Real-time Imaging of Methane Gas Leaks Using a Single-pixel Camera

We demonstrate a camera which can image methane gas at video rates, using only a single-pixel detector and structured illumination. The light source is an infrared laser diode operating at 1.651µm tuned to an absorption line of methane gas. The light is structured using an addressable micromirror array to pattern the laser output with a sequence of Hadamard masks. The resulting backscattered light is recorded using a single-pixel InGaAs detector which provides a measure of the correlation between the projected patterns and the gas distribution in the scene. Knowledge of this correlation and the patterns allows an image to be reconstructed of the gas in the scene. For the application of locating gas leaks the frame rate of the camera is of primary importance, which in this case is inversely proportional to the square of the linear resolution. Here we demonstrate gas imaging at ∼25 fps while using 256 mask patterns (corresponding to an image resolution of 16x16). To aid the task of locating the source of the gas emission, we overlay an upsampled and smoothed image of the low-resolution gas image onto a high-resolution color image of the scene, recorded using a standard CMOS camera. We demonstrate for an illumination of only 5mW across the field-of-view imaging of a methane gas leak of ∼0.2 litres/minute from a distance of ∼1 metre. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Direct quantitative analysis using flame ionisation detection. the construction and performance of the FIDOH detector, " J. Passive infrared imaging sensor for standoff detection of methane leaks, " (SPIE, 2004), vol. 5584 of Chemical and Biological Standoff Detection II, pp. 93–99. Development of a pulsed backscatter-absorption gas-imaging system and its application to the visualization of natural gas leaks, " Appl. Real-time gas-correlation imaging employing thermal background radiation, " Opt. Imaging of methane gas using a scanning, open-path laser system, " New J. Hyperspectral imaging of gases with a continuous-wave pump-enhanced optical parametric oscillator, " Opt. A portable remote methane sensor using a tunable diode laser, " Meas. An open-path, hand-held laser system for the detection of methane gas, " J. near-field terahertz imaging of hidden objects using a single-pixel detector, " Sci. Fast wavelength multiplexing of a white-light supercontinuum using a digital micromirror …


Introduction
Graphene has been shown to be a prototypical two-dimensional material with exceptional physical properties [1]. However, the difficulty of creating an optical bandgap in graphene stimulated the search for other monolayer materials [2]. Layered transition metal dichalcogenides have attracted considerable attention due to their usability in fabricating electronic devices [3][4][5]. Monolayer MoS 2 has shown the surprising property of being photoluminescent [6,7], which renders this material also interesting for optical and optoelectronic [8,9] applications. Recently, photoluminescence of monolayer MoSe 2 [10] and WSe 2 [11] has been reported. Here, we investigate photoluminescence emission and absorption of MoS 2 , MoSe 2 , and WSe 2 monolayers and elucidate the nature of the layerdependent phonon modes via high-resolution Raman spectroscopy.

Sample preparation and crystal structure
MoSe 2 and WSe 2 single crystals are grown by the vapor phase transport method [12]. As a reference, naturally grown MoS 2 is also investigated. Layered transition metal dichalcogenides of the form MX 2 (M = Mo, W and X = Se, S) crystallize in a strongly covalently bound X-M-X sandwich structure [13]. Consecutive X-M-X layers are weakly bound by the van der Waals interaction. Layered transition metal dichalcogenides appear in different modifications, distinguished by their stacking orders. The X-M-X layers of our investigated three material systems may crystallize as a hexagonal 2H structure belonging to the space group P63/mmc (point group D 6h ) with two MX 2 molecules inside the unit cell or as rhombohedral polytype 3R with three molecular layers per unit cell (R3m) [14]. Therefore, we perform X-ray diffraction measurements on suitably oriented single crystals of MoS 2 , MoSe 2 , and WSe 2 with a Seifert XRD 3000PTS diffractometer. For all samples we find a reflection unique to the 2H polytype (data not shown), i.e. all investigated materials belong to the 2H polytype. To obtain few-down to monolayer material the crystals are mechanically exfoliated [2] onto SiO 2 /Si substrates. The number of layers is determined by optical interference and atomic force microscopy (AFM) measurements [15,16]. Figure 1 shows an optical micrograph, AFM image, and AFM line scan in contact mode of a flake of WSe 2 . Micronsized regions of different heights in the range of nanometers are clearly identified. The AFM step height from a monolayer to the bilayer amounts to 0.7 nm (line scan in Fig. 1b), which is in excellent agreement with previous AFM studies (0.67 nm) [16]. The increased step height of 0.9 nm from the substrate to the monolayer material is attributed to adsorbates or other interactions between the monolayer and the substrate [17].

