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966 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38. NO. IO. OCTOBER 1991 Tunable Diode Laser Spectroscopy for Isotope Analy sis-Detection of Isotopic Carbon Monoxide in Exhaled Breath Peter S. Lee, Richard F. Majkowski, and Thomas A. Perry Abstract-A high resolution tunable infrared diode laser spectroscopy system was developed for isotope analysis with sensitivity at ppb levels. Such a system is ideally suited for de- tection and measurement of minute amounts of infrared active compounds present in a huge noninfrared active background such as air. The operation and capabilities of the system were demonstrated b measurin physiological levels of isotopic car- bon monoxide, kI6O and '3C160, naturally present in exhaled human breath with essentially no sample preparation. The sim- plicity in obtaining such data suggests that fundamental phys- iological information may be derived from noninvasive mea- surements. This makes the system potentially useful for many biomedical applications. INTRODUCTION ADIOISOTOPES have been extensively used as R tracers. Many investigations, however, preclude their use either because there are no suitable radioisotopes for some elements (e.g., the longest lived radioisotope of ox- ygen, oxygen-15, has a half-life of 2 min), or because radiation exposure raises health, environmental, or waste disposal concerns. The application of stable isotopes as tracers predates that of radioisotopes [l], [2] but, because of the lack of a simple and versatile detection method, routine application of stable isotopes has thus far been limited. Mass spectro- metry is the traditional method for detection of stable iso- topes, but it requires extensive efforts to distinguish and measure chemically different molecules with the same nominal mass; an example is detecting a minute amount of carbon monoxide I2CI60 in the high background of ni- trogen I4Nl4N present in exhaled human breath. In previous papers, we presented a tunable diode laser spectroscopy system for isotope analysis [3], [4]. This system combines the specificity of the infrared absorption spectra of isotopic molecules and the resolution and spec- tral power density of diode lasers [5] with a unique dual path cell matched to the expected isotopic absorbances. Manuscript received January 23. 1990; revised January 8. 1991. P. S. Lee is with the Department of Biomedical Science. General Motors Research Laboratories. Warren, MI 48090. R. F. Majkowski was with the Department of Physics, General Motors Research Laboratories. Warren, MI 48090. He is now with Lawrence Technological University, Southfield, MI 48075. T. A. Perry is with the Department of Physics, General Motors Research Laboratories. Warren, MI 48090. This resulted in an isotope analysis system that is simple, versatile, and specific. However, the sensitivity of this approach is limited by the luminescence background and the ability to measure direct spectral transmission. To fur- ther enhance the detection sensitivity and to eliminate the small luminescent background that is present along with lasing emission, we added to this system the techniques of wavelength modulation and second-harmonic detec- tion. This system is ideally suited for detection and mea- surement of small quantities of compounds present in a large background of air with minimal or no sample prep- aration required, since the main constituents of air (nitro- gen, oxygen, and argon) are transparent to infrared radia- tion. This paper describes the stable isotope diode laser system and presents a sample application for the detection of background levels of isotopic carbon monoxide in ex- haled human breath. METHODS A. Wavelength Modulation and Harmonic Detection Wavelength modulation and harmonic detection pro- vides superior signal to noise ratio compared to conven- tional spectroscopy for weak optical absorptions [6], [7]. As the laser is slowly tuned over the spectral feature of interest, the wavelength of measurement is modulated at kHz frequency and with a window of the order of the spectral bandwidth. The detector output is processed by a frequency and phase selective amplification system (such as a lock-in amplifier) which is referenced to the modu- lation frequency. When the detection system is tuned to the fundamental of the modulation frequency, the output is proportional to the first derivative of intensity with re- spect to the optical frequency. Likewise, if the system is tuned to the second harmonic of the modulation frequency the output is proportional to the second derivative of the spectral signal (the mathematical relationship is presented in the Appendix). It is important to note that the deriva- tive spectroscopy is insensitive to any dc component of the signal, such as the broad luminescence background which may amount to - 1 % of the total laser emission. This nonlasing emission would, otherwise, contribute a constant intensity background and place a limit on the ac- curacy of straight absorption experiments. 0018-9294/91/1000-0966$01.00 0 1991 IEEE

