Toward single-ended absorption spectroscopy probes based on backscattering from rough surfaces: H₂O vapor measurements near 1350 nm

Abstract

We demonstrate feasibility of a new class of absorption spectroscopy sensors which use return scattering from native surfaces such as the piston of an automotive engine. Our demonstration experiment collects backscatter through a 2-mm-diameter aperture, consistent with a small sensor footprint. A 20 mW DFB laser is used, but only 10 µW is collected. We studied the noise associated with motion of the rough surface and found an RMS level of 7 %. Wavelength modulation spectroscopy (WMS) was used to overcome this noise. We demonstrate WMS spectra of H₂O vapor with a SNR of >400 for DFB scan ranges of 0.82 and 37 cm⁻¹.

1 Motivation

Given line-of-sight optical access in practical test articles such as engines, absorption spectroscopy is a proven tool for measuring gas properties [1–6]. However, line-of-sight access can be challenging to install into practical test articles, and the challenge is exacerbated when multiple lines of sight are used to obtain spatial information [7, 8]. Accordingly, spectroscopic probes have seen intense development in recent years [9–12], through to commercial products (e.g., LaVision ICOS-Temperature). In this paper, a probe refers to an optical sensor that penetrates a wall of the device under test and monitors gas properties internal to the device. Furthermore, in this paper, probes are considered single ended: each probe is intended to be used alone, requiring no opposing probe or optical surface in view of the probe.

Probes for monitoring gases within practical devices (e.g., spark-plug-mounted temperature probes [11]) generally monitor a small volume of gas near the wall penetration. In a common probe architecture [10, 11], a small mirror is affixed at the tip of the probe, suspended in the gas under test; sensor light propagates through the gas and is returned to the probe body by the mirror. Unfortunately, the invasive nature of such probes [10, 11] reduces their usefulness. For example, in one study [10], cold temperature biases of over 1000 K appeared to arise from heat transfer to physical probe components.

The present work aims to remove the mirror of the common probe and allow the return signal to come from scattering off the far wall of the device, as shown in Fig. 1. Accordingly, the probe benefit of ease of installation is retained, while the invasive drawbacks are mitigated.

Fig. 1

Representative backscatter probe design. Small aperture, a, is desired, because it is consistent with a small overall probe diameter, ϕ. The scattering surface could be a combustor wall, as noted, or an engine piston, or another native surface

Our proposed probe geometry shown in Fig. 1 closely resembles a probe in the literature [13]. The difference is that our approach relies on backscattering from a natural surface of the device under test rather than a rough surface that is part of the probe.

Figure 1 shows the case of 1:1 imaging, where s _i  = s _o ; however, magnification M ≠ 1 can be used. For clarity, Fig. 1 shows a case where the probe diameter ϕ is on the order of the wall spacing s _o ; more commonly, ϕ ≪ s _o . Typically, ϕ values of 4–25 mm are desirable, for articles with s _o of 25–400 mm. A typical low-throughput scenario has a/s _o  = 0.06 and an absorbing combustor wall. We tested a case with a/s _o  = 0.06 where the rough wall surface was represented by a ~ 500-μm-thick layer of candle flame soot on an aluminum plate; a throughput of 1 ppm was found. Thus, the ability of the probe to manage throughput values down to 1 ppm is desirable.

The sensing goal is path-averaged measurements of gas temperature and/or species mole fractions in the test gas region between the probe and the far wall. Generally, purge gas (e.g., dry nitrogen) must be delivered to the space between the lens and the PD as shown to eliminate absorption interference. Measurement repetition rates of 0.01–30,000 Hz are desirable, depending on the application. The test gas pressure is typically in the range of 1–30 bar.

Among the most challenging of possible measurement scenarios is a case where the throughput is 1 ppm, the desired repetition rate is 30,000 Hz, and the gas pressure is 30 bar. While this scenario is theoretically tractable, we chose in this initial work to relax the scenario to a throughput of 500 ppm, repetition rates of ≤10 Hz, and a gas pressure of 1 bar. We also demonstrate that the extension to 30 bar is straightforward. Future extension toward ~1 ppm throughput and ~30,000 Hz will generally require higher power sources, as in [14]. Fortunately, spectroscopic laser sources are now becoming commercially available at powers above 250 mW (e.g., Photodigm PH852DBR280CM). Furthermore, amplifiers with even higher output powers are readily available (e.g., Keyopsys CTFA-PB-PM-40-BW3-B130-FA-FA features 10 W output power and operates in the 1900–2050 nm range, suitable for H₂O sensing).

2 Experimental setup

To begin to assess the performance of the probe design shown in Fig. 1, we constructed the related laboratory setup shown in Fig. 2.

