Detection Limits - Analytical Chemistry (ACS Publications)

Report

Detection Limits

and Spectral Interferences in Atomic Emission Spectrometry

The detection limit serves as both the foundation and the skeleton of the basic methodology ofan analytical technique

D

etection limits are important figures of merit in all branches of analytical chemistry. In routine analyses, they are intuitively interpreted as the lowest concentration that one can determine with a particular method. In research and instrument development, where one is primarily concerned with the experimental determination of numbers that reflect the power of the method or the instrument, detection limits are used to promote methods or instruments and their manufacturers. The true content of detection limits is the set of relationships that describes the dependence of the detection limits on the physical variables of the analytical systems they characterize. Because discussions of detection limits are scattered throughout the literature and sometimes

P.W.J.M. Boumans Philips Research Laboratories 0003 - 2700/94/0366 -459A/$04.50/0 © 1994 American Chemical Society

are incoherent or ambiguous, it has been difficult to understand this content. However, it is my view that the messages detection limits convey now have been unified; the means exist for systems to communicate concrete messages about strong and weak features that are hidden behind the numerical values of detection limits. Detection limits are usually determined experimentally with ideal samples that contain only analytes at very low concentrations. Such detection limits provide useful information about the intrinsic performance of instruments, particularly if the measurements are obtained according to procedures that include the acquisition of additional data. The results may provide insight into system diagnosis, possible improvements, optimal exploitation of new technologies, and unbiased communication of results that can be unambiguously interpreted beyond the strict environment in which they were collected.

A real sample comprises a matrix that may adversely affect the detection limit, the precision, and the accuracy of the measurement. In atomic emission spectrometry (AES), for example, the matrix may substantially worsen the detection limit, chiefly because of spectral interference. A detailed analysis has not only revealed the precise reasons for this problem but has also uncovered ways that it can be addressed. AES is a field in which the study of the fundamental aspects of detection limits has received considerable attention. Developments in instrumentation, particularly the advent of steady plasma sources such as the inductively coupled plasma (ICP), have fostered in-depth investigations whose results can be extended and applied to all AES methods with either liquid or solid sampling. With proper adaptations, these results can also be applied to atomic mass and fluorescence spectroscopy, including X-ray fluores-

Analytical Chemistry, Vol. 66, No. 8, April 15, 1994 459 A

Report cence spectroscopy. Although detection limits will be discussed here in terms of ICP-AES (1,2), there is no limit on the scope of applications. Historical perspective For the measurement of detection limits and the theoretical discussion of their de pendence on system variables, either of two approaches may be followed (3) : the SNR approach, which uses the signal-tonoise ratio (SNR), or the SBR-RSDB ap proach, which uses the signal-to-back ground ratio (SBR) and the relative standard deviation of the background (RSDB). Each approach is correct, and each yields the same detection limits. Over the past 50 years, however, a major problem has been that protagonists of one ap proach did not understand the essentials of the other approach. Nevertheless, con cepts from one were used with the other, which caused not only confusion but also horrible errors. Fortunately, it now ap pears that this problem has disappeared. Kaiser described the basis of the SBRRSDB approach (4), but its acceptance outside continental Europe was ham pered, possibly because it was published in German but more likely because it was originally associated with photographic detection, which has lost much of its at traction since the early 1960s. In photo graphic detection, noise is manifested as fluctuations in optical density ("blacken ing") and a difference between a line sig nal and the background is primarily ob served as a difference in optical densities. Because a photographic emulsion has a logarithmic response, a density differ ence translates into a difference between the logarithms of two intensities (x), which is equivalent to the logarithm of an intensity ratio (log xA/xB). This is the ori gin of the ratio concept underlying SBR and RSDB. Further development of the theory expanded its scope beyond photo graphic detection. Using the source back ground as a natural reference level greatly facilitates the practical application of phys ical relationships as well as the transfer of data on detection limits and related quan tities between equipment. Thus, one can avoid the cumbersome absolute intensity calibrations with a standard source, which would be required in the SNR approach to 460 A

Figure 1 . Block diagram illustrates the dependence of SBR, RSDB, and detection limit on the characteristics of the source, spectrometer, and detector when background is defined in terms of radiant energy only. The SBR value that dictates the detection limit is the SBR as measured, which depends on the SBR in the source, the physical width of the spectral line, and the bandwidth of the spectrometer. The relevant value of RSDB may be directly measured or calculated from an RSDB function in which the coefficients for the noise contributions have been previously measured under conditions representative of the pertinent equipment. (Adapted with permission from Reference 16.)

exchange information between different equipment or laboratories. Flame emission spectrometrists in the 1950s and 1960s and plasma source emis sion spectrometrists in the 1970s and 1980s, particularly in North America, viewed the photographic plate as a curi ous antiquity. They did not see a need to use European idiosyncracies such as SBR and RSDB in their work, which was domi nated by the straightforward SNR concept (5). They did borrow the SBR concept for optimization purposes, but blending SBR and SNR turned out to be a ticklish en deavor. This confusing situation has been clari fied by a detailed theoretical analysis of both approaches and their interrelation ship (3, 5-7). Practical applications of the SBR-RSDB approach to assess classical ICP systems using photomultipliers (PMTs) as detectors (6, 7-9) and ad vanced ICP systems based on array detec tors (10-12) suggest that this approach is finding wider acceptance. This fact, cou pled with the recent design and publica tion of software for data collection and

