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Abstract
In order to increase the optical path and related sensitivity of photometers, multiple axial-reflection of parallel light-beam inside a capillary cavity is one of the most effective ways. However, there is a non-optimum trade-off between optical path and light intensity, e.g., smaller aperture on cavity mirror can increase multiple axial-reflection times (i.e., longer optical path) due to the lower cavity-loss, but it would also reduce coupling efficiency, light intensity, and related signal-to-noise ratio. Herein, an optical beam shaper, which is composed of two optical lenses with an apertured mirror, was proposed to focus the light beam (i.e., increasing coupling efficiency) without deteriorating beam parallelism and related multiple axial-reflection. Thus, by combining the optical beam shaper with a capillary cavity, large optical path enhancement (10-fold of capillary length) and high coupling efficiency (>65%) can be realized simultaneously, where the coupling efficiency was improved 50-fold. An optical beam shaper photometer (with a 7 cm long capillary) was fabricated and applied to detect water in ethanol with a detection limit of 12.5 ppm, which is 800-fold and 32∼80 fold lower than that of the commercial spectrometer (1 cm cuvette) and previous reports, respectively.
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1. Introduction
Photometers (including spectrometers) are widely used for the detection of liquid samples [1–4]. Compared to conventional cuvettes, liquid waveguide capillaries can provide a long optical path for highly sensitive detection, while maintaining a small sample volume [1–3,5,6]. However, for normal liquid waveguide capillaries (e.g., Teflon amorphous fluorinated polymer capillary), their optical path is only nearly equal to its physical length without a further enhancement (Fig. 1(a)) [2,3,5,6]. In addition, increase of capillary length would increase the risk of gas bubble accumulation and lead to bulky apparatus [2,6].
Fig. 1. Light propagation in the capillary cavity. (a) Multiple radial-reflection (MRR), (b) multiple axial-reflection (MAR), and (c) MAR with OBS. Where β is the tilt angle of mirror-2, and the OBS is the optical beam shaper.
Multiple reflection inside capillary is an effective way to enhance optical path without elongating capillary, and it can be classified as multiple radial-reflection (MRR) and multiple axial-reflection (MAR), which occurs between the capillary sidewalls and end-faces, respectively. As for MRR (Fig. 1(a)), each reflection only leads to a small increase in optical path (nearly equal to the capillary i.d.) [7–10], so numerous reflections were required, which would lead to severe attenuation of light intensity and related signal-to-noise ratio (the attenuation can reach ∼106 even for silvered capillary [10]). In comparison, for MAR (Fig. 1(b)), each reflection can lead to a large increase in optical path (equal to capillary length). Thus, MAR can more effectively increase the optical path with less reflection times (i.e., low attenuation).
However, for MAR in a capillary cavity, there is a non-optimum trade-off between optical path (decided by MAR times) and coupling efficiency. As shown in Fig. 1(b), in order to realize MAR between the two mirrors at capillary end-faces, parallel light-beam with low divergent angle was required to avoid the incidence of light onto capillary sidewall (i.e., avoid MRR), and two apertured mirrors were used to construct an optical cavity as well as introducing the light beam into/outside the capillary cavity. It can be found that smaller aperture on the mirror (i.e., lower loss of the cavity) can increase MAR times (i.e., longer optical path), but it would also lead to lower coupling efficiency (i.e., lower light intensity) because the parallel light-beam should maintain its parallelism and cannot be focused. The low coupling efficiency would deteriorate the signal-to-noise ratio and related detection limit.
It should be noted that as shown in Fig. 1(b), the above trade-off would be eliminated if the diameter of parallel light-beam is small enough, which can make high coupling efficiency achievable without focusing. However, the parallel light-beam normally has a large diameter, due to the diffraction effect. For example, the parallel light-beam obtained from the collimator of single-mode fiber has a parallel light-beam diameter larger than 0.5 mm (beam divergence of 0.15 degree) [11], while the collimator of multi-mode fiber has a parallel light-beam diameter larger than 4 mm (beam divergence of 0.5 degree) [12]. Moreover, even if small parallel light-beam can be obtained, it is still difficult to control the optical path, because the incidence of small parallel light-beam onto small aperture is by accident.