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966 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38. NO. IO. OCTOBER 1991

Tunable Diode Laser Spectroscopy for Isotope Analy sis-Detection of Isotopic Carbon

Monoxide in Exhaled Breath Peter S. Lee, Richard F. Majkowski, and Thomas A. Perry

Abstract-A high resolution tunable infrared diode laser spectroscopy system was developed for isotope analysis with sensitivity at ppb levels. Such a system is ideally suited for de- tection and measurement of minute amounts of infrared active compounds present in a huge noninfrared active background such as air. The operation and capabilities of the system were demonstrated b measurin physiological levels of isotopic car- bon monoxide, k I 6 O and '3C160, naturally present in exhaled human breath with essentially no sample preparation. The sim- plicity in obtaining such data suggests that fundamental phys- iological information may be derived from noninvasive mea- surements. This makes the system potentially useful for many biomedical applications.

INTRODUCTION ADIOISOTOPES have been extensively used as R tracers. Many investigations, however, preclude their

use either because there are no suitable radioisotopes for some elements (e.g., the longest lived radioisotope of ox- ygen, oxygen-15, has a half-life of 2 min), or because radiation exposure raises health, environmental, or waste disposal concerns.

The application of stable isotopes as tracers predates that of radioisotopes [l], [2] but, because of the lack of a simple and versatile detection method, routine application of stable isotopes has thus far been limited. Mass spectro- metry is the traditional method for detection of stable iso- topes, but it requires extensive efforts to distinguish and measure chemically different molecules with the same nominal mass; an example is detecting a minute amount of carbon monoxide I2CI60 in the high background of ni- trogen I4Nl4N present in exhaled human breath.

In previous papers, we presented a tunable diode laser spectroscopy system for isotope analysis [3], [4]. This system combines the specificity of the infrared absorption spectra of isotopic molecules and the resolution and spec- tral power density of diode lasers [5] with a unique dual path cell matched to the expected isotopic absorbances.

Manuscript received January 23. 1990; revised January 8. 1991. P. S. Lee is with the Department of Biomedical Science. General Motors

Research Laboratories. Warren, MI 48090. R. F. Majkowski was with the Department of Physics, General Motors

Research Laboratories. Warren, MI 48090. He is now with Lawrence Technological University, Southfield, MI 48075.

T. A . Perry is with the Department of Physics, General Motors Research Laboratories. Warren, MI 48090.

This resulted in an isotope analysis system that is simple, versatile, and specific. However, the sensitivity of this approach is limited by the luminescence background and the ability to measure direct spectral transmission. To fur- ther enhance the detection sensitivity and to eliminate the small luminescent background that is present along with lasing emission, we added to this system the techniques of wavelength modulation and second-harmonic detec- tion. This system is ideally suited for detection and mea- surement of small quantities of compounds present in a large background of air with minimal or no sample prep- aration required, since the main constituents of air (nitro- gen, oxygen, and argon) are transparent to infrared radia- tion. This paper describes the stable isotope diode laser system and presents a sample application for the detection of background levels of isotopic carbon monoxide in ex- haled human breath.

METHODS A . Wavelength Modulation and Harmonic Detection

Wavelength modulation and harmonic detection pro- vides superior signal to noise ratio compared to conven- tional spectroscopy for weak optical absorptions [ 6 ] , [7]. As the laser is slowly tuned over the spectral feature of interest, the wavelength of measurement is modulated at kHz frequency and with a window of the order of the spectral bandwidth. The detector output is processed by a frequency and phase selective amplification system (such as a lock-in amplifier) which is referenced to the modu- lation frequency. When the detection system is tuned to the fundamental of the modulation frequency, the output is proportional to the first derivative of intensity with re- spect to the optical frequency. Likewise, if the system is tuned to the second harmonic of the modulation frequency the output is proportional to the second derivative of the spectral signal (the mathematical relationship is presented in the Appendix). It is important to note that the deriva- tive spectroscopy is insensitive to any dc component of the signal, such as the broad luminescence background which may amount to - 1 % of the total laser emission. This nonlasing emission would, otherwise, contribute a constant intensity background and place a limit on the ac- curacy of straight absorption experiments.

