WPCW 2 BD ZT 3|WHPLJ IIISi - CR (100 % super/sub)b)HPCR_100.PRSx  @8;HjX@ L X` hp x (#%'0*,.8135@8:,%,&s-'.a6TechnicalTechnical Document Style$)D (a) . a2TechnicalTechnical Document Style%<6  ?  A.   a3TechnicalTechnical Document Style&9Wg  2  1.   a4TechnicalTechnical Document Style'8bv{ 2  a.   24(.)/*:0+0a1TechnicalTechnical Document Style(F!<  ?  I.   a7TechnicalTechnical Document Style)(@D i) . a8TechnicalTechnical Document Style*(D a) . PleadingHeader for numbered pleading paper+P@n   $] X X` hp x (#%'0*,.8135@8:4<5qI=6=7M>Document[2]rM Document Style;H)M ;H;H;H;H^)M 4*    Document[7]rM Document Style;H)M ;H;H;H;H^)M 5  ` ` ` Right Par[1]rM Right-Aligned Paragraph Numbers;H;H;H;H^)M 68 @  Right Par[2]rM Right-Aligned Paragraph Numbers;H;H;H;H^)M 7A@` ` `  ` ` ` 2A8?9?:V@;ADocument[3]rM Document Style;H)M ;H;H;H;H^)M 80    Right Par[3]rM Right-Aligned Paragraph Numbers;H;H;H;H^)M 9J` ` ` @  ` ` ` Right Par[4]rM Right-Aligned Paragraph Numbers;H;H;H;H^)M :S` ` `  @  Right Par[5]rM Right-Aligned Paragraph Numbers;H;H;H;H^)M ;\` ` `  @hhh hhh 2E<A=B>vC?HDRight Par[6]rM Right-Aligned Paragraph Numbers;H;H;H;H^)M w` ` `  hhh@ppp ppp Document[1]rM Document Style;H)M ;H;H;H;H^)M ?F    ׃  2rG@5EAEB?FCFTechnical[5]rM Technical Document Style)M ;H;H;H;H^)M @&!"  . Technical[6]rM Technical Document Style)M ;H;H;H;H^)M A&#$  . Technical[2]rM Technical Document Style)M ;H;H;H;H^)M B*%&    Technical[3]rM Technical Document Style)M ;H;H;H;H^)M C''(   2IDGE9HFHGoITechnical[4]rM Technical Document Style)M ;H;H;H;H^)M D&)*   Technical[1]rM Technical Document Style)M ;H;H;H;H^)M E4+%,     Technical[7]rM Technical Document Style)M ;H;H;H;H^)M F&-.  . Technical[8]rM Technical Document Style)M ;H;H;H;H^)M G&/0  . 2DPHe&JIpJJsJnKHeading 2rM Underlined Heading Flush Left;H;H;H;H^)M HYZ Heading 1rM Centered Heading;H)M ;H;H;H;H^)M I[ \ Ã  Bullet ListrM Indented Bullet List)M ;H;H;H;H^)M J]^` ` ` "m+O6^;C]ddCCCdCCCCddddddddddCCȲY~~wCN~sk~CCCddCYdYdYCdd88d8ddddJN8ddddYYdYddddddCddddddddd8YYYYYY~Y~Y~Y~YC8C8C8C8ddddddddddYdddddsdYYYYYYYd~Y~Y~Y~YddddddddC8C8C8C8oNd~8~8~8~8~8dvddddJJJkNkNkNkN~8~8~8dddddddYYYd~8dJkN~8dddddCddCCCWxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNdddCYQQddddddFddddFCChhd44ddzzdddwooChdF"Ȑdhd岲dCCȐzȲxCddodȐȅdCdYdsȐ]ȐȐȧzȐUwŐdȐYYCCCCѐz~ozoY~NYdYC8YooYdYzsdzdd~YYzozzzzNd88YYYzYzzzzCCdddddddzzzzzzzzzzzzzzzzzzzNNNNNNNdddddddddddddddddddd888888888888YYYYYYYYYYYYYYYYYYYzzzzzzzzzzzzzzzzzzzzCs~CzCddYCx2vPZLUW"m+O6^,,CTTe,,,T,,,,TTTTTTTTTT,,EcT^`MJc`%JYHy`eOhVVT```[Q,,,CC,HMHMH1MM H tMMMM/C1MJtJJ@;C;TTTTTT,TTTTTTCTQ cHcHcHcHcHr^HMHMHMHMH% % % % `MeMeMeMeM`M`M`M`M[JcH`MeMeM[J`MOMcHcHcH^H^H^H^H`MMHMHMHMHcMcMcMcMcMcM`M`M% % % % l@JYHH H H H0H `M`[`M`MeMeMyV/V/V/VCVCVCVCT1T1T1`M`M`M`M`M`Mt[JQ@Q@Q@`MH `MV/VCT1[J[J`MeM`M,CC,,,WddddddddddddddddddddddddddddddddddddddddN```CTT,EJJTTT66T44CCT4,,CCT11TTRReCC`C[{{QQ,CC4"``C`F``C充C,,`O``````````x,CcTJT`cC,T`CTM`hV``````````H``````oYQh`9O```````C```````;````;```````````````````````````````````````````,```,```,```,`````````````cJTHJCcHM>Q9`MeH% YCcEyJ`JT9eM`MOHOO;T>[Hm^`@j[ceJ>M MHHeHJe[[,,TTTTTTTJJJJJJJJJJJJJJJJJJJ>>>>>>>MMMMMMMMMMMMMMMMMMMM MMMMMMMHHHHHHHHHHHHeeeeeeeeeeeeeeeeeeee,McM`%e[c%[HC;,x?xxx,x6X@8;X@?xxx,ťx `B;X?xxx,#,x6Nh ;XHo8wC;,:zXw P7XPd!T,,,NpTxP7P ? Ԋ .,=, XT X     @12/29/94: Page @@12/29/94: Page 2/3/95: Page @ PROTOCOL FOR THE USE OF EXTRACTIVE FOURIER TRANSFORM INFRARED (FTIR) SPECTROMETRY FOR THE ANALYSES OF GASEOUS  ? b EMISSIONS FROM STATIONARY SOURCES ă INTRODUCTION The purpose of this document is to set general guidelines for the use of modern FTIR spectroscopic methods for the analysis of gas samples extracted from the effluent of stationary emission sources. This document outlines techniques for developing and evaluating such methods and sets basic requirements for reporting and quality assurance procedures.  ?  1.0 NOMENCLATURE 1.1 Appendix A lists definitions of the symbols and terms used in this Protocol, many of which have been taken directly from American Society for Testing and Materials (ASTM) publication E 13190a, entitled "Terminology Relating to Molecular Spectroscopy." 1.2 Except in the case of background spectra or where otherwise noted, the term "spectrum" refers to a doublebeam spectrum in units of absorbance vs. wavenumber (cmé1). 1.3 The term "Study" in this document refers to a publication that has been subjected to EPA or peerreview.  ?8  2.0 APPLICABILITY AND ANALYTICAL PRINCIPLE 2.1 Applicability. This Protocol applies to the determination of compoundspecific concentrations in single and multiplecomponent gas phase samples using doublebeam absorption spectroscopy in the midinfrared band. It does not specifically address other FTIR applications, such as singlebeam spectroscopy, analysis of openpath (nonenclosed) samples, and continuous measurement techniques. If multiple spectrometers, absorption cells, or instrumental linewidths are used in such analyses, each distinct operational configuration of the system must be evaluated separately according to this Protocol. 2.2 Analytical Principle. 2.2.1 In the midinfrared band, most molecules exhibit characteristic gas phase absorption spectra that may be recorded by FTIR systems. Such systems consist of a source of midinfrared radiation, an interferometer, an enclosed sample cell of known absorption pathlength, an infrared detector, optical elements for the transfer of infrared radiation between components, and gas flow control and measurement components. Adjunct and integral computer systems are used for controllingh),** the instrument, processing the signal, and for performing both Fourier transforms and quantitative analyses of spectral data. 2.2.2 The absorption spectra of pure gases and of mixtures of gases are described by a linear absorbance theory referred to as Beer's Law. Using this law, modern FTIR systems use computerized analytical programs to quantify compounds by comparing the absorption spectra of known (reference) gas samples to the absorption spectrum of the sample gas. Some standard mathematical techniques used for comparisons are classical least squares, inverse least squares, crosscorrelation, factor analysis, and partial least squares. Reference A describes several of these techniques, as well as additional techniques, such as differentiation methods, linear baseline corrections, and nonlinear absorbance corrections.  ?H  3.0 GENERAL PRINCIPLES OF PROTOCOL REQUIREMENTS  The characteristics that distinguish FTIR systems from gas analyzers used in instrumental gas analysis methods (e.g., EPAMethods 6C and 7E) are: (1) Computers are necessary to obtainand analyze data; (2) chemical concentrations can be quantified using previously recorded infrared reference spectra; and (3) analytical assumptions and results, including possible effects of interfering compounds, can be evaluated after the quantitative analysis. The following general principles and requirements of this Protocol are based on these characteristics. 3.1 Verifiability and Reproducibility of Results. Store all data and document data analysis techniques sufficient to allow an independent agent to reproduce the analytical results from the raw interferometric data. 3.2 Transfer of Reference Spectra. To determine whether reference spectra recorded under one set of conditions (e.g., optical bench, instrumental linewidth, absorption pathlength, detector performance, pressure, and temperature) can be used to analyze sample spectra taken under a different set of conditions, quantitatively compare "calibration transfer standards" (CTS) and reference spectra as described in this Protocol. (Note: The CTS may, but need not, include analytes of interest). To effect this, record the absorption spectra of the CTS (a) immediately before and immediately after recording reference spectra and (b)immediately after recording sample spectra. 