block diagram computer simulation of analytical instruments

cases, simula- tions may be the only feasible way to obtain useful results. Even when this is not true, simulations help to clar- ify information obta...
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BLOCK DIAGRAM COMPUTER SIMULATION OF ANALYTICAL INSTRUMENTS Edward Voigtman LGRT-102 (Chemistry) University of Massachusetts at Amherst Amherst, MA 01003-0035

There are many varieties of analytical instrument computer simulations and probably j u s t as many reasons for doing them, but there is one fundamental goal of all such efforts: the promise of insights that would be far more tedious to obtain through traditional e x p e r i m e n t a l or theoretical techniques. In some cases, simulations may be the only feasible way to obtain useful results. Even when this is not true, simulations help to clarify information o b t a i n e d by o t h e r m e a n s . This aspect is p a r t i c u l a r l y useful in teaching, where the goal is to effectively impart an understanding of the material at hand. In this 0003 - 2700/93/0365-1029A/$04.00/0 © 1993 American Chemical Society

REPORT I will focus on the principles of t h e a n a l y t i c a l i n s t r u m e n t computer simulations t h a t I have been using recently. Several examples will show how a n d why t h e s e t y p e s of simulations are useful for both r e search and teaching.

REPORT Is it possible to construct computer simulations t h a t are quantitatively accurate in t h e i r modeling of both the signals and relevant noises in an analytical i n s t r u m e n t and t h a t are implemented in such a way t h a t the simulation program model a p p e a r s to be e s s e n t i a l l y t h e s a m e as t h e "block diagram" of the instrument? Simulating the block diagram of the i n s t r u m e n t is i m p o r t a n t because it

makes the models more intuitive in appearance, operation, description, and documentation, and because the modularity of the models facilitates error correction. For spectrometric instruments, the answer to this question is a qualified yes. The qualification is necessary b e c a u s e some t e c h n i q u e s a r e too complicated or ill-understood to be simulated in a quantitative fashion. Even in the best cases, it is impractical to e x p e c t a t w o - d i m e n s i o n a l block diagram to behave exactly like the three-dimensional instrument it r e p r e s e n t s . However, surprisingly, some techniques are highly amenable to such modeling. Several such techniques will be illustrated. Prerequisites To perform these simulations, several prerequisites must be satisfied.

ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993 · 1029 A

REPORT First, we need a simulation program "engine," preferably based on a desk­ top microcomputer system. The en­ gine receives user input for the de­ sired s t a r t i n g and ending t i m e s of the simulation, the desired time of e a c h of t h e s i m u l a t i o n s t e p s (or number of steps), and the number of simulations to perform. Basically, we need to follow the time evolution of the digital representation of the mod­ eled "real" system; the essential pa­ rameters are when to start, when to stop, and how finely the t i m e axis needs to be divided. By taking these actions we are assuming that the sim­ ulations are intrinsically time-based, which is t r u e for many simulations but clearly is not for all simulations of possible interest. The second requirement is t h a t the s i m u l a t i o n e n g i n e use "blocks" to represent instrument components or functionalities. These blocks are func­ tional pieces of the computer code, with their own graphic icons, input and o u t p u t connectors, a n d dialog boxes for entry of user-specified data and necessary operational p a r a m e ­ ters. They are coded to represent, as accurately as the underlying equa­ tions and the digital representation allow, the behavior of the correspond­ ing component in the "real" system. The program must use "interconnec­ tions" (either lines or arrows) to rep­ resent the flow of chemical, electronic, or optical i n f o r m a t i o n a m o n g t h e blocks. These restrictions necessarily follow from the requirement that the simulation model be its own block di­ agram. The third requirement is t h a t the information p a t h s along t h e i n t e r ­ connections be m u l t i d i m e n s i o n a l , r a t h e r t h a n simply temporal se­ quences of r e a l n u m b e r s . P u t a n ­ other way, it must be possible for in­ terconnections to allow the passage of multicomponent arrays of values, rather t h a n only single values, with each simulation time step. This re­ quirement is necessary because it is not possible to model all of the es­ sential optical and chemical informa­ tion with temporal sequences of real values. For example, spectrometric instru­ ments deal with light, so spectromet­ ric simulation models must be able to deal with the passage of "light" through the interconnected optical component blocks in t h e model. If only the intensity of the light is of significance, then a sequence of real values (the light intensity value at each simulation time step) is a d e ­ quate. B u t if polarization is impor­ tant, then optical vectors are the ap­

