Squared), William K. Reagen, Ph.D. (3M) and Perry W. Logan (3M).
TABLE 2. REPRESENTATIVE INFRARED DATA FOR THE COMPOUNDS OF TABLE 1
NOTE: The Limit of Detection (LOD) may vary from laboratory to laboratory, analyst to analyst, instrument to instrument, and day to day. Therefore, any determination of this value should be performed under the same conditions used for sample analysis and reported only with those analyses. It is stressed that the values below are only conservative estimates of the expected performance of this method.
| Compound | Analytical Region (cm$^{-1}$) | Reference Spectrum Filenames$^a$ | LOD at 10m$^b$ (ppm) | Max. conc. at 10m$^c$ (ppm) | Max. RSA$^d$ (abs-cm-1) | Reference Spectrum Source |
| Aromatic Hydrocarbons |||||||
| Benzene | 3000 - 3150 | 015mav01.spc | 0.32 | 149 | .0360 | EPA$^e$ |
| o-xylene | 709 - 781 | 171mav01.spc | 0.65 | 150 | .0444 | EPA$^e$ |
| m-xylene | 782 - 805 | 172mav01.spc | 1.36 | 146 | .0377 | EPA$^e$ |
| p-xylene | 749 - 840 | 173mav01.spc | 1.17 | 151 | .0561 | EPA$^e$ |
| Styrene | 738 - 944 | 147mav01.spc | 1.84 | 150 | .0363 | EPA$^e$ |
| Toluene | 701 - 768 | tolmav01.spc | 1.16 | 463 | .0499 | EPA$^e$ |
| Aliphatic hydrocarbons |||||||
| n-Hexane | 2778 - 3051 | 095mav01.spc | 0.10 | 150 | .0639 | EPA$^e$ |
| Ketones |||||||
| Acetone | 1163 - 1265 | 192mav01.spc | 0.95 | 148 | .0211 | EPA$^e$ |
| 2-Butanone | 1127 - 1235 | mekmav01.spc | 0.27 | 463 | .0233 | 3M$^f$ |
| Alcohols |||||||
| Methanol | 941 - 1100 | 104mav01.spc | 0.28 | 151 | .0447 | EPA$^e$ |
| Halogented Hydrocarbons |||||||
| Methylene Chloride | 701 – 789 | 117mav01.spc | 0.31 | 150 | .0620 | EPA$^e$ |
| Vinylidene Fluoride | 1080 – 1215 | dfemav05.spc | 0.21 | 25.7 | .0930 | 3M$^f$ |
| Trichloroethylene | 762 – 966 | tcemav01.spc | 0.43 | 464 | .1071 | 3M$^f$ |
| Tetraflouroethylene | 1080 – 1215 | tfemav05.spc | 0.17 | 25.7 | .0930 | 3M$^f$ ​ |
| Aldehydes |||||||
| Formaldehyde$^g$ | 2727 – 2844 | 087bb.spt | 0.40 | 1125 | .0267 | EPA$^{e,g}$ |
| Epoxides |||||||
| Ethylene Oxide | 3059– 3070 | 084mav01.spc | 0.11 | 138 | .0025 | EPA$^e$ |
| Ethers |||||||
| Tetrahydrofuran | 2750 - 3085 | thf405.spc | 0.18 | 41 | .0782 | 3M$^f$ |
| Inorganic Compounds |||||||
| Nitrous Oxide | 1226- 1333 | n2omav01.spc | 0.36 | 904 | .0301 | 3M$^f$ |
| Carbon Disulfide | 2109 - 2200 | 028mav01.spc | 0.13 | 151 | .0123 | EPA$^e$ |
| Sulfur Dioxide$^h$ | 1290 - 1410 | so2.spc | 0.35 | ~200$^g$ | .1394 | NIST$^h$ |
| Ammonia | 998 - 1131 | nh3mav01.spc | 0.77 | 470 | .0363 | 3M$^f$ |
| Inorganic Acids |||||||
| Hyrdogen Flouride | 4034 - 4206 | 21hfrav | 0.93 | 15.8 | 0.15 | 3M$^f$ |
$^a$ Used in LOD calculations; averaged spectra from the quoted libraries; data available from the authors. $^b$ Approximate Limit of Detection (LOD) for a 10 meter absorption pathlength. Typical values of the RSA, the quoted Analytical Regions, and the quoted reference spectral data were used to calculate the LOD as described in Appendix E, Equation E1.
$^c$ The maximum ppm-m value available for the compound in the quoted reference spectrum source.
$^d$ Maximum Squared Residual Area (RSA) in the specified Analytical Regions consistent with the quoted LOD values. See Appendix E, Section 1.
$^e$ See Reference 10. Average absorbance and accepted standard concentration values for the low-concentration pairs of spectra were used. Interferograms were truncated to 0.5 cm-1 resolution and triangular apodization was employed.
$^f$ Data available from the authors.
$^g$ From EPA reference spectra recorded at 100° C (Reference 10).
$^h$ NIST Standard Reference Database #79 (Reference 9). The quoted maximum concentration for SO2 is based on linearity studies of 0.5 cm-1 resolution spectra with triangular apodization. Non-linear absorbance leads to errors of less than 10% at 1000 ppm-m.
​APPENDIX A. Terminology.
absorption cell—a structure which contains a fluid sample, but allows light to pass through a sample at known temperature, pressure, and absorption path length.
absorption band—a contiguous wavenumber region of a spectrum (equivalently, a contiguous set of absorbance spectrum data points) in which the absorbance passes through a maximum or a series of maxima.
absorption pathlength—the distance, measured in the direction of propagation of the beam of radiant energy, between the surface of the specimen on which the radiant energy is incident and the surface of the specimen from which it is emergent.
absorbance (units: abs)—in terms of the incident and transmitted intensities I$_0$ and I, the absorbance A is given by A = -log(I/I$_0$). From a pair of FTIR single beam spectra A (the background spectrum) and B (the sample spectrum), the sample absorbance for each wavenumber value (with index i) in the spectra is approximated by A$_i$ = -log(B$_i$/A$_i$).
absorbance linearity—a characteristic of (ideal) absorbance spectrum; for such a spectrum, the measured absorbance is described by Beer's Law (Equation C1).
absorptivity—a measure of the fraction of the incident infrared radiation that is absorbed by a particular compound per molecule and per absorption pathlength; see equation C1.
analytical region—a contiguous wavenumber region (equivalently, a contiguous set of absorbance spectrum data points) used in the quantitative analysis for one or more analytes. Note: The quantitative result for a single analyte may be based on data from more than one analytical region.
analyst—a person familiar with and experienced in performance of all aspects of this FTIR-based method. Analysts m ay perform any portion(s) of the method, and must perform certain portions of the method (see also "operator").
analyte—a compound whose concentrations in a sample is of interest and must be accurately quantified (see also "interferant").
aperture—an optical device which physically restricts the diameter of the optical beam.
apodization—modification of the interferogram through its multiplication by a weighing function whose magnitude varies with the position of the interferometer's moving element.
background spectrum—the single beam spectrum obtained with all system components and without sample present (or in the presence of a non-absorbing gas replacing the sample).
baseline—any line (or smooth function of wavenumber) drawn on an absorption spectrum to establish a reference point that represents a function of the radiant power incident on a sample at a given wavelength.
Beer's Law—the direct proportionality of the absorbance of a compound in a homogeneous sample to its concentration. See Equation C1, which also describes the more general case of gas mixtures.
calibration transfer standard (CTS) gas—a gas standard of a compound used to measure the sample absorption pathlength; see Step 7, Step 11, Appendix B (Section 1), and Appendix D, (Section 5).
cm$^{-1}$—see wavenumber
compound—a substance possessing a distinct, unique molecular structure.
concentration—the quantity of a compound contained in a unit quantity of sample. The unit "ppm" (number, or mole, basis) is recommended, and is equivalent to the volume basis for ideal gases.
concentration-path length product (CCP)—the mathematical product of concentration of the species and the
​absorption pathlength. For reference spectra, this is a known quantity; for sample spectra, it is the quantity directly determined from Beer's Law. The units "ppm-meters" (ppm-m) are recommended.
data quality objectives—parameters pertaining to a certain application of this method, including the estimated LOD values for each compound.
de-resolve—to form spectra of lower resolution (higher FW HM) from spectra of higher resolution (lower FW HM); see Reference 2 (Appendix K) and Reference 11 for de-resolution procedures and programs.
detector linearity—a characteristic of an (ideal) IR detector; for such a detector, the measured detector output voltage, when plotted against the total IR in a broad-band IR signal incident on the detector, would form a straight line.
double beam spectrum—a transmittance or absorbance spectrum derived by dividing the sample single beam spectrum by the background spectrum.
Note: The term "double-beam" is used elsewhere to denote a spectrum in which the sample and background interferograms are collected simultaneously along physically distinct absorption paths. Here, the term denotes a spectrum in which the sample and background interferograms are collected at different times along the same absorption path.
extractive—the type of spectroscopy which includes extracting and transporting a sample stream from gases at a certain location to an absorption cell, and isolating the sample in the absorption cell for analysis. Other types of spectroscopy in which the sample is not isolated in an absorption cell include "remote", "open path", and "local open path" techniques.
filter—(1) A device made of inert materials which physically removes solid and liquid phase particles from a gas stream. (2) An optical device which transmits some fraction of the radiation incident on it; "neutral density" and "mesh" filters transmit an approximately constant fraction of the incident radiation at all wavelengths over a specified wavelength range.
FFT (Fast Fourier transform)—a discrete (digital) approximation to an FT (Fourier transform; see below) involving the factoring of the original data into sparse matrices containing mostly zeros.
FT (Fourier transform)—the mathematical process for converting an analytical (non-discrete) amplitude-time function to an amplitude-frequency function, or vice versa.
FTIR (Fourier transform infrared) spectrometer—an analytical system that employs a source of mid-infrared radiation, an interferometer, an enclosed sample cell of known absorption pathlength, an infrared detector, optical elements that transfer infrared radiation between components, and a computer system. The time-domain detector response (interferogram) is processed by a Fourier transform to yield a representation of the infrared power vs. infrared frequency. See Figures C1 and C2.
FTIR spectrometry—use of an FTIR system to perform quantitative measurements.
FTIR system—the combination of an FTIR spectrometer and a sample interface.
