Bidimensional Optical Path Estimation and Correction Algorithm for ATR‐FTIR Spectra of Complex Mixed Solutions

Peng Shan; Menghao Zhi; Teng Liang; Guodong Pan; Zhigang Li; Zhonghai He

doi:10.3788/AOS250599

Acta Optica Sinica, Volume. 45, Issue 15, 1530001(2025)

Bidimensional Optical Path Estimation and Correction Algorithm for ATR‐FTIR Spectra of Complex Mixed Solutions

Peng Shan^1,2, Menghao Zhi^1,2、*, Teng Liang^1,2, Guodong Pan^1,2, Zhigang Li^1,2, and Zhonghai He^1,2

¹Hebei Key Laboratory of Micro-Nano Precision Optical Sensing and Measurement Technology, Qinhuangdao 066004, Hebei , China

²College of Information Science and Engineering, Northeastern University, Shenyang 1010819, Liaoning , China

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Figures & Tables(11)

Fig. 1. Real data spectra. (a) γ-PGA fermentation broth spectra; (b) blood spectra

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Fig. 2. Summary of multiplication parameters of OPLECm experiment. (a) Multiplication parameters based on γ-PGA fermentation broth spectra in the training set; (b) multiplication parameters based on γ-PGA fermentation broth in the test set; (c) multiplication parameters based on blood spectra in the training set; (d) multiplication parameters based on blood spectra in the test set

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Fig. 3. Summary of inner and outer parameters of Bi-OPLECm experiment based on γ-PGA fermentation broth spectra. (a) Outer parameters on the training set; (b) outer parameters on the test set; (c) inner parameters of glucose and sodium glutamate on the training set; (d) inner parameters of glucose and sodium glutamate on the test set

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Fig. 4. Summary of inner and outer parameters of Bi-OPLECm experiments based on blood spectra. (a) Outer parameters on the training set; (b) outer parameters on the test set; (c) inner parameters of blood glucose and triglyceride on the training set; (d) inner parameters of blood glucose and triglyceride on the test set

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Fig. 5. Scatter plots of quantitative analysis models for γ-PGA fermentation broth data processed using three methods. (a) Scatter plot for glucose mass concentration prediction; (b) scatter plot for sodium glutamate mass concentration prediction

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Fig. 6. Scatter plots of quantitative analysis models for blood data processed using three methods. (a) Scatter plot for blood glucose mass concentration prediction; (b) scatter plot for triglyceride mass concentration prediction

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Table 0. [in Chinese]

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Table 0. [in Chinese]

input： spectral matrix X

output： inner parameter $a_{j} (j = 1, \dots, N)$ and outer parameter $p = {[p_{1}, p_{2}, \dots, p_{M}]}^{T}$

1） $a_{i, j} = 1$ ∥Initialize all inner parameters to 1

2） for n=1∶10

3） ∥Keep the parameter a_j fixed. Solve for p， RMSEC and RMSEP.

$\underset{p, A}{m i n} \frac{1}{2} \{{‖U_{s} U_{s}^{T} p - p‖}_{2}^{2} + \sum_{j = 1}^{N} \frac{{‖U_{s} U_{s}^{T} p ⊙ a_{j} ⊙ c_{j} - p ⊙ a_{j} ⊙ c_{j}‖}_{2}^{2}}{{[m a x (c_{j})]}^{2}}\}, p \geq 1, a_{j} \geq 1$

4） ∥Transform the original spectral matrix.

$X_{n + 1} = \frac{1}{p} ⊙ X_{n} = [\begin{matrix} U_{s s} & U_{t t} \end{matrix}] [\begin{matrix} Σ_{s s} & 0 \\ 0 & Σ_{t t} \end{matrix}] {[\begin{matrix} V_{s s} & V_{t t} \end{matrix}]}^{T}$

5） ∥Keep the parameter p fixed. Solve for a_j of each component and the final RMSEC and RMSEP in round n.

$\underset{a_{j}}{m i n} \sum_{j = 1}^{N} \frac{{‖U_{s} U_{s}^{T} p ⊙ a_{j} ⊙ c_{j} - p ⊙ a_{j} ⊙ c_{j}‖}_{2}^{2}}{{[m a x (c_{j})]}^{2}}, a_{j} \geq 1$

6） end

7） ∥Select the optimal p anda_j according to RMSE.

Table 1. Quantitative analysis of glucose experimental results
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Table 1. Quantitative analysis of glucose experimental results
Method r LVs RMSEC RMSEP R $_{t r n}^{2}$ R $_{t s t}^{2}$ MAE_trn MAE_tst
None 9 1.864 2.439 0.954 0.923 1.315 1.955
OPLECm 15 8 1.977 2.382 0.948 0.926 1.284 1.735
Bi-OPLECm 13 11 1.631 1.801 0.964 0.957 1.085 1.365

Table 2. Quantitative analysis of sodium glutamate experimental results
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Table 2. Quantitative analysis of sodium glutamate experimental results
Method r LVs RMSEC RMSEP R $_{t r n}^{2}$ R $_{t s t}^{2}$ MAE_trn MAE_tst
None 10 0.510 0.929 0.993 0.978 0.400 0.730
OPLECm 15 11 0.464 0.926 0.994 0.978 0.361 0.708
Bi-OPLECm 2 12 0.440 0.827 0.995 0.982 0.343 0.683

Table 3. Quantitative analysis of blood glucose experimental results
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Table 3. Quantitative analysis of blood glucose experimental results
Method r LVs RMSEC RMSEP R $_{t r n}^{2}$ R $_{t s t}^{2}$ MAE_trn MAE_tst
None 4 1.765 1.801 0.576 -1.128 1.244 1.468
OPLECm 15 4 1.760 1.759 0.578 -1.030 1.224 1.432
Bi-OPLECm 18 3 1.788 1.467 0.565 -0.411 1.255 1.255

Table 4. Quantitative analysis of triglycerides experimental results
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Table 4. Quantitative analysis of triglycerides experimental results
Method r LVs RMSEC RMSEP R $_{t r n}^{2}$ R $_{t s t}^{2}$ MAE_trn MAE_tst
None 2 0.775 2.108 0.097 -0.05 0.616 1.127
OPLECm 15 2 0.681 1.828 0.302 0.211 0.534 0.976
Bi-OPLECm 7 3 0.456 1.190 0.688 0.665 0.369 0.753

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Peng Shan, Menghao Zhi, Teng Liang, Guodong Pan, Zhigang Li, Zhonghai He. Bidimensional Optical Path Estimation and Correction Algorithm for ATR‐FTIR Spectra of Complex Mixed Solutions[J]. Acta Optica Sinica, 2025, 45(15): 1530001

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