# Quantitative Evaluation of Broadband Photoacoustic Spectroscopy in the Infrared with an Optical Parametric Oscillator

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

_{2}windows, transmitting 90% of the incoming light intensity and allowing the constant measurement of the remaining idler wave’s intensity after passage through the cell, ${I}_{\mathrm{M}}$, with a resolution of 3%. The systematic uncertainty is more than twice as high as the total loss of laser power due to absorption in the sample cell ∼$1.6\%$ of ${I}_{\mathrm{A}}$ which therefore can be safely neglected in the renormalization of the measured amplitudes. The second, less intense, idler wave component which emerges from the beam splitter ${I}_{\mathrm{W}}=0.07\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{I}_{0}$, was directed to a combined wavemeter and spectrum analyzer. The wavemeter provided the adjusted wavelength with a nominal accuracy of $1\times 10{}^{-4}\phantom{\rule{0.166667em}{0ex}}\mathrm{nm}$ at a resolution of $6\times 10{}^{-4}\phantom{\rule{0.166667em}{0ex}}\mathrm{nm}$. In spectrum analyzer mode the FWHM of the idler beam could estimated to be less than 500 pm. More details regarding the setup can be found in Saalberg et al. [11] and Bruhns et al. [17] where an almost identical setup was used.

#### 2.2. Measurements

## 3. Results and Interpretation

#### 3.1. Quantitative Evaluation of the Obtained Broadband PAS Spectra for Methane, Ethane and Propane

#### 3.2. Analysis and Quantitative Evaluation of Prominent Absorption Lines

#### 3.3. Estimation of the Signal-to-Noise Ratio (SNR) and the Limit of Detection (LOD)

_{exp}and a corresponding hypothetically equivalent lowest detection limit LOD

_{hyp}which would occur if the OPO tuning could exactly be matched to ${\sigma}_{\mathrm{FTIR}}^{\mathrm{max}}({\lambda}_{\mathrm{k}})$ at maximum OPO output power. The hypothetical value describes the system independently of the distribution of the ${\lambda}_{\mathrm{i}}$ and fluctuations in the output power and is therefore better representing the potentials of the OPO system. The results are summarized in Table 3. A detailed description of the exact procedures involved is given in [28].

## 4. Simulation of Deconvolution of Photoacoustic Spectra of Gas Mixtures

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AI | Artificial Intelligence |

FTIR | Fast Fourier transformation in the infrared |

FWHM | Full-width-half-maximum |

IR | Infrared |

LOD | Limit of detection |

MEMS | Microelectromechanical systems microphone |

NA | Natural abundance |

OPO | Optical-parametric oscillator |

PAS | Photoacoustic spectroscopy |

PPLN | Periodically poled lithium niobate |

SNR | Signal-to-noise ratio |

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**Figure 3.**$\mathrm{d}N/\mathrm{d}\lambda $ for the propane measurement in bins of $0.1\mathrm{nm}$. The enhancement of the distribution for $0.6\mathrm{nm}\lesssim \mathrm{d}\lambda \lesssim 1.1\mathrm{nm}$ is due to non-continuous phase matching at the periodically poled lithium niobate (PPLN) crystal.

**Figure 4.**Broadband photoacoustic absorption spectrum (PAS), ${I}_{\mathrm{PAS}}({\lambda}_{\mathrm{i}})$ (blue) in (a.u.), for methane at $c=99.1\phantom{\rule{0.166667em}{0ex}}\mathrm{ppm}$ for $N=1350$ discrete values of ${\lambda}_{\mathrm{i}}$. The normalized standard reference spectrum ${I}_{\mathrm{ref}}^{\mathrm{a}.\mathrm{u}.}({\lambda}_{\mathrm{i}})$ shown in red was calculated from the HITRAN database. The average relative error of ${I}_{\mathrm{PAS}}({\lambda}_{\mathrm{i}})$ with respect to the reference spectra, $\overline{\delta {I}_{\mathrm{rel}}}$ is 15.0(14)% (see text for the definition of $\overline{\delta {I}_{\mathrm{rel}}}$). The red abscissa on the right side refers to the cross section ${\sigma}_{\mathrm{FTIR}}({\lambda}_{\mathrm{i}})$ and is for guidance only.