FTIR system configuration—the set of parameters required to reproduce, as closely as possible, results from a particular FTIR system at a later time. This set includes (at least) the nominal MIL, the absorption pathlength, the apodization function, the gas temperature, the gas pressure, the zero filling factor, the measured wavenumbers of specific water absorption bands, the sources of the reference library spectra, the integration time, the detector type and serial number, the detector gain (including hardware and software settings).
FTIR system response time—the minimum time required for the output of an FTIR system to accurately reflect a sudden change in the sample gas composition; see Appendix B, Section 5.
frequency,—v the number of cycles per unit time; for light, $\scriptstyle {v=s\backslash \lambda }$, where's is the speed of light and λ is the light's wavelength. Unlike the speed and wavelength, which are medium-dependent, the frequency of light is independent of the medium through which the light travels. Th e term "frequency" is often used to ​denote the wavenumber (w, cm$^{-1}$) in FTIR spectroscopy because (in a given medium) the wavenumber is proportion al to the frequency v. (See Appendix C, Section 4, and "wavenumber" in this Appendix.)
full-width-half-maximum (FWHM)—for a single, symmetric absorption band, the full width of the band (in cm$^{-1}$) between its 50% relative maxim um absorption levels.
impinger—a device constructed of inert materials which passes a gas stream through a liquid phase.
infrared source—a device which emits a pattern, stable in intensity and wavelength profile, of infrared radiation over a wide range of infrared wavelengths. High temperature filaments or ceramic elements, in conjunction with appropriate focusing optics, are often employed.
infrared detector—a device which (ideally) produces a voltage proportional to the total infrared power incident on it. Examples are 1) the mercury-cadmium -telluride (MCT) detector, which requires cooling (and is often cooled to liquid nitrogen temperature), and 2) the deuterated triglycine sulfate (DTGS) detector, often operated at ambient temperature.
interferogram—record of the IR detector's response to the modulated component of the interference signal measured as a function of retardation.
interferometer—device that divides a beam of radiant energy into two or more paths, generates an optical path difference between the beams, and recombines them in order to produce repetitive interference maxima and minima as the optical retardation is varied.
integration time—the total time over which the interferometric results of single scans are averaged to produce an interferogram (and its subsequent single- and double-beam spectra). Most software packages allow selection of the number of scans rather than the integration time. The integration time is approximately equal to (but is always less than) the time interval over which the selected number of scans is actually executed.
interferant—a compound whose presence in a sample spectrum must be taken into account to accurately determine one or more analyte concentrations, but whose concentration need not be accurately determined.
least squares fitting (LSF) algorithm—a calculation whereby one or more com pound concentrations are estimated from a sample spectrum by minimizing the squared error in Beer's Law within a defined analytical region (see Equations C1 through C6).
limit of detection (LOD, ppm)—for a defined FTIR system configuration and sample matrix, an estimate of the lowest detectable concentration of a specific analyte based on the FTIR system's RSA and the analyte's integrated absorbance for a selected analytical region.
line—see absorption band
linewidth—see full-width-half-maximum (FWHM) and minimum instrumental linewidth (MIL).
metering valve—a gas valve allowing reproducible adjustments of a gas stream flow rate on the order of 2% of the valves full flow rate.
mid-infrared (MIR)—the region of the electromagnetic spectrum from approximately 400 to 5000 cm$^{-1}$.
minimum instrumental linewidth (MIL)—for a given FTIR spectrometer and FTIR system configuration, the minimum measured FWHM for any absorption band. In wavenumbers, the MIL is often estimated as the reciprocal of the retardation expressed in centimeters. The MIL depends on the choice of apodization function, and is often larger than the MIL estimated from the retardation.
multi-pass cell—an absorption cell which uses mirrors to pass the infrared radiation through the gas sample more than once; this leads to an absorption pathlength larger than the physical length of the cell (see also "White cell").
mm Hg—a measure of pressure difference which results in the vertical displacement of a column of liquid ​mercury by one millimeter. A pressure difference of one atmosphere (atm) is equal to 760 mm Hg, to 1.01 × 10$^5$ Pascals (Pa), and to 14.7 pounds per square inch (psi).
operator—a person familiar with and experienced in performance of only some aspects of this FTIR-based method. Operators may perform many portions of this method, but specific portions of the method (see above) must be performed by an "analyst".
peak—see absorption band
qualitative analysis—examination of sample spectra to determine the presence or absence of particular compounds in a sample.
quantitative analysis—estimation of the actual concentrations of a specific set of compounds using a specific set of analytical regions.
reference spectra—absorption spectra of gases with known chemical compositions, recorded at a known absorption pathlength, which are used in the quantitative analysis of gas samples.
relative wavenumber accuracy (RWA, %)—the percent difference in wavenumber values measured by an FTIR spectrometer relative to a reference library standard. The RWA is estimated through spectral comparisons of the wavenumbers of two isolated water vapor absorption. See Appendix B, Section 3.
residual squared area (RSA)—a measure of the noise (random and systematic) and/or spectral artifacts for an absorbance spectrum in some analytical region; see Appendix B, Section 2 for a mathematical definition. The RSA can be used to estimate the LOD for a given compound measured with a given FTIR system configuration.
retardation—optical path difference between two beam's in an interferometer; also known as "optical path difference" or "optical retardation." In the case of a standard Michelson interferometer, the retardation is simply twice the distance moved by a mirror in the interferometer during a scan.
rotameter—a device indicating the volumetric flow rate of a gas by the vertical displacement of an object suspended by the gas stream.
sampling location—the point in space at which sample gases enter the sample interface.
sample interface—that part of the FTIR system which comes in contact with the sample and/or calibration gas es. It includes the sample probe, sample filter, sample line, sample pump, gas valves, internal surfaces of the absorption cell, pressure gauge, sample rotameter, the vent lines, and the calibration components (gas cylinders, regulators, and rotameters).
scaling—application of a multiplicative factor to the absorbance values in a spectrum.
scan—digital representation of the detector output obtained during one complete motion of the interferometer's moving assembly or assemblies.
single beam spectrum—Fourier-transformed interferogram, representing the relative detector response vs. wavenumber.
    Note: The term "single-beam" is used elsewhere to denote any spectrum in which the sample and background interferograms are recorded on the same physical absorption path; such usage differentiates such spectra from those generated using interferograms recorded along two physically distinct absorption paths (see "double-beam spectrum" above). Here, the term applies (for example) to the two spectra used directly in the calculation of transmittance and absorbance spectra of a sample.
system zero (SZ) spectrum—the absorbance spectrum of a non-absorbing gas (nitrogen or zero air) acquired using those portions of the sampling interface used to acquire actual sample gases.
transmittance, T—the ratio of radiant power transmitted by the sample to the radiant power incident on the ​sample. Estimated in FTIR spectroscopy by forming the ratio of the single-beam sample and background spectra; often presented in %T (100 × T) in spectral representations.
uncertainty—a mathematical quantity determined in a least-squares fitting procedure, used to estimate the likely error in the determination of the sample concentration in a procedure; see Equations C1-C6.
wavelength λ,—the physical distance between successive maxima in the electromagnetic waves which comprise light. The wavelength and speed of light depend on the medium through which the light travels.
wavenumber, w—the reciprocal of the wavelength, also the number of wavelengths of light per unit length, usually expressed in the units cm$^{-1}$. As is true of both the speed and wavelength of light, the wavenumber is dependent on the medium through which the light travels. (See Appendix C, Section 4, and "frequency" in this Appendix.)
wavenumber adjustment—reassignment of the cm$^{-1}$ values associated with single- and/or double beam spectra. Adjustments may be made locally by shifting or stretching the wavenumber scale, or globally stretched by changing the laser wavenumber during the FFT.
White cell—alternate name for a "multi-pass" absorption cell (see above) indicating its inventor.
zero filling—the addition of zero-valued points to the end of a measured interferogram. In most computer programs, specification of a zero filling "factor" of N results in an interferogram with N times as many points as the original interferogram.
​APPENDIX B . System Tests.
These procedures must be conducted at least once on new or significantly altered (by replacement of components, dis- and reassembly, etc.) systems. The tests described in Sections B2 and B4 must also berepeated during either the pre-test preparations or quality assurance procedures. In all cases, activate the FTIR system and allow sufficient time for the infrared source, the infrared detector, and (if required) the temperature control systems to stabilize before proceeding.
B1 Absorption pathlength
Obtain one or more absorbance spectra of a calibration transfer standard (CTS) gas (ethylene at 200 to 300 ppm-meters is recommended) at the gas temperature and pressure of a reference CTS spectrum of the same compound. For each spectrum, calculate the indicated absorption pathlength according as
${L_{S}}={\frac {{L_{R}}{P_{R}}{A_{S}}}{{P_{S}}{A_{R}}}}$ Equation B1
where $L_{S}$ = pathlength indicated by the sample CTS spectrum (meters). $L_{R}$ = pathlength of the reference CTS spectrum (meters). $A_{S}$ = area of the reference CTS spectrum (abs cm$^{-1}$). $A_{R}$ = area of the reference CTS spectrum (abs cm$^{-1}$). $P_{S}$ = pressure of the sample CTS spectrum (mm Hg). $P_{R}$ = pressure of the reference CTS spectrum (mm Hg).
When multiple CTS spectra are available, assign to $L_{S}$ the mean of the single-spectrum $L_{S}$ results. The reference CTS spectrum pathlength and concentration used must be based on multiple, high-quality gas standards and physical length measurements (see Appendix D, Section 5). The analyst must document criteria for the selection of the analytical region and any baseline correction procedures employed.
B2 Residual Squared Area
Note: If the following calculations are performed during testing or as part of the QC procedures (steps 14 through 17), perform them using a workspace air spectrum instead of the “water vapor (absorbance) spectrum” described in the two paragraphs below.
Use the integration time selected for field testing in recording the spectra described below. Record a background spectrum of dry N$_2$ gas or zero air. Using a suitable impinger, humidify the N$_2$ or zero air stream and record a single-beam spectrum at an absolute pressure between 725 and 795 mm Hg. Form the absorbance spectrum of this water vapor sample from the single beam spectra. Assign the spectrum a unique filename and save it for the calculations described below.
