Correlation-Based Approaches to Time-Resolved Fluorimetry

Instrumentation G. M. Hieftje Department of Chemistry Indiana University Bloomington, Ind. 47405

G. R. Haugen Department of Chemistry Lawrence Livermore Laboratory Livermore, Calif. 94550

Correlation-Based Approaches to Time-Resolved Fluorimetry In the past two years, several new techniques have been introduced for the measurement of nanosecond and subnanosecond fluorescence processes (1-5). Because these methods use relatively simple instrumentation and offer exceptional time resolution and accuracy, they compete favorably with more established approaches. In this paper, an introduction to these new methods is provided, and their capabilities and limitations are assessed. Because the new correlation-based techniques have their bases in a field termed linear response theory, let us briefly review the basic precepts of that field. Linear Response Measurements

During the measurement of fluorescence decay curves, one attempts to determine the response of a fluorescing molecule to a pulse of radiation that perturbs it. That is, the perturbing light pulse creates a transient overpopulation of a chosen excited state, which then decays with time. In turn, this decay can be monitored by following the time-dependent fluorescence of the molecule. This time-dependent decay, which is the information sought, can be viewed as the impulse response function of the fluorescing sample, according to linear response theory (6). Conveniently, individuals working with linear response theory have developed alternative approaches to obtain the same kind of information; these alternative schemes can be applied profitably to time-resolved fluorimetry. To understand these alternative schemes, let us view impulse-response measurements from a more general 0003-2700/81 /0351-755AS01.00/0 © 1981 American Chemical Society

viewpoint. As seen in Figure 1, an impulse response is elicited from any system that is perturbed by an extremely brief (impulsive) energy source. Ideally, the impulsive perturbation should be infinitely narrow; that is, it should approach a mathematical delta function. If this goal is realized, the Fourier transform of the perturbing pulse will be flat; in other words, it will contain all frequencies. Therefore, the response elicited by the perturbation should also contain all frequencies, except those that have been distorted, attenuated, or phase shifted. Accordingly, it seems reasonable that alternative perturbing waveforms could be used to obtain the

same information, obviating the need for brief, high-energy pulses. Of course, the alternative waveform, like the impulse, must contain a broad range of frequencies. The most general waveform of this kind is broadband or "white" noise. White noise, like a delta function, contains all frequencies. However, the frequency components in the noisy waveform are unrelated in phase. Therefore, the response of the tested system to a noisy perturbation will also appear noisy. However, the noisy response will not be the same as the perturbing waveform, but will have frequency components that are attenuated, distorted, and phase-shifted

In

Out Instrument

Time

Time

Figure 1. Generation of an impulse response function by application of an impulse (mathematical delta function). The system undergoing testing might be an instrument, a chemical system, or, in the present discussion, a fluorescing sample. In this case, the perturbing impulse is a brief pulse of exciting light ANALYTICAL CHEMISTRY, VOL. 53, NO. 6, MAY 1981 • 755 A

seconds, stringent instrumental requirements are placed on the correlation fluorimeter of Figure 4. First, the monitored fluorescence fluctuations must be observed on a nanosecond time scale, requiring an extremely fast correlation computer. In addition, because of the necessary short-term nature of the fluctuations, the source . must be modulated at frequencies beyond 1 GHz. Let us first examine sources that exhibit such high-frequency fluctuations and might therefore prove suitable for correlation fluorimetry.

Autocorrelation

White Noise

Impulse

Figure 2. Autocorrelation of a random waveform such as white noise produces an impulse

much like those in the impulse when it is employed. From these considerations, it is evident that the noisy response contains the same information as the impulse response function but that the information has a different form. The "trick" is then to process the information in the noisy response to make it appear like the more familiar impulse response. The trick to be used in this case is correlation (7). As portrayed in Figure 2, autocorrelation of a random waveform (white noise) produces a delta function. This result occurs because autocorrelation phase relates all frequency components in a waveform. When this phase registration occurs, all the frequency components add constructively at the phase-related point. However, at all other locations, the waves cancel each other, to produce a net value of zero. Therefore, the overall result is the production of a sharp, impulselike waveform. Similarly, it is possible to produce the impulse response function simply by cross-correlating a random waveform that perturbs a tested system with the apparently noisy response it elicits. This behavior, shown schematically in Figure 3, can be understood by recalling that autocorrelation is merely the cross-correlation of a waveform with itself. In the present case, however, the random perturbing function is being cross-correlated with a waveform that resembles it, but which has removed from it or changed within it several frequency components. Therefore, the resulting correlation waveform cannot rise and fall with infinite sharpness as does the delta function, but instead changes more slowly. In other words, it is identical to the impulse response function.

