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Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

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profitable to observe the spectra obtained in CDC13 so- lution, where effects from crystal structure are removed. As in the previous discussion, the vibrational bands at ~200 cm -1 can be assigned to the ~ A1 vibration of the hydrogen bond. ACKNOWLEDGMENT Financial support of this research by a grant from the Department of Energy (Officeof Basic Energy Sciences) is gratefully acknowledged. 1. C. J. Pedersen, J. Am. Chem. Soc. 89, 7017 (1967). 2. D. J. Cram, Applications of Biochemical Systems in Organic Chemistry, J. B. Jones, C. J. Sih, and D. Perlman, Eds. (John Wiley & Sons, New York, 1976), Part II, p. 815. 3. J.-M. Lehn, Pure Appl. Chem. 50, 871 (1978). 4. 0. Nagano, A. Kobayashi, and Y. Sasaki, Bull. Chem. Soc. Jpn 51, 790 (1978). 5. R. M. Izatt, B. L. Haymore, and J. J. Christensen, J. Chem. Soc. Chem. Commun. 1308 (1972). 6. G. S. Heo and R. A. Bartsch, J. Org. Chem. 47, 3557 (1982). 7. R. Chevert, A. Rodrigue, M. Pigeon-Gosselin, and R. Savoie, Can. J. Chem. 60, 853 (1983). 8. J.-P. Behr, P. Dumas, and D. Moras, J. Am. Chem. Soc. 104, 4540 (1982). 9. I. Goldberg, Inclusion Compounds 2, J. L. Atwood, J. E. D. Davies, and D. D. McNicol, Eds. (Academic Press, London, 1984), p. 303. 10. I. M. Kolthoff, W.-J. Want, and M. K. Chantooni, Jr., Anal. Chem. 55, 1202 (1983). 11. A. Rinch, P. N. Gates, K. Radcliffe, F. N. Dickson, and F. F. Bent- ley, Chemical Applications of Far Infrared Spectroscopy (Aca- demic Press, New York, 1970). 12. R. J. Jakobsen, J. W. Brasch, and Y. Mikawa, Appl. Spectrosc. 22, 641 (1968). 13. A. T. Tsatsas, R. W. Stearns, and W. M. Risen, Jr., J. Am. Chem. Soc. 94, 5247 (1972). 14. S. He, J. Wu, and T. Change, Revue de Chimie Minerale 20, 737 (1983). 15. W. J. Hurley, I. D. Kuntz, Jr., and G. E. Leroi, J. Am. Chem. Soc. 88, 3199 (1966). Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements ROBERT SAMS and ALAN FRIED* National Bureau of Standards, Center for Analytical Chemistry, Gaithersburg, Maryland 20899 There are various potential sources of systematic error in tunable-diode- laser absorption measurements. In this paper, we discuss two such sources that are associated with multimode lasing. The first is caused by sec- ondary modes which are passed by a monoehromator and are absorbed by lines not intentionally being studied. In the second source of error, different spatial modes may appear in different arms of a double-beam system. Both types of errors can give rise to rather dramatic systematic errors in frequency and concentration calibrations. Index Headings: Infrared; Diode lasers; Analytical methods; Spectro- scopic techniques. INTRODUCTION Photometric absorption techniques have long been used to study various gas molecules of atmospheric im- portance in both the laboratory and the earth's atmo- sphere. Quantitative determination of the concentration of such molecules under different conditions of pressure and temperature, however, first requires an accurate knowledge of line-center frequencies, intensities, and widths, and of line shapes. Tunable diode lasers (TDL), with their inherently high spectral resolution approach- ing 10 -4 cm -I, their broad frequency coverage spanning the entire near-IR region, and their continuous tunabil- ity over small frequency intervals, are ideally suited for these line-parameter measurements. Unfortunately, TDL absorption measurements are susceptible to many different types of systematic errors such as a nonuniform laser scanning rate, 1 an apprecia- Received 19 April 1985. * Author to whom correspondence should be sent. ble laser linewidth relative to the absorption feature un- der study, 2 and the presence of multimode lasing) All can have rather dramatic effects upon quantitative ab- sorption measurements. In the last case, systematic errors associated with multimode lasing can be further mani- fested in a variety of different ways. Diode lasers usually emit their output frequency si- multaneously in several longitudinal modes. These modes, which are typically separated by a few cm -1, can be eliminated by a monochromator. However, multi- mode lasing can also take place where two or more lasing modes are very closely spaced in frequency and thus are not rejected by the monochromator. Mucha, 3 in an ex- cellent study involving water-vapor line-parameter de- terminations, discusses some of the systematic errors arising from such satellite modes. In the present study, which was carried out on various rotational-vibrational absorption lines in the v3 band of NO2 near 6 #m, we discuss two additional sources of systematic error associated with multimode lasing. Not only can both of these error sources give rise to signifi- cant systematic errors in TDL measurements in the di- rect absorption mode, but also one of them can affect second harmonic measurements as well. Undoubtedly, a few diode laser experimentalists may be aware of these sources, but to our knowledge, these sources have not been discussed in the literature. EXPERIMENTAL The experimental apparatus is illustrated schemati- cally in Fig. 1. The output of a tunable diode laser (Spec- 24 Volume 40, Number 1, 1986 0003-7028/86/4001-002452.00/0 APPLIED SPECTROSCOPY © 1986 Society forApplied Spectroscopy
Transcript
Page 1: Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

