Analytical and Numerical Characterization of Autocorrelation and Perturbation-Correlation Moving-Window Methods

Moving-window (MW) approaches to two-dimensional correlation spectroscopy (2D-COS) make it possible to characterize spectral changes occurring in a narrow range of perturbation variable (e.g., time, temperature, and concentration). Despite the wide range of application, the physical meanings of MW correlation intensities have been only qualitatively associated with the direction and curvature of spectral intensity change with regard to a perturbation variable. Here are full and simplified analytical expressions of autocorrelation moving-window (ACMW) and synchronous and asynchronous perturbation-correlation moving-window ( s-PCMW and as-PCMW) intensities. When the window is set sufficiently narrower than the bandwidth of spectral change, the square root of ACMW intensity and s-PCMW intensity becomes proportional to the first order derivative, and as-PCMW intensity becomes proportional to the negative of the second order derivative. This paper demonstrates that both ACMW and PCMW profiles can be significantly altered by non-uniform perturbation spacing. It is also found that intensity noise can cause ACMW to display a false offset drift. This analytical and numerical characterization of the two MW correlation intensities elucidates their physical meanings and ascertains the analysis conditions for reliable interpretation.