It should also be noted that cavity ring-down/enhanced-absorption spectroscopy (CRDS/CEAS) [13,14] has also been proposed for increasing optical path. However, its performance deteriorates rapidly with cavity loss, so special solvent with low absorbance was required for detecting liquid samples [13–15].
Meanwhile, ethanol is a renewable and clean fuel compared with traditional fossil fuels [16–21], and it also has wide applications in the fields of pharmaceutical, biological and chemical industry [16–18,22,23]. Detections of water in ethanol (WIE) is important for ethanol quality monitoring [16–19,24–28]. In comparison with traditional titration method, which is time-consuming [16,22–26], optical methods have advantages of fast detection, easy operation and high sensitivity [17,18,29,30]. Currently, several optical methods such as colorimetry [16,22,24,25], fluorometry [17,26–29] and NIR spectrometry [19–21,23,31] have been applied to detect WIE with a detection limit in a range of 1∼1.2 × 104 ppm [16,22,24,25], 20∼1000 ppm [17,26–29] and 400∼1000 ppm [19,20], respectively. As for colorimetry and fluorometry, time-consuming chemical reactions with reagents (e.g., chromogenic reagent [16,22,24,25] and fluorescent dyes/probes [17,26–29]) was required. As for NIR spectrometry, which is normally based on cuvette, whose optical path is very limited, the detection limit is as high as 400∼1000 ppm. Thus, WIE detection with fast speed, easy operation, and high sensitivity (with a detection limit less than tens of ppm level) is still a challenge.
Herein, an optical beam shaper (OBS), which combines two optical lenses with an apertured mirror (Fig. 1(c)), was proposed for MAR in the capillary cavity. The OBS can focus light beam (i.e., increasing coupling efficiency) without deteriorating beam parallelism and related MAR. Thus, by combining the OBS with capillary cavity, large optical path enhancement (10-fold of capillary length) and high light intensity (coupling efficiency >65%) in capillary can be realized simultaneously, where the coupling efficiency was improved ∼ 50-fold. An OBS photometer was fabricated and applied to detect WIE with a detection limit of 12.5 ppm, which is 800-fold lower than that of commercial spectrometer (PerkinElmer) with 1 cm cuvette at the same operating wavelength of 1300 nm. The OBS photometer features compact and high sensitivity.
2. Materials and methods
2.1 Apparatus and concept
As shown in Fig. 2, the OBS photometer consists of (1) a 7 cm-long metal capillary with a 4.3 mm i.d. and polished inner surface, (2) two apertured plane mirrors (silver coated quartz-plates with a reflectivity ∼97.5%, ME2S-P01, Thorlabs [32]) attached on the front and back end-face of the metal capillary, i.e., mirror-1 and mirror-2, respectively, (3) an OBS formed by inserting mirror-1 between two lenses (i.e., the front-lens and back-lens, GLH21, Heng Yang Guang Xue Inc.), (4) a light source (tungsten lamp, SLS201/M, Thorlabs) with a 1300 nm band-pass filter, and (5) a photodetector (PDA10CS-EC, Thorlabs). The two apertured mirrors are the same, where a central disc-aperture with a diameter of 0.5 mm was fabricated on the silver film by removing the silver coating. The mirror-1 was aligned vertically with the metal capillary, while mirror-2 was tilted with an angle of β (i.e., deviated from the vertical direction of metal capillary), and the apertures locate on the central axis of metal capillary. In order to prevent the OBS from contacting with detection sample, a quartz plate was placed between the OBS and metal capillary (metal capillary was sealed by the quartz plate).
Fig. 2. (a) Schematic diagram and (b) optical image of the OBS photometer. Where the optical beam shaper (OBS) is formed by inserting an apertured mirror between two lenses.
As shown in Fig. 2(a), the OBS was used to focus light beam (i.e., increasing coupling efficiency) without deteriorating beam parallelism. The mirror-1 is located at the focal plane of both front-lens and back-lens. The focal lengths of the front-lens and back-lens of mirror-1 are 5.6 and 3.0 mm, respectively, and the focal length of the back-lens of mirror-2 is 10 mm. By using the front-lens, the light beam from tungsten lamp was focused into a tiny spot, and then it can transmit through the aperture of mirror-1 (i.e., coupled into the capillary cavity) with high coupling efficiency. Then, by using the back-lens, the coupled light can be transformed into parallel light for high performance MAR between the mirror-1 and mirror-2.
