A Deconvolution Technique for Determining the Intrinsic Fluorescence Decay Lifetimes of Crude Oils

M. F. QUINN,* S. J O U B I A N , F. AL-BAHRANI , S. AL-ARURI, and O U S S A M A A L A M E D D I N E Electronics Department, Engineering Division, Kuwait Institute [or Scientific Research, P.O. Box 24885, 13109, Safat, Kuwait (M.F.Q., S.J., F.A., S.A.) and Kuwait Scientific Center (IBM), P.O. Box 4175, Safat, Kuwait (O,A.)

A simple deconvolution procedure using FT was developed for deter- mining the average lifetime of samples excited by a nitrogen laser pumped dye laser operating at 428 nm. To overcome the noise limitations imposed by including higher frequency harmonics in the analysis, we used an alternative approach. This approach relied on taking the Fourier trans- form at 21 subharmonic frequencies and using an appropriate weighting procedure in the calculation of amplitude and lifetime of the sample impulse respom~e. A single exponential decay was assumed.

Index Heading~,~: Fluorescence; Fluorescence spectroscopy; Fluorescence lifetimes.

INTRODUCTION

Ultraviolet/visible radiation induced luminescence from plants, rocks, oils, etc., may be used to characterize these species. 1,2 The spectral features are frequently used for the characterization. However, the temporal behavior of the luminescence (generally the lifetimes or decay times are measured) has been considered as a possible char- acterization parameter, particularly where spectral fea- tures are not easily identified2 ,4 Measurements of this nature are often carried out with the use of a laser to excite luminescence in the species under investigation. One of the problems encountered in lifetime determi- nations is that the excitation laser pulse width is very often of the same order of magnitude as the lifetime of the species under investigation, i.e., a few hundred pi- coseconds (ps) to 20 nanoseconds (ns). It is necessary in these circumstances to deconvolute, using mathematical techniques, ~he excitation pulse profile from the mea- sured luminescence pulses. 5 In addition, it is generally necessary to deconvolute the finite response of the de- tection electronics in order to determine the intrinsic lifetimes of the species.

A fluorescence lifetimes measuring system was set up in our laser laboratory to measure fluorescence lifetimes of species wiLh decay times in the range 200 ps to 50 ns. The fluorescence lifetimes of many materials of interest fall within this range. A mathematical procedure was developed to deconvolute the laser pulse and detection electronics response from the measured pulse, thus al- lowing for the determination of intrinsic lifetimes. The measurement and deconvolution procedures are de- scribed below.

Received 19 June 1987; revision received 6 October 1987. * Author to whom correspondence should be sent.

EXPERIMENTAL SYSTEM

The experimental system for exciting the lumines- cence in the sample was described previously2 A dye laser pulse (duration 3-4 ns), tuned to 428 nm, was fo- cused on the sample. The resulting luminescence was collected by an optical system and directed onto a mono- chromator, where wavelength dispersion occurred. The bandwidth of the monochromator was set to 8 nm. By sequentially scanning over 20 nm steps, we were able to cover a spectral range from 460 nm to 720 nm.

The luminescence light collected at the selected wave- length band was led through an optical light guide onto the cathode of a high-speed photomultiplier (Hama- matsu R955, risetime 1 ns). The output of the photo- multiplier was led to a digitizer (Tektronix 7912 AD), where signal averaging and waveform digitization oc- curred. The digitized signal was then transferred to an IBM-PC and eventually to an IBM 4341 mainframe com- puter for processing.

THEORETICAL CONSIDERATIONS

The observed decay curves from the fluorescent sam- ple, excited by a short laser pulse, are distorted by the finite duration of the excitation pulse and by the limited frequency response of the detection system. Assuming linear behavior of the fluorescence and the apparatus, the measured decay curve [ ( t ) is given by the convolution integral:

f ( t ) = l ( t ) * h ( t ) * a ( t ) (1)

where:

l ( t ) = excitation pulse h ( t ) = impulse response of sample a ( t ) = impulse response of apparatus.

Similarly, the measured apparatus response e (t) to the laser excitation pulse (without sample) is:

e ( t ) =- l ( t ) * a ( t ) . (2)

If it is assumed that a (t) is independent of wavelength, then, since convolution is commutative, the following relation is valid:

[ ( t ) = e ( t ) * h ( t ) . (3)

That is, the measured apparatus response acts like an excitation pulse, as far as fluorescence decay is con-

406 Volume 42, Number 3, 1988 0003-7028/88/4203-040652.00/0 APPLIED SPECTROSCOPY © 1988 Society for Applied Spectroscopy

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FIG. I. Fluorescence deconvolution using FFT gives the impulse response h(t) of the fluorescence from a laser-excited crude oil sample. Ordinate: amplitude (arbitrary units); abscissa: time (ns).

cerned. In the frequency domain, the above equation can be easily deconvoluted:

H(w) = F(~o)/E(~o) (4)

where H(w), F(¢o), and E(¢o) are the Fourier transforms of h(t), [(t), and e(t), respectively. A direct retransfor- mation of H(~0) into the time domain by discrete inverse FFT would yield a signal h(t), which represents the oil response.