profi table to observe the spect ra obta ined in CDC13 so- lution, where effects f rom crystal s t ructure are removed. As in the previous discussion, the vibrat ional bands at ~200 cm -1 can be assigned to the ~ A1 vibrat ion of the hydrogen bond.

ACKNOWLEDGMENT

Financial support of this research by a grant from the Department of Energy (Office of Basic Energy Sciences) is gratefully acknowledged.

1. C. J. Pedersen, J. Am. Chem. Soc. 89, 7017 (1967). 2. D. J. Cram, Applications of Biochemical Systems in Organic

Chemistry, J. B. Jones, C. J. Sih, and D. Perlman, Eds. (John Wiley & Sons, New York, 1976), Part II, p. 815.

3. J.-M. Lehn, Pure Appl. Chem. 50, 871 (1978). 4. 0. Nagano, A. Kobayashi, and Y. Sasaki, Bull. Chem. Soc. Jpn 51,

790 (1978). 5. R. M. Izatt, B. L. Haymore, and J. J. Christensen, J. Chem. Soc.

Chem. Commun. 1308 (1972).

6. G. S. Heo and R. A. Bartsch, J. Org. Chem. 47, 3557 (1982). 7. R. Chevert, A. Rodrigue, M. Pigeon-Gosselin, and R. Savoie, Can.

J. Chem. 60, 853 (1983). 8. J.-P. Behr, P. Dumas, and D. Moras, J. Am. Chem. Soc. 104, 4540

(1982). 9. I. Goldberg, Inclusion Compounds 2, J. L. Atwood, J. E. D. Davies,

and D. D. McNicol, Eds. (Academic Press, London, 1984), p. 303. 10. I. M. Kolthoff, W.-J. Want, and M. K. Chantooni, Jr., Anal. Chem.

55, 1202 (1983). 11. A. Rinch, P. N. Gates, K. Radcliffe, F. N. Dickson, and F. F. Bent-

ley, Chemical Applications of Far Infrared Spectroscopy (Aca- demic Press, New York, 1970).

12. R. J. Jakobsen, J. W. Brasch, and Y. Mikawa, Appl. Spectrosc. 22, 641 (1968).

13. A. T. Tsatsas, R. W. Stearns, and W. M. Risen, Jr., J. Am. Chem. Soc. 94, 5247 (1972).

14. S. He, J. Wu, and T. Change, Revue de Chimie Minerale 20, 737 (1983).

15. W. J. Hurley, I. D. Kuntz, Jr., and G. E. Leroi, J. Am. Chem. Soc. 88, 3199 (1966).

Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

R O B E R T S A M S a n d A L A N F R I E D * National Bureau of Standards, Center for Analytical Chemistry, Gaithersburg, Maryland 20899

There are various potential sources of systematic error in tunable-diode- laser absorption measurements. In this paper, we discuss two such sources that are associated with multimode lasing. The first is caused by sec- ondary modes which are passed by a monoehromator and are absorbed by lines not intentionally being studied. In the second source of error, different spatial modes may appear in different arms of a double-beam system. Both types of errors can give rise to rather dramatic systematic errors in frequency and concentration calibrations. Index Headings: Infrared; Diode lasers; Analytical methods; Spectro- scopic techniques.