As shown in Fig. 1(c), the parallel light reflected by mirror-2 would be refocused by the back-lens. It was noted that the refocused light should not incident onto the aperture again (i.e., does not escape from the aperture of mirror-1), so the beam propagation direction needs to be slightly tilted. The tilt angle of beam propagation was caused by the tilt angle (β) of the mirror-2, which deviated from the vertical direction of metal capillary. The tilted mirror-2 was realized by insertion a thin quartz plate (70 um thick) between the mirror-2 and the T-connector (Fig. 2(a)), which was used to fixed the metal capillary. The value of tilt angle (β) was decided by the insertion depth of the thin quartz plate. In this case, the tilt angle is 0.93 degree. After reflected by mirror-1, the refocused light will be transformed into parallel light again by the back-lens. Thus, the beam can maintain its parallelism when it experiences MAR between the mirrors.
For the OBS, high coupling efficiency can be obtained even for small aperture by using the front-lens, and light parallelism can be achieved and maintained by using the back-lens. Meanwhile, owing to the small aperture and parallel light beam, high performance MAR (long optical path) can also be realized.
2.2 Reagents and methods
Analytical grade ethanol was purchased from Dalian Bonuo Biological Reagent Factory. A series of WIE solutions (sample W9∼W1) were prepared with water content ranging from 12.5 ppm to 5 × 104 ppm by using the successive dilution method (Supplement 1). Moreover, the ethanol without adding water was employed as blank solution for calibration.
The performance of photometers was investigated by measuring the absorbance of WIE solutions at 1300 nm. The absorbance measurement was carried out by sample switching between the WIE solution and the blank solution. In order to avoid the high-concentration contamination, the samples were measured in sequence from low to high concentration (i.e., from W9 to W1). The transmission spectra of ethanol and water were shown in Fig. S2 (see Supplement 1). The spectra were measured by using the OBS photometer, and the 1300 nm band-pass filter was replaced with a linear variable filter (900∼1700nm, Vortex) for spectrum measurement. It was noted that at 1300 nm, ethanol has an absorption peak, while water has an absorption valley. Thus, 1300 nm was chosen as the operating wavelength of the OBS photometer.
For comparison, a metal capillary photometer (it has the same structure with the OBS photometer except that the OBS and the apertured mirrors were removed) and a commercial spectrophotometer (PerkinElmer Lambda 950) with 1.0 cm cuvette were also employed to measure the WIE solutions. It was noted that for the metal capillary photometer, the light beam was transformed into parallel beams by the collimator and then passed through the capillary directly without multiple reflections, and the optical path is equal to the capillary length (7 cm).
3. Theoretical analysis
3.1 Theoretical calculation
The analysis was carried out by using ray optics for simplicity, because the size of capillary and the aperture (500 µm) is much larger than the wavelength of operating light (1.3 µm). It was noted that the reflectivity of lens surface (∼3.3%) is much lower than that of the silver mirror (∼97.5%), so the reflection on lens surface was neglected in analysis for simplicity.
As shown in Fig. 3(a), the optical cavity was formed between the two apertured mirrors (mirror-1 and mirror-2), and the effective reflectivity of the mirror (RE) can be calculated as RE = R × (1-SA), where R is the reflectivity of the silvered mirror (97.5%), and SA is the area ratio of the aperture to the beam cross-section (SA = r2/rc2, r and rc are the aperture radius and beam-radius, respectively). Thus, the effective transmissivity of the mirror (TE) can be calculated as TE = 1-RE = (1-R) × (1-SA)+SA. It was noted that the cavity enhancement can increase with RE, so larger beam radius rc is preferred (the maximum rc is equal to the inner radius of metal capillary, i.e., 2rc = 4.3 mm).
Fig. 3. (a) Schematic diagram and (b) analysis mode of MAR with OBS. Where β is the tilt angle of mirror-2, and the OBS is the optical beam shaper.
