Precision evaluation of Raman densimetry for carbon dioxide: improvement by correction for the drift effect

Junji Yamamoto; Yuuki Hagiwara

doi:10.1364/AO.507939

Applied Optics
Vol. 63,
Issue 5,
pp. 1402-1410
(2024)
•https://doi.org/10.1364/AO.507939

Precision evaluation of Raman densimetry for carbon dioxide: improvement by correction for the drift effect

Junji Yamamoto and Yuuki Hagiwara

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Junji Yamamoto and Yuuki Hagiwara, "Precision evaluation of Raman densimetry for carbon dioxide: improvement by correction for the drift effect," Appl. Opt. 63, 1402-1410 (2024)

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Abstract

To evaluate the precision of the wavenumber difference between the two main Raman bands of ${{\rm CO}_2}$ (designated as $\Delta$, an index of ${{\rm CO}_2}$ density), we performed theoretical calculations for the uncertainties of the peak positions of the ${{\rm CO}_2}$ Raman bands, and measured Raman spectra of ${{\rm CO}_2}$ under the conditions used for the calculations. The $\Delta$ precision improves with increased peak intensity, but the peak intensity–precision relation does not hold beyond an intensity threshold corresponding to the measurement time of 1–2 min. Correction for temporal variation of $\Delta$ by fitting a linear function to the data distribution improved the $\Delta$ precision to ${\pm} {0.0005}\;{{\rm cm}^{- 1}}$ at best, corresponding to ${{\rm CO}_2}$ density precision as ${\pm} {0.00015}\;{{\rm g/cm}^3}$.

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Supplementary Material (1)

Name	Description
Supplement 1	Tables S1–S5

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (9)

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Symbol	Parameter	Unit
$a / 2$	Half inclusion angle	radian
$C$	One-half of the matrix of the second derivatives of the $χ^{2}$	—
$f$	Focal length of the concave mirror in the spectrometer	cm
$I$	Peak intensity	$e^{-}$
$k$	Grating constant	µm
$v_{c}$	Peak center position	${c m}^{- 1}$
$v_{i}$	Raman shift allocated to the $i$ -th bin	${c m}^{- 1}$
$R_{I}$	Intensity ratio ( $< 1$ )	—
$w_{P i x e l}$	Pixel width of CCD detector and CMOS detector	µm
$Γ$	Full width at half maximum	${c m}^{- 1}$
$Δ x$	Pixel resolution	${c m}^{- 1} / p i x e l$
$λ$	Wavelength	nm
$σ_{Δ}$	Precision of $Δ$	${c m}^{- 1}$
$σ_{i}$	Shot noise	$e^{-}$
$σ_{ω}$	Uncertainty of wavenumber	${c m}^{- 1}$

$I_{w}$	$σ_{Δ}$	$σ_{Δ L}$ ^a		Time^b
$e^{-}$	${c m}^{- 1}$	${c m}^{- 1}$	$σ_{Δ L} / σ_{Δ}$	s
CCD-g1200
$8.56 E + 01$	0.11798	0.11540	0.98	1
$5.88 E + 02$	0.04259	0.03664	0.86	2
$1.25 E + 03$	0.02103	0.01713	0.81	4
$6.11 E + 03$	0.01153	0.00803	0.70	16
$2.23 E + 04$	0.01164	0.00865	0.74	60
$1.14 E + 05$	0.01429	0.00601	0.42	300
$4.18 E + 05$	0.01200	0.00619	0.52	1050
$1.99 E + 06$	0.01024	0.00949	0.93	5100
CCD-g1800
$2.07 E + 02$	0.04902	0.03998	0.82	2
$2.18 E + 02$	0.03493	0.03492	1.00	2
$6.34 E + 02$	0.02339	0.02339	1.00	4
$1.65 E + 03$	0.01481	0.00967	0.65	10
$3.79 E + 03$	0.01041	0.01028	0.99	20
$4.16 E + 03$	0.00975	0.00871	0.89	20
$7.62 E + 03$	0.00627	0.00569	0.91	40
$2.39 E + 04$	0.00692	0.00501	0.72	120
$3.90 E + 04$	0.00559	0.00461	0.83	200
$5.62 E + 04$	0.00732	0.00381	0.52	260
$1.16 E + 05$	0.00416	0.00291	0.70	582
$2.20 E + 05$	0.00857	0.00402	0.47	1040
$3.11 E + 05$	0.00602	0.00531	0.88	1540
$3.86 E + 05$	0.00700	0.00669	0.96	1820
$4.19 E + 05$	0.00611	0.00442	0.72	1980
$2.18 E + 06$	0.00472	0.00389	0.82	9880
CMOS-g1800
$1.33 E + 03$	0.01168	0.01000	0.86	1
$4.47 E + 03$	0.00523	0.00453	0.87	4
$1.34 E + 04$	0.00445	0.00258	0.58	12
$4.45 E + 04$	0.00186	0.00171	0.92	40
$1.28 E + 05$	0.00135	0.00107	0.79	120
$4.30 E + 05$	0.00197	0.00118	0.60	400
$1.28 E + 06$	0.00289	0.00077	0.27	1200
$3.76 E + 06$	0.00434	0.00050	0.12	3600
$1.07 E + 07$	0.00565	0.00088	0.16	10800