From this water vapor spectrum, subtract a scaled spectrum (see Appendix A) formed from the water vapor reference spectrum to be used in subsequent quantitative analyses. The scaling factor may be varied to minimize the absorbance in the resulting difference spectrum in the various analytical regions to be used in the analyses. Subtract a constant offset, a linear function, or a quadratic function from the difference spectrum in each analytical region to form a residual spectrum R for each region. For each residual spectrum R with discrete absorbance value $R_{i}$ for i = p to q, in the wavenumber range $w_{p}$ to $w_{q}$, the residual squared area (RSA) is defined as:
​$RSA={\frac {[{w_{p}}-{w_{q}}]}{q-p+1}}{\sqrt {\sum _{i=p}^{i=q}{\frac {{(R_{i})}^{2}}{q-p}}}}$ Equation B2
The RSA has the dimensions (abs cm$^{-1}$), and serves as a measure of the integrated absorbance of spectral noise and water subtraction artifacts over the analytical region. The RSA is compared to the total absorbance of a compound in the same region to estimate the LOD for the compound in that region (see Appendix D, Section 9 and Appendix E, Section 1).
The calculation described above assumes that water is the only significant infrared absorber in the samples besides the analytes, and that only one analyte absorbs in any analytical region. If other analytes or interferants are present, a more conservative RSA may be estimated by adding the absorbance of the additional compounds to the difference spectrum using a set of suitable reference spectra, then subtracting their absorbance using a different set of reference spectra.
B3 Minimum Instrumental Linewidth (MIL)
Evacuate the absorption cell to a pressure below 100 mm Hg and record a background spectrum. Obtain a workspace air sample at an absolute pressure of approximately 300 mm Hg. Record the absorbance spectrum of this low-pressure sample. Measure at the FW HM (full width at half maxim um) linewidth, in absorbance, of at least two isolated water vapor lines (for example, the lines near 1918 cm$^{-1}$ and 2779 cm$^{-1}$). The MIL is the mean of these FW HM measurements.
B4 Wavenumber Reproducibility
Note: If this calculation is performed during testing or as part of the QC procedures (see Steps 6 and 10), perform these determinations using a workspace air spectrum instead of the water vapor absorbance spectrum described in Section B2.
Using a water vapor spectrum recorded as described in Section B2, determine the center wavenumber values w$_{S1}$ and w$_{S2}$ of two isolated water vapor absorption features; the peaks near 1918 cm$^{-1}$ and 2779 cm$^{-1}$ are suggested, though any other pair of isolated lines separated by 500 cm$^{-1}$ or more is suitable. Compare these results to those center wavenumber values w$_{R1}$ and w$_{R2}$ and for the same absorbance features in the water vapor wavenumber standard associated with the reference library to be used in quantitative analyses as follows: Calculate the relative wavenumber accuracy (RW A) in percent for each of the two absorption bands according to
$RWA=ABS(w_{Rt}-w_{st})$ for i = 1, 2. Equation B3
Compare the maximum of these two values to the MIL for the FTIR system (see Section B3). If the ratio RWA/MIL exceeds 2%, adjustment of the wavenumber scale for the sample spectra may be required.
Mathematical wavenumber adjustments may be made locally by shifting or stretching the wavenumber scale, or globally stretched by changing the laser wavenumber during the FFT. However, large shifts (on the order of 5% or more of the MIL) indicate that the system requires physical adjustments, such as re-alignment of the laser system responsible for control of the interferometer's moving element. In addition, mathematical wavenumber adjustments require some sort of interpolation procedure in conjunction with the quantitative spectral analysis, and those procedures may result in spectral mismatches whose effects on the accuracy of the analysis are not easily quantified.
The necessity of such wavenumber adjustments depends, in part, on the widths of the absorption peaks of the compounds involved in the spectral analysis. Because many of the absorption bands of water—a nearly ubiquitous interferant in workspace air IR analysis—are very narrow, an accurate analysis usually requires the relatively stringent limits placed above on the RWA to MIL ratio. However, it is possible to obtain accurate results when this ratio exceeds the recommended limit, especially when only broad absorbance features are actually employed. The analyst may choose ​to approve analytical results obtained when this ratio exceeds the recommended limit.
B5 System Response Time
Direct N$_2$ or zero air through the entire sample interface and record spectra at approximately 30 second intervals. Abruptly replace the N$_2$ or zero air gas flow with CTS gas and continue to record spectra. The system response time is the subsequent time required for the FTIR system to generate an absorbance spectrum in which the CTS compound's calculated concentration reaches 95% of the final (stable) concentration value indicated in later spectra.
B6 Detector Linearity
For the chosen optical configuration, attenuate the power incident on the detector by either 1) modifying the aperture setting or 2) placing filters (neutral density or mesh) in the infrared beam path (see Figure A1). At approximately 100%, 50% and 25% of the system full IR power level, collect pairs of background and CTS spectra. Compare the areas of the CTS bands for the three spectra and verify that they are equal to within 5% of their mean value. If they are not, apply software linearization corrections to the interferometric data according to the manufacturer's instructions. If this option is unavailable, it is necessary to either 1) characterize the system non-linearity and/or apply appropriate concentration corrections or 2) operate the system with attenuation sufficient to ensure linear detector response.
​APPENDIX C. General Description of FTIR Spectrometry.
C1. FTIR Spectrometer Components
Figure C1. FTIR Spectrometer Components and Beam Path
Figure C1 illustrates the basic FTIR spectrometer configuration required for gas phase analyses. The infrared radiation emitted by the infrared (IR) source contains energy at all wavelengths between 2.0 and 20 microns; this is the portion of the electromagnetic spectrum usually referred to as the "mid-infrared" (MIR). In the units typically employed in FTIR spectroscopy (wavenumbers, or cm$^{-1}$), this is the wavenumber range 5000 to 500 cm$^{-1}$. The IR radiation passes through an interferometer, where the motion of an optical element-usually a mirror-optically modulates the infrared beam. The modulated IR beam then enters an absorption cell through a window (typically made of KBr or ZnSe) and interacts with the gases of interest. The physical length over which this interaction takes place is the "absorption pathlength." In "multi-pass" (or "White") absorption cells, mirrors within the cell direct the IR beam through the sample gas many times; in such cells, the absorption path length can be from 4 to 50 (or more) times the cell's physical length. (A larger absorption pathlength generally leads to greater sensitivity.) The IR beam then exits the sample cell via a second window and is re-focused onto an IR detector. Because this extractive technique requires the transport of gas samples through the FTIR absorption cell, the design and integrity of the sampling system is of great importance. It is also important that the sampling system allow the operator to perform all the necessary calibration and sampling procedures without compromising the speed and flexibility of the analytical system. Figure C2 illustrates a sampling system con figuration that meets these requirements, though other configurations are possible. A computer controls the actions of the interferometer and records the voltage output of the IR detector throughout the motion of the interferometer's optical element. Ideally, the detector voltage is proportional to the total power in the IR beam. The computer must accurately record the detector voltage as a function of the position of the moving element in the interferometer, so a secondary, laser-based optical system is usually used to measure the moving element's position very precisely. In most circumstances, the motion of the mirror or other optical element is repeated many times, and the resulting individual "scans" are ​"co-added" (averaged) to reduce the system's residual noise area (RSA). A plot of the resulting IR power-vs.-position signal, referred to as an interferogram, is shown in Figure C3. This interferogram is the co-added result of 64 scans with only nitrogen gas (and some low level of water vapor) present in the absorption cell. Nitrogen is one of the few compounds which does not interact with infrared radiation, so this interferogram very closely represents the fundamental FTIR system response in the absence of a sample. Note that the signal is relatively large near the beginning of the interferogram, where the “zero phase difference (ZPD) burst” is located. The ZPD is often used to rapidly obtain an estimate of the IR signal strength during alignment of the optical system.
Figure C2. Sampling Components and Sample Paths
Figure C3. Sampling Components and Sample Paths
​C2. The Fast Fourier Transform (FFT)
Every data point in the interferogram contains intensity information about every infrared wavelength transmitted from the source to the detector. It is possible to recover the intensity information as a function of wavelength through application of a Fast Fourier Transform (FFT), from which the FTIR technique's name is derived. This digital transformation of the interferogram can be thought of as the mathematical inverse of the optical modulation applied to the infrared beam as it passes through the interferometer. Its function is similar to that of the human brain and ear, which provide intensity information (loudness) versus wavelength (pitch) for complex signals (sound waves) incident on the eardrum. (Note that, as for an interferogram, each point in a complex sound wave contains intensity information about every pitch contained in the wave. Yet the ear and brain allow a symphony audience to immediately perceive, for instance, that the piccolo is playing very loudly while the tuba is playing very quietly.) Reference 15 (Chapter 3) provides a complete mathematical description of the FFT.
C3. Instrument Resolution, Apodization Function, and Minimum Instrumental Linewidth (MIL)
Most software packages supplied with FTIR systems provide several options associated with the collection of data and application of the FFT. These typically include – at least – the nominal "instrument resolution" (specified in cm$^{-1}$) and the "apodization function" (e.g., "Boxcar" and "Triangular"). These parameters are very important in quantitative spectroscopy, and are addressed in turn below.
The instrument resolution is the most fundamental and important instrument parameter. It specifies the nominal minimum full-width-at-half-maximum (FWHM, in cm$^{-1}$) of any spectral "peak" (or "line") in the final instrument output. Every FTIR instrument has a minimum FWHM determined by the maxim um distance traversed by the interferometer's moving element during a single scan. (For the basic Michelson interferometer, the FWHM in cm$^{-1}$ is equal to (2d)$^{-1}$, where d is the distance in cm traversed by a moving mirror during a scan.) Clearly, instruments with low FWHM provide more spectral information than instruments with higher FWHM capability. However, this additional information comes at high costs associated with the design, construction, size, mechanical stability, portability, speed, and residual noise area (RSA) of the instruments.
It is important to recognize the two uses of the word “resolution” in the nomenclature used to describe FTIR spectrometers: Instruments of high resolving power, or “high resolution,” provide spectral features of low FWHM; when the nominal resolution is specified in units of cm$^{-1}$, a lower cm$^{-1}$ specification corresponds to higher resolving power, or “higher resolution”. Most commercially available FTIR spectrometers suitable for field use provide FWHM values greater than or equal to 0.5 cm$^{-1}$—that is, they are systems whose nominal spectral resolution is specified as a number higher than 0.5 cm$^{-1}$. Most of the instruments capable of higher resolution (lower FWHM) are suitable for use only in very stable laboratory environments.