Raman spectroscopy
Raman spectroscopy has been shown to be a powerful tool to determine the exact number of layers of exfoliated MoS 2 . The energy, width, and amplitude of the vibrational modes are strongly influenced by the thickness of the flakes [17]. We investigate the vibrational modes of mono-and few-layer MoSe 2 and WSe 2 with high-resolution Raman spectroscopy. We use a Horiba LabRAM HR spectrometer with an excitation wavelength of 514.5 nm. The measurements are performed in a confocal micro configuration using a 100x microscope objective lens and a motorized xyz stage with 100 nm step size. Using a 2400 l/mm grating and a confocal pinhole of 100 µm the spectral resolution is below 1 cm −1 . The power of laser excitation measured below the microscope objective lens is 15 µW for MoS 2 and 68 µW for both MoSe 2 and WSe 2 . For bulk WSe 2 500 µW is used. All measurements are performed at room temperature. For simplicity we denote all vibrational modes with the irreducible representations of the D 6h point group of bulk material. A group-theoretical analysis predicts four Raman active modes for the D 6h group [18], i.e. three in-plane modes E 1g , E 1 2g , and E 2 2g , and one out-of-plane mode A 1g (Fig. 2). In our experiment only E 1 2g and A 1g are accessible. The E 2 2g mode is at very low frequencies (~30 cm −1 ), and the E 1g mode is forbidden in backscattering geometry on a basal plane [19].

MoS 2
For bulk MoS 2 we observe both the in-plane E 1 2g mode at 383.5 cm −1 and the out-of-plane A 1g mode at 408.6 cm −1 (data not shown), in agreement with previous studies [17][18][19][20][21][22][23]. The separation between the two modes decreases with decreasing thickness of the material, which is an excellent indicator for the number of layers in MoS 2 [22][23][24].