0018-9294/91/1000-0966$01.00 0 1991 IEEE

LEE er U / . : TUNABLE DIODE LASER SPECTROSCOPI 967

Signal

Reference 4 D'A Lock-In

I

Beam Spllner

Selectable Dual Path Cell

Hw Ne Laser

Modulation

. - - - . - . . . Monochromator1 . . _ _ - . -. . IChopPeri

Fig. 1. Schematic diagram of the tunable diode laser isotope analysis sys- tem. An off-axis parabola was used to collimate the IR radiation. This min- imizes optical interference by preventing laser light reflection from a col- limating lens. A chopper (shown in dotted line) was used for conventional absorption spectroscopy.

In the present system (Fig. l ) , the modulation is pro- vided by the signal generator built into the current supply (SP5820 control module, Laser Photonics). A lock-in am- plifier (SR5 10, Stanford Research Systems) referenced to

. the modulation frequency detected the second harmonic signal.

B. Diode Laser Isotope Analysis System and Computer Interface

The schematic diagram of the diode laser isotope anal- ysis system is shown in Fig. 1. The laser was a double heterojunction growth with a PbTe active layer and PbEuSeTe confinement layers [5] , operating typically around 120 K and 0.3 A. The laser was housed in a liquid nitrogen dewar-based temperature stabilization system. The dewar housing is a Precision Cryogenic Systems model PIR 107. The laser mounting and temperature sta- bilization system, designed and fabricated in house, con- sisted of the laser diode, temperature sensing diode, con- trol heater element, thermal link to the dewar cold stage, radiation shielding, and optical elements. At the operating temperature of the laser (typically around 120 K), the temperature could be controlled to within f 2 mK over a 2 h period as measured from a near Doppler limited spec- tral absorption line.

The scanning of the spectrum was accomplished by fine tuning the infrared laser emission through stepwise ramp- ing of the injection current. In the present system, the SR510 lock-in amplifier has a built in digital to analog channel with 13 bits of resolution from - 10.24 to + 10.24 V, providing a voltage increment of 2.5 mV (the incre- ment could be made finer using a voltage divider). The transfer function of the laser current supply is 20 mA/V. Thus, a 1.5 V external input to the current supply would provide a stepwise ramping current of 30 mA and scan the spectrum in 600 steps. The laser light was collimated by a 75 mm focal length (150 mm working distance), 90" off-axis parabola (Optical Filter Corp.). The collimated light passed through the sample cell, and focused onto a liquid N, cooled InSb detector (Model 40742, Santa Bar-

bara Research). The analog signal from the detector was digitized through a 13 bit A/D converter built into the lock-in amplifier. The spectrometer system was con- trolled by a software package with a PC/AT which com- manded the lock-in to drive the current supply, read the digital data from the lock-in, graphed the data in real time, and stored the data on the hard disk for subsequent anal- ysis.

There were several sample cells which could be in- serted in the optical path. A multireflection 20 m path length White cell (Foxboro) was used for low concentra- tion gas measurements. There was also an interconnecting dual path cell. This cell had a variable path length (0.5- 20.0 mm) short cell and a long cell (500 mm) which also allowed for a multiple pass configuration (maximum 3.5 m). This combination of cells gives a broad range of path lengths. The absorption intensities of two isotopic species with greatly different concentrations can be made similar by using the appropriate combination of these cells. Thus, the dynamic range problem associated with processing vastly different isotopic concentrations can be eliminated if a ratio measurement is desired.

A He-Ne laser, a pellicle beam splitter and a plane re- flecting mirror mounted on a kinematic base were used to facilitate the alignment of IR laser radiation. The align- ment was accomplished by adjustment of the optical ele- ments so that the He-Ne laser radiation was colinear with the IR path from the laser diode to the detector.