propriate m e a n s for conveying t h e necessary information; a number of possibilities exist. For t h e s i m u l a ­ tions described here, the Jones and the Mueller optical calculi are used to represent light as it passes from one optical component block to the next. These optical calculi have somewhat complementary characteristics and are described elsewhere (1, 2). The final requirement is t h a t the simulation program allow u s e r s to program the component blocks needed to construct the spectromet­ ric instrument models. In the models information will flow from block to block via input and output connec­ t o r s . E a c h block m u s t b e p r o ­ grammed to process the information received and to pass it along through its output connections. The simula­ tion engine gives each block its tim­ ing information, but the blocks have to do the rest, so it is necessary for each block to be programmed in all aspects ( i n t e r n a l b e h a v i o r a l code, block icon, number of inputs and out­ puts, and error handling). As a prac­ tical matter, it is also important that t h e p r o g r a m m i n g l a n g u a g e of t h e block support matrix operations be­ cause this is the only reasonable way to i m p l e m e n t t h e r e q u i s i t e optical calculus operations. The blocks are "working stores" of what we have learned (and published in the literature) about the behavior of t h e components of spectrometric i n s t r u m e n t s . We w a n t this knowl­

edge to be " a l i v e " a n d accessible r a t h e r t h a n "dead" on the p r i n t e d page. We w a n t to avoid reinventing the wheel whenever we need to per­ form a new type of simulation. Satisfying the prerequisites The computer simulation program Extend (Imagine That, Inc., San Jose, CA) meets our requirements. It uses a Macintosh computer system at the Macintosh Plus level or above. The program comes with standard li­ b r a r i e s of p r e p r o g r a m m e d compo­ n e n t blocks t h a t a r e user-selected from s t a n d a r d d r o p - d o w n m e n u s , but the libraries do not contain opti­ cal component blocks and have only a few generic electronic component blocks. However, it is relatively easy to c u s t o m - p r o g r a m blocks, a n d I have released—as copyrighted share­ ware—a collection of 144 optical cal­ culus and electronic signal-processing component blocks. These blocks, ar­ ranged in four libraries collectively named "Voigt fx," are available via anonymous file transfer protocol in the MacSciTech shareware archives on t h e I n t e r n e t . (The p a t h is MacSciTech/Chem, and the machine name is ra.nrl.navy.mil.) A functional demonstration copy of Extend, with disabled saving and printing capabili­ ties, is also available. A m o n g m a n y o t h e r blocks, t h e Voigt fx libraries provide blocks for implementing any arbitrary, static Jones or Mueller matrices, and they

Figure 1. Instrument model for simulating the measurement of optical transmittance. Light source has 1 -μ\Λ/ intensity and «· 1% Gaussian-distributed, band-limited (1 mHz-10 Hz) Mf intensity noise. Preamplifier noise is - 50 nV/(Hz)1'2. This model can be used as a chromatogram generator.

