Abstract:
Novel methods and laser spectroscopic systems for accurately measuring the concentration of compounds are disclosed herein. The disclosed methods utilize a modulation cancellation technique resulting in a significantly increase in the sensitivity and accuracy of laser spectroscopic measurements. In general, the methods and systems utilize modulation phase-shifting and amplitude attenuation to cancel the signals detected from at least two modulated light beams. Thus, any signal detected will be directly proportional to the concentration measurement.

Description:
TECHNICAL FIELD OF THE INVENTION 
     The present invention relates to techniques in laser spectroscopy. More particularly, this invention relates to wavelength modulation spectroscopy. 
     BACKGROUND OF THE INVENTION 
     Concentration ratio measurements via laser spectroscopic methods have been in use for many years. The most commonly studied elements have been carbon ( 13 C/ 12 C), distantly followed by hydrogen (D/H). The two main measurement methods are based on emission spectra and absorption spectra. Initially, quantitative determination of concentration ratios via the emission spectra of molecular transitions was inaccurate and not useful. At the same time, the absorption spectra lacked the resolution needed to characterize overlapping but isotopically different molecular transitions. This was mainly due to lack of power at monochromatic wavelengths. With the advent of lasers in the late 1960&#39;s, this limiting factor was eliminated, and high-resolution characterization of polyatomic species with isotopic substitution was possible. It was not until the completion of laser absorption studies in controlled laboratory settings that quantitative emission studies became useful. 
     Laser isotopic studies of carbon in methane and other short chain hydrocarbons continued for academic purposes until the late 1980&#39;s. In the 1990&#39;s, little scientific work was done in the field of carbon isotopic measurements in hydrocarbon gases. Since the 1990&#39;s, the academic focus has shifted to laser isotopic studies of inorganic polyatomic molecules. Commercialized applications of  13 C/ 12 C measurements have been used in medical research (measuring exhaled carbon dioxide), and in geological research for determining inorganic characterization of water and carbon in sandstone/mudstones, pyrite, sphalerite, galena and calcite. In the analysis of exhaled CO 2 , light emitted by a CO 2  laser is used to measure isotope ratios. Inorganically bound isotopes of sulfur, oxygen, and hydrogen have also been studied with lasers for geological and environmental purposes. 
     Although much improved, current laser spectroscopic methods still possess some shortcomings. For example, in the context of a sample that contains two chemical species A and B having concentrations [A] and [B], respectively, concentrations are typically calculated from measurements of very small deviations of R=[A]/[B] ratio from the same ratio R st  in the reference (standard) sample. The most common application where such measurements are required is isotopomer abundance quantification. In this case, the deviation from standard is commonly expressed as 
     
       
         
           
             
               
                 
                   
                     δ 
                     [ 
                     
                       % 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       o 
                     
                     ] 
                   
                   = 
                   
                     
                       
                         R 
                         - 
                         
                           R 
                           st 
                         
                       
                       