ure 4. In the correlation fluorimeter, a randomly modulated light source is employed instead of one that is pulsed. In turn, the random fluctuations in light intensity from the source are cross-correlated with the apparently random fluctuations in fluorescence it generates; from the correlation computer an output should result that is the desired fluorescence decay curve. As we will show later, some configurations will permit the use of a spectrum analyzer in place of the correlation computer. Because the correlation computer will probably be electronic in nature, it must process electrical rather than optical signals and will therefore require a fast photodetector to monitor fluorescence fluctuations; fluctuations in the modulated source intensity will be monitored from the source modulator itself. In the instrument, excitation and emission monochromators would probably be incorporated to enable the experimenter to select specific wavelengths to excite the desired fluorophore and at which fluorescence is to be measured. Because fluorescence decay curves are seldom longer than several nano-

Sources

The most general source for producing high-frequency fluctuations is a simple white-light lamp like a tungsten bulb. Although such a lamp cannot be modulated at high frequencies, it inherently produces quantum noise that is by nature extremely broadband (i.e., white). Unfortunately, the light from such a source also generates shot noise from any photodetector used to monitor fluorescence fluctuations. Careful mathematical analysis (8) then shows that such a source, if used with correlation fluorimetry, would yield under optimal conditions a signal-to-noise ratio no higher than one! Clearly, the source would be unsuitable for such an application. What is needed is a source having a modulation amplitude much higher than that produced by quantum noise. Such a source is a continuous-wave (CW) laser. Laser mode noise, which is often discussed but poorly characterized, can be qualitatively described as the "beating" of laser modes with each other. This beating produces in the output of the laser an apparent amplitude modulation at discrete frequencies separated by an amount equal to the laser's mode spacing. Moreover, these beats extend to frequencies as high as the laser's emission band-

Out Random Perturbation

System under Test

Impulse Response Cross Correlator Function

Linear Response Fluorimetry

Translating these concepts to the measurement of fluorescence lifetimes establishes instrumental requirements for a correlation fluorimeter (2). Such a fluorimeter might appear as in Fig-

Figure 3. From linear response theory, a system to be tested can be perturbed with a random waveform and still yield the impulse response function (fluorescence decay curve in the present study). However, it is necessary to employ cross-correlation to phase-relate the frequency components in the perturbing and response waveforms

756 A • ANALYTICAL CHEMISTRY, VOL. 53, NO. 6, MAY 1981

Fluorescence Cell Source Excitation Monochromator Emission Monochromator

Random Modulator Cross-Correlation Signal

Correlation Computer

High-Speed Photodetector

Spectrum Analyzer

Figure 4. Schematic diagram of a hypothetical correlation fluorimeter. See text for discussion (reproduced with permission from reference 2)

width. Because the mode spacing in a laser is equal to c/2L, where c is the speed of light and h is the distance be tween the laser's mirrors, a CW laser will appear to be amplitude modu lated at frequencies of c/2L, 2c/2L, 3c/2L,. . . nc/2L, where η is the num ber of modes oscillating within the laser. For typical ion lasers (e.g., an argon ion laser), L is ~ l m , making c/2L = 150 MHz. Moreover, in such a laser, as many as 30 modes oscillate, indicating that the laser will appear to be amplitude modulated at discrete frequencies of 150 MHz, 300 MHz, 450 MHz, etc., up to frequencies as high as 4.5 GHz. Because these amplitude modulations are relatively large, the laser serves as a nearly ideal source for correlation fluorimetry.