1030 A · ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993

also provide a pair of blocks that allow u s e r s to p r o g r a m a r b i t r a r y , t i m e - d e p e n d e n t J o n e s or M u e l l e r matrices; the entire Jones and Mueller optical calculi are available for use in simulation models. Users may also program their own custom optical calculus components, which may be necessary to obtain blocks not in the Voigt fx libraries (the software provides the necessary source code for transmitting and receiving Jones vectors for Jones calculus and Stokes vectors for Mueller calculus). E v e n t h i s m a y n o t be e n o u g h , though. Fiber optics a r e a case in point. Extend can actually pass dynamic a r r a y s of u p to five d i m e n sions along its interconnections. This ability m a k e s it relatively easy to implement simulations involving, for example, complex p a r a x i a l optics. There are many other possibilities because arrays can be used to represent vectors, tensors, matrices, and other geometric objects. To add techniques to the software, access to t h e expressions t h a t provide t h e d e s i r e d q u a n t i t a t i v e d e scription of the process to be modeled is required, and then the blocks need to be p r o g r a m m e d . How well t h i s works depends on the complexity of the real process and the desired mathematical model, and how long the u s e r is willing to wait for t h e s i m u l a t i o n to r u n . E x t e n d i n g t h e simulations to encompass nonspectrometric techniques a p p e a r s to be feasible, b u t e x t e n s i o n s a r e b e s t done by those with expertise in the specific areas. One further caveat: The released Voigt fx libraries a r e restricted to monochromatic spectroscopies. However, the extension to polychromatic operation has been accomplished and the polychromatic blocks will be r e leased in the near future. The goal

Our goal is to put block diagrams on the computer screen, give each block its necessary information, specify the simulation time parameters, and then r u n t h e simulation. We w a n t the simulation output to represent, as accurately as possible, t h e time behavior of both the signal and the relevant noises. We want the models to provide results as quickly as possible, consistent with accuracy and robustness considerations. In addition, we want to use the models for exploration purposes, trying out various component parameters and instrument configurations and playing hunches j u s t to see w h a t h a p p e n s . Intuition, after all, is something that

Figure 2. Typical temporal response produced by the model in Figure 1. Peak parameters are listed in Table I.

Table I. Gaussian peak parameters for the simulated chromatogram generator in Figure 1 Peak no. 1 2 3

Peak concentration (M)

Retention time (s)

Standard deviation (s)

0.001 0.003 0.005

1 3 5

0.1 0.15 0.2

is learned and can be sharpened. P e r h a p s t h e e a s i e s t w a y to see how this works is to s t a r t with Figure 1, which shows a simple instrument designed to measure the t r a n s m i t t a n c e of a n a b s o r b i n g s a m p l e . The model c o n t a i n s a noisy l i g h t source, a n a b s o r p t i o n flow cell, a concentration temporal profiles block, a photodetector and t r a n s i m pedance preamplifier block, a noise generator block (for modeling detector a n d preamplifier noise), a n d a digital storage oscilloscope. For this model, the light source has l ^ W int e n s i t y a n d a p p r o x i m a t e l y 1% of Gaussian - distributed, band - limited (1 m H z - 1 0 Hz) 1 / / i n t e n s i t y noise. This light source is rather weak and noisy, as a real light source might be. In the model, the output of the light source block is a s t r e a m of noisy J o n e s vectors, one per s i m u l a t i o n time step. Suppose that the absorber was not

Molar absorptivity (L/mol cm) 300 200 500

present and that the light source was connected directly to the photodetector and the preamplifier block. The photodetector would then convert the a r r i v i n g noisy J o n e s v e c t o r s into noisy photocurrents, represented by real numbers. To do this, the photodetector first calculates t h e noisy light intensities of the Jones vectors by summing the squares of the components of the J o n e s vectors. Then the photodetector multiplies by its responsivity (in A/W) as specified in the block's dialog box. Next, the "current-to-voltage converter" portion of the block produces noisy output voltages by multiplying by the transimpedance (in V/A) as specified in the dialog box. Therefore, the output of the block is a sequence of real numbers, representing the noisy, photoinduced voltages. T h e effect of p h o t o d e t e c t o r a n d preamplifier noise is modeled by the noise generator block and yields real

ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993 · 1031 A

REPORT values t h a t correspond to even nois­ ier photoinduced voltages, which are captured and displayed by the digital storage oscilloscope. The noise gen­ erator block also allows for exporta­ tion of the data as ASCII text files. For Figure 1, the responsivity is 0.1 A/W and the transimpedance is 1000 V/A; t h e r e f o r e , t h e m e a n o u t p u t voltage should be 1 μW χ 0.1 A/W χ 1000 V/A = 100 uV. Now c o n s i d e r t h e full model in Figure 1. In a real system, t h e a b ­ sorption cell is a vessel containing the absorbing species t h a t serves to determine the absorption pathlength. In Figure 1, the pathlength is 1 cm and the block is used to model a flow cell (i.e., the block is similar to a n a b s o r b a n c e flow cell u s e d in H P L C ) . T h e t r a n s m i t t a n c e of t h e flow cell is determined by the sum of the absorbances of the species flow­ ing through the cell. This absorbance

is time-dependent because the spe­ cies are assumed to be independent and noninteracting as they pass through the flow cell. In a real absorbance flow cell con­ nected to the output of an HPLC col­ umn, the eluting chemical sub­ s t a n c e s t h e m s e l v e s would be t h e sources of the absorbances. To model t h i s , t h e block labeled " G a u s s i a n peak profiles" is used. As seen from its dialog box in Figure 1, this block m a y be u s e d a s t h e s o u r c e of a s many as 30 independent concentra­ tion temporal profiles. For each con­ c e n t r a t i o n profile, t h e peak shape and its associated shape parameters m a y be u s e r - s p e c i f i e d , a n d e a c h peak may have independent values of molar absorptivity (L/mol cm), op­ tical activity (OA, °/cm M), and cir­ cular dichroism (CD, 7 c m M). Peaks may be fully resolved or may overlap in an arbitrary fashion.

Table II. Gaussian peak parameters for the simulated chromatogram generator in Figures 3, 5, and 6 Peak no. 1 2 3 4 5

Retention time (s)

Standard deviation (s)

1 2 3 4.5 5

0.1 0.1 0.1 0.2 0.25

Molar absorptivity (L/mol cm) 100 1 1 10 10

OA (°/cm M)

CD (7cm M)

0.1 10 0.1 10 -10

0.1 0.1 100 0.1 100

Concentration is 0.001 M for all five peaks.

Figure 3. Instrument model for simulating the measurement of absorbance using a simple double-beam system. Light source has 1 -μνν intensity and - 0.12% Gaussian-distributed, band-limited (1 mHz-10 Hz) Ml intensity noise. Preamplifier noise is - 3 nW(Hz)1'2. R is reflectivity. 1032 A · ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993

The m a n n e r in which t h i s block works with the absorption cell block is crucial to understanding how the simulations work. With each simula­ tion step, the time-dependent peak concentrations are computed. These values, multiplied by their respective peak's molar absorptivity, yield the time-dependent absorptivities (cm - 1 ). Similar calculations may be made for the OA and the CD. A 3 1 row by 6-column array of values, in­ cluding the summed absorptivities, OAs, and CDs, is passed to the ab­ sorption cell at each simulation step. The absorption cell uses these passed values to calculate the total absor­ b a n c e , n e t OA (deg), a n d n e t CD (deg), which a r e used to construct the proper optical calculus matrix for the block. W h e n the incident light source optical vector a r r i v e s , it is multiplied by the calculated matrix of the absorption cell block, resulting in an optical vector t h a t is passed to the output of the block. Table I shows the specified peak shape p a r a m e t e r s for the model in Figure 1. In each case, the OAs and t h e CDs were a s s u m e d to equal 0; the simulation s t a r t i n g and ending times were 0 and 6 s, respectively, and the time per simulation step was 0.01 s. Running the model on a Mac­ intosh Ilfx takes 8 s of real time and gives results typical of those shown in Figure 2. As expected, the Gaus­ s i a n c o n c e n t r a t i o n profiles do not give Gaussian transmittance profiles a n d t h e o u t p u t v o l t a g e is r a t h e r noisy because of the deliberate use of a light with low intensity (1 μW), a small t r a n s i m p e d a n c e (1000 V/A), and a high photodetector and pream­ plifier noise (~ 50 nV/(Hz) 1 / 2 ). The b l a n k level is about 100 μ ν , as ex­ pected. The peak absorbances may be calculated u s i n g t h e t r a n s m i t ­ tance values at the known retention t i m e s of t h e p e a k s a n d t h e m e a n blank value of 100 μ ν ; the calcula­ tions are possible because of the ab­ sence of time c o n s t r a i n t s in any of the six blocks in Figure 1. Running the simulation many times d e m o n s t r a t e s t h a t the noise v a r i e s from r u n to r u n . T h u s it is possible to examine the effects of sig­ nal averaging, gated integration, matched filtering, S a v i t z k y - G o l a y filtering, and a variety of other sig­ nal-processing techniques. The data files a r e also e a s i l y e x p o r t e d (as ASCII text files) for further process­ ing with other programs. There are many other possibilities, even with this simple model, and they are best explored by trying them. This is one of the major strengths of the method:

