- Email: [email protected]
Relative intensity calibration of single-beam near-infrared spectrometers
058d-fJ539/91$3.00+0.00 Q 1991 Pcgamm Ress pk
SpzctrochimimAcfa, Vol. 47A. No. 9110, pi. 1119-1187.1991 Printed in Great Britain
Relative intensity calibration of single-beam near-infrared spectrometers C. J. PETIT,* G. M. WARNES, P. J. HENDRA AND M. JUDKINS Department of Chemistry, University of Southampton, Southampton SO9 5NH, U.K. (Receioed 4 Feburary 1991; infinal form and accepted 9 April 1991) Ahstraet-A method of correcting near-infrared emission spectra for variations in spectrometer response with wavelength is described. This method has been applied to a Fourier transform Raman instrument but should be equally valid for any single-beam emission spectrometer working in the near-infrared. The method is intended for use in normal analytical labs, and as such involves no expensive or complicated equipment and is simple to apply.
INTRODUCTION
ALL optical spectrometers have a complex response profile as a function of wavelength. This is due to the transmission/reflection characteristics of their constituent optical components and the response of the detector. This profile is most unlikely to be constant with wavelength. As a result the spectra recorded are not an accurate description of the light emitted or adsorbed by the sample, but are the convolution of this light and the instrumental response profile. If no correction is made for this then relative band areas will vary from spectrometer to spectrometer for an identical sample. A prototype Fourier transform (IT)-Raman instrument, developed at Southampton University, was used in these experiments and is described elsewhere [l, 21. The instrument uses a room temperature InGaAs detector, a quartz beamsplitter and four dielectric transmission filters (for the elimination of the Rayleigh line [3]). The spectral performance of these elements is shown in Fig. 1.t To rectify the problem of spectral response, absorption spectrometers generally record two spectra; the spectrum of the source alone and that of the source attenuated by the sample. This is achieved by the use of sample and reference beams or, in the case of FT instruments, by recording a separate “background” spectrum. In either case the system response is normalised by ratioing the sample spectrum against the reference (or background) spectrum. Thus, provided there is adequate light transmission across the entire spectral range the precise details of the response profile are unimportant. However, this scheme cannot be used for emission instruments, and to obtain the true spectra the instrumental response function must be known. In principle there are two ways to obtain the instrumental function. First, it would be possible to measure the characteristics of all the optical components and the response of the detector individually and multiply them together. This would not only be impractical, but would be subject to the cumulative errors from each measurement. Alternatively the spectrum of a precisely known light distribution could be recorded. For example, standard lamps, rotational Raman spectra and fluorescence profiles could be used. Standard lamps in general are difficult to produce and quantify and are therefore expensive. Normal filament lamps do not generally have a constant temperature across the whole filament and therefore the viewed output can be sensitive to the lamps’ positioning. The filament’s output will also change with age [4,5]. Rotational Raman spectra have precisely known intensity outputs, but although these could be used for correction purposes each line would produce only a discrete point correction and many points would be needed to produce even a vague correction profile.
* Author to whom correspondence should be addressed. t The best currently available transmission tiltet’s have less oscillation on their profiles than those shown here. However, any oscillation of the transmission profile will be enlarged by the need to use several filters and the need for correction remains. 1179
1180
C.J. PEITY et al. 1~0
0,8
1
0.4
0.2
0 800
1000
t200
1400
1600
1800
Wavelength Inm] 100
.,
Reflection Trace
/
~
Transmission Trace
40~
30--
2O
10
soo 100
-
soo
10~0
1200
1400 leoo Wavelength / n m
tsoo
2ooo
z2oo
24oo
-
90
80
70 60
J
50 40
3o 20
0
"
~
. . . .
Wavelength / n m
Fig. 1. The spectral response of (a)InGaAs detector at room temperature and when liquid nitrogen cooled, (b) quartz beamsplitter, and (c) the set of four dielectric transmission filters, used for Ray|eigh line rejection.