**Figure 5.**Broadband PAS absorption spectrum ${I}_{\mathrm{PAS}}({\lambda}_{\mathrm{i}})$ (blue) in (a.u.) for ethane at $c=95.5\phantom{\rule{0.166667em}{0ex}}\mathrm{ppm}$ for $N=1345$ discrete values of ${\lambda}_{\mathrm{i}}$. The normalized standard reference spectrum ${I}_{\mathrm{ref}}^{\mathrm{a}.\mathrm{u}.}({\lambda}_{\mathrm{i}})$ (red) was calculated from the HITRAN database. The average relative error, $\overline{\delta {I}_{\mathrm{rel}}}=$ 8.7(11)%, is small. The inset shows the wavelength region between $3330\mathrm{nm}$ and $3370\mathrm{nm}$ featuring ${I}_{\mathrm{PAS}}({\lambda}_{\mathrm{i}})$ and ${I}_{\mathrm{ref}}^{\mathrm{a}.\mathrm{u}.}({\lambda}_{\mathrm{i}})$ in detail. The selected region is dominated by sharp resonances. The high resolution cross section data set, ${\sigma}_{\mathrm{FTIR}}({\lambda}_{\mathrm{k}})$, was taken from the HITRAN database and appropriately rescaled (green). Resonances which remained fully unresolved are highlighted with a red circle. Partially resolved resonances are indicated with a yellow circle and accurately resolved ones with a green circle. The cause for the limited resolving capability is discussed in the text.

**Figure 6.**Broadband PAS absorption spectrum ${I}_{\mathrm{PAS}}({\lambda}_{\mathrm{i}})$ (blue) in arbitrary units (a.u.) for propane at $c=99.3\phantom{\rule{0.166667em}{0ex}}\mathrm{ppm}$ for $N=1349$ discrete values of ${\lambda}_{\mathrm{i}}$. The normalized standard reference spectrum ${I}_{\mathrm{ref}}^{\mathrm{a}.\mathrm{u}.}({\lambda}_{\mathrm{i}})$ (red) was calculated from the absorption cross section ${\sigma}_{\mathrm{FTIR}}({\lambda}_{\mathrm{k}})$ in the HITRAN FTIR database. The average relative error, $\overline{\delta {I}_{\mathrm{rel}}}$ derived from the 1349 measured wavelengths, after correction for the contaminations, ${\lambda}_{\mathrm{i}}$ is 7.1(6)%, the lowest value of all three test gases.

**Figure 7.**Rescaled absorption cross section ${\sigma}_{\mathrm{FTIR}}$ of propane for the line at $3369.7628\mathrm{nm}$ at $297\mathrm{K}$ and $1025\mathrm{h}\mathrm{Pa}$ as published by HITRAN (green). The blue circles show the discrete values for ${I}_{\mathrm{PAS}}({\lambda}_{\mathrm{i}})$ and the red ones depict the associated reference intensity ${I}_{\mathrm{ref}}^{a.u}({\lambda}_{\mathrm{i}})$. The high resolution ${\sigma}_{\mathrm{FTIR}}({\lambda}_{\mathrm{k}})$ is displayed in green colour with its corresponding intensity scale given by the red abscissa on the right.

**Figure 8.**EUREQA analysis of a simulated PAS spectra with 960‰ ethane and 40‰ propane admixture. Selected training points for pattern recognition are annotated with a light blue dot, whilst validation points used to quantify the quality of the fit are indicated with a dark blue dot. Note that the best solution model as found by EUREQA is highlighted in blue.

**Figure 9.**$\Delta {c}_{\mathrm{fit}}$ as obtained from the comparison between the EUREQA fit and simulated mixed ethane $\Delta {c}_{\mathrm{fit}}^{\mathrm{e}}$ (red dots) and propane $\Delta {c}_{\mathrm{fit}}^{\mathrm{p}}$ (blue dots) spectra based on the current measurements. For relative admixtures with ${c}_{\mathrm{rel}}\ge 40,$ EUREQA is able to retrieve the concentration with an accuracy better than ${10}^{-1}=10\%$ (blue area). The dotted lines are depicted to guide the eyes.

**Table 1.**Parameters of the measured broadband ${I}_{\mathrm{PAS}}$ spectra for methane, ethane and propane and related quantitative benchmark parameters as derived from EUREQA.

Measurement | EUREQA-Fit | ||||||||
---|---|---|---|---|---|---|---|---|---|

$\mathit{c}$/ppm | ${\mathit{\lambda}}_{\mathbf{min}}$/nm | ${\mathit{\lambda}}_{\mathbf{max}}$/nm | $\mathit{N}$ | $\overline{\mathit{\delta}{\mathit{\lambda}}_{\mathbf{i}}}$/nm | ${\mathit{I}}_{\mathbf{PAS}}^{\mathbf{tot}}$/a.u. | $\overline{\mathit{\delta}{\mathit{I}}_{\mathbf{rel}}}$/% | ${\mathit{\xi}}_{\mathbf{cor}}$ | ${\mathit{R}}^{\mathbf{2}}$ | |

Methane | 99.1 | 3272.0361 | 3526.8055 | 1350 | 0.1887(3025) | 464.1 | 15.0(14) | 1.0288 | 0.8260 |

Ethane | 95.5 | 3275.2941 | 3526.8729 | 1345 | 0.1870(2926) | 1593.9 | 8.7(11) | 0.9959 | 0.9759 |

Propane | 99.5 | 3275.3858 | 3526.9183 | 1351 | 0.1865(2931) | 2170.7 | 7.1(6) | 0.9996 | 0.9760 |

**Table 2.**Comparison of the position and FWHM of selected resonance lines in diluted methane, ethane and propane test gases as obtained by PAS and the corresponding FTIR reference values.