                         R 
                         st 
                       
                     
                     × 
                     1000 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The existing spectroscopic approaches to measure δ require precise separate measurements of the absorption lines for A and B with the subsequent numerical calculation of δ. This approach requires an extremely high accuracy of measurement because practically important δ ranges are between ˜1% to 0.1%. For example, in traditional approaches the required or desired measurement accuracy for [B] may be 10 −4 . In practice, making such precise measurements is extremely difficult due to small variations in temperature, pressure, and other external factors. 
     The most common tool for this type of measurements is a mass-spectrometer (MS). MS provides the required accuracy, but there are a number of shortcomings associated with this technology. Mass spectrometers are expensive, bulky and in general can not be used in the field. A sample preparation is required that can potentially affect the isotopic composition. Confusion between molecules or molecular fragments with similar masses is possible. 
     Infrared molecular absorption spectroscopy is considered as a viable alternative to MS, but few groups have succeeded in achieving the required accuracy even in laboratory experiments Current optical instrumentation for determination of isotopic composition is based on separate precise measurements of the strength of absorption lines corresponding to two isotopes with the subsequent numerical comparison. Hence, a small difference between isotopic compositions of the analyzed sample and the reference sample is determined as a difference between two large numbers (concentration ratios). Some of the issues adding to the error of such an approach are: the temperature and pressure dependence of the absorption line intensity; non-linearity of laser tuning; baseline distortions caused by spurious interference fringes and far wings of the irrelevant strong absorption lines; and isotopic fractionation in the sampling procedure. 
     Another problem with present laser spectroscopic techniques has been the detection of species with broad irresolvable absorption features, which is a characteristic of many polyatomic molecules. In such cases, a semiconductor laser usually can not be wavelength modulated with a swing sufficient to cover the whole absorption feature. Thus, detection of such molecules would require amplitude modulation of the laser radiation. The scattered and subsequently absorbed light creates an incoherent background, making low-level concentration measurements difficult. 
     Accordingly, there is a need for a simple method of accurately measuring small deviations in concentration ratios using laser spectroscopy. It is further desired to provide a laser spectroscopic method to detect minute concentrations of complex molecules. 
     SUMMARY OF THE INVENTION 
     Novel methods and laser spectroscopic systems for accurately measuring concentrations of compounds are disclosed herein. The disclosed methods utilize a modulation cancellation technique resulting in the detection of a signal which is directly proportional to δ in Equation 1. Thus, the disclosed methods and systems significantly increase the sensitivity and accuracy of laser spectroscopic measurements. 
     These and other needs in the art are addressed in one embodiment by a method for measuring a concentration of a first and a second compound in a sample composition. The method comprises providing at least a first and a second modulated light beam having a first and a second wavelength, respectively. The second modulated light beam is phase shifted from the first modulated light beam. The method also comprises passing the first and the second modulated light beam through a reference composition. The reference composition comprises a reference concentration of the first and the second compound. In addition, the method comprises detecting a reference signal resulting from the absorption of the first and second modulated light beam by the reference composition. Moreover, the method comprises adjusting the amplitude of the second modulated light beam such that no reference signal is detected. Additionally, the method comprises passing the first modulated light beam and the second modulated light beam through a sample composition. The method further comprises detecting a sample signal so as to measure the concentration of the first and the second compound in the sample composition. 
     In another embodiment, a method for measuring the concentration of a compound having a background wavelength and an absorption wavelength comprises providing at least a first and a second modulated light beam, wherein the second modulated light beam is phase shifted from the first modulated light beam. The method also comprises tuning the first modulated light beam to the background wavelength of the compound and the second modulated light beam to the absorption wavelength of the compound. Moreover, the method comprises tuning the amplitude of the second modulated light beam such that no signal is detected when the first and the second modulated light beam are passed through a composition lacking the compound. In addition, the method comprises passing the first and the second modulated light beam through a sample composition. The method further comprises detecting a signal indicative of the concentration of the compound in the sample composition. 
     In a further embodiment, a laser spectroscopic system comprises a first and a second light source. The first and said second light source emit a first and second modulated light beam, respectively. The second beam is phase shifted from the first modulated light beam. Furthermore, the system comprises a sample cell including a sample detector. The sample cell contains a sample composition comprising a first and a second compound. The first and said second modulated light beam pass through the sample cell. The system additionally comprises a reference cell including a reference detector. The reference cell contains a reference concentration of the first and the second compound. The first and said second modulated light beam pass through said reference cell. Moreover, the system comprises an attenuator coupled to said reference detector and said second light source. The attenuator controls the second light source to match the amplitude of the second modulated light beam to the amplitude of the first modulated light beam such that no signal is detected from the reference detector. 
     The foregoing has broadly outlined the features and technical advantages of the present invention in order that the detailed description of the invention that follows may be better, understood. Additional features and advantages of the invention will be described hereinafter that form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and the specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the scope of the invention as set forth in the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the invention, reference is made to the accompanying drawings, wherein: 
         FIG. 1  is a schematic of a modulation cancellation method according to an embodiment of the invention; and 
         FIG. 2  is a schematic of a second embodiment of the present modulation cancellation method as applied to chemical species with broad unresolved species. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , an embodiment of a laser spectroscopic system  100  is shown schematically and in general, includes first and second light sources  101 ,  102 , a polarization combiner-splitter  161 , a sample cell  111 , and a reference cell  112 . First and second light source  101 ,  102  typically each comprise a tunable laser device. However, first and second light source  101 ,  102  may comprise any suitable light emitting device. In certain embodiments, first and second light source  101 ,  102  comprise distributed-feedback diode lasers. Alternatively, first and second light source  101 ,  102  are quantum cascade lasers. First light source  101  generates a first modulated light beam  121  and second light source  102  generates a second modulated light beam  122 . As defined herein, a modulated light bean is a beam of radiation in which the wavelength or amplitude of the beam of radiation is varied or modulated at a particular modulation frequency. 
     In further embodiments, laser spectroscopic system includes a first and second beam splitter  104 ,  106 . First and second beam splitter  104 ,  106  split first and second beams  121 ,  122  and direct each respective beam to first and second polarization controllers  141 ,  143 , and first and second calibration cells  151 ,  153 , respectively. First and second cells  151 ,  153  typically each comprise a photodetector such as a photodiode, although other types of photodetectors may be utilized. In general, each cell  151 ,  153  contains a reference concentration of a compound. Specifically, first cell  151  contains a reference concentration of a first compound while second cell  153  contains a reference concentration of a second compound. The photodetector from each cell is coupled to a controller  184  which in turn is coupled to first and second current controllers  105 ,  107 . First and second current controllers  105 ,  107  adjust the wavelength of first and second light sources  101 ,  102 . 
     According to another embodiment, system  100  also includes a controller  184  such as a low-power digital signal microprocessor. However, any suitable microprocessors may be used with the laser spectroscopic system  100 . Other examples of suitable processors include without limitation, field programmable gate arrays, microcontrollers, programmable logic devices, application specific integrated circuits and the like. As shown in  FIG. 1 , in an embodiment, controller  184  is coupled to reference cells  151 ,  153  and current controllers  104 ,  105  for line-locking first and second light source  101 ,  102 . In other embodiments, additional controllers (not shown) may be coupled to first and second lock-in amplifiers and first and second light source  101 ,  102 . The additional controllers may be used to calibrate or tune the modulation frequency of first and second modulated light beams  121 ,  122  in embodiments utilizing resonant acoustic detectors. 
     In embodiments, controller  184  includes memory. Memory may comprise volatile (e.g., random access memory) and/or non-volatile memory (e.g., read only memory (ROM), electrically-erasable programmable ROM (EEPROM), Flash memory, etch). In a preferred embodiment, memory is flash memory. Memory may be used to store data or code (e.g., software, discussed below) that is executed by the controller  184 . The executable code may be executed directly from the non-volatile memory or copied to the volatile memory for execution therefrom Laser spectroscopic system  100  may also include memory external to controller  184 . This external memory is generally coupled to controller  184  and may comprise either volatile or non-volatile memory. 
     In general, first and second compound may be any material or chemical. Additionally, the first and second compound may be a gas or a liquid. In preferred embodiments, the second compound is an isotope of the first compound. By way of example only, the first compound may comprise H 2   16 O while the second compound may comprise H 2   18 O. Other examples of the first and second compounds include without limitation,  12 C- and  13 C-containing species,  32 S- and  34 S-containing species,  14 N and  15 N containing species, or H- and D-containing species. 
     In one embodiment, the system  100  includes a polarization combiner-splitter  161  which combines first and second beam  121 ,  122  into a combined beam (not shown) and splits it into a first and second combined beam  123 ,  124  as seen in  FIG. 1 . However, the first and second modulated light beams  121 ,  122  may be combined by any suitable means including, without limitation, a wavelength division multiplexer, a polarization combiner, or diffraction grating. In addition, the system  100  may incorporate a separate beam combiner and beam splitter to combine first and second beam  121 ,  122  and split the combined beam. 