During the initial setup, a half meter grating mono- chromator was used to provide approximate wavelength identification and to filter out unwanted laser modes. Once the proper conditions were established, the monochro- mator was bypassed in all the subsequent experiments.

C. Collection and Analysis of Breath Samples

Volunteer human subjects were asked to breathe into an impermeable gas sampling bag (Anspec). The contents were then purged to remove trapped air. A fresh sample was then exhaled into the bag, and introduced into a glass flask with a liquid N2 cold finger to remove moisture. This was the only sample preparation step that was performed. The purpose was to keep unnecessary moisture from the optical cells. A portion of the sample was then introduced into the optical cell for quantitative and isotopic analysis of CO.

Calibration curves relating signal intensity and concen- tration (partial pressure in ppb to ppm in air) were ob- tained for isotopic spectral lines. Samples with different concentrations were prepared by mixing and dilution of 9.472 ppm total CO in air (Scott Speciality Gases EPA Protocol Gas) with compressed air (Scott Specialty Gases Hydrocarbon Free). The mixtures were prepared using two mass flow controllers with a flow range of 0-500 mL/min (Scott Specialty Gases, model 52-36AlV-50 and model 52-36E-4 control unit). Isotopic abundances for I2CI60 and 13C'60 were obtained from the AFCRL (Air Force Cambridge Research Laboratory) compilation [8].

968 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38, NO. IO, OCTOBER 1991

RESULTS

The diode laser emission could be broadly tuned over - 300 cm-I by varying the heat sink temperature (tuning rate - 5 cm-'/K), and fine tuned over - 1-2 cm-' by varying the injection current (tuning rate - 30 cm-'/A). Fig. 2(a) shows the absorption spectrum of carbon mon- oxide (10 torr, path length 0.5 m) scanned about a laser mode centered at about 2046 cm-I. Three isotopic lines, 13Ci60 P(13) at 2045.777 cm-I, 12C180 P(12) at 2046.070 cm-I, and I2CI6O P(23) at 2046.276 cm-I, can be clearly detected. Fig. 2(b) shows the second derivative spectrum over the same region. The curvature of the background, in Fig. 2(a), induced by the laser emission is clearly ab- sent in the second derivative spectrum, Fig. 2(b).

The second derivative signals (peak to peak) for the I2CI60 P(3) line at 2131.632 cm-l and the I3CI6O R(9) line at 2131.005 cm-I were determined. For constant iso- topic molecular concentration (9.344 ppm '*cl60, or 0.1049 ppm 13C160) but different pressures, there is seemingly linear response at pressure below about 10 torr. At higher pressures the second harmonic signal deviates significantly from a projected linear response. The results are shown in Fig. 3(a) and (b), respectively. The nonlin- ear response at higher pressures is expected. As shown in the Appendix, if the conditions for an optically thin sam- ple (i.e., weak absorption) or for a constant spectral ab- sorption coefficient at line center (i.e., low pressure or high but constant pressure) are no longer valid, the sec- ond-harmonic signal is not linearly proportional to con- centration.

At a constant operating pressure of 30 torr, the rela- tionship between second harmonic signal and isotopic molecular concentration was determined. As shown in Fig. 4, a linear response was observed for the I2Ct60 P(3) line at a concentration of 1-10 ppm in air. Likewise, a linear response was also observed for the I3CI6O R(9) line at a concentration of 0.01-0.1 ppm in air. Linear regres- sion analyses indicate correlation coefficients of 0.9994 and 0.9975, respectively. Since we could detect the pres- ence of minute amounts of carbon monoxide in the com- pressed air used to blend the reference gas, the level of this impurity was corrected in all the samples. It is noted that the second-harmonic signal is linearly proportional to varying concentrations at a constant pressure of 30 torr (Fig. 4). But, at 30 torr, it clearly deviates from a linear response with varying pressures (Fig. 3). These obser- vations indicate that a decrease in spectral absorption coef- ficient at line center due to pressure broadening is the main reason for the nonlinear response of signals with varying pressures (see Appendix). Consequently, a linear rela- tionship between signal and concentration can be ex- pected for any one of the following three experimental conditions:

1) experiments conducted at low pressure (5 torr or be- low), or

2) experiments conducted at a constant pressure, or 3) the line strength rather than the spectral absorption

0.2110 q-J f

0.0978 0.05 30 I

(b) Laser C u m (mA)

Fig. 2 . (a) Absorption spectrum of carbon monoxide ( I O torr, 0.5 m path '

length) scanned by a laser mode centered at 2046 c m - ' . (b) The second derivative spectrum over the same region.

l*l@ 0.1049ppm

I I I ~ I * ~ ~ ~ I 0 50 100

Total Pressure (Tom)

(b) Fig. 3. (a) Second harmonic signal as a function of total sample pressure for the "C"0 P(3) vibration rotation line. All the samples had a constant concentration of 9.344 ppm "Cl'O in air. (b) Second harmonic signal of the "C"0 R(9) line as a function of total sample pressure. The concentra- tion of 'k"0 in all the samples was constant at 0 .1049 ppm in air.

LEE et al. : TUNABLE DIODE LASER SPECTROSCOPY 969

0.00 5.0 10.0 10.0 ' " . I " '

0.01 0.00 0.05 0.10

Concentration (ppm I%%)

Fig. 4. Second harmonic signal versus CO concentration at a constant sample pressure of 30 torr (in air) for isotopic "C"O and 'C"O.

coefficient at line center is used (i.e., integrated peak area is used).

The levels and isotopic composition of carbon monox- ide, I2CI6O and ' 3C i60 , naturally present in exhaled breath were determined in a group of volunteers.' The levels of I2CI6O fall between 1.6 to 2.4 ppm for non smokers, and between 12 and 15 ppm for smokers, with measurements from a light smoker in between the two groups. Likewise, the levels of isotopic I3CI6O fall between 0.02 and 0.03 ppm for nonsmokers, and between 0.14 and 0.18 ppm for smokers, again with light smoker's data in between the two groups. This is shown in Fig. 5. There is an overall deviation from AFCRL isotopic abundance, indicating general enrichment of the heavier I3C isotope in the car- bon monoxide present in exhaled breath. Although these results are preliminary and no special efforts were made to guarantee a purely alveolar sample, they demonstrate the usefulness of the system for noninvasive biomedical testing for the following reasons: 1 ) no preparation of breath sample is needed other than removal of water va- por, and even this is not a necessity; 2) extremely high sensitivity ( - ppb) can be easily obtained with a moder- ately long absorption path (a 20 m multireflection path was used in the present experiment, whereas 100-1000 m folded paths are commercially available); and 3) even with a nonoptimized data handling system, the spectral infor- mation for a complete scan over a laser mode was ob- tained in a matter of minutes.

With careful selection of the laser emission mode, high detection sensitivity down to sub-ppb levels can be easily achieved. The consistency of the measurements can be demonstrated by the absolute as well as the relative abun- dance of isotopic molecules. While the bulk of the data presented in this paper were obtained using an in house fabricated 10- 15 pm mesa stripe laser, these consistency

' A protocol for the experiments was approved by the General Motors Human Research Committee.

/ /

0 . 0 0 / a - v I ' 0 5 ' I ' 2 . ' 0.0 5.0 10.0 15.0

12cl@ in Exhaled Breath (ppm)

Fig. 5 . Isotopic carbon monoxide naturally present in exhaled human breath. Deviation from projected AFCRL isotopic abundance (dotted line) indicates general enrichment of the "C isotope which was especially no- ticeable in the smokers.

measurements were obtained using a commercial 4 pm buried layer laser (Laser Photonics). At a total CO con- centration of 2.37 ppm in air (total sample pressure 10 torr), the standard deviation for the relative abundance of I2CI8O to I2CI6O measured over a period of 2-3 h was found to be 0.5 %. The standard deviation for the absolute concentration of 12C'80 at 4.92 ppb was 1.5%. There was no difference in the standard deviation for the relative abundance of two isotopic molecules measured either within a single laser emission mode or across two emis- sion modes. This is consistent with the specified accuracy of k l % gain accuracy for the lock-in amplifier used in the present experiment.