I N T R O D U C T I O N

Pho tomet r i c absorpt ion techniques have long been used to s tudy various gas molecules of a tmospher ic im- por tance in bo th the labora tory and the ear th ' s a tmo- sphere. Quant i ta t ive de te rmina t ion of the concentra t ion of such molecules under different conditions of pressure and t empera tu re , however, first requires an accurate knowledge of l ine-center frequencies, intensities, and widths, and of line shapes. Tunab le diode lasers (TDL), with their inherent ly high spectral resolution approach- ing 10 -4 cm -I , their broad f requency coverage spanning the entire nea r - IR region, and their cont inuous tunabi l - ity over small f requency intervals, are ideally sui ted for these l ine -paramete r measurements .

Unfor tunate ly , T D L absorpt ion measu remen t s are susceptible to m a n y different types of sys temat ic errors such as a nonuni form laser scanning rate, 1 an apprecia-

Received 19 April 1985. * Author to whom correspondence should be sent.

ble laser l inewidth relative to the absorpt ion fea ture un- der study, 2 and the presence of mul t imode las ing) All can have ra ther d ramat ic effects upon quant i t a t ive ab- sorption measurements . In the last case, systematic errors associated with mul t imode lasing can be fur ther mani- fested in a var ie ty of different ways.

Diode lasers usually emi t their ou tpu t f requency si- m u l t a n e o u s l y in s eve ra l l o n g i t u d i n a l modes . T h e s e modes, which are typical ly separa ted by a few cm -1, can be el iminated by a monochromator . However, mult i - mode lasing can also take place where two or more lasing modes are very closely spaced in f requency and thus are not rejected by the monochromator . Mucha, 3 in an ex- cellent s tudy involving water -vapor l ine -paramete r de- terminat ions , discusses some of the sys temat ic errors arising f rom such satelli te modes.

In the presen t study, which was carr ied out on various ro ta t ional -vibra t ional absorp t ion lines in the v3 band of NO2 near 6 #m, we discuss two addi t ional sources of sys temat ic error associated with mul t imode lasing. No t only can bo th of these error sources give rise to signifi- cant sys temat ic errors in T D L measu remen t s in the di- rect absorpt ion mode, bu t also one of t hem can affect second harmonic measu remen t s as well. Undoubtedly , a few diode laser exper imenta l i s t s m a y be aware of these sources, bu t to our knowledge, these sources have not been discussed in the l i terature.

E X P E R I M E N T A L

The exper imenta l appa ra tus is i l lustrated schemati- cally in Fig. 1. The ou tpu t of a tunable diode laser (Spec-

24 Volume 40, Number 1, 1986 0003-7028/86/4001-002452.00/0 APPLIED SPECTROSCOPY © 1986 Society for Applied Spectroscopy

Page 2: Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

Cold Head Diode Laser

OAP OAP

Chopper OAP

OAPS Detecto~

Vertically Displaced Beams ~.. Detector B /

" " ~ ) I ~ L__~___ =

VDFMP Absorption Cell

OAP: Off Axis Parabola BS: Beam Splitter

ETALON

\ Sample Cell

BS

VDFMP: Vertically Displaced Flat Mirror Pair FIG. 1. Schematic of experimental apparatus. In each vertically displaced flat-mirror pair (one at the entrance and one at the exit of the monochromator) one mirror is above the plane of the figure.

