Trading Wavelength for Absorbance Resolution: Predicting the Performance of Array Detection Systems

CHRIS W. B R O W N Department o[ Chemistry, University of Rhode Island, Kingston, Rhode Island 02881

Mid-infrared spectra of liquid mixtures measured at 4 cm -I resolution and near-infrared spectra of synthetic natural gas samples measured at 2 c m - ' resolution were convoluted to determine the effect of low resolution on multicomponent analyses of these samples . The resolution of the liquid samples could be degraded to almost 100 cm-' before significant effects on the quantitative results were observed. The minor components in the natural gas samples were sensitive to degrading the resolution; however, the major components, methane and ethane, and the B T U values were unaffected until the resolution was degraded to over 100 nm ( ~ 6 0 0 cm -1 at 1225 nm). The convoluted spectra were also displayed across a simulated array detector to determine the effect of the number of pixels on quantitative analysis. Excellent resul ts were obtained on the convoluted spectra of both the liquid and gas mixtures with 32 elements . The liquid samples could be analyzed with as few as 8 pixels.

Index Headings: Near-infrared; Array detectors; Convolution; Gas-phase spectra; Diode arrays; Multicomponent analysis; Principal component regression; Quantitative analysis; Computer applications; Infrared; Spectroscopic techniques.

INTRODUCTION

From the early days of commercial spectroscopic in- strumentation, resolution has been an important factor in selecting an appropriate instrument. One spectrom- eter rather than another is purchased because its reso- lution is better. However, is high resolution really need- ed? The answer is yes, if we are trying to determine a physical property such as bond length which can be cal- culated from the frequencies of closely spaced vibration- al-rotational lines. Moreover, there was a time when peak separation was a strict requirement for identification and/ or quantitative analysis. However, this requirement no longer exists due to developments in modern pattern recognition techniques.

Instead of using peak position and/or intensities of selected bands for identification and quantitation, we can now treat the entire spectral pattern. Pattern rec- ognition techniques of principal component analysis (PCA) 1-~ and partial least-squares (PLS) analysis 7-~1 of full spectra have been successfully used for quantitative analysis of multicomponent systems. PCA has also been used for searching infrared spectral libraries. ~2-~6 These processes use all or selected parts of spectra and do not rely on selection of peak positions or heights.

During the last decade, there has been an increase in the number of spectrometers built with array detection systems. This holds especially true for the UV-visible region, but the technology is developing rapidly towards the use of arrays in most commercial near-IR spectrom- eters. Eventually, there will be commercial array spec- trometers covering the entire optical spectral region.

Received 17 December 1992.

In the present study, we have investigated the effects of degrading resolution and the use of (simulated) array detectors on the analysis of a liquid mixture in the mid- IR and a gas mixture in the near-IR. The results from the present investigation were used to design a low-res- olution diode array system for measuring the BTU con- tent of natural gas. Spectra from a prototype instrument will be compared with those predicted in the present study.

EXPERIMENTAL

Spectral Measurements. Mid-infrared spectra of the liquid samples were measured on a Bio-Rad Model FTS40 spectrometer (Cambridge, MA) with a 25-#m-pathlength cell with AgC1 windows. Spectra were measured at a resolution of 4 cm -1 with the use of 64 scans. The near- infrared gas-phase spectra were measured on a Bio-Rad Model FTS40N near-IR spectrometer equipped with a quartz beamsplitter and a liquid N2-cooled InSb detec- tor. Gases were contained in a 10-cm-long high-pressure gas cell and measured at a pressure of 100 psia. Pressures were measured with a Druck Limited (Leicestershire, England) Model PDCR135 pressure transducer.

Near-IR spectra of the gases were also measured on a diode array spectrometer, which is a prototype for a BTU monitoring system. This instrument consists of a tung- sten-halogen source, a bifurcated fiber-optic interface to a 5-cm-long high-pressure gas cell, 17 an American Ho- lographic (Littleton, MA) Model 100s spectrograph with a grating blazed at 1225 nm covering the range of 1100 to 1450 nm, and a prototype 32-element Ge array detec- tor built by EG&G Judson (Montgomeryville, PA). Analog signals from the array were passed to a trans- impedance amplifier (built by Judson) and to a 32-chan- nel 16-bit A/D converter Series PCI from Burr Brown/ Intelligent Instrumentation (Tucson, AZ).

