Fourier transform spectrometry in the ultraviolet

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Anne P. Thorne Blackett Laboratory Imperial College London SW7 282, U.K.

Sixteen years ago Horlick and Yuen (I) contributed an article to these pages on “Atomic Spectrochemical Measure- ments with a Fourier Transform Spec- trometer.” Some years later, again in these pages, Faires (2) wrote on “Fouri- er Transforms for Analytical Atomic Spectroscopy.” Progress in Fourier transform spectrometry (FTS) has ac- celerated over the last five years, and the time seems right for a new assess- ment of its role in atomic spectrochem- istry.

FT-IR has, of course, been a well- established technique for much longer than 16 years, but it is FT-UV that is relevant to analytical atomic spectroscopy-both in the emission and the absorption modes-and especially in the wavelength region between 250 and 190 nm where the sensitive lines of most elements are found. Two questions therefore arise. First, what are the difficulties and constraints of extending FTS into the UV, and to what extent have they been overcome? Second, if the technical problems can be or have been solved, does FTS offer significant advantages over dispersive grating

0003-2700/9 1 /0363-057A/$02.50/0 @ 1991 American Chemical Society

spectrometry for analytical atomic spectroscopy? Following a summary of the essential features of the technique, I will try to answer these two questions (in reverse order) before going on to discuss my view of the proper role of FTS in atomic spectrometry a t present. Finally, I offer the customary hostage to fortune by speculating on the future.

FTS: A quick guide

This section should be regarded as a sketch map to help those unfamiliar with FTS to reach a vantage point from which they can survey both the useful- ness of the technique and the difficulties of the road ahead to shorter wave-

lengths. A fuller treatment is given in standard texts (3-5), and a more spe- cific background for the type of high- resolution atomic spectroscopy discussed here can be found in References 6 and 7.

We start with the Michelson interferometer, in which a collimated light beam is divided at a beam splitter into two coherent beams of equal amplitude that are incident normally on two plane mirrors. The reflected beams recom- bine coherently at the beam splitter to give circular interference fringes at in- finity, focused by a lens at the plane of the detector. For monochromatic light of wavelength A0 and intensity B(Ao), the intensity at the center of the fringe

Figure 1. (a) Symmetric interferogram and (b) its cosine transform, consisting of the true spectrum (shaded black in this figure and in Figures 3 and 4) and its mirror image.

ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991 5 7 A

INS'TRUMEN 7A7lON

pattern as a function of the optical path difference x between the two beams is given by the familiar two- beam interference relation

I , = B(h)[ l + cos (27rx/X,)] =

B(ao)(l + cos 27raox) (1)

where the wavenumber a is defined by a = 1/X = v/c, normally measured in cm-l (Y is the frequency of light in s-l and c is the speed of light in cm s-l). If x is changed by scanning one of the mirrors, the recorded intensity (the interferogram) is a cosine of spatial frequency 60. Its temporal frequency is given by fo = uao where u is the rate of change of optical path, or twice the mirror speed. A scan speed of 1 mm/s puts f into the audiofrequency range, and the interferometer can be regarded as a de- vice for converting optical frequencies to audiofrequencies: f = UQ = ( U / C ) Y .

If the source contains more than one frequency, the detector sees a super- position of such cosines.

I o ( x ) = [ B(a)(l + cos 27rax)do (2)

Subtracting the constant intensity JtB(a)da corresponding to the mean value of the interferogram ( I ( x ) ) leaves Equation 3.

lom B(a) cos (27rax)da (3)

The right-hand side of Equation 3 contains all the spectral information in the source and is the cosine Fourier transform of the source distribution B(a) . The latter can therefore be recovered by the inverse Fourier transform

B(a) = [ I ( x ) cos (27rax)dx (4)

Actually the Fourier transform not only reproduces B(a) but also necessarily adds a mirror image B(-a) at negative frequencies (Figure 1). This can easily be verified by direct integration for the simple case of the monochromatic source B(ao), and it is under- standable because the relation cos 27rux = cos 27r(-a)x ensures that B(a) and B(-a) produce identical interfero- grams. Negative frequencies are un- real, but the mirror image enters into the consideration of aliasing below.