MoSe 2
For bulk MoSe 2 the A 1g mode shifts about 150 cm −1 towards lower wavenumbers compared to MoS 2 [25-27], which is also confirmed by calculations [28]. Indeed, we observe this out-ofplane mode in the spectral range of 240.5 -242.5 cm −1 , depending on the number of layers (Fig. 3). Our high experimental resolution allows us to observe a splitting of the out-of-plane Raman A 1g line for the first time. Starting from one Raman line for mono-and bilayer MoSe 2 it splits into two for three and four layer material. For five layers of MoSe 2 , three Raman lines appear. The spectral positions of the two maxima for three layers of MoSe 2 are arranged almost symmetrically with respect to the monolayer line. The range of the observed splittings is 2.4 -3.2 cm −1 . This effect is due to the so-called Davydov splitting, which appears due to the presence of more than one MoSe 2 molecule in the unit cell [18,24,25]. For the Raman active A 1g mode the Se atoms in all layers oscillate in phase with respect to the corresponding center molybdenum atom, which does not move (Fig. 2, A 1g ). The splitting occurs due to a varying number of phase shifts of 180° between the layers (Fig. 4). A phase shift of 180° between two layers is defined by the movement of the Se atoms: both top and bottom Se atoms within one layer move away from the molybdenum atom, while at the same time top and bottom Se atoms in the adjacent layer move towards the Mo atom and vice versa. Due to the weak interaction between the layers, the vibration frequencies of the in-phase and out-ofphase modes are almost degenerate [18]. However, each two adjacent layers vibrating in phase cause a small shift towards higher frequencies (indicated in Fig. 4 as a red dashed line), while two adjacent layers oscillating out of phase cause a shift towards lower frequencies by approximately the same amount (indicated in Fig. 4 as a green dotted line). Obviously, for a monolayer only one Raman active out-of-plane mode (A′ 1 , see Fig. 4) appears, since the unit cell contains only one MoSe 2 molecule and no translation symmetry along the c axis exists. For a bilayer with two MoSe 2 molecules per unit cell the situation is similar to bulk material with only one Raman active out-of-plane mode. However, the mode shifts towards higher wavenumbers compared to the monolayer due to the interlayer interaction. For few layer material with an odd number of layers only out-of-plane modes which preserve the symmetry elements of the monolayer A′ 1 out-of-plane mode are Raman active. For our consideration, the most important symmetry element for these modes is the mirror plane σ h indicated in Fig. 4. Therefore, for three layer material two Raman active outof-plane modes are expected. For the first mode all layers are in phase, while for the second mode the center layer is 180° out of phase with respect to the two outer layers. The energies of these modes are arranged almost symmetrically to the monolayer mode, because the interlayer interactions induce an increase (decrease) of the energy for the first (second) mode.
For an even number of layers the out-of-plane modes with the same symmetry elements as the A 1g mode are Raman active. These modes exhibit an inversion center. Thus, for four layer material again two out-of-plane modes are Raman active. For the first mode all layers are in phase. For the second mode, the two outer layers are vibrating in opposite phase to the two inner layers. In five layer material one expects four different Raman active modes with none, one, two, and three layers being 180° out of phase with respect to the two outer layers. Two of these modes (with one and three inner layers vibrating out of phase) exhibit the same interlayer interaction and thus are degenerate. Indeed, we observe three maxima for the five layer material at 242.04 cm −1 , 240.12 cm −1 , and 238.03 cm −1 .
We now turn to the in-plane E 1 2g mode, which appears at higher wavenumbers than A 1g in MoSe 2 . In bulk MoSe 2 a weak vibrational mode was previously experimentally verified at 286 cm −1 [10,[25][26][27][28]. Here, this mode is found at 287.2 cm −1 for monolayer and at 285.9 cm −1 for bilayer MoSe 2 , indicating the same stiffening with decreasing numbers of layers as for MoS 2 . Interestingly, at 353 cm −1 we observe a previously unknown Raman line for few-layer MoSe 2 . The intensity of this mode is strongest for bilayer material and is reduced as the number of layers increases. Using similar considerations as above, we can assign this line to the B 2g mode. This mode is inactive in bulk, but becomes Raman active due to the breakdown of translation symmetry in few layers. Besides these sharp lines (~1 cm −1 ), there are multiple broader maxima resulting from second order Raman processes (data not shown).

WSe 2
For bulk WSe 2 , we find two distinct Raman signals at 248.0 and 250.8 cm −1 (Fig. 5). This doublet was also previously reported in a measurement of a WSe 2 crystal at a temperature of T = 80 K [30]. The two lines are also in agreement with a recent calculation [28], predicting both the E 1 2g and the A 1g mode to be close to 250 cm −1 . For few-layer WSe 2 we only find a single maximum, the position of which changes with the number of layers. Presently, it is not clear whether this single maximum is due to only one of the two lines, or the two modes are almost degenerate and cannot be resolved. Moreover, we also find a broad side maximum at 260 cm −1 and a small signature at 309 cm −1 for the bilayer. The latter can be assigned again to the normally inactive B 2g mode [21,28]. As for MoSe 2 , there are multiple broader maxima resulting from second order Raman processes (data not shown).
In summary, we find that Raman spectroscopy is an excellent tool to unambiguously pinpoint the number of sheets of the layered dichalcogenide materials MoSe 2 and WSe 2 .

Photoluminescence emission
Recently, the transformation of MoS 2 from an indirect semiconductor in its bulk form to a direct semiconductor in case of a monolayer has been experimentally demonstrated [6,7]. As a consequence, substantial photoluminescence emission was detected. For bulk MoS 2 , the fundamental indirect band gap originates from a transition from the top of the valence band at the Γ point to the bottom of the conduction band, which is about halfway between the Γ and Κ point. The direct band gap for bulk MoS 2 is higher in energy and occurs at the K point. The situation drastically changes, if the number of layers of MoS 2 is decreased. The energy of the fundamental indirect band gap increases, until it crosses the direct gap transition, which is virtually unchanged in energy [31]. In this way, monolayer MoS 2 becomes a direct band gap semiconductor and the photoluminescence intensity drastically increases with decreasing number of layers. We now compare the photoluminescence emission of MoSe 2 , WSe 2 , and MoS 2 . A confocal microphotoluminescence setup is used to excite the sample with a continuous wave laser (λ = 532 nm), which is focused by a 100x microscope objective lens (NA = 0.9). Photoluminescence (PL) emission is collected by the same objective, dispersed with a f = 150 mm spectrometer and detected by a nitrogen cooled charge coupled device. All measurements are performed at room temperature.