3.3 Evaluation of FTIR Analyses. The applicability, accuracy, and precision of FTIR measurements are influenced by a number of interrelated factors, which may be divided into two classes: 3.3.1 SampleIndependent Factors. Examples are system configuration and performance (e.g., detector sensitivity and infrared source output), quality and applicability of reference absorption spectra, and type of mathematical analyses of the0*,** spectra. These factors define the fundamental limitations of FTIR measurements for a given system configuration. These limitations may be estimated from evaluations of the system before samples are available. For example, the detection limit for the absorbing compound under a given set of conditions may be estimated from the system noise level and the strength of a particular absorption band. Similarly, the accuracy of measurements may be estimated from the analysis of the reference spectra. 3.3.2 SampleDependent Factors. Examples are spectral interferants (e.g., water vapor and CO2) or the overlap of spectral features of different compounds and contamination deposits on reflective surfaces or transmitting windows. To maximize the effectiveness of the mathematical techniques used in spectral analysis, identification of interferants (a standard inital step) and analysis of samples (includes effect of other analytical errors) are necessary. Thus, the Protocol requires postanalysis calculation of measurement concentration uncertainties for the detection of these potential sources of measurement error.  ?  4.0 PRETEST PREPARATIONS AND EVALUATIONS Before testing, demonstrate the suitability of FTIR spectrometry for the desired application according to the procedures of this section. 4.1 Identify Test Requirements. Identify and record the test requirements described below in 4.1.1 through 4.1.5. These values set the desired or required goals of the proposed analysis; the description of methods for determining whether these goals are actually met during the analysis comprises the majority of this Protocol. 4.1.1 Analytes (specific chemical species) of interest. Label the analytes from i = 1 to I. 4.1.2 Analytical uncertainty limit (AUi). The AUi is the maximum permissible fractional uncertainty of analysis for the ithĠanalyte concentration, expressed as a fraction of the analyte concentration in the sample. 4.1.3 Required detection limit for each analyte (DLi, ppm). The detection limit is the lowest concentration of an analyte for which its overall fractional uncertainty (OFUi) is required to be less than its analytical uncertainty limit (AUi). 4.1.4 Maximum expected concentration of each analyte (CMAXi,ppm). 4.2 Identify Potential Interferants. Considering the chemistry of the process or results of previous Studies, identify potential interferants, i.e., the major effluent constituents and0*,** any relatively minor effluent constituents that possess either strong absorption characteristics or strong structural similarities to any analyte of interest. Label them 1 through Nj, where the subscript "j" pertains to potential interferants. Estimate the concentrations of these compounds in the effluent (CPOTj, ppm). 4.3 Select and Evaluate the Sampling System. Considering the source, e.g., temperature and pressure profiles, moisture content, analyte characteristics, and particulate concentration), select the equipment for extracting gas samples. Recommended are a particulate filter, heating system to maintain sample temperature above the dew point for all sample constituents at all points within the sampling system (including the filter), and sample conditioning system (e.g., coolers, waterpermeable membranes that remove water or other compounds from the sample, and dilution devices) to remove spectral interferants or to protect the sampling and analytical components. Determine the minimum absolute sample system pressure (Pmin, mmHg) and the infrared absorption cell volume (VSS, liter). Select the techniques and/or equipment for the measurement of sample pressures and temperatures. 4.4 Select Spectroscopic System. Select a spectroscopic configuration for the application. Approximate the absorption pathlength (LS', meter), sample pressure (PS', kPa), absolute sample temperature TS', and signal integration period (tSS, seconds) for the analysis. Specify the nominal minimum instrumental linewidth (MIL) of the system. Verify that the fractional error at the approximate values PS' and TS' is less than one half the smallest value AUi (see Section 4.1.2). 4.5 Select Calibration Transfer Standards (CTS's). Select CTS's that meet the criteria listed in Sections 4.5.1, 4.5.2, and 4.5.3. Note: It may be necessary to choose preliminary analytical regions (see Section 4.7), identify the minimum analyte linewidths, or estimate the system noise level (see Section4.12) before selecting the CTS. More than one compound may be needed to meet the criteria; if so, obtain separate cylinders for each compound. ƌ# 4.5.1 The central wavenumber position of each analytical region lies within 25 percent of the wavenumber position of at least one CTS absorption band. 4.5.2 The absorption bands in 4.5.1 exhibit peak absorbances greater than ten times the value RMSEST (see Section4.12) but less than 1.5 absorbance units. 4.5.3 At least one absorption CTS band within the operating range of the FTIR instrument has an instrumentindependent linewidth no greater than the narrowest analyte absorption band;h),** perform and document measurements or cite Studies to determine analyte and CTS compound linewidths. 4.5.4 For each analytical region, specify the upper and lower wavenumber positions (FFUm and FFLm, respectively) that bracket the CTS absorption band or bands for the associated analytical region. Specify the wavenumber range, FNU to FNL, containing the absorption band that meets the criterion of Section 4.5.3. 4.5.5 Associate, whenever possible, a single set of CTS gas cylinders with a set of reference spectra. Replacement CTS gas cylinders shall contain the same compounds at concentrations within 5 percent of that of the original CTS cylinders; the entire absorption spectra (not individual spectral segments) of the replacement gas shall be scaled by a factor between 0.95 and 1.05 to match the original CTS spectra. 4.6 Prepare Reference Spectra. Note: Reference spectra are available in a permanent soft copy from the EPA spectral library on the EMTIC (Emission Measurement Technical Information Center) computer bulletin board; they may be used if applicable.ƌ# 4.6.1 Select the reference absorption pathlength (LR) of the cell. 4.6.2 Obtain or prepare a set of chemical standards for each analyte, potential and known spectral interferants, and CTS. Select the concentrations of the chemical standards to correspond to the top of the desired range. 4.6.2.1 CommerciallyPrepared Chemical Standards. Chemical standards for many compounds may be obtained from independent sources, such as a specialty gas manufacturer, chemical company, or commercial laboratory. These standards (accurate to within 2percent) shall be prepared according to EPA Protocol 1 (see Reference D) or shall be traceable to NIST standards. Obtain from the supplier an estimate of the stability of the analyte concentration; obtain and follow all the supplier's recommendations for recertifying the analyte concentration. 4.6.2.2 SelfPrepared Chemical Standards. Chemical standards may be prepared as follows: Dilute certified commercially prepared chemical gases or pure analytes with ultrapure carrier (UPC) grade nitrogen according to the barometric and volumetric techniques generally described in Reference A, SectionA4.6. 4.6.3 Record a set of the absorption spectra of the CTS {R1}, then a set of the reference spectra at two or more concentrations in duplicate over the desired range (the top of the range must be less than 10 times that of the bottom), followed by a second set of CTS spectra {R2}. (If selfprepared0*,** standards are used, see Section 4.6.5 before disposing of any of the standards.) The maximum accepted standard concentrationpathlength product (ASCPP) for each compound shall be higher than the maximum estimated concentrationpathlength products for both analytes and known interferants in the effluent gas. For each analyte, the minimum ASCPP shall be no greater than ten times the concentrationpathlength product of that analyte at its required detection limit. 