Anal. Chem. 1980, 52, 101-104
LITERATURE CITED
101
(8) C. T. Burt, T. Glonek, and M. Barany, Science. 195, 145-49 (1977). (9) T. W. Gurley and W. M. Ritchey, Anal. Chem., 47, 1444-46 (1975). (IO) D. Canet, G. C. Levy, and I. R . Peat, J . Magn. Reson.. 18, 199-204
(1) J. R. Van Wazer, "Determination of Organic Structures by Physical Methods", F. C. Nachod and J. J. Zuckerman, Eds., Academic Press, New York, 1971, p 323. (2) J. R. Van Wazer and T. Glonek, "Analytical Chemistry of Phosphorus Compounds", M. Halmann. Ed., Wiley, New York, 1972, p 151. (3) M. M. Crutchfield, C. H. Dungan, J. H. Letcher, V. Mark, and J. R. Van Wazer, "31PNuclear Magnetic Resonance", Interscience Division of John Wiley, New York, 1967. (4) G. Marvel, "Annual Reports on NMR Spectroscopy", E. F. Mooney, Ed., Academic Press, New York, 1973, p 1. (5) T. C. Farrar and E. D. Becker, "Pulse and Fourier Transform NMR", Academic Press, New York, 1974. (6) F. Kasler, "Quantitative Analysis by NMR Spectroscopy", Academic Press, New York. 1973. (7) D. E. Leyden and R. H. Cos, "Analytical Applications of NMR", Interscience Division of John Wiley, New York, 1977.
(1975). (11) D. E Jones and H. Sternlicht, J . Magn. Reson., 6 , 167-87 (1972). (12) J. W. Cooper, "Topics in Carbon-I3 NMR Spectroscopy", Vol. 2, G. C. Levy, Ed., Interscience Division of John Wiley, New York, 1976, p 392, (13) R. R. Ernst and W. A. Anderson. Rev. Sci. Instrum., 37, 93-102 (1966). (14) S. W. Dale and M. E. Hobbs, J . P h y s . Chem., 75, 3537-46 (1971). (15) W. E. Morgan and J. R. Van Wazer, J . Am. Chem. Soc.. 97, 6347-52 (1975). (16) T. W. Gurley and W. M. Ritchey, Anal. Chem., 48, 1137-40 (1976).
RECEIVED for review May 2, 1979. Accepted October 25, 1979. We thank the Institute Mondial dii Phosphate, Paris, France, for financial support and interest in this work.
Dual Beam Fiber Optic Time-of-Flight Spectrometer W. B. Whitten" and H. H. Ross Analytical Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830
persion to wavelength dispersion. For a hypothetical fiber with a fused silica core, transit time dispersion with wavelength has been calculated to range from 0.07 ns nm-' km a t 900 nm to 1.1ns nm-' km-' a t 400 nm ( 1 ) . Modal dispersion can be estimated from the fiber bandwidth; for example, a bandwidth of 1 GHz km-' would correspond to a Gaussian full width a t half maximum of 0.4 ns km Fiber attenuation can be a problem a t the shorter wavelengths. While attenuations of less than 5 d B km-' are not unusual in the near infrared, the attenuation a t 400 nm might be as much as 50 d B km-'. As noted in our earlier study ( I ) , transmitted intensity can be increased substantially with only a small decrease in spectral resolution if the fiber is shortened because the transmission decreases exponentially while resolution increases linearly with fiber length. Time-correlated single photon counting techniques were used for our prototype spectrometers in both this and the previous study. The light pulses are generated by a weak spark source and attenuated so that a t most a single photon is detected per flash. The detected photons will have a wavelength distribution identical to the spectrum which would be measured by the detector under qteady, high intensity conditions. T h e arrival time relative to the flash can be determined with subnanosecond precision with commercially available instrumentation. After a large number of flashes, the transit time distribution of the detected photons is obtained. This distribution can then be related to the wavelength distribution if the dispersive properties of the fiber are known. Our earlier spectrometer ( I ) was based on an 1100-m fiber in a single beam configuration. T h a t is, sample absorbance was measured by alternately placing a sample and blank in the light path. This procedure is subject to several sources of error, the most important of which is probably variation of the spectral output of the source during the time of the measurement. In the present investigation, a dual beam spectrometer has been constructed with the original fiber divided into two unequal lengths. Photons passing through the two fibers arrive at the detector at somewhat different times so that the sample and blank spectra can be measured concurrently. Recause all measurements are in the time do-
A dual beam spectrometer has been constructed whlch uses the variation in light velocity with wavelength In an optical fiber to provide spectral dispersion in the time domain. Two fibers of different lengths constitute the sample and reference channels which are time-delay multiplexed and monitored by a single photomuitlpller. Thne-correlated single photon counting techniques provide the necessary timing accuracy for satisfactory spectral resolution.