We have demonstrated the detection of isotopic carbon monoxide naturally present in exhaled human breath at levels far below those reported in the literature [9]-[ 1 11. The ease with which such measurements can be made suggests that new fundamental physiological information can be derived from non-invasive testing using only a breath sample. Rigorous efforts are under way to improve and expand these measurements by: 1) collecting more consistent end tidal air samples such as those collected with a Rahn End Tidal Breath Sampler [12]; and 2) col- laborating with medical institutions to obtain samples from subgroups of the general population for possible identifi- cation of medical disorders.

DISCUSSION A . Biomedical Applications

It is conceivable that a number of simple, noninvasive and nonradioactive biomedical, clinical, and field diag- nostic applications can be developed using this system. A few examples are: diabetes, liver function, alcoholic cir- rhosis, malnutrition, lean body mass, total body water,

~

970 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 38. NO. IO, OCTOBER 1991

fat malabsorption, blood disorders, jaundice, ileal dys- function, drug metabolism, lung function, energy expen- diture (caloric requirement), protein turnover/synthesis, lactase deficiency (milk intolerance), small intestine bac- terial overgrowth, inborn errors of metabolism. Some po- tential diagnostic procedures have already been demon- strated in clinical research using either radioactive isotopes or stable isotope/mass spectrometry [ 131, [ 141. However, because of the radiation safety restrictions or the technical difficulties, even those diagnostic techniques already demonstrated to be feasible remain generally un- available as routine procedures.

We have demonstrated the measurement of isotopic carbon monoxide in exhaled breath. Such measurements should be useful in the following studies:

I ) Study related to the catabolism of heme protein- Carbon monoxide is endogenously produced along with billirubin from the catabolism of heme protein on a mole per mole basis [ 15]-[ 181. Since hemoglobin comprises over 90% of the total body heme, monitoring of endoge- nously produced CO in subjects who refrain from smok- ing should be a good indicator for a number of blood dis- orders that result in the alteration of red blood cell catabolism rate [ 191-[21].

2) Study that may be related to the catabolism of heme protein-Jaundice is caused by high levels of billirubin in circulating blood. An increased concentration of billiru- bin can be caused either by the excessive destruction of red blood cells, or by interference with the mechanism of billirubin excretion through the bile. A noninvasive test based on the detection of endogenously produced CO could be developed for infant jaundice.

3) Study related to the formation of hemoglobin- Hemoglobin, specifically the a-methene bridge carbon atom of the heme ring [20], [22], is the precursor of CO. It is synthesized in living cells from starting materials de- rived from food sources. The isotopic composition for a given element in various food sources is known to have natural variations that reflect the isotopic fractionation through different biochemical pathways [23], [24]. In- deed, isotopic variations were observed for I3C in expired CO2 among different human individuals [25], and the preferential use of I6O in consumed oxygen associated with respiration has been reported [26]. The detection of less abundant isotopic specie in the endogeneously pro- duced CO could provide unique information on the di- etary history of the subjects.

Other molecules such as carbon dioxide, water, am- monia, formaldehyde, hydrogen peroxide etc, can be de- tected and measured noninvasively in the breath. Indeed, the applicability of the system can be extended to almost any infrared active molecules. This is because of the ex- tremely high spectral resolution and spectral power den- sity of the individual diode laser, and the broad range of wavelengths for which diode lasers are available. The sensitivities required for most diagnostic tests would be much less demanding than the ppb levels demonstrated

for the present system. This would be especially true if the particular isotopic specie comes from the intake of labelled compounds, for example, the detection of excess expired 13C02 from oral administration of I3C enriched glucose [27]. Most screening procedures using natural levels of endogenously produced molecules would also require lower sensitivities, since only the most abundant isotopic specie need to be detected. The higher sensitivi- ties (ppb or sub-ppb levels) would only be required in the detection of less abundant isotopic specie and in the assay of biological tissues where isotope analysis can be made on CO (oxygen isotope) or CO2 (carbon isotope) resulting from pyrolysis or combustion of the sample.