tra Physics, Laser Analytics Div.)t was collimated into a 6-mm-diameter beam with the use of an all-reflective optical system similar to that employd by Jennings. 4 Ap- proximately 10% of the beam (the reference beam) was split off with a pellicle beamsplitter and was directed through a three-inch Ge etalon for frequency calibra- tion. The main beam passed through two absorption cells, a 50-cm cell and a 16-cm cell, placed in series. The long- er one, which was used for NO2 absorption measure- ments, was connected to calibrated 10-and 1000-Torr MKS Baratron pressure transducers. The smaller cell was fixed in place and was used to establish the opaque limit for each absorption line under study. Both cells were independently connected to their own vacuum sys- tems. The sample and reference beams were imaged on the entrance slit of a monochromator. As shown in Fig. 1, this was accomplished with the use of a pair of ver- tically displaced flat mirrors at both the entrance and exit of the monochromator. After passage through the monochromator, which was employed for gross mode se- lection, both beams were again separated and each was

t To adequately describe materials and experimental procedures, it was occasionally necessary to identify commercial products by man- ufacturer's name or label. In no instance does such identification imply endorsement by the National Bureau of Standards, nor does it imply that the particular products or equipment are necessarily the best available for the purpose.

focused onto the surface of a HgCdTe detector. Both detector outputs were directed into a computer through a pair of lock-in amplifiers and a 12-bit analog-to-digital converter (ADC) board. The pair of lock-in amplifiers and the ADC board were calibrated and were found to be linear to better than 0.1%.

We first carried out the absorption measurements with both cells evacuated to record the 100% transmission baseline. Selected mixtures of NO2 in air were next al- lowed to flow through the 50-cm absorption cell under pressures typically around 1.5 kPa (11 Torr). Absorption scans were recorded by computer as the diode was slowly scanned through each absorption feature. Scanning was accomplished with the use of the computer and a 12-bit digital-to-analog converter. A complete scan of an indi- vidual region took approximately 8 min. Etalon scans were recorded simultaneously. No further attempts were carried out in this study to thermostat this etalon to minimize fringe temperature drifts. However, the spin splitting between resolved NO2 lines is known accurately enough so as to allow a convenient check on our fre- quency calibration. In most cases the etalon fringe spac- ings resulted in splittings that were within ± 3.5 % of the measured splittings. 5,6 After recording the absorption features, we filled the 16-cm cell with pure NO2 at pres- sures around a few Torr until the mode absorption be- came opaque. All absorption lines under study were then rescanned. The beam was also shuttered to indicate the

APPLIED SPECTROSCOPY 25

Page 3: Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

i I I

A 151,15~_

ll j!

I 1 I I I F I

1 4 2 , 1 2 ± 114,8

.01622 cm "1

FIG. 2A. Direct absorption and etalon scans of NO~ lines in the 1603.6 cm i region as a function of diode current (X-axis). The 114,s+ absorp- tion line occurs at 1603.7069 ~ and the etalon-free spectral range at 296 K is 0.01622 cm -1. The N02 sample is a 2280-ppm mixture of N02 in air, The nominal cell length is 50 cm and the total pressure is 1.6 kPa (11.8 Tort).

I I ] I E I I I I I

C / j ~ r i m a ry r v I ode Absorption

Secondary Mode Absorption

I I I J I ] I I I

Fro. 2C. Display of secondary-mode absorption (lower trace) super- imposed on the absorption spectrum of the primary mode of 2A. The two peaks marked by arrows in the lower trace indicate absorption from a small amount of the primary mode leaking through. The cor- responding primary-mode absorption leaking through near the other two peaks gives rise to the broadened appearance. The axes are the same as in 2A.

amount of stray radiation in other lasing modes. Using this set up and these procedures, we observed some very interesting mode behavior, as will now be discussed.

RESULTS AND DISCUSSION

Mucha shows in his paper 3 that a satellite mode from one particular laser, approximately 0.02-0.04 cm -t from the center of a water-vapor line under study, caused a systematic decrease by as much as 30 % in the line-cen- ter absorption coefficient. This laser, furthermore, pro- duced structure on the opaque limit scan that could not be satisfactorily explained. In the present study, we ob- served this same type of structure in our opaque limit scans of NO2 in the 1603.6 cm- ' region.

