Anal. Chem. 1907, 5 9 , 783-786
LITERATURE CITED
for the elements a t very low concentration (e.g., P b and U).
CONCLUSIONS This work has shown that, although analyses with external calibrations are usually more subject to errors arising from ionization interferences (caused by concomitant elements) in ICP-MS, unless the matrix of the standard solutions used to calibrate closely matches that of the samples, they can nevertheless be used rather efficiently in many cases, provided that an adequate correction for drift is made. The methods of standard additions provides, in general, more accurate results than external calibrations as it compensates for ionization interferences. Finally, the isotope dilution technique gives by far the most accurate and precise results, but it requires two isotopes free of isobaric interferences, and equilibration of the spike isotope with the analyte must be achieved in order to assure their identical behavior during any sample treatment preceding the analysis.
ACKNOWLEDGMENT The authors thank Ralph Sturgeon and Scott Willie for preparing the riverine water concentrates used in the standard additions analyses. Registry No. H20, 7732-18-5; Na, 7440-23-5; Mg, 7439-95-4; K, 7440-09-7; Ca, 7440-70-2; Al, 7429-90-5; V, 7440-62-2; Cr, 7440-47-3; Mn, 7439-96-5; Cu, 7440-50-8; Zn, 7440-66-6; Sr, 7440-24-6; Mo, 7439-98-7; Sb, 7440-36-0; Ba, 7440-39-3; U, 7440-61-1; As, 7440-38-2; Co, 7440-48-4; Ni, 7440-02-0; Cd, 7440-43-9; Pb, 7439-92-1.
703
(1) Douglas, Donald, J.; Houk, Robert S. Prog. Anal. At. Spectrosc. 1985, 8 , 1-18. (2) Gray, Alan L. Spectrochim. Acta, Part 8 1985, 4 0 8 , 1525-1537. (3) Houk, Robert S. Anal. Chem. 1986, 5 8 , 97A-105A. (4) Olivares, J. A,; Houk, R. S. Anal. Chem. 1988, 5 8 , 20-25. (5) Tan, Samantha, H.; Horllck, Gary Appl. Spectrosc. 1988, 4 0 , 445-460. (6) McLaren, J. W.; Mykytiuk, A. P.; Willie, S. N.; Berman. S. S. Anal. Chem. 1985, 5 7 , 2907-2911. (7) McLaren, J. W.:Beauchemin, Diane; Berman, S. S. Anal. Chem., in press. (8) Vaughan, M. A,; Horlick, Gary Appl. Spectrosc. 1988, 4 0 , 434-445. (9) McLeod, C. W.; Date, A. R.; Cheung, Y. Y. Spectrochim. Acta, Part 6 1986, 4 1 6 , 169-174. (10) Doherty, William; Vander Voet, Anthony Can. J . Spectrosc. 1985, 30(6),135-141. (11) Gregoire, D. C. SSC Workshop on Applications of ICP-MS; Toronto, Canada, 1985. (12) Taylor, Howard, E.; Garbarino, John R. Winter Conference on Plasma Spectrochemistry; Hawaii, 1986. (13) Date, Alan R.; Gray, Alan L. Spectrochim. Acta, Part 8 1985, 4 0 6 , 115-122. (14) Boomer, D. W.; Powell, M. J. Can. J . Spectrosc. 1986, 3 7 , 104-109. (15) Koirtyohann, S. R.; Jones, J. S.; Jester C. P.; Yates, D. A. Spectrochim. Acta, Part8 1981, 368,49-59. (16) Beauchemin, Diane: McLaren, James ICP I n f . News/. 1985, 11(7). 44 1-446. (17) Sturgeon, R. E.; Berman, S. S.; Wiiiie, S. N.; Desaulniers, J. A. H. Anal. Chem. 1981, 5 3 , 2337-2340. (18) McLaren, J. W.; Beauchemin, Diane; Berman, S. S. J . Anal. At. Spectrom ., In press. (19) CRC Handbook of Chemistry and Physics, 58th ed.: Weast, Robert C.; Ed.; The Chemical Rubber Co.; Cleveland, OH, 1977; pp 8271-8354. (20) Sturgeon, R. E., Ottawa, ON,Canada, 1986, unpublished results.
