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Anal. Chem. 1988, 60, 2212-2218
ported for AB was 7.5 ng of As (13),this is 25 times worse than the present AB HPLC detection limit of 300 pg reported in Table 11, largely due to the superior sensitivity of ICP-MS. With the column removed (flow injection mode), the limit of detection of AB improves to 70 pg, almost comparable to that of GFAAS. For AB, which was moderately retained, the detection limit of the HPLC mode was estimated to be about 10 times worse than that of the continuous nebulization mode, despite chromatographic band broadening, increased noise due to shorter measurement time, and the use of relatively high salt content in the mobile phase.
ACKNOWLEDGMENT We thank W. R. Cullen, Department of Chemistry, University of British Columbia for synthesizing arsenobetaine and arsenocholine. LITERATURE CITED
Arsenic Symposium, Gaithersburg, MD; Van Nostrand Reinhokl: New York, 1983. (6) Edmonds, J. S.; Francesconi, K. A.; Cannon, J. R.; Raston, C. L.; Skelton, B. W.; White, A. H. TetrahedronLen. 1977, 18, 1543-1546. (7) Cannon, J. R.; Edmonds, J. S.; Francesconi, K. A.; Raston, C. L.; Saunders, J. B.; Skebn, B. W.; White, A. H. Aust. J. Chem. 1981, 34, 787-798. (8) Shiomi, K.; Shinagawa, A.; Azumi, M.; Yamananka, H.; Kikuchi, T. Compn. Biochem. Physiol., C: Comp. Pharmacol. 1983, 74C, 393-396. (9) Luten. J. B.; RiekweCBooy, G.; Greef, J. v. d.; ten Noever de Brauw, M. C. Chemosphere 1883, 12, 131-141. (10) Lawrence, J. F.; Michaiik, P.;Tam, G.; Conacher. H. B. S. J . Agic. food Chem. 1986, 34, 315-319. (11) Kurosawa. S.; Yasuda, K.; Taguchi, M.; Yamazaki. S.;Toda, S.; Morita, M.: Uehwo,T.; Fuwa, K. ANc. Bbl. Chem. 1980, 44, 1993-1994. (12) Kaise, T.; Watanabe. S.; Ito, K.; Hanaoka, K.; Tagawa, S.; Hirayama, T.; Fukul, S. Chemosphere 1987, 16, 91-97. (13) Francesconi, K. A.; Micks, P.; Stockton, R. A.; Irgoiic, K. J. Chemosphere 1985, 14, 1443-1453. (14) Matsuto, S.; Stockton, R. A.; Irgolic, K. J. Sci. Total Environ. 1986, 48, 133-140. (15) Norin, H.; Christakopouios. A. Chemosphere 1982, 1 1 , 287-298. (16) Lau, B. P. Y.; Michaiik, P.; Porter, C. J.; Kroiik, S. Biomed. Environ. Mess Spechom. 1987, 14 723-732. (17) Berman, S. S.; Sturgeon, R. E. Fresenius’ 2. Anal. Chem. 1987, 326, 712-715. (18) Siu, K. W. M.; Berman, S. S. Talsnta 1984. 31, 1010-1012. (19) Voth-Beach, L. M.; Shrader, D. E. Spectroscopy (Springfiekl, Oreg.) 1988, 1 , 49-59. (20) Lunde, G. EHP, Environ. Health Perspect. 1977, 19, 47-52. (21) Crecelius, E. A. EHP, Environ. Health Perspect. 1877, 19, 147-150. (22) Edmonds, J. S.; Francesconi, K. A. Nature (London) 1977, 265, 436. (23) Morita, M.; Uehiro, T.; Fuma, K. Anal. Chem. 1981, 53, 1606-1808. ~
(1) Lewis, R. J.; Tatken, R. L. Reg&try of Toxic Effects of Chemical Sub-
stances; U.S. Department of Heatth, Education and Welfare: Cincinnati, OH, 1978. (2) Peoples, S. A. Review of Arsenical PestlCMes; Woolson, E. A., Ed.; ACS Symposium Series 7; American Chemical Society: Washington, DC, 1974 pp 1-12. (3) Vahter, M.; Marafante, E.; Dencker, L. Scl. Total Environ. 1983, 30, 197-21 1. (4) Marafante, E.; Vahter, M.; Dencker, L. Sci. Total. Environ. 1984, 34, 223-240. (5) Zingaro, R. A.; Bottino. N. R. Biochemistry of Arsenlc: Recent Developments; Lederer, W.H., Fensterhein, R. J., Eds.; Proceedingsof the
RECEIVED for review March 14,1988. Accepted July 1,1988.
Anomalous Intensities of Apodized and Unapodized Magnitude Spectra Judy P. Lee, Kim H. Chow, and Melvin B. Comisarow* Department of Chemistry, University of British Columbia, Vancouver, British Columbia, Canada V6T 1 Y6
While the valley helght between the peaks of two overlapping spectral lines could be expected to decrease monotonically as the frequency difference between the two lines Increases, In actuality, the valley helght between two overlapping peaks in a Fourier transform magnltude spectrum oscllletes as the frequency between the peaks increases. This phenomenon can cause the apparent magnitude resoiutlon to Increase as the llne separation decreases. A resolution criterion based upon the helght of a valley between two overiapplng peaks is pointless when the phenomenon Is operatlve. When the phenomenon Is present, the apparent position of the spectral lines can be dlsplaced from the true spectral positlon. The severity of the phenomenon Is a function of the windowlng function, the amount of relaxation In the time domain signal, and the peak separation. The presence of the phenomenon can be predlcted from the llne separatlon and can be confirmed by changing the windowlng functlon and by computer matching to the experimental spectrum.