Single-beam NIR spectrometry
1181
The use of a filament lamp has been reported [6] for the correction of conventional scanning Raman instruments. The correction required for a conventional instrument is in general small. In PI’-Raman instruments however, the reflection-transmission profiles of the optical components involved are highly variable across the spectral range. This can mean that a large correction function is needed. The method reported here uses an electric furnace as a blackbody emitter whose temperature, T, can be measured accurately. The emission profile was calculated from the Planck distribution which describes the energy density, p(A, T) J rne2, emitted from a blackbody in the wavelength interval rZto 1+ drl:
(1) where h = Planck’s constant = 6.626 x 10Su Js c = Velocity of light = 2.998 X 108ms-’ k=
Boltzmann’s constant = 1.381 x 10Su JK-‘.
The brightness of the source, B(A, T) Wm-*ster-‘, is given by
The detection system used in the instrument registers photon events rather than the integrated energy with time. If we correct for this, by introducing a factor llhv, and express the equation in wavenumbers, o, substituting from Eqn (1) we have
B(w, T )6w = elOOkcdkT_
1 &I.
Fig. 2. The theoretical furnace output nonnalised to the measured output.
(3)
C. J. PETIT et
al.
Fig. 3. A typical correction curve. Data is at 4 cm-’ resolution and is shown unsmoothed.
PREPARATION OFCORRECTION CURVES A suite of correction curves is needed-one for each resolution normally used. This is in order to represent accurately the required shape of the instrument profile and to provide correction curves with the same data point interval as the spectra with which they must be multiplied. Since use of the correction curve should not significantly increase noise levels of the spectra being corrected, it is essential to obtain high quality spectra of the furnace. For this reason spectra should be accumulated for a period considerably longer than is used for general spectra, to ensure lower levels of noise. An electrical tube furnace, filled with small pieces of firebrick (to provide an emission surface), was used as a blackbody. The furnace was aligned such that the alignment HeNe laser beam, on the optical axis of the instrument, passed along the axis of the tube. Any edge effects from the tube are considered to be negligible since it is an extended source (approximately 50 mm diameter) and since the front face of the furnace is at a much lower temperature than the tube. The measured output curve from the furnace is smooth (except for water absorption lines discussed later), and it is therefore assumed that the brick material used has no absorptions in the region of interest. Since the aim of the experiment is to produce a relative correction it is of no consequence if the furnace behaves as a “greybody” rather than an ideal blackbody-only the shape of the output is relevant. An ideal cavity radiator emits from a “small” aperture in order that radiation escaping the system does not disturb the thermal equilibrium within the cavity. The extent to which our furnace approximates to a cavity furnace was checked by introducing a small (5 mm diameter) aperture to the front of the tube furnace. This did not significantly change the shape of the emission profile, and we therefore assume that (to a reasonable approximation) our furnace behaves as a “greybody”. The temperature was monitored using a high temperature thermocouple packed within the firebrick. The voltage applied to the furnace was adjusted such that the temperature stabilised at an accurately known value around 1300 “C. After the temperature reading stabilised a period of about 20 min was allowed before recording the spectra to ensure all emission occurred at the same temperature. Signal intensity received by the instrument was controlled by attenuation. Spatial attenuation by changing the distance between the furnace and the entrance aperture of the instrument, to adjust the solid angle collected, gave a coarse adjustment. Finer adjustment was achieved by using neutral reflection attenuators placed directly before the collection optics. In this way the
Single-beamNIR spectrometry
1183
Fig. 4. Curves of ideal blackbody output, plotted at various temperatures from Eqn (3).
signal could be adjusted to fall within the dynamic range of the detection system, and to give a large signal-to-noise ratio. Having acquired this spectrum a personal computer was used to generate the theoretical output of the furnace from Eqn (3), with the same data point interval as the measured furnace spectrum. The temperature of the furnace fluctuated by no more than +Z”C over the time period of the data acquisition and an average value was used for the calculation. The theoretical curve was normalised to the furnace spectrum (Fig. 2). A point-by-point division of the theoretical curve by the measured spectrum gives a correction function by which subsequent spectra may be multiplied. This process assumes the closest point of the instrument response profile, to the theoretical curve, to be perfect (a correction factor of l.O), and corrects all other points relative to this. A typical correction curve is shown in Fig. 3. The second ET-Raman instrument in our laboratory is fitted with rejection filters from Barr Associates whose cut-off may be moved closer to the Rayleigh line by angling them with respect to the instrument’s optical axis [7]. The detector may also be operated cooled, at any temperature down to 77 K, for improved signal-to-noise levels [8]. Both of
4
Ccrmotlcn Curve (raw date)
1 B -
Effeot of Smccthfng
P p
-
iI: ok,,,,,,,,,,,,,,,,,,, 45c
4m
s50
Remen ShlR
300
I cm
-’