There are three important modifica- tions to these simple relations. First, the interferogram is never totally symmetric about x = 0, and to recover the full spectral information it is necessary to take the complex rather than the cosine Fourier transform. Second, the

Flgure 2. (a) Top-hat truncation function of the interferogram extending from 0 to f~ and (b) its transform, the instrument function sinc 2aL sin PaaLl(2aaL).

interferogram is recorded to a finite path difference L rather than to infin- ity. Third, the interferogram is actually recorded by sampling it a t discrete intervals Ax. Equation 4 thus becomes

shape recorded from an ideal monochromatic input is sinc 2(a - a& (Fig- ure 2). The first zero of this function is at (a - a,) = f 1/2L; this value defines the resolution of the instrument:

N

B(a) = 1 I(pAx)e-2"i"pA" (5) p = - N

where NAx = L and p is the index number of the sample.

The consequence of the first modification is that the recovered spectrum is complex, and a phase correction has to be applied to rotate it back into the real plane. The effect of the finite path difference, which effectively multiplies the infinite interferogram by a top-hat (boxcar) function of width 2L, is to con- volute the spectrum with the Fourier transform of the top-hat function.

2L s i n c 2 d (6)

This sinc function is the instrument function of the spectrometer: The line-

(7)

The third modification, the discrete sampling, has the effect of replicating the computed spectrum a t wavenumber intervals of l /Ax. To see why, consider Equation 5. If a is replaced by a f l/Ax, the argument of the exponen- tial is increased by 27rip, an integral number of 27r, which leaves it un- changed. The replication also applies to the negative imageB(-a), and it can be seen from Figure 3a that the negative part of the first replication will overlap the positive part of the original unless l /Ax > 2um, where a, is the highest frequency in the source. The condition for avoiding overlap is Ax I 1/20,, or Ax I XJ2, which is the Ny- quist sampling theorem. The replication is known as aliasing. Figure 3a can be interpreted as the unfolding of a stack of Z-fold paper (Figure 3b), each sheet of which has width Aa where

Figure 3. (a) Spectral band of maximum wavenumber a,,,, together with its negative image, replicated at wavenumber intervals I /Ax and (b) representation of this replication by folding the spectrum at intervals of the free spectral range Aa = 112A.x.

58 A ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991

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INSTRUMEN TATION

AU = 1/2Ax (cm-l)

In Equation 8, Au is known as the alias width and is equivalent to the free spectral range. Any real information on, say, page 3 (third alias) of the stack will be indistinguishable from the replica on that page of the spectrum on page 1 (first alias). Suppose, however, that there is actually no real signal at low frequencies, perhaps because the detector is insensitive to long wavelengths. As illustrated in Figure 4, it is then permissible to undersample the interferogram, knowing that the information on page 3 really belongs there and cannot have come from page 1. One must, of course, be sure that pages 4, 5 . . . are also blank, and it is also necessary to use a bandpass filter to avoid folding in the noise from all these other pages.

The quantity N introduced in Equa- tion 5 is a number of some significance. As defined there ( N = L/Ax), it is evidently the number of independent points in the interferogram (because in principle 0 to -L contains the same information as 0 to +L). Using Equa- tions 7 and 8 gives N = Au/6u, so N is also the number of resolution elements (independent spectral points) in the free spectral range. If the maximum wavenumber um comes at the end of the nth alias, nN is numerically equal to the resolving power R

N = L/Ax = u/6u (9)

and

nN = nAu/6u = u,/6u = R (10) Grating versus FT spectrometry Equation 10 brings out a similarity to grating spectrometry: nN is the theo- retical resolving power of a grating of N rulings used in the nth order. This re-

sult is not too surprising, for N is simply the number of samples taken by the grating of the incident wavefront. Why build an interferometer to go through the motions of ruling a grating every time one wants a spectrum, instead of buying a grating ruled by someone else in the first place? Of course it is conve- nient to be able to make a free choice of N, but there must be better reasons.

