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Abstract
We propose a unique way to design multipass cells (MPCs), which combines cost-efficient spherical mirrors with the high-density pattern of astigmatic mirrors. Such functionality was accomplished using at least three standard spherical mirrors appropriately tilted, which breaks the parallelism between them. A genetic algorithm (GA) supported the cell configuration optimization. A 16 m and 23.8 m optical path length (OPL) MPC was developed, practically realized, and proved by a time-of-flight (TOF) experiment to demonstrate the principle. Finally, CO2 detection at 2004nm obtaining 0.4 ppmv limit of detection (LOD) using wavelength modulation spectroscopy (WMS) with 10 s averaging was performed.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Trace gas detection using optical techniques is a rapidly growing application of laser spectroscopy. Environmental pollution and industrial processes monitoring imply that compact, laser-based gas sensors are highly demanded on the market [1,2]. Generally, to achieve high sensitivity in absorption spectroscopy, a long optical path is required [3], which becomes a key factor affecting the overall size of the sensor. Hence, the use of a MPC enables the implementation of compact gas sensors. Currently, there are several different types of MPCs commonly used in industry and research. The most basic one is a Herriott MPC [4] formed by two parallel spherical mirrors, which creates stable elliptical spot patterns. This particular MPC is easy to use, robust, and its OPL is adjustable. Moreover, its pattern shape and OPL can be easily determined using analytical equations [5]. Unfortunately, its pattern density is low, which is a fundamental limitation on getting long OPLs while simultaneously maintaining compactness. This kind of MPC design can be improved by using astigmatic mirrors with different foci on their perpendicular axes to create dense Lissajous figures instead of elliptical patterns [6]. However, due to the complex manufacturing process of astigmatic mirrors, their implementation significantly increases the price of such a MPC and limits the flexibility in terms of OPL configuration. Another frequently used MPC based on three spherical mirrors (primarily rectangular) with equal foci is a White cell [7]. Its OPL can be easily adjusted by tilting one of the side mirrors. High aperture beams can be coupled to the MPC, and denser patterns are obtainable compared to the classical Herriott MPC. Recently, a toroidal MPC has been introduced [8]. In this particular solution, compact size and adjustable OPL can be obtained, but its fabrication cost and complexity are high.
Out-of-lab applications of laser-based gas analyzers usually impose a size and weight limit. Therefore, a technological race takes place in the development of miniature and effective MPCs. For instance, So et al. [9] has presented a Herriott-type MPC with dense patterns, which was followed later by an even more compact design with a folded optical path [10]. A similar solution has been additionally demonstrated by Liu et al. [11]. The dense astigmatic pattern can also be obtained by using cylindrical instead of astigmatic mirrors [12,13], or three mirrors [14] in the Herriott MPC configuration. The miniature MPCs with long OPL have also been realized using the toroidal [15–18] and full sphere [19] concepts. Contrary to the standard Herriott MPC, the dense-pattern cells, especially when astigmatism is considered, require numerical simulations to determine their optimal configurations [9,14,15,19,20].
In this paper, we propose a unique way to design and construct MPCs, combining the cost efficiency of spherical mirrors with the high-density pattern of astigmatic mirrors. An astigmatic pattern is obtained using at least three standard spherical mirrors and appropriate tilting, which breaks the parallelism. The MPC mirrors are placed in a way similar to the White cell or the MPC presented in [14]. However, its principle of operation is significantly different (explanation in the next paragraph), which we have initially introduced in previous works [21,22]. The most straightforward three mirrors setup was also investigated by Zhong et al. [23]. However, this concept is limited in achieving an optimal OPL to volume ratio (OPL/V). Here, based on the design principles, a compact MPC with four spherical mirrors is comprehensively investigated. A 16 m and 23.8 m OPL MPC was developed and empirically tested (exceptionally low 80 cc volume can be achieved [21] similar to toroidal MPCs [17,18]) using a bow-tie-like configuration. To confirm that the developed MPC is useful for laser spectroscopy applications, we demonstrate CO2 detection at 2004nm (4990 cm-1), with a 0.4 ppmv LOD at 10 seconds of averaging using the WMS technique. It is equal to a minimum fractional absorption (MFA) of 9.5×10−5. Moreover, to speed up the MPC design process, an automatic procedure with an implemented GA was developed. It allows for determining the optimal MPC configuration with predefined input parameters, such as initial geometry, total OPL, operating temperature range, and mirror positions.
