Significance of Correction for Detector Temperature in Infrared Emission Spectroscopy

G ~ B O R K E R E S Z T U R Y * and J A N O S M I N K Central Research Institute for Chemistry, Hungarian Academy o[ Sciences, P.O. Box 17, H-1525 Budapest, Hungary (G.K.); and Institute of Isotopes, Hungar- ian Academy of Sciences, P.O. Box 77, H-1525 Bu- dapest, Hungary (J.M.)

Index Headings: Blackbody radiation; IR emission spectroscopy; Tem- perature estimation.

INTRODUCTION

In the May 1991 issue of this journal, DeBlase and Compton 1 published a comprehensive review bringing together most of the basic knowledge on IR emission spectroscopy available in the literature up to 1988. Dis- cussing the role of the temperature of the sample and detector, the authors show a series of blackbody curves, both computer-generated and measured ones, for differ- ent temperatures and draw the following conclusion:

The computer-generated blackbody c u r v e s . . , can be used to carry out an internal check of sample temper- ature spectroscopically. By searching for the best fitted theoretical curve which matches the experimental sin- gle-beam spectrum, one can determine the sample temperature during the emission measurement. 1

The idea is clear but it has not been developed properly, and some important details of the procedure seem to be ignored or overlooked by the authors. In our opinion the above statement is valid with good approximation only if the temperature of the detector is much lower than that of the blackbody. If not, correction for the detector temperature must be made as outlined below.

Instrumental distortions are usually compensated for by means of multiplying the measured spectrum by the instrument response function. This operation, however, cannot compensate for the effect in question: it does not take into account the changes of sample temperature, and it will never reproduce the zero spectrum observed when the sample and detector are at the same temper- ature. The appropriate correction should also include subtraction of the emission spectrum of the detector.

Depending on the detector temperature, subtraction of the "detector emission spectrum" can lead to signif- icant decrease in intensity and to a shift in the maximum of measured blackbody emission curves to higher fre- quencies, as seen in the examples of Fig. 1. For instance, if a blackbody emitter is at 400 K, the maximum of the corresponding theoretical curve is near 772 cm -1 (curve C in Fig. 1). However, using a room-temperature DTGS detector and supposing that its emission is close to that of a blackbody (e.g., at 300 K, curve A), we expect the detected radiation to have the shape of curve B in Fig. 1 with the maximum shifted to near 950 cm 1--a fre- quency that would otherwise correspond to a blackbody temperature of 492 K. If a liquid-N2-cooled MCT detec- tor is used or, in general, if the difference between the temperatures of the sample (Tbb) and detector (T,~et) is sufficiently great (e.g., Tbb > 4Tdet), the shift of the max- imum may become negligible. (However, correction for instrument self-emission has increasing importance with low-temperature detectors, unless the whole instrument is cooled.)

Thus, in order to make a fair comparison or meaningful search of the theoretical blackbody curves for temper- ature determination, both the theoretical curves and the measured spectra should be corrected. For this purpose we are suggesting the procedure described below.

Correction of the Measured Emission Spectrum for In- strument Self-Emission and Instrument Response. Since self-emission of the instrument may give rise to inverted interferograms (ZPD peak turned upside down), sub- traction of instrument self-emission from the measured blackbody emission should be done in the interferogram

DISCUSSION

Computer-generated blackbody curves are based on Planck's distribution law that assumes detection of all emitted radiation, i.e., a detector temperature of 0 K. ~= Laboratory-generated blackbody curves, however, are most often measured with MCT or DTGS detectors kept at liquid-N2 or room temperature, respectively. It is ob- -~ vious that if the temperature difference between the blackbody (sample) and the detector is not great enough, the measured single-beam spectrum, as it is, will deviate significantly from the theoretical blackbody emission curves, no matter how great the collection angle of the emission attachment. (A trivial proof of this statement z is the fact that emission of a room-temperature sample cannot be measured with a room-temperature detector.)

Received 1 December 1991; revision received 15 June 1992. * Author to whom correspondence should be sent.

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FIG. 1, Computer-generated blackbody radiation curves for 300 (A), 400 (C), and 500 K (E). Curves B and D give differences C - A and E - A, respectively.

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3000

FIG. 2. Blackbody emission spectra obtained using a Digilab FTS- 20C spectrometer (DTGS detector, KBr optics), and computer-gen- erated (uncorrected) blackbody radiation curves for 100 and 60°C (top and bottom pairs, respectively).

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FIG. 3. Blackbody emission spectra as in Fig. 2 and computer-gen- erated blackbody curves for 100 (top) and 60°C (bottom) corrected for detector temperature (29°C).

stage. The difference is then Fast Fourier Transformed (FFT), and the resulting single-beam spectrum, L(v, T), is divided by the instrument response function R(D (de- termined in a separate measurement) to obtain the cor- rected single-beam blackbody emission spectrum, L*(v, T):

L*(~, T) = FFT{IT - IT(aet)}/R(~') = LO', T) /R(v)

where Iv is the interferogram of the blackbody emission at T, and IT(~eO is the interferogram of the instrument self-emission (measured as emission of the blackbody at detector temperature).

Correction of the Series of Theoretical Blackbody Ra- diation Curves. Deviation of the detector temperature from 0 K can be taken into account by subtraction of the curve H(v, Tdet) corresponding to blackbody radiation at detector temperature from the blackbody radiation curves calculated for different temperatures:

H*(v, T) = H,O,, Ti) - f.H(~,, Tde,)

where the use of a constant factor, f, may be justified to take into account the deviation of radiation properties (or surface reflectivity) of the detector from those of the blackbody.

