1. Introduction

Residual amplitude modulation (RAM) [1,2], arising from direct intensity modulation of the laser, has long been a major limiting factor in tunable diode laser spectroscopy (TDLS) with wavelength or frequency modulation (WMS and FMS respectively), particularly if signal recovery is implemented at the modulation frequency (i.e. if 1f or first harmonic detection is used). The RAM gives rise to a high background signal in 1f-detection with the small absorption signal superimposed. Signal amplification is limited by saturation of the detection electronics by the high background and there are significant sensitivity/resolution issues in the digital acquisition of signals. The origin of RAM in WMS and its distorting effects on various harmonic signals have been studied in great detail in several papers [3–5]. To circumvent the problem of high background signals, detection at twice the applied modulation frequency (2f or second harmonic detection) has been favoured, although, even for 2f-detection, a background signal arising from the RAM has been reported [6]. To address the problem more generally, electronic cancellation of RAM has also been attempted by a few authors. In two earlier double-beam-double-detector schemes, two different detectors were used to cancel the common-mode noise and baseline [7,8]. In the most recent attempt, a digitally generated 2f component with appropriately adjusted amplitude and phase has been added to the laser current modulation [9]. To date, it appears that no concerted effort has been made to eliminate the RAM at the optical level in TDLS-WMS and thereby make 1f detection a viable option. Recently, two new calibration-free methods, namely the RAM method [10], and the Phasor decomposition (PD) method [11], have been reported for the recovery of absolute absorption line shapes from the 1st harmonic signals. In both these techniques the predominant factor that fundamentally limits the sensitivity is the high RAM background. Elimination of the RAM would increase the sensitivity of both these methods, and the PDM in particular could then be exploited to its full potential. In this paper a simple and robust fiber-optic technique to eliminate the concentration-independent RAM component at the optical level is presented. This potentially offers the possibility of 1f, shot noise limited detection for calibration-free direct recovery of the absolute gas absorption lines.

The approach taken to suppress the RAM in this work is to split the modulated laser output power into two paths, one directed through a gas cell and the other through a fiber delay line, and then to recombine them just before the photo-diode detector. The sinusoidal modulation frequency/delay are chosen to ensure a π phase difference between them at the combiner. The amplitudes of the anti-phase intensity-modulated signals are balanced using a variable optical attenuator in the delay line arm, so that, in the absence of gas or off-line, they cancel at the combiner output. The resulting dc signal is rejected by the lock-in amplifier (LIA) making the output zero and thus eliminating the high background RAM signal. In the presence of gas the imbalance at the output directly reflects the concentration-dependent absorption of the gas. Here we describe the experimental system and the mathematical justification of the technique and demonstrate validity through measurements made by the RAM method [10] on methane/nitrogen mixtures compared to theoretical traces derived from HITRAN data.

2. Experimental details

Figure 1 shows the experimental system. An OKI 1651nm DFB laser with a built-in isolator is controlled by a Thorlabs LDC 210 current controller and TEC 210 temperature controller. Two Agilent 33250A 80MHz arbitrary waveform generators are used to apply a slow 5-Hz ramp and a 100 kHz sinusoid to the laser current for wavelength scanning and modulation. The output of the DFB is split by an OptoSci 1x4 fiber-optic splitter, with two outputs going to the gas cell (path length 5.9cm between GRIN lenses [10]) and the SMF-28 fiber delay line respectively. In order to introduce a phase shift of π to the signal component going through the delay fiber the required length of the delay fiber is given by$L=c/2nf$, where f is the modulation frequency and n is the refractive index of the fiber. The fiber length L is approximately 1km for a modulation frequency of 100 kHz and a typical value of 1.5 for n. A small adjustment of the modulation frequency is necessary to compensate for the small difference between assumed and actual values of both L and n. An important consideration in the choice of the modulation frequency is that the corresponding fiber length (that varies inversely as f) should be much longer than the coherence length of the laser in order to minimize optical interference. The coherence length of the DFB laser was determined to be ~43 m for a linewidth of 7 MHz which is much smaller than the fiber length. The outputs of the gas cell and the delay fiber after attenuation by a variable optical attenuator (Thorlabs VOA50-APC) pass through two polarization controllers (Thorlabs FPC562) to establish orthogonal polarization states for the two combining optical signals and thereby minimize optical interference noise at the 3dB coupler / combiner. The VOA is used to adjust their relative amplitudes so that they cancel at the output of the coupler. It was found necessary and sufficient to attenuate the output from the fiber delay arm only, because due to the appreciable loss through the gas cell that signal is weaker than the delayed signal by default. The output is detected by an InGaAs photodiode (OptoSci LNP-2) whose output is fed to a PerkinElmer 7280 DSP lock-in amplifier. To implement the RAM technique [10], 1f detection is performed with the LIA detection phase adjusted to null the classic WMS derivative signal and isolate the RAM components from it. The final output is observed on a Tektronix TDS 3014B 200MHz digital storage oscilloscope from which data is captured using a LabVIEW program.