'.
It has recently been shown that a fiber optic waveguide can serve as the dispersing medium in a time-of-flight optical spectrometer ( I ) . Characteristic features of time domain spectrometers include inherent time resolution, mechanical rigidity, and single detector operation. In this paper, we show how the combination of time delay with fiber length and wavelength dispersion can be used for dual beam operation of a fiber optic time-of-flight spectrometer. Orofino and Unterleitner (2) suggested that optical fibers be used for spectrometry in the time domain. The group velocity, ug, of a light pulse in a dispersive medium is given by
vg = c / n (1
X dn +; c)
In this expression, c is the velocity of light in vacuum and n, the index of refraction, is a function of wavelength, A. For a graded index, multimode fiber (31, all rays of a given wavelength will have about the same transit time, T , as a ray passing along the center of the fiber of length L T
= L/U,
(2)
Franks et al. ( 4 , 5 )studied the pulse broadening due to modal dispersion and wavelength (material) dispersion in a commercial graded index fiber and found that sufficient spectral resolution could be obtained to calculate the attenuation vs. wavelength of the fiber. The spectral resolution which can be obtained from a fiber optic spectrometer will be limited by the ratio of modal dis0003-2700/80~0352-0101$01 .OO/O
c
1979 American Chemical Society
102
ANALYTICAL CHEMISTRY,VOL. 52, NO. 1, JANUARY 1980
Figure 1. Block diagram of the single beam fiber optic time-of-flight spectrometer
Flgure 2. Block diagram of the dual beam fiber optic time-of-flight spectrometer
main, the instrument again requires no moving parts.
JNSTRUMENTATION A block diagram of the single beam spectrometer configuration is shown in Figure 1. Light from an Ortec model 9352 spark
source is focused by a microscope objective lens onto the fiber. In the earlier investigation, the sample and appropriate filters were placed in the narrow cone of light emerging from the source. The fiber is a Corning Corguide 5050 fiber, 1119 m long, wound in a single layer as described previously (I). The fiber is butted against the face of a cooled RCA C31034 photomultiplier tube (-30 "C). The phototube signal is amplified by two stages of an Ortec 574 timing amplifier and then processed by an Ortec 473A constant fraction discriminator. The discriminator pulse is used to stop an Ortec 457 time-to-pulse height converter which is started by a trigger signal from the light pulser; a BNC 7030 digital delay generator is used. The voltage pulses from the time-to-pulse height converter are sorted into a histogram of photon counts vs. transit time by a Tracor Northern TN1706 pulse height analyzer. The same instrumentation is used for the dual beam spectrometer but now the fiber is divided into two unequal lengths, nominally 525 and 550 m. A block diagram is shown in Figure 2. In this configuration, the light from the source is made parallel by a microscope lens, split by a beam splitter cube so that it passes through the sample or blank cuvettes (1-cm square), and then focused by two additional microscope lenses onto the two fibers. The other ends of the two fibers are butted against the photomultiplier face. Because of the difference in length between the sample and reference fibers, one spectrum is delayed with respect to the other. The two spectra can therefore be measured together if a suitable range is chosen for the time-to-pulse height converter. Time calibrations were performed with the crystal controlled digital delay generator which has f O . l ns jitter. Transit timewavelength measurements for the two fibers were made by placing interference filters before the beam splitter. The filters were checked for maximum transmission wavelength on a Cary 14 spectrophotometer. The spark gap was run with an O2atmosphere which gives a shorter duration spark at long wavelengths and has considerably less spectral structure than a lamp run in air ( I ) . The time response of various components could be checked by inserting a short fiber of about 1 m in length in place of the longer fibers. A fast source was constructed with a Ferranti XD21 gallium phosphide light emitting diode (6). The diode was driven in the reverse, avalanche, mode by an avalanche transistor circuit similar to that described by Andrews (7). The overall time response of this combination--diode source, short fiber, photo-