Analytical Chemistry, Vol. 66, No. 8, April 15, 1994

processing using the SBR-RSDB ap proach (13), reflects my belief that the approach offers distinct advantages. Principles Detection limit and background-limited noise. Conventionally, a detection limit (C] ) is experimentally defined as the ana lyte concentration that yields a net analyte signal (xA) equal to k times the standard deviation (σΒ) of the background (xH) kcs„

(1)

where c0 is the concentration yielding a net analyte signal xA. Equation 1 is the formulation of the detection limit in terms of the SNR theory. The right-hand side of the equation is the quotient of the net signal at the detection limit (kaB) and the sensitivity (xjc0). The numerical value of the factor k is im portant in the context of the statistical in terpretation of the detection limit as a practical analytical figure of merit (14). For the sake of uniformity, the use of k = 3 is generally recommended. The use of

k = 2 y 2 is preferable in fundamental discussions to emphasize the statistical interpretation and to ease connecting the detection limit with precision (3). The standard deviation σ Β is usually determined by measuring the variability of the background signal using an analytefree "blank" sample. In Equation 1 it is assumed that near the detection limit the system is limited by background noise. The complications inherent in the treat ment of the situation in which both back ground and analyte signal noise are cov ered (15) is of little interest here. This is because it may be disputed whether the conditions under which analyte signal noise perceptibly contributes to the total noise at the detection limit are acceptable as a basis of viable analytical methods. If such conditions occur, usually as a result of a lack of detector sensitivity, the rele vant system is far from optimal. SBR-RSDB approach. Equation 1 es sentially contains the quotient of the back ground noise (σΒ) and the net analyte signal (xA); only the value of the quotient has meaning in comparisons of results obtained on diSerent equipment. Numeri cal values of σ Β and xA in terms of units such as volts, amperes, or counts have meaning only if used in the context of the same instrument. Transfer of data be tween equipment requires the use of a standard source for intensity calibrations. This impractical approach is rarely used in analytical laboratories. A viable alternative is to normalize σ Β and xA to the background signal xB, de fined as the readout signal obtained for the radiant background of the source (i.e., without possible contributions from detec tor dark current or readout offsets). This is the essence of the SBR-RSDB ap proach, which is formalized by dividing the numerator and the denominator of Equation 1 by xB. The common form of this equation is cL = k χ 0.01 χ RSDB χ - ^ -

which is equal to c0/SBR, is often pre ferred. Clearly this equation should yield ex actly the same detection limit as Equa tion 1. The difference is not in the final results but in the ease with which the de tection limit can be broken down into practically measurable functions. To avoid absolute measurements, the SBR-RSDB approach uses two relative quantities, SBR and RSDB. They can be unambiguously determined experimen tally for any system and can be expressed as functions of the physical variables of the system. This approach permits a de tailed assessment of the system and an unbiased comparison of different systems. Figure 1 (16) illustrates this concept schematically for the variables associated with the three components of an emission spectrometric system: source, spectrome ter, and detector. This concept has been examined theoretically (3,6, 7) and prac tically (8-11), and tools for further appli cations are available (17). The SBR function Figure 1 shows that the measured SBR ([SBR]meas) depends on both the source and the spectrometer. The term "source" refers to the combination of the excitation

source and the sample introduction de vice. Actually, only a part of the source is used for observations; this part is charac terized by the "source SBR" ([SBR]source), which is dictated by typical source param eters such as temperature, sample trans port efficiency, type of discharge gas, and gas flow rates. Recognition that the source SBR is a characteristic independent of the spec trometer is paramount. The spectrometer converts the source SBR into the mea sured SBR on the basis of two variables: the physical width of the spectral line and the spectral bandwidth of the spectrome ter. The result of a rigorous treatment of the pertinent relationships in terms of spectral radiances may be condensed into a simple equation in which the measured SBR is the product of the source SBR and fopt, which is a function of the physical width of the spectral line and the band width of the spectrometer (3,17). This function has been determined semiempirically for the ICP using general physical principles, and its appropriate ness has been independently confirmed theoretically (9). The semiempirical func tion has been used to construct the curves in Figure 2 (18) for spectral lines having physical widths ranging from 1 to 16 pm.

(2)

where RSDB is the relative standard devi ation of the background (expressed as a percentage) and SBR is associated with concentration c0. Because a numerical value of SBR has a defined meaning only if the value of c0 is also stated, the use of the background equivalent concentration,

Figure 2. Line sensitivity (left) and signal-to-background ratio (right) as functions of spectral bandwidth for lines with physical widths ranging from 1 to 16 pm. For comparison, the diagrams include a curve that represents the behavior of continuous background. The curves are based on calculations using a semiempirical model that involves a slight discontinuity. (Adapted with permission from Reference 18.)

