Efficient Model-free Deconvolution of Measured Ultrafast Kinetic Data

1. Purpose of this work Relevance of model-free deconvolution A direct model-free deconvolution methodhas beenimplemented, using a genetic algorithm.The method has beenthoroughly testedon femtosecond pump-probe transient absorption andfluorescence upconversion data. Mostly used method to evaluate ultrafast kinetic data: Reconvolution =least-squares fitting of a suitable model functiono(t)convolved with the distortion function s(t) Problem:reconvolution requires a particular kinetic model, which is usually not known prior to kinetic inference. Model-free deconvolutionenables to get undistorted kinetic data without presupposing any particular kinetic model. Additional advantage:instrumental distortion parameters can be determined without any correlation with kinetic and photochemical parameters, as there is no need for an additional adjustable „zero time” parameter. What is deconvolution? To get the undistorted kinetic function o(t)from the detected (convolved) signal i(t), the spread function s(t) should be known andthe integral equation (Eq. C) should be solved. The procedure yielding an estimate of the original o(t) functionis calleddeconvolution. creation operators to generate one individualof the initial population loweredamplitude smoothenedsteplike jumps shallower rise and descent rise anddecaysteepening ”cutoff” of the first few data convolution results in: temporalcompression amplitudeincrease  = temporally widened signal Efficient Model-free Deconvolutionof Measured Ultrafast Kinetic Data Ernő Keszei and Péter Pataki Department of Physical Chemistry, and Reaction Kinetics Laboratory, Eötvös University (ELTE) H-1518 Budapest, P.O. Box 32, Hungary; e-mail: keszei@chem.elte.hu Convolution in ultrafast laser chemistry Experiment:femtosecond pump-probe transient absorption femtosecond fluorescence upconversion Limitation:due to uncertainty relation:100 fs ≤ pulse width Problem:characteristic times of the studied reactions and the temporal width of the laser pulse are comparable Result of the measurement: adistorted curve(image, i);theconvolutionof the kinetic response function (object, o)and the instrumental distortion function (spread, s) (Eq. C) Pros and contras of direct deconvolution Model-free deconvolution using a genetic algorithm • Advantages:2 • Does not require any prior knowledgeof the kinetic mechanism • After deconvolving the detected signal,it is mucheasier to find the appropriate mechanism • Instrumental response parameters can be determinedwithout correlationwith kinetic and photochemical parameters • Difficultiesof „classical” signal processing methods:2,3,4 • Possible appearence ofmathematically acceptable, butphysically nonsensesolutions as artefacts • Unavoidable low-frequency wavy oscillations and high frequency noise • Artefacts can largegely be reduced using a genetic algorithmfor deconvolution, due to the highly flexible genetic operators 1) To get the undistorted signal, these effects should be inversed randomlygenerated initialpopulation bestdeconvolved(”winner”) This is achieved by:1) creation of an initial population (whose members represent fairly good solutions) 2) evolution of the population by crossover random mutation natural selection 2) fine-tuning of the population members (to best reproduce the detected signal when convolved with the instrumental response) genetic operators Code of the deconvolution procedure via genetic algorithm1 Tests on simulated kinetic data1 Kinetic mechanism used to testtransient absorption: consecutive two steps reaction: Implementation: a package of user defined Matlab functions and scripts Input:a project descriptor text file with parameters of the creation of initial population and evolution operators + files containing measured data Initial conditions: [A] = 1, [B] = [C] = 0 at t = 0. Kinetic response function (F): Output:all input parameters in the same format as the project descriptor, measured input data and all results in a matrix format as a text file + a four-panel graphical window τ1= 200 fs, τ2= 500 fs; transient absorption with residual bleaching: A = 5, B= 30, C= – 10 Spread:255 fs fwhm Gaussian Experimental error:random noise with a normal distribution of 2% variance of the maximum amplitude. Code available athttp://keszei.chem.elte.hu/GA Test on real-life experimental data1 time domain results frequency domain results signal processing results Tests were also performed on experimental fