Multi-exponential Lifetime Extraction in Time-logarithmic Scale

Methods are proposed for estimating real lifetimes and corresponding coefficients from real-valued measurement data in logarithmic scale, where the data are multi-exponential, i.e. represented by linear combinations of decaying exponential functions with various lifetimes. Initial approximations of lifetimes are obtained as peaks of the first derivative of the data, where the first derivative can, e.g, be calculated in the spectral domain using the cosine Fourier transform. The coefficients corresponding to lifetimes are then estimated using the linear least squares fitting. Finally, all the coefficients and the lifetimes are optimized using the values previously obtained as initial approximations in the non-linear least squares fitting. We can fit both the data curve and its first derivative and allow simultaneous analysis of multiple curves.