4.6.4 Permanently store the background and interferograms in digitized form. Document details of the mathematical process for generating the spectra from these interferograms. Record the sample pressure (PR), sample temperature (TR), reference absorption pathlength (LR), and interferogram signal integration period (tSR). Signal integration periods for the background interferograms shall be tSR. Values of PR, LR, and tSR shall not deviate by more than 1 percent from the time of recording {R1} to that of recording {R2}. 4.6.5 If selfprepared chemical standards are employed and spectra of only two concentrations are recorded for one or more compounds, verify the accuracy of the dilution technique by analyzing the prepared standards for those compounds with a secondary (nonFTIR) technique as follows: 4.6.5.1 Record the response of the secondary technique to each of the four standards prepared. 4.6.5.2 Perform a linear regression of the response values (dependant variable) versus the accepted standard concentration (ASC) values (independent variable), with the regression constrained to pass through the zeroresponse, zero ASC point. 4.6.5.3 Calculate the average fractional difference between the actual response values and the regressionpredicted values (those calculated from the regression line using the four ASC values as the independent variable). 4.6.5.4 If the average fractional difference value calculated in Section 4.6.5.3 is larger for any compound than the corresponding AUi, the dilution technique is not sufficiently accurate and the reference spectra prepared are not valid for the analysis. 4.7 Select Analytical Regions. Using the general considerations in Section 7 of Reference A and the spectral characteristics of the analytes and interferants, select the analytical regions for the application. Label them m = 1 to M. Specify the lower, center and upper wavenumber positions of each analytical region (FLm, FCm, and FUm, respectively). Specify the analytes and interferants which exhibit absorption in each region. 4.8 Determine Fractional Reproducibility Uncertainties. Using Appendix E, calculate the fractional reproducibility0*,** uncertainty for each analyte (FRUi) from a comparison of {R1} and {R2}. If FRUi > AUi for any analyte, the reference spectra generated in Section 4.6 are not valid for the application. 4.9 Identify Known Interferants. Using Appendix B, determine which potential interferant affects the analyte concentration determinations. If it does, relabel the potential interferant as "known" interferant, and designate these compounds from k = 1 to K. Appendix B also provides criteria for determining whether the selected analytical regions are suitable. 4.10 Prepare Computerized Analytical Programs. 4.10.1 Choose or devise mathematical techniques (e.g, classical least squares, inverse least squares, crosscorrelation, and factor analysis) based on Equation 4 of Reference A that are appropriate for analyzing spectral data by comparison with reference spectra. 4.10.2 Following the general recommendations of Reference A, prepare a computer program or set of programs that analyzes all the analytes and known interferants, based on the selected analytical regions (4.7) and the prepared reference spectra (4.6). Specify the baseline correction technique (e.g., determining the slope and intercept of a linear baseline contribution in each analytical region) for each analytical region, including all relevant wavenumber positions. 4.10.3 Use programs that provide as output [at the reference absorption pathlength (LR), reference gas temperature (TR), and reference gas pressure (PR)] the analyte concentrations, the known interferant concentrations, and the baseline slope and intercept values. If the sample absorption pathlength (LS), sample gas temperature (TS) or sample gas pressure (PS) during the actual sample analyses differ from LR, TR, and PR, use a program or set of programs that applies multiplicative corrections to the derived concentrations to account for these variations, and that provides as output both the corrected and uncorrected values. Include in the report of the analysis (see Section 7.0) the details of any transformations applied to the original reference spectra (e.g., differentiation), in such a fashion that all analytical results may be verified by an independent agent from the reference spectra and data spectra alone. 4.11 Determine the Fractional Calibration Uncertainty. Calculate the fractional calibration uncertainty for each analyte (FCUi) according to Appendix F, and compare these values to the fractional uncertainty limits (AUi; see Section4.1). If FCUiĠ>AUi), either the reference spectra or analytical programs for that analyte are unsuitable. 4.12 Verify System Configuration Suitability. Using Appendix C, measure or obtain estimates of the noise level (RMSEST,absorbance) of the FTIR system; alternatively, construct0*,** the complete spectrometer system and determine the values RMSSm using Appendix G. Estimate the minimum measurement uncertainty for each analyte (MAUi, ppm) and known interferant (MIUk, ppm) using Appendix D. Verify that (a)MAUiĠ<(AUi)(DLi), FRUi < AUi, and FCUi < AUi for each analyte and that (b) the CTS chosen meets the requirements listed in Section 4.5.  ?@  5.0 SAMPLING AND ANALYSIS PROCEDURE 5.1 Analysis System Assembly and LeakTest. Assemble the analysis system. Allow sufficient time for all system components to reach the desired temperature. Then determine the leakrate (LR) and leak volume (VL), where VL = LR tSS. Leak volumes shall be 4 percent of VSS. 5.2 Verify Instrumental Performance. Measure the noise level of the system in each analytical region using the procedure of Appendix G. If any noise level is higher than that estimated for the system in Section 4.12, repeat the calculations of Appendix D and verify that the requirements of Section 4.12 are met; if they are not, adjust or repair the instrument and repeat this section. 5.3 Determine the Sample Absorption Pathlength. Record a background spectrum. Then, fill the absorption cell with CTS at the pressure PR and record a set of CTS spectra {R3}. Store the background and unscaled CTS single beam interferograms and spectra. Using Appendix H, calculate the sample absorption pathlength (LS) for each analytical region. The values LS shall not differ from the approximated sample pathlength LS' (see Section 4.4) by more than 5 percent. 5.4 Record Sample Spectrum. Connect the sample line to the source. Either evacuate the absorption cell to an absolute pressure below 5 mmHg before extracting a sample from the effluent stream into the absorption cell, or pump at least ten cell volumes of sample through the cell before obtaining a sample. Record the sample pressure PS. Generate the absorbance spectrum of the sample. Store the background and sample single beam interferograms, and document the process by which the absorbance spectra are generated from these data. (If necessary, apply the spectral transformations developed in Section 5.6.2). The resulting sample spectrum is referred to below as SS. Note: Multiple sample spectra may be recorded according to the procedures of Section 5.4 before performing Sections 5.5 and 5.6.ƌ# 5.5 Quantify Analyte Concentrations. Calculate the unscaledanalyte concentrations RUAi and unscaled interferant concentrations RUIK using the programs developed in Section 4. Tocorrect for pathlength and pressure variations between the reference and sample spectra, calculate the scaling factorh),** RLPSĠ=(LRPRTS)/(LSPSTR). Calculate the final analyte and interferant concentrations RSAi = RLPSRUAi and RSIk = RLPSRUIk. 