Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) has emerged as a critical analytical technique for characterizing complex mixed solutions, including glutamate fermentation broths and biological fluids such as blood. However, its quantitative accuracy is often compromised by the interplay of physical and chemical factors. Physical variations, such as fluctuations in optical path length, refractive index mismatches, and light scattering, introduce multiplicative scaling distortions across spectral bands. Concurrently, chemical interactions, such as hydrogen bonding between analytes and solvents or conformational changes in macromolecules, generate component-specific spectral shifts. Traditional correction methods, primarily developed for near-infrared (NIR) spectroscopy, typically rely on a single global scaling factor to address multiplicative effects. These approaches fail to disentangle the spatially heterogeneous distortions inherent to ATR-FTIR spectra, where physical and chemical effects are tightly coupled. To overcome this limitation, we proposed the bidimensional modified optical path length estimation and correction algorithm (Bi-OPLECm), which introduces a dual-layer parameterization framework to systematically decouple and correct these effects.

Bi-OPLECm employs a hierarchical model to decompose multiplicative distortions into two distinct layers. The first layer addresses sample-wide physical effects through a single outer parameter that accounts for global variations in optical path length and refractive index. The second layer incorporates analyte-specific inner parameters to model chemical interactions that differentially alter spectral bands associated with individual components. The algorithm iteratively optimizes these parameters using an alternating strategy over ten cycles. Initially, the inner parameters were fixed while the outer parameter was estimated via constrained least-squares optimization within a low-dimensional subspace defined by spectral singular values. Subsequently, the outer parameter was held constant while each inner parameter was calibrated by minimizing the root mean squared error (RMSE) of partial least squares (PLS) regression models during both calibration and prediction phases. Spectral datasets were partitioned into training and test subsets using the SPXY algorithm at a 3∶1 ratio, ensuring representative sampling across mass concentration ranges. PLS models were further refined through five-fold cross-validation to determine the optimal number of latent variables, balancing model complexity and predictive performance.

The efficacy of Bi-OPLECm was validated on two datasets: γ-PGA (151 samples containing glucose and sodium glutamate) and blood (106 samples containing glucose and triglycerides). For the γ-PGA dataset, Bi-OPLECm reduces the RMSEP by 26.2% for glucose from 2.439 to 1.801 and 11.0% for sodium glutamate from 0.929 to 0.827 compared to uncorrected spectra. In blood analysis, improvements are even more pronounced, with RMSEP reductions of 18.5% for blood glucose from 1.801 to 1.467 and 43.5% for triglycerides from 2.108 to 1.190. When benchmarked against the traditional single-parameter OPLECm method, Bi-OPLECm achieves RMSEP reductions of 24.4%, 10.7%, 16.6%, and 34.9% for the four analytes, respectively. These improvements are accompanied by substantial increases in test set R2 values, reflecting enhanced model robustness and predictive reliability. The success of Bi-OPLECm lies in its ability to isolate physical effects—common to all spectral features—from chemical distortions that selectively influence specific functional groups. For instance, hydrogen bonding between glutamic acid molecules and water alters carboxylate absorption bands, while glucose hydroxyl stretching modes are sensitive to solvation dynamics. By resolving these distinct contributions, the algorithm mitigates overcorrection and undercorrection artifacts common in single-factor methods.

Bi-OPLECm represents a significant advancement in multiplicative effect correction for ATR-FTIR spectroscopy. By integrating a global physical scaling factor with analyte-specific chemical adjustment parameters, the algorithm effectively addresses the spectral heterogeneity inherent to complex mixtures. The alternating optimization framework ensures stable parameter estimation and guards against overfitting, as evidenced by consistent cross-validation results. Practical applications span industrial bioprocess monitoring, clinical diagnostics, and environmental analysis, where accurate quantification of multicomponent systems is essential. Future work will explore adaptive parameterization schemes for dynamic systems and integration with deep learning architectures to further enhance computational efficiency. Our study not only extends the methodology of ATR-FTIR spectroscopy but also provides a generalizable solution for correcting multiplicative distortions in other vibrational spectroscopy modalities.