Iterative optimization technology (IOT), a method that predicts the component composition from only the infrared (IR) spectra of the pure components and mixtures by using Beer's law, has been proposed to reduce the number of calibration samples for process analytical technology in the pharmaceutical industry. However, IOT cannot be applied to mixtures that have wavelength regions where Beer's law does not hold, such as liquid mixtures. The objective of this study is to apply IOT to liquid mixtures to realize a calibration-minimum method. We propose a novel calibration-minimum method that formulates spectral changes by polynomials of the mole fractions considering reasonable boundary conditions for online monitoring. The prediction ability of the proposed method was verified by three case studies: two binary mixtures and one ternary mixture. The model selection strategy, conditions for calibration, and estimation of missing pure component spectra are also discussed. This research represents a step towards advanced calibration-minimum methods.

迭代优化技术（IOT）是一种通过使用比尔定律仅从纯组分和混合物的红外（IR）光谱预测组分组成的方法，已被提出来减少制药过程分析技术的校准样品数量行业。但是，IOT不能应用于波长范围不符合比尔定律的混合物，例如液体混合物。这项研究的目的是将IOT应用于液体混合物，以实现最小校准方法。我们提出了一种新颖的最小定标方法，该方法考虑了在线监测的合理边界条件，通过摩尔分数的多项式来制定光谱变化。通过三个案例研究验证了该方法的预测能力：两种二元混合物和一种三元混合物。还讨论了模型选择策略，校准条件和估计的纯组分光谱缺失。这项研究代表了朝着先进的最小标定方法迈出的一步。