5.6 Determine Fractional Analysis Uncertainty. Fill the absorption cell with CTS at the pressure PS. Record a set of CTS spectra {R4}. Store the background and CTS single beam interferograms. Using Appendix H, calculate the fractional analysis uncertainty (FAU) for each analytical region. If the FAU indicated for any analytical region is larger than the required accuracy requirements determined in Section 4.1, then comparisons to previously recorded reference spectra are invalid in that analytical region, and the analyst shall perform one or both of the following procedures: 5.6.1 Perform instrumental checks and adjust the instrument to restore its performance to acceptable levels. If adjustments are made, repeat Sections5.3, 5.4 (except for the recording of a sample spectrum), and 5.5 to demonstrate that acceptable uncertainties are obtained in all analytical regions. 5.6.2 Apply appropriate mathematical transformations (e.g., frequency shifting, zerofilling, apodization, smoothing) to the spectra (or to the interferograms upon which the spectra are based) generated during the performance of the procedures of Section 5.3. Document these transformations and their reproducibility. (how ?) Do not apply multiplicative scaling of the spectra, or any set of transformations that is mathematically equivalent to multiplicative scaling. Different transformations may be applied to different analytical regions. Frequency shifts shall be smaller than onehalf the minimum instrumental linewidth, and must be applied to all spectral data points in an analytical region. The mathematical transformations may be retained for the analysis if they are also applied to the appropriate analytical regions of all sample spectra recorded, and if all original sample spectra are digitally stored. Repeat Sections 5.3, 5.4 (except the recording of a sample spectrum), and 5.5 to demonstrate that these transformations lead to acceptable calculated concentration uncertainties in all analytical regions.  ?  6.0 POSTANALYSIS EVALUATIONS Estimate the overall accuracy of the analyses performed in Section 5 as follows: 6.1 Qualitatively Confirm the Assumed Matrix. Examine each analytical region of the sample spectrum for spectral evidence of unexpected or unidentified interferants. If found, identify the interfering compounds (see Reference C for guidance) and add them to the list of known interferants. Repeat the procedures of Section 4 to include the interferants in the uncertainty calculations and analysis procedures. Verify that the MAU and FCU values do not increase beyond acceptable levels for the application requirements. Recalculate the analyte0* ,** concentrations (Section 5.5) in the affected analytical regions. 6.2 Quantitatively Evaluate Fractional Model Uncertainty (FMU). Perform the procedures of either Section 6.2.1 or 6.2.2: 6.2.1 Using Appendix I, determine the fractional model error (FMU) for each analyte. 6.2.2 Provide statistically determined uncertainties FMU for each analyte which are equivalent to two standard deviations at the 95% confidence level. Such determinations, if employed, must be based on mathematical examinations of the pertinent sample spectra (not the reference spectra alone). Include in the report of the analysis (see Section 7.0) a complete description of the determination of the concentration uncertainties. 6.3 Estimate Overall Concentration Uncertainty (OCU). Using Appendix J, determine the overall concentration uncertainty (OCU) for each analyte. If the OCU is larger than the required accuracy for any analyte, repeat Sections 4 and 6.  ?0  7.0 REPORTING REQUIREMENTS  ?  [Documentation pertaining to virtually all the procedures of Sections 4, 5, and 6 will be required. Software copies of reference spectra and sample spectra will be retained for some  ? minimum time following the actual testing.]  ,**  ?  8.0 REFERENCES A)Standard Practices for General Techniques of Infrared Quantitative Analysis (American Society for Testing and Materials, Designation E 16888).ƌ# B)The Coblentz Society Specifications for Evaluation of Research Quality Analytical Infrared Reference Spectra (Class  ?@ II); Anal. Chemistry 47, 945A (1975); Appl. Spectroscopy 444,  ? pp. 211215, 1990. ƌ# C)Standard Practices for General Techniques for Qualitative Infrared Analysis, American Society for Testing and Materials, Designation E 125288.ƌ# D)"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, EPA600/477027b, August 1977.ƌ# ,**  ? % APPENDIX A ă DEFINITIONS OF TERMS AND SYMBOLS׃  ?  A.1 Definitions of Terms  ?x  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.ƌ#  ?`  absorption pathlength in a spectrophotometer, 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.ƌ#  ?  analytical region a contiguous wavenumber region (equivalently, a contiguous set of absorbance spectrum data points) used in the quantitative analysis for one or more analyte.ƌ# Note: The quantitative result for a single analyte may be based on data from more than one analytical region.ƌ#  ?  apodization modification of the ILS function by multiplying the interferogram by a weighing function whose magnitude varies with retardation.ƌ#  ?p  background spectrum the single beam spectrum obtained with all system components without sample present.ƌ#  ?  baseline any line 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.ƌ#  ?  Beers's law the direct proportionality of the absorbance of a compound in a homogeneous sample to its concentration.ƌ#  ?@  calibration transfer standard (CTS) gas a gas standard of a compound used to achieve and/or demonstrate suitable quantitative agreement between sample spectra and the reference spectra; see Section 4.5.1.ƌ#  ?(#  compound a substance possessing a distinct, unique molecular structure.ƌ#  ?%  concentration (c) ĩ the quantity of a compound contained in a unit quantity of sample. The unit "ppm" (number, or mole, basis) is recommended.ƌ#  ?(  concentrationpathlength product the mathematical product of concentration of the species and absorption pathlength. For reference spectra, this is a known quantity; for sample0* ,** spectra, it is the quantity directly determined from Beer's law. The units "centimetersppm" or "metersppm" are recommended.ƌ#  ?   derivative absorption spectrum a plot of rate of change of absorbance or of any function of absorbance with respect to wavelength or any function of wavelength.ƌ#  ?@  double beam spectrum a transmission or absorbance spectrum derived by dividing the sample single beam spectrum by the background spectrum.ƌ# Note: The term "doublebeam" 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.ƌ#  ?  fast Fourier transform (FFT) a method of speeding up the computation of a discrete FT by factoring the data into sparse matrices containing mostly zeros.ƌ#  ?  flyback interferometer motion during which no data are  recorded.ƌ#  ?P  Fourier transform (FT) the mathematical process for convertingan amplitudetime spectrum to an amplitudefrequency spectrum, or vice versa.ƌ#  ?p  Fourier transform infrared (FTIR) spectrometer an analytical system that employs a source of midinfrared 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 timedomain detector response (interferogram) is processed by a Fourier transform to yield a representation of the detector response vs. infrared frequency.ƌ# Note: When FTIR spectrometers are interfaced with other instruments, a slash should be used to denote the interface; e.g., GC/FTIR; HPCL/FTIR, and the use of FTIR should be explicit; i.e., FTIR not IR.ƌ#  ?(#  frequency , v the number of cycles per unit time.  ?$  infrared the portion of the electromagnetic spectrum containing wavelengths from approximately 0.78 to 800 microns.ƌ#  ?'  interferogram, I(%) record of the modulated component of the interference signal measured as a function of retardation by the detector.ƌ# h) ,**Ԍ ?  interferometer device that divides a beam of radiant energy into two or more paths, generate 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.ƌ#  ?  linewidth the full width at half maximum of an absorption band in units of wavenumbers (cmé1).ƌ#  ?  midinfrared the region of the electromagnetic spectrum from approximately 400 to 5000 cmé1.ƌ#  ?`  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.