1. Introduction

Tunable diode laser spectroscopy (TDLS) has been proven to be a successful technique for trace-gas environmental monitoring [1–4]. By using frequency modulation (FM) or wavelength modulation (WM) methods, TDLS can measure optical absorption in atomic or molecular samples, with a high resolution and sensitivity in real time. In FM-TDLS, for instance, the minimum detectable absorption could be as low as 10^-7 [1]. The high sensitivity originates from the dramatically increased signal-to-noise ratio (SNR), which can be expressed as

I is the intensity of light arriving at the detector and κ describes the absorption signal. N_sI, β√I, and N_t are the laser source noise, the detector quantum noise and the detector thermal noise, respectively. N_sI, which is induced by the fluctuations of the laser source, dominates at low frequencies but can be suppressed efficiently by going to high frequencies (Ns∝1/f). In FM-TDLS where the laser source is modulated at radio frequencies, β√I and N_t (light-intensity independent) instead dominate, and therefore, the SNR can be improved by increasing the laser intensity. This ultimately corresponds to quantum limited measurements.

Apart from the absorptive technique just described, a group of zero-background methods exists. Here a spectroscopic signal (I_S) rises from a zero or low background. For instance, laser-induced fluorescence spectroscopy produces a signal only when the laser frequency is tuned to the molecular absorption line. This technique is sensitive enough to track a single ion or atom [5, 6]. Likewise, in photo-acoustic spectroscopy, the acoustic signal appears solely when the laser wavelength matches an absorption line to excite the molecules [7]. A further example is polarization spectroscopy, developed for low absorption signal applications by Wieman and Hänsch [8]. Here a crossed polarizer placed in front of the detector will normally block out the linearly polarized laser light background. Only at the line center the polarization plane is rotated by the polarized sample and a signal occurs from zero back-ground providing a higher sensitivity compared with standard saturation spectroscopy [9]. The SNR of such zero-background techniques is described by

Here, a high SNR can still be obtained even if NsIS (Ns≪1) dominates in the absence of high-frequency modulation. Most importantly, the small quantity I_s now replaces the large quantity I when measuring small signals.

In the present paper, we propose and demonstrate, as we believe, for the first time, a TDLS scheme working on a zero background. By using laser beams with equal strength but with a phase shift of π causing destructive interference in a Michelson interferometer, the recorded light intensity can be balanced out to zero. When one light beam used for gas probing suffers an absorption induced by a gas sample, the balance is disrupted and a non-zero signal appears. In the paper, we demonstrate, through theoretical analysis and experimental work, that the zero-background TDLS presented can improve the SNR compared with a direct absorption TDLS. It should be mentioned that a similar principle was used by Dakin et al. to create a spectroscopically structured broadband light source for correlation spectroscopy [10].

 

Fig. 1. (a). Schematic diagram of zero-background TDLS; (b) the principle for forming the zero background.

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2. Measurement principle and analysis

As shown in Fig. 1(a), a fiber-optic Michelson interferometer is employed in a destructive interference mode to form a zero output intensity, which constitutes the background for the spectroscopic signal to be recorded. It is worthwhile noting that fiber-optics is not necessary for the proposed technique, thus making it also very suitable in the IR region, where fibers are not readily available. We demonstrated the technique by using a fiber-optic Michelson interferometer only because of its proper compatibility with the light source. When the optical path difference (OPD) of the two arms is adjusted to zero, the intensity of the light at the detector in the absence of gas absorption can be expressed as $I_B=\frac{1}{4}P{\left(1-k\right)}^2$, where P is the laser power and k (0<k<1) is a balance factor for intensities of the two interfering light beams. If k is close to 1, a very low light intensity, i.e. a zero background, can be achieved (see Fig. 1(b)). When the laser wavelength is tuned to the absorption line of the sample, which is inserted in one arm of the Michelson interferometer, an absorption (A) is induced in this arm and the balance is perturbed. The light intensity _S I at the detector in the presence of an absorption increases to $I_s=\frac{1}{4}P{\left(1-k\sqrt{1-A}\right)}^2$. By defining δ=1-k, I_S can be approximately written as

Figure 2(a) shows the calculated values of _S I as A increases from 0 to 0.1, for different unbalance factors δ. One can see that when δ=0, both the signal and the responsivity( $\frac{\partial I_s}{\partial A}$) rapidly drop to zero for small A. However, the responsivity for measuring a small signal can be improved by a non-zeroδ (see the second term in Eq. (3)). As an amplification coefficient, δ is comparable with the bias angle θ in a polarization spectroscopy [8].