Standard Samples. Analytical-grade solvents from Mallinckrodt were used for the liquid samples. All liquid mixtures were prepared in volume ratios. The samples of natural gas were prepared at the University of Oklahoma ~s and were pre-treated prior to the measure- ment according to the protocol discussed previously. 19

Data Processing. All the spectra were processed on a personal computer. Spectral processing was performed with Lab Calc software (Galactic Industries, Salem, NH) using computer programs written in Array-Basic. The mid-IR spectra were convoluted with a slit function ex- pressed in wavenumbers, whereas the near-IR spectra were converted from wavenumber to wavelength (nm) and convoluted with a slit function expressed in wave- length. The conversion to wavelength was performed so that the resulting spectra could be used to predict the

Volume 47, Number 5, 1993 0003-7028/93/4705-061952.00/0 APPLIED SPECTROSCOPY 619 © 1993 Society for Applied Spectroscopy

~J

Z < f13

.5 0 (,9 f13

Array Spectrum

Array Detector

Convoluted

Original

12'00 14'00 WAVELENGTH (nm)

FIG. 1. Nea r - IR spec t ra of na tu ra l gas. F rom top to bot tom: 32-channel a r ray spec t rum; 32-e lement a r ray detector; convolu ted to 10 nm; orig- inal spec t rum.

performance of a spectrograph/array detection system that is linear in wavelength. Spectra were convoluted with a Gaussian-shaped slit function. The spectra were converted from absorbance to % transmission prior to the convolution and converted back to absorbance fol- lowing the convolution. For simulation of an array de- tector, the % transmission spectra were "displayed" across a selected number of pixels, each having equal, finite widths. The values in each pixel were averaged to produce the array spectra and then converted back to the absorbance domain. The entire process is demon- strated in Fig. 1, where the original spectrum of natural gas is compared with one convoluted with a 10-nm slit width, displayed on the 32 "pixels" of a array detector, and then the values in each pixel are averaged to produce the array spectrum of 32 channels. These spectra are all shown in the absorbance domain for comparison, but the calculations were all performed in % transmission.

* J - -

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0

0 1 s'oo 1 o'0o WAVENUMBER (CM-1)

Fro. 2. Mid-IR spectrum of the three pure components in the liquid mixtures.

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40"

20"

O , m

30 C M - I ~

20 CM- 1 ~ j ~

10 C M - I ~ J ~

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15'00 1000 WAVENUMBER (CM-1)

FIG. 3. Mid - IR s p e c t r u m of a 5/2/3 l iquid mix tu re of 1,2,4-tr imethyl- benzene/p-xylene/m-xylene. From bo t t om to top: original, and con- voluted to 10, 20, 30, and 40 cm 1.

RESULTS AND DISCUSSION

Mid-Infrared Spectra of Liquid Mixtures. Mid-infra- red spectra of 16 mixtures of 1,2,4-trimethylbenzene, p-xylene, and m-xylene were measured. Spectra of the pure components from 850 to 1850 cm -1 are shown in Fig. 2; all three components have a band below 850 cm -1 which is very strong and nonlinear at the pathlength of the present measurements, so that region was not in- cluded in the analysis.

The effects of convolution on a typical liquid mixture sample can be seen in Fig. 3 after the application of four different slit functions from 10 to 40 cm -1. All the spectra were convoluted with slit functions from 10 to 200 cm -1 in increments of 10 cm -1. To determine the effects of lower resolution on multicomponent analysis, we ana- lyzed the 16 mixtures of 1,2,4-trimethylbenzene/p-xy- l ene /m-xy lene with principal component regression (PCR) using the me thod of successive average orthogonalization 19 to form the loading vectors. The re- sults on cross-validation of the spectra at resolutions from 20 up to 200 cm -~ are shown in Fig. 4. Cross-vali- dation was performed with the method of "leave-one- out." All samples except one are used in the training set

SEP CROSS-VALIDATION OF 16 LIQUID MIXTURES 1.6 1.4

1.2

1

0.8

0.6

0.4

0.2

0

FIG. 4.