ƌ#  ?H  retardation, % optical path difference between two beams in an interferometer; also known as "optical path difference" or "optical retardation." ƌ#  ?h  scan digital representation of the detector output obtained during one complete motion of the interferometer's moving assembly or assemblies.ƌ#  ?  scaling application of a multiplicative factor to the absorbance values in a spectrum.ƌ#  ?  single beam spectrum Fouriertransformed interferogram,representing the detector response vs. wavenumber. ƌ# Note: The term "singlebeam" 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 "doublebeam spectrum" above). Here, the term applies (for example) to the two spectra used directly in the calculation of transmission and absorbance spectra of a sample.ƌ#  ?  standard reference material a reference material, the composition or properties of which are certified by a recognized standardizing agency or group.ƌ# Note: The equivalent ISO term is "certified reference material."ƌ#  ?%  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 singlebeam sample and background spectra.ƌ#  ?h)  wavenumber ,  vA  the number of waves per unit length. 0*,**ԌNote: The usual unit of wavenumber is the reciprocal centimeter, cmé1. The wavenumber is the reciprocal of the wavelength, , when  is expressed in centimeters.ƌ#  ?   zerofilling the addition of zerovalued points to the end of a measured interferogram.ƌ# Note: Performing the FT of a zerofilled interferogram results in correctly interpolated points in the computed spectrum.ƌ#  ?`  A.2 Definitions of Mathematical Symbols  ?  A, absorbance the logarithm to the base 10 of the reciprocal of  the transmittance (T).ƌ# 1dddddddd (1) 1 (1) !#\ dd<X=FUNC {A~=~log SUB 10~{left(1 over T right)}~=~log sub 10 T} x6X@8;X@x6X@8;X@x6X@8;X@Alog10{1{8TlogV10Tvgn ^$##H ##X!!#$  ?h AAIim band area of the ith analyte in the mth analytical region,  at the concentration (CLi) corresponding to the product of its required detection limit (DLi) and analytical uncertainty limit (AUi) .ƌ#  ?P  AAVim average absorbance of the ith analyte in the mth analytical  region, at the concentration (CLi) corresponding to the product of its required detection limit (DLi) and analytical uncertainty limit (AUi) .ƌ#  ?8 ASC, accepted standard concentration ĩ the concentration value assigned to a chemical standard. ƌ#  ?  ASCPP, accepted standard concentrationpathlength product for a chemical standard, the product of the ASC and the sample absorption pathlength. The units "centimetersppm" or "metersppm" are recommended. ƌ#  ?x  AUi, analytical uncertainty limit the maximum permissible fractional uncertainty of analysis for the ith analyte concentration, expressed as a fraction of the analyte concentration determined in the analysis.ƌ#  ?`"  AVTm average estimated total absorbance in the mth analytical region.ƌ#  ?$  CKWNk estimated concentration of the kth known interferant.  ?H&  CMAXi estimated maximum concentration of the ith analyte.  ?'  CPOTj estimated concentration of the jth potential interferant. 0h),**\#!0Ԍ ?  DLi, required detection limit for the ith analyte, the lowest concentration of the analyte for which its overall fractional uncertainty (OFUi) is required to be less than the analytical uncertainty limit (AUi).ƌ#  ?  FCm center wavenumber position of the mth analytical region.  ?x  FAUi, fractional analtyical uncertainty calculated uncertainty in the measured concentration of the ith analyte because of errors in the mathematical comparison of reference and sample spectra.ƌ#  ?`  FCUi, fractional calibration uncertainty calculated uncertainty in the measured concentration of the ith analyte because of errors in Beer's law modeling of the reference spectra concentrations.ƌ#  ?H  FFLm lower wavenumber position of the CTS absorption band associated with the mth analytical region.ƌ#  ?  FFUm upper wavenumber position of the CTS absorption band associated with the mth analytical region.ƌ#  ?  FLm lower wavenumber position of the mth analytical region.  ?  FMUi, fractional model uncertainty calculated uncertainty in the measured concentration of the ith analyte because of errors in the absorption model employed.ƌ#  ?  FNL lower wavenumber position of the CTS spectrum containing an absorption band at least as narrow as the analyte absorption bands.ƌ#  ?  FNU upper wavenumber position of the CTS spectrum containing an absorption band at least as narrow as the analyte absorption bands.ƌ#  ?  FRUi, fractional reproducibility uncertainty calculated uncertainty in the measured concentration of the ith analyte because of errors in the reproducibility of spectra from the FTIR system.ƌ#  ?  FUm upper wavenumber position of the mth analytical region.  ?`"  IAIjm band area of the jth potential interferant in the mth analytical region, at its expected concentration (CPOTj).ƌ#  ?$  IAVim average absorbance of the ith analyte in the mth analytical  region, at its expected concentration (CPOTj).ƌ#  ?'  ISCi or k, indicated standard concentration the concentration from the computerized analytical program for a singlecompound reference spectrum for the ith analyte or kth known interferant.ƌ# 0*,**Ԍ ?  kPa kiloPascal (see Pascal).  ?  LS' estimated sample absorption pathlength.  ?   LR reference absorption pathlength.  ?  LS actual sample absorption pathlength.  ?@  MAUi mean of the MAUim over the appropriate analytical regions.  ?  MAUim, minimum analyte uncertainty the calculated minimum concentration for which the analytical uncertainty limit (AUi) in the measurement of the ith analyte, based on spectral data in the mth analytical region, can be maintained. ƌ#  ?  MIUj mean of the MIUjm over the appropriate analytical regions.  ?  MIUjm, minimum interferant uncertainty ĩ the calculated minimum concentration for which the analytical uncertainty limit CPOTj/20 in the measurement of the jth interferant, based on spectral data in the mth analytical region, can be maintained. ƌ#  ?  MIL, minimum instrumental linewidth the minimum linewidth fromthe FTIR system, in wavenumbers.ƌ# Note: The MIL of a system may be determined by observing an absorption band known (through higher resolution examinations) to be narrower than indicated by the system. The MIL is fundamentally limited by the retardation of the interferometer, but is also affected by other operational parameters (e.g., the choice of apodization).ƌ#  ?  Ni number of analytes.  ?   Nj number of potential interferants.  ?  Nk number of known interferants.  ?@  Nscan the number of scans averaged to obtain an interferogram.  ?  OFUi the overall fractional uncertainty in an analyte concentration determined in the analysis (OFUi = MAX{FRUi, FCUi, FAUi, FMUi}).ƌ#  ?#  Pascal (Pa) metric unit of static pressure, equal to one Newton per square meter; one atmosphere is equal to 101,325 Pa; 1/760 atmosphere (one Torr, or one millimeter Hg) is equal to 133.322 Pa.ƌ#  ?'  Pmin minimum pressure of the sampling system during the sampling  procedure. ƌ#  ?0*  PS' estimated sample pressure.0*,**Ԍ ? ԙ PR reference pressure.  ?  PS actual sample pressure.  ?   RMSSm measured noise level of the FTIR system in the mth analytical region.ƌ#  ?x  RMSD, root mean square difference a measure of accuracy determined by the following equation:ƌ# 1 (1) !1dddddddd (1) uA#6 dddddJndd<XLFUNC {RMSD~=~SQRT {{left(1 over n right)}~{SUM FROM {i~=~1} TO n~}e_i ^2}} x6X@8;X@x6X@8;X@x6X@8;X@RMSD5<15_nn`+it+1Se:2iJ+OTNSSR9g9n Iu$####!A#$X X where: @n =L the number of observations for which the accuracy is determined.ƌ# @0ei =@ the difference between a measured value of a property and its mean value over the n observations. ƌ# Note: The RMSD value "between a set of n contiguous absorbance values (Ai) and the mean of the values" (AM) is defined as ƌ#  ?P a#6dddddd ndd<fXgFUNC {RMSD~=~ SQRT {{left(1 over n right)}~{SUM FROM {i~=~1} to n} {left(A sub i~~A sub M right)^2}}} x6X@8;X@x6X@8;X@x6X@8;X@RMSD5<15_nn`+it+1%Ai A M! !2J+J~ TNSSR9g9n Ie lf$##P##!a#$ RSAi the (calculated) final concentration of the ith analyte.  ?  