A simple, compact and versatile tunable diode laser isotope analysis system would meet the requirements for the development of diagnostic procedures and functional tests for the general population under free living condi- tions. These procedures would be noninvasive, are non- radioactive, require no hospitalization, and provide dy- namic evaluations.

B. Isotopic Primary Standards The precise analysis of isotopic composition is usually

accomplished in mass spectrometry through ratio mea- surements of isotopic ion beams. The ratio of the isotopic ion beams (current or voltage) is proportional to the true isotopic abundance ratio with the proportionality constant dependent upon a number of factors [28]:

a fractionation factor due to capillary constriction of viscous into molecular flow during gas inlet;

a factor due to difference in ionization cross section of isotopic molecules;

a factor to account for the collection yields (such as focusing conditions) of the isotopic ion beams;

a factor due to unequal gains (dynamic range) of am- plifiers, etc.

For most work, the proportionality constant is difficult to determine. Furthermore, long term stability in ion beam ratios is difficult to maintain. Consequently, the concept of differential comparison and the del (%o) notation was introduced, and the isotopic abundance is expressed as the relative difference in ratio between a sample and a stan- dard [29]. In the del expression, the proportionality con- stant is canceled out, and the difference in long term drift between the sample and the standard remains most likely the same. For this purpose, primary standards such as SMOW (Standard Mean Ocean Water) [30], and V-SMOW [31] for hydrogen and oxygen, or PDB (PeeDee Belem- nite) for carbon [32] were defined. Reference standards, typically CO2 (there is none for CO at the current time), were then derived from primary standards and used in the differential comparison measurements. However, uncer- tainties due to undetermined equations arising from over- lapping isotopic ions of the same nominal mass [28] may still persist even in the standards. Because of the high spectral resolution of the diode lasers, the problem of un-

LEE er 01.: TUNABLE DIODE LASER SPECTROSCOPY 97 1

determined equations is eliminated if a diode laser based system is used. It should also be noted that the necessity of having to determine the isotopic abundance as a rela- tive difference in ratio is not critical here, since none of the fractionation problems mentioned above exist in this type of high resolution spectroscopy.

APPENDIX ' The laser intensity I(v) can be expanded about fre-

quency is, as is is slowly tuned by ramping the diode laser current

(n) -

n.

CU

I(v) = y (v - V ) "

where I ( " ) ( i s ) is the nth derivative of Z(v) with respect to v evaluated at is.

To generate the harmonic signal, a small sinusoidal modulation of amplitude a and angular frequency w is su- perimposed on the diode laser ramping current,* resulting in

v = V + a sin ut (2) then

(3)

Sin" ut can be expanded into a sum of multiple angle sine and cosine functions [33]

sin ut for n odd. I n! + (- 1)@ - ' ) / 2 ( n - 1 ) / 2 !

(4)

sinn ut = 7 cos nut - n cos (n - 2)wt (- [

n(n - 1) 2

+- COS ( n - 4)wt +

n! + (- 1 p - 2 ) / 2 cos (n - 2 ) / 2 !

n! 1 n / 2 ! 2"

+ - . - for n an even

. . .

2ur]

integer. (5)

'Part of the formulation is taken from 16). [71. and 1341. 'Harmonic signal can also be generated by nonsinusoidal modulation such

as triangular wave where the contribution of each Fourier component will be considered.

Substituting (4) and (5) into (3) and rearranging terms, the signal with angular frequency 2w has the form

For small modulation amplitude a , the intensity at 2w is proportional to the second derivative of I(v) with respect to v.

The incident laser intensity IJv) is related to the trans- mitted intensity I(v) by the Beer-Lambert law

I(v) = Zo(v) exp [-a(v) * I p ] (7)

where a(v) is the spectral absorption coefficient, 1 and p are the path length and pressure (concentration), respec- tively.