In Fig. 2A, the TDL is scanned through a number of transitions in this region. The two strongest lines shown, the 151.t5± and the 142,12±, are actually unresolved spin- split doublets, and the two weakest lines, the 114,8_ and the 114,s+, are spin-split pairs that are just resolved. Only in the case of the weaker resolved lines will we continue to use the _+ notation to delineate the spin-split lines.

I I I l I I I I

Shuttered Z e r o

FIG. 2B. Opaque limit scans of NO= lines in the same region recorded by filling a 16-cm cell with approximately 0.4 kPa (3 Tort) of pure NO=. The axes are the same as in 2A.

The low-finesse etalon trace recorded simultaneously at the bottom of Fig. 2A does not show the presence of any other modes. However, the opaque limit scans of these same transitions shown in Fig. 2B do indicate the pres- ence of other lasing modes. Not only are the opaque limits different from the shuttered 0 % transmission level, but also the opaque limit scans for the first three lines show considerable structure. Furthermore, this struc- ture in all cases gives additional absorption compared with the nonstructured opaque limit of the 114.8+ line. The source of this structure, which we have seen on nu- merous occasions, was found to be caused by a secondary mode being absorbed simultaneously by NO2 lines dif- ferent from the primary lines shown in Fig. 2A. In this particular case the secondary mode, which was passed by the monochromator, was approximately 2.2 cm -1 from the primary mode. This occurred despite the fact that the slit widths were adjusted to yield a theoretical mono- chromator bandpass less than 1.3 cm -1. The decrease in the monochromator rejection was invariably caused either by our not properly filling the monochromator grating or by the fact that the acceptance angle of the monochromator was greater than that anticipated, be- cause of a slightly different spatial orientation of the secondary mode. It should be pointed out, however, that the same opaque limit structure could just as well have been caused by a close-lying satellite secondary mode passed by the monochromator. In fact, this has been observed during the course of other studies.

Employing a high-finesse confocal interferometer, such as proposed by Jennings, 7 would be an important ad- junct to the above opaque limit measurements. This in- terferometer should immediately reveal the presence of such secondary modes, even close-lying satellite modes. However, as in the present case where secondary-mode absorption occurs near the primary-mode absorption, appropriate experimental steps and/or corrections must still be applied to eliminate systematic errors. Estimates for such systematic errors will be discussed shortly.

Lasing in different modes will not only have different

26 Volume 40, Number 1, 1986

Page 4: Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

frequencies but can also be different spatially. In Fig. 2C, we display the NO2 absorption spectrum due to the secondary mode (lower trace) superimposed on the ab- sorption spectrum of the primary mode of Fig. 2A. We achieved this by adjusting the optical alignment of the off-axis parabola that focuses the radiation at the chop- per, shown on the right side of Fig. 1, so as to optimize the throughput of the secondary mode instead of the primary mode. All other experimental conditions in- cluding the starting current and scanning rate were maintained constant in an at tempt to establish a com- mon current axis for this overlay. The absorption due to the secondary mode was found to occur in the QQ branch of NO2, approximately 2.2 cm -1 higher than the 1603.6 cm 1 region of the primary mode. This display directly indicates the absorption features responsible for the structured opaque limit scans shown in Fig. 2B. The two absorption peaks on the secondary-mode scan that are marked by arrows indicate absorption due to a small amount of the primary mode leaking through. These two features were very useful because they provide addition- al information on the spectral relationship between the two modes. The primary-mode absorptions leaking through near the other two peaks are also present; how- ever, they are closer to the secondary-mode absorption features and thus appear as broadened lines. In the ab- sence of the primary-mode absorption, each of the QQ branch lines in the lower trace of Fig. 2C would have the same shape.

In all three cases, the additional absorption caused by the second mode clearly explains the opaque limit struc- ture shown in Fig. 2B; the second mode appears slightly to the right of the 151,15 and 114.8 peaks and slightly to the left of the 142,12 peak. In accordance with the non- structured opaque limit observed in Fig. 2B, the l14.s+ peak is not coincident with any secondary-mode absorp- tion features.