Based on the above RE and TE, the analysis can be carried out by using traditional cavity enhancement theory [4]. The light intensity I(α) transmitting through the cavity can be calculated as follows [4]:
Then, optical path of the OBS photometer can be calculated via the absorbance (A) of the sample:
According to Eq. (1) and (2), the dependence of optical path on aperture size (r) and absorbance coefficient (α) was calculated and shown in Fig. 4. It is clear that optical path can increase rapidly with shrinking aperture, due to the decrease of cavity loss. With an aperture diameter of 0.5 mm, an optical path as long as 180 cm can be obtained, which corresponds to 25-fold enhancement of optical path (i.e., a 25-fold of the metal capillary length). When the aperture diameter increases to 4.3 mm (i.d. of metal capillary), which means the non-existence of mirrors, the optical path would decrease to 7 cm (equal to metal capillary length).
Fig. 4. Dependence of OP on absorption coefficient and aperture size for OBS photometer. Where r and rc is the aperture radius and beam-radius, respectively.
As shown in Fig. 4, the optical path increases with decreasing α, and it becomes saturated when α is less than 10−4 cm−1. While, when α increases to a certain value (e.g., α > 0.1 cm−1), the enhancement on optical path disappears (i.e., disappearing of MAR), because the light beam was severely attenuated by the detected sample before it was reflected by the mirror. This phenomenon agrees with previously reports [7–10].
Finally, coupling efficiency was analyzed. For traditional MAR without OBS, small aperture would lead to low coupling efficiency, because the light cannot be focused (light parallelism needs to be maintained). Thus, when a parallel beam (beam diameter of 4.3 mm) incident onto an apertured mirror (aperture diameter of 0.5 mm), the coupling efficiency is only 1.3% if without OBS.
In comparison, for the MAR with OBS, the coupling efficiency can be greatly improved, because the light can be focused without deteriorating its parallelism. Herein, for the tungsten lamp with pigtailed output-fiber (fiber diameter of 1 mm), the light source can be regarded as a spot light (spot diameter of 1 mm) with a divergence angle of 25 degrees. The spot light can be easily focused into a smaller spot (diameter < 0.5 mm), so it can transmit through the apertured mirror (aperture diameter of 0.5 mm) with a high coupling efficiency. The output power of the tungsten lamp is 138.3 mW, the light power coupled into the capillary via OBS is 89.9 mW, so the measured coupling efficiency with OBS can reach 65% (i.e., 89.9/138.3), which is improved 50-fold compared with the coupling efficiency without OBS (1.3%). The input power of photodetector is 0.35 mW, and the lower input power is resulted from that the 1300 nm band-pass filter before the photodetector can block most of the light power of the tungsten lamp (broad spectrum lamps).
3.2 Simulation
For simplicity, some approximations were made in following simulation. (1) The light beam that focused into the capillary through the aperture of mirror-1 was simplified as a point light source at the center of the aperture, and the light source has 20 rays with a divergence angle of 25 degrees (Fig. 5(b)). (2) Due to the symmetry of the light beam and the capillary, only the two-dimensional plane along the central axis of the metal capillary was considered in the simulation.
Fig. 5. Simulation of light path in the OBS photometer. (a) The structure of photometer, (b) the light entering the capillary through the aperture of mirror-1, and (c) the light reflected by the tilted mirror-2.
Simulation of light path inside the capillary of the OBS photometer was shown in Fig. 5 by using ray tracing of COMSOL. As shown in Fig. 5(b)-(c), the length of optical path was indicated by the color bar, and the end point of ray propagating was indicated by red dot. As shown in Fig. 5(b), owing to the enlarged diameter of the parallel beam transformed by the back lens of mirror-1, only a few number of rays can escape from the aperture of mirror-2 (the aperture is much smaller than the beam diameter), and most rays can be reflected by the tilted mirror-2 and then continue to propagate parallelly in the capillary with a tilt angle of 2β. As shown in Fig. 5(c), when the reflected rays reach mirror-1 again, only a few number of rays escaped from the aperture of mirror-1 due to the tilt angle (2β) of the beam, and most rays can be reflected by mirror-1 for continuing MAR. Thus, the rays can maintain its parallelism while experiencing MAR between the mirrors.