pulse response function (fluorescence decay curve) can then be calculated by Fourier transformation of the mea sured power spectrum. An instrument useful for correlation fluorimetry based on a power spec trum measurement is portrayed in Figure 5 (1). To appreciate how this instrument performs, let us perform two hypothetical experiments. In the first experiment, the sample cell shown in Figure 5 will be filled with a scattering suspension, so the photodetector monitors fluctuations in scat tered radiation that mimic those in

the laser. In this case, the microwave spectrum analyzer will produce a plot that shows the frequency composition of the laser's fluctuations; such a plot reveals that the laser's output radiant power fluctuates over a broad range of discrete frequencies. In the second experiment per formed with the apparatus of Figure 5, we will monitor the fluctuations in sample fluorescence induced by the fluctuating laser light. Although the laser's discrete-frequency fluctuations all occur simultaneously, we can un derstand their effect by considering the frequency components individual ly. For the lowest frequency compo nents (recall c/2L = 150 MHz for a laser whose cavity is 1 m long), the fluorescing molecule's excited state would be short enough in lifetime to enable it to follow the variations in laser output intensity. Therefore, the excited-state population of the fluorophore will increase and decrease as the laser varies, producing a similar fluc tuation in fluorescence. Accordingly, the spectrum analyzer will register a large amplitude in fluorescence fluctu ation at that particular frequency. In contrast, high-frequency fluctuations in the laser cannot be followed by the fluorophore's excited-state popula tion, because of the finite excitedstate lifetime. Accordingly, there will be no fluctuations in fluorescence at the high frequencies, and the ampli tudes at those frequencies plotted by the spectrum analyzer will be low. Clearly, between these extremes a slow roll-off will occur. More impor tantly, the form of the roll-off can be understood by recognizing that it is

Scattering

Cross-Correlation Computer

Calculation of the correlation func tion for correlation fluorimetry has taken two forms. In the first approach, it is recognized that nanosecond corre lators are relatively complex, and an alternative function is calculated from which the correlation waveform can be deduced. In the second approach, the correlation function is itself evaluated directly. Spectrum Analysis Approach. The first of these approaches is based on the fact that the autocorrelation function of a waveform is the Fourier transform of its power spectrum. Whereas it would seem at first glance difficult to determine a nanosecond correlation function, it is relatively straightforward to measure a gigahertz power spectrum, simply through use of a microwave spectrum analyzer. If desired, a waveform related to the im

Laser

Frequency Detector

Fluorescence

Sample

Spectrum Analyzer

Frequency

Figure 5. Illustration of the spectrum analysis route to correlation fluorimetry. Hy pothetical instrument shown on left. Top spectrum on right reflects frequency com position of laser mode noise; bottom spectrum indicates the high-frequency roll-off in these fluctuations, which would be expected in sample fluorescence excited by the laser


Laser

AVG

Figure 6. Cross-correlation route to linear response fluorimetry. Laser might be ei ther CW (containing mode noise) or mode-locked (repetitively pulsed). BS, beam splitter, which reflects part of laser power to high-speed photodetector D2; C, sample cell (for molecular fluorimetry) or flame (for atomic fluorescence); D 1 , fast photodetector to monitor sample fluorescence; M, microwave mixer serving as high-speed multiplier; AVG, low-pass filter serving as time averager; Δ Χ , spatial displacement of detector D2, which produces the time delay (τ) needed in crosscorrelation; C12 (τ), cross-correlation output (fluorescence decay curve) suitable for tracing on a strip-chart recorder

the frequency-domain equivalent of the time-domain exponential decay. Thus, the roll-off should be Lorentzian, which is the Fourier transform of an exponential. Significantly, excitedstate lifetimes can be found directly from the Lorentzian plot without re sorting to Fourier transformation into the time domain. Using suitable units for the horizontal axis, it is possible to extract the excited-state lifetime as simply the reciprocal of the Lorent zian half-width. The frequency-domain plots that are obtained using the power-spec trum approach are seldom as clean as those portrayed in Figure 5 (1). In stead, one finds that the discrete-fre quency peaks caused by laser mode noise are not all the same amplitude, ' requiring that the corresponding fluo rescence plots be normalized. That is, the mode-noise amplitudes at any two frequencies are often different, pro ducing different amplitudes in the flu orescence fluctuations at those frequencies. However, at any frequen cy, the fluorescence fluctuations are proportional to those in the mode noise; normalization then involves simply dividing the peak amplitudes measured in the fluorescence plot by those observed in the scattering exper iment. Such normalization, it has been found (2), yields excellent Lorentzian plots from which the desired lifetime information can be extracted. Impor tantly, such division in the frequency domain is equivalent to deconvolution in the time domain. Deconvolution is ordinarily necessary in time-resolved

fluorimetry but, significantly, becomes trivial when this method is employed. Correlation Fluorimeter. In the second approach to correlation fluo rimetry, an optoelectronic network is constructed to measure directly the cross-correlation function between the fluctuating laser source and the re sulting fluorescence variations. A sim plified schematic diagram for such a device is shown in Figure 6. To under stand the operation of this correlation fluorimeter, it is useful to remember the nature of the correlation process, which can be represented by equation 1. Cl, 2 (τ) =

lim — J_+T

Bx(t) B2(t - r) di (1)