A different appearance in the opaque limit scans of spin-split components like the 114,8+ and l14,s_ lines is an obvious indication of the presence of additional mode absorption, be it caused by either secondary modes passed by the monochromator which are close or by those far removed from the primary mode. Both line compo- nents are close in frequency and in intensity (within 10% ) and, therefore, should give rise to identical opaque limits. In fact, all four peaks of Fig. 2A should give rise to identical opaque limits. On a previous day in which a different optical alignment and diode current and tem- perature were employed, identical opaque limits were in fact observed for the 151,15, the 142,12, and the 114,8+ peaks. As expected, the limits were nonstructured. By incor- rectly using the wrong opaque limit, one can incur sys- tematic errors. In the present example of Fig. 2A and 2B, the determination of concentration based upon the 151,1~, the 142,12, and the 114.8_ lines would be low, by 4.0%, 9.8%, and 5.5%, respectively, if the maximum absorption of each opaque limit were employed instead of the correct value given by the l14,s+ line. As shown in Fig. 2C, the secondary-mode absorption features near the 142.12 and the 114.s_ peaks appear so close to the absorption features of the primary mode (approximately 0.003 and 0.004 cm -1, respectively) that attaining the opaque limit at lower NO2 pressures had no effect on

the appearance of the structure. Only in the case of the 151,15 line (approximately 0.007 cm -1 from the primary- mode absorption) did a lower pressure help to eliminate the structure on the opaque limit. In contrast, by further increases in the pressure of the absorbing gas, the max- imum absorption of each opaque limit scan further in- creases, giving rise to even larger systematic errors. Eventually, the secondary-mode absorption will also saturate, and all structure on the opaque limit scan will disappear. In his water vapor study, 3 Mucha shows this type of structural change as a function of pressure. The difficulty in determining the correct opaque limit due to this cause, even at low saturation pressures, may have been responsible for the 30 % systematic decrease in ab- sorption coefficient observed by Mucha.

This particular source of systematic error can be ex- pected whenever multimode lasing occurs in the study of polyatomic molecules where there is a high density of lines. The extent of the error is dependent on the strength and position of the secondary-mode features relative to that of the primary mode, as well as the line strength of the additional absorption features causing the struc- tured opaque limit. Fortunately, one can readily detect the presence of this type of error by carefully scanning a number of opaque absorption features in each spectral region of interest. The correct opaque limit should thus be found.

In addition to hindering the correct determination of the opaque limit, secondary-mode absorption features such as those shown in Fig. 2C may also cause additional absorption on the lower pressure scans where the ab- sorption measurements are carried out. This type of error would result in a positive bias in line strength or con- centration determinations, exactly opposite in sign to the previous error discussed above. The net bias would obviously depend upon the relative magnitude of both errors. However, in general, one adjusts the experimen- tal conditions such that the primary mode contains most of the intensity. Thus, only in cases where the second- ary-mode absorption is appreciably stronger than that of the primary mode will a significant positive bias oc- cur. Most of the time, the former bias will dominate. To guarantee this, it becomes important to identify the sec- ondary-mode absorption features so that the magnitude of the additional absorption can be calculated. In the present case, indicated by Fig. 2C, we estimate from the secondary-mode intensity, position, and appropriate line strengths that this second source of systematic error contributes less than 1% to the line-center absorption of all three peaks. Subsequent line-fitting of the 114,8_ and 114,8+ peaks confirmed this; the residuals of the fit from both lines were less than 1% and revealed no sys- tematic structure on the 114,8_ component relative to the unperturbed 114,8+ component. However, when this sec- ond type of error starts to become appreciable, mea- sured linewidths should become unduly broadened and, thus, pressure-broadening measurements would readily be affected. Alternatively, the presence amidst normal peaks of a peak with an unexplainable and exceptionally large linewidth should be an indication of this type of error. The more subtle case, as observed by Mucha, 3 where both modes fall within the same absorption-line profile would also give rise to exceptionally large line-

APPLIED SPECTROSCOPY 27

Page 5: Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

A

f B

J FIG. 3. (A) Direct absorption scan of NO~ in the 1603.6 cm -1 region showing spurious mode absorption feature marked by an arrow. (B) Same spectral scan as in 3A only spurious absorption was eliminated by realignment of the optics.

widths. For this reason, we recommend, as does Mucha, ~ frequent scanning of absorption features where the line- width can be accurately calculated when one is perform- ing a series of intensity measurements.