Fig. 2

Setup used to make initial tests of backscatter probe performance. The source was a fiber-coupled 20 mW DFB laser

A distributed feedback (DFB) laser (NEL NLK1B5GAAA) operating near 1350 nm was used as the source. It can access relevant H₂O vapor transitions. The laser light is delivered by single-mode fiber to the collimating lens (Newport 5723-H-C, 6.2 mm focal length). The beam is then directed at a rough surface (Thorlabs ground glass diffuser DG-101500-F01, measured RMS roughness = 0.358 µm). The position of the collimating lens was adjusted to focus the beam slightly, forming a 400-µm-diameter spot at the rough surface. An iris was used in front of the collimating lens to limit interference associated with backscatter returned to the collimating lens. The rough surface was chucked into a lathe (Central Machinery 93212) so that the rough surface could be rotated at variable speed ω = 0–ω = 300 rad/s. The rotation allows controlled testing of the effects of motion of the rough surface. The laser spot on the rough surface was positioned at a radius r = 1 cm from the center of rotation. The second iris with an aperture of d = 2 mm was used to represent the small lens in the probe (Fig. 1). The scattered spot was then imaged at unity magnification by a biconvex lens (Thorlabs LB1761C, 25.4 mm focal length) onto an InGaAs photodiode detector (Thorlabs PDA20CS-EC-NOWIN-SP). The detector is operated at 30 dB gain where its 3 dB bandwidth is 660 kHz. The total system throughput from the fiber to the PD is 500 ppm. The fiber-coupled output power from the DFB laser is typically 20 mW; accordingly, the power reaching the detector is typically 0.01 mW. The detector signal was sampled at a rate of 2 MS/s by a flexible-resolution digitizer (National Instruments PXI-5922).

3 Noise

Incorporating rough surfaces into absorption spectroscopy experiments (as in Figs. 1, 2) allows uncommon noise sources to become relevant. We considered three sources: interference arising from optical path differences (OPDs) due to scattering, variation of speckle with wavelength, and variation of speckle with motion.

It is common for OPDs from reflections or birefringence to plague absorption spectroscopy, e.g., reflections from windows produce the ubiquitous etalon interference. Inclusion of a scattering surface presents additional opportunities for OPDs: for example, when a laser beam strikes a scattering surface at non-normal incidence, various path lengths exist between the source and the surface. Such OPDs can in principle manifest as noise due to interference that varies with laser wavelength. Theoretically, one can minimize scattering OPDs by imaging the rough surface onto the photodiode [13], as shown in Figs. 1 and 2. For our tests (Fig. 2), we estimate the relevant OPDs to be <5 µm, resulting in a free spectral range of >2000 cm⁻¹, large enough to be inconsequential.

The speckle pattern present in the backscattered radiation varies with wavelength. These variations can manifest as signal changes [15], because the signal collection system collects only a portion of the speckle field. The situation is similar to wavelength variation of fiber modal noise [16, 17]; fortunately, due to the length scales involved, the speckle field in the scattering case tends to vary much less dramatically as laser wavelength is tuned.

For a spectral change of Δν (cm⁻¹), the intensity correlation coefficient is given by [18].

$${\rho_I} = \exp \left( { - 16{\pi^2}h_{\text{RMS}}^2\Delta {\nu^2}} \right)$$

(1)

Here, h _RMS is the RMS roughness of the surface (0.358 μm in our case). Accordingly, the spectral change needed to significantly change the speckle pattern is commonly calculated as [18].

$$\Delta {\nu_{\text{decorrelate}}} = \frac{1}{{2\sqrt 2 \pi {h_{\text{RMS}}}}}$$

(2)

Δν _decorrelate for our case is therefore 3144 cm⁻¹. Δν _decorrelate is usually much greater than the absorption feature widths of interest, even for surfaces significantly rougher than the one we used. Accordingly, wavelength-dependent speckle effects are generally inconsequential in absorption spectroscopy; for example, standard baseline fitting approaches will generally remove the signal changes. By contrast, in the case of fiber modal noise, it is common for small changes such as Δν _decorrelate = 0.01 cm⁻¹ to substantially change the speckle pattern, and accordingly, baseline fitting is usually ineffective at removing fiber modal noise.

To estimate the magnitude of the signal changes due to wavelength tuning, we first estimate the number of collected speckles for Fig. 2, following the literature [19]:

$$N = \frac{{{a^2}{D^2}}}{{1.44{{\left( {1 + M} \right)}^2}{\lambda^2}{F^2}}}$$

(3)

Here, a is the aperture diameter (2 mm, see Fig. 2), D is the diameter of spot size on the detector (400 μm), M is the magnification (1 in this case), and F is the lens focal length (25.4 mm). The calculation yields N = 94.