     In at least one embodiment, the system  100  comprises an attenuator  190 . Attenuator may be any device known to one of ordinary skill in the art used to adjust the intensity of a light beam. Depending on the embodiment, attenuator  190  may be used to adjust first or second beam  121 ,  122 . In the embodiment shown in  FIG. 1 , attenuator is coupled to second lock-in amplifier  167 . As will be described in more detail below, attenuator  190  may utilize signals from reference detector  117  via second lock-in amplifier  167  to adjust intensity of second beam  122 . 
     In an embodiment, system  100  comprises a sample cell  111  and a reference cell  112 . Sample and reference cells  111 ,  112  generally comprise sample and reference detectors  115 ,  117  which serve to detect signals from sample and reference cells  111 ,  112 , respectively. In any case, first and second cells  111 ,  112  generate sample and reference output signals  131 ,  132 , respectively. Moreover, sample and reference cell  111 ,  112  contain the sample and reference compositions, respectively. The sample composition generally comprises a concentration of the first and the second compound while the reference composition comprises a known or reference concentration ratio of the first and second compound. As will be described in further detail below, the described apparatus is used to determine whether the sample composition contains a concentration ratio of the compounds different than the reference composition. 
     According to one embodiment, sample and reference detectors  115 ,  117  are used to detect the absorption of the combined beams  123 ,  124  by the sample composition and the reference composition. More specifically, the detector  115  in sample cell  111  detects a signal generated because of the absorption of the first and second modulated light beam in combined beam by the sample composition. In a particular embodiment, detector  115  is an acoustic detector such as a microphone, a quartz tuning fork, etc. In other embodiments, detector  115  is a photodetector such as a photodiode. However, detector may be any suitable detector capable of detecting absorption of light by a compound. Similarly, reference detector  117  may comprise a photodetector, an acoustic detector, or any other suitable detector. 
     Sample detector  115  may be coupled to a first lock-in amplifier  165 , Likewise, reference detector  117  may be coupled to a second lock-in amplifier  167 . First lock-in amplifier  165  is generally coupled to an output device or a microprocessor to process the data generated from sample cell (not shown). On other hand, second lock-in amplifier  167  is typically coupled to an attenuator  190  as shown in  FIG. 1 . Attenuator  190  is preferably used to adjust the amplitude of second modulated light beam  122  in response to a signal received from second lock-in amplifier  167 . 
     Another embodiment of a laser spectroscopic system  200  is shown in  FIG. 2 . Such an embodiment may be used to detect minute concentrations of complex, polyatomic molecules. In this embodiment, system  200  includes first and second light sources  201 ,  202 , a beam combining device  261 , and a sample cell  211 . Beam combining device  261  may comprise a polarization combiner as described above. Sample cell  211  includes a detector  215 . As with other embodiments, detector  215  may comprise an acoustic detector, a photodetector, or other suitable detector in this embodiment, system  200  does not require a dual line-locking feedback loop as shown in  FIG. 1 . Nor does system  200  implement a reference cell. Although not shown in  FIG. 2 , it is contemplated that other devices known to those of skill in the art for laser spectroscopy may be incorporated into system  200  such as microcontrollers, lock-in amplifiers, sensors, etc. 
     In one embodiment, a method of measuring a concentration of a first and a second compound in a sample composition comprises the following steps: a) providing at least a first and a second modulated light beam having a first and a second wavelength, respectively, wherein the second modulated light beam is phase shifted from the first modulated light beam; b) passing the first and the second modulated light beam through a reference composition, wherein said reference composition comprises a reference concentration of the first and the second compound; c) detecting a reference signal resulting from the absorption of the first and second modulated light beam by the reference composition; d) adjusting the amplitude of the second modulated light beam such that no reference signal is detected; e) passing the first modulated light beam and the second modulated light beam through a sample composition; and f) detecting a sample signal so as to measure the concentration of the first and a second compound in the sample composition. 
     Referring now to  FIG. 1 , in a preferred embodiment, first and second modulated light beams  121 ,  122  are wavelength-modulated or amplitude-modulated with the same modulation frequency f, but different phase. In other words, first and second modulated light beams  121 ,  122  generally have equal modulation frequencies, but opposite phase. However, other embodiments may incorporate different modulation frequencies. Unless otherwise noted, as defined herein, phase-shifting refers to adjusting or shifting the modulation phase of a light beam. As will be described in more detail below, the modulation of the second beam  122  may be phase-shifted 180° from first beam  121 . However, second beam  122  may be phase-shifted to any appropriate phase to cancel a signal from first beam  121 . For example, if the signals from sample and reference detector  115 , 117  are detected at twice the modulation frequency, the phase shift may be 90°. In some embodiments, injection current modulation may be imposed on top of the DC current that is used to power light sources  101 ,  102 . 