RSIk the (calculated) final concentration of the kth known interferant. ƌ#  ?   tscan, scan time ĩ time used to acquire a single scan, not including flyback.ƌ#  ?x  tS, signal integration period the period of time over which an interferogram is averaged by addition and scaling of individual scans. In terms of the number of scans Nscan and scan time tscan, tS = Nscantscan.ƌ#  ?`"  tSR signal integration period used in recording reference spectra.ƌ#  ?$  tSS signal integration period used in recording sample spectra.  ?H&  TR absolute temperature of gases used in recording reference spectra.ƌ#  ?(  TS absolute temperature of sample gas as sample spectra are recorded.ƌ# @0*,**! #}Ad#a@Ԍ ?  TP, Throughput manufacturer's estimate of the fraction of the total infrared power transmitted by the absorption cell and transfer optics from the interferometer to the detector.ƌ#  ?  VSS volume of the infrared absorption cell, including parts of attached tubing.ƌ#  ?x  Wik weight used to average over analytical regions k for quantities related to the analyte i; see Appendix D.ƌ# Note that some terms are missing, e.g., BAVm, OCU, RMSSm, SUBS, SICi, SACi, SS,**  ? % APPENDIX B ă X X b IDENTIFYING SPECTRAL INTERFERANTS׃  ?  B.1 General B.1.1 Assume a fixed absorption pathlength equal to the value LS'. B.1.2 Use band area calculations to compare the relative absorption strengths of the analytes and potential interferants. In the mth analytical region (FLm to FUm), use either rectangular or trapezoidal approximations to determine the band areas described below (see Reference A, Sections A.3.1 through A.3.3); document any baseline corrections applied to the spectra. B.1.3 Use the average total absorbance of the analytes and potential interferants in each analytical region to determine whether the analytical region is suitable for analyte concentration determinations. Note: The average absorbance in an analytical region is the band area divided by the width of the analytical region in wavenumbers. The average total absorbance in an analytical region is the sum of the average absorbances of all analytes and potential interferants.ƌ#  ?  B.2 Calculations B.2.1 Prepare spectral representations of each analyte at the concentration CLi = (DLi)(AUi), where DLi is the required detection limit and AUi is the maximum permissible analytical uncertainty. For the mth analytical region, calculate the band area (AAIim) and average absorbance (AAVim) from these scaled analyte spectra. B.2.2 Prepare spectral representations of each potential interferant at its expected concentration (CPOTj). For the mth analytical region, calculate the band area (IAIjm) and average absorbance (IAVjm) from these scaled potential interferant spectra. B.2.3 Repeat the calculation for each analytical region, and record the band area results in matrix form as indicated in Figure B.1. B.2.4 If the band area of any potential interferant in an analytical region is greater than the onehalf the band area of any analyte (i.e., IAIjm > 0.5 AAIim for any pair ij and any m), classify the potential interferant as known interferant. Label the known interferants k = 1 to K. Record the results in matrix form as indicated in Figure B.2. 0*,**ԌB.2.5 Calculate the average total absorbance (AVTm) for each analytical region and record the values in the last row of the matrix described in Figure B.2. Any analytical region where AVTmĠ>2.0 is unsuitable.   FIGURE B.1 Presentation of Potential Interferant Calculations X X ,L,L ,,"LL$Analytical Regions  ,,"LL$1 . . . . M  ,,"LL$ ,","H ""I""I""IAnalyte Labels 1 ,,"LL$AAI11 . . . AAI1M . ,,"LL$ . . . ,,"LL$ . . I ,,"LL$AAII1 . . . AAIIM  ,,"LL$ Potential Interferant Labels 1 ,,"LL$IAI11 . . . IAI1M . ,,"LL$ . . . ,,"LL$ . . J ,,"LL$IAIJ1 . . . IAIJM   FIGURE B.2 Presentation of Known Interferant Calculations  ,,"LL$Analytical Regions  ,,"LL$1 . . . . M  ,,"LL$ Analyte Labels 1 ,,"LL$AAI11 . . . . AAI1M . ,," . . . ,,"LL$ . . I ,,"LL$AAII1 . . . . AAIIM Known Interferant,,"LL$  Labels 1 ,,"LL$IAI11 . . . . IAI1M . ,,"LL$ . . . ,,"LL$ . . K ,,"LL$IAIK1 . . . . IAIKM Total Average,,"LL$  Absorbance,,"LL$ AVT1,,/ AVTM $,**  ? % APPENDIX C ă ~ESTIMATING NOISE LEVELS  ?   C.1 General C.1.1 The rootmeansquare (RMS) noise level is the standard measure of noise in this Protocol. The RMS noise level of a contiguous segment of a spectrum is defined as the RMS difference (RMSD) between the absorbance values which form the segment and the mean value of that segment (see Appendix A). C.1.2 The RMS noise value in doublebeam absorbance spectra is assumed to be inversely proportional to: (a) the square root of the signal integration period of the sample single beam spectra from which it is formed, and (b) to the total infrared power transmitted through the interferometer and absorption cell. C.1.3 Practically, the assumption of C.1.2 allow the RMS noise level of a complete system to be estimated from the following four quantities: (a)RMSMAN the noise level of the system (in absorbance units), without the absorption cell and transfer optics, under those conditions necessary to yield the specified minimum instrumental linewidth, e.g., Jacquinot stop size.ƌ# (b)tMAN the manufacturer's signal integration time used to determine RMSMAN.ƌ# (c)tSS the signal integration time for the analyses.ƌ# (d)TP the manufacturer's estimate of the fraction of the total infrared power transmitted by the absorption cell and transfer optics from the interferometer to the detector.ƌ#  ?x  C.2 Calculations C.2.1 Obtain the values of RMSMAN, tMAN, and TP from the manufacturers of the equipment, or determine the noise level by direct measurements with the completely constructed system proposed in Section 4. C.2.2 Calculate the noise value of the system (RMSEST) as follows: 5#6*dddddv ndd<XGFUNC {RMS sub EST~=~ {RMS sub MAN ~~TP~SQRT{t sub ss over t sub MAN }}}x6X@8;X@x6X@8;X@x6X@8;X@RMSESTRMSMANTP ct~ /ss_tV +MANTNSSR5$##%##!#$0h),***#-.0  ? % APPENDIX D ă ESTIMATING MINIMUM CONCENTRATION MEASUREMENT UNCERTAINTIES (MAU and MIU)׃  ?  D.1 General Estimate the minimum concentration measurement uncertainties for the ith analyte (MAUi) and jth interferant (MIUj) based on the spectral data in the mth analytical region by comparing the analyte band area in the analytical region (AAIim) and estimating or measuring the noise level of the system (RMSEST or RMSSm). Note: For a single analytical region, the MAU or MIU value is the concentration of the analyte or interferant for which the band area is equal to the product of the analytical region width (in wavenumbers) and the noise level of the system (in absorbance units). If data from more than one analytical region is used in the determination of an analyte concentration, the MAU or MIU is the mean of the separate MAU or MIU values calculated for each analytical region.ƌ#  ?  D.2 Calculations D.2.1 For each analytical region, set RMS = RMSSm if measured (Appendix G), or set RMS = RMSEST if estimated (Appendix C). D.2.2 For each analyte associated with the analytical region, calculate 3ddddd dd<XFUNC {MAU sub im~=~{left(RMS right)```left(DL sub i`` right)``` left(AU sub i`` right)``` left(FU sub m`````FL sub m``right) OVER AAI sub im }}x6X@8;X@x6X@8;X@x6X@8;X@MAUimuRMSDL{iAUi cFU /m cFL /m _AAI+ +imw` cGdk\else lg  e l$####!#$ D.2.3 If only the mth analytical region is used to calculate the concentration of the ith analyte, set MAUi = MAUim. D.2.4 If a number of analytical regions are used to calculate the concentration of the ith analyte, set MAUi equal to the weighted mean of the appropriate MAUim values calculated above; the weight for each term in the mean is equal to the fraction of the total wavenumber range used for the calculation represented by each analytical region. Mathematically, if the set of analytical regions employed is {m'}, then the MAU for each analytical region is 0',**#"0 #ddddd dd<XUFUNC {MAU sub i~=~ SUM from { VERT 50 {k``IN``\{m  \}}}``W sub ik~~MAU sub ik~}x6X@8;X@x6X@8;X@x6X@8;X@!MAUi+k+{!+m+}t!WikA!MAUik'!d+Iq+$#### !