Fig. 5. The edge of spectral cut-off, raw and smoothed data. SA(A)17:9-E
a
1184
C. J. PETTYet al.
Raman Shift/cm
Fig. 6. Raw and corrected spectra of: (a) an 80: 20 mixture of PEES: PESES polymers. The raw data shows the characteristic filter oscillation on the high background which is removed by correction. Scan conditions were 350 mW laser power at sample, 4 cm-’ resolution, 16 scans (approximately 1 min scanning time); (b) methyl iodide: this shows the effect of severe band attenuation close to the filters’ cut-off. Scan conditions were 500 mW laser power at the sample, 4 cm-’ resolution, 16 scans.
these adjustments alter the instrument response profile and it is impractical to prepare correction curves for each set-up using the furnace arrangement. It is therefore intended that a lamp with a large area element be used as a secondary standard; preparing a corrected spectrum of the lamp once, using the furnace, should enable the lamp to be used to correct for subsequent instrument response profiles. This method will of course be subject to the problems of filament lamps discussed earlier, although the use of a lamp with a large area element should reduce the positional sensitivity. The need for an expensive calibrated lamp is avoided by correcting against the furnace (since the lamp is used as a secondary standard, the shape of its output profile is no longer important). It has been suggested that spectrometers be fitted with a lamp as standard which would have as flat a profile as possible in the region of interest. This output would be assumed to be perfectly flat and the spectrometer’s recording of the lamp would be ratioed directly with subsequent spectra as a means of correction. In order to get as “flat” a response as possible from the sauce the temperature of the lamp should be selected such that the maxima in the output lies around the centre of the spectral region. In our particular Raman instrument the spectral region is roughly 1.06-1.85 pm wavelength. We might expect the temperature required to give maximum output in the centre of this region to
Single-beam NIR spectrometry
1185
MO-
O 4occ
Sam
1 ,_
m Raman Shin I
1WO
‘>
,
0
cd
Fig. 6(b).
be calculated from Weins’ displacement law: 2,,T= constant.
(4)
The constant has been measured as 2.9 X 10S3mK. This suggests a temperature of 1988 K for a central maxima. The emissivity of tungsten varies as a function of wavelength [9] and therefore tungsten lamps are not accurately described by the equations so far quoted for a blackbody [lo]. A more serious problem, however, is that spectrometers record spectra with wavenumbers on the abscissa, not wavelengths, and the form of the blackbody output is very different when considered in terms of frequencies [ll]. Figure 4 shows the blackbody output plotted on a wavenumber versus counts per second scale [these curves are described by Eqn (3)]. As can be seen from the diagram the maximum occurs below the region in which we are interested (approximately lOOOO-58oocm”), and to provide a maximum at the centre of this region requires temperatures in excess of what could easily be achieved using a lamp (the melting point of tungsten is about 3650 K). Consequently the output cannot be considered “flat” across the spectral region, and a correction curve would still need to be calculated by ratioing in the same way as we have done with the furnace. LIMITATIONSOF THE CORRECTIONPROCESS
The process is intended only to produce a relative correction of spectral bands with respect to each other. There is no external intensity standardisation involved and
1186
C. .I. P~rrv et al.
therefore spectra are not presented on an absolute scale. In practice this means that spectra run on different instruments under the same conditions (resolution, apodisation, etc.) should appear the same; ordinate axis scales, for each instrument, will still be independently arbitrary. In spectra run at high resolution, groups of sharp absorption bands due to water in the air are visible on the spectra of the furnace. These will produce positive peaks on the correction curve and may therefore create small errors in the profile of bands falling in this region of the spectrum. Since the atmospheric conditions are subject to change, and light from a sample and that from the furnace have different path lengths before reaching the detector, the magnitude of the absorptions will be different in each case. Therefore, the correction curve produced by the furnace cannot be used to correct accurately for absorptions in sample spectra. However, unless a sample has a particularly large background, or a band in the sample coincides with an absorption band, virtually no light will be present at the correct frequency to be absorbed. Consequently the absorptions, and the effects of their presence in the correction curves, will generally have a negligible effect in Raman spectra and may be ignored. If these peaks must be removed from the correction curves, this may be done by applying a Savitsky-Golay smoothing function, which will also reduce any residual noise on the curve. However, this has the effect of altering the shape of any part of the curve which has a sharp change of gradient, for example the cut-off at either end of the spectral region, and will therefore reduce the reliability of the relative heights of peaks in these regions (Fig. 5). This method produces spectra which are independent of the instrumental factors in the system. This means that spectra run on equivalent instruments should be “identical” after correction. Because of the v4 factor in the Raman effect however, spectra of a sample run at different excitation wavelengths would not be identical even after our instrumental correction. This occurs because exciting with different wavelengths leads to a different distribution of scattered light from the sample. Because this is a “natural” phenomenon of the Raman effect we have chosen not to include it in our correction process; to do so however requires only that spectra be divided by the v4 function.