2. Principle of operation of the astigmatic multipass cell based on spherical mirrors
In the classical White cell [7], based on three mirrors (Fig. 1(a)), astigmatism is negligible due to its principle of operation. The center of curvature of mirror M3 is placed halfway between the other two symmetrically mounted mirrors M1 and M2. Also, the center of curvatures of mirrors M1 and M2 lies on the mirror M3 surface. Therefore, any beam reflected from mirror M1 is imaged to the same point of mirror M2. The first reflection of the input beam occurs at the center of M1. The beam is then reflected symmetrically with respect to the optical axis of M3. Consequently, a pattern consisting of only a single or double line shape on the mirror M3 can be obtained, thus limiting the number of non-overlapping passes and the OPL (Fig. 1(a)).
Fig. 1. The difference in principle of operation of: a) White cell with the longest possible OPL of 2 m and its pattern on M3 b) 3 spherical mirrors MPC with broken symmetry with the OPL of 10 m. Both designs have a maximum pattern density without leakage. The red line in the left-hand column indicates the input beam.
Compared to the White cell, our design (Fig. 1(b)) enables to obtain a dense astigmatic pattern, despite being based on three standard spherical mirrors. Two conditions have to be satisfied to enable such a pattern to emerge. First, the distance between the opposite mirrors must not be equal to its radius of curvature r. Second, the input beam has to enter the cell off-axis of mirror M3. Due to the fact that the mirrors are not parallel to each other, unlike in the Herriott cell, the radial symmetry of such a setup is not preserved. This in turn allows for creating a Lissajous pattern, which is usually found only in configurations using expensive astigmatic mirrors. Moreover, mirrors M1 and M2 can be placed at different distances and angles relative to mirror M3 to maximize their surface coverage by the laser beam. As a result, the pattern can be much denser than in classical Herriott or White cells, without parasitic beam overlapping.
In order to present the difference between the White cell and the proposed design, we have performed GA-aided ray-tracing simulations using self-developed software in C++ [24]. GA is an optimization and search problem algorithm class based on biologically inspired mutation, selection, and crossing operators. The GA starts from a set (population) of MPC configurations with different mirrors positions and angles. In a single iteration, the selection operator chooses the better half of the configurations based on a fitness function. Then the mutation operator randomly modifies mirrors positions and angles of the selected configurations. The iteration process is repeated until satisfying the boundary conditions (desired OPL, output beam quality).
During the optimization, real Gaussian laser beams are considered, which enable to monitor the beam shape during the GA operation and ensures no light leakage, which might occur at mirror edges and input/output apertures. The beam was composed of 300 traces for the GA optimization process and 10000 traces for the visualization patterns depicted in Fig. 1. The fitness function of the GA takes into account: mirrors’ parameters and their positions, input and output beam shape, beam overlap (distance of main beam spot to other rays or interferences at detector area), beam leaks (a part of the beam that escapes from the mirror borders or apertures), OPL (difference between the desired and obtained path length), and thermal stability (temperature range of operation). As a result of the GA operation, 10000 MPC configurations have been analyzed (mirrors patterns and OPL). As an outcome, the optimum mirror positions and the input and output angles of the laser beams were determined. The performed optimization procedure was made with the following assumptions: 25 mm focal length spherical mirrors and measurement laser beams with a Gaussian profile and the FWHM of 2 mm. In the case of the White cell configuration (Fig. 1(a)) with a mirror separation r of 50 mm, two mirrors with 12 mm diameter (M1, M2) and M3, with a dia. of 25 mm, the OPL of 2.2 m was obtained (equal to 43 reflections), without beam overlap. The minimal volume of the designed cell is equal to 18 cc, which is limited by the mirror's shape and distance.
Using the proposed concept with a broken symmetry (BS), a dense astigmatic pattern can be obtained (Fig. 1(b)), and the OPL increases significantly to 10 m. This approach requires using three identical spherical mirrors with a clear aperture of 25 mm. In order to maximize the pattern density, distances between M1 to M3 and M2 to M3, and angels α, β were optimized by the GA, and calculated equal to 46.4 mm, 44.1 mm, and 16.9°, 14.7°, respectively. The minimal internal volume of 35 cc based on mirror shapes and their distances is almost twice as the White cell. However, the OPL/V of the BS MPC is 0.29, which is significantly higher than the standard White cell (0.12). Moreover, it should be noted that to realize the 10 m OPL using the standard White cell configuration; the distance r has to be increased 5 times, thus significantly expands the dimensions of the cell.
