2:45 PM - 3:00 PM
[MTT38-05] Ultimate precision of intensity ratio measurements by Raman spectroscopy: Approaches from simulation, experiment, and theory
Keywords:Raman spectroscopy, Isotope ratio, Fluid inclusion, Noise, Carbon isotope ratio
Introduction
Raman spectroscopy has been established as one of the most versatile quantitative analytical methods in materials science research due to its non-destructive analysis and high spatial resolution. In recent years, improvements and developments in non-destructive local isotope analysis methods for H2O, CO2, CH4, HCO3-, CO32-, N2, humic acid, calcite, etc. using Raman spectroscopy have been carried out (e.g., Yamamoto and Hagiwara 20221), but the accuracy is still far from being applicable to isotope ratio measurements for natural samples. For example, regarding the accuracy of CO2 carbon isotope ratio measurements, which are relatively well studied among these, Arakawa et al. (2007)2 and Yokokura et al. (2020)3 reported a measurement accuracy of 1σ = 20‰ and 1σ = 8.7‰, respectively. The reasons for the improved accuracy in Yokokura et al. (2020)3 may be attributed to the longer focal length of the spectrometer, the improved pixel resolution, and the longer measurement time, but it is still unclear which factors contribute most to the improvement in measurement precision. In this study, optical simulations, experiments, and theoretical calculations were carried out to identify the parameters that have a significant influence on the precision of the intensity ratios in Raman spectroscopic analysis.
Methods
First, we built a model for optical simulations. The model can automatically generate arbitrarily shaped spectra by varying various parameters, such as spectral resolution, laser linewidth, laser wavelength, centre position, slit width, grating groove density, spectrograph focal length, spectrograph magnification, half inclusion angle, grating width, pixel size, vertical binning width, exposure time, integration number, CCD sensitivity, dark noise, and readout noise, etc. For each condition, 100-300 spectra were generated and fitted to determine their spectral characteristics and their uncertainties. These processes were repeated under various conditions to obtain relationships between uncertainties and parameters.
Experiments were then carried out on CO2 fluid sealed in a high-pressure optical cell at a pressure of 30 MPa, varying the analysis conditions, such as grating, exposure time, number of readouts, readout speed and gain. For each condition, the measurements were repeated 20-50 times to determine the spectral properties and their uncertainties.
Finally, we introduced several approximations to deduce the uncertainties in the intensity ratios of spectra with pure Gaussian and Lorentzian profiles. For this purpose, we made the following seven assumptions: 1) the variance of the noise is equal to the signal at all points; 2) the pixel resolution is constant; 3) the peaks are sufficiently large such that they are almost zero outside the sampling region; 4) the measurement error is Gaussian distribution; 5) the function is sufficiently dense in Δx steps and is not sampled and the sum is well represented by the integral; 6) Baseline uncertainties are negligible; 7) peaks do not interfare with each other. The results show that the measurement accuracy σαIG(Gaussian) and σαIL(Lorentzian) for the best intensity ratio achievable under the shot noise limited conditions can be described as functions of intensity I, bandwidth Γ, and pixel resolution Δx using the following equations
σαIG =[(ln2/π)1/2(16αI/7Is){(Δxw/Γw)+αI(Δxs/Γs)}]1/2
σαIL ≒[(0.77αI/Is){(Δxw/Γw)+αI(Δxs/Γs)}]1/2
where the subscripts "w" and "s" refer to the spectral characteristics of the weaker and stronger of the two peaks respectively. Also, αI = Iw/Is.
Results
Our simulations, experiments, and theoretical calculations show that four factors are important in the intensity ratio measurements: 1) intensity of the weak peak, 2) ratio of pixel resolution to bandwidth, 3) saturation of detecter, and 4) (readout noise + dark noise)/shot noise. In a previous study2, it was pointed out that the position of the data points constituting the peak could have a significant effect on the precision of the intensity ratio measurements, but our simulation results negated this possibility, which is consistent with experimental data of Yokokura et al. (2020)3.