CONCLUSIONS
Using this method spectra may be successfully corrected for the instrument response function. The process is simple enough to be carried out in any laboratory and once the correction functions are determined they need only be changed if the optical set-up varies. In situations where instrumental conditions change frequently, a secondary standard may be used to facilitate the generation of correction functions unique to each set-up. Computer software has been written within our research group to automate the correction of spectra and all recent publications have used spectra corrected in this way [12]. Correction requires less than 10 s per spectrum. Acknowledgements-One of us, CHRISPE~Y, would like to thank Perkin-Elmer U.K. for financial support. We would also like to thank the Office of Naval Research for continued generous funding of this project.
REFERENCES [l] [Z] [3] [4] [5] [6] [7]
A. Crookell, P. J. Hendra, H. M. Mould and A. J. Turner, J. Raman Spectrosc. 21, 85(1990). P. J. Hendra and H. A. Mould, Int. Lab. 18,34 (1988). D. J. Cutler, Specfrochim. Acta 46A, 131 (1990). R. D. Larrabee, J. Opt. Sot. Am. 49,619 (1959). C. R. Barber, J. Opt. Sot. Am. 23,238 (1946). D. P. Strommen and K. Nakamoto, Laboratory Raman Spectroscopy. Wiley, New York (1984). H. A. Macleod, Thin Film OpticalFifters (2nd edn). Adam Hilger, New York (1982).
Single-beam NIR spectrometry [8] [9] [lo] [ll] [12]
1187
E. N. Lewis, V. F. KaIansky and I. W. Levin, Appl. Spectrosc. 43, 156 (1989). J. C. Devos, P/rys& 20, 690 (1954). D. Halliday and R. Resnick, Physics (combined 3rd edn). Wiley, New York (1978). A. P. Thome, Spectrophysics (2nd edn). Chapman & Ha& London (1988). G. Ellis, P. J. Hendra, C. M. Hodges, T. Jawhari, C. H. Jones, P. Le Barazer, C. Passingham, I. A. M. Royaud, A. Sanchez-Blazquez and G. M. Wames, Analyst 114,lOfX (1989).
SpzctrochimimAcfa, Vol. 47A. No. 9110, pi. 1119-1187.1991 Printed in Great Britain
Relative intensity calibration of single-beam near-infrared spectrometers C. J. PETIT,* G. M. WARNES, P. J. HENDRA AND M. JUDKINS Department of Chemistry, University of Southampton, Southampton SO9 5NH, U.K. (Receioed 4 Feburary 1991; infinal form and accepted 9 April 1991) Ahstraet-A method of correcting near-infrared emission spectra for variations in spectrometer response with wavelength is described. This method has been applied to a Fourier transform Raman instrument but should be equally valid for any single-beam emission spectrometer working in the near-infrared. The method is intended for use in normal analytical labs, and as such involves no expensive or complicated equipment and is simple to apply.