A directly recovered impulse response h(t), for a typ- ical crude oil sample, is shown in Fig. 1. We calculated the function h (t) by taking the inverse fast Fourier trans- form (FFT) of H(w). It is easily seen that the signal is totally submerged in noise and that the application of the (FFT) procedure is unacceptable. The reason for such a large noise can be explained by referring to the locus of H(~0) plotted in Fig. 2. The initial part of this curve (the first two harmonics are labelled 0 and 1) rough-

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F(w) Locus of H(w) [first 15 harmonics], where H(w) = E~)" Ordinate: imaginary axis; abscissa: real axis.

ly fits a semicircle. Taking further harmonics leads pro- gressively to larger and larger oscillations, which have random directions. The source of these oscillations lies in the error of the quotient F(w)/E(w).

The functions F(w) and E(w) become smaller with higher w, but their quotient can take any value if their associated errors, AF(w) and AE(w), are roughly constant in magnitude, i.e.,

F(~) + AF(~) tt(o:) + AH(~) = (5)

E(~) + ~E(~)

and H(w) shows strong fluctuations with decreasing E(~0) and F(w).

To show the behavior more clearly, we have plotted in Fig. 3 the locus of H(w) for the first fifteen harmonics only (labeled 0-14). The semicircular behavior in the upper quadrant in Fig. 3 [indicating an exponential h (t)], is readily apparent. Uncertainties start to predominate at the fifth harmonic and eventually lead to the total submergence of the true signal in noise by the eleventh harmonic.

Assuming eL first-order sample decay of the form

h*(t) = A exp - (t/r) (6)

where r represents an "effective" time constant of the various species composing the sample, the following equation may be applied:

H*(o:) = Ar/(io:r + 1) (7)

where H*(w) :is an "effective" sample transfer function. By fitting tt*(o:) with H(~) in the Fourier space, one

can determine the intrinsic parameters A and r of the sample. It car, easily be shown then that:

1~At = Real E(~o)/F(o:) (8a)

and

1/A = Imag E(w)/wF(w). (8b)

Any set of E(~0) and F(~0), determined for a given fre- quency ~0 ¢ 0, is sufficient to determine A and r. However, it is better to determine the above quotients for a large number of frequencies and to calculate l iAr and 1/A by least-squares fitting techniques.

Because of the limitations imposed by taking a large number of harmonics as mentioned above, an alternative approach was necessary.

This approach was based on the following:

If Wo defines the fundamental frequency (first har- monic), then the Fourier transform g(~0) of f(t) may be calculated at 21 subharmonic equidistributed frequen-

~0o 2~o 10¢0o 20¢°° covering the range 0 to cies 0, 10' 10 . . . . 10 "'" 1--0-' 2Wo, where

g(w)=~__+=f(t)e-i~tdt._ (9)

With the use of this procedure, 21 subharmonic values of the quotients E(w)/F(w) and E(w)/wF(¢o) may be de- termined. A and r may then be determined by least- squares fitting techniques through the 21 sets of values.

The use of subharmonics in the direct FT calculation was found to yield the best results, provided a suitable weighting procedure was utilized in the calculations. The weighting procedure is briefly discussed below.

Since E(w) and F(w) are determined numerically [from experimentally measured time functions e(t) and f(t)], a number of errors are introduced into the procedure. These are as follows:

1. Measurement errors on e(t) and f(t).

408 Volume 42, Number 3, 1988

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FIG. 4. The effective averaged first-order decay lifetimes of (a) a light, (b) a medium, and (c) a heavy crude oil, in 13 fluorescence wavelength channels. The oils were excited by a nitrogen laser pumped dye laser operating at 428 nm. Ordinate: fluorescence lifetime (ns); abscissa: wavelength (nm).

2. Errors due to replacing the continuous FT by a dis- crete one.

3. Calculation errors.

These errors influence the two quantities Real E(o~)/ F(o~) and Imag E(w)/o~F(w) to different extents, as shown below.