Then, the variation in the total collected signal associated with wavelength-dependent speckle can be derived from the literature [15, 20] as:

$$\frac{\Delta I}{{{I_{\text{o}}}}} = \frac{{\sqrt {1 - {\rho_I}} }}{\sqrt N }\;$$

(4)

The largest spectral change Δν relevant to our experiments here is Δν = 37 cm⁻¹ (Fig. 7); even at this large value of Δν, Eq. (4) yields ΔI/I _O  = 1.7 × 10⁻³, which is small enough to be inconsequential. Our experiments do not have sufficient baseline flatness over a 37 cm⁻¹ scan to allow us to observe such a small effect. In summary, wavelength-dependent speckle effects are generally negligible both due to large Δν _decorrelate and small ΔI/I _O . A notable exception would be a surface such as Spectralon™ that provides volume scattering rather than a pure surface effect; for such materials, h can become ~4 orders of magnitude larger than tested here, resulting in problematic values (small Δν _decorrelate and large ΔI/I _O ). Initial tests of a thermal barrier coating (TBC) on a gas turbine engine parts suggest that the coating exhibits volume scattering and interferes with measurements of the type presented in this paper.

The speckle pattern present in the backscattered radiation also varies with motion, such as caused by vibration of the rough surface. We experimentally tested the associated noise by rotating the rough surface as shown in Fig. 2. The RMS noise level was 0.07 (7 %). The theoretical RMS noise level is 0.10 (10 %), calculated as N^−½, where N is the approximate number of speckles (94 in this case). Theoretically, the RMS noise level does not depend upon the surface roughness, as can be seen from Eq. (3). The noise is shown in Fig. 3 for speeds of v = 0, 0.3, and 3 ms⁻¹ (v = ω × r). The noise is periodic; the period is consistent with the lathe rotation speed (e.g., in the bottom trace, the period of 0.02 s = 2π/ω = 2π/(300 rad/s).

Fig. 3

Time trace of speckle noise for three cases: v = 0, v = 0.3 ms⁻¹, and v = 3 ms⁻¹. The RMS noise level for the bottom panel is 0.07

Fast Fourier transforms (FFTs) of the traces shown in Fig. 3 are presented in Fig. 4. For the 0.3 ms⁻¹ case, significant noise extends to about 2.5 kHz, and for 3 ms⁻¹, to about 25 kHz. Accordingly, an absorption spectroscopy modality that is immune to noise up to ~25 kHz is desirable for the probe application. The highest speed presented, 3 ms⁻¹, represents very strong vibration: a surface vibrating with an amplitude of ±48 mm at 10 Hz or ±4.8 mm at 100 Hz would have a peak speed of 3 ms⁻¹.

Fig. 4

Power spectrum of experimental noise for three cases: v = 0, v = 0.3 ms⁻¹, v = 3 ms⁻¹. For the 0 and 0.3 ms⁻¹ cases, the full 0.5-s-duration time traces were used to compute the power spectrum. For the 3 ms⁻¹ case, only a 0.025-s-duration excerpt was used

4 Selection of WMS

As described in Fig. 2, we chose to use a DFB laser in our backscatter probe work, because DFB lasers feature much higher output power than common swept-wavelength sources such as VCSELs [21, 22]. Next, we chose scan-wavelength rather than fixed-wavelength absorption spectroscopy, at least for the initial work. Scan-wavelength results provide feature shape information, which is helpful when interpreting results at high temperature and pressure, where uncertainties in lineshape models can be significant. Scan-wavelength results also can reveal wavelength-dependent interference that arises. Finally, to allow measurements up to 30 bar, broad wavelength scans are desirable, so we considered only approaches that are compatible with temperature tuning of a DFB laser. Although other DFB modulation strategies might be competitive, wavelength modulation spectroscopy (WMS) is the obvious choice under these constraints. WMS is an established approach that allows rejection of the speckle motion noise below 25 kHz during relatively slow wavelength scans, as from temperature tuning.

To enable WMS, two function generators (Agilent 33250A) were used in conjunction with a 50-ohm combiner (Mini-Circuits, ZFRSC-42) to apply low-frequency sawtooth and high-frequency sinusoidal modulation to the DFB laser through a current source (ILX Lightwave LDX-3620B).

5 Results

In a first experiment, the DFB laser injection current was varied according to a sawtooth function having a repetition rate of f _s = 1 Hz, causing the laser to scan from 7404.69 cm⁻¹ to 7405.51 cm⁻¹. Superposed on the sawtooth function is a sine function at f _m = 10 kHz. The sine function induces a 10 kHz modulation depth of 0.088 cm⁻¹. In post-processing, a digital dual-phase lock-in amplifier based on a low-pass tenth-order Butterworth filter is used to extract the WMS-1f and WMS-2f signals with a bandwidth of 1 kHz. Results are shown in Fig. 5. In direct absorption, this atmospheric pressure H₂O vapor feature has a peak absorbance of 0.134.