The reasons normally applicable in the IR are the multiplex (Fellgett’s) and throughput (Jacquinot’s) advantages, both of which significantly improve the signal-to-noise ratio (S/N). The multiplex advantage is a consequence of IR detector noise limitations and does not apply in the UV or visible regions (nor, usually, in the near-IR) where noise is not detector limited. I t can sometimes become a disadvantage, as we shall see. The throughput advantage is the consequence of division of amplitude (by the beam splitter) rather than division of wavefront (by the grating). The interferometer can use a circular entrance aperture with an area some 2 orders of magnitude greater than the slit area of a grating spectrometer of the same resolution. When photon shot noise is the dominant source of noise, so that noise is equal to the square root of the signal, this larger signal can lead to an improvement in S/N of -1 order of magnitude.

Less well known is the wavenumber (Connes’) advantage. The wave- numbers in the transform are derived directly from the sampling intervals, which in turn are determined from the interference fringes of a He-Ne laser following the same path as the signal beam. This results in an accurately lin- ear wavenumber scale with a reproducibility that depends only on the stabil- ity of the laser. The alignment of the laser can introduce a scaling factor of the order of 1/R, so that reference stan-

Figure 4. A band-limited spectrum at high frequency. (a) The interferogram is undersampled so that the band falls in the third alias (Ax = 3/20,,,). (b) The folded spectrum shows that there is no ambiguity provided that no real spectral information exists in the regions u < 2Aa and a > 3Aa.

dards are still required for absolute wavelengths more accurate than, say, l: lO5. In principle, however, only one such reference is required to determine the scaling factor, in contrast to the set of standards spaced out over the wavelength range that is required to cali- brate a grating spectrometer.

The high resolution attainable has already been mentioned. Simply by extending the scan length, the width of the instrumental function can be reduced to the point where it has a negligible effect on the observed line profile. In most of the sources used in atomic spectroscopy the true linewidths are determined by Doppler broadening, and in practice u/6uo (or X/GXo) is usually in the range lo5 (light element at -6000 K) to lo6 (heavy element at room temperature). Allowing two to three resolution points per Doppler width, this calls for a resolving power R from 200000 to 2 million. The lower end of this range would require a large grating spectrometer or an echelle with a predisperser, whereas the upper end is simply unattainable with any form of grating.

It can easily be shown (8) that when the instrumental width is reduced to below half the Doppler width, the re- sultant convolved profile is almost indistinguishable from a pure Gaussian, and the undesirable ringing shown in Figure 2 is damped down to less than 0,001 of the peak intensity. As a matter of fact it is not necessary to live with the sinc function even if the line is not fully resolved: FTS offers the ability to change the instrument profile by ma- nipulating (mathematically) the way in which the interferogram is truncated at the ends of the scan, and it is possible to suppress the ringing at the expense of an increase in linewidth, a process known as apodising.

The last important feature of FTS is that it necessarily gives a complete spectral record over the entire spectral bandpass seen by the detector, rather like a vastly superior photographic plate. Obviously this can be a mixed blessing. If one is interested only in half a dozen spectral lines, nearly all the information is redundant; but in a number of applications-and I will give some examples below-this global record is invaluable.