     Hereinafter, the first and second compound to be measured are referred to as A and B while the concentration of first and second compound are denoted by [A] and [B]. In an embodiment, first and second modulated light beams  121 ,  122  are emitted from first and second light source  101 ,  102  and are directed to first and second beam splitters  104 ,  106 . Preferably, the central wavelengths of first and second light source  101 ,  102  are tuned to the absorption wavelength of the first and second compound, A and B, respectively. Thus, the magnitude of the signal detected by a detector from first light source  101  after passing through the sample composition in sample cell  111  is dependent on the peak absorption and width of the spectroscopic line of A (in its turn, peak absorption is proportional to [A]), the radiation power from first light source  101 , and the modulation depth of first light source  101 . Similarly, the magnitude of the signal detected by a detector from second light source  101  after passing through a sample composition will depend on the peak absorption mid width of the spectroscopic line of  13  (in its turn, peak absorption is proportional to [B]), the radiation power from second light source  102 , and the modulation depth of second light source  102 . 
     The first and second beam  121 ,  122  are initially split to line-lock first and second light source  101 ,  102 . More particularly, first calibration cell  151  contains a reference concentration of A while second calibration cell  153  contains a reference concentration of B. Photodetector in each calibration cell  151 ,  153  provides a signal at the wavelength at which A and B absorb light, respectively. For example, first calibration cell  151  may contain a reference concentration of C 12  and second calibration cell  153  may contain a reference concentration of C 13 , a carbon isotope. The signals from the calibration cells  151 ,  153  are relayed to controller  184  to detect the wavelength error. Controller  184  performs a computation on the wavelength error signal, and sends this error factor to current controllers  105 ,  107  to adjust the wavelength of first and second light source  101 ,  102 . This feedback loop ensures that first and second light sources  101 ,  102  are emitting light at the appropriate wavelength corresponding to the absorption lines of A and B in sample cell. This wavelength control is known as “line-locking.” In particular embodiments, the line-locking may be accomplished by a 3f technique, where f is the wavelength modulation frequency of the light beam emitted from the light sources  101 ,  102 . 
     In a further embodiment, after passing through beam splitters  104 ,  106 , the polarization of the first and second beam  121 ,  122  may be altered or adjusted by passing the beams through polarization controllers  141 ,  143 . The polarization controllers adjust polarization of first and second beam  121 ,  122  so that the beams may be combined by a polarization combiner or another appropriate device. In an embodiment, first and second beams  121 ,  122  are combined into a combined beam and then split into first and second combined beams  123 ,  124  by polarization combiner-splitter  161  as shown in  FIG. 1 . Each combined beam  123 ,  124  thus comprises both first and second beam  121 ,  122 , preferably in identical proportions. 
     Preferably, first and second combined beam  123 ,  124  each have equal intensities. That is, combined beam is split evenly into first and second combined beam  123 ,  124 . However, it is contemplated that other embodiments may utilize different ratios of intensity between first and second combined beam. First combined beam  123  is directed to sample cell  111  while second combined beam  124  is directed to reference cell  112 . Because first and second beam  121 ,  122  are line-locked to first and second compound, respectively, as first and second combined beam pass through sample and reference cell  111 ,  122 , the first and second compound present in both the sample and reference composition will absorb the energy from first and second beam in each combined beam. In an alternative embodiment, it is contemplated that the combined beam need not be split into first and second combined beam  113 ,  135 , but instead a combined beam may pass through reference cell  112  and sample cell  111  in series (not shown). 
     The absorption of radiation by first and second compound is measured by sample and reference detectors  115 ,  117  in sample and reference cell  111 ,  112 , respectively. As mentioned above, any suitable means may be utilized to measure the absorption signals detected in sample and reference cell  111 ,  112 . According to one embodiment, the absorption of the combined beams  123 ,  124  by the sample composition and the reference composition may be detected by photoacoustic detection. More specifically, the detectors  115 ,  117  in sample cells  111 ,  112  detect an acoustic signal generated because of the absorption of the first and second modulated light beam in combined beam by the sample composition. In embodiments using photoacoustic detection, quartz tuning forks may be used in the reference and sample cells to measure the absorption signals. In other embodiments, photodetection may be used to detect absorption by the first and second compound. 
     After passing through second polarization controller  143 , second modulated light beam  122  is directed at an attenuator  190  before entering polarization combiner  161 . Alternatively, attenuator  190  may be placed before polarization controller  143  and thus, second modulated light beam  122  is directed to attenuator  190  before passing through polarization controller  143 . In preferred embodiments, the intensity of second modulated light beam  122  may be adjusted by using attenuator  190  to null the signal from reference detector  117 . In another embodiment, by adjusting the power P 2  of second beam  122  and/or its modulation depth, the corresponding signal may be made equal in magnitude but opposite in phase to the signal generated by absorption of first modulated light beam  121  to null the signal from reference detector  117 . 
     As disclosed above, the modulation of second light source  102  is phase shifted with respect to the wave modulation of first light source  101 . In some embodiments, such as 2f photoacoustic detection, second beam  122  is phase shifted by 90° such that the signals generated by first and second light source  101 ,  102  in the reference cell will be opposite in sign and cancel each other. Put another way, the two signals in the reference cell  112  are balanced in such a way that no generation of signal occurs and the detector  117 , does not detect any signal S ref :
 