Fig. 5

2f/1f signal of f _m  = 10 kHz for two cases: v = 0.3 ms⁻¹, v = 3 ms⁻¹. The excess noise in the 3 ms⁻¹ case is due to speckle motion

The results are not significantly contaminated by speckle noise for slow lathe rotation speeds (e.g., the v = 0.3 ms⁻¹ speed shown). However, for higher rotation speeds (e.g., the v = 3 ms⁻¹ speed shown), the speckle noise falls within the bandwidth of both the 2f and 1f lock-in amplifiers, contaminating the 2f/1f signal. The reader may verify in Fig. 4 the presence of excess speckle noise at ~10 kHz for v = 3 ms⁻¹ but not for v = 0.3 ms⁻¹. The highest noise (e.g., near 0.2 s in Fig. 5) occurs when the 1f signal is smallest; the speckle noise contamination is approximately constant during the scan so it is relatively strong when the 1f signal is small.

In a second test, we used a modulation frequency of f _m = 120 kHz to avoid the speckle noise. This increase of f _m causes the speckle noise to fall to negligible levels within the 1f and 2f lock-in amplifier bandwidths (110–130 kHz and 230–250 kHz). Both 1f = 120 kHz and 2f = 240 kHz also avoid spurious noise (see Fig. 4). Results, shown in Fig. 6, demonstrate successful reduction of speckle noise contamination by increasing the modulation frequency f _m. For the data shown in Fig. 6, the sawtooth repetition rate was increased to f _s = 10 Hz, the lock-in amplifier bandwidth was increased to 10 kHz, and the modulation depth at 120 kHz is 0.093 cm⁻¹. At these same conditions, we replaced the rotating diffuser with a stationary automotive engine piston (GM Europe GmbH #55567347) and obtained results similar to the one shown in Fig. 6.

Fig. 6

2f/1f signal of f _m = 120 kHz for v = ωr = 3 ms⁻¹ using the setup shown in Fig. 2. Tests on a stationary automotive piston in the same setup yield similar results

To demonstrate the ability to monitor higher-pressure gas, we used temperature tuning to scan the DFB laser over a broad wavelength range (7391–7428 cm⁻¹). The test operates again on the rotating rough surface. The test begins by setting the DFB laser temperature to −5 °C, the minimum operating temperature recommended by the manufacturer. Once stabilized at −5 °C, a constant heating current is applied to the Peltier element. Accordingly, the DFB laser temperature increases in an approximately linear fashion. When the laser reached 75 °C, the maximum recommended operating temperature, the heating current was turned off. In our case, the temperature sweep took 4.5 s. In principle, continuous scanning is possible with this approach, but we only used a single scan here. Other temperature tuning mechanisms (e.g., rapid thermal cycling of a laser [23]) might be used to reduce temperature scanning durations. The gas pressure was maintained at 1 atm for simplicity. Accordingly, a modulation frequency of f _m = 120 kHz at a depth of 0.093 cm⁻¹ was used again throughout the temperature scan. Results are shown in Fig. 7. A baseline fit has been applied to the data of Fig. 7 to subtract the effects of residual amplitude modulation (RAM), as in [24].

Fig. 7

2f/1f signal for temperature tuning of the DFB laser for a duration of 4.5 s. These results demonstrate the ability to obtain broader spectra, as is beneficial for inferring gas properties at high pressure

In an actual high-pressure case, a higher modulation depth is generally preferred. Although we did not use a higher modulation depth, we verified that our system could easily achieve a modulation depth of 0.32 cm⁻¹ as used previously for measurements up to 25 atm [25].

6 Conclusions and outlook

We have demonstrated the ability to measure WMS spectra with SNR >400 using backscatter from rough surfaces moving at speeds up to 3 ms⁻¹. Surfaces tested include a commercial diffuser and a piston from an automotive engine. Using the commercial diffuser, the throughput was 500 ppm for collection through a 2-mm-diameter aperture. The results motivate development of absorption spectroscopy probes based on backscatter from native surfaces such as engine components. WMS spectra were measured at repetition rates up to 10 Hz. Extension toward ~1 ppm throughput and ~30 kHz repetition rate will generally require amplified lasers and higher modulation frequencies. Additional benefits await backscatter absorption spectroscopy, such as the possibility to monitor multiple paths through the test gas using a single probe, following an approach similar to that of Seidel et al. [26, 27] but using a scattering surface rather than a retro-reflective foil.