Problems and solutions for the UV The loss of the multiplex advantage and the reduced benefit of the throughput advantage were for very many years taken as adequate reasons for not venturing to shorter wavelengths. A stronger deterrent was the tightening of the optical and mechanical toler-

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INSTRUMEN 7ArION

Figure 5. Optical arrangement of the Imperial College interferometer. A is the entrance aperture; B is the beam splitter; C, and C2 are the catseye retroreflectors: D, and D2 are the detectors: MI is the collimating mirror: M2 and M3 are the focusing mirrors: M4, M5. and M6 are folding mirrors: L is the controlling laser; and LD is the laser detector.

ances required. The normal requirement for two-beam interferometry is a maximum discrepancy of X/4 on the re- combining wavefronts. This puts an upper limit of kX/8 on each of the optical surfaces involved, or f 2 5 nm at 200 nm. The requirement that the scanning mirror stay aligned to this tolerance during the scan translates to an angular tolerance (for a 20-mm beam) of -0.5 arc second.

Most instruments built for the visible and the near-UV have tackled the angular problem by replacing the plane mirrors by retroreflectors, in the form of catseyes. The incoming and outgoing beams are then always parallel, but tilting the catseye introduces a shear into the outgoing beam. The al- lowable shear tolerance of about 10 pm at 200 nm sets a limit of some four arc seconds on the tilt. This same shear tolerance applies to the guidance system, which constrains the motion of the catseye along the optic axis of the interferometer. The one advantage of going to shorter wavelengths is that the scan distance becomes shorter: A resolving power of 2 million at 200 nm requires a maximum optical path difference of 20 cm, or a physical displace- ment of A10 cm from zero path difference.

Finally in this list come the require- ments of the sampling system. To work unaliased to below 200 nm requires a sampling interval of not more than 90 nm, or one-seventh of a He-Ne laser fringe (Equation 8). In practice it is frequently possible and desirable to work in the second or a higher alias (using, e.g., a solar-blind detector insensitive above 300 nm), but it is still necessary to subdivide the laser fringes rather than to use whole fringes or mul- tiples of them as is done in the IR. Ran- dom errors in the sampling steps ap-

pear as noise in the transformed spectrum, and in practice sampling steps must be accurate to about one part in 1000 (about 0.1 nm) if one wants to keep the sampling noise a t a negligible level.

In addition to these formidable optical and mechanical constraints, the handling of the data is not a trivial problem. The number of data points is, as we have seen, numerically equal to the resolving power, and there is little incentive for attempting UV-FTS if one cannot exploit the full useful resolving power of a million or so. (Such high resolving powers are not normally required, or indeed attainable, in the IR.) However, computer technology has advanced so much in recent years that data acquisition, manipulation, and storage can no longer be regarded as a limitation on UV-FTS; the time taken for a million-point FFT (fast Fourier transform), for example, has dropped over the last decade from a few hours on a minicomputer to a few minutes on a PC, and a spectrum that once filled all of a demountable 16-in. hard disk now resides happily in a small fraction of the PC disk.

The feasibility of high-resolution FTS in the visible and near-UV was first demonstrated on the large, high- performance instruments at the Na- tional Solar Observatory (NSO) in Kitt Peak, AZ, and at Orsay, France; Refer- ences 9 and 10 describe these instruments, and Reference 10 gives details about the earlier Orsay instruments. At Imperial College we set out to design and build a compact high-resolution FTS specifically for the UV down to 180 nm (11); this has been operating, with more or less continuous improvements, since 1986. Figure 5 shows the optical arrangement: I t is an f/25 spectrometer o ~ l y 1.5 m long with maxi-

mum resolution 0.025 cm-l (resolving power 2 million at 200 nm).

Over about the same period a very large FT spectrometer, modeled on the NSO instrument but designed for high resolution from 20 pm to 200 nm, was built by Los Alamos National Labora- tory (12). This instrument has in fact been little, if a t all, used at its short wavelength end. In the commercial sphere, Bomem and Bruker have ex- tended the ranges of their IR-vis instruments to shorter wavelengths, and Chelsea Instruments makes a commercial version of the Imperial College FT spectrometer.

UV-FTS is therefore feasible and practicable, but not yet readily avail- able. Given a spectrometer that can re- solve true lineshapes and measure enormous numbers of wavelengths with unprecedented accuracy over a wide spectral range, to what practical problems should it be applied?

