Precision in Peak Parameter Estimation for the Pseudo-Voigt Profile: A Novel Optimization Approach for High-Precision Analysis via Mixing Parameter Control

Abstract

High-precision measurement of peak parameters such as intensity (I), peak position (ω_c), full width at half-maximum (Γ), and area (A) is pivotally important for advancing scientific research. Achieving high-precision requires elucidating the physical principles governing measurement precision and establishing guidelines for optimizing analytical conditions. Although the pseudo-Voigt profile is a widely used line-shape model, the underlying principles governing the precision of its parameter estimation remained unclear. For this study, we developed a model to quantify the parameter estimation precision under arbitrary conditions by integrating theoretical analysis, numerical calculations, and Monte Carlo simulations. Our quantification results indicate that when the mixing parameter (η) is fixed, the precision of I, Γ, and A is proportional to {Δx/ΓI}^0.5, whereas the precision of ω_c is proportional to {ΓΔx/I}^0.5, where Δx denotes the sampling interval. Furthermore, the analytical precision exhibits η-dependence: for I and Γ, when the profile becomes more Lorentzian, the absolute value of the covariance between Γ and η as well as between I and η increases, thereby degrading their estimation precision. This finding suggests that in addition to conventional methods such as improving the signal-to-noise ratio and reducing sampling interval, appropriately controlling η can be an effective strategy for optimizing precision. For instance, if broadening effects (e.g., instrumental or Doppler broadening) are deliberately introduced to tune η from 1 to 0, then this alone improves Γ estimation precision by a factor of 3.7, equivalent to a 14-fold increase in signal intensity. Furthermore, when the effect of increased Γ due to broadening is considered, even greater improvements in precision can be achieved. Overall, our model provides a foundational framework for research on peak parameter estimation. It serves as an alternative approach to error estimation when experimental evaluation is challenging and as a quantitative tool for assessing precision gain from instrument upgrades.