Analytical

Chemistry,

Vol. 66, No. 8, April 15, 1994

461 A

Report The left-hand diagram illustrates the behavior of the line sensitivities and the continuous background as functions of spectral bandwidth. Accordingly, lines that have the same intensity at 1-pm bandwidth may differ by 1 order of magnitude in intensity at 20-pm bandwidth. Logically, the broader the lines the more closely they resemble a continuum and the less their increase in intensity "lags" behind that of the continuum. The corollary is that an SBR decreases with increasing bandwidth (the narrower the line, the sharper the decrease), as illustrated in the right-hand diagram. Calculations involving the function/opt permit the conversion of SBRs, and thus detection limits, between spectrometers or the reduction of the values of measured SBRs to the corresponding values of source SBRs. This approach can remove bias in assessments of the detection capabilities of different sources without the need to make observations on the same spectrometer. The practical application of the approach requires the availability of data on physical linewidths, knowledge of the bandwidth of the relevant spectrometers and, for convenience, the availability of a computer program to perform the calculations. For the ICP, the physical widths of - 350 prominent lines of 65 elements have been measured with a high-resolution spectrometer (19). A computer program (in IBM-PC format) (17) is associated with a database of measured physical linewidths (19) or, for spectral lines broadened by hyperfine structure, as the result of modifications of the original data made during the development of the program and in interaction with it. It enables the user to perform calculations and to view simulated line profiles, with SBR+1 as an ordinate, on the screen. By default the calculations are performed for linewidths valid in an ICP with a Doppler temperature of 6300 K, but the temperature used by the program may be varied between 100 and 10,000 K. New data may also be included in the database. Figure 3, which is based on this software, is equivalent to Figure 2 and primarily covers the behavior of three real spectral lines (curves with points). The behavior is peculiar because the Cu and Ce lines are doublets and the In line is a 462 A

"How large are the effects of bandwidth correction under practical conditions of spectrochemical analysis?" The data in Table 1, computed with the simulation program and the associated database (17), give a general idea of the magnitude. The computed increase in SBR for changes in bandwidth is shown from a higher to a lower value, for example, from 25 to 3 pm (symbolized as 25/3 in the table heading). The results are based on spectral lines with physical widths in a range between 1 and 20 pm; the high values are associated with hyperfine structure composites. This range is common for sources such as ICPs that have a Dopi " ' 1 1 1 1 1 ' pler temperature on the order of 6000 K. 0 5 10 15 20 25 30 Bandwidth (pm) It is clear from these data that a change in bandwidth affects spectral lines Figure 3. SBR as a function of of varying physical width differently. The spectral bandwidth for t w o maximum effect ranges from a factor of 8 doublets (Cu and Ce) and a triplet to a factor of 1.1; a factor of 2-3 is the (In). most common. Bandwidth corrections in The curves with points are for the actual structures; those without points represent the comparisons of detection limits do not behavior if the strongest component is treated have a dramatic effect, but because they as an isolated, simple line. The data are systematic, they may remove bias underlying the curves were obtained with a spectrum simulation program using measured, from the assessments. physically resolved spectra as the primary This type of data is useful in a typical data. The various curves have been research situation in which the primary normalized. (Adapted with permission from Reference 17.) interest may be in assessing the capabilities of sources separate from the spectrometers. In contrast, if the capabilities of a particular, complete (commercial) intriplet. The multiplet structure is well restrument are being assessed, it is the unsolved at a very low bandwidth, but the components merge into each other as the modified results that are important. bandwidth increases. The SBR behavior, Bandwidth determination. In principle, orginally that of a single narrow line, the bandwidth of a spectrometer may be changes into that of a broad line. If each estimated as the spectral slit (i.e., the line consisted of only the strongest comproduct of the slit width and the reciproponent, its SBR would behave as depicted cal linear dispersion [5,20]). However, as by the corresponding curves without the spectral slit decreases below 15 pm, points. aberrations increasingly enhance the Bandwidth correction of SBRs and de- practical bandwidth above the value of the spectral slit, which makes an experimentection limits. The crucial question is,

Table 1 . Factor increase in SBR associated with a given decrease in bandwidth Upper and lower bandwidth (pm) PHW

Line (pm) Ho 345600 Nb 309415 Mn 260569 Ag 328068 W 218936


(pm)

25/3

25/5

25/10

20/3

20/5

20/10

10/3

10/5

- 20.4 - 7.5 - 3.8 2.2 1.1

1.5 2.0 3.8 6.0 7.9

1.7 2.0 3.5 4.6 4.9

1.5 1.8 2.4 2.5 2.5

1.3 1.6 3.1 4.8 6.3

1.5 1.6 2.8 3.7 3.9

1.3 1.5 1.9 2.0 2.0

1.0 1.1 1.6 2.4 3.2

1.1 1.1 1.5 1.9 2.0

tal determination mandatory. This may be done conveniently with one or more ICP lines that have small physical widths (21). The RSDB function