UV-FTS for analytical chemistry For the physicist there are several obvious answers to this question: hyperfine structure and isotope shifts in atomic spectra, rotational structure of elec- tronic bands in molecular spectra, gen- eration of accurate secondary wavelength standards, high-quality wavelength measurements for term analysis, relative intensity measurements for branching ratios and hence transition probabilities, lineshape investigations for study of collisional processes, and so on.

For the analytical chemist the answers are less obvious. For atomic emission spectroscopy the excellent resolution and wavelength reproducibility are clearly advantageous, particularly for the line-rich spectra of the rare- earth and actinide elements, where there are often severe spectral interfer- ences. The wide spectral coverage al- lows a choice of analytical lines and a choice that can be made after the data have been recorded.

There is, however, a well-known un- favorable feature of FTS that has been discussed in a number of papers (1,2,8, 13, 14). It is commonly known as the “multiplex disadvantage,” but i t should really be regarded as a “Fourier disadvantage,” which can be potential- ly enhanced by the true multiplex disadvantage. The origin of the problem is that when random noise is added to the interferogram on the left-hand side of Equation 3, the transform of the noise is added to the spectrum on the right- hand side of the equation. The Fourier transform of random noise is “white noise,” which has the same mean intensity at all frequencies. The noise from every line in the spectral band contrib-


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Utes to the noise at every point in the spectrum.

Consider first a case where photon noise is dominant. Ignoring for the mo- ment the throughput advantage, it can be shown (5, 6) that the ratio of the mean signal to the noise in a Fourier transform spectrum is the same as that in a grating spectrum of the same spectral bandwidth, resolution, and scan time. In other words, the multiplex advantage is broadly neutral. Because the Fourier transform noise level is almost constant, FTS gains in S/N at points in the spectrum where the signal is above the mean and loses where it is below.

For an emission spectrum this situa- tion is much better than it looks at first, because the mean signal in the Fourier transform is the average over all N spectral elements, not just over the lines. By way of illustration, if the spectrum is dominated by m strong lines of approximately equal intensity I , occu- pying one resolution element each, the mean signal is mI/N. The fraction m/N can be regarded as the “filling factor’’ for this hypothetical spectrum. For a properly resolved real emission spectrum, even a line-rich one, this filling factor is usually only a fraction of 1%, so the two instruments give approximately equal S/N for a weak line of intensity I. If we now include the throughput advantage of FTS, this crossover point drops to about I. Lines weaker than this are more likely to be detected by a grating spectrometer. Evidently FTS is not the best way of looking for ultratrace elements in the presence of strong lines of matrix elements. Furthermore, detection limits can no longer be quantified because they vary with the concentration of the matrix element(s) and the spectral bandwidth used (14) .

Matters are made worse if the dominant noise is multiplicative, as for example fluctuations in emission intensity from an inductively coupled plasma (ICP). In this case there is a true multiplex disadvantage of a factor 1/N1/2 working against FTS, and the throughput advantage is lost. Ratio recording might be expected to help here, and a subsidiary advantage of the retroreflectors used in most UV-FT inter- ferometers is the accessibility of the second output beam (see Figure 5) that can be used for this purpose. Although ratio recording reduces the effect of source fluctuations, it certainly does not remove them, probably because they are true variations in plasma temperature and density that do not affect all spectral lines in the same way. An important point is that this flicker/ fluctuation noise is not “white.” The characteristics of the noise seen in the

transformed spectrum depend on both the source and the spectrometer, so it is hardly surprising that not all authors agree on them.

Fortunately there is a considerable choice of sources that can be run in a photon-noise-limited manner. Experi- ence gained with ICP-FTS indicates that the main source of noise is the nebulizer rather than the plasma itself. If the analyte is introduced in the form of a vapor, the ICP behaves as a photon-noise-limited source. Hollow cathode lamps have been used for years as thoroughly well-behaved sources for FTS, and recent work has shown that Grimm discharge lamps are similarly well behaved (15).