1 J. Yamamoto and Y. Hagiwara, Anal. Sci. Adv. 2022, 3, 269-277.
2 M. Arakawa, J. Yamamoto, and H. Kagi, Appl. Spectrosc. 2007, 61, 701-705.
3 L. Yokokura, Y. Hagiwara, and J. Yamamoto, J. Raman Spectrosc. 2020, 51, 997-1002.
Raman spectroscopy has been established as one of the most versatile quantitative analytical methods in materials science research due to its non-destructive analysis and high spatial resolution. In recent years, improvements and developments in non-destructive local isotope analysis methods for H2O, CO2, CH4, HCO3-, CO32-, N2, humic acid, calcite, etc. using Raman spectroscopy have been carried out (e.g., Yamamoto and Hagiwara 20221), but the accuracy is still far from being applicable to isotope ratio measurements for natural samples. For example, regarding the accuracy of CO2 carbon isotope ratio measurements, which are relatively well studied among these, Arakawa et al. (2007)2 and Yokokura et al. (2020)3 reported a measurement accuracy of 1σ = 20‰ and 1σ = 8.7‰, respectively. The reasons for the improved accuracy in Yokokura et al. (2020)3 may be attributed to the longer focal length of the spectrometer, the improved pixel resolution, and the longer measurement time, but it is still unclear which factors contribute most to the improvement in measurement precision. In this study, optical simulations, experiments, and theoretical calculations were carried out to identify the parameters that have a significant influence on the precision of the intensity ratios in Raman spectroscopic analysis.
Methods
First, we built a model for optical simulations. The model can automatically generate arbitrarily shaped spectra by varying various parameters, such as spectral resolution, laser linewidth, laser wavelength, centre position, slit width, grating groove density, spectrograph focal length, spectrograph magnification, half inclusion angle, grating width, pixel size, vertical binning width, exposure time, integration number, CCD sensitivity, dark noise, and readout noise, etc. For each condition, 100-300 spectra were generated and fitted to determine their spectral characteristics and their uncertainties. These processes were repeated under various conditions to obtain relationships between uncertainties and parameters.
Experiments were then carried out on CO2 fluid sealed in a high-pressure optical cell at a pressure of 30 MPa, varying the analysis conditions, such as grating, exposure time, number of readouts, readout speed and gain. For each condition, the measurements were repeated 20-50 times to determine the spectral properties and their uncertainties.
Finally, we introduced several approximations to deduce the uncertainties in the intensity ratios of spectra with pure Gaussian and Lorentzian profiles. For this purpose, we made the following seven assumptions: 1) the variance of the noise is equal to the signal at all points; 2) the pixel resolution is constant; 3) the peaks are sufficiently large such that they are almost zero outside the sampling region; 4) the measurement error is Gaussian distribution; 5) the function is sufficiently dense in Δx steps and is not sampled and the sum is well represented by the integral; 6) Baseline uncertainties are negligible; 7) peaks do not interfare with each other. The results show that the measurement accuracy σαIG(Gaussian) and σαIL(Lorentzian) for the best intensity ratio achievable under the shot noise limited conditions can be described as functions of intensity I, bandwidth Γ, and pixel resolution Δx using the following equations
σαIG =[(ln2/π)1/2(16αI/7Is){(Δxw/Γw)+αI(Δxs/Γs)}]1/2
σαIL ≒[(0.77αI/Is){(Δxw/Γw)+αI(Δxs/Γs)}]1/2
where the subscripts "w" and "s" refer to the spectral characteristics of the weaker and stronger of the two peaks respectively. Also, αI = Iw/Is.
Results
Our simulations, experiments, and theoretical calculations show that four factors are important in the intensity ratio measurements: 1) intensity of the weak peak, 2) ratio of pixel resolution to bandwidth, 3) saturation of detecter, and 4) (readout noise + dark noise)/shot noise. In a previous study2, it was pointed out that the position of the data points constituting the peak could have a significant effect on the precision of the intensity ratio measurements, but our simulation results negated this possibility, which is consistent with experimental data of Yokokura et al. (2020)3.
1 J. Yamamoto and Y. Hagiwara, Anal. Sci. Adv. 2022, 3, 269-277.
2 M. Arakawa, J. Yamamoto, and H. Kagi, Appl. Spectrosc. 2007, 61, 701-705.
3 L. Yokokura, Y. Hagiwara, and J. Yamamoto, J. Raman Spectrosc. 2020, 51, 997-1002.