Thefirstapproach to formulating the RSDB function expressed it in terms of the coefficients for source flicker noise, shot noise, and detector noise, and the background readout signal. For many years, the use of the equation in this form was justified because in all practical situa tions, detector noise was negligible. Re cently, when systems with non-negligible detector noise were included (7,8), the equation was refined as

An additional feature of this approach is that the magnitudes of the terms in the RSDB equation reveal the relative impor tance of the various noise sources. This allows detailed analysis of the system; comparisons with other systems; and pre dictions of the effects of changing proper ties of the system, categorized according to source (background radiance), spec trometer (throughput, bandwidth), and detector (sensitivity, dark current), as illustrated in Figure 1.

RSDB = 1+

(3)

The background signal (zB) is expressed as the readout signal per unit time, and the equation also contains the detector's dark current signal (zD), expressed in the same readout units (per unit time) as zB. The various versions of the RSDB function contain a set of coefficients whose values can be determined experi mentally and subsequently can be substi tuted as parameters characteristic of the system. In turn, this implies that values of RSDB can be determined with the equa tion by inserting the numerical values of easily and precisely measurable variables into the relevant RSDB equation. The advantage of this approach is that one obtains far more consistent RSDB values than would be found with the com mon procedure of direct, repeated mea surements of RSDB. The use of an RSDB function, based on straightforward physi cal principles, that incorporates experi mentally determined numerical values of coefficients represents the application of a type of smoothing technique. On the other hand, use of an RSDB equation with particular coefficient values requires that the system remain constant. The system should be checked regularly by a direct RSDB determination based on a small set of measurements. Comparison of the value obtained from the check with the value derived from the equation will im mediately show whether the system still behaves properly (i.e., whereby a toler ance of a factor of 2 may be acceptable).

0 100 200 300 400 500 Background signal (readout units/s)

0 100 200 300 400 500 Background signal (readout units/s) Figure 4. RSDB assessments of t w o ICP spectrometer systems. (a) System A and (b) System B. The points are the experimental results from which the coefficients in Equation 3 have been determined. Curves a and c are the corresponding fitted curves, respectively; other curves represent extrapolations. Curves a, b, and c represent three different integration times (τ): 5.36, 10, and 1 s, respectively; Curve d is for an extrapolation to dark current zero and τ = 5.36 s. If the systems could be made free of shot noise and thus become flicker-noise dominated, Curve f would apply with o B = 0.8% (system A) and a B = 1.5% (system B). Curve g is the corresponding extrapolation to a B = 0.4% and a B = 0.75%. Curve e shows what would happen to the actual systems if the flicker noise could be reduced to the latter values and if τ were 5.36 s for both systems. (Adapted with permission from Reference 8.)

Assessment of spectrometers. Figure 4 shows the use of RSDB in assessing sev eral ICP spectrometers (8). The examples presented here refer to a 1-m (Spectrome ter A) and a 0.4-m (Spectrometer B) monochromator with - 8- and 12-pm bandwidths, respectively. The spectrome ters were different, as were the ICPs and the nebulizers, which were also assessed; both systems were equipped with photomultipliers as detectors. The points in the diagrams are experi mental data obtained at 10 different (ana lytical) wavelengths ranging from 193.8 to 324.8 nm. A smoothing technique used with Spectrometer A provided an effective integration time of 5.36 s in contrast to Spectrometer B, in which the actual and effective integration time was 1 s. This difference in integration time is reflected in the curves fitted through the experi mental points: Curve a in Figure 4a and Curve c in Figure 4b. Thesefitsprovided for the numerical values of the coefficients ceB and β in Equation 3; the third coeffi cient, zD, was obtained by a direct mea surement. Once the coefficients are known, Equa tion 3 can be used to calculate RSDB for a variety of conditions, in particular other integration times, dark currents, and shotand flicker-noise coefficients. Thus, it al lows extrapolations to desirable or ideal ized conditions. The figures show several curves, most of which are based on ex trapolations. From these curves, one can conclude that Spectrometer A is shot-noise limited because Curve a lies well above Curve f, which represents the flicker noise limit (aB = 0.8%) for this system. The smooth ing technique, which leads to an effective integration time of 5.36 s, is essential to keep RSDB at a reasonable level. If it were not used (Curve c with τ = 1 s), the sys tem's performance would be poor. Dark current reduction or ICP flicker noise reduction (actually nebulizer stabil ity improvement) would affect RSDB only marginally. This can be deduced from the fact that the relevant curves (b, d, and e) are close to Curve a. For an appreciable improvement of RSDB at low wave lengths, both photon and dark current shot noise should be reduced. This can be achieved by increasing the throughput of the spectrometer and/or the sensitivity of