If the quotient of two complex quantities Yl and Y2 is designated by y (i.e., y = YJY2) and if y~ = R~e i*', Y2 = R2ei% and R1 - ~ R2 -~ const -~ A (absolute error on Ri), then by straightforward error calculation it can be shown that

AR = A{Real y} = (Real y)(1 + Itan(¢l - ¢2)]) • (1/R~ + 1 / R 2 ) A (10a)

and

AI = A{Imag y} = (Imagy) (1 + ]cot(¢~ - ¢2)1) • ( l / R 1 + 1/R2) A. (10b)

It can easily be shown that AR = A/. The weighing factors for the fitting procedure are then

(A/AR) 2 for the real part

and

(A/Az) 2 for the imaginary part.

These errors have been computed for all subharmonic frequencies and used as weights in the least-squares fit- ting procedure.

RESULTS AND DISCUSSION

With the use of the above procedures it was possible to rapidly determine the closest fitting average lifetime based on first-order decay analysis. Typical results are presented in Figs. 4 and 5.

In Fig. 4, the lifetimes of three representative samples of crude oil are shown as a function of fluorescence wave- length band. These oils could be classified as (a) light (approximately 36 API), (b) medium (approximately 27 API), and (c) heavy (approximately 15 API). These curves are consistent with those reported in the literature. 7,8 We carried out a test of the goodness of the calculated life- time constant by reconvolving the calculated oil impulse response h( t ) with the excitation pulse e( t ) to regenerate f ( t ) . A regenerated f ( t ) is shown in Fig. 5 together with the original measured f(t) used to calculate the lifetime. A comparison of the two curves shows that the procedure is functioning correctly, giving a good averaged estimate of the fluorescence decay of the oil.

In these lifetime calculations presented above, the re- sponse of the apparatus was assumed to be independent of wavelength. However, it is well known 9 that the re- sponse of photomultiplier detectors is slower in the red region of the spectrum than in the blue region. To ac- count for this, we investigated the response of the pho- tomultiplier (Hamamatsu R955) used in our measure- ments. We were unable to detect any wavelength dependence in the system response and therefore con- cluded that any variations were smaller than 200-300 ps--i.e., below the measurement capability of our sys- tem.

The advantages of using the above procedure are as follows:

1. It is a relatively simple deconvolution approach. 2. It is an approach which is ideally suited to the rapid

determination of decay constants of large batches of samples.

We have used this technique to calculate the lifetimes for 14 different spectral bands of more than 500 oil sam-

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ples. D u r i n g these d e t e r m i n a t i o n s , we e s t i m a t e d the t ime for a s ingle d e c o n v o l u t i o n to be a p p r o x i m a t e l y 2.2 s, us ing a sy s t em I B M 4341 a n d A P L as the p r o g r a m m i n g lan- guage.

ACKNOWLEDGMENTS

The authors wish to acknowledge the support of the Kuwait Institute for Scientific Research (KISR), the Kuwait Environmental Protection Agency (EPC), and the Kuwait Scientific Center (IBM). We also wish to acknowledge the excellent advice given by Dr. Nabil Alyassini (KISR) and Dr. Samir Atassi (KSC/IBM) throughout the duration of the work.

1. L. Celander, K. Fredriksen, B. Yalle, and S. Svanberg, Investigation of Laser-induced Fluorescence with Applications to Remote Sens- ing of Envi,mnmental Parameters, Final Report G1PR-149 (De- partment of Physics, Goteborg Institute of Physics, Chalmers Uni- versity of Technology and the University of Goteborg, Sweden, 1978).

2. E. W. Chappelle, F. M. Wood, Jr., J. E. McMurtrey III, and W. W. Newcomb, Appl. Opt. 23, 134 (1984).

3. R. T. V. Kung and I. Itzkan, "New Concept for the Remote Mea- surement of Oil Fluorescence Conversion Efficiency," in Proceedings of the lOth International Symposium on Remote Sensing of En- vironment (1975), pp. 231-241.

4. J. P. deNeufville, A. Kasdan, and R. J. L. Chimenti, Appl. Opt. 20, 1279 (1981).

5. U. P. Wild, A. R. Holzwarth, and H. P. Good, Rev. Sci. Instruments 48, 1621 (1977).

6. M. F. Quinn, M. S. A1-Ajeel, and F. A. A1-Bahrani, Journal of Lu- minescence 33, 53 (1985).

7. R. M. Measures, H. R. Houston, and D. G. Stephenson, Optical Engineering 13, 494 (1974).

8. D.M. Rayner and A. G. Szabo, A Laboratory Study of the Potential of Time-Resolved Laser Fluorosensors, Report Number By-76-1 (RC) (National Research Council of Canada, Division of Biological Sci- ences, Montreal, 1976).

9. D. M. Rayner, A. E. McKinnar, A. G. Szabo, and P. A. Hackett, Canadian Journal of Chemistry, 54, 3246 (1976).

410 Volume 42, Number 3, 1988