20 40 60 80 100 120 140 160 180 200 RESOLUTION IN CM-1

[ ] TRIMETHYL-BENZENE [ ] P-XYLENE [ ] M-XYLENE

Effect of convolut ion on the cross-val idat ion of the 16 l iquid mix tu re spectra. S t a n d a r d error of predic t ion (SEP) vs. resolution.

620 Volume 47, Number 5, 1993

3 0 -

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10,

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4 C H A ~

16 CHANNELS~~

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FIG. 5. S imula ted array spec t ra of a l iquid mix ture with, f rom bo t tom FIG. 7. to top, 32, 16, 8, and 4 channels , tion.

1500 20'00 2500 WAVELENGTH (nm)

Near - IR spec t rum of na tura l gas measu red at 2 c m - ' resolu-

for calibration to predict the concentration of the one left out. That sample is returned to the set and the pro- cedure repeated for each of the samples in the standard set. The resulting errors for the entire set are used for the standard error of prediction (SEP), which is plotted in Fig. 4 for each of the resolutions. Basically, the errors do not increase much until a slit function of 100 cm -1 is used. There are some fluctuations in the errors of the individual components with resolution, but there is not a pronounced trend in the results at lower resolutions.

The effects of different size array detectors are shown in Fig. 5. All the spectra shown in Fig. 3 were stored at 2-cm -1 increments; this approach is the same as using a 500-element array detector. For smaller simulated ar- rays, equal numbers of these 500 values were "displayed" across each element of the array. The spectrum convo- luted to 40 cm -1 was used to form simulated arrays with 32, 16, 8, and 4 channels. These simulated spectra are shown in Fig. 5.

The effects of the number of array elements on the SEPs from cross-validation are shown in Fig. 6. In going from 500 to 32 elements in the optical plane, the errors

SEP 5

4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ .. . . . . . . . . . . . . .

V~ 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

o ~ - ~ ~ ~ 500 32 16 8

# CHANNELS [ ] TRIMETHYL-BENZENE [ ] P-XYLENE [ ] M-XYLENE

FIG. 6. Effect of the n u m b e r of a r ray e lements on the cross-val idat ion of the 16 l iquid mix tu re spec t ra a t 40 cm-1 resolution. S t anda rd error of predic t ion (SEP) vs. n u m b e r of channels .

for trimethylbenzene increased slightly, whereas those for p-xylene and m-xylene decreased. There was a slight increase in the errors for trimethylbenzene and p-xylene with 16 and 8 channels, but the only major increase in errors for all three components occurred when only 4 elements were used. Basically, 32 channels supplied enough "resolution" to give results as good as 500 chan- nels, whereas 16 and 8 channels provided comparable results.

Near-Infrared Spectra of Natural Gas Mixtures. The near-infrared spectrum of a natural gas sample from 1000 to 2500 nm is shown in Fig. 7. Spectra of all of the gas standards were measured at a pressure of 100 psia. Twen- ty-four standard gas samples were used in the training set for this study. The range of concentrations for the components in these standards is given in Table I. An industry standard gas sample certified by the Institute of Gas Technology (IGT) was used to test the accuracy and precision of the model; its concentrations are also

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APPLIED SPECTROSCOPY 621

TABLE I. Compos i t i on o f s tandard gas mixtures .

Mole percent Mole percent Component s tandard mixtures IGT s tandard

Methane 83.1181-97.3850 90.64 Ethane 0.5068--8.1035 3.99 Propane 0.2412-4.8335 0.998 Butane 0.0585-0.4292 0.299 iso-Butane 0.0423-0.3934 0.302 Pentane 0.0223-0.1276 0.102 iso-Pentane 0.0234-0.1305 0.101 Hexane 0.0141-0.1035 • .. Carbon dioxide 0.7742-2.1222 1.00 Nitrogen 0.0000-3.9449 2.52

given in Table I. Ten separate samples of this gas were analyzed for accuracy and precision measurements.