There are three important roles for FTS in atomic spectroscopy that exploit its strengths rather than its weak- nesses. The first has already been mentioned: analysis of complex spectra in which the sheer number of lines leads to problems of spectral overlap and identification.

The second is the provision of a high- quality database along the lines advo- cated by Boumans, Scheeline, and oth- ers in a recent workshop held to define the need for fundamental reference data (16). The demand for accurate wavelengths, intensities, and true linewidths and shapes of all possible interfering lines in a window around each important analytical line is one that FTS is extremely well qualified to meet. The needs of analytical chemists here overlap to a considerable extent those of astrophysicists, who are also

struggling with an inadequate database, particularly for the astrophysical- ly abundant transition elements. In solar spectroscopy, any line of inter- est is likely to be blended with a line of one of these elements, especially iron, or with one of the large number of un- identified lines. The completeness and quality of the data that can be provided by FTS are illustrated by Figure 6, which is a section 0.8 nm wide of a broadband spectrum (453-217 nm) from a steel hollow cathode lamp, showing lines of Fe, Cr, and Ni. The resolution (1 pm in this region) gives true source linewidths. The separa- tion of the close Fe(1)-Cr(1) pair is only 6 pm. The three weak Cr(I1) lines do not appear in the MIT tables (1 7).

The third role is the measurement of lineshapes and intensities for diagnostic work on plasmas, particularly for the study of temperatures, densities, and excitation processes in ICPs and glow discharges. An example of this work is the determination of excitation temperatures (18) and gas kinetic (Doppler) temperatures (19) for Fe- group elements in an ICP. A different manifestation of this role is illustrated by Figure 7 (20), which shows the effect of microwave boosting (21) on the 324-nm resonance line of copper emit- ted by a Grimm lamp running a t 20 mA. The line profiles are shown in Fig- ure 7a with the normal dc glow discharge and in Figure 7b with the microwave boost. The basic doublet structure comes from the hyperfine splitting

Ni(l)

Ni(l)

I I I

Figure 6. A 0.8-nm-wide section of a broadband (453-217 nm) spectrum from a steel hollow cathode. The resolution is 1 pm, which is about half the true linewidth. The Fe(l) and Cr(l) lines at 301 nm, 6 pm apart, are clearly separated. The three weak Cr(ll) lines (marked with asterisks) are not listed in the MIT tables (77 ) .

ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991 63 A

INSTRUMEN 7ArION

Flgure 7. The 324-nm resonance line of Cu(l) excited in a Grimm lamp at 20-mA current with a resolution of 0.06 cm-' (0.6 pm). (a) Spectrum with a Cu cathode and normal dc discharge, (b) spectrum with a Cu cathode and microwave boost, and (c) spectrum obtained with an AI cathcde containing 1 % Cu. The two hyperfine components in (b) and (c) appear as four components in (a) because of self-reversal. (Adapted with permission from Reference 20.)

of the ground state, but in Figure 7a each of the hyperfine components is further split by self-reversal. The intensity ratio of the two components should be 53, and the equal intensities in Figure 7b indicate strong self-absorption. This is confirmed by the profiles recorded in Figure 7c with copper impurity in an aluminum cathode. In- spection of the complete spectrum, of which a small section is reproduced in Figure 8, shows that the microwave boost has a dramatic effect on the relative intensities of different lines and on the S/N of the resonance lines. The wavelength accuracy and completeness of the spectral record make it relatively easy to compare large numbers of lines in spectra taken under different running conditions.

UV-FTS: Future prospects Physicists and astrophysicists are always greedy for shorter wavelengths, and efforts are being made to extend the spectral range of FTS beyond the spectrosil cutoff at about 178 nm. Fig- ure 9 shows a section of the vacuum- UV spectrum of a platinum hollow

cathode lamp a t a resolution of 0.2 pm, in which two of the lines have been expanded to show the resolved hyperfine structure.