Mathematically, correlation is sim ply a process involving multiplication, time shifting, and time averaging. To generate the cross-correlation [Ci,2 (τ)] between two waveforms [Bi(t) and B2(t)], the two waveforms must be multiplied, their product time-averaged, and the time average expressed as a function of a delay or displacement (τ) between the two waveforms. This mathematical opera tion is implemented in a straightfor ward way in the instrument of Figure 6. Fast photodetectors are employed to monitor the laser and fluorescence signals, respectively, and these signals are sent to an optoelectronic network, which performs the cross-correlation.


Multiplication, which must be done in an extremely high-speed system, is ac complished in a microwave mixer, a common component which serves well as a multiplier over several decades. After this multiplication step, time av eraging is accomplished through use of a simple low-pass electronic filter. Fi nally, displacement of the waveforms with respect to each other can be ac complished by means of an optical delay line. That is, an increment in delay can be effected just by displac ing spatially one of the detectors with respect to the other. In particular, be cause light travels at 3 Χ 10 10 cm/s, moving one of the detectors back a distance of 1 m will delay the optical signal it receives by approximately 3 ns. Accordingly, changing the position of the detector then enables one to smoothly vary the temporal displace ment between the two waveforms. A strip-chart recorder connected to the output of the averager (low-pass filter) will then trace out the fluorescence decay curve as displacement is swept (3). To understand more readily the op eration of this cross-correlation fluo rimeter, let us consider using a deter ministic (repetitively pulsed) input waveform rather than a random one (4). That is, let us use a mode-locked laser rather than one that operates in a CW fashion. In such a mode-locked (repetitively pulsed) laser, it can be shown that the time behavior of the laser's output amplitude has the same frequency composition as the mode noise in the CW laser, even though the waveforms are different. In particular, the output of a mode-locked laser is a train of extremely narrow pulses that appears at a rather high frequency. Typical values are 1-200 ps for the pulse width and 80-100 MHz for the pulse repetition rate. If such a laser is employed in the correlation fluorime ter, the photodetector used to monitor it will generate an electrical pulse which mimics that of the laser. In ad dition, the photomultiplier employed to monitor fluorescence will also pro duce a pulsed output in response to the laser's excitation. These wave forms are shown schematically in Fig ure 7. When the waveforms produced by the two photodetectors are multi plied, the product is a waveform that is zero except during the time when the laser pulse strikes the photodetec tor monitoring it. During that time, the output of the multiplier is propor tional to the product of the ampli tudes of the laser and the fluorescence decay curve. Therefore, this product signal is a time-sampled representa tion of the fluorescence signal at one particular time in its history. Because the laser is repetitively pulsed, this time sampling occurs over and over

Fluorescence Signal

Photodiode Signal

Multiplier Output

Cross Correlation

Figure 7. Schematic illustration of concept behind correlation fluorimetry. It is as sumed that a repetitively pulsed laser is used as excitation source. See text for dis cussion again, so t h a t t i m e averaging of t h e p r o d u c t p r o d u c e s a value t h a t can be displayed on a s u i t a b l e device (e.g., s t r i p c h a r t recorder) a n d which is pro p o r t i o n a l to t h e p r o d u c t of laser a n d fluorescence signal a m p l i t u d e . S p a tially displacing t h e d e t e c t o r which m o n i t o r s either pulse t h e n shifts t h e two waveforms t e m p o r a l l y w i t h re s p e c t t o e a c h other, a n d t h e r e b y per m i t s s a m p l i n g at a different p o i n t on t h e decay curve. Clearly, t h e D C (av eraged) value registered on t h e m o n i toring device will also reflect t h i s c h a n g e d value. S m o o t h l y sweeping t h e d i s p l a c e m e n t of t h e t w o d e t e c t o r s should t h e n p e r m i t t h e e n t i r e decay curve t o be traced. In essence, t h e op toelectronic cross-correlator b e h a v e s like a boxcar i n t e g r a t o r in t h i s appli cation (9). A l t h o u g h t h i s s t r a i g h t f o r w a r d ex p l a n a t i o n m i g h t seem less e l e g a n t t h a n t h e e x p e r i m e n t in which a CW laser is employed, it can be shown t h a t a pulsed laser p r o d u c e s higher signalto-noise ratios. Careful analysis of var ious m o d u l a t i o n a n d d e t e c t i o n s c h e m e s has b e e n carried o u t a n d h a s shown t h i s l a t t e r a p p r o a c h t o be a m o n g t h e m o s t useful (8). Comparison with Other Techniques I t is a p p r o p r i a t e t o c o m p a r e t h e cor relation fluorimetric a p p r o a c h with o t h e r s c o m m o n l y used for m e a s u r i n g excited-state lifetimes. T h e m o s t com m o n of t h e s e m e t h o d s , t h e t i m e - c o r r e lated single-photon t e c h n i q u e (10), of fers high t i m e resolution, exceptional ly high sensitivity, a n d relatively accu