The effects of convolution on the natural gas spectrum with slits of 10, 30, and 50 nm for the region of 1100 to 1450 nm are shown in Fig. 8. A considerable amount of the band definition is lost by 50 nm. Multicomponent analysis results for the cross-validation of spectra in the same spectral region convoluted in the range of 20 to 120 nm are shown in Fig. 9. Convoluting at increasingly larger slit widths affects the components having the lowest con- centrations first. The errors for the components of lowest concentrations such as the butanes and pentanes are large even at a slit width of 4 nm. The maximum con- centration of the pentanes is 0.25 mole % in the 24 sam- ples. The relative standard error for the pentanes at 4 nm is greater than 90 % ; however, since the total pentane concentration is so small, the absolute error is also small. Moreover, the number of loading vectors used in the PCR modeling was selected on the basis of the lowest BTU values, i.e., the model was not optimized for the individ- ual components. The errors for BTU, methane, and eth- ane do not show significant increases until the simulated slit widths are greater than 100 nm.

As a general test for the model, the IGT industry stan- dard gas was used for determining the accuracy and pre- cision of an "unknown." The % accuracy is defined as the average of the relative absolute differences between the known and predicted values, whereas the precision is the relative standard deviation. The % accuracy values

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4 20 40 6O 80 Y

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RESOLUTION IN NM

[ ] BTU [ ] METHANE [ ] ETHANE

[ ] PROPANE [ ] BUTANES [ ] PENTANE$

FIG. 10. Effect of convoluting the spectral region of 1100 to 1450 nm on the To accuracy of 10 samples of the IGT s tandard gas.

as a function of resolution are shown in Fig. 10. The relative error for BTUs remains almost constant in the range of 0.2 to 0.259 from 4 to 80 nm slit widths and starts to increase only at a slit width of 100 nm. In gen- eral, the errors for the components with the lowest con- centrations such as propane, butanes, and pentanes ex- hibit a slow increase from 4- to 100-nm slit widths, although the pentanes exhibit an initial decrease before starting to increase. However, the errors for methane and ethane decrease with convolution and do not show sig- nificant increases until 80 nm. Again, we should empha- size that the principal component model used to predict the values for the IGT standard was optimized for BTUs and not for the individual components.

The % precision values for the 10 samples of the IGT standard are given in Fig. 11. The errors for the butanes increase with increasing slit widths, but the errors for BTUs and the other components are almost constant up until 80 nm, at which point they all exhibit significant increases.

Simulated array spectra of a natural gas sample in the 1100-1450 nm region, which had been convoluted to 10 nm, are shown displayed on 400, 32, 16, and 8 pixels in Fig. 12. The effect of the simulated array detector on the accuracy of predicting BTUs and component concentra-

200

4 20 40 60 8O 100 120

RESOLUTION IN NM [ ] BTU [ ] METHANE [ ] ETHANE

[ ] PROPANE [ ] BUTANES [ ] PENTANES

Fro. 9. Effect of convoluting the spectral region of 1100 to 1450 nm on the relative To errors for BTU and 5 component groups for the cross- validation of 24 s tandard samples.

lOO

00 . . . . . I

,

_ 20 ..... O

N 4 ..... 3 . . . . . .

2 . . . . . .

1 . . . . . .

o 4 20 40 60 80 100 RESOLUTION IN NM

[] BTU [] METHANE [] ETHANE

[ ] PROPANE [ ] BUTANES [ ] PENTANES

FIG. 11. Effect of convoluting the spectral region of 1100 to 1450 nm on the To precision of 10 samples of the IGT s tandard gas.