INTRODUCTION
ALL optical spectrometers have a complex response profile as a function of wavelength. This is due to the transmission/reflection characteristics of their constituent optical components and the response of the detector. This profile is most unlikely to be constant with wavelength. As a result the spectra recorded are not an accurate description of the light emitted or adsorbed by the sample, but are the convolution of this light and the instrumental response profile. If no correction is made for this then relative band areas will vary from spectrometer to spectrometer for an identical sample. A prototype Fourier transform (IT)-Raman instrument, developed at Southampton University, was used in these experiments and is described elsewhere [l, 21. The instrument uses a room temperature InGaAs detector, a quartz beamsplitter and four dielectric transmission filters (for the elimination of the Rayleigh line [3]). The spectral performance of these elements is shown in Fig. 1.t To rectify the problem of spectral response, absorption spectrometers generally record two spectra; the spectrum of the source alone and that of the source attenuated by the sample. This is achieved by the use of sample and reference beams or, in the case of FT instruments, by recording a separate “background” spectrum. In either case the system response is normalised by ratioing the sample spectrum against the reference (or background) spectrum. Thus, provided there is adequate light transmission across the entire spectral range the precise details of the response profile are unimportant. However, this scheme cannot be used for emission instruments, and to obtain the true spectra the instrumental response function must be known. In principle there are two ways to obtain the instrumental function. First, it would be possible to measure the characteristics of all the optical components and the response of the detector individually and multiply them together. This would not only be impractical, but would be subject to the cumulative errors from each measurement. Alternatively the spectrum of a precisely known light distribution could be recorded. For example, standard lamps, rotational Raman spectra and fluorescence profiles could be used. Standard lamps in general are difficult to produce and quantify and are therefore expensive. Normal filament lamps do not generally have a constant temperature across the whole filament and therefore the viewed output can be sensitive to the lamps’ positioning. The filament’s output will also change with age [4,5]. Rotational Raman spectra have precisely known intensity outputs, but although these could be used for correction purposes each line would produce only a discrete point correction and many points would be needed to produce even a vague correction profile.
* Author to whom correspondence should be addressed. t The best currently available transmission tiltet’s have less oscillation on their profiles than those shown here. However, any oscillation of the transmission profile will be enlarged by the need to use several filters and the need for correction remains. 1179
1180
C.J. PEITY et al. 1~0
0,8
1
0.4
0.2
0 800
1000
t200
1400
1600
1800
Wavelength Inm] 100
.,
Reflection Trace
/
~
Transmission Trace
40~
30--
2O
10
soo 100
-
soo
10~0
1200
1400 leoo Wavelength / n m
tsoo
2ooo
z2oo
24oo
-
90
80
70 60
J
50 40
3o 20
0
"
~
. . . .
Wavelength / n m
Fig. 1. The spectral response of (a)InGaAs detector at room temperature and when liquid nitrogen cooled, (b) quartz beamsplitter, and (c) the set of four dielectric transmission filters, used for Ray|eigh line rejection.
Single-beam NIR spectrometry
1181
The use of a filament lamp has been reported [6] for the correction of conventional scanning Raman instruments. The correction required for a conventional instrument is in general small. In PI’-Raman instruments however, the reflection-transmission profiles of the optical components involved are highly variable across the spectral range. This can mean that a large correction function is needed. The method reported here uses an electric furnace as a blackbody emitter whose temperature, T, can be measured accurately. The emission profile was calculated from the Planck distribution which describes the energy density, p(A, T) J rne2, emitted from a blackbody in the wavelength interval rZto 1+ drl:
(1) where h = Planck’s constant = 6.626 x 10Su Js c = Velocity of light = 2.998 X 108ms-’ k=
Boltzmann’s constant = 1.381 x 10Su JK-‘.
The brightness of the source, B(A, T) Wm-*ster-‘, is given by
The detection system used in the instrument registers photon events rather than the integrated energy with time. If we correct for this, by introducing a factor llhv, and express the equation in wavenumbers, o, substituting from Eqn (1) we have
B(w, T )6w = elOOkcdkT_
1 &I.
Fig. 2. The theoretical furnace output nonnalised to the measured output.
(3)
C. J. PETIT et
al.
Fig. 3. A typical correction curve. Data is at 4 cm-’ resolution and is shown unsmoothed.