 S   ref   =k   ref ( P   1   [A]   ref   −P   2   [B]   ref )=0  (2)
 
where k ref  describes responsivity of the reference detector  117  and P 1 , P 2  are optical powers of first and second light source  101 ,  102 , respectively. The signal dependence on the modulation index has been omitted for simplicity, and the spectroscopic line peak absorbance is represented by the concentration of the corresponding species. It follows from (2) that
 
 P   2   =P   1   [A]   ref   /[B]   ref   =P   1   R   ref   (3)
 
     Without being limited by theory, it is believed that if the ratio R=[A]/[B] is the same in sample cell  111  as R ref  in reference cell  117  and both samples are at the similar pressure and temperature conditions, the balanced radiation will not generate the response in the sample detector  115  either. If R is not equal to R ref , the sensor response gives:
 
 S=k ( P   1   [A]−P   2   [B] )  (4)
 
     Simple substitutions using (3), (1), and the definition of R give:
 
 S= 1/1000 ×kP   1   [B]R   ref ×δ  (5)
 
     Thus, any signal measured from the sample detector  115  in  FIG. 1  will be directly proportional to δ. In Equation (5) R ref  is known by definition, P 1  is constant and can be either monitored directly or derived from S ref  when second light source  102  is turned off, and k[B] can be derived from S when first light source  101  is off. In an alternative embodiment, the amplitude of first beam  121  may be adjusted using an attenuator (not shown) to adjust its amplitude or intensity with respect to the amplitude of second beam  122  to produce the same result above. 
     Any signal detected from sample detector is relayed to first lock-in amplifier  165  which is tuned to the modulation frequency of the light sources  101 ,  102 . Likewise, signal from reference detector  117  is amplified by second lock-in amplifier  167  which is tuned to the modulation frequencies of the light sources  101 ,  102 . Any signal detected from reference detector  117  indicates that the amplitude of second beam  122  needs to be attenuated. Accordingly, the signal from second lock-in amplifier is used in conjunction with attenuator  190  as part of a feedback loop to control the amplitude of second beam  122 . 
     In another embodiment, a method for measuring the concentration of a compound having a background wavelength and an absorption wavelength comprises: a) providing at least a first and a second modulated light beam, wherein the second modulated light beam is phase shifted from the first modulated light beam, b) tuning the first modulated light beam to the background wavelength of the compound and the second modulated light beam to the absorption wavelength of the compound, c) tuning the amplitude of the second modulated light beam such that no signal is detected in the absence of the compound when the first and the second modulated light beam are passed through a sample composition, d) passing the first and the second modulated light beam through a sample composition, and e) detecting a signal indicative of the concentration of the compound in the sample composition. 
     Referring to  FIG. 2 , first modulated light beam  221  from first light source  201  may be tuned to the background wavelength of the compound&#39;s absorption spectrum, while the second modulated light beam  222  from second light source  202  may be tuned to a target compound&#39;s absorption wavelength. In a preferred embodiment, the modulation of second modulated light beam  222  is phase-shifted from the modulation of first modulated light beam  221 . For example, second modulated light beam  222  may have a 180° phase shift from first modulated light beam  221 .  FIG. 2  shows an embodiment with rectangular amplitude modulation of light beams  221 ,  221 , but the amplitude modulation may be sine or any other waveform. As above, the emissions of first light source  201  and second light source  202  may be combined to be collinear and form a combined beam  225  by using a polarization combiner or other suitable device. Combined beam  225  may pass through a sample cell  211  containing a sample composition with an unknown concentration of the target compound. 
     Furthermore, the modulation amplitudes of first and second modulated light beams  221 ,  222  may be adjusted or tuned such that no signal is detected in the absence of the target compound, A, in a sample composition. If the concentration [A] is not equal to zero, the signal detected at the modulation frequency will be proportional to the concentration [A]. 
     A signal resulting from the absorption of the combined first and second light beams  221 ,  222  may be measured by any suitable means, including without limitation photoacoustic detection and photodiode detection. The target compound is preferably a compound that exhibits broad unresolved absorption features in laser spectroscopy. More particularly, the target compound may comprise a background wavelength and a target absorption wavelength. Such compounds are usually complex, polyatomic molecules. Without limitation, examples of such compounds include isoprene, nerve gases, hydrazine, rocket fuel components, or combinations thereof. 
     Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations may be made herein without departing from the spirit and scope of the invention as defined by the appended claims.