${\mathit{\lambda}}_{\mathbf{res}}$/nm | ${\Delta}_{{\mathit{\lambda}}_{\mathbf{res}}}$/${10}^{-5}$ | FWHM/nm | ${\Delta}_{\mathbf{FWHM}}$/% | EUREQA-Fit | ||||
---|---|---|---|---|---|---|---|---|

PAS | FTIR | PAS | FTIR | $\mathit{\eta}$ | ${\mathit{R}}^{\mathbf{2}}$ | |||

Methane | 3280.5219 | 3280.6543 | −4.036 | 0.568 | 0.641 | −11.50 | 0.5313 | 0.9354 |

3291.1426 | 3291.0667 | 2.306 | 0.599 | 0.738 | −18.84 | 0.6196 | 0.9976 | |

3368.6480 | 3368.5638 | 2.500 | 0.745 | 0.996 | −25.16 | 0.6205 | 0.9231 | |

3391.9170 | 3392.0495 | −3.906 | 1.636 | 1.376 | 18.85 | 0.1047 | 0.7012 | |

3428.1770 | 3428.1805 | −0.102 | 2.321 | 2.361 | −1.69 | 0.0005 | 0.8692 | |

3465.8520 | 3465.7252 | 3.659 | 3.317 | 2.823 | 17.49 | 0.2794 | 0.6394 | |

Ethane | 3336.7143 | 3336.8223 | −3.237 | 0.275 | 0.178 | 54.46 | 1.0000 | 0.9416 |

3340.5772 | 3340.6186 | −1.389 | 0.158 | 0.197 | −19.83 | 0.9999 | 0.9981 | |

3348.2759 | 3348.1813 | 2.825 | 0.176 | 0.181 | −3.14 | 0.9995 | 0.9990 | |

3351.9117 | 3351.8977 | 0.418 | 0.139 | 0.179 | −22.06 | 0.5437 | 0.9954 | |

3355.6083 | 3355.9151 | −0.203 | 0.231 | 0.198 | 18.17 | 0.9994 | 0.9999 | |

Propane | 3369.8481 | 3369.7503 | 2.902 | 0.653 | 0.792 | −17.62 | 0.5056 | 0.8014 |

3463.6431 | 3463.7889 | −4.209 | 2.268 | 2.072 | 9.44 | 0.5533 | 0.8147 |

**Table 3.**Experimental and hypothetical detection limits (LOD) and signal-to-noise (SNR) ratios of the OPO driven broadband PAS system.

Experiment | Hypothetical | ||||
---|---|---|---|---|---|

${\mathit{I}}_{\mathbf{PAS}}^{\mathbf{max}}({\mathit{\lambda}}_{{\mathbf{i}}^{\mathbf{*}}})$/a.u. | ${\mathbf{LOD}}_{\mathbf{exp}}$/ppb | ${\mathbf{SNR}}_{\mathbf{exp}}$ | ${\mathbf{LOD}}_{\mathbf{hyp}}$/ppb | ${\mathbf{SNR}}_{\mathbf{hyp}}$ | |

Methane | 11.4747 | 13.6 | 143.4 | 3.0 | 227.9 |

Ethane | 16.4530 | 7.1 | 205.7 | 2.4 | 270.3 |

Propane | 9.3811 | 13.2 | 117.3 | 4.9 | 137.3 |

Nitrogen | 0.0800 | 1.0 |

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**MDPI and ACS Style**

Bruhns, H.; Wolff, M.; Saalberg, Y.; Spohr, K.M.
Quantitative Evaluation of Broadband Photoacoustic Spectroscopy in the Infrared with an Optical Parametric Oscillator. *Sensors* **2018**, *18*, 3971.
https://doi.org/10.3390/s18113971

**AMA Style**

Bruhns H, Wolff M, Saalberg Y, Spohr KM.
Quantitative Evaluation of Broadband Photoacoustic Spectroscopy in the Infrared with an Optical Parametric Oscillator. *Sensors*. 2018; 18(11):3971.
https://doi.org/10.3390/s18113971

**Chicago/Turabian Style**

Bruhns, Henry, Marcus Wolff, Yannick Saalberg, and Klaus Michael Spohr.
2018. "Quantitative Evaluation of Broadband Photoacoustic Spectroscopy in the Infrared with an Optical Parametric Oscillator" *Sensors* 18, no. 11: 3971.
https://doi.org/10.3390/s18113971