PREPARATION OFCORRECTION CURVES A suite of correction curves is needed-one for each resolution normally used. This is in order to represent accurately the required shape of the instrument profile and to provide correction curves with the same data point interval as the spectra with which they must be multiplied. Since use of the correction curve should not significantly increase noise levels of the spectra being corrected, it is essential to obtain high quality spectra of the furnace. For this reason spectra should be accumulated for a period considerably longer than is used for general spectra, to ensure lower levels of noise. An electrical tube furnace, filled with small pieces of firebrick (to provide an emission surface), was used as a blackbody. The furnace was aligned such that the alignment HeNe laser beam, on the optical axis of the instrument, passed along the axis of the tube. Any edge effects from the tube are considered to be negligible since it is an extended source (approximately 50 mm diameter) and since the front face of the furnace is at a much lower temperature than the tube. The measured output curve from the furnace is smooth (except for water absorption lines discussed later), and it is therefore assumed that the brick material used has no absorptions in the region of interest. Since the aim of the experiment is to produce a relative correction it is of no consequence if the furnace behaves as a “greybody” rather than an ideal blackbody-only the shape of the output is relevant. An ideal cavity radiator emits from a “small” aperture in order that radiation escaping the system does not disturb the thermal equilibrium within the cavity. The extent to which our furnace approximates to a cavity furnace was checked by introducing a small (5 mm diameter) aperture to the front of the tube furnace. This did not significantly change the shape of the emission profile, and we therefore assume that (to a reasonable approximation) our furnace behaves as a “greybody”. The temperature was monitored using a high temperature thermocouple packed within the firebrick. The voltage applied to the furnace was adjusted such that the temperature stabilised at an accurately known value around 1300 “C. After the temperature reading stabilised a period of about 20 min was allowed before recording the spectra to ensure all emission occurred at the same temperature. Signal intensity received by the instrument was controlled by attenuation. Spatial attenuation by changing the distance between the furnace and the entrance aperture of the instrument, to adjust the solid angle collected, gave a coarse adjustment. Finer adjustment was achieved by using neutral reflection attenuators placed directly before the collection optics. In this way the
Single-beamNIR spectrometry
1183
Fig. 4. Curves of ideal blackbody output, plotted at various temperatures from Eqn (3).
signal could be adjusted to fall within the dynamic range of the detection system, and to give a large signal-to-noise ratio. Having acquired this spectrum a personal computer was used to generate the theoretical output of the furnace from Eqn (3), with the same data point interval as the measured furnace spectrum. The temperature of the furnace fluctuated by no more than +Z”C over the time period of the data acquisition and an average value was used for the calculation. The theoretical curve was normalised to the furnace spectrum (Fig. 2). A point-by-point division of the theoretical curve by the measured spectrum gives a correction function by which subsequent spectra may be multiplied. This process assumes the closest point of the instrument response profile, to the theoretical curve, to be perfect (a correction factor of l.O), and corrects all other points relative to this. A typical correction curve is shown in Fig. 3. The second ET-Raman instrument in our laboratory is fitted with rejection filters from Barr Associates whose cut-off may be moved closer to the Rayleigh line by angling them with respect to the instrument’s optical axis [7]. The detector may also be operated cooled, at any temperature down to 77 K, for improved signal-to-noise levels [8]. Both of
4
Ccrmotlcn Curve (raw date)
1 B -
Effeot of Smccthfng
P p
-
iI: ok,,,,,,,,,,,,,,,,,,, 45c
4m
s50
Remen ShlR
300
I cm
-’
Fig. 5. The edge of spectral cut-off, raw and smoothed data. SA(A)17:9-E
a
1184
C. J. PETTYet al.
Raman Shift/cm
Fig. 6. Raw and corrected spectra of: (a) an 80: 20 mixture of PEES: PESES polymers. The raw data shows the characteristic filter oscillation on the high background which is removed by correction. Scan conditions were 350 mW laser power at sample, 4 cm-’ resolution, 16 scans (approximately 1 min scanning time); (b) methyl iodide: this shows the effect of severe band attenuation close to the filters’ cut-off. Scan conditions were 500 mW laser power at the sample, 4 cm-’ resolution, 16 scans.
these adjustments alter the instrument response profile and it is impractical to prepare correction curves for each set-up using the furnace arrangement. It is therefore intended that a lamp with a large area element be used as a secondary standard; preparing a corrected spectrum of the lamp once, using the furnace, should enable the lamp to be used to correct for subsequent instrument response profiles. This method will of course be subject to the problems of filament lamps discussed earlier, although the use of a lamp with a large area element should reduce the positional sensitivity. The need for an expensive calibrated lamp is avoided by correcting against the furnace (since the lamp is used as a secondary standard, the shape of its output profile is no longer important). It has been suggested that spectrometers be fitted with a lamp as standard which would have as flat a profile as possible in the region of interest. This output would be assumed to be perfectly flat and the spectrometer’s recording of the lamp would be ratioed directly with subsequent spectra as a means of correction. In order to get as “flat” a response as possible from the sauce the temperature of the lamp should be selected such that the maxima in the output lies around the centre of the spectral region. In our particular Raman instrument the spectral region is roughly 1.06-1.85 pm wavelength. We might expect the temperature required to give maximum output in the centre of this region to
Single-beam NIR spectrometry
1185
MO-
O 4occ
Sam
1 ,_
m Raman Shin I
1WO
‘>
,
0
cd
Fig. 6(b).