#$ where the weight Wik is defined for each term in the sum as 1dddddddd (1) 1dddddddd (1) D# ddddddd<XFUNC {W sub {ik}~=~ left( ~FM sub k````FL sub k~ right)``` left(`SUM from { VERT 50 {p``IN``\{m  \}}}[`FM sub p`` ``` FL sub p`] right) sup {1}}x6X@8;X@x6X@8;X@x6X@8;X@!Wik!FMk!FLkF+p +{p+m +} ![% !FM pP !FLE p !]1!E!+ !aRelTg#TnI+D$##x## !#$ D.2.5 Repeat Sections D.2.1 through D.2.4 to calculate the analogous values MIUj for the interferants j = 1 to J. Replace the value (AUi)(DLi) in the above equations with CPOTj/20; replace the value AAIim in the above equations with IAIjm.@ ,**!#$ # @  ?   % APPENDIX E ă  DETERMINING FRACTIONAL REPRODUCIBILITY UNCERTAINTIES (FRU)׃  ?   E.1 General To estimate the reproducibility of the spectroscopic results of the system, compare the CTS spectra recorded before and after preparing the reference spectra. Compare the difference between the spectra to their average band area. Perform the calculation for each analytical region on the portions of the CTS spectra associated with that analytical region.  ?(  E.2 Calculations E.2.1 The CTS spectra {R1} consist of N spectra, denoted by S1i, i=1, N. Similarly, the CTS spectra {R2} consist of N spectra, denoted by S2i, i=1, N. Each Ski is the spectrum of a single compound, where i denotes the compound and k denotes theset {Rk} of which Ski is a member. Form the spectra S3 according to S3i = S2iĩS1i for each i. Form the spectra S4 according to S4i = [S2i+S1i]/2 for each i. E.2.2 Each analytical region m is associated with a portion of the CTS spectra S2i and S1i, for a particular i, with lower and upper wavenumber limits FFLm and FFUm, respectively. E.2.3 For each m and the associated i, calculate the band area of S4i in the wavenumber range FFUm to FFLm. Follow the guidelines of Section B.1.2 for this band area calculation. Denote the result by BAVm. E.2.4 For each m and the associated i, calculate the RMSD of S3i between the absorbance values and their mean in the wavenumber range FFUm to FFLm. Denote the result by SRMSm. E.2.5 For each analytical region m, calculate the quantity FMm = SRMSm(FFUmĩFFLm)/BAVmă E.2.6 If only the mth analytical region is used to calculate the concentration of the ith analyte, set FRUi = FMm. E.2.7 If a number pi of analytical regions are used to calculate the concentration of the ith analyte, set FRUi equal to the weighted mean of the appropriate FMm values calculated above. Mathematically, if the set of analytical regions employed is {m'}, then 1dddddddd (1) 1 (1) #\+dd<XTFUNC {FRU sub i~=``SUM from {VERT 50 {k ``IN`` \{m  \}}} W sub ik ```FM sub k}x6X@8;X@x6X@8;X@x6X@8;X@!FRUi+k+{+m+}!Wik{!FMpk'!8+jIE+$##H&##X!#$ where the Wik are calculated as described in Appendix D.0h),**\+#@-0  ? % APPENDIX F ă vDETERMINING FRACTIONAL CALIBRATION UNCERTAINTIES (FCU)׃  ?   F.1 General F.1.1 The concentrations yielded by the computerized analytical program applied to each singlecompound reference spectrum are defined as the indicated standard concentrations (ISC's). The ISC values for a single compound spectrum should ideally equal the accepted standard concentration (ASC) for one analyte or interferant, and should ideally be zero for all other compounds. Variations from these results are caused by errors in the ASC values, variations from the Beer's law (or modified Beer's law) model used to determine the concentrations, and noise in the spectra. When the first two effects dominate, the systematic nature of the errors is often apparent; take steps to correct them. F.1.2 When the calibration error appears nonsystematic, apply the following method to estimate the fractional calibration uncertainty (FCU) for each compound. The FCU is defined as the mean fractional error between the ASC and the ISC for all reference spectra with nonzero ASC for that compound. The FCU for each compound shall be less than the required fractional uncertainty specified in Section 4.1. F.1.3 The computerized analytical programs shall also be required to yield acceptably low concentrations for compounds with ISC=0 when applied to the reference spectra. The limits chosen in this Protocol are that the ISC of each reference spectrum for each analyte or interferant shall not exceed that compound's minimum measurement uncertainty (MAU or MIU).  ?X  F.2 Calculations F.2.1 Apply each analytical program to each reference spectrum. Prepare a similar table as that in Figure F.1 to present the ISC and ASC values for each analyte and interferant in each reference spectrum. Maintain the order of reference file names and compounds employed in preparing FigureF.1. F.2.2 For all reference spectra in Figure F.1, verify that the absolute value of the ISC's are less than the compound's MAU (for analytes) or MIU (for interferants). F.2.3 For each analyte reference spectrum, calculate the quantity (ASCISC)/ASC. For each analyte, calculate the mean of these values (the FCUi for the ith analyte) over all reference spectra. Prepare a similar table as that in Figure F.2 to present the FCUi and analytical uncertainty limit (AUi) for each analyte. (,**  Y #Xt4 PoGzXP#%FIGURE F.1 | Presentation of Accepted Standard Concentrations (ASC's) and Indicated Standard Concentrations (ISC's) r ddx !v} dd r $ EP P P @@@@@P$  Compound Name   + Reference C Spectrum  File Name & & %]ASC $*(ppm) 5vISC (ppm) 9( 'Analytes Interferants + i=1..................I /!j=1.................J.EP P @@P    v. < < < < < < < < 0        0         0       < 0 > > > > > > > >     E  %FIGURE F.2 5  Presentation of Fractional Calibration Uncertainties (FCU's) Nand Analytical Uncertainties (AU's) r !v} dd  A&dX}99 r  s@ @ P $ !Analyte "#Name-_ ,FCU ,(%)4 3AU 3(%)s@ @ P X L L       Ls#x  @8;X@#,**  ? % APPENDIX G ă MEASURING NOISE LEVELS׃  ?  G.1 General The rootmeansquare (RMS) noise level is the standard measure of noise. The RMS noise level of a contiguous segment of a spectrum is the RMSD between the absorbance values that form the segment and the mean value of the segment (see Appendix A).  ?(  G.2 Calculations G.2.1 Evacuate the absorption cell or fill it with UPC grade nitrogen at approximately one atmosphere total pressure. G.2.2 Record two single beam spectra of signal integration period tSS. G.2.3 Form the double beam absorption spectrum from these two single beam spectra, and calculate the noise level RMSSm in the M analytical regions.,**  ? % APPENDIX H ă DETERMINING SAMPLE ABSORPTION PATHLENGTH (LS) AND FRACTIONAL ANALYTICAL UNCERTAINTY (FAU)׃  ?  H.1 General Reference spectra recorded at absorption pathlength (LR), gas pressure (PR), and gas absolute temperature (TR) may be used to determine analyte concentrations in samples whose spectra are recorded at conditions different from that of the reference spectra, i.e., at absorption pathlength (LS), absolute temperature (TS), and pressure (PS). Appendix H describes the calculations for estimating the fractional uncertainty (FAU) of this practice. It also describes the calculations for determining the sample absorption pathlength from comparison of CTS spectra, and for preparing spectra for further instrumental and procedural checks. H.1.1 Before sampling, determine the sample absorption pathlength using least squares analysis. Determine the ratio LS/LR by comparing the spectral sets {R1} and {R3}, which are recorded using the same CTS at LS and LR, and TS and TR, but both at PR. H.1.2 Determine the fractional analysis uncertainty (FAU) for each analyte by comparing a scaled CTS spectral set, recorded at LS, TS, and PS, to the CTS reference spectra of the same gas, recorded at LR, TR, and PR. Perform the quantitative comparison after recording the sample spectra, based on band areas of the spectra in the CTS absorbance band associated with each analyte.  ?  H.2 Calculations H.2.1 Absorption Pathlength Determination. Perform and document separate linear baseline corrections to each analytical region in the spectral sets {R1} and {R3}. Form a one ?x dimensional array A R containing the absorbance values from all segments of {R1} that are associated with the analytical regions; the members of the array are ARi, i = 1, n. Form a similar one ? dimensional array A S from the absorbance values in the spectral set {R3}; the members of the array are ASi, i = 1, n. Based on  ?