 

Fig. 2. Calculated results of (a) responsivity and (b) SNR for an increasing absorption ratio, for different values of δ. The gray dashed curve in (b) shows the SNR of a direct absorption TDLS.

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Further, the SNR of the system, which determines the minimal detectable signal and sensitivity, is calculated assuming that the noise _{s S} N I in Eq. (2) still dominates (otherwise it is in the quantum limited range and the SNR can be improved by increasing the laser power):

The corresponding calculated results are shown in Fig. 2(b). It is obvious that when δ=0 (I_B=0, i.e. zero background), Eq. (4) turns to a constant _s 1/N, which means that a good SNR can be achieved independent of the signal _S I or the absorption A. For real-world applications, SNR curves of δ≠0 are calculated. From Fig. 2(b), obviously better SNR can be seen compared with that of the direct absorption spectroscopy (gray dashed curve), which is known to have a s SNR≈A N. For instance, when δ=0.05 (corresponding to that the intensity ratio of the interfering light beams is 0.9), the SNR of the method presented is 17 times better than that of the direct absorption spectroscopy, when an absorption ratio of 0.01 is considered.

A trade-off can be seen by comparing Figs. 2(a) and 2(b). The unbalance factor δ can improve the responsivity on the one hand; while the increased background will certainly decrease the SNR on the other hand. Thus, a suitable value for δ should be carefully chosen depending on different applications.

3. Experiment and results

An experimental set-up was constructed as shown in Fig. 1(a). A distributed feed-back (DFB) diode laser module (Denselight, DL-BF12-CLS051B-S1648) is employed. The wavelength of this single longitudinal mode laser is around 1648.21 nm, for measuring absorption lines of methane, CH₄ [11]. The laser module has an inner current and temperature (I & T) controller. The laser wavelength can be tuned by controlling the driving current with an external voltage signal. After passing through an optical isolator (for avoiding reflected light to damage the laser source), the light enters a fiber-optic Michelson interferometer, which is formed by a 1:1 fiber coupler and two reflecting mirrors. A 10 cm long gas cell, filled with a 12 mbar gas mixture (15% CH₄ and 85% air), is inserted in one arm (i.e., the gas sensing arm) of the Michelson interferometer. The glass windows of the gas cell are tilted to avoid reflected light entering the system. A fiber-optic polarization controller in the other arm (i.e., the reference arm) is used to balance the polarization states of the interfering light beams. A section of fiber can compensate the OPD between the two arms for avoiding etalon effect when the laser wavelength is scanned. The coupling efficiency of the fiber collimators can be adjusted by tuning the angles of the mirrors and therefore equal light strength can be obtained in the two beams of interfering light. The output port of the Michelson interferometer is connected to an InGaAs detector (New Focus 2033), the signal of which is recorded by a DAQ card (NI-6154) installed in a personal computer. The same card also provides controlling signal for the DFB laser module.

 

Fig. 3. (a). Measured light intensity corresponding to the reference arm (gray) and the gas sensing arm (dark); (b). SNR comparison between direct absorption TDLS (gray curve at top) and the system presented (dark curve at bottom). The inset of (b) shows that the calculated spectrum agrees with the measured one.