Although dense astigmatic pattern-based MPCs tend to have relatively poor spot beam shape causing interferences between spots, also on the output, appropriate sensor design permits their implementation in sensitive and selective laser-based spectroscopy applications [25]. The astigmatism of the beam can be reduced using mirrors with longer focal lengths. However, this increases the MPC size. In the presented configuration, the negative influence of astigmatism was limited by proper MPC optimization using the GA (minimization of leakage on subsequent bounces around the output hole). Moreover, the output beam was further conditioned using an iris diaphragm placed before the detector. In the end, we have developed a long OPL, compact, thermally stable, and cost-effective MPC based on only commonly available spherical mirrors.
3. Towards optimal astigmatic pattern MPC configuration
Optical sensors for field-deployed applications require compact, mechanically stable MPCs with the OPL as long as possible to obtain the desired sensitivity. As shown above, increasing the OPL can be achieved while maintaining a compact size by appropriately re-configuring the mirrors to achieve a dense astigmatic pattern in the MPC. Further improvement in the OPL can be made by increasing the number of mirrors, which translates into an extension in the path traveled by light in a single set of reflections inside the cell. It also results in additional possible combinations of the beam reflections between them. There are two types of reflections in such MPCs: rotating - when a laser beam reflects each mirror one by one and returning - when a laser beam reflects back at the last mirror. Exemplary MPC configurations with the number of mirrors greater than 2 are shown in Fig. 2. If an MPC with three mirrors is considered, only two setups are possible (Fig. 2(a), (b)). However, when we take into account the possibility of using more than three mirrors, the number of solvable configurations increases significantly and choosing the optimal one is challenging.
Fig. 2. Astigmatic pattern MPC exemplary configurations based on 3 to 6 spherical mirrors. The red line shows a rough laser beam path inside each MPC.
These configurations differ in many factors, such as achievable OPL, minimum volume, mechanical complexity, angles of reflections, thermal stability, etc. In order to choose the most effective compact astigmatic dense pattern MPC configuration with the longest OPL, we have calculated the single roundtrip OPL per volume ratio (OPL/V). The calculations performed with the CAD software assumed: a) the use of spherical mirrors with the diameter and focal lengths of 25 mm, b) the distance between successive mirrors set to around 50 mm, c) common input and output aperture located in one of the mirrors, d) the same number of roundtrips at each investigated MPC (the same density patter at each mirror). The obtained results are summarized in Table 1, where: one roundtrip means the distance traveled by light from the input to the output mirror aperture, while the calculated volume is limited by the outer contour of appropriately positioned mirrors (no kinematic mounts are assumed).
Table 1. Comparison of different MPC configurations with regard to the OPL/V ratio.
As a reference for this comparison, we have taken the two astigmatic mirror MPC with the same constraints in terms of dimensions and number of roundtrips (pattern density) as for the MPCs based on spherical mirrors. To compare the MPCs configurations, the roundtrip OPL/V was calculated. It is clear that the returning configurations with the dense astigmatic pattern based on spherical mirrors allow obtaining a higher OPL/V than in a rotating MPC. Moreover, all of the returning configurations based on commonly available spherical mirrors outperform a standard MPC with two astigmatic mirrors. Their OPL/V ratio is at least 30% greater. The best OPL/V was obtained for the 6 mirror configuration, which is slightly complicated in practical implementation. Therefore, as a compromise between OPL/V ratio, compactness, and complexity for the final optimization and further laser spectroscopy experiments, four mirrors, bow-tie-like, returning type configuration was chosen (Fig. 2(d)).
Further optimizations for the chosen bow-tie-like configuration (Fig. 3(a)) were performed using the self-developed GA-based software for the following constraints and requirements: a) mirrors diameter and focal length of 25 mm, b) 90° angle between the mirrors surface and base plate (to simplify the MPC fabrication and adjustment procedure), c) OPL temperature stability range of at least 10°C (the simulations took into account the thermal expansion coefficient of the aluminum baseplate), d) OPL longer than 10 m, e) 2 mm Gaussian input laser beam, f) centrally located 3 mm aperture size of input mirror, g) 99% reflectivity of mirrors. Based on these requirements, the algorithm calculated two stable solutions as a result of the optimization of the mutual mirror's position and the introduction of the input beam through the central hole in mirror M1. For the same intracavity geometry, the OPL of 16 m (306 reflections) and 23.8 m (450 reflections) are obtainable when the angle of the input beam is properly adjusted. The calculated mirror patterns, including the information about the input beam angles for these two configurations, are depicted in Fig. 3(b). It is seen that the longer OPL results in a denser mirror spot pattern and more effective use of the mirror surface. At the same time, the requirements for the precision of the input beam coupling are comparable for both configurations.