INTRODUCTION Resolution Criteria. Spectral resolution is conventionally defined for a single spectral line as the line width at some chosen fraction of the peak height divided by the spectral
position. For a spectral line located at frequencyf , whose line width at some fraction of the peak height is Af, the resolution for the single line could be defined as resolution = f / A f
(1)
An alternate criterion of resolution involves two overlapping lines, where resolution is defined in terms of the height of the valley between the lines. For example, in mass spectrometry it is conventional to define resolution in terms of the peak separation required to give a 10% valley between the peaks (11, whereas in optical spectroscopy it is conventional to define resolution by the Rayleigh criterion (2),which corresponds to a peak separation having an 81.057% ( 8 / 9 )valley between the peaks. Figure 1 illustrates the definitions of resolution discussed above for a single peak (Figure 1a) and two overlapping peaks (Figure Ib,c). It seems intuitively obvious that the valley height, V in Figure 1,would montonically decrease as the separation between the peaks increases. In this work we show that for Fourier transform magnitude spectra this intuition is erroneous and that the valley height, V ,oscillates with increasing peak separation. Moreover, the apparent individual positions of the component peaks are displaced from the true spectral position. Both the displacement and the intensities are also functions of the phase of the time signals that lead to the magnitude spectra. The oscillation phenomenon, which to
0003-2700/S8/0360-2212$01.50/00 1988 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 60, NO. 20, OCTOBER 15, 1988
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of analog signals, each of the form given by
A
f ( t ) = cos u t
(a1
(2)
For all of these FT spectrometers, the analog time signal is sampled N times, at a sample rate S, to give a discrete time domain signal. The amount of time T, required for this sampling step is called the acquisition time and is given by
T =N/S 0
(3)
The discrete FT process converts the N-point discrete time signal into a N / 2 discrete complex spectrum consisting of a discrete real spectrum and a discrete imaginary spectrum. Each of these spectra is defined only at the particular frequencies m = 0, 1 , 2, ... N / 2 - 1 (4) f,,, = m / T
I
f
where m is called the index of the discrete spectrum. The discrete frequency spacing in both these spectra is given by frequency spacing = 1 / T
Af
Y
Flguro 1. Resolution criteria. The resolution is defined by eq 1 where f is the spectral frequency (or position) and A f is a distance increment on the frequency (position) scale. Part a gives the resolution criterion derived from a single spectral peak. In this case A f is the line width at some chosen fraction of the peak height and f is the spectral frequency. For purposes of illustration in part a, A f is chosen to be the line wMth at 50% of the peak height, but in general, any fraction of the peak hd@t could be chosen. Parts b and c show the "two-peak criterion" of resolution. The resolution is defined by eq 1 where f is as for part a and A f is the peak separation when the valley height V Is some chosen fraction of the maximum amplitude. Part c shows how we have defined V for the situation where the individual peaks have auxiliary maxima.
our knowledge has not been previously demonstrated for apodiied spectra, can be explained in terms of the nonadditive nature of magnitude spectra. Fourier Transform Spectrometers. For any chemical spectrometer,the peak h e shape and resolution are controlled by factors that are characteristic both of the sample and of the instrument. Instrumental effects can be particularly pronounced in Fourier transform (FT) spectrometers due to the ease of application of numerical data manipulation techniques. In FT spectrometers the spectrometer produces a signal characteristic of the entire sample, which is stored in the computer of the spectrometer. For Fourier transform infrared (FT-IR) (3) spectrometers, the signal is the spatially dispersed interferogram of the absorption spectrum of the sample. For FT-NMR ( 4 ) )Fourier transform ion cyclotron resonance (ICR) (fill),and M' microwave (12) spectrometers, the signal is a time domain signal from a spectroscopically excited sample. This time domain signal consists of a sum
(5)
where T i s given by eq 3. Equation 5 gives what is called the discrete resolution of the spectrum. The frequency spectrum may be presented as the absorption spectrum, which ideally is identical with the real spectrum, the magnitude spectrum, which is the modulus (the square root of the sum of the squares of the real and the imaginary spectra) of the complex spectrum, or the power spectrum, which is the square of the magnitude spectrum. Windowing and Apodization. One advantage of FT spectrometers is that the line shape and resolution can be changed by multiplication of the stored signal by a special function, called a window, prior to Fourier transformation. The process is known as windowing in the time domain or apodization in the frequency domain. Recently we have completed a survey of windows for the damped signals that occur in FT-NMR, FT-ICR, and FT-microwave spectroscopies and we have proposed a dynamic range criterion (13,241for selection of the most appropriate window for any particular case. The principal advantage of apodization is a reduction of ripple and narrowing of the spectral line near the base line and a concomitant reduction in the interference of one peak with nearby peaks. For the magnitude mode our selected windows are the rectangle window, R(t),(correspondingto no windowing)
R ( t ) = 1.0 0