RECEIVED for review August 29, 1986. Accepted November 7, 1986.
Optical Cells with Partially Reflecting Windows as Nonlinear Absorbance Amplifiers Purnendu K. Dasgupta* and Jae-Seong Rhee Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-4260
An etalon, where the dlelectrlc spacer Is a weakly absorbing solution, forma a nonllnear absorbance ampllfler. The observed net absorbance Is equal to -log [10-3A’4(l R,)/( 1 10-A’2Rw)]where R , Is the reflectance of the windows and A Is the absorbance of the same solution in a conventional cell. Reasonable agreement between theory and experiment Is observed for a coherent source. For conventional sources, the observed amplification factor is much higher due to beam dlvergence, multlpath effect, and multiple beam interference.
-
-
The measurement of smaller and smaller optical absorbance values is a continued preoccupation of the trace analyst. In recent years, the approaches to this problem have included exploitation of the thermal lensing effect ( I ) , utilization of long path capillary cells (2),or reflective helical cells (3). For the modified cell designs mentioned above, it has been shown (3)that the nonlinear absorbance amplification effect (i.e., the fact that the effective path length of the cell, 6, increases with decreasing value of tC, t being the molar absorptivity and C the molar concentration) is due to a multipath effect originating from finite beam divergence. While nonlinear absorbance amplification, which not only facilitates measure-
ments of low absorbance but extends the attainable dynamic range as well, has obvious utilitarian consequences ( 2 ) ,the necessary cell designs or configurations are essentially inapplicable to situations which potentially stand to benefit the most from the ability to measure very low absorbance values. As an example, the utility of optical absorbance detection in open-tubular liquid chromatography, which employs column diameters of the order of 15 km (4)are limited because dispersion considerations dictate that the only permissible cell geometry involves the column itself; i.e., the incident beam is orthogonal to the column long axis and the physical path length is equal to the column diameter. Increasing the physical path length by using an angle of incidence different from orthogonal is of limited utility because of increasing light conduit action of the column wall; this phenomenon will also limit the utility of multipass schemes, e.g., in a White cell (5), aside from increasing the cell volume. Fabry-Perot interferometry as well as laser resonant cavities make use of the well-known optical device, etalon, in which a dielectric is bounded by two partially reflecting surfaces (6). Normally, the dielectric is transparent to the optical region of interest. The results of replacing the nonabsorbing dielectric in an etalon with an absorbing solution (or conversely, the results of replacing the normally transparent cell windows
0003-2700/87/0359-0783$01.50/00 1987 American Chemical Society
784
ANALYTICAL CHEMISTRY, VOL. 59, NO. 5, MARCH 1, 1987
/ //
0.6
0.9 8
0.97 Y 0.96 0.95 0.91
I
1
0
3
2
4
0
Figure 1. Absorbance amplification factor as a function of conventional absorbance, reflectivities ranging from 0.4 to 0.9, computed according to eq 11 and 12.
of an optical cell with partially reflective ones), to our knowledge, have never been documented, either experimentally or theoretically. Such a modification can be done to any conceivable optical cell, and we intend to show in this work that this results in nonlinear absorbance amplification.