- 4 - 2
0
2
TIME
4
6
8
IO
(lis)
Figure 3. Time dependence of spark lamp at 500 nm L ' ( t ) l L ' q max (crosses). Also shown is the normalized asymmetrical portion, L r(t)l (Llpmax W ) used for the correction (solid curve)
multiplier, and electronics-was less than 0.7 ns. The light emitting diode has a fairly broad spectral output, from 550 to nearly 900 nm, so these diodes might be useful spectral sources under some circumstances. The response times with the Ortec lamp were longer, as discussed below.
NUMERICAL ANALYSIS Sample absorbance vs. wavelength was calculated from the sample spectrum and interpolated values for the blank spectrum at corresponding wavelengths. (The two fibers have somewhat different dispersion because of the length difference.) T h e instrumental absorbance (blank vs. blank) was subtracted to correct for the variation in instrumental response with wavelength. Dark counts were negligible. It was noticed in preliminary measurements that the slow decay of the spark lamp caused a n appreciable reduction in spectral resolution and a shape distortion of absorbance peaks. The long wavelength pulses are transmitted by the fiber with much less attenuation than those of short wavelength. Since the detector cannot discriminate between short wavelength photons and photons from the tails of faster long wavelength pulses, the apparent absorbance of a sample a t shorter wavelengths can be reduced by long wavelength stray light. Such distortions were not a serious problem with the single beam spectrometer because the fiber was twice as long with proportionally higher dispersion. Fortunately, it is possible to make an approximate correction to the measured spectrum because of the asymmetrical shape of the lamp pulse, shown in Figure 3. The normalized lamp response shown here was measured with a 1-m fiber with the same time interval per channel as the absorbance measurements with the long fibers. The asymmetrical part of the lamp response, here divided by the peak height times the full width at half maximum, is also shown. These latter data will be used to correct t h e absorbance results. It is convenient to make the corrections in the time domain since the experimental results are obtained as the number of photons counted per time interval or channel. Functions of time (or wavelength converted to the equivalent transit time)
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
will be expressed as functions of the time, t,, corresponding to the nth channel. T h e time dependence of the lamp intensity, L(ti),can be separated into two components: one part, Lp, which is symmetrical about the peak value and an asymmetrical tail, L,,
103
which can be rewritten, O(tk)
=
L(tJ)C(tl-,)T(tk-l)
r
=
I
J
L(t])T’(tk-J)
(9)
The quantity, T‘, given by Here, the integer i indexes the intervals used to measure the lamp time dependence with i = 0 corresponding to the time of peak intensity. If the symmetrical part is only a single channel wide, the measured output of the fibers can be readily corrected for the tail contribution. Now, consider the response of the entire system: lamp, sample, fibers, etc. Let the integer k index the channels in which the output counts are stored. The number of photons, O ( t k ) counted by the detector for channel k, Le., between times ( t k - t k - 1 ) / 2 and ( t k t k + * ) / 2 , will be given by
+