It is fun to run the models and see what happens. More detailed examples

Suppose we specify five peaks, with the parameters shown in Table II. The first three peaks are resolved and exhibit significant absorbance, OA, and CD. The last two peaks are wider than the first three peaks and overlap. Both exhibit absorbance and have substantial OAs, though of op­ posite signs, but only the last peak exhibits significant CD. These peak parameters are placed in a copy of the concentration pro­ files block, called "concentration pro­ files,*" which has its output con­ nected to a "circular activity*" block. This two-block combination repre­ sents a simple model of an HPLC column connected to a flow cell and is used in the models in Figures 3, 5, and 6, with the parameters given in Table II. Now suppose we want to measure the absorbances of these five peaks. What instrumental configuration is needed? One possible answer is pro­ vided by Figure 3, which shows a simple double-beam absorbancemeasuring system. The absorbance may be obtained by taking the nega­ tive log of the transmittance (trans­ mitted light intensity divided by the incident light intensity). Alterna­ tively, the proportionate preampli­ fier voltages may be used instead of the intensities. What happens when the model is run, with starting and ending times of 0 and 6 s, respectively, and a time step of 0.01 s? Typical results, avail­ able in 15 s of real time, are shown in Figure 4a. All of the absorbances for the resolved peaks are as ex­ pected from Table II, and the last two peaks significantly overlap. The noise is too small to appear in the plot because the double-beam config­ uration provides excellent light source noise rejection and because the preamplifier noises are too small; this is evident when the concentra­ tions of the peaks are reduced. If the OAs of the peaks, rather than the absorbances, were of inter­ est, a different measurement scheme would be needed. One possibility is shown in Figure 5, where the chromatogram generator and the circular activity block are the same as in Fig­ ure 3. This simple configuration ap­ pears from time to time in different guises (3, 4), and its principles of op­ eration are easily understood. Light, with its plane of polarization ori­ ented at +45°, is incident upon the flow cell. In the absence of net OA in

the flow cell, the beam exits with its plane of polarization still at +45°. The polarizing beamsplitter resolves the beam into χ and y components, where χ orientation is defined as 0° and y orientation is defined as 90°, which have equal intensities. Ne­ glecting photodetector and preampli­ fier noises, the respective photoinduced voltages, Vx and V„, are equal. If net OA is present in the flow cell, the plane of polarization is rotated away from +45° so that the polarizing beamsplitter resolves the rotated beam into unequally intense components. Then 7X and Vy are also unequal. Recovery of the Ο A is via the following expression (4): 1 180

the flow cell with alternating hand­ ednesses of circularly polarized light (or, more generally, elliptically polar­ ized light). One possible measure­ ment scheme is shown in Figure 6. The principle of operation of the in­ strument is straightforward. The photoelastic modulator, driven by the squarewave from the function generator, converts noisy, linearly