THEORY Consider a Fabry-Perot etalon with entrance and exit window reflectances and transmittances of R, and T,, respectively. We further assume that the windows each absorb a finite fraction of the incident radiation, A,, called absorptance in physical optics. (Most texts on physical optics discuss Fabry-Perot interferometry in detail, ref 6 is a good example). For the classic Febry-Perot etalon, the transmitted light consists of peaks a t discrete frequencies separated in wavenumber by 1/2b where b is the spacing between the windows (i.e., the peaks will be separated by 0.5 cm-l for a pathlength of 1 cm). The peak transmission, defined as the ratio of transmitted to incident energy at the transmitted wavelength and is given by is denoted by ItmJIi
When the interposing dielectric is nonabsorbing, and since A,
+ T, + R,
=1
(2)
J
i
1
-log A
-log
i
A
Figure 2. Absorbance ampliitlon factor as a function of conventional absorbance, reflectivities ranging from 0.9 1 to 0.99, computed ac-
cording to eq 11 and 12. erenced against a conventional cell, both containing an essentially nonabsorbing medium, is therefore
A, = -log T, = -log
(6)
(Itmax/Ii3)
We now consider the situation when the etalon cell is filled with a dielectric medium of absorbance A. It is convenient to consider that each window has a layer of absorbing material of absorbance A/2 associated with it. Light must each time travel through this layer and only the transmitted fraction, 10-A'2, is subject to window absorption, reflection, and transmission. It is necessary therefore to substitute 10-A12T, and 10-A/2R, for T, and R,, respectively, in all the pertinent equations. The new absorbance of the cell system containing the absorbing dielectric, A:, analogous to eq 6 is given by
(
A,' = -log
10-A/2T,
)I/BI
1 - 10-A/2R,
(7)
where
Equations 1, 4,and 6 combine to A, = -log
(
TW2
~R,'i'(l - R,)
eq 1 takes the more familiar form
)
(9)
Equations 7 and 8 combine to
(3) A,' = -log The finesse of the etalon, 3, is defined to be the ratio of the separation of the adjacent transmitted maxima to the halfwidth of the transmitted peaks and is given by
3 = 7rRw'I2/ (1- R,)
(4)
Consideration of eq 1 (or eq 3) and eq 4 together yields the overall light throughput through the etalon; the overall transmittance T,averaged over many transmission peaks is thus
10-AT,2 (1- 10-A/2R,)~( 10-A/2R,)1/2
The net absorbance increase, A p t , due to the presence of the absorbing medium, is obtained by substracting eq 9 from eq 10 A,"et = -log
(
1 0 - 3 ~ / 4 ( 1- R,)
1 - 10-A/2R,
(11)
The absorbance amplification factor, CY, is then given by a = Aenet/A
The background absorbance, A,, of an etalon cell, when ref-
)
(12)
Values of CY, calculated according to eq 11and 12 are plotted vs. A in Figures 1 and 2. The high and nonlinear absorbance amplification, especially at high values of R,, is clearly evident.
ANALYTICAL CHEMISTRY, VOL. 59, NO. 5, MARCH 1, 1987
785
Y
;10.0
f U
$
I
4
c a
1
5.0
n
1 nm s l i t
:
n 4
1.0 1.0
2:o -log
3:O A
Figure 3. Observed absorbance amplification factors for etalon absorption cells with r , = r 2 = 0.062, 0.44, and 0.75 respectively: slit width, 4 nm: CuSO, standards, 550 nm.
The derivation of eq 11,however, does not take into account beam divergence. Even with a coherent source, beam divergence cannot be completely avoided. Although absorbance amplification occurs in principle only around a limited number of wavelengths that are effectively transmitted by the interferometer, the effect of beam divergence is to cause more wavelengths to satisfy the conditions for maximum transmission. Additionally, beam divergence, with multiple reflections occurring, brings in the multipath effect (3),and may result in greater nonlinearity than predicted by eq 11. For a perfectly collimated beam, absorbance amplification will occur only around ZtmaXwhere the number of round trips is limited only by the finesse. Equation 11should therefore be regarded as the lower limit of absorbance amplification experimentally attainable a t low absorbance values. I t is also clear that if an etalon cell is used in a conventional spectrophotometer with a divergent source, multiple beam interference will play an important role and effects from Fizeau fringes (6) cannot be ignored. However, a comprehensive mathematical elucidation of the situation with a divergent source is beyond the scope of the simple theory presented above.