Computer Search for Best Matching Theoretical Curve. Apart from measurement noise, L* is expected to have a shape similar to H*; thus the set of H* curves can be searched against L* to find the closest match to estimate the temperature thereby. Alternatively, H(v, T~et) can be added to L*(~, T), and the resulting spectrum can be compared to the original theoretical blackbody emission curves, Hi(~,, Ti).

Dividing the measured emission spectrum by the in- strument response function has been recommended by

Griffiths, 2 who noted in addition that it was theoretically possible but rather difficult to estimate the temperature of the sample from the spectra. However, correction of the theoretical curves for detector temperature, which is needed to get the correct instrument response function as well, is a new approach in our procedure.

We have tested the feasibility of the above method by

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FIG. 4. Ins t rument response functions obtained for the Digilab FTS- ~20C spectrometer using a laboratory blackbody sample emitting at 100 (top) and 60°C (bottom).

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a6oo z~oo z6oo I~oo 16oo ~oo NRVENUMBEFI

FIO. 5. Emission spectrum of a laboratory blackbody sample at 60°C measured with a room-temperature detector and corrected for instru- ment response (noisy curve) compared to the theoretical blackbody radiation curve corrected for detector temperature (smooth curve).

measurements on a laboratory blackbody sample with a Digilab FTS-20C spectrometer equipped with a room- tempera ture DTGS detector. Single-beam emission spectra of the blackbody (a metal disk covered by mat black paint) were recorded at sample temperatures of 100 and 60°C and corrected for instrument self-emission as suggested above. The resulting single-beam blackbody emission spectra (L*) are plotted in Fig. 2 in a common energy density scale. The two smooth curves in Fig. 2 are the theoretical blackbody emission curves (Hi) cor- responding to the same two temperatures. Although no attempt has been made to adjust the absolute intensities by a more suitable scaling, the great differences in rel- ative intensities indicate that the measured blackbody spectra cannot be directly compared to the theoretical curves.

Correction of the theoretical curves by subtracting the curve corresponding to the actual detector temperature (29°C) from them leads to corrected blackbody curves (H*), shown in Fig. 3. Note that, this time, the relative intensities show a remarkably good correspondence to the measured ones, and in addition the positions of the maxima seem to have shifted to the right place.

The correspondence can be evaluated by dividing the measured curves by the corresponding corrected theo- retical ones to generate the instrument response func- tion, R (v), that is supposed to be independent of sample temperature. Figure 4 testifies that, apart from different noise levels in the region above 1800 cm -1, the R(D curves obtained for 100 and 60°C are very much the same; there- fore, the proposed correction scheme (with a one-to-one subtraction, i.e., f = 1) seems to be basically justified.

The corrected single-beam emission spectrum ob- tained for 60°C according to the first step of the proposed procedure (i.e., as the ratio of the spectrum measured at 60°C and the instrument response function determined at a higher temperature) deviates a little from the cor- rected theoretical curve H* (v, 60 °) in the region between 1300 and 400 cm -1, as shown in Fig. 5, although the overall shapes are very similar. The redundant bump near 830 cm -~ in the experimental curve suggests that correction for instrument self-emission has not been quite successful.

Once a good instrument response function is obtained, it can be used to simulate the measured single-beam

blackbody emission spectra, L*(T), for different tem- peratures by multiplying the corrected theoretical curves H*(,, T) by R(v). Note that this procedure can be used to generate lower-temperature blackbody reference spec- tra with a higher signal-to-noise ratio than what can reasonably be measured.

One more remark needs to be made regarding the use of theoretical blackbody emission curves. In Ref. 1 and in this work, a form of Planck's distribution law ex- pressed in the wavenumber domain as

H(v, T) = c l v 3 / [ e x p ( c 2 v / T ) - 1]

is used, where c2 = h c / k = 1.4388 cm. K, and ~ is expressed in cm-L Constant c~ may have different values (e.g., Cl = 2 7 r h c = 1.2482' 10 -~ erg. cm) depending on what kind of energy density is used. (In our case, c~ played the role of an arbitrary scaling factor to control the plot height.) The above function yields curves with maxima given by Wien's displacement law as ~mo, (cm-1) = 1.93. T. It is worth pointing out that Planck's distribution law and Wien's displacement law formulated for the wavelength domain as

H ( X , T ) = 2 7 r c 2 h / { X S [ e x p ( h c A k T ) - 1]}

and

Xma. (#m) = 0.2829/T,

respectively (see, e.g., Refs. 3 and 4), are not compatible with modern FT spectrometers producing spectra at con- stant resolution in frequency, since they are valid for constant resolution in wavelength. Thus, contrary to the example given in Ref. 2, the maximum of blackbody ra- diation for 300 K can be observed at 579 cm -1 instead of 10 #m (1000 cm -~) with a liquid-N2-cooled or lower-tem- perature detector. Note also that, for blackbody radia- tion curves H*(,, T) corrected for the detector temper- ature, the dependence of the maximum position on temperature cannot be described by a simple linear re- lationship.

1. F. J. DeBlase and S. Compton, Appl. Spectrosc. 45, 611 (1991); Erratum, ibid., 45, 1209 (1991).

2. P. R. Griffiths, Am. Lab. 7, 37 (1975). 3. P. V. Huong, in Advances in Infrared and Raman Spectroscopy,

R. J. H. Clark and R. E. Hester, Eds. (Heyden, London, 1978), Vol. 4, Chap. 3, pp. 85-107.

4. R. M. Goody, Atmospheric Radiation, Part I: Theoretical Basis (Oxford University Press, London, 1964), pp. 29-31.

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