`" the model A S = r A R + E , determine the leastsquares estimate of  ?(# r', the value of r which minimizes the square error E2 . Calculate the sample absorption pathlength LS = r'(TS/TR)LR. H.2.2 Fractional Analysis Uncertainty. Perform and document separate linear baseline corrections to each analytical region in  ?' the spectral sets {R1} and {R4}. Form the arrays A S and A R as  ?' described in Section H.2.1, using values from {R1} to form A R,  ?( and values from {R4} to form A S. Calculate the values 1 (1) 1dddddddd (1) !$#6dddddjndd<cXFUNC {NRMS sub E~=~ SQRT{{SUM from {i=1} to n} ``left[A sub Si~~{left( T sub R over T sub S right)}``{left( L sub S over L sub R right)}``{left(P sub S over P sub R right)}``A sub Ri``right]^2 }}x6X@8;X@x6X@8;X@x6X@8;X@NRMSEqn!+i+1ASi_cT/R__T+S? cL /S? _L +R cP /S _P +R ARi2q+!oToNSoSoR+Itvtw}~hiI oI pB h i) o) p"  h i o p cand00*,**#!0Ԍ$####!!#$A#ddddd#dd<:XFUNC {IA sub AV~=~{1 over 2 }``{Sum from {i=1} to n}`` {left[A sub Si``+``` {left ( T sub R over T sub S right)}``{left( L sub S over L sub R right)}``{left(P sub S over P sub R right)}`` A sub Ri``right]}~ }x6X@8;X@x6X@8;X@x6X@8;X@IAAV <1 _2n+ik+1IASicTD/R_TD+S cL$ /S _L$ +R cP /S _P +R Ai Ri+ Ivw5}5~LhLiop, h, i o p  h iq oq pj :߷$####!A#$ The fractional analytical uncertainty is defined as }a#<dddddBdd<X)FUNC {FAU ~=~{NRMS sub E over IA sub AV}}x6X@8;X@x6X@8;X@x6X@8;X@FAUcNRMS/E-_IA"+AV,}$##( ##!a#$P,**1#!#J A<#`aP  ? % APPENDIX I ă DETERMINING FRACTIONAL MODEL UNCERTAINTIES (FMU)׃  ?  I.1 General To prepare analytical programs for FTIR analyses, the sample constituents must first be assumed; the calculations in this appendix, based upon a simulation of the sample spectrum, verify the appropriateness of these assumptions. The simulated spectra consist of the sum of single compound reference spectra scaled to represent their contributions to the sample absorbance spectrum; scaling factors are based on the indicated standard concentrations (ISC) and measured (sample) analyte and interferant concentrations, the sample and reference absorption pathlengths, and the sample and reference gas pressures. No bandshape correction for differences in the temperature of the sample and reference spectra gases is made; such errors are included in the FMU estimate. The actual and simulated sample spectra are quantitatively compared to determine the fractional model uncertainty; this comparison uses the reference spectra band areas and residuals in the difference spectrum formed from the actual and simulated sample spectra.  ?P  I.2 Calculations I.2.1 For each analyte (with scaled concentration RSAi), select a reference spectrum SAi with indicated standard concentration ISCi. Calculate the scaling factors #ddddddd<$func { RA sub i ~=~{{T sub R}```{L sub S}```{P sub S}~ {RSA sub i} } over {{T sub S}```{L sub R}```{P sub R}~ {ISC sub i}} }x6X@8;X@x6X@8;X@x6X@8;X@RAicT7/RcLF/ScPU/ScRSAj/i_T7+S_LF+R_PU+R_ISCj+i4 $ߡ$####!#$and form the spectra SACi by scaling each SAi by the factor RAi. I.2.2 For each interferant, select a reference spectrum SIk with indicated standard concentration ISCk. Calculate the scaling factors #t'ddddddd<$func { RI sub k ~=~{{T sub R}```{L sub S}```{P sub S}~ {RSI sub k} } over {{T sub S}```{L sub R}```{P sub R}~ {ISC sub k}} }x6X@8;X@x6X@8;X@x6X@8;X@RIkcT7/RcLF/ScPU/ScRSIj/k_T7+S_LF+R_PU+R_ISCj+k4 $ߡ$##`"##!#$and form the spectra SICk by scaling each SIk by the factor RIk. I.2.3 For each analytical region, determine by visual inspection which of the spectra SACi and SICk exhibit absorbance bands within the analytical region. Subtract each spectrum SACi and SICk exhibiting absorbance from the sample spectrum SS to@0*,**!#8!t'#*@ form the spectrum SUBS. To save analysis time and to avoid the introduction of unwanted noise into the subtracted spectrum, it is recommended that the calculation be made (1) only for those spectral data points within the analytical regions, and (2)for each analytical region separately using the original spectrum SS. I.2.4 For each analytical region m, calculate the RMSD of SUBS between the absorbance values and their mean in the region FFUm to FFLm. Denote the result by RMSSm. I.2.5 For each analyte i, calculate the quantity #tddddd dd <Tfunc { FM sub m ~=~{{RMSS sub m}```{left(``FFU sub m`` ```FFL sub m ``right) }```{AU sub i}` ``{DL sub i} } over {{AAI sub i}``` {RSA sub i}} }x6X@8;X@x6X@8;X@x6X@8;X@FMmcRMSS/mcFFU/m*cFFL /m cAU /i cDL /i,_AAI+i+_RSA +ipcY1e lT$##` ##!#$for each analytical region associated with the analyte. I.2.6 If only the mth analytical region is used to calculate the concentration of the ith analyte, set FMUi=FMm. I.2.7 If a number of analytical regions are used to calculate the concentration of the ith analyte, set FMi equal to the weighted mean of the appropriate FMm values calculated above. Mathematically, if the set of analytical regions employed is {m'}, then #,dddddmdd <XRFUNC {FMU sub i~=~ SUM from { VERT 50 {k``IN``\{m  \}}}W sub ik ~ FM sub k~}x6X@8;X@x6X@8;X@x6X@8;X@!FMUi+k+{!+m+}H!Wik!FMk'!d+Iq+$#### !#$where Wik is calculated as described in Appendix D.@8 ,**!t# ,#< @  ? % APPENDIX J ă DETERMINING OVERALL CONCENTRATION UNCERTAINTIES (OCU)׃ The calculations in previous sections and appendices estimate the measurement uncertainties for various FTIR measurements. The lowest possible overall concentration uncertainty (OCU) for an analyte is its MAU value, which is an estimate of the absolute concentration uncertainty when spectral noise dominates the measurement error. However, if the product of the largest fractional concentration uncertainty (FRU, FCU, FAU, or FMU) and the measured concentration of an analyte exceeds the MAU for the analyte, then the OCU is this product. In mathematical terms, set OFUi = MAX{FRUi, FCUi, FAUi, FMUi} and OCUi = MAX{RSAi*OFUi, MAUi}.  !,**  ?  - Outline Table of Contents ă #TxP7pP#    INTRODUCTIONp"#d 1 1.0 NOMENCLATUREp"#d 1 2.0 APPLICABILITY AND ANALYTICAL PRINCIPLEp"#d 1 3.0 GENERAL PRINCIPLES OF PROTOCOL REQUIREMENTSp"#d 2 4.0 PRETEST PREPARATIONS AND EVALUATIONSp"#d 3 4.1 Identify Test RequirementsƘ!p"#d 3 4.2 Identify Potential InterferantsƘ!p"#d 3 4.3 Select and Evaluate the Sampling SystemƘ!p"#d 4 4.4 Select Spectroscopic SystemƘ!p"#d 4 4.5 Select Calibration Transfer Standards (CTS's)Ƙ!p"#d 4 4.6 Prepare Reference SpectraƘ!p"#d 5 4.7 Select Analytical RegionsƘ!p"#d 6 4.8 Determine Fractional Reproducibility UncertantiesƘ!p"#d 6 4.9 Identify Known InterferantsƘ!p"#d 7 4.10 Prepare Computerized Analytical ProgramsƘ!p"#d 7 4.11 Determine the Fractional Calibration UncertantyƘ!p"#d 7 4.12 Verify System Configuration SuitabilityƘ!p"#d 7 5.0 SAMPLING AND ANALYSIS PROCEDUREp"#d 8 5.1 Analysis System Assembly and LeakTestƘ!p"#d 8 5.2 Verify Instrumental PerformanceƘ!p"#d 8 5.3 Determine the Sample Absorption PathlengthƘ!p"#d 8 5.4 Record Sample SpectrumƘ!p"#d 8 5.5 Quantify Analyte ConcentrationsƘ!p"#d 8 5.6 Determine Fractional Analysis UncertaintyƘ!p"#d 9 6.0 POSTANALYSIS EVALUATIONSp"#d 9 6.1 Qualitatively Confirm the Assumed MatrixƘ!p"#d 9 6.2 Quantitatively Evaluate Fractional Model Uncertainty (FMU)Ƙ!p`"#c 10 6.3 Estimate Overall Concentration Uncertainty (OCU)Ƙ!p`"#c 10 7.0 REPORTING REQUIREMENTSp`"#c 10 8.0 REFERENCESp`"#c 11 APPENDIX ADEFINITIONS OF TERMS AND SYMBOLSp`"#c 12 APPENDIX BIDENTIFYING SPECTRAL INTERFERANTSp`"#c 20 APPENDIX CESTIMATING NOISE LEVELSp`"#c 22 APPENDIX DESTIMATING MINIMUM CONCENTRATION MEASUREMENT UNCERTAINTIES (MAU and MIU)p`"#c 23 APPENDIX EDETERMINING FRACTIONAL REPRODUCIBILITY UNCERTAINTIES (FRU)p`"#c 25 APPENDIX FDETERMINING FRACTIONAL CALIBRATION UNCERTAINTIES (FCU)p`"#c 26 APPENDIX GMEASURING NOISE LEVELSp`"#c 28 APPENDIX HDETERMINING SAMPLE ABSORPTION PATHLENGTH (LS) AND (FRACTIONAL ANALYTICAL UNCERTAINTY (FAU)p`"#c 29 APPENDIX IDETERMINING FRACTIONAL MODEL UNCERTAINTIES (FMU)p`"#c 31 APPENDIX JDETERMINING OVERALL CONCENTRATION UNCERTAINTIES (OCU)p`"#c 33