EXPERIMENTAL SECTION Mirror-type beam splitters, with nominal reflectivities of lo%, 50%, and 75%, were obtained from Edmund Scientific Co. (Barrington, NJ). These were cut into -12 mm X 30 mm strips (3 mm thickness). A quartz flow cell with a large aperture (11 X 7 mm) was chosen for this work. To measure the conventional absorbance A , the spectrophotometric instrument (Model 559, equipped with a double monochromator, Perkin-Elmer) was zeroed with water in the cell and a series of acidified copper sulfate solutions of varying concentration sipped into the cell by a peristaltic pump and measured at 550 nm with a slit width of 4 or 1nm (a separate series of measurements were carried out for each slit width) under flow conditions (ca. 0.5 mL/min) with 2-5-s integration. To measure A:, the partial mirrors (with mirror surfaces nearest to the cell) were taped to the cell windows on either side. The cell compartment of the instrument was modified to accept the resulting much thicker cell and the absorbances of the same series of copper sulfate solutions were measured after zeroing with water. Experiments with a coherent source were conducted in a dark room using an argon-ion laser (Spectra Physics), the same flow cell as before with or without attached partial mirrors, and a silicon photodetector with an intensity readout (Spectra Model 901 photometer/radiometer). The 514.5-nm line of the laser was isolated with an appropriate filler. The detector readings were manually processed to obtain the reported A and A,‘ absorbance values. The actual reflectivities of the mirrors used were measured at the laser wavelength to be 6.2,44, and 75%, respectively. The
-
2.0 log A
3.0
Flgure 4. Calculated (eq 12, dashed line) vs. observed absorbance amplification factors (open circles), for a coherent source, 514.5 nm, R, = 0.75, compared to spectrophotometer measurements, slit widths of 1 and 4 nm (closed symbols).
absorptance values (A,) were difficult to measure accurately; our best estimates for the three respective mirrors are 0.02,0.04, and 0.05, respectively; the literature value of a 50 nm thick silver film (R, = 0.94) is 0.05 (6).
RESULTS AND DISCUSSION The experimental amplification factors, a , obtained for the three different reflectivities, R, = 0.062, 0.44, and 0.75, are shown in Figure 3. Presumably due to significant beam divergence occurring in the spectrophotometer measurement system, the observed amplification factors are substantially higher, especially at low absorbances, than values calculated from eq 11and 12. The experimental results obtained for a coherent source with the etalon cell of R, = 0.75 are shown in Figure 4 along with the predictions from eq 11and 12 shown as the dashed line. The predicted plateau value a t low absorbance levels is somewhat lower than that experimentally observed. It should be noted, however, that all our calculations have been performed on the basis that the source bandwidth is significantly larger than the bandwidth of the peaks transmitted by the etalon. This is not true with the laser source used in this work. In principle, it should be possible to “tune” the etalon cell for matching one of the transmission bands to that of the source by carefully controlling the tilt of the cell as in interferometric experiments. However, the etalon used in this work is far from perfect; it is likely that surface variations over the significant area of beam incidence and the limited finesse of the cell used would have allowed a significant portion of the incident radiation to match the transmission criteria. Clearly, in the absence of a perfect overlap, sensitivity enhancement can occur for only that portion of the incident radiation which is effectively transmitted. Nevertheless, the experiments are meaningful in that the transmitted light intensity is measured on a comparative basis, with water or sample being aspirated into the cell, without disturbing the cell or the rest of the optical setup. The sharper fall off of a with increasing A relative to the expectations from eq 11 and 12 remain, however, unclear. Figure 4 also shows that for the spectrophotometer measurement system, the observed value of CY acutely depends on slit width. This supports the contention that the disagreement of the observed value of a with eq 11and 1 2 is due to beam divergence (which nonetheless facilitates the desired objective of nonlinear amplification further). The values of A, measured for the cells with R, = 0.44 and 0.75 ( A , = 0.04 and 0.05, respectively) were 0.650 and 1.158 compared to the respective values of 0.635 and 1.23 computed according to eq 9, in reasonable agreement. In the spectro-
786
ANALYTICAL CHEMISTRY, VOL. 59, NO. 5, MARCH 1, 1987
:,R
0.75
0
Flgwe 5. The spectra of a holmium oxide filter with and without partial
mirrors (R, = 0.75) on each side. Full scale span is the same for both scans; considerable base-line offset is required for the etalon spectra. Note that at these high absorbances, stray light effect is Significant and the registered absorbances for the etalon spectra would have been even higher without stray light effects.