Fig. 3. The GA optimized bow-tie-like MPC: a) geometrical layout based on four mirrors with a diameter and focal length equal to 25 mm, b) spot patterns for the two calculated stable solutions with an OPL of 16 m and 23.8 m, c) the stencil for coarse mirrors positioning on the base plate (vertices correspond to A-H points whose coordinates are one of the results of the simulations), d) stencils with pattern holes for fine mirrors alignment (a direct result of the performed simulations with the self-developed software).
4. Practical realization of the MPC
In order to speed up and simplify the alignment procedure of the proposed bow-tie-like MPC with a dense astigmatic pattern, a special stencil for coarse mirror positioning on an aluminum base plate was prepared (Fig. 3(c)). Its shape and dimensions were specified based on the coordinates of the A-H points defining the edges of the mirrors, which are a direct outcome of our GA-aided simulations. The laser-cut steel stencil was placed on the aluminum baseplate of the MPC to enable the coarse alignment of silver-coated mirrors mounted in kinematic holders. In line with the simulation's constraints, the surface defined by the edges of the mirrors was set right away perpendicular to the base plate. The final and fine alignment of the mirrors’ angles and the input laser beam was carried out using additional stencils (Fig. 3(d)) placed directly in front of each of the mirrors. The holes in these stencils correspond to several initial reflections spot patterns which positions were directly generated from the simulations. They were manufactured with high precision using laser micromachining. Therefore, to obtain the required OPL and patterns, the mirror angles can be precisely adjusted in a step-by-step procedure by monitoring the consecutive beam reflections. In the case of the investigated bow-tie-like MPC configuration, analyzing the first 6 reflections on each mirror was sufficient for achieving the desired OPL.
Confirmation that the adjustment was carried out correctly and that the intended OPL was achieved was made using the TOF technique according to the scheme depicted in Fig. 4(a). 8 ns laser pulses generated at 1550 nm (semiconductor laser diode modulated by an intensity electro-optical modulator and subsequently amplified in an erbium-doped fiber amplifier) were passed a BK7 wedge and divided into a reference and probe beam. The reference pulses were focused with an off-axis parabolic mirror onto a fast photodetector (FGA04 InGaAs, 2 GHz), while the probe pulses were coupled to the MPC, and the exiting beam was finally collected at the same photodetector. The measured TOF (Fig. 4(b)) were 54 ns and 80 ns, which corresponds to an OPL of 16.1 m and 23.9 m, respectively. The obtained results are in very good agreement with the performed simulations (16 m and 23.8 m), especially considering the maximum distance measurement error of 15 cm caused by the limited performance of the oscilloscope used in the experiment (350 MHz bandwidth with a 2 GHz sampling rate). To confirm if the obtained mirror patterns agree with the results of the simulation, we compared images captured with a camera with beam-spot patterns calculated by the GA algorithm. The comparison for the mirror M4 is presented in Fig. 4(c) (the upper image shows the simulated pattern, the lower one is taken with a camera), which confirms the excellent correlation between simulation and the experimentally obtained results.
Fig. 4. a) Scheme of the experimental setup for the optical path-length measurement (PLS – Pulsed Laser Source, OM – Off-axis Mirror, W – BK7 Window, PD – Photodetector), b) the measured time delays for the 16 m and 23.8 m configurations (the input pulses were attenuated to be at the same scale as the pulses exiting the MPC), c) visual comparison between the M4 mirror patterns (the upper one is simulated while the lower one is a camera image), d) visualization of the optimized MPC with the OPL of 23.8 m.
The TOF measurement was also helpful for fine MPC adjustment, where the overall transmittance was maximized by optimizing the mirrors and input beam positions. It has to be highlighted that when the intracavity geometry was optimized and fixed, the switch between the OPLs was achieved by simply changing the input beam coupling angle. There is no need for MPC mirrors realignment. The presented MPC can be easily modified so that only one OPL is achievable. The fully optimized MPC with an OPL of 23.8 m is depicted in Fig. 4(d) (to better illustrate the mirror patterns an additional green alignment laser was coupled into the cell, which did not require realignment of the MPC).