MoSe 2
The energy of the indirect gap of bulk MoSe 2 is in the near-infrared [32] at 1.1 eV (1.13 µm). The direct A and B excitons are higher in energy at 1.57 eV (790 nm) and 1.82 eV (682 nm) [33,34]. Figure 6a shows the photoluminescence spectrum of one, two, and three layers of exfoliated MoSe 2 . The observed emissions from monolayer and bilayer MoSe 2 exhibit a single prominent maximum at 1.57 eV (792 nm) and 1.54 eV (807 nm), respectively. Both emission lines are asymmetric with a steep edge at the high energy side and a broader tail at the low energy side. The peak positions vary slightly ( ± 5 nm) from sample to sample due to different environments caused by adsorbates or potential variations at the SiO 2 surface [35]. The PL intensities from the monolayer material are 10 -20 times stronger than those of the bilayer material. The emission from the trilayer material shows two broad maxima at 1.53 and 1.35 eV (812 and 922 nm). The PL intensity decreases again by one order of magnitude as compared to the bilayer. The observed PL intensity maximum in photoluminescence for monolayer MoSe 2 is in excellent agreement with the known direct A exciton in the corresponding bulk material. This observation corroborates recent photoluminescence data of MoSe 2 [10] and model calculations [31,36,37] for other transition metal dichalcogenides, which show that the indirect gap increases in energy, while the direct gap at the K point stays at about the same energy when decreasing the thickness from bulk to monolayer material. The valence band maximum and the conduction band minimum at the K point (direct gap) originate predominately from the strongly localized d orbitals at metal atom sites. Since the metal atoms are located in the middle of the X-M-X unit cell, there are only minimal interlayer interactions [6]. Therefore, the direct gap barely changes with decreasing layers. The observed decrease of PL intensity of MoSe 2 of one order of magnitude per additional layer is in accordance with measurements of MoS 2 [6]. The asymmetry of both monolayer emission maxima might be related to the presence of surface bound excitons as found for MoS 2 [38]. Already for bilayer MoSe 2 a direct band gap was predicted at the K point of the Brillouin zone [37], which could explain the single emission maximum of the measured photoluminescence. Only the MoSe 2 trilayer exhibits two well-separated maxima with one being at the same energy as for the bilayer (related to the A exciton) and the other assigned to the indirect band gap.  Figure 6b shows prominent photoluminescence of monolayer WSe 2 centered at 1.65 eV (752 nm). The emission has the same asymmetry as for MoSe 2 . Bilayer WSe 2 emits at 1.54 eV (806 nm) with a side maximum of 1.60 eV (773 nm). Interestingly, the PL intensity of the WSe 2 bilayer is only reduced by a factor of 4 compared to the monolayer. For a trilayer of WSe 2 , the side maximum nearly stays at the same position, while the main emission shifts towards a lower energy of 1.46 eV (849 nm). The smaller emission maxima of the bi-and trilayer again arise from the A exciton. The stronger maximum at the lower energy side is assigned to the indirect band gap, in agreement with previous studies on MoS 2 [6]. Our photoluminescence data are in excellent agreement with [11]. Differences in the relative intensities of the emission maxima might be related to the different excitation wavelength of 514 nm.

Photoluminescence emission vs. absorption of atomically thin MoS 2 , MoSe 2 , and WSe 2
To gain insight into the efficiency of the photoluminescence emission process we first investigate the role of absorption for each monolayer material. Due to multiple reflections at the interfaces of the MX 2 /SiO 2 /Si structure, the absorption of laser light used for excitation is different as compared to a free-standing MX 2 monolayer. Since the Si substrate is nontransparent, one may use simple reflectivity measurements and the intensity of the Raman emission from the Si substrate at 528 nm, i.e. 520 cm −1 in the Raman signal, to extract the absorption of the MX 2 monolayers. A sketch of the optical system is given in Fig. 7. The absorption of the monolayer (neglecting scattering) is given by