Optimisation of digital noise filtering in the deconvolution of ultrafast kinetic data

Ultrafast kinetic measurements in the sub-picosecond time range are always distorted by a convolution with the instrumental response function. To restore the undistorted signal, deconvolution of the measured data is needed, which can be done via inverse filtering, using Fourier transforms, if experimental noise can be successfully filtered. However, in the case of experimental data when no underlying physical model is available, no quantitative criteria are known to find an optimal noise filter which would remove excessive noise without distorting the signal itself. In this paper, we analyse the Fourier transforms used during deconvolution and describe a graphical method to find such optimal noise filters. Comparison of graphically found optima to those found by quantitative criteria in the case of known synthetic kinetic signals shows the reliability of the proposed method to get fairly good deconvolved kinetic curves. A few examples of deconvolution of real-life experimental curves with the graphical noise filter optimisation are also shown.