For an optically thin sample (i.e., a(v) * 1 - p << I ) , and at the line center frequency (i.e., da(v, , ) /dv = 0), the dominant term of the second harmonic signal is

The first term in (8) is a dc offset which should be small since the curvature of ZJv,) is very small, and the second term indicates that the second-harmonic signal is linearly dependent on concentration. It can be shown that for low absorption and at the line center, the fourth-order contri- bution in (6) is also linear, and the overall second har- monic signal is linear in concentration (pressure).

The spectral absorption coefficient a(v) is related to the line strength S by the line shape function +(v - v,,) [341, U51

a(v) = s 4 ( v - V(,) . (9)

The line shape can be described by a Voigt profile [34]

(10) 1

Y D +(v - v,) = - (In 2/7r) 'I2I/(b, x)

where - ,'2 e . V(b, X ) = - dy (Voigt function) !yw b2 + (x -

b = (In 2 ) ' / 2 y c / y D (ratio of collision broadened linewidth yc to Doppler linewidth yD)

x = (In 2 ) 1 / 2 ( v - v,)/yD (distance from line center frequency normalized by the Doppler linewidth)

yo = v. (2k T In 2 / m ) ' / * (Doppler linewidth)

and where C is the velocity of light, k is the Boltzmann

C

972 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 38. NO. IO. OCTOBER 1991

constant, T i s the absolute temperature, and m is the mo- lecular mass.

At low pressure, the Voigt function reduces to Gauss- ian (Doppler broadening)

at line center frequency yo , the Voigt function reduces to a constant, and the spectral absorption coefficient be- comes a constant (at constant temperature).

At high pressure, the Voigt function reduces to Lo- rentzian (collision broadening)

- 1 Y, a (v - vJ2 + Y f ’

Equations (lo), ( 1 1 ) , or (12) along with (6) and (7) can be used to calculate the magnitude of the harmonic signal.

ACKNOWLEDGMENT The authors wish to express their sincere thanks to D.

L. Partin and C. M. Thrush for providing the diode laser, D. K . Lambert for the help in alignment with the off axis parabolic mirror, R. A. Gorski for help in plumbing the gas handling system, and J . B. D’Arcy for advice on blending the gas mixture. They also wish to thank R. M. Schreck, C. C. Green and J . P. Heremans for discussions and support during the progress of the work.

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LEE er crl . : TUNABLE DIODE LASER SPECTROSCOPY 973

Peter S. Lee received the undergraduate degree including five patents, on these varied subjects While at GMRL he a l w in cheniistry from the Ndtional Taiwan Univer- taught physics at the University of Detroit (1955-1958), Detroit Institute sity, Taipei, the Ph D degree in physical chem- of Technology (1958-1979), and Lawrence Technological University istry from the University of Illinois, Urbana- (1979-present) In September 1987, he retired from GMRL and remained Champaign. and post-graduate training from the on the physics faculty at LTU He is al\o a conwitant to GMRL on diode University of California, Irvine laser\ and their applications

He worked in the Department of Medicine, University of Illinoi\ Medical School, Chicago He joined General Motors Research Laboratories i n 1977 and has worked i n area$ of diesel euhau\t emissions, isotope tracers, diode laser spectrw-

copy and applications, and biosensors

Richard F. Majkowski wa\ born in Detroit, MI. on April 18. 1930. He received the undergraduate and terminal graduate degrees in physics from the University of Detroit. Detroit. MI.

He joined the General Motors Research Labo- ratories, Warren, MI. in 1955. There he worked on magnetics, emission spectroscopy and plasma physics, laser in combustion research and data processing. holography, and the development of lead salt diode lasers and their applications. He has authored or coauthored over 30 publications.

Thomas A. Perry received the B.S . degree from the University of Michigan, Ann Arbor, with dual majors in physics and chemistry in 1980, the M.S. degree in physics from the University of Wiscon- sin, Madison, in 1982, and the Ph.D. degree in physics from the University of Michigan in 1985.

He joined General Motors Research in 1985 and has been active in areas of growth and character- ization of new materials and also application of spectroscopy as diagnostic tool.