Report the PMT and decreasing the PMT dark current. For Spectrometer B, it is clear that the flicker noise limit (Curve f) is higher (a B = 1.5%), but in the absence of a smoothing technique, performance with the actual integration time of 1 s is shotnoise limited (Curve c). However, if smoothing were applied (τ = 5.36 s), the system would be close to being flickernoise dominated. Consequently, improv ing the ICP and nebulizer stability (a B = 0.75%) would greatly affect the overall per formance (Curve e), making it better than that of Spectrometer A. The focal length of Spectrometer Β is smaller than that of A, which fosters a higher throughput and lower shot-noise level. However, it also entails a poorer spectral bandwidth, which partly offsets the gain in RSDB as a result of increased SBR. The detailed analysis of the spectrome ters in terms of SBR, RSDB, and detection limit (8) shows that there is little statisti cal mystery and much straightforward physics in the behavior of SBRs, RSDBs, and detection limits, not only in research laboratories but also on commercial in struments. Even small variations among sets of detection limits obtained with dif ferent equipment can be explained in de tail using a rational approach. The use of the SBR-RSDB approach made it possible to reveal the separate roles of the dark currents of the PMTs (detector shot noise), the sensitivity of these PMTs in conjunction with the back ground radiant flux at the detector (pho ton shot noise), the effective integration time (detector and photon shot noise), the nebulizers and ICPs (source flicker noise), and the spectral bandwidths of the spectrometers in connection with the physical widths of the lines (SBR and pho ton shot noise). The consistent application of the SBRRSDB approach during the development and evaluation of a new type of ICP array spectrometer (10,11,22) not only demon strated the applicability of this approach to array detectors but also fostered inno vation. R S D of n e t l i n e s i g n a l : p r e c i s i o n

Very often it is not the detection limit but the precision of an analytical method, ex pressed in terms of the RSD or the confi 464 A

dence interval of the concentration, that is crucial. Precision depends primarily on the RSD of the measured net line signal (RSDN) if the statistical error in the cali bration is neglected. RSDN, in turn, is dictated by the fluctuations in the mea sured background signal and the mea sured gross line signal. The latter in cludes the fluctuations in the emitted net line signal (analyte flicker noise). These dependencies imply that precision and detection limit are functionally interre lated, at least to a certain extent (i.e., at the detection limit, RSDN is always 50% if, in Equation 1, k = 2 γ 2 and is - 50% if k = 3). Also, if the limit of determination (cD) is defined as the concentration asso ciated with a 10% RSD, then cn = 5eL. At higher concentrations the connec tion between detection limit and precision is even further disrupted. Figure 5 illus trates the dependence of RSDN on the ratio of the concentration present to c L for several values of parameter aA, which is the flicker noise coefficient associated with the emitted net line signal. The curves represent the function (3,12),

RSDN

104

(4)

which is valid for the situation in which a A = a B and SBR « 1 in the vicinity of the detection limit. The first condition, a A = a B , may hold in practice, but this is not

Figure 5. Plots of the relative standard of the net line signal (RSDN) as a function of the ratio of the concentration present to the detection limit. (Adapted with permission from References 3 and 23.)


necessarily so. The second condition, SBR « 1, implies that the system under consid eration is background noise limited. This assumption means that, in the vicinity of the detection limit, analyte signal noise does not perceptibly contribute to RSDB. This assumption avoids complications in the discussion and it also makes sense in practice because, as indicated above, it is doubtful whether a substantial contribution from analyte signal noise near the detection limit can be accepted as a basis for viable analytical methods (3). Equation 4 can be derived as a limiting case from a general equation written with SBR instead of c/cL. At the high end of the concentration range (i.e., for large SBR) and if the detector noise is assumed to be negligible (γ ~ 0), Equation 4 may be con verted into (12) RSDN

+ —

(5)

Equation 5 is less trivial than it might seem at first sight; it indicates how higher precision can be obtained in emission spectroscopy. We are accustomed to situ ations in which the shot-noise term ($/xA) in Equation 5 is negligible, and thus RSDN is fully dictated by analyte flicker noise (RSDN = a A ). In this case, the prac tical lower limit of RSDN in ICPs is ~ 0.5-1%. Although using PMTs as detec tors will provide some improvement by establishing ratios of analyte signals with respect to an internal standard signal (24), this approach is not ideal and it is complex instrumentally. Array detectors, in their present stage of development, offer far better opportuni ties because virtually simultaneous mea surements can be made at adjacent wave lengths in the spectrum. This opens up the possibility for exploiting correlations in such a way that the flicker-noise term in Equation 5 becomes negligible with re spect to the shot-noise term (12). The corollary is that at high concentrations RSDN will follow the shot-noise curve (i.e., the broken curve in Figure 5) instead of leveling off to the flicker-noise limit. Recently this ideal has been shown to ex ist as an experimental reality (11,22). This development, which exploits cor relations of intensities at closely spaced wavelengths through the use of multivari ate approaches, might eventually lead to

an improvement of the precision (for rela tively high concentrations) in ICP-AES from the present value of 1% to 0.1%, mak ing it competitive with that of X-ray fluo rescence (12). The precision at the detec tion limit will not improve fundamentally (Equation 5) and will remain at 50% if