 

Fig. 1 Experimental setup.

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3. Analytical treatment of RAM nulling

The reduction in transmission due to wavelength dependent absorption in the vicinity of a gas line is quantified by Beer’s Law,$I_t(\lambda )=I_0(\lambda )e^{-\alpha (\lambda )Cl}$, where I₀(λ) and I_t(λ) are the incident and transmitted intensities respectively, α(λ), is the wavelength dependent absorption coefficient, C is the gas concentration expressed as a fraction of the total molecular density and l is the path length through the gas. For weak absorption this may be approximated by$I_t(\lambda )=I_0(\lambda )[1-\alpha (\lambda )Cl]$. In a TDLS-WMS system with such weak absorption the signals at the output of the gas sensing region may be found using a simple Taylor series expansion of the absorption line shape function, α(λ) [10]. Including the laser direct intensity modulation terms and expressing the variables as functions of wavelength rather than frequency as in [10], this results in the following expression for the primary first harmonic terms, only strictly applicable at modulation indices, m, of less than 0.2 [10,11] -

Here, λ_c denotes the slowly-varying centre wavelength set by the ramp, δλ(λ_c) is the peak wavelength deviation, and ψ denotes the phase separation [3],between the intensity and wavelength modulation of a DFB laser. The first two terms arise from the direct laser intensity modulation and may be referred to respectively as the concentration-independent RAM, and the concentration-dependent RAM (collectively as$\Delta I({\lambda }_c)\cos \omega t{[1-\alpha ({\lambda }_c)Cl]}_{}$, simply the RAM signal). The third term is the classic WMS 1st harmonic/1st derivative signal arising from the interaction of the laser’s wavelength/frequency modulation with the gas line. The first term, when recovered by a LIA, gives rise to the high background output signal with the other two terms representing the deviations around it, arising from the presence of the gas.

In the RAM technique [10], the LIA signal detection phase is aligned at ψ-90° to null the first derivative signal and only the isolated RAM signals are recovered, again with the gas absorption signal, term 2, sitting on a high background signal, term 1. The overall aim of the RAM nulling technique reported here is to eliminate the high background signal through destructive interference at the signal frequency. With reference to Fig. 1 and assuming no gas, the signals arriving at the output of the fiber combiner, OP₁, from the gas cell and the delay line are of nearly equal amplitude (balanced by the VOA) and are anti-phase (due to the delay/modulation frequency choice). Hence, in the absence of gas or off-line, they cancel presenting only a high average DC level to the LIA resulting in a zero output. An imbalance results from the presence of gas and a non-zero LIA output arises, essentially from term 2 of Eq. (1). However, the elimination of the background leads to a complication in signal normalization because the concentration-dependent absorption signal now appears on a zero background. A simple mathematical formulation of the RAM nulling mechanism shows that it is relatively straightforward to extract a normalization method.

Given the above, the output at OP₁, in the absence of gas (or off-line) can be written:

In the presence of gas in the cell, the signal in that arm gets multiplied by a factor e^-α(λc)Cl due to the absorption. The resulting output, OP_1gas, is then given by,

Again, it is easy to see that OP_1gas sits on a near-zero background since off-line, $e^{-\alpha Cl}=1$. Subtracting (2) from (3) and reorganizing we get

The denominator of the last term in Eq. (4),$\Delta I_1({\lambda }_c)\cos \omega t$, is simply the output at OP₁ with the delay fiber arm disconnected from the coupler. As well as being crucial to recovering the gas absorption line shape, it also serves as a convenient normalization factor that accounts for any changes in background laser intensity and the wavelength dependencies of the laser output and the two couplers as regards the gas cell arm. In practice a fiber-optic switch inserted between the VOA and the coupler can be used to block the signal from the delay fiber line whenever this needs to be measured. Alternatively, it could be obtained using a fiber tap coupler inserted between the gas cell and the system output coupler, provided the relationship between the tap output and OP₁ is known and stable over the required wavelength range. In either case it can be obtained with or without gas in the cell, the former simply requiring a curve fit to the off-line data. The system output signal, OP₁, with or without gas, does not sit exactly on a zero background but has a small sloping background through zero due to the different wavelength dependencies of the different directions through the couplers, particularly evident at low gas concentration. (Initial experiments with wavelength-flattened couplers have shown a marked reduction of this slope.) The subtraction of the no-gas signal in the numerator of the last term Eq. (4) puts the data on an exactly zero background before normalization and calculation of the gas transmission. OP_{1 no gas} can be obtained without gas in the cell or from a curve fit to the off-line data in the OP_{1 gas} signal.