Vx - VA

where θ is the ΟA in degrees. In Fig­ ure 5, this equation is implemented by the "equation" block, available in Extend's generic library. This block is quite powerful; it is like having BASIC in a block. How well does Figure 5 work? Running it with starting and ending times of 0 and 6 s, respectively, and a time step of 0.01 s (in 26 s of real time) yields results such as those in Figure 4b. Again, the plot displays very little noise because the OAs are large, the photodetector and pream­ plifier noises are very small, and this scheme is essentially a double-beam configuration. The oppositely signed OAs of peaks 4 and 5 are evident. Also the absorbances have had little effect on the measurement. Another possibility involves mea­ suring the CD. This involves probing

Figure 4. Typical temporal response produced by the model in (a) Figure 3 and (b) Figure 5. Peak parameters are listed in Table II.

Figure 5. Instrument model for simulating the measurement of optical activity. Light source has 1 -μνν intensity and « 0.12% Gaussian-distributed, band-limited (1 mHz-10 Hz) Ml intensity noise. Preamplifier noise is - 3 nV/(Hz)1'2. Equation is given in text. ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993 · 1033 A

REPORT polarized light into noisy, circularly polarized light. The handedness al­ ternates, at 100 Hz, between right circular polarization (RCP) and left circular polarization (LCP). In the absence of CD in the flow cell, both the RCP and the LCP are equally ab­ sorbed. In the presence of a net CD, the RCP and the LCP are unequally absorbed, resulting in a 100-Hz square wave variation in the trans­ mitted light intensity. The lock-in amplifier (LIA) provides phasesensitive detection (demodulation) of the photoinduced voltages, extract­ ing any CD signal at 100 Hz, while rejecting the low-frequency transmittance envelope of the photoinduced voltage. Running Figure 6 with starting and ending times of 0 and 6 s, re­ spectively, and a time step of 1 ms, yields the result shown in Figure 7. The photoinduced voltage, offset by —1 V to avoid evoking the step re­ sponse of the LIA, is shown at the top of the figure. The LIA output is shown at the bottom. The model sim­ ulates peaks 3 and 5, which have significant CD response, as expected, and the plot is noisy. This is because of the single-beam nature of the measuring scheme and the use of a small LIA time constant of 0.1 s. Ideally, the time constant should be long relative to the period of the ref­ erence frequency, which is 10 ms in Figure 6, but not long relative to the peak widths to be recovered. With longer simulated chromatographic peaks, measured in minutes rather than seconds, the time constant could be increased and the noise would be reduced. However, the sim­ ulation run time (467 s of real time) would be greatly increased. A nonmodulated CD measurement config­ uration, analogous to the absorbance and OA schemes, would be much faster in terms of simulation time. Whether it would provide better per­ formance is another matter. The three examples in Figures 3, 5, and 6 clearly show that the flow cell yields a response dependent on precisely how the flow cell is probed (i.e., on the type of instrument of which it is a p a r t ) . None of the three instrument schemes is opti­ mal in any sense, so it is likely that better performance may be obtained by using different instrument con­ figurations. The easiest way to find out is to start with a model that uses real experimental parameters, from the laboratory or the litera­ ture, and then widen the scope of the exploration. It pays to be care­ ful and methodical, but it is essen­

Figure 6. Instrument model for simulating the measurement of circular dichroism. Light source has 1 -μ\Λ/ intensity and - 0.12% Gaussian-distributed, band-limited (1 mHz-10 Hz) Ml intensity noise. Preamplifier noise is - 3 nV/ (Hz)1'2.