* = 2\/2. However, this precision will then be reached at a concentration that is 10 times lower. In other words, if the curves in Figure 5 were plotted as a func tion of concentration instead of c/cL, they would shift to the left by 1 order of magni tude along the concentration axis. Line interference and true detection limit It is common knowledge that line interfer ence is the most severe problem of emis sion spectrometry. Equally common is an intuitive understanding of line interfer ence. However, the questions of what it actually is, why it is a such a severe prob lem, and what progress has been made in recent years to cope with it remain. Figure 6 elucidates the concept of line interference. The curve marked "Blank" represents the profile of an interfering line produced by the matrix of a sample. It contributes a signal x1 at the peak wave length λ3 of an analysis line, which con tributes a signal xA. Together the two lines produce the profile marked "Spiked," which is shown superimposed on a contin uous background of magnitude %. It is the curve "Spiked" that forms the only direct information in a sample spectrum from which the correct value of xA must be derived. Two problems are apparent: finding the correct position for measuring the sum xB + x1+ xA and finding the correct value of xl to be subtracted from the sum. Establishing the value of % does not present a real difficulty. Generally, xl should come from an external information source, either a blank spectrum of the matrix or equivalent information stored in a database. However, even if xl is known, the difficulty of locating λ3 remains. Perhaps surprisingly, modern spec trometers do not yet have sufficient me chanical and optical stability to obviate this problem, which was first recognized by Boumans and Vrakking (23,25,26). We developed an approach to quantify the magnitude of the error in terms of the

true detection limit. The introduction and elaboration of this concept subsequently induced others to further investigate the interference problem and to devise alter nate approaches (27,28). Various considerations have prompted the following definition of the true detec tion limit (23,25, 26) ν C

L,true

=

g

C

IEC

+

C

L, conv

W

tration that can be determined with a pre cision of 50% but in a sample where the matrix produces interference on the analy sis line. In Equation 6, cIEC is the analyte concentration equivalent to xx, thus χλ di vided by the sensitivity (SA) of the analy sis line; cUcoav is the conventional detec tion limit (23, 25,26)

Vnv = * ^ . 0 1 x R S D B x [ % c C

which, like the detection limit defined by Equation 2 for pure water, is the concen-

Analysis lines free from interference or ones that have minimal interference, which must be corrected for, should be selected.

Figure 6. Line profiles observed for a blank solution of an interfering species and the same solution spiked with analyte. The peak of the analysis line is located at wavelength λΑ. To determine the net line signal (xA), an accurate measurement of the gross signal (xB + x, + xA), the interfering line signal (χ,), and the continuous, flat background signal (xB), which may contain contributions from line wings, must be made. (Adapted with permission from Reference 26.)

WEC

+

c

IEc]

+ (*)

This equation is analogous to that for the detection limit for pure water written in terms of the background equivalent con centration cBEC ct = k χ 0.01 χ RSDB χ cBEC

(8)

instead of as c0/SBR as in Equation 2. The conventional detection limit contains the sum of the equivalent concentrations re lated to background from pure water (c BEC ), line wings or continua associated with the matrix (c WEC ), and the interfer ing line (cIEC). The term "conventional detection lim it" has been coined because convention ally one would be inclined to treat the background contributions from wings, continua, and the interfering line as sim ple background enhancements (29). In view of the problems pointed out above, this treatment is unrealistic and is the rea son that the additional term at the righthand side of Equation 6 was introduced. This term contains a parameter v, the value of which is likely to lie between 0 and 2. Generally ν = 2 and ν = 0 will be reached only with the aid of multivariate approaches, including the use of ad hoc collected information on analyte and inter fering species. Accuracy, line selection, and true detection limit Accuracy, line selection, and true detec tion limit are closely interrelated. Clearly, if the presence of an interfering line is not recognized, the result of the analysis will be inaccurate. Therefore analysis lines free from interference or ones that have minimal interference, which must be cor rected for, should be selected. If this se lection must be made a priori, then some knowledge of the sample composition and a database (line coincidence table) are indispensable. There has been ample dis-