where T(tk) includes the sample and fiber transmission coefficients, photomultiplier quantum yield, and the wavelength variation of the lamp intensity, all at the wavelength corresponding to the transit time, t k . (In this discussion, the wavelength variation of the lamp time dependence has been neglected. Inclusion of the actual variation would be only a slight complication.) T(tk)is the quantity which is needed for calculation of the sample absorbance, A(X) after the transit times are converted t o wavelength, in
A(X) = log
Tblank(X)
-
1%
TsarnpIe(X)
(5)
There will be some channel before which there will be no significant counts, usually because of lack of photomultiplier response a t long wavelengths. The first channel, say channel m, to have a detectable number of counts will not have any contribution from tails of longer wavelength light because these wavelengths are cut off. The tail of the pulse arriving a t channel m will contribute, however, to the signal at channels m + 1, etc. The quantity T(t,) can be evaluated from Equation 4 with i = 0, so that the contribution of light pulse m a t channel m + i is just
T(tm)Lt(tJ= O ( t m ) L t ( t J / L p ( t , )
(6)
This quantity can be subtracted from all channels after m for which Lt(t,) is significant. All channels are subsequently corrected for the tails of light pulses where peaks arrive a t tm+l, t m f 2 , etc. The corrected output should then be
Lp (tO)T(tk). T h e above results apply only when most of the lamp intensity is emitted during a single channel. The time per channel is usually chosen to be less than the full width at half maximum of the light pulse to obtain optimum resolution. T h e analysis must therefore be modified to account for the effectively broader lamp time dependence. We start by assuming that the experimental lamp intensity, which has a width greater than one channel, can be approximated by broadening an ideal one-channel wide lamp response as used above. Let the ideal lamp intensity be L ( t J as before and let the broadened intensity, which is the experimentally obtained quantity, be L’(t,). We can express L’(tr)as a convolution of L(t,) with a broadening function, C(t,,),
C is assumed to be normalized so that L’and L have the same area. Then we can write
T’(tk-])
=
C(tl-])T(tk-l)
(10)
1
is an effective transmission coefficient for the fiber, sample, etc., but now with decreased resolution because of the broadening function, C. T‘ is therefore proportional to the output which would be obtained if the lamp pulse had no tail. The values of T’(tk)could be found from O(t,) by the process described above for T ( t &if the ideal lamp time dependence were known. In the spirit of the approximations used for these corrections, we assume that the one channel wide peak of the has the same area as the symideal lamp intensity, Lp(to), metrical part of the experimental intensity, L 6 Lp(t0)
=
E L’p(tr)
L’p
maxw
(11)
1
where L ’p rnax and W are the peak value and full width a t half maximum of Lb. Furthermore, since L’, is a slowly varying function of time, we have used the experimental values of L’t instead of L , to calculate the corrected spectra. The errors introduced by these approximations will be substantial only within a time W from the lamp intensity peak. The correction process is therefore to subtract the quantities O(tk)L’t(tr)/(L’p
maxw)
from the i values of 0(tk+J,for each value of t k starting before the longest wavelength light has arrived, t,. The values of L ,; L ’p -, and W are obtained from the time dependence of the flash as measured with the 1-m fiber. The number of counts remaining in each channel will now be proportional to T’. After converting to an equivalent wavelength scale for both the sample and reference spectra, the absorbance can be evaluated from Equation 5 with T replaced by T’. Corrections to the experimental spectrum for the symmetrical portion of the lamp time dependence and for the photomultiplier and electronic timing errors would require a formal deconvolution. Such processes greatly magnify the random noise present in the data (8). A partial deconvolution (8)could be performed if somewhat enhanced resolution were desired a t the expense of signal-to-noise ratio.