Figure 7. Typical temporal response produced by model in Figure 6.

tial to be adventurous — a much better instrument design may be only a few blocks away! The choice of software is of pri­ mary importance in determining the ease and efficiency of modeling ana­ lytical instrument behavior. Trying to do the simulations shown in Fig­ ures 3, 5, and 6 (each took less than 10 min to set up) using BASIC, For­ tran, Pascal, C, a spreadsheet, or one of the mathematical processing pro­

1034 A · ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993

grams would be a very daunting en­ deavor! The near future

A drawback of the simulations used currently is that they are monochro­ matic. Frequently, this deficiency is insignificant (5-12), but sometimes it is essential to be able to process spectra. The optical calculus compo­ nent blocks have been extended so that polychromatic operation—over

as many as 1024 wavelengths or optical frequencies—is now available. This extension of the software h a s not been officially released, but a p plications have been presented ( 2 5 16) and will soon be published. A n o t h e r useful a d d i t i o n to t h e software would be I/O support for common data acquisition boards. Extend has built-in serial port support in its user-accessible programming language t h a t provides a way to interface with d a t a acquisition h a r d ware. Extend also supports the use of external function code (i.e., Hypercard XFCNs), so it is easy to add XFCNs for s t a n d a r d B A S I C - l i k e Peek and Poke functions. These are being added to the Voigt fx libraries. Extend will very likely be ported to the Windows environment by early to m i d - 1 9 9 4 , a n d t h e P o w e r P C based RISC processor systems will become available at about the same t i m e . Both of t h e s e d e v e l o p m e n t s bode well for u s e r s of t h e s i m u l a tions described, particularly with regard to the polychromatic version of the software, and it a p p e a r s to be only a matter of time before the Macintosh operating system is available on high-speed workstations.

England Academic Analytical Chemis­ try Conference, Kennebunkport, ME, October 1991. (1) Shurcliff, W. A. Polarized Light, 1st éd.; (16) Voigtman, E. Presented at the 76th Harvard University Press: Cambridge, Canadian Society for Chemistry Confer­ MA, 1962. ence and Exhibition, Sherbrooke, Que­ (2) Kliger, D. S.; Lewis, J. W.; Randall, C. E. Polarized Light in Optics and Spectros- bec, Canada, June 1993. copy, 1st éd.; Academic Press: Boston, 1990. (3) Chem. Eng. News 1990, 68(49), 29. (4) Dawson, J. B.; King, P. R.; Duffield, R. J.; Ellis, D. J. /. Anal. At. Spectrom. 1989, 4, 245. (5) Voigtman, E. Anal. Chim. Acta 1991, 246, 9. (6) Voigtman, E. Appl. Spectrosc. 1991, 45, 890. (7) Kale, U.; Voigtman, E. Appl Spectrosc. 1992, 46, 1636. (8) Voigtman, E. Spectrochim. Acta. 1992, 47B, Ε1549. Edward Voigtman received a B. S. degree (9) Voigtman, E. Anal. Chem. 1992, 64, 2590. from Rensselaer Polytechnic Institute in (10) Voigtman, E. Anal. Instrum. 1993, 1972 and a Ph.D. in physical chemistry 22,43. from the University of Florida in 1979. (11) Voigtman, E. Anal. Chim. Acta., in He was a postdoctoral associate under the press. (12) Voigtman, E. Presented at the Sci­ direction of James Winefordner for several entific and Engineering Applications of years and then joined the faculty at the the Macintosh Conference, Woburn, University of Massachusetts in 1986. His MA, August 1993. research interests include laser-based pho(13) Voigtman, E. Presented at the toacoustic and two-photon ionization Northeast Regional Meeting of the American Chemical Society XXI, Am­ studies in liquid solutions, theoretical in­ herst, MA, June 1991. vestigations of signal-to-noise theory, and (14) Voigtman, E. Presented at the quantitative computer simulations of American Chemical Society Meeting, spectrometric techniques. (Internet: New York, NY, August 1991. voigtman@chemistry. Umass. edu) (15) Voigtman, E. Presented at the New

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ANALYTICAL CHEMISTRY, VOL. 65, NO. 23, DECEMBER 1, 1993 · 1035 A