5. CO2 detection using the optimized MPC
To demonstrate that the proposed dense astigmatic pattern MPC can be effectively used in gas sensors, laser detection of carbon dioxide (CO2) was performed. The MPC with the OPL of 23.8 m was sealed and filled with 200 ppm CO2 in N2 at 533 hPa of pressure. The chosen CO2 concentration used in the experiment was approximately half of the concentration in the Earth's atmosphere [26], which enabled initial validation of the MPC for applications in non-complex out-of-lab sensors. A CO2 transition located at 4990 cm-1 was targeted. As a laser source, we have used a ∼2004nm single-mode laser diode (EP2004-0-DM, Eblana Photonics). The exiting beam was collected with an off-axis mirror (OM) onto the surface of a high sensitivity detector (PDA10DT-EC, Thorlabs.). In the first experiment, we have used the direct absorption spectroscopy approach employing the setup is depicted in Fig. 5(a). The laser current was modulated to sweep the emitted wavelength through the chosen absorption line (a ramp signal with a frequency and amplitude of 100 Hz, 200 mV was used, respectively). The signal from the detector was collected with an oscilloscope (800 kHz acquisition frequency). The obtained results presented in Fig. 5(c) are in very good agreement with a simulation obtained based on the HITRAN database [27] (the standard deviation of the residual signal was at the level of 0.19%).
Fig. 5. Results of laser-based detection of 200 ppm CO2 at 533 hPa in the 23.8 m MPC, a) setup used for direct absorption measurements, b) setup used for WMS detection technique, c) signal registered for direct absorption measurements; the bottom panel shows the residual signal, d) the registered 2f WMS signal modulated with 2 kHz sine and 2 Hz sawtooth ramp; the bottom panel shows a measurement for the MPC purged with N2, e) Allan Deviation of WMS top values.
Further investigation of the developed MPC performance, especially its impact on parasitic fringes in the detected signal, has been done using WMS technique (Fig. 5(b)). The current of the laser diode was modulated with a 50 mV, 2 kHz sinewave signal superimposed onto a 200 mV, 2 Hz sawtooth ramp by the low noise, 2 Mega Samples Per Second (MSPS), 16-bit Digital/Analog Converter (DAC), while the detected signal was acquired with low noise 2 MSPS, 16-bit Analog/Digital Converter (ADC), both self-implemented in the processing unit based on an ARM Cortex-M7 microcontroller. The measured 2f WMS signal of 200 ppm CO2 in N2 at 533 hPa and pure N2 is presented in Fig. 5(d). The measured signal with a standard deviation of 4.2 is depicted in the lower panel of Fig. 5(d). The LOD was calculated at a level of 0.4 ppm based on top of 2f, 2 Hz signal with 10 s averaging (Fig. 5(e)), which is comparable with previously reported experiments [28–30]. The performed experiments confirm that the proposed dense pattern MPC can be used as a very compact, relatively non-complex and inexpensive (in comparison to astigmatic-mirror based configurations) component for gas sensors operating at ppm detection levels, e.g. for CO2 monitoring.
6. Summary
In this work, we demonstrate the new concept of a compact MPC with the extended OPL. By properly breaking the parallelism between spherical mirrors, dense astigmatic patterns were created without using any astigmatic mirror. The optimization process aimed at obtaining a MPC with the best possible parameters for defined constraints was automated by the self-developed software based on the direct ray-tracing technique and GA. The results of the simulations were successfully verified experimentally on the example of the four mirrors, bow-ties like MPC, which was chosen as a compromise between OPL/V ratio, compactness, and complexity. A practically realized MPC based on spherical mirrors was characterized by an OPL of 16 and 23.8 m confirmed with TOF measurements. Its suitability for laser-based gas spectroscopy was also experimentally verified within the direct absorption and WMS setups. The compactness, stability, and cost-effectiveness of the proposed MPC design make it a competitor to commercially available solutions such as traditional Herriott-type or astigmatic multipass absorption cells. Furthermore, applying standard, commonly available spherical mirrors reduces the fabrication costs, simultaneously preserving the benefits of astigmatic mirror-based MPCs.
Funding
Narodowa Agencja Wymiany Akademickiej (PPI/APM/2018/1/00031/U/001).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [27].
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