It is entirely possible that secondary-mode absorption can occur far enough away from the primary-mode ab- sorption so as not to affect the primary-mode absorption scans carried out under low pressure. However, the ab- sorption features may still be close enough so that the opaque limit scan, due to self-broadening, will contain absorption features from both modes. The scans for the 151.1~ peak appear to fall under this category. Under such conditions, the only systematic error that would arise is one associated with proper determination of the correct opaque limit.

Secondary-mode absorption far enough removed from the primary-mode absorption will show up as a spurious line. This is shown by the marked feature (with an ar- row) of Fig. 3A, for which no assignment could be found. Subsequent optical realignment eliminated this feature, as shown in Fig. 3B. As in all cases where secondary- mode absorption occurs, this second lasing mode hap- pens to occur at the same diode conditions of tempera- ture and current as the primary mode, even though its frequency is vastly different. We have seen this type of artifact many times, and thus one should keep in mind that the recorded spectrum is really a plot of transmis- sion as a function of diode current; each lasing mode will have a different frequency axis. In order to avoid such errors associated with artifact lines, one should make extensive use of line-assignment compilations.

The second major source of systematic error that we wish to discuss concerns the spatial behavior of multi- mode lasing. We have demonstrated in two different

28 Volume 40, Number 1, 1986

A

Reference Beam

ary Beam

B Reference Beam \

• ary Beam

FIG. 4. (A) Direct absorption scans of NO2 in both the primary and reference arms of a double-beam instrument taken by alternate place- ment of a 16-cm cell in each arm. The alignment is such that different spatial modes are present in each arm. (B) Similar scan as in 4A taken in another spectral region. The alignment is such that both the sample and reference arms contain the same spatial modes•

cases that changing the optical alignment can dramati- cally affect the mode distribution• Each mode can be emitted in a preferred direction with a given focal pa- rameter (f/#). Most diode laser spectrometers utilize more than one arm to achieve frequency or concentra- tion calibrations. However, unless precautions are taken, all double-beam instruments are subject to the possibil- ity that each arm may be transmitting a different frac- tion of each spatial mode, or worse yet, entirely different spatial modes. This is shown in Fig. 4A, where we dis- play NO2 absorption scans taken when a 16-cm cell filled with NO2 was alternately placed in the sample and ref- erence arms of our double-beam set up. The reference trace clearly shows the presence of many different lines from an additional mode(s) not appearing on the pri- mary trace. In addition, both traces show vastly differ- ent contours. This is a result of different mode intensi- ties and a different monochromator transmission for each beam. This behavior, which we have observed on a num- ber of occasions, is obviously dependent upon the char- acteristics of each individual diode laser. In Fig. 4B, we show a similar scan in a different spectral region when proper alignment is achieved. In this case, the sample and reference arms each contain the same spatial modes. The systematic errors that may arise from this source include: (1) line misidentification, (2) incorrect frequen- cy calibration using a reference cell or etalon in a ref- erence arm, and (3) incorrect concentration calibration in second-harmonic (second-derivative) experiments where a concentration reference cell is employed in a

Page 6: Potential Sources of Systematic Errors in Tunable-Diode-Laser Absorption Measurements

reference arm. This last source may be particularly sig- nificant since many researchers routinely employ a con- centration reference cell in a reference arm for field and laboratory calibrations of their double-beam instru- ment. This type of error, however, can easily be detected and eliminated. During each experimental run, one should place an absorption cell either in an arm common to both beams or, alternately, in both beams and record the absorption scans. As shown, gross differences should be immediately obvious and can be corrected by chang- ing the optical alignment.

