An Improved Wavelength Modulation Spectroscopy Based on Natural Logarithm and Hilbert Transform for Oxygen Detection Within Pharmaceutical Vials

Tunable diode laser absorption spectroscopy (TDLAS) based on wavelength modulation spectroscopy (WMS) is widely used for gas concentration measurement due to its rapid detection, high accuracy, and non-destructive nature. However, traditional WMS produces unreliable results for residual oxygen detection in pharmaceutical vials due to laser attenuation caused by glass walls. Although advanced methods such as ln-WMS and WMS-2f/fattempt to overcome this limitation, they suffer from algorithmic inflexibility or high computational cost. This paper introduces ln-Hilbert-WMS, an improved technique that integrates natural logarithm processing with the Hilbert transform. This method effectively isolates gas absorption components from laser intensity variations while simultaneously enabling harmonic extraction, laser intensity elimination, and offset noise suppression. A detection system for oxygen within pharmaceutical vials is established for validation. Experimental results demonstrate that the method can accurately measure the oxygen concentration without being affected by variations in vial transmittance. Furthermore, comparative analysis under different offset-noise conditions, together with FPGA implementation results, shows that the proposed method provides greater algorithmic generality than ln-WMS while requiring lower computational cost than WMS-2f/f. In pharmaceutical vial testing, ln-Hilbert-WMS achieves the best detection performance, with a standard deviation of 0.45% and an RMSE of 0.51%, outperforming traditional WMS, ln-WMS, and WMS-2f/ftechniques.