photometer system used, measurement noise is dependent, under the experimental conditions and absorbance ranges used, on the overall light throughput. The noise levels observed with the etalon cells containing water were the same as those of conventional cells containing a solution which has an absorbance equal to the measured A , value of the etalon cell; i.e., noise levels in these experiments are dependent on the overall light throughput and not on the cell type. The intrinsic source noise present in the single beam measurement system used with the coherent source made accurate measurement of system noise impossible. The spectra of a holmium oxide filter, with and without partial mirrors on each side, are shown in Figure 5; the amplification is evident for the absorption bands shown. It is clear that for any system inherently limited by detector noise (as opposed to flow and thus cell-related noise), the etalon-cell concept may be of significant utility. High amplification factors are easily attained, albeit a t the cost of light throughput. In conventional liquid chromatography, a typical
system is detector noise limited only when pure solvents, transparent at the monitoring wavelength, are being used and the pumping system is free from pulsations. This situation does not exist in many cases; certainly detector noise is not the limiting factor in postcolumn reaction systems (7). However, when conventional optical detectors are adapted for open tubular liquid chromatography (8),due to the extremely small path length, the system is frequently detector noise limited. This situation is particularly likely to benefit from the etalon cell concept. However, if it is possible to use high-power focused sources such that the detector is not light-starved, the etalon cell is of potential utility in absorbance amplification in many other situations and is applicable to all conceivable optical cells physically bounded by windows. The etalon cell concept can be extended to flow cells where the entrance and exit windows are optical fibers, the terminal leads being partially silvered, a design of special utility with laser-based sources. Theoretically, a more intriguing problem is the behavior of a system where one or more partial mirrors are interposed between the entry and exit windows.
ACKNOWLEDGMENT This paper was made possible only through the constructive criticism offered by J. M. Harris, University of Utah.
LITERATURE CITED (1) (2) (3) (4) (5) (6)
Jansen, K. L.; Harris J. M. Anal. Chem. 1985, 57, 2434-2436. Lei, W.; Fujiwara, K.; Fuwa, K . Anal. Chem. 1983, 55. 951-955. Dasgupta, P. K . Anal. Chem. 1984, 5 6 , 1401-1403. Jorgenson. J. W.; Guthrie, E . J. J . Chromatogr. 1983, 255, 335-348. White, J . U . J . Opt. SOC.A m . 1942, 32, 285-288. Hecht. E.; Zajac A. Optics; Addison-Wesley: Reading, MA, 1979; pp 301-319. (7) Cassidy, R. M.; Elchuk, S.;Dasgupta, P. K. Anal. Chem. 1987, 5 9 , 85-190. (8) Ishii, D.; Takeuchi, T . J , Chromarogr. Scl. 1980, 18, 432-472.
RECEIVED for review March 18, 1986. Accepted November 10, 1986. This research was supported by the Office of Basic Energy Sciences, U.S. Department of Energy, Division of Chemical Sciences through Grant No. DE-FG05-84ER-13281. However, this paper has not been subject to review by the DOE and no endorsements should be inferred.