be calculated from Weins’ displacement law: 2,,T= constant.
(4)
The constant has been measured as 2.9 X 10S3mK. This suggests a temperature of 1988 K for a central maxima. The emissivity of tungsten varies as a function of wavelength [9] and therefore tungsten lamps are not accurately described by the equations so far quoted for a blackbody [lo]. A more serious problem, however, is that spectrometers record spectra with wavenumbers on the abscissa, not wavelengths, and the form of the blackbody output is very different when considered in terms of frequencies [ll]. Figure 4 shows the blackbody output plotted on a wavenumber versus counts per second scale [these curves are described by Eqn (3)]. As can be seen from the diagram the maximum occurs below the region in which we are interested (approximately lOOOO-58oocm”), and to provide a maximum at the centre of this region requires temperatures in excess of what could easily be achieved using a lamp (the melting point of tungsten is about 3650 K). Consequently the output cannot be considered “flat” across the spectral region, and a correction curve would still need to be calculated by ratioing in the same way as we have done with the furnace. LIMITATIONSOF THE CORRECTIONPROCESS
The process is intended only to produce a relative correction of spectral bands with respect to each other. There is no external intensity standardisation involved and
1186
C. .I. P~rrv et al.
therefore spectra are not presented on an absolute scale. In practice this means that spectra run on different instruments under the same conditions (resolution, apodisation, etc.) should appear the same; ordinate axis scales, for each instrument, will still be independently arbitrary. In spectra run at high resolution, groups of sharp absorption bands due to water in the air are visible on the spectra of the furnace. These will produce positive peaks on the correction curve and may therefore create small errors in the profile of bands falling in this region of the spectrum. Since the atmospheric conditions are subject to change, and light from a sample and that from the furnace have different path lengths before reaching the detector, the magnitude of the absorptions will be different in each case. Therefore, the correction curve produced by the furnace cannot be used to correct accurately for absorptions in sample spectra. However, unless a sample has a particularly large background, or a band in the sample coincides with an absorption band, virtually no light will be present at the correct frequency to be absorbed. Consequently the absorptions, and the effects of their presence in the correction curves, will generally have a negligible effect in Raman spectra and may be ignored. If these peaks must be removed from the correction curves, this may be done by applying a Savitsky-Golay smoothing function, which will also reduce any residual noise on the curve. However, this has the effect of altering the shape of any part of the curve which has a sharp change of gradient, for example the cut-off at either end of the spectral region, and will therefore reduce the reliability of the relative heights of peaks in these regions (Fig. 5). This method produces spectra which are independent of the instrumental factors in the system. This means that spectra run on equivalent instruments should be “identical” after correction. Because of the v4 factor in the Raman effect however, spectra of a sample run at different excitation wavelengths would not be identical even after our instrumental correction. This occurs because exciting with different wavelengths leads to a different distribution of scattered light from the sample. Because this is a “natural” phenomenon of the Raman effect we have chosen not to include it in our correction process; to do so however requires only that spectra be divided by the v4 function.
CONCLUSIONS
Using this method spectra may be successfully corrected for the instrument response function. The process is simple enough to be carried out in any laboratory and once the correction functions are determined they need only be changed if the optical set-up varies. In situations where instrumental conditions change frequently, a secondary standard may be used to facilitate the generation of correction functions unique to each set-up. Computer software has been written within our research group to automate the correction of spectra and all recent publications have used spectra corrected in this way [12]. Correction requires less than 10 s per spectrum. Acknowledgements-One of us, CHRISPE~Y, would like to thank Perkin-Elmer U.K. for financial support. We would also like to thank the Office of Naval Research for continued generous funding of this project.
REFERENCES [l] [Z] [3] [4] [5] [6] [7]
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