Dynamic mathematical model of a non-dispersive infrared (NDIR) absorption spectroscopy measurement system for transient gas analysis

Non-dispersive infrared (NDIR) absorption spectroscopy is widely used for quantitative gas analysis; however, the steady-state use of the Beer–Lambert law alone does not describe transient signals and temperature dependent behavior frequently encountered under practical flow conditions. Here, the effects of flow rate and cell temperature on transient NDIR responses are experimentally characterized, and a unified dynamic formulation is presented. The detection cell is modeled as a linear time-invariant system with a characteristic time constant τ = V/v (V: cell volume, v: volumetric flow rate), and, under isothermal operation, absorbance is expressed as the convolution of the input concentration with the instrumental impulse response. This representation accounts for response delays and waveform asymmetry under time-varying composition and flow, and it provides implementation-ready procedures for response correction and calibration in dynamic measurements. The formulation offers specification-level guidance beyond instrument-specific fixed settings and is expected to improve quantitative reliability for challenging sample matrices (e.g., powders, concrete, and liquids), thereby broadening NDIR applicability beyond conventional steel analysis.