Standard FTIR operating software always provides options for recording spectra with FW HM values higher than the instrument's actual lower FWHM limit. These options simply move the mirror (or other optical element) through only some fraction of its maximum possible travel. Operating the instrument in this manner results in larger FWHM values ("lower" resolution, and shorter interferograms) than the instrument is mechanically capable of providing. Spectra of lower resolution (higher FWHM) provide less information, but can be generated more quickly and, in most cases, with lower RSA than spectra of higher resolution.
The instrument operator can also choose the apodization function to be used in the generation of FTIR spectra. Apodization is a mathematical alteration of the interferogram that can be performed before application of the FFT. Several standard alteration functions have been devised, and each affects the final absorption spectrum of the sample gas in a different way. As with the selection of instrument resolution, each choice has its advantages and drawbacks. The simplest choice, known as the "boxcar apodization" function, results in the lowest FWHM but also in relatively low S/N ratio. (Spectra generated with the boxcar function are often referred to as “unapodized” spectra.) Other choices (triangular, Norton-Beer, and several other apodization functions) provide higher S/N ratio at the cost of higher FWHM values and other tradeoffs in quantitative spectroscopy. Reference 15 provides a more thorough description of the characteristics of various apodization functions.
For a given instrument configuration—which includes the nominal spectral resolution and the choice of apodization function—every FTIR system is capable of generating absorption bands with a minimum instrumental linewidth (MIL). Unlike the actual spectral resolution (which has several accepted physical ​definitions—see Reference 15, Chapter 1, Section IV) and nominal spectral resolution parameters, the MIL is a parameter which is readily measured to the accuracy required for practical applications of FTIR spectrometry. It can be measured using the water absorption bands present in low-pressure works pace air samples (see Appendix B, Section 3).
C4. Single Beam Spectra
The mathematical result of the FFT (applied to an apodized IR interferogram) is a called a single beam spectrum. Single beam spectra represent the infrared power transmitted through the FTIR spectrometer as a function of the infrared "wavenumber" $w$, which is usually expressed in the units of reciprocal centimeters (cm$^{-1}$). The wavenumber is actually a measure of the frequency, rather than the wavelength, of the infrared radiation. In a vacuum, the wavelength and frequency are related through the equation $\textstyle {\nu =s/\lambda }$, where λ is the wavelength (cm), ν is the frequency (sec$^{-1}$, or Hz), and s(cm/sec) is the speed of light, equal to 2.99792954×10$^{10}$ in a vacuum. In these units, the wavenumber in cm$^{-1}$ is given by the equation $\textstyle {w=1/\lambda =\nu /s}$. Figure C4 presents the single beam spectra for two samples consisting mainly of nitrogen gas (≥99%) but with different concentrations (≤ 1%) of water vapor. The vertical scales of the two spectra are nearly identical, but they have been offset for clarity. The detected infrared power in certain wavenumber regions is clearly lower in the high moisture sample, indicating both the qualitative nature and strength of water's absorption of infrared radiation.
C5. Double-Beam Spectra - Transmittance and Absorbance
Combinations of pairs of single beam, such as the pair of spectra S and B shown in Figure C4, are referred to as double beam spectra; they provide the quantitative basis for FTIR spectroscopy. One type of double
Figure C4. Single Beam Spectra of N2 at Different Moisture Levels.
​beam spectrum is the transmittance. The percent transmittance of a sample gas possessing the single-beam spectrum S—with respect to the background single-beam spectrum B—is defined as T(%)=100 * S/B; a transmittance value is defined for each wavenumber value of the two spectra. If the background spectrum B closely represents the response of the FTIR system to a transparent sample, then the percent transmittance T closely approximates the percentage of the infrared radiation transmitted by the sample (represented by the spectrum S). Because water is the only absorbing compound present in the single-beam spectrum B, the spectrum T (shown in Figure C5) closely approximates the percent transmittance spectrum of water.
The same pair of spectra define the (double beam) absorbance A of the sample through the equation A = -log$^{10}$(S/B). The absorbance spectrum of water, as approximated by the two single-beam spectra S and B, is shown in Figure C6. The absorbance is the desired quantity because it appears in the general linear absorption model known as Beer's Law (see below).
Figure C5. Double Beam Transmittance Spectrum of Water
​C6. Beer's Law
Figure C6. Double Beam Absorbance Spectrum of Water
The absorbance spectrum of a sample gas is determined from single beam spectra of an infrared-transparent gas (the background spectrum) and the sample gas (see Section 5). The fundamental relationship connecting the absorbance spectrum of a sample gas to the concentrations of the compounds comprising the sample is referred to as Beer’s Law. This relationship can be written as
$A_{1}=\sum _{j=1}^{M}{L_{S}}{a_{ij}}{c_{j}}$ (Equation C1) where
| $i$ | = | an index labeling the frequencies of the observed absorbance values in the sample’s absorbance spectrum. |
| $A_{i}$ | = | the observed absorbance of a sample at the ith wavenumber (abs). |
| $L_{S}$ | = | the sample absorption pathlength (meters). |
| $j$ | = | an index labeling the absorbing compounds comprising the sample. |
| $a_{ij}$ | = | the absorptivity of the jth compound at the ith wavenumber (abs/ppm/meter). |
| $C_{j}$ | = | the volumetric concentration of the jth compound (ppm). |
| $M$ | = | the number of absorbing compounds in the sample. |
The procedures described in this method are all related to the parameters which comprise Beer’s Law. The following list describes these procedures and relationships in a general context:
1) Record a reference absorbance spectrum for each interesting compound of a nitrogen-diluted sample of the pure compound, at a known concentration and pathlength, then divide the absorbance at each point in that spectrum by the product of the concentration and pathlength. This process yields the absorptivity spectrum ($a_{ij}$), or reference spectrum, for each compound.
​2) Measure the absorbance $A_{i}$ for the mixture of compounds (see Steps 5 and 9 above).
3) Determine the pathlength $L_{S}$ for the current measurement of $A_{i}$ (see Steps 5 and 7 above).
4) Select the analytical region—that is a set of frequencies, corresponding to the possible values of the index i—which are to be used to determine the concentration of each compound, and then mathematically invert Equation C1 to determine the desired concentrations $C_{j}$. (Appendix E addresses the topic of spectral analysis in detail.)
NOTE: The true absorptivity for a single gaseous compound is a characteristic only of the compound's structure. However, details of the FTIR system performance and operation affect the observed absorptivity and its accuracy. Similarly, FTIR measurements provide only an approximation of the true absorbance spectrum of a mixture of gaseous compounds, though it is, under many circumstances, a sufficiently accurate approximation. It is the responsibility of the analyst to verify and ensure that the reference and sample spectra provide a sufficiently accurate quantitative analysis according to Beer's Law. The following sections of this Appendix describe the mathematics of such an analysis. Appendix D addresses the topics of developing and using reference spectral libraries. Appendix E provides an illustrative example of the design and evaluation of the quantitative analytical process.
C7. Determining Concentrations with Least Squares Fitting Algorithms.
When a sample gas contains only one absorbing compound, Equation C1 simplifies to
$A_{i}={L_{S}}{a_{ij}}C_{j}$ (Equation C2)
This means that in any analytical region where only one gas absorbs, any one (of the usually many) absorbance spectrum values $A_{i}$ can be used to yield the concentration $C_{j}$.
The absorbance area $A_{s}$ for single-component spectrum in an analytical region (from i = p to i = q) can be written as
${A_{S}}={\sum _{i=p}^{i=q}}A_{i}={\sum _{i=p}^{i=q}}{L_{S}}{a{ij}}{C_{j}}={L_{S}}{C_{j}}{\sum _{i=p}^{i=q}}{a_{ij}}={L_{S}}{C_{j}}{A_{R}}$ (Equation C3)
where $A_{R}$ is the area in the reference spectrum for that compound in the same analytical region. (This is the basis of the absorption path length $L_{S}$ calculation described in Step 7 and Appendix B, Section 1.) Because calculation of the absorbance area involves many points in the sample spectrum, Equation C3 leads to much more accurate results than the single-point calculation represented by Equation C2.
However, when many absorbing compounds are present in a sample, the absorption patterns of the various compounds often overlap. In this case, there is usually not an isolated analytical region for each compound in which only that compound absorbs infrared radiation; no single absorbance point and no simple absorbance area is suitable for determining any of the component concentrations. In this case, the simplest method for determining concentrations is to use a least square's fitting (LSF) algorithm.
LSF algorithms use the fact that there is some set of estimated concentrations $D_{j}$ which minimizes the "squared error" in Beer's Law for any given analytical region, for any set of compounds. The only requirement on the chosen analytical region is that it must contain a sufficient number of data points; since each FTIR spectrum contains many thousands of absorbance values, this requirement is nearly always fulfilled. If we use the estimated concentrations $D_{j}$ (rather that the true concentrations $C_{j}$) in Beer's law, they will lead to some estimated error $e_{i}$ at each value of i (that is, at each point in the analytical region we choose). Equation C1 becomes:
${A_{i}}={e_{i}}+{\sum _{j=1}^{M}}{L_{S}}{a_{ij}}{D_{j}}$ (Equation C4)
The estimated squared error (or "variance") in Beer's Law using the estimated concentrations is:
​ $E^{2}={\sum _{t=1}^{N}}{(e_{t})}^{2}={\sum _{t=1}^{N}}{[{\sum _{j=1}^{M}}({L_{S}}{a_{ij}}{D_{j}})-{A_{t}}]}^{2}$ (Equation C5)
where N represents the number of absorbance values in the analytical region. Reference 16 demonstrates that 1) for N > M there is a unique set of estimated concentrations $D_{j}$ which minimizes the estimated squared error; 2) this set of values is calculable from the known quantities in Equations C1 through C5; and 3) estimates $\sigma _{j}$ of the uncertainties in the quantities $D_{j}$ are also calculable from the same quantities. The value </math>3\sigma_j</math> is generally accepted as a conservative estimate of the statistical uncertainty in the related estimated LSF concentration (see Reference 3).
The estimated LSF error at each point in the analytical region,
${e_{i}}={A_{i}}{\sum _{j=1}^{M}}{L_{S}}{a_{i}j}{D_{j}}$ (Equation C6)
is usually stored following the analysis as a “residual spectrum,” which can provide an estimate of the LODs for other compounds. In addition, the residual spectrum and the concentration uncertainties can allow the analyst to detect and identify compounds which are actually present in the sample gas but which were not included in the mathematical analysis. Appendix E provides an example illustrative of these procedures.