Report cussion on the lack of adequate databases, and various solutions to this problem have been proposed (30). The measurement and use of highly resolved spectra have been worked out extensively for a portion of the very complex spectra of rare earth elements (REEs) (31). This work has culminated in the design and publication of a program for spectrum simulation, including the manipulation of composite spectra (32). Crucial is the storage of data in physically resolved form, which permits simulating spectra for any user-specified spectral bandwidth by convolution of the physical spectrum and the instrument function. This makes the database, in principle, independent of the spectrometer. However, the amount of work involved in data acquisition is too comprehensive to extend the database beyond that for a limited number of REE analysis lines. This severely restricts the use of this approach for practical purposes. The program is very powerful because it provides insight into the line interference problem and the scope of presentday chemometric approaches intended to overcome this problem. The program's features include the visualization of spectra in 80-pm-wide spectral windows centered around REE analysis lines for mixtures of REE samples having a composition specified by the user. For example, Figure 7a shows the spectrum around the La analysis line at 333.749 nm for a 1000 pg/mL Nd solution with 0.25 ug/ mL La, which is precisely 10 times the true limit of determination or 50 times the true detection limit under these conditions. This spectrum is for the extremely high-resolution case corresponding to 1-pm bandwidth (i.e., virtually physical resolution). The effect of increasing the bandwidth to a value more realistic in practice (10 pm) is illustrated in Figure 7b. At this resolution, the analyte concentration of 0.25 pg/mL is less than half the true limit of determination instead of 10 times its value. The true detection limit is also the ideal criterion for line selection in trace analysis (23); the criterion should take into account both the intrinsic detection capability of the line (i.e., the detection limit for pure water) and the effect of the interference from the sample matrix. This 466 A

is precisely what the true detection limit covers. The simulation program includes a feature for applying this approach within the restrictions set by the database. This is didactically useful but, because of database limitations, has restricted value in practice. On the other hand, the introduction of these concepts has recently stimulated additional work on spectral interferences involving REEs in a form that is more rational and more universally appli-

cable than the format used in classical tables (33, 34). Although studies have demonstrated the deficit of these classical tables as to coverage, accuracy, and appropriateness, they are still used because we lack better alternatives. Many more data points are needed. More important, studies have definitively demonstrated that line interference may worsen the true detection limits, compared with the ideal ones for

Figure 7. Simulated spectra for a 10OO pg/mL Nd solution with and without 0.25 pg/mL La as analyte. (a) Spectral bandwidth: 1 pm and (b) spectral bandwidth: 10 pm. The difference between the spectra of the blank and spiked solution is indicated by the red line in the center of the spectral window, which is located at the 333.749-nm line for La. The ordinate scale of the spectra in part has been expanded (x4) and peaks have been truncated. (Adapted with permission from Reference 32.)


pure water, by orders of magnitude. This circumstance severely hampers trace analysis in samples with matrices that pro duce line-rich spectra. It is not surprising that several research groups are pursuing this area. Line interference: remedies Figures 7a and 7b not only illustrate a fea ture of the spectrum simulation program, but also demonstrate that an increase in spectral resolution reduces the disastrous effect of line interference on the true de tection limit. Although in this case more than 1 order of magnitude is gained, im provements are limited to the common, practical range of bandwidths between 5 and 15 pm. To achieve dramatic effects, other approaches are required, in particu lar multicomponent or multivariate tech niques. One of these, known as Kalman filter ing, was successfully explored and elabo rated by van Veen and his co-workers, among others. The most recent result is the forthcoming publication of a program called "KAAS" (Dutch for cheese) (28). The essence of their approach is the judi cious collection of additional spectral in formation about analytes and interfering species so that the magnitude of interfer ing line signals (*,) can be accurately pre dicted. In terms of Equation 6, this means that the value of parameter ν is reduced to zero. This additional information is ob tained from scans instead of simple peak height measurements. If the value of ν is reduced to zero, the true detection limit becomes equal to the conventional detec tion limit. The effect of line interference is thus reduced to that produced by a simple background enhancement equal to xv A further consequence is that the con ventional detection limit may now be used as the criterion for line selection, which avoids some complications and is more straightforward (35). This approach also lowers the requirements on the dynamic range of databases for the initial, tentative line selection preceding the definitive measurements involving Kalman filtering (36). Jinfu Yang and co-workers (37) have made an in-depth analysis of the fac tors affecting the parameter ν in Equation 6 and also established the conditions un der which Kalman filtering tends to bring the sketched profits and when it does not.