If ICP-FTS is going to be useful in analytical chemistry, the outstanding need is to reduce source noise, particularly with respect to sample introduction. Because ICPMS makes similar demands, an approach to photon noise limitations seems a not unreasonable hope. For glow discharge lamps (GDLs)-in which samples are introduced by sputtering directly from the solid state-this happy state of affairs already exists, and GDL-FTS is a technique waiting to be exploited.

Even for the photon-noise-limited case, the matrix noise difficulty re- mains. It can certainly be reduced by isolating parts of the input spectrum, either with an auxiliary coarse mono- chromator or with suitable filters (22, 23), but this sacrifices the wide spectral coverage that is in other respects an advantage. A more attractive approach is to exploit this same wide coverage to correlate signals from many different lines of the same element, either in the spectrum (23) or in the interferogram (24). The spectral correlation can be done very precisely, thanks to the excellent wavelength reproducibility; for m lines of similar intensity the signals

37 Finn nn nnn

AI cathode 15 mA, 1200 V

unboosted

30 000 Wave

Cu 324.7 nm

c

AI cathode 15 mA, 870 V

microwave boost

Figure 8. Part of the Grimm lamp spectrum from an AI cathode with 1 % Cu, showing the changes resulting from the microwave boost. (a) The overall change in appearance between 400 and 250 nm. The arrows indicate the Cu resonance lines. (b) Expanded plots of the 324.7-nm Cu resonance line. The SIN is increased from 50 to 640 by the microwave boost, but running conditions have not been optimized for the unboosted lamp.


f

-,, I . I, I r' ",,

4800 55000 55200 55400 55600 55800 56000 56200 56400 1

Wavenumber (cm-l)

1

60C

0

Wavenumber (cm-1)

Figure 9. Approach to the current short wavelength limit of FTS, illustrated by part of the spectrum of a Pt hollow cathode lamp at 20 mA with a resolution of 0.06 cm-' (0.2 pm). (a) A section 6 nm wide extending down to 176 nm, (b) expanded plot of the R(l) line at 182 nm, and (c) expanded plot of the R(ll) line at 177 nm. The lines in (b) and (c) are marked with asterisks in (a).

add coherently to give a factor m while the noise adds incoherently to give m1/2, an improvement in S/N of m1/2. Faires gives an actual example for Fe in Reference 23. This type of data pro- cessing makes maximum use of the large quantity of information that has necessarily been acquired, but it obviously requires a different approach to calibration and to limits of detection.

Finally, what about atomic absorption spectroscopy? The high resolution of FTS makes continuum-source multielement AAS an attractive possibility, but there are two hurdles to sur- mount. The first is the requirement for an absorption cell running continuous- ly and quietly for the length of the scan (-1 min). The second is the character- istic noise distribution. For a quasi- continuous light source the spectral filling factor discussed above is close to unity: The noise from the entire unin- teresting background is distributed throughout the spectrum, including the bottom of the absorption troughs. For this reason much FTS absorption work is done with a restricted spectral band pass, which reduces the scope of the method.

A more exciting possibility is atomic magneto-optic rotation (AMORS) (25). If the absorption cell is placed between crossed polarizers in a magnetic field, light from the background source is transmitted only near a resonance

line where the plane of polarization is rotated by the Faraday effect. An absorption spectrum thus appears as an emission spectrum, with a very small filling factor and high S/N. A number of problems associated with background intensity and quadratic concentration dependence must be ad- dressed, but the method does appear to be a very promising one.

It is not easy to see a role for FTS in routine analytical applications, but for many difficult nonroutine problems, database acquisition, and diagnostic purposes it is already a viable and valu- able technique just waiting to be fully exploited. Improvements in methods of sample introduction would extend the range of problems for which it could provide important advantages over grating spectrometers. A significant change in data handling and calibration techniques would also be required.