The above description illustrates a simple and easily-interpreted LSF analysis. More sophisticated LSF analytical techniques, possibly more accurate for particular types of samples, are described in the literature (see, for example, Reference 18 and references therein).
C8 Calibration Transfer and Reference Libraries
Equations C1 through C6 demonstrate the importance of quantities $L_{S}$ (the absorption pathlength) and $a_{ij}$ (the absorptivity) in FTIR spectrometry. Accurate determinations of these quantities allow the use of reference libraries for quantitiative analyses without the necessity of compound-specific field calibrations. The system tests described in the procedures and in Appendix B are intended to ensure suitability of the system configuration for such calibration transfers, as are the requirements of obtaining CTS spectra in field. Appendix D describes procedures for recording and processing reference library spectra.
C9 Corrections to Deviations from Beer’s Law Exhibited by FTIR Spectra
Beer’s Law is based on fundamental, well-established physical principles. It holds absolutely for gas samples which are at thermal equilibrium and dominated by induced (rather than spontaneous) emission and absorption processes. (See Note A1 below). However, this is not to say that the absorbance, as measured by an FTIR spectrometer, follows Beer’s Law under all conditions. Deviations from Beer’s Law in FTIR spectra are often observed; however, they indicate inaccuracies in the FTIR spectra, not “violations” of Beer’s Law. For example, deviation from Beer’s Law is commonly exhibited by sets of single-component reference spectra recorded over a range of absorbance levels. At large enough values of the absorbance, the points $A_{i}$ of stronger absorption bands of such spectra no longer increase linearly with the concentration-pathlength product ${L_{R}}{C_{j}}$; this is why Table 2 specifies a maximum ppm-m value for the listed reference spectra. If the assumption of detector linearity does not hold (see Appendix B), similar effects are often present in reference and sample spectra; this is the basis for the system test described in Appendix B, Section 6.
Mathematical correction of the concentration estimates $D_{j}$ derived from Beer’s Law can often reduce the error in sample analyses when either type of non-linear effect occurs. Figure C7 provides an example of such a correction. The actual and calculated ppm-m values for a set of reference spectra are plotted against each other; a “piece-wise linear” approximation to the pattern is shown by the solid line, and the dashed line indicates the ideal linear behavior based on the spectrum of lowest absorbance. At any ppm-m value indicated in a Beer’s Law sample analysis (that is, for any y-axis value up to approximately 900 ppm-m in the example), reasonably accurate values are available from the corresponding x-axis position of the solid line. If the analyst ​employs such corrections, he or she should also calculate the residual (Equation C6) using the reference spectrum which minimizes the squared error (Equation C5). FTIR analysts and manufacturers have devised other correction procedures to improve the sample analysis accuracy in such circumstances, and these are included in some commercially available software packages.
Note: Intense infrared radiation, such as that produced by some lasers, can induce non-equilibrium populations of a molecule’s rotation-vibration energy states. However, the thermal infrared sources used in commercially available FTIR spectrometers are much weaker than such lasers. In gases at atmospheric pressure, the commercially available thermal sources induce transition rates between quantum energy states which are small compared to those of the competing collisional relaxation processes, and cannot induce non-equilibrium energy state populations. In addition, the induced transition rates related to absorption and emission at mid-infrared frequencies are much larger than the corresponding spontaneous (natural) emission rate. As a result, all accurate FTIR measurements at mid-infrared frequencies obey Beer’s Law to within the uncertainty related only to the S/N ratio of the measured spectra.
​APPENDIX D. Purposes, Preparation, and Use of Reference Spectral Libraries.
D1. Purposes of Reference Spectral Libraries
FTIR analyses rely on the availability of libraries of spectral information on the compounds of interest. For gases, the measured absorbance of a single component is often completely independent of the concentrations of other gases comprising the sample, and single-component reference spectra are usually employed. (For condensed phases, there are often strong interactions between components, and reference spectral libraries of mixtures are usually required.) Reference libraries may be used for quantitative measurements of analyte concentrations, for the mathematical removal of spectral features of interferants in a mixture, or simply for the identification of compounds in a mixture. Clearly, the required level of quantitative accuracy of the library is different for these three tasks; the highest quality is required for analyte concentration determinations, while no quantitative information is required for interferant removal and compound identification.
A useful characteristic of extractive FTIR spectrometry is that it provides accurate field measurements for many compounds, but requires field calibration procedures involving only two compounds. The water vapor available in every ambient air sample serves to calibrate the wavenumber (x) axes of FTIR absorbance spectra; a single calibration transfer standard (CTS) gas serves to calibrate their concentration-related (y) axes. When these two field calibrations are combined with an appropriate reference spectral library describing additional compounds, the measurement capability of the technique is practically limited only by the quality and scope of the reference library. If the reference library is carefully prepared and properly employed, this characteristic can lead to greatly lowered field test costs, since the calibration materials need be handled only once, and only in the laboratory.
D2. Reference and Field FTIR System Configurations
In the ideal case, the reference library can be prepared on the field instrument, but this is often impractical; the reference library is usually prepared on specific laboratory systems and employed in measurements made with many field systems. Reference libraries recorded on a specific instrument provide accurate quantitative analyses for spectra recorded on other instruments only when the configurations of the various systems are compatible. The following table lists compatibility considerations for the reference system configuration parameters.
Table D1. Reference and Field System Configuration Parameters. :
| Parameter | Requirements for Reference and Field Systems |
| minimum instrumental linewidth | Reference MIL must be less than or equal to field MIL. See Appendix B, Section 3 for MIL measurement technique. |
| gas temperature | Reference temperature within 20°C of field temperature. Density corrections based on ideal gas law are accurate over only this narrow temperature range, and their exact accuracy is compound-dependent. |
| gas pressure | Reference pressure within 20% of absolute field pressure. Pressure corrections based on ideal gas law are accurate over at least this range, but their accuracy is compound-dependent. Atmospheric pressure is recommended for all measurements. |
| apodization function | Reference and field apodization functions must be the same. A single set of reference interferograms (background and sample) can be used to generate a multiple sets of absorbance spectra using different apodization functions. |
| zero filling factor | Reference and field zero filling factors must be the same. A single set of reference interferograms (background and sample) recorded with no zero filling can be used to generate a multiple set of absorbance spectra using different zero filling factors. |
| wavenumber accuracy | Characterized by the position of water absorption bands in a wavenumber standard spectrum (see below); if additions to an existing library are being made, care must be taken to match the x-axes of all spectra as closely as possible. ​ |
| integration time | Reference integration times (for both background and sample interferograms) should be greater than or equal to expected field integration times. For reference libraries, the longest practical integration time is recommended. |
| detector type and serial number | If an MCT or other potentially non-linear detector is employed in the reference system, IR attenuation may be required to ensure linearity; see Appendix B, Section 6; because each detector may exhibit linearity to a specific degree, the serial number of the detector should be included in any specification of the system configuration. |
D3. Wavenumber Standard Spectra
Except in extremely dry conditions, the IR absorption by water vapor in workspace air is detectable at even very short absorption pathlengths. The wavenumber positions of water vapor indicated by the reference system allow the analyst to confirm the wavenumber accuracy of sample spectra recorded on a different FTIR system in the field. Reference spectra used for this purpose are referred to here as the wavenumber standard spectra.
Every spectrum in a reference library should be associated with a wavenumber standard spectrum collected under the identical system configuration; even when the reference FTIR system is in a stable environment, it is recommended that a wavenumber standard spectrum be recorded daily with the system.
Before recording reference spectra, the analyst should check the most recent wavenumber standard spectrum against previous wavenumber standard spectra in the library; see Appendix B, Section 4 for recommended calculations. If the wavenumber reproducibility of the system is poor, the resulting reference spectra may not be suitable for quantitative use on other field systems.
D4. Obtaining and Preparing Standard Reference Gases
The accuracy of any FTIR quantitative analysis is limited by the accuracy of the concentrations of the gas standards used in preparing the reference library. It is therefore important to use gas standards of the highest available quality. NIST-traceable gravimetric standards are available from many commercial sources, and are quoted to 2% accuracy in many circumstances; EPA has also published guidance on the preparation of "Protocol 1" gases (see Reference 17), though these are available for only a limited number of compounds. Users should obtain documentation from the gas vendors regarding the analytical techniques applied and the stability limits (concentration and time) of the compounds in the cylinders. When possible, an alternative analytical method should be used to verify the quoted cylinder concentrations, especially for compounds which are reactive, corrosive, or have relatively high boiling points.
If cylinder standards are not available for a compound, the analyst may prepare reference gases based on gravimetric, barometric, or dynamic methods. In any case, the related mass, pressure, and flow measurements should be made with NIST-traceable equipment whenever possible. In general, methods which provide a stream of standard gas (dynamic methods) provide more reliable results than static methods, since the concentrations of static gases are more prone to change when reactions between the standards and the sampling system or absorption cell surface can occur.
D5. Determining the Reference Absorption Pathlength
The accuracy of any FTIR quantitative analysis is limited by the accuracy to which the pathlength of the absorption cell used in preparing the reference library is known. For single-pass absorption cells through which a collimated IR beam is passed, the pathlength can be physically measured to high accuracy. For multi-pass cells, the nominal pathlength can be estimated from the base pathlength and the number of passes. However, because focused beams and curved mirrors are required in multi-pass cells, the pathlength estimated in this fashion can differ significantly from the actual pathlength. Because of this, combinations of physical and spectroscopic measurements with multiple CTS gas standards (see below) and single-pass absorption cells should be employed to determine the actual pathlength of multi-pass absorption cells.
​D6. Recording CTS Spectra
The CTS (calibration transfer standard) gas is used to characterize the absorption pathlengths of the reference and field FTIR systems. Ethylene in nitrogen, at concentrations leading to between 100 and 300 ppm-meter concentration-pathlength values for the systems, is recommended; for ethylene, spectra with ppm-m values greater than 300 begin to exhibit non-linear absorbance, and must be carefully analyzed (see Sections D8 and D9 below). Standards of this gas with 2% accuracy are readily available, and both the EPA and NIST libraries contain ethylene spectra which can be used to link those libraries to measurements performed with field instruments. However, almost any other stable compound with appropriate IR absorption characteristics can be used in developing an independent reference library and for accurate field measurements.
In the field, CTS spectra must be recorded both before and after sample spectra are acquired using the same system configuration employed in recording the sample spectra (see Steps 7 and 11 above).