r a t e lifetime m e a s u r e m e n t s . Also, like t h e correlation fluorimetric m e t h o d , it p r o d u c e s complete fluorescence decay curves (or t h e i r f r e q u e n c y - d o m a i n c o u n t e r p a r t s ) , enabling one t o verify e x p o n e n t i a l behavior in a m o n i t o r e d signal. T h e r e f o r e , it is with t h i s m e t h od t h a t p r i m a r y c o m p a r i s o n will be made. I n t e r m s of sensitivity, one would a n t i c i p a t e t h e single-photon m e t h o d t o be superior. Moreover, because t h a t m e t h o d relies u p o n t h e d e t e c t i o n of single p h o t o n s , light source intensities m u s t be very low, resulting in very lit tle p h o t o d e c o m p o s i t i o n of a m o n i t o r e d s a m p l e . However, t h e necessary t i m e for d e v e l o p m e n t of c o m p l e t e flu orescence d e c a y curves is often incon veniently long with t h e single-photon a p p r o a c h , especially for long-lived fluorophores. F o r e x a m p l e , it is n o t u n c o m m o n for c o m p l e t e curves t o re q u i r e i n s t r u m e n t a l t i m e s as long as one h o u r for such a m e t h o d , c o m p a r e d t o m e a s u r e m e n t t i m e s of 6 s t o 1 m i n for correlation fluorimetry. T i m e resolution in t h e two tech niques should be c o m p a r a b l e , espe cially if laser sources are employed. W i t h such a source, t h e s i n g l e - p h o t o n a p p r o a c h would g e n e r a t e s o m e w h a t b e t t e r t e m p o r a l r e s p o n s e (11), since it relies for t i m e resolution u p o n d e t e c tion only of t h e leading edge of a p h o t o d e t e c t o r pulse; in c o n t r a s t , correla tion fluorimetry r e q u i r e s d e t e c t i o n of t h e entire p h o t o d e t e c t o r response curve. However, it is m o r e c o m m o n t o employ h i g h - p r e s s u r e flash l a m p s as sources in s i n g l e - p h o t o n fluorimetry,