(24) Meyers, S. A; Tracy, D. H. Spectrochim. Acta 1983,38B, 1237. (25) Boumans, P.WJ.M.; Vrakking, J.J.A.M. Spectrochim. Acta 1985, 40B, 1085,1107. (26) Boumans, P.W.J.M.; Vrakking, J.J AM. Spectrochim. Acta 1987, 42B, 819. (27) van Veen, E. H.; Bosch, S.; de Loos-Vollebregt, M.T.C. Spectrochim. Acta 1994, 49B, 1691. (28) van Veen, Ε. Η.; Bosch, S.; de Loos-Vollebregt, M.T.C. Spectrochimica Acta Elec tronica included in Spectrochim. Acta, in press. (29) Boumans, P.WJ.M.; McKenna, R. J.; Bosveld, M. Spectrochim. Acta 1981,36B, References 1031. (1) Inductively Coupled Plasma Emission Spec (30) Needs for Fundamental Reference Data troscopy; Boumans, P.W.J.M., Ed.; John for Analytical Atomic Spectroscopy; Bou Wiley and Sons: New York, 1987. mans, P.W.J.M.; Scheeline, A, Eds.; Spe (2) Inductively Coupled Plasmas in Analytical cial Issue, Spectrochim. Acta 1988,43B Atomic Spectrometry; Montaser, Α.; (1), 1-127. Golightly, D. W., Eds.; VCH Publishers: (31) Boumans, P.WJ.M.; ZhiZhuang, H.; Vrak New York, 1987,1992. king, J.J.A.M.; Tielrooy, J. A; Maessen, (3) Boumans, P.W.J.M. Spectrochim. Acta FJ.MJ. Spectrochim. Acta 1989,44B, 31. 1991,465,917. (32) Boumans, P.WJ.M.; van Ham-Heijms, (4) Kaiser, H. Spectrochim. Acta 1947,3, 40. AH.M. Spectrochimica Acta Electronica (5) Ingle, J. D., Jr.; Crouch, S. R. Spectrochemincluded in Spectrochim. Acta 1991, 46B, ical Analysis; Prentice-Hall International: E1863. Englewood Cliffs, NJ, 1988. (33) Daskalova, N.; Velichkov, S.; Kras(6) Boumans, P.W.J.M. Spectrochim. Acta nobaeva, N.; Slavona, P. Spectrochimica 1990, 45B, 799. Acta Electronica included in Spectrochim. (7) Boumans, P.WJ.M. Spectrochim. Acta Acta 1992,47B, E1595. 1990,45B, 431. (34) Velichkov, S.; Daskalova, N.; Slavona, P. (8) Boumans, P.W.J.M.; Ivaldi, J. C; Slavin, Spectrochimica Acta Electronica included W. Spectrochim. Acta 1991,46B, 641. in Spectrochim. Acta 1993,48B, E1743. (9) Mermet, J. M.; Carré, M.; Fernandez, Α.; (35) van Veen, E. H.; Oukes, F. J.; de LoosMurillo, M. Spectrochim. Acta 1991, Vollebregt, M.T.C. Spectrochim. Acta 46B, 941. 1990,45B, 1109. (10) Barnard, T. W.; Crockett, M. I.; Ivaldi, (36) Boumans, P.WJ.M. Spectrochim. Acta J. C; Lundberg, P. L.Anal. Chem. 1993, 1990,45B, 1121. 65,1225. (37) Yang, J.; Piao, Z.; Zeng, X. Spectrochim. (11) Barnard, T. W.; Crockett, M. I.; Ivaldi, Acta 1993,48B, 543. J. C; Lundberg, P. L.; Yates, D. A; Le(38) Zhang, P.; Littlejohn, D.; Neal, P. Spectro vine, P. A; Sauer, D. J. Anal. Chem. chim. Acta 1993, 48B, 1517. 1993, 65,1231. (12) Boumans, P.WJ.M./. Anal. At. Spectrom. 1993,8, 767. (13) Borer, M. W.; Sesi, N. N.; Starn, T. K.; Hieftje, G. M. Spectrochimica Acta Electronica included in Spectrochimica Acta 1992,47B, E1135. (14) Boumans, P.W.J.M. Spectrochim. Acta 1978,33B, 625. (15) Boumans, P.W.J.M. Spectrochim. Acta 1991,46B, 936. (16) Boumans, P.WJ.M. Spectrochim. Acta 1991,46B, 926. (17) Boumans, P.WJ.M.; van Ham-Heijms, A.H.M. Spectrochimica Acta Electronica P. W.J.M. Boumans has been active in the included in Spectrochim. Acta 1991,46B, field of analytical atomic emission spectros E1545. copy for 40 years. He obtained his Ph.D. in (18) Boumans, P.W.J.M.; Vrakking, J.J.A.M.; Heijms, A.H.M. Spectrochim. Acta 1988, analytical chemistry from the University of Amsterdam (1961), where he worked until 43B, 1377. he joined Philips Research Laboratories (19) Boumans, P.WJ.M.; Vrakking, J.J.A.M. Spectrochim. Acta 1986,41B, 1235. (PRL) in Eindhoven, The Netherlands, in (20) Olesik, J. W. In Inductively Coupled 1968. He retired from PRL in 1991 and in Plasma Emission Spectroscopy; Boumans, P.WJ.M., Ed.; John Wiley and Sons: New 1994 from his position as Editor-in-Chief of Spectrochimica Acta Β after a 22-year af York, 1987; p. 466. (21) Mermet, J. M.J. Anal. At. Spectrom. filiation with that journal. Although he re 1987,2,681. mains a visiting professor at Strathclyde (22) Ivaldi, J. C; Barnard, T. W. Spectrochim. University (Scotland), he has decided to Acta 1993,48B, 1265. concentrate more on the study of art, gen (23) Boumans, P.W.J.M. FreseniusZ. Anal. eral history, and art history. Chem. 1979,299,337.

Although approaches such as Kalman filtering are powerful, they still suffer from the disadvantage that knowledge about possible interferences and their concen trations is not available a priori. A new chemometric approach capable of allow ing researchers to predict the presence of an interfering line when the sample com position is not known has been recently described by Zhang and co-workers. (38).


Detection Limits - Analytical Chemistry (ACS Publications)

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