Photoacoustic diagnostics of fast photochemical and photobiological processes. Analysis of inverse problem solution

Photoacoustic (PA) diagnostics is a time-resolved experimental technique that measures transient photoinduced volume changes on the nano- and microsecond time-scales. The technique has been used to study the energetics and dynamics of chemical and biochemical reactions initiated by absorption of light. The dynamics of the volume changes and associated relaxation processes can be restored from PA-waveforms by solving an ill-posed problem of deconvolution. For the systems with known relaxation kinetics scheme this problem is usually solved by an iterative approximation algorithm. In complex photoactive systems (e.g. photosynthetic samples), where information about kinetics of fast photoinduced volume changes is not available, an algorithm of direct deconvolution must be used. The implementation of one of the linear deconvolution algorithms (Tikhonov's alpha-regularization) for the PA-diagnostics is therefore considered. The problem of the optimal choice of experimental set-up, and restoration algorithm is analyzed by a numerical simulation. It is shown that the quality of PA-diagnostic experiment is mainly determined by a transfer function converting the relaxation spectrum to the spectrum of output electric signal. The analytical expressions to calculate this function (so called PA-filter) are presented. The performance of two widely used schemes of PA-diagnostics are then directly compared. The time-resolution of the PA-diagnostics in analysis of simultaneous bi-exponential decay is evaluated, and the relationship between the resolving power and parameters of the experimental set-up (signal-to-noise ratio, sampling rate, shape of the PA-filter) is found. The advantage of front face irradiation scheme with piezopolymer film detector for time-resolved measurements is demonstrated.