CONCLUSIONS

In this study, we have shown how multimode lasing can dramatically affect the appearance and quantitative accuracy of diode-laser absorption measurements. Such systematic errors, however, can be minimized if one per- forms repeated measurements under different experi- mental conditions and takes the following precautions: (1) Frequently scan and observe the shape of the opaque limits of many different lines in the region of interest using as low a pressure as possible; (2) ascertain the

correct opaque limit from these measurements and iden- tify lines perturbed by secondary-mode absorption; (3) frequently record lines whose widths can be accurately calculated and compared with the observed spectra; and (4) check the spatial characteristics of each arm of a multiple-beam instrument using an absorption cell. A high-finesse confocal interferometer will greatly facili- tate these efforts by helping to identify the presence and relative positions of secondary modes. Unless these pre- cautions are taken, tunable-diode-laser absorption mea- surements may contain errors in the 5 to 30% range or larger.

1. J. J. Hillman, D. E. Jennings, and J. L. Faris, Appl. Opt. 18, 1808 (1979).

2. L. L. Strow, J. Quant. Spectrosc. Radiat. Transfer 29, 395 (1983). 3. J. A. Mucha, Appl. Spectrosc. 36, 141 (1982). 4. D. E. Jennings, Appl. Opt. 19, 2695 (1980). 5. R. Toth, unpublished results from the jet propulsion laboratory. 6. V. M. Devi, B. Fridovich, G. D. Jones, D. G. S. Snyder, P. P. Das,

J.-M. Flaud, C. Camy-Peyret, and K. N. Rao, J. Mol. Spectrosc. 93, 179 (1982).

7. D. E. Jennings, Appl. Opt. 23, 1299 (1984).

Molecular Vibration Frequency Assignment of Dimethylsilanediol

T H I E N D. HO Analytical Research, Dow Corning Corporation, Midland, Michigan 48640, and Department of Chemistry, Central Michigan University, Mr. Pleasant, Michigan 48859

The fundamental molecular vibration frequencies of dimethylsilanediol were studied and assigned based upon data collected by infrared and Raman spectroscopy, and upon the literature of analogous compounds. Dimethylsilanediol and dimethylsilane-d2-diol were prepared by the hy- drolysis of dimethoxydimethylsilane with water and deuterium oxi~le, respectively. The purity of dimethylsilanediol was verified by a gas chro- matographic technique. This research found the S iOH deformations of dimethylsilanedioi to absorb at 1175 cm -1 and 1060 cm i. Index Headings: Dimethylsilanediol; Molecular vibration; Infrared.

INTRODUCTION

Dimethylsi lanediol , Me2Si(OH)2, is the parenta l monomer of a whole series of important polymeric prod- ucts, 1 polydimethylsiloxanes. This monomer holds in- terest as a possible treating agent, plasticizer, and chem- ical intermediate to more complex silicone materials as well as being one of the few water-soluble silicones. 2 A number of physical characteristics of this monomer have been studied by several investigators2 -9 However, a de-

Received 11 March 1985; revision received 19 April 1985.

tailed frequency assignment for the fundamental molec- ular vibrations has not been reported.

Dimethylsilanediol is assumed to belong to symmetry group C2v and executes thirty-three fundamental vibra- tions, of which eleven are A1 type, active in both infrared and Raman spectroscopy; six are As type, active only in Raman; and eight are B1 and eight more B2 vibrations, active in both infrared and Raman.

In this work, a series of spectroscopic measurements, mostly by infrared, was performed to assign the funda- mental vibrations of dimethylsilanediol. The author ob- tained infrared and Raman spectra of dimethylsilane- diol, dimethylsilane-d2-diol, and tetramethyldisiloxane- 1,3-diol for comparision between them and with the spectra of the analogous compounds in order to assign the frequencies of those bands which appear in the mid- infrared region, from 4000 cm -1 to 400 cm -1. The skeletal bending vibrations of dimethylsilanediol were believed to fall in the far-infrared region. They were only tenta- tively assigned, based on data collected from infrared and Raman spectra.

A number of diorganosilanediols and tetraorganodi- siloxane-l,3-diols have been prepared in which the or- ganic groups are larger than methyl2 Dimethylsilanediol

Volume 40, Number 1, 1986 0003-7028/86/4001-002952.00/0 APPLIED SPECTROSCOPY 29 © t986 Society for Applied Spectroscopy


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