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In order to prove that the system presented can reduce system noise extremely well and hence improve the SNR, we add extra noise on the scanning voltage (0.5–2.3V) of the DAQ card. The noise in the laser intensity is artificially enlarged to 6.5% of the maximum intensity value, together with noise in laser frequency and phase. Principally, all these three types of noise can be suppressed by the presented balanced Michelson interferometer. However, considering the intensity measurement in a direct absorption TDLS, the phase noise can be ignored and since the frequency noise transfers into effective intensity noise, we only study the intensity noise in the measurements. The intensities of the light passing through the reference and gas sensing arms are measured independently. From the results shown in Fig. 3(a), they overlap very well until absorption lines of CH₄ appear around 1648.22 nm, which corresponds to 1.7 V scanning voltage. The data after 2.1 V, where the laser unfortunately exhibits mode jumps, are not used in later experimental results. The transmission spectrum of CH₄, i.e. the ratio of the curves in Fig. 3(a), is shown as the noisy gray curve in Fig. 3(b). It fits well with the calculated results of two R6 absorption lines of CH₄, using the HITRAN database [11]. Here, a direct absorption TDLS suffers from a bad SNR (3.1) even in the presence of an obvious absorption signal of about 20%. If instead the horizontal position of the mirror in the reference arm is tuned to adjust the Michelson interferometer working in a destructive interference mode, a low-intensity background is achieved, and an increasing signal instead of a signal reduction due to absorption appears at 1.7 V. From the dark curve at the bottom of Fig. 3(b), we can see that the SNR (13.8) is improved by 4.5 times, which is close to the calculated result, 5 times higher SNR for a perfect (δ=0) zero-background TDLS, compared to a direct absorption measurement for the case when the absorption is 20 % (beyond the upper range in Fig. 2(b)). As an imperfection, we noted that the laser wavelength tunes considerably faster after 1.4 V when the controlling voltage is linearly scanned, which explains the kink in the curve. The non-zero background shown in the curve is induced by a non-zero δ obtained in practice, even with efforts to minimize it as much as possible in the experiment. This shows the limitation on the minimal detectable signal when the absorption becomes small and the SNR decreases dramatically, as illustrated in Fig. 2(b).

 

Fig. 4. (a). Oscillating pattern with an envelope including spectroscopic information; (b) and (c) show the details of windows b and c in (a).

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4. Discussion

Without any extra stabilizing scheme, the destructive interference setting of a Michelson interferometer cannot be kept for a long term. For better system performance, an interferometer with a stable OPD should be built. One possibility is to construct a closed-loop controlling circuit for the Michelson interferometer, in a similar way as used, e.g. in a build-up optical cavity [12]. By detecting the light intensity at the output port of the interferometer, a specific algorithm, e.g. a proportional-integral-derivative (PID) algorithm can control a piezo-driven mirror to lock the OPD of the interferometer working in destructive interference and a zero-background can be stably maintained. Another possibility is to use a self-stabilized interferometer, e.g. a Sagnac fiber loop [13]. In such an interferometer, two interfering light beams always pass through the same optical path and the destructive interference condition is naturally kept at the output port. In the fiber loop a smart scheme should be included to induce differential absorption (due to the gas) between the light beams propagating clockwise and counter-clockwise. In such a design, many advantages are expected compared with the Michelson interferometer demonstrated in the proof-of-principle work in this paper. For instance, if a Michelson interferometer is employed in real applications, the balance factor of the two arms will degrade because of, e.g., mechanical instability, and phase noise will be induced in long optical paths of flowing sample gas. However, all these problems can be naturally solved in case the interfering light components always experience the same optical path.

Instead of developing complicated close-loop electronics to stabilize the interferometer, we find that if an active fast modulation is applied on the OPD, the slow drift is replaced by an oscillating pattern where the constructive and destructive interference is achieved alternatingly. It could be realized by shaking one of the mirrors piezo-electrically. The modulation range should be larger than one wavelength but sufficiently small that the etalon effects are not appearing, considering that the laser wavelength scans at the same time. For demonstration, we move the reference mirror swiftly on the linear stage. From the measured result shown in Fig. 4(a), we can see in one scan of the controlling voltage, that the interference pattern oscillates rapidly between destructive and constructive conditions. If the minimal values (corresponding to destructive conditions) are utilized, an increasing signal positioned on a low background (see Fig. 4(b)) can also be obtained, similarly as in Fig. 3(b). Although the integrated signal intensity is reduced, (which is already described in Eq. (3)), we believe that the SNR can be improved. Evidence is shown in Fig. 4(c). The noise corresponding to the destructive condition is obviously decreased compared with that corresponding to the constructive one. The noise in this modulation mode is even lower than for the case without modulation (compare with bottom curve of Fig. 3(b); note that the same extra noise is still applied), since N_s∝1/f. On the other hand, the spectral sampling is decreased as a penalty in this case. However, the basic features of the new technique introduced are still clearly demonstrated.

5. Conclusion

In conclusion, we have demonstrated an efficient method to decrease the noise in TDLS by operating at a close-to-zero background, without any high-frequency modulation on the light source. This is achievable by using a Michelson interferometer set to destructive interference. The method has similarities to polarization spectroscopy, but is a linear spectroscopy method. A fiber-optic implementation was demonstrated, constituting a realistic approach for real-world gas monitoring. The proposed technique is particularly attractive in applications where high-frequency modulation is difficult to realize.