Symbol	Parameter	Unit
$a / 2$	Half inclusion angle	radian
$C$	One-half of the matrix of the second derivatives of the $χ^{2}$	—
$f$	Focal length of the concave mirror in the spectrometer	cm
$I$	Peak intensity	$e^{-}$
$k$	Grating constant	µm
$v_{c}$	Peak center position	${c m}^{- 1}$
$v_{i}$	Raman shift allocated to the $i$ -th bin	${c m}^{- 1}$
$R_{I}$	Intensity ratio ( $< 1$ )	—
$w_{P i x e l}$	Pixel width of CCD detector and CMOS detector	µm
$Γ$	Full width at half maximum	${c m}^{- 1}$
$Δ x$	Pixel resolution	${c m}^{- 1} / p i x e l$
$λ$	Wavelength	nm
$σ_{Δ}$	Precision of $Δ$	${c m}^{- 1}$
$σ_{i}$	Shot noise	$e^{-}$
$σ_{ω}$	Uncertainty of wavenumber	${c m}^{- 1}$

$I_{w}$	$σ_{Δ}$	$σ_{Δ L}$ ^a		Time^b
$e^{-}$	${c m}^{- 1}$	${c m}^{- 1}$	$σ_{Δ L} / σ_{Δ}$	s
CCD-g1200
$8.56 E + 01$	0.11798	0.11540	0.98	1
$5.88 E + 02$	0.04259	0.03664	0.86	2
$1.25 E + 03$	0.02103	0.01713	0.81	4
$6.11 E + 03$	0.01153	0.00803	0.70	16
$2.23 E + 04$	0.01164	0.00865	0.74	60
$1.14 E + 05$	0.01429	0.00601	0.42	300
$4.18 E + 05$	0.01200	0.00619	0.52	1050
$1.99 E + 06$	0.01024	0.00949	0.93	5100
CCD-g1800
$2.07 E + 02$	0.04902	0.03998	0.82	2
$2.18 E + 02$	0.03493	0.03492	1.00	2
$6.34 E + 02$	0.02339	0.02339	1.00	4
$1.65 E + 03$	0.01481	0.00967	0.65	10
$3.79 E + 03$	0.01041	0.01028	0.99	20
$4.16 E + 03$	0.00975	0.00871	0.89	20
$7.62 E + 03$	0.00627	0.00569	0.91	40
$2.39 E + 04$	0.00692	0.00501	0.72	120
$3.90 E + 04$	0.00559	0.00461	0.83	200
$5.62 E + 04$	0.00732	0.00381	0.52	260
$1.16 E + 05$	0.00416	0.00291	0.70	582
$2.20 E + 05$	0.00857	0.00402	0.47	1040
$3.11 E + 05$	0.00602	0.00531	0.88	1540
$3.86 E + 05$	0.00700	0.00669	0.96	1820
$4.19 E + 05$	0.00611	0.00442	0.72	1980
$2.18 E + 06$	0.00472	0.00389	0.82	9880
CMOS-g1800
$1.33 E + 03$	0.01168	0.01000	0.86	1
$4.47 E + 03$	0.00523	0.00453	0.87	4
$1.34 E + 04$	0.00445	0.00258	0.58	12
$4.45 E + 04$	0.00186	0.00171	0.92	40
$1.28 E + 05$	0.00135	0.00107	0.79	120
$4.30 E + 05$	0.00197	0.00118	0.60	400
$1.28 E + 06$	0.00289	0.00077	0.27	1200
$3.76 E + 06$	0.00434	0.00050	0.12	3600
$1.07 E + 07$	0.00565	0.00088	0.16	10800

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (6)

Tables (2)

Equations (9)

Applied Optics