According to the simulation (Supplement 1 and Fig. S1), when the tilt angle (β) of mirror-2 is less than 0.93 degrees, light rays begin to escape from the aperture of mirror-1, and the amount of escape rays would increase with decreasing β. With decrease of β to 0.67 degrees, all the rays would escape from the aperture of mirror-1 (Fig. S1e), and the optical path of rays that directly transmitted through the aperture of mirror-2 can decrease to capillary length (7 cm). It should be noted that, with the increasing β, the rays tend to incident onto capillary sidewall and related MAR times would decrease. Thus, the optimum tilt angle of mirror-2 is 0.93 degrees, which is a result of compromise between light escape and MAR times.
4. Results and discussion
Performance of the OBS photometer was investigated by measuring the WIE samples. Measurement results of the WIE samples were shown in Fig. 6(a)-(d) (all the results were provided in Supplement 1). The time, when switching takes place between the WIE solution and the blank solution, is marked by the red arrows in Fig. 6. VWIE and Vblank are output voltage of the photodetector when WIE solution and the blank solution are introduced into the capillary, respectively. The signal increases rapidly when switching from WIE- to blank-solution, and it decreases vice versa. It was noted that “transient peak” induced by sample switching was observed (Fig. 6), which deceases with signal ΔV. The peak may result from Schlieren effect [8,33,34], i.e., the undesired optical reflection at the interface of two switching samples.
Fig. 6. Measurement results of the WIE sample (a) W1 (5 × 104 ppm), (b) W4 (400 ppm), (c) W8 (25 ppm) and (d) W9 (12.5 ppm) by using the OBS photometer. VWIE and Vblank are output voltage of the photodetector when WIE and blank solutions are introduced into the capillary, respectively, and the signal is expressed as ΔV = Vblank–VWIE.
As shown in Fig. 6, the VWIE, Vblank and corresponding signal ΔV (ΔV = Vblank–VWIE) can be obtained and used for calculating the absorbance (AOBS) of WIE solutions (Supplement 1). As shown in Fig. 6(d), the measured ΔV is 0.3 mV, and its corresponding absorbance is 2.7 × 10−4 absorbance unit (AU) (Supplement 1). The output voltage decreases slowly with increasing measurement time, which mainly results from the gas bubble accumulation on the inner surface of the capillary and the drift of light power of the light source. Smaller ΔV is hard to be discriminated from the noise, so the detection limit of OBS photometer is 12.5 ppm (sample W9). The long-term (more than 75 min) measurement curve of ethanol solution by using the OBS photometer was shown in the Fig. S5 (Supplement 1). The noise level remains stable during the measurement period, and the detection limit is mainly decided by the noise level. So, the detection limit of the long-term detection is also expected to reach 12.5 ppm and the OBS photometer is stable for a long-term detection.
For comparison, the WIE solutions were also measured by using the metal capillary photometer and the commercial spectrophotometer (Supplement 1). Dependence of the absorbance on water content was plotted in Fig. 7(a), where AOBS, AMC, and Acuvette is the WIE absorbance measured by using the OBS photometer, the metal capillary photometer, and the commercial spectrometer at 1300 nm, respectively. It is clear that Acuvette is linearly proportional to the water content, because the cuvette has a constant optical path of 1 cm (OPcuvette =1 cm). The noise in the measurement curve (Fig. 6) is mainly caused by the inherent noise of the detector and light source as well as the flowing liquid in capillary. The noise level varies little for different WIE samples. So, the error bar does not clearly increase at low values of AOBS and AMC.
Fig. 7. Dependence of the (a) measured absorbance and (b) related optical path on the absorption coefficient of WIE samples. AOBS, AMC, and Acuvette is the absorbance measured by using the OBS photometer, the metal capillary photometer, and the commercial spectrometer at 1300 nm, respectively, AEF is the absorbance enhancement factor (AEF = AOBS/Acuvette), OPOBS and OPMC is the optical path of the OBS photometer and the metal capillary photometer, respectively.