References

(1) Horlick, G.; Yuen, W. K. Anal. Chem. 1975,47,775 A.

(2) Faires, L. M. Anal. Chem. 1986, 58, 1023 A.

(3) Bracewell, R. N. The Fourier Trans- form and Its Applications; McGraw-Hill: New York, 1965.

(4) .Griffiths, P. R. Chemical Infrared Fou- rier Transform Spectroscopy; Wiley: London and New York, 1975.

(5) Chamberlain, J. The Principles of In- terferometric Spectroscopy; Wiley: Chichester, U.K., 1979.

(6) Brault, J. W. Proceedings of the 15th Annual Advanced Course of the Swiss Society of Astrophysics and Astronomy, Geneva; Sauverny, Switzerland, 1985.

(7) a. Spectrometric Techniques; Vanasse, G., Ed.; Academic Press: New York, 1977; Vol. I, Chapter 1. b. Spectrometric Tech- niques; Vanasse, G., Ed.; Academic Press: New York, 1981; Vol. 11, Chapters 1-3.

(8) Thorne, A.P. J. Anal. At . Spectrom. 1987,2,227.

(9) Brault, J. W. Ossni. M e n . Oss. Astrofis. Arcetri 1979,106,33.

(10) Luc, P.; Gerstenkorn, S. Appl. Opt. 1978,17,1327.

(11) Thorne, A. P.; Harris, C. J.; Wynne- Jones, I.; Learner, R.C.M.; Cox, G. J . Phys. E 1987,20,54.

(12) Palmer, B. A. Proceedings of the Opti- cal Society of America Meeting in Santa Fe; Optical Society of America: Washing- ton, DC, 1989.

(13) Stubley, E. A.; Horlick, G. Appl. Spec- trosc. 1985,39,805.

(14) Faires, L. M. Spectrochim. Acta 1985, 40B, 1473.

(15) Broekaert, J.A.C.; Brushwyler, K. R.; Monnig, C. A.; Hieftje, G. M. Spectro- chim. Acta 1990,45B, 769.

(16) Boumans, P.W.J. et al. Spectrochim. Acta 1988,43B(l).

(17) Harrison, G. R. MIT Wavelength Ta- bles; Wiley: New York, 1939.

(18) Faires, L. M.; Palmer, B. A.; Engle- man, R.; Niemczyk, T. Spectrochim. Acta 1984,39B, 819.

(19) Faires, L. M.; Palmer, B. A.; Brault, J. W. Spectrochim. Acta 1985,40B, 135.

(20) Thorne, A. P. Spectrosc. World 1990, 2,24.

(21) Steers, E.B.M.; Leis, F. J. Anal. At . Spectrom. 1989,4,199.

(22) Stubley, E. A.; Horlick, G. Appl. Spec- trosc. 1985,39,811.

(23) Faires, L. M. J. Anal. Appl. Spectrom. 1987,2,585.

(24) Ng, R.C.L.; Horlick, G. Appl. Spec- trosc. 1985,39,834.

(25) Dawson, J. B.; King, P. R.; Driffield, R. J.; Ellis, D. J. J . Anal. At . Spectrom. 1989,4,245.

Anne P. Thorne took her B.A. degree in physics at Oxford University, fol- lowed by a D. Phil., also at Oxford, on hyperfine structure in atomic spectroscopy. After a two-year fellowship at Harvard University, doing research on molecular beams under the direc- tion of Norman Ramsey, she was ap- pointed in 1955 to a lectureship in the physics department at Imperial Col- lege, where she is still working. She has taught a variety of courses, and her research has been in atomic structure and laboratory astrophysics, mainly using interferometric techniques. She is currently collaborating on different FTS-related projects with Harvard College Observatory, Lund University, and the European Space Agency.

ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991 65 A

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Fourier transform spectrometry in the ultraviolet