4. Experimental results

Figure 2 demonstrates the significant reduction in the high, concentration-independent background achieved by the RAM nulling technique for three concentrations of methane in nitrogen (10%, 1% and 0.1%) at a pressure of approximately 1 bar. The time-indexed (not wavelength-referenced yet) LIA output signals have been plotted. Clearly, the background level in the nulled case is nominally zero, but with a small sloping non-zero component noted above, arising from the wavelength dependencies of the couplers. The non-nulled signal slope is dictated by the downward slope of the ΔI(λ_c) term that is governed by the nature of the DFB laser’s current-intensity curve. For each case the sensitivity setting of the LIA was different and maximized without causing saturation. Clearly for the non-nulled cases it becomes harder to cleanly recover signals for low concentrations due to the high background. The significant reduction in background allowed the LIA sensitivity/gain to be increased greatly without saturation and if required, the recovered absorption signals can be selectively amplified further before being digitized in order to reduce the effects of quantization noise.

 

Fig. 2 LIA signals for 10%, 1% and 0.1% methane in nitrogen for (a) RAM-nulled case, and (b) Non-nulled case, showing the large background level that obscures the absorption signal.

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To fully validate the method for the recovery of absolute gas transmission line shapes, the signals presented in Fig. 2 for the 10% and 1% mixtures were fully processed and compared with theoretical Voigt profiles derived from HITRAN spectral data. Firstly, the recovered data was processed according to Eq. (4) and then the time-indexed horizontal scale was converted to a wavelength scale using the simultaneously recorded output signal from the accurately characterized fiber resonator connected to one of the ports of the 1x4 coupler as before [10,11]. The modulation indices, m (the ratio of the wavelength sweep to the half line width of the gas line), for the recovered 10% and 1% signals were calculated to be 0.61 and 0.65 respectively. For such high m values the recovered gas line profiles are distorted by the contributions from the higher order terms of the Taylor series expansion, neglected in Eq. (1). Hence, the appropriate correction factors [10,11] to take account of this were applied to yield the absolute gas transmission functions. These are presented in Fig. 3 with theoretical Voigt profiles calculated from HITRAN data for comparison. The excellent agreement between the experimental results and the theoretical plots proves that the accuracy of measurement has not been compromised by the RAM nulling technique and its data processing algorithm.

 

Fig. 3 Relative transmission for methane for (a) concentration 10.13%, pressure 1.067 bar temperature 22.6°C, and (b) concentration 1.02%, pressure 1.082 bar and temperature 23.6°C.

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5. Conclusion

A method to optically eliminate the high concentration-independent RAM component in TDLS-WMS has been successfully demonstrated and it has been shown that extraction of the absolute transmission through a gas sample is possible with high accuracy. The long-term stability of the RAM nulling condition is excellent, with no need for adjustments over many hours of experimentation. In any case, small drifts with time are acceptable as it is sufficient to substantially reduce, rather than exactly cancel, the background RAM signal, since any small remnant signal (e.g. as arising from the wavelength dependence of the couplers) is removed by subtraction of the no-gas signal (see Eq. (4)). The fiber delay line length is more than 20 times the coherence length of the laser under cw conditions, and even greater under modulation. Hence, even for worst case conditions of beam polarization, the interference noise is minimal. Under conditions of crossed polarization, the interference noise remains stably less than the receiver noise over long periods of time. If required active polarization control can be applied easily to maintain this condition. With these features, this new RAM nulling technique, in principle, can lead to improvements in sensitivity for 1st harmonic detection schemes such as the RAM and PD methods. However, in the current system, etalon fringes arising from the parallel faces of the GRIN lenses in the gas cell are the main limitation to high sensitivity and indeed prevent any meaningful study of sensitivity in relation to detector or optical noise. A new gas cell, based on a con-focal lens arrangement with superior anti-reflection coatings, has been designed to greatly suppress the etalon effects. A full and meaningful study of sensitivity awaits its incorporation into the system and will be reported later.