RESULTS The values of transit time relative to 2560 ns a t various interference filter wavelengths are given in Table I. I t can be seen t h a t the dispersion increases markedly on going to the shorter wavelengths. The different times for the two fibers result from the difference in length and hence, the different dispersions. In Figures 4 and 5 are shown, respectively, the spectrum of a sample of K M n 0 4 in 1 N H2S04without and with the correction for the lamp time dependence described above (crosses). Also shown as a solid curve is a spectrum of the same sample measured on a Cary 14 spectrophotometer. In addition to improving the spectral resolution, the correction restores the peak absorbance values to their proper size by eliminating the stray long wavelength light. For these measurements, a Corning CS 4-70 filter was placed ahead of the beamsplitter to attenuate the near infrared. DISCUSSION The dual beam spectrometer described above demonstrates several of the novel features associated with fiber optic spectrometry in the time domain: time dispersion, time-delay
104
ANALYTICAL CHEMISTRY, VOL. 52, NO. 1, JANUARY 1980
--T
Table I. Transit Time vs Wavelength for Sample and Reference Fibers, Relative to 2560 ns transit time, ns reference sample fiber fiber
wavelength, nm 697.5 677 660 639 620 600 580 559 54 1 5 20 501 48 1 460 441 418 398
170.3 172.3 174.8 177.1
50.6 53.2 55.8 58.1 61.3 63.9 67.4 71.9 76.1 81.6 87.1 93.6 101.9 110.6 120.0 131.9
x
180.6
183.9 187.4 191.3 195.8 201.9 207.4 214.8 224.2 231.9 243.9 257.4
-r------1
2 I
400
[
l
450
500
l 550
I
i
l
600
650
700
WAVELENGTH (nm) Figure 5. Same as Figure 4 but corrected for lamp time response
construct an improved dual beam spectrometer in which both sample and reference channels consisted of a series of fibers with dispersions and attenuations optimized for various wavelength ranges. The range to be measured would be selected by the digital delay generator. While these investigations have been implemented with single photon counting techniques, the principles are valid as well for single pulse, high intensity analogue measurements. I t is through these single pulse measurements t h a t the advantages of subnanosecond time resolution and rapid spectral acquisition can be realized.
W
0 Z
0
v, m
a
ACKNOWLEDGMENT
't
~ I
400
We thank J. M. Ramsey for designing and constructing the photomultiplier voltage divider circuit and for many helpful discussions.
1 ' I
I
450
500
I
I
I
550
600
650
I 700
WAVELENGTH (nrn) Figure 4. Absorbance vs. wavelength, KMnO, in 1N H,SO,, uncorrected for lamp time response. Crosses represent fiber optic measurements; solid curve, conventional spectrophotometer
multiplexing of two channels, and multiwavelength spectrometry with a single detector and rigid system. Because the fibers are only half as long as in the previous study, the effective spectral range is shifted about 50 nm to shorter wavelengths. Since resolution increases with shorter wavelength, it may be possible to obtain useful resolution with much shorter fibers and wavelengths. One could conceivably
LITERATURE CITED
I
Whitten, W. B.; Ross, H. H. Anal. Chem. 1979, 51. 417. Orofino, T. A.; Unterleitner, F. C. 'Appl. Opt. 1976, 15, 1907. Olshansky, R.; Keck, D. E. Appl. Opt. 1976, 15, 483. Franks, L. A.; Nelson, M. A , ; Davies. T. J. Appl. Phys. Leff. 1975, 2 7 , 205. (5) Franks, L. A.; Nelson, M. A,; Davies, T. J.; Lyons, P.; Golob, J. J . Appl. Phys. 1977, 48, 3639. (6) Lo, C. C.; Leskovar, B. I€€€ Trans. Nucl. Sci. 1974, NS-21, No. 1, 93. (7) Andrews, J. R. Rev. Sci. Insfrum. 1974, 4 5 , 22. (8) Bronk, E. V.; Whitten, W. B. Nucl. Instrum. Methods 1973, 106, 319. (1) (2) (3) (4)
RECEIVED for review August 24, 1979. Accepted October 30, 1979. Oak Ridge National Laboratory is operated for the US. Department of Energy by Union Carbide Corporation under Contract W-7405-eng-26. This article was supported by the Basic Energy Sciences.
~