It was noted that AOBS is not linear with the absorption coefficient (α) at low values, since the optical path of the OBS photometer increases with decreasing α. In order to explain the reason more clearly, the transmitted light can be classified as the single-pass light (direct transmission from the aperture of mirror-1 to the aperture of mirror-2) and the multi-pass light (MAR between mirror-1 and mirror-2 at the end-faces of the capillary), the optical path (Lop) of the single-pass light and the multi-pass light is equal to Lphy and N × Lphy, respectively, Lphy is length of the metal capillary. According to Beer’s law, the intensity of the transmitted light can be expressed as I(α)=I0×exp(-α×Lop). Thus, for the WIE with high water content (e.g., α > 0.001 cm−1), the multi-pass light is highly attenuated, and its intensity is much lower than that of the single-pass light, due to the large absorption-coefficient (α) and its much longer optical path. In this case, the single-pass light would play a dominant role in absorbance detection with Lop = Lphy. In contrast, when the absorption-coefficient is decreased with decreasing water content (e.g., α < 0.0001 cm−1), the intensity of the multi-pass light will increase more rapidly than that of the single-pass light, and then it begins to play a more important role with Lop = N × Lphy. Thus, with decreasing absorption coefficient, the optical path increases from Lphy towards N × Lphy.
Based on the measured absorbance (Fig. 7(a)), optical path of the OBS photometer (OPOBS) can be obtained via OPOBS = AEF × OPcuvette according to Beer’s law [35], where AEF is the absorbance enhancement factor (AEF = AOBS/Acuvette at the same water content). Similarly, the optical path of metal capillary photometer (OPMC) can also be calculated from the measured absorbance. By using the commercial spectrometer as standard, the absorption coefficient (α) of the WIE samples can be obtained via α=Acuvette/OPcuvette [4], where OPcuvette =1 cm.
With the obtained optical path and α, their relationship was plotted in Fig. 7(b). It can be observed that for the OBS spectrometer, a maximum OPOBS of 72 cm, which corresponds to a 10-fold optical path enhancement (10 times of metal capillary length), was realized. In comparison, the OPMC is only 7 cm (well matches with the physical length of metal capillary), because MAR does not occur in the metal capillary photometer.
It was noted that although the measured curve (Fig. 7(b)) is similar with the theoretical curve (Fig. 4), the measured OPOBS (72 cm) is smaller than the theoretical value (180 cm) with an aperture diameter (2r) of 0.5 mm. The main reason may be that the tilt angle of mirror-2 (Fig. 1(c)) causes the decrease of related MAR times.
For the OBS photometer, the detection limit (12.5 ppm) is 800-fold lower than that (104 ppm) of the commercial spectrometer (Supplement 1). The improvement on detection limit is manly resulted from the long optical path (72 cm) and the high coupling efficiency (i.e., high light intensity and signal-to-noise ratio). For comparison, performance of WIE detection by using the previous NIR spectrometer [19–21,23] were summarized in Table 1. The detection limit (12.5 ppm) of the OBS photometer is 32∼80 fold lower than that of previous reports on WIE detection by using NIR spectrometers (400∼1000 ppm) [19,20], whose operating wavelength was set at 1400∼1500 nm (the absorption coefficient of water at 1400∼1500 nm is ∼25 times larger than that at 1300 nm). Moreover, it was noted that the reported Fourier transform NIR spectrometer are normally bulky and expensive [20,21]. For performing real-time monitoring, the spectrometer/photometer needs to be compact and portable. The dimensions and weight of the OBS photometer can meet the requirements of portability.
Table 1. Summary of the performance of WIE detection by using the previous NIR spectrometer
5. Conclusions
An OBS, which consists of two optical lenses with an apertured mirror, was proposed to focus light beam (i.e., increasing coupling efficiency) without deteriorating beam parallelism and related MAR. By using the front-lens of OBS, the light beam was focused into a tiny spot, and then it can transmit through the aperture of mirror with high coupling efficiency. Then, by using the back-lens of OBS, the coupled light can be transformed into parallel light for MAR between the two mirrors at capillary end-faces. Thus, for MAR inside a capillary, the non-optimum trade-off between optical path and light intensity can be eliminated. By combining the OBS with a capillary cavity, large optical path enhancement (10-fold of capillary length) and high coupling efficiency (>65%) can be obtained simultaneously, where the coupling efficiency was improved 50-fold. An OBS photometer (with a 7 cm long capillary) was fabricated and applied to detect WIE with a detection limit of 12.5 ppm at the operating wavelength of 1300 nm, which is 800-fold and 32∼80 fold lower than that of commercial spectrometer (1 cm cuvette) and previous reports, respectively. The OBS photometer features compact and high sensitivity.
Funding
National Natural Science Foundation of China (61774027, 62074023).
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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