leading t o poorer t i m e resolution b u t a t lower cost t h a n in t h e correlation fluorimetric m e t h o d . P e r h a p s t h e m o s t significant a d v a n tage of t h e new l i n e a r - r e s p o n s e - b a s e d t e c h n i q u e s is their ability t o m e a s u r e decay t i m e s of self-luminous samples. A l t h o u g h such s a m p l e s d o n o t ordi narily arise in c o n v e n t i o n a l solution fluorimetry (except for some p h o s p h o r e s c e n t or c h e m i l u m i n e s c e n t samples), t h e y are u n a v o i d a b l e w h e n t h e fluo rescence of a t o m s is m e a s u r e d . U n d e r s t a n d a b l y , t h e single-photon t e c h n i q u e c a n n o t t o l e r a t e t h e presence of stray p h o t o n s , such as those e m i t t e d b y h o t a t o m s in a flame or b y t h e flame itself, since such p h o t o n s will cause pretriggering of t h e detection s y s t e m a n d t h u s yield e r r o n e o u s decay curves. In c o n t r a s t , t h e r e is n o p e n a l t y t o be p a i d in correlation fluorimetry w h e n l u m i n o u s s a m p l e s a r e employed, except for a slight loss in signal-tonoise r a t i o caused b y p h o t o d e t e c t o r shot noise. It is in t h i s l a t t e r class of m e a s u r e m e n t s t h a t correlation fluo r i m e t r y should find its g r e a t e s t appli cation. In our laboratories, we are employ ing such t e c h n i q u e s for t h e m e a s u r e m e n t of s t e a d y - s t a t e lifetimes of a t o m s in vapor cells a n d in analytical sources such as flames a n d p l a s m a s . In a d d i t i o n , we have found t h e basic con cepts e m b o d i e d in linear response t h e o r y t o have i m p o r t a n t application in t h e m e a s u r e m e n t of a b r o a d r a n g e of t i m e - d e p e n d e n t chemical p h e n o m e na; t h e s e applications c u r r e n t l y are being explored. I n c l u d e d a m o n g t h e m are new a p p r o a c h e s t o t h e m e a s u r e m e n t of p h o t o l y t i c reaction r a t e s , r a d ical-initiated chemical reactions, a n d t h e s t u d y of s t a t e - t o - s t a t e kinetics. It is our h o p e a n d belief t h a t t h e s e same concepts will be useful t o m a n y read ers a n d will prove to be powerful tools in chemical analysis, m e a s u r e m e n t , and characterization. Acknowledgment T h e a u t h o r s are i n d e b t e d t o R. E. Russo, J. M. R a m s e y , a n d B . H i t e s for t h e i r assistance in p r e p a r i n g some of t h e figures used in t h i s p a p e r . Work on this paper was supported in part by the Public Health Service through NTH grant GM24473 and by the Office of Naval Research. References (1) Hieftje, G. M.; Haugen, G. R.; Ram sey, J. M. Appl. Phys. Lett. 1977, 30, 463-6. (2) Hieftje, G. M.; Haugen, G. R.; Ramsey, J. M. In "New Applications of Lasers to Chemistry"; Hieftje, G. M., Ed., ACS Symposium Series no. 85; American Chemical Society: Washington, D.C., 1978; ρ 118. (3) Dorsey, C. C ; Pelletier, J. M.; Harris, J. M. Rev. Sci. Instrum. 1979,50, 3336. (4) Ramsey, J. M.; Hieftje, G. M.; Continued on page 765 A

Haugen, G. R. Appl. Optics 1979, 18, 1913 20 (5) Ramsey, J. M.; Hieftje, G. M.; Haugen, G. R. Rev. Sci. Instrum. 1979, 50 997-1001 (6) Hieftje, G. M.; Vogelstein, Ε. Ε. In "Modern Fluorescence Spectroscopy"; Wehry, E. L., Ed., Plenum: New York, N.Y., in press. (7) Horlick, G.; Hieftje, G. M. In "Con temporary Topics in Analytical and Clinical Chemistry"; Hercules, D. M.; Hieftje, G. M.; Snyder, L. R.; Evenson, Μ. Α., Eds.; Plenum: New York, N.Y., 1978; Vol. 3, ρ 153. (8) Ramsey, J. M. Ph.D. Dissertation, In diana University, 1979. (9) Hieftje, G. M. Anal. Chem. 1972, 44 (7),69A-78A. (10) Shaver, L. Α.; Cline-Love, L. J. In "Progress in Analytical Chemistry"; Simmons, I. L.; Ewing, G. W., Eds., Ple num: New York, N.Y., 1976; Vol. 8, ρ 249. (11) Koester, V. J.; Dowben, R. M. Rev. Sci. Instrum. 1978, 49, 1186-91.

Gary Hieftje

Gil Haugen Gary Hieftje is professor of chemistry at Indiana University. He received his PhD in 1969 from the University of Illinois under the direction of H. V. Malmstadt. His research interests in clude the investigation of basic mech anisms in atomic emission, absorp tion, and fluorescence spectrometric analysis, and the development of atomic methods of analysis. He is also interested in on-line computer con trol of chemical instrumentation and experiments, the use of time-resolved luminescence processes for analysis, the application of information theory to analytical chemistry, and the use of stochastic processes to extract basic and kinetic chemical informa tion. Gil Haugen is a senior scientist asso ciated with the Chemistry and Mate rials Science Department at Law rence Livermore National Laborato ry. He received his PhD in chemistry from the University of Southern Cali fornia in 1960. His interests are in chemical kinetics, photochemistry, and the application of lasers in chem ical measurements.

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Correlation-Based Approaches to Time-Resolved Fluorimetry

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