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fI3 f~

a3

< 1-

0 260 400 CHANNEL #

Fro. 12. Simulated array spectra of natural gas with 400, 32, 16, and 8 array elements.

tions of the IGT standard gas is shown in Fig. 13. There is a significant increase in the errors for the components with the lower concentrations in going from 400 to 32 elements; however, the BTU and methane values are predicted very well with 32 elements. The error for the BTU is slightly less with 32 elements than it is with 400.

The goal of this research was to design a monitor that could provide real-time predictions of BTU values on- line with an accuracy better than 0.25%. The results showed that this goal could be accomplished in the spec- tral range of 1100 to 1450 nm with an accuracy of 0.21% with 32 elements. During this investigation various sec- tions of the near-IR spectra between 1000 and 2500 nm were examined with different convolutions and simulat- ed arrays. The best results were obtained for the region 1300 to 1530 nm using 10-nm resolution and a 32-element array. The accuracy and precision were 0.136 and 0.185 %, respectively. However, a grating blazed at 1225 nm for the 1100-1450 nm region was readily available, and sec- ond-best results were obtained for this region; thus, the prototype BTU monitor was constructed with this grat- ing.

100

8O

6O

O 0 °<4

3 2 1 o

4OO 32 16 8

# OF ELEMENTS

[ ] BTU [ ] METHANE [ ] ETHANE

[ ] PROPANE [ ] BUTANES [ ] PENTANES

Fro. 13. Effect of number of array elements in the spectral region of 1100 to 1450 nm on the To accuracy of 10 samples of the IGT standard gas.

w O

O 09 [ n <

.1 ~ L

I'0 2'0 3'0 CHANNEL #

FIG. 14. Simulated and actual array spectrum of a gas sample with a 32-element array detector.

Near-Infrared BTU Monitor. The BTU monitor was calibrated with the use of 17 of the standard gases at 20 psi. The lower pressure was required for field tests of the monitor unit, which will be discussed in a later report. The spectra of the standard gases were measured under flow-through conditions in order to simulate field con- ditions. The cell was first opened to atmospheric pressure for 5 s so that the ambient pressure could be measured. It was then opened to N2 gas at 20 psi for 10 s, and the background spectrum measured (signal averaged) for 15 s. Finally, it was opened to the natural gas sample for 15 s, and the sample spectrum measured for 15 s. The ratio of this spectrum to the background spectrum of N2 was stored for each sample.

A typical spectrum from the BTU monitor is compared with one obtained from the FT-IR after convolution to 10 nm and displayed on a simulated 32-element array in Fig. 14. The spectra are nearly identical. Differences are due to the fact that the wavelength range displayed on each pixel is not exactly the same for the simulated and real array spectra. Again, ten samples of a standard gas were used to determine the accuracy and precision of the BTU monitor. The accuracy was 0.25 % and the precision 0.31%. Both of these are on the same order as those predicted for this spectral region from the simulation study.

CONCLUSIONS

The goal of this study was to explore the possibility of trading resolution in wavelength with resolution in absorbance. The latter actually corresponds to improving the signal-to-noise ratio. Convolution is a method of spectral smoothing which produces higher signal-to-noise ratios at the expense of (wavelength) resolution. The premise that high (wavelength) resolution is needed in all situations is not true, especially considering the cur- rent sophistication of pattern recognition techniques. As we have clearly showed herein, multicomponent analy- ses, even on gases, can be performed at much lower res- olutions as long as there is a good signal-to-noise ratio. Simulation of a diode array detection system proved

APPLIED SPECTROSCOPY 623

wor thwhi l e for des ign ing a n d p red i c t i ng the p e r f o r m a n c e of a B T U mon i to r . Resu l t s on the ac tua l m o n i t o r were very close to those p r ed i c t ed f rom the s i m u l a t i o n s t u d y a n d s u p p o r t the use of s i m u l a t i o n in the des ign of spec- t r o m e t e r s for specific ana ly t i c a l app l ica t ions .

ACKNOWLEDGMENT

The author wishes to express his appreciation to the Gas Research Institute (Chicago) for partial support of this research.

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624 Volume 47, Number 5, 1993