When developing reference spectra, the analyst must record CTS spectra at least daily; each reference spectrum should be associated with at least one CTS spectrum. The analyst must use the same system configuration employed in recording the reference spectra, with one exception: The integration time used for the CTS spectra may be less than that used for the reference spectra, if the quality of the resulting CTS spectra is still sufficient for an accurate determination of the absorption pathlength. It is highly recommended that the analyst store all the interferograms from which the CTS absorbance spectra are generated, including all background interferograms. The interferometric data provide the most direct method of verifying the FFT calculations and/or adding reference absorbance spectra for other apodization function choices.
D7. Recording Reference Spectra
Before recording reference spectra, verify that the requirements specified for system checks, system configuration parameters, gas standards, absorbance pathlength determinations, and CTS spectra described in the pertinent sections of this Appendix and Appendix B have been met. Additional checks of the sample gas pressure and temperature should also be made periodically as the spectra are recorded.
It is highly recommended that the analyst store all the interferograms from which the reference absorbance spectra are generated, including all background interferograms. The interferometric data provide the most direct method of verifying the FFT calculations and/or adding reference absorbance spectra for other apodization function choices.
Beer’s Law (Equation C1) describes the fundamental linearity of the infrared absorbance versus concentration. However, the resolution (and other) limitations of instruments typically used to generate field FTIR spectra often lead to non-linear behavior for many compounds, even at low absorbance levels. The expected accuracy of FTIR-based measurements results for a particular compound can be achieved only when 1) the reference absorbance is characterized at a sufficient number of concentration-pathlength values, up to some maximum value, and 2) the sample absorbance associated with any compound represents a value lower than that of the maximum concentration-pathlength value represented in the reference library for that compound.
For each analyte, the analyst should record two reference spectra at each of two concentration values (that is, at least four spectra) at a single absorption path length; the two concentrations should be separated by no more than a factor of ten, and a maxim um factor of five is recommended. After recording these spectra, the analyst must 1) permanently record the system parameters and the maximum measured concentration path length product and 2) characterize the linearity of the absorbance across the measured concentration-pathlength range (see Section D8). It may be necessary to record additional reference spectra for the analyte if either the absorbance linearity or maximum concentration-path length value proves unsuitable for later field measurements.
D8. Linearity Checks
The performance of linearity checks on a set of reference spectra is an important aspect of FTIR spectrometry, and is best illustrated by a practical example. The following example is based on a series of reference measurements performed in the 3M Environmental Laboratory on the compound tetrafluoroethylene, hereafter referred to as TFE.
​Five absorbance spectra for TFE are shown in Figure D1. These spectra were recorded over the entire mid-IR wavenumber range, but only that portion of the spectra showing the most intense TFE absorption bands is included in the Figure. Each of the spectra was calculated by mathematically averaging a number of TFE absorbance spectra recorded with the system configuration parameters given in Table D2, and a linear baseline correction was applied to each of these spectra over the range illustrated in Figure D1.
The reference gas samples were generated by diluting with N$_2$ the output of a single standard gas cylinder of TFE. The TFE concentration of the standard cylinder was determined (by the gas vendor) according to NIST-traceable gravimetric measurements, and the flow rates of the cylinder gas were measured with a NIST-traceable volumetric device.
Figure D1. Reference Absorbance Spectra of TFE (x-axis truncated)
​One technique to check for the linearity of this set is to form a normalized average of these five spectra and then use it in a linear analysis of the five original spectra. The normalization consists of dividing each spectrum by its concentration-pathlength product; these values, based on the CTS-derived pathlength of 10.23 meters, are given with the actual gas concentrations and new spectral filenames in Table D3. Figure D2 illustrates the normalized spectra, all of which represent spectra of concentration-product values 1.00 ppm-meters. These spectra are nearly equal to one another, as predicted by Beer’s Law. Only the spectrum tfe01n.spc, based on the original 25.53 ppm spectrum, is easily discernable from the other spectra in the Figure.
Table D2. System Configuration Parameters for TFE Reference Spectra (see Figure D1). :
| System Configuration Parameters | Values/Notes |
| MIL (cm$^{-1}$) | 0.5 |
| integration time (sec) | 1080 (120 sec/spectrum × 9 spectra) |
| absorption pathlength (m) | 10.23 |
| gas temperature (C) | 15 |
| gas pressure (mm Hg) | 760 (±10) |
| apodization function | Triangular |
| zero filling factor | zero |
| detector type | MCT |
| detector gain (hardware) | jumpers BCD |
| detector gain (software) | 1 |
| reference CTS spectra | j2kety.spc |
| wavenumber standard spectrum | j2kety.spc |
Table D3. Normalization Factors TFE Spectra :
| Original Spectrum | Concentration (ppm) | Concentration-Pathlength Product (ppm-meter) | Normalized Spectrum |
| tfe01.spc | 2.50 | 25.5 | tfe01n.spc |
| tfe02.spc | 6.63 | 67.8 | tfe02n.spc |
| tfe03.spc | 13.3 | 133 | tfe03n.spc |
| tfe04.spc | 20.4 | 208 | tfe04n.spc |
| tfe05.spc | 25.1 | 257 | tfe05n.spc |
Figure D2. Normalized Reference Absorbance Spectra of TFE
Table D4 shows the results of a linear least-squares analysis using the average normalized spectrum as a single reference spectrum (with concentration-pathlength product 1.00 ppm-meters) over the analytical range 1050 to 1400 cm$^{-1}$. The bias in the linear method is clearly evident in the fourth column of the Table, which indicates that the analysis yields concentrations which are slightly too high at the lowest concentration and slightly too low at the highest concentration. The average of the last column in the table, which represents the absolute percent difference between the actual and calculated concentrations, the “fractional calibration uncertainty” (FCU; see Reference 2), is 3.2%. This value represents the average error over the concentration range for these reference spectra to be expected from the linear analysis up to the maximum concentration-pathlength value used in the analysis (257 ppm-meter). If additional accuracy is required, non-linear analyses or corrections such as those discussed above (Appendix B, Section 9) can be employed.
Table D4. Results of Linear Least Squares Analysis for TFE Reference Spectra. :
| TFE Reference Spectrum | Calculated Concentration (ppm) | Actual Concentration (ppm) | Actual Calculated Concentration (ppm) | Absolute Percent Difference |
| tfe01.spc | 2.69 | 2.50 | 0.19 | 7.7 |
| tfe02.spc | 6.64 | 6.63 | 0.01 | 0.2 |
| tfe03.spc | 12.8 | 13.0 | -0.2 | 1.4 |
| tfe04.spc | 19.8 | 20.4 | -0.6 | 2.9 |
| tfe05.spc | 24.2 | 25.1 | -0.9 | 3.7 |
​D9. Calculating the Limit of Detection (LOD)
The estimated LODs are the concentrations – for the given system configuration, reference spectra, and analytical region – at which each compound’s absorbance area is equal to the RSA. For a specified system configuration and analytical region, an estimate of the LOD for a compound can be made from the absorbance area of a reference spectrum in that region (${A_{R}}$, absorbance-cm$^{-1}$), the reference spectrum concentration-pathlength product (CPP, ppm-m), the sample absorption pathlength ($L$, meters), and the RSA values (absorbance-cm$^{-1}$) as
$LOD={\frac {(CCP)(RSA)}{L{A_{R}}}}$ Equation D1
A simple trapezoidal approximation of ${A_{R}}$ over the analytical region of interest, including baseline corrections when necessary, is suitable for the LOD estimate. The RSA is formed from the product of the FTIR system’s typical root-mean-square noise level in absorbance and the width of the analytical region in cm$^{-1}$ (see Appendix B, Section 2); the RSA estimate should reflect the error incurred in subtracting known spectral interferences. Appendix E, Section 1 presents detailed examples of RSA and LOD calculations.
D10. Using Existing Reference Libraries
The analyst may use any of the publicly available reference libraries for quantitative analyses, but it is strongly recommended that quantitative results for analytes be based only on spectra from libraries which meet the requirements discussed in this Appendix. If the reference library consists of spectra recorded at a spectral resolution different from that of the field system, the analyst must 1) de-resolve the spectra mathematically to that of the field data and 2) ensure that the library data are suitably linear over the desired measurement range at the spectral resolution of the field system.
​ APPENDIX E. Example Calculations.
This Appendix uses an analysis of tetrafluoroethylene (TFE) and 1,1-difluroethylene (DFE) in workplace air to illustrate the calculations of residual squared area (RSA) and limits of detection (LODs). The topics of designing, applying and verifying, and correcting a spectral analysis are also addressed below.
The FTIR system configuration assumed for this set of calculations is given below. These parameters are consistent with the LOD values presented in Table 2.
| MIL: | 0.5 cm$^{-1}$ |
| absorption pathlength: | 10 meters |
| apodization function: | triangular |
| gas temperature: | 293 K |
| gas pressure: | 760 Torr |
| zero filling factor: | none |
| wavenumbers of water bands: | 1918 cm$^{-1}$ and 2779 cm$^{-1}$ |
| reference library sources: | 3M Environmental Laboratory |
| integration time: | 70 seconds (64 scans) |
| detector type: | MCT |
| detector gain-hardware: | Gain jumpers A, D, and H |
| detector gain-software: | 1.0 |
E1. Residual Squared Area (RSA), Analysis Design, and Limits of Detection (LODs)
The analysis is to be carried out in workspace air, so the only potential spectral interferences are due to water and carbon dioxide. Figure E1 illustrates example reference spectra of TFE, DFE, and water. (The water spectrum shown is typical of workspace air samples; carbon dioxide does not absorb in any of the spectrum. As a result, the limited spectral region shown in Figure E2 is actually of the greatest interest for an analysis of DFE and TFE in workspace air.
Shown in greater detail in Figure E2 are the three reference spectra and two possible analytical regions. Analytical region 1, from 1370 to 1295 cm$^{-1}$, includes water bands which interfere with the TFE absorbance in the sample spectra. Analytical Region 2 (1215 to 1100 cm$^{-1}$) may be the best choice for analyzing samples for both TFE and DFE (though the weaker features near 3000 cm$^{-1}$ remain an option for DFE); it avoids the TFE interference with water, but necessarily includes some spectral overlap between the two analytes. Until the relative TFE, DFE, and water concentrations in the samples are known, it is unclear which of the two regions will provide better concentration estimates for TFE, so calculations for both regions are described below.
Estimation of the LODs for TFE and DFE requires a calculation of the residual square area (RSA) in the actual sample spectra over the selected analytical regions. The RSA represents an estimate, based on the assumed sample matrix and available reference spectra, of the residual absorbance (see Equation A6) which will be used to calculate the concentration uncertainties from the actual sample spectra.
The reader should note that the RSA and derived LOD are only estimates. If the actual sample matrix differs substantially from that of the sample matrix assumed in the performance of these estimates, the actual concentration uncertainties and LODs may differ substantially from the RSA and LOD values obtained in the calculations described below. For workplace air samples, water is the only interfering compound which is certain to appear in any of the analytical regions considered below. A realistic ​
Figure E1. Absorbance Reference Spectra of TFE, DFE, and Water
Figure E2. Possible Analytical Regions
Figure E3. Water Spectra 1295 to 1080 cm-1
Figure E4. Water Spectra 1370 to 1295 cm-1
​estimate of the RSA is therefore available by forming the mathematical difference of two water spectra—of substantially different water concentrations—recorded using the same FTIR system configuration. For each analyte, this estimate assumes that only water and that analyte will absorb substantially in the actual sample spectra. Later analyses based on the actual sample matrix could lead to either lower or higher concentration uncertainty and LOD estimate ; examples of such analyses are detailed below.
Figures E3 and E4 illustrate two absorbance spectra recorded using the system configuration described above. They represent spectra of workspace air at approximately 20% and 40% relative humidity. The upper trace in each Figure is slightly offset for clarity.
Figure E5 shows two residual spectra formed by subtracting scaled versions of the lower-absorbance spectrum from the higher-absorbance spectrum. The scaling factors were determined in independent LSF analyses over the two analytical regions. Linear baseline corrections (offset and slope) were also determined during the analyses, so the mean value of each residual spectrum is zero. (These calculations were performed by using the ANOVA data analysis tool in Microsoft Excel 97). The residual squared area (RSA) values for the residual spectra are defined in Equation C2, and the related calculations are presented in Table E1. (The calculations also were performed in the program Excel by applying the function STD EV to the regression residuals.)
Figure E5. Water Residual Spectra
Table E1. Results of RSA Analysis from Water Reference Spectra. :
| Analytical Region (cm$^{-1}$) | Calculated Scaling Factor | Scaling Factor Uncertainty (1 σ) | Residual RMS Standard Deviation (absorbance) | RSA (absorbance -cm$^{-1}$; Eq. B2) |
| 1370-1295 | 1.636 | 0.003 | 0.00575 | 0.431 |
| 1215-1080 | 1.870 | 0.008 | 0.00069 | 0.093 |
An estimate of the LODs (ppm) for the two compounds—for the specified system configuration—can be made from the absorbance areas of the reference spectra over these analytical ranges (A$_R$,absorbance-cm$^{-1}$), the reference spectra concentration-path length products (CPP, ppm-m), the sample absorption pathlength L (meters), and the RSA values (absorbance-cm$^{-1}$) derived above. The absorbance areas were determined using a standard trapezoidal approximation without baseline correction. (For these spectra, baseline corrections lead to values which differ from those quoted by less than 3%, and have been neglected below.) Figure E6 shows the spectral features of TFE and DFE used to calculate the A$_r$ for the reference spectra tfeav05.spc (CCP = 256.7 ppm-m) and dfea v05.spc (CCP = 1 97.8 ppm-m).
The estimated LODs are the concentrations—for the given system configuration, reference spectra, and analytical region—at which each compound's absorbance area is equal to the RSA. Mathematically, the LOD estimates are given by
$LOD={\frac {(CCP)(RSA)}{L{A_{R}}}}$ Equation E1
Table E2 lists the pertinent quantities and resulting LODs for DFE and TFE in the two analytical regions considered. The results indicate that the analytical region from 1215 to 1080 cm$^{-1}$ is likely to provide the most reliable TFE concentrations.
Table E2. LODs for TFE and DFE from RS A Analysis of Water Reference Spectra. :
| Analytical Region (cm$^{-1}$) | Compound | Reference Spectra | Reference Spectra | Reference Spectra | System Configuration | System Configuration | System Configuration |
| Analytical Region (cm$^{-1}$) | Compound | File Name | CCP (ppm-m) | Absorbance Area (abs-cm$^{-1}$) | RSA (abs-cm$^{-1}$) | L (m) | Estimated LOD (ppm) |
| 1370-1295 | TFE | tfe05.spc | 256.7 | 16.03 | 0.431 | 10.0 | 0.69 |
| 1215-1080 | TFE | tfe05.spc | 256.7 | 13.97 | 0.093 | 10.0 | 0.17 |
| 1215-1080 | DFE | dfe05.spc | 197.8 | 8.72 | 0.093 | 10.0 | 0.21 |
Figure E.6 TFE and DFE Spectra for Absorbance Area Calculations
E2. LSF Determinations of TFE and DFE Concentrations
Presented in this section is a description of a least squares fit (LSF) analysis for the two compounds TFE and DFE in ambient air samples. As is always the case before actual measurements are taken, no actual sample data for mixtures of the compounds in the assumed matrix (ambient air) were available as these analyses were performed. Accordingly, the following description is based on synthetic spectra generated from available reference spectra for TFE, DFE, and water.
In order to not overestimate the effectiveness of the FTIR technique, the noise levels in the synthetic sample spectra were artificially raised, and the reference spectra used are not those most likely to provide an optimal analysis. This is the most prudent course available to an analyst attempting to predict the performance of the FTIR method under essentially unknown conditions, and it is the course recommended by the authors to analysts who find themselves in this common situation.
Estimates of the LOD for this sample matrix (see Appendix E, Section 1) indicate that the analytical region from 1215 to 1080 cm$^{-1}$ will likely provide the most reliable TFE and DFE concentrations. The system configuration parameters used in those estimates are assumed to hold in the following description.
E2A. Generation and Analysis of Synthetic Sample Spectra of TFE and DFE
Table E3 describes the mathematical generation of synthetic samples for the following LSF analysis description. Each sample spectrum consists of the sum of scaled reference spectra for TFE (tfe4.spc, CCP = 208.3 ppm-m), DFE (dfeav05.spc, CCP = 197.8 ppm-m) and water (wat02bl.spc). The scaling factors indicated in Table E3 were used to generate synthetic sample spectra at the listed concentrations and the assumed absorption pathlength of 10.0 meters.
Table E3. Parameters Used to Generate Synthetic Sample Spectra Containing TFE, DFE, and Water. :
| TFE Scaling Factor | TFE Synthetic Conc. (ppm) | DFE Scaling Factor | DFE Synthetic Conc. (ppm) | H2O Scaling Factor | Synthetic Sample Spectrum File Name |
| 0 | 0 | 0 | 0 | 0.6 | S001.spc |
| 0 | 0 | 0 | 0 | 1.2 | S002.spc |
| 1.200 | 25.0 | 1.264 | 25.0 | 0.6 | S551.spc |
| 1.200 | 25.0 | 0.253 | 5.00 | 0.6 | S511.spc |
| 0.240 | 5.00 | 1.264 | 25.0 | 0.6 | S151.spc |
| 1.200 | 25.0 | 1.264 | 25.0 | 1.2 | S552.spc |
| 1.200 | 25.0 | 0.253 | 5.00 | 1.2 | S512.spc |
| 0.240 | 5.00 | 1.264 | 25.0 | 1.2 | S152.spc |
A spectrum representing random absorbance noise was added to each synthetic spectrum. The noise spectrum was generated using the function RANDOM within the program GRAMS/32 V4.1 1 (Galactic, Inc.; see the Array Basic User’s Guide, V4.1, page 31 6); similar functions are also available in Microsoft Excel. For the noise spectrum, the root mean square absorbance noise N$_{RMS}$ (see also equation C2, which defines the RSA), calculated over the appropriate analytical region(s) according to
$N_{\text{RMS}}={\sqrt {\sum _{l=p}^{l=q}{\frac {(R_{l})^{2}}{q-p}}}}$Equation E2
was 0.00034 in the region 1438 to 1282 cm$^{-1}$; this is very close to the value obtained from actual absorbance spectra (provided by MID AC Corporation) recorded with the quoted system configuration in the region 1005 to 932 cm$^{-1}$.
The synthetic spectra represent four different mixtures of TFE and DFE (including one "mixture" which contains neither compound), each at two different moisture levels.
Table E4 lists the results of a LSF analysis (program 4FTIMD V15, Rho Squared; see Reference 18) for TFE, DFE, and water in the analytical region 1215 to 1080 cm$^{-1}$ using the reference spectral files TFE3.spc (CCP = 133 .2 ppm-m) and dfeav04.spc (CCP = 133.3 ppm-m), and wat01bl.spc. Note that these are not the same reference spectra which were used in the generation of the synthetic sample spectra, and that the results for water are in arbitrary units. The analysis included the determination of two baseline correction parameters along with the compound concentrations.
Table E4. Original LSF Results for Original Synthetic Sample Spectra Containing TFE, DFE, and Water. :
| Synthetic Sample Spectrum File Name | TFE Synth. Conc. (ppm) | TFE LSF Result (ppm) | TFE LSF 3σ Uncert. (%) | DFE Synth. Conc. (ppm) | DFE LSF Result (ppm) | DFE LSF 3σ Uncert. (%) | H$_2$O LSF Result (arb) | H$_2$O LSF 3σ Uncert. (%) |
| S001.spc | 0 | 0.02 | 52.5 | 0 | 0.07 | 13.7 | 1.12 | 1.23 |
| S002.spc | 0 | 0.03 | 32.2 | 0 | 0.14 | 8.95 | 2.24 | 0.80 |
| S551.spc | 25.0 | 24.41 | 0.26 | 25.0 | 24.30 | 0.29 | 0.87 | 11.8 |
| S511.spc | 25.0 | 24.43 | 0.25 | 5.00 | 4.88 | 1.43 | 0.87 | 11.5 |
| S151.spc | 5.00 | 4.88 | 0.41 | 25.0 | 24.33 | 0.09 | 1.07 | 3.04 |
| S552.spc | 25.0 | 24.43 | 0.26 | 25.0 | 24.35 | 0.29 | 1.99 | 5.20 |
| S512.spc | 25.0 | 24.45 | 0.26 | 5.00 | 4.95 | 1.43 | 1.99 | 5.11 |
| S152.spc | 5.00 | 4.90 | 0.43 | 25.0 | 24.39 | 0.10 | 2.19 | 1.56 |
| Average Abs. % Concentration Difference | | 2.24 | | | 2.34 | | | |
| Average Abs. % Concentration Uncertainty | | | 0.31 | | | 0.61 | | 6.38 |
The LSF results for the non-zero TFE and DFE spectra are consistently good, being different from the synthetic concentrations less than 3% in every case. Listed in the Table for TFE and DFE are the average percent differences between the synthetic concentrations and those derived from the LSF analysis, which are 2.24% and 2.34%, respectively.
The concentration uncertain ties listed in Table E4 are the statistically determined 3σ values from the LSF analyses. Included in the last row of the Table are the average percent concentration 3σ uncertainties for the non-zero TFE and DFE spectra. These percent uncertainty parameters and the visual appearance of the LSF residual spectra are important indicators of the quality of the least squares analysis, and are discussed further in the following section.
Though they are not included in the averages presented in the last two rows of Table 3, the TFE and DFE results for the two synthetic spectra which contain no absorption features of TFE and DFE (S001 and S002) are of interest and importance. The LSF concentration results are small. (Their maximum is 0.14 ppm). They are smaller in each case than the LOD estimates of Table E2, and their corresponding 3σ uncertainties from this LSF analysis are smaller still. Unfortunately, no consensus exists on the exact mathematical relationship between the LODs calculated as described in this document and the 3σ concentration uncertainties. This statement is supported by the contents of Section A2 in Reference 3—a consensus document —which prescribes three different methods for calculating LODs (or, in the terminology of Reference 3, "minimum detectable concentrations"). These three prescriptions include one similar to the LOD method prescribed in this document, and one which is based on the concentration uncertainties derived from spectra similar to S001 and S002. In this limited example, two of the three prescriptions included in Reference 3 provide very different results, and they indicate that the LOD calculation described in this document provides the most conservative estimate—that is, the highest estimate—of the three LOD prescriptions of Reference 3.
​E2B. Analyses of Synthetic Sample Spectra with an Interfering Compound
Every compound-specific quantitative analytical technique, including FTIR spectrometry, can fail to provide accurate results when interfering compounds appear in a sample. However, the results of a mathematical FTIR spectral analysis designed for a particular set of compounds provides clues to its failure in the presence of interferants. An experienced analyst can often adjust the analysis to accommodate the interferants and provide accurate results.
To illustrate this important aspect of FTIR spectrometry, a synthetic interference was introduced to the spectra described in Table E3. Scaled versions of a reference spectrum (hfpav06.spc, 256.6 ppm-m) of the compound hexafluoropropylene (HFP), representing the compound at two concentrations (5.00 and 10.0 ppm), were added to the original synthetic spectra. The resulting final synthetic sample spectra are described in Table E5 below. The least squares analysis described above for TFE and DFE only, when applied to these spectra containing spectral features of HFP, gives the results shown in Table E6 below.
Table E5. Parameters Used to Generate Synthetic Sample Spectra Containing TFE, DFE, Water, and HFP. :
| Original Synthetic Sample Sepctrum File Name | HFP Scaling Factor | HFP Synthetic Conc. (ppm) | Final Synthetic Sample Spectrum File Name |
| S001.spc | 0.195 | 5.00 | S0011.spc |
| S002.spc | 0.390 | 10.0 | S0022.spc |
| S551.spc | 0.195 | 5.00 | S5511.spc |
| S151.spc | 0.195 | 5.00 | S1511.spc |
| S512.spc | 0.195 | 5.00 | S5121.spc |
| S511.spc | 0.390 | 10.0 | S5112.spc |
| S552.spc | 0.390 | 10.0 | S5522.spc |
| S152.spc | 0.390 | 10.0 | S1522.spc |
Table E6. Original LSF Results for Final Synthetic Sample Spectra Containing TFE, DFE, Water, and HFP :
| Synthetic Sample Spectrum File Name | TFE Synth. Conc. (ppm) | TFE LSF Result (ppm) | TFE LSF 3σ Uncert. (%) | DFE Synth. Conc. (ppm) | DFE LSF Result (ppm) | DFE LSF 3σ Uncert. (%) | H$_2$O LSF Result (arb) | H$_2$O LSF 3σ Uncert. (%) |
| S0011.spc | 0 | 1.00 | 39.6 | 0 | -1.58 | 26.5 | 1.65 | 0.89 |
| S0022.spc | 0 | 2.01 | 39.5 | 0 | -3.16 | 26.4 | 3.29 | 1.78 |
| S5511.spc | 25.0 | 25.06 | 1.51 | 25.0 | 22.65 | 1.89 | 1.43 | 43.3 |
| S5112.spc | 25.0 | 25.73 | 2.90 | 5.00 | 1.57 | 53.8 | 1.99 | 61.4 |
| S1511.spc | 5.00 | 5.53 | 6.64 | 25.0 | 22.67 | 1.84 | 1.63 | 37.0 |
| S5522.spc | 25.0 | 25.73 | 2.90 | 25.0 | 21.05 | 4.01 | 3.10 | 39.2 |
| S5121.spc | 25.0 | 25.09 | 1.52 | 5.00 | 3.29 | 13.1 | 2.55 | 24.4 |
| S1522.spc | 5.00 | 6.20 | 11.87 | 25.0 | 21.09 | 3.96 | 3.30 | 36.4 |
| Average Abs. % Concentration Uncertainty | | | 4.56 | | | 13.1 | | 40.3 |
The results shown in the last rows of Table E4 (those of the original LSF analysis without HFP interference) and Table E6 (those of the original LSF analysis with HFP interference) are clearly quite different. Averaged over the six synthetic spectra containing TFE and DFE in each case, the (absolute) percent concentration uncertainties for TFE, DFE, and H$_2$O are greater for the spectra with HFP interference. For TFE and DFE, the average percent uncertainties of Table E6 are over ten times greater than those of Table E4.
This exercise shows that:
* For sample spectra containing substantial TFE and DFE concentrations, the HFP interference causes large increases in the TFE and DFE relative absolute concentration uncertainties.
* For sample spectra containing low or zero concentrations TFE and DFE, the relative absolute uncertainties are NOT a reliable indicator of the HFP interference. However, for such spectra, the concentration results themselves are often clearly unreliable; note that the DFE concentration results are negative and large compared to the LOD estimate for this compound. (Note also that negative concentration results which are small compared to the LOD are statistically valid, and do not necessarily indicate a failure of the analysis.)
If the concentration results show anomalies such as those noted above, the residual spectra from the analyses will also exhibit anomalous behavior. This is illustrated in Figure E7, which shows the residual spectra for four analyses. Compared to the residual spectra resulting from analyses of spectra without the HFP interference, those with HFP interference show large absorbance features which cannot be modeled by the three reference spectra employed. The analyst needs to identify the interfering compound before proceeding. This can often be done by visually comparing the suspect residual spectra to reference spectra of a number of likely interferants, as illustrated in Figure E8.
Figure E7. Residual Spectra with and without HFP Interference
Figure E8. Comparison of Residual, Sample and Reference Spectra
Figure E9. Original LSF Residual and HFP Reference Spectra
Figure E8 show's that the positions of three major relative maxima in the residual spectrum (top trace) correspond well to only one of the nine candidate reference spectra in the lower traces of the Figure. (The nine spectra shown are all of light, partially or fully fluorinated hydrocarbons.) An additional absorbance band from this single reference spectrum also corresponds to a large peak in both of the sample spectra (second and third traces from top of the Figure).
A closer examination of this reference spectrum—that of HFP, of course—is illustrated in Figure E10. It clearly shows a close relationship between the shape of the residual spectrum and the absorption features of HFP. The relationship is not exact because the sample spectrum has had incorrect amounts of the compounds TFE and DFE subtracted, and this distorts the residual spectrum.
Though this identification is tentative, it can be tested by including HFP in the LSF analysis. Table E7 shows the TFE, DFE and water concentrations resulting from an analysis identical to those described above except for the addition of HFP as a fourth compound. (As usual, an HFP reference spectrum different from the one used to add the synthetic interference was employed in the analysis.) To facilitate comparisons with the preceding tables, the HFP results have been excluded from Table E7; they were in all cases similar in quality to those obtained for the other compounds.
The results show that inclusion of HFP in the analysis yields results of the original (high) quality shown in Table E3 for TFE, DFE, and water. The percent relative uncertainties are slightly higher in the final analysis than in the original analysis; this is to be expected because the same amount of spectral information is being used to determine an additional parameter in the final analysis. The quality of the analysis could probably be further improved by extending the analytical region to include the entire HFP absorbance band shown in Figure E9. ​
Table E7. Final LSF Results for Final Synthetic Sample Spectra Containing TFE, DFE, Water, and HFP :
| Synthetic Sample Spectrum File Name | TFE Synth. Conc. (ppm) | TFE LSF Result (ppm) | TFE LSF 3σ Uncert. (%) | DFE Synth. Conc. (ppm ) | DFE LSF Result (ppm ) | DFE LSF 3σ Uncert. (%) | H$_2$O LSF Result (arb) | H$_2$O LSF 3σ Uncert. (%) |
| S0011.spc | 0 | 1.00 | 39.6 | 0 | -1.58 | 26.5 | 1.65 | 0.89 |
| S0022.spc | 0 | 2.01 | 39.5 | 0 | -3.16 | 26.4 | 3.29 | 1.78 |
| S5511.spc | 25.0 | 24.43 | 0.27 | 25.0 | 24.27 | 0.33 | 0.87 | 12.1 |
| S5112.spc | 25.0 | 24.45 | 0.27 | 5.00 | 4.81 | 1.72 | 0.88 | 12.34 |
| S1511.spc | 5.00 | 4.91 | 0.44 | 25.0 | 24.27 | 0.11 | 1.08 | 3.23 |
| S5522.spc | 25.0 | 24.46 | 0.28 | 25.0 | 24.27 | 0.35 | 1.99 | 5.51 |
| S5121.spc | 25.0 | 24.45 | 0.27 | 5.00 | 4.92 | 1.63 | 1.99 | 5.25 |
| S1522.spc | 5.00 | 4.94 | 0.57 | 25.0 | 24.29 | 0.14 | 2.20 | 2.05 |
| Average Abs. % Concentration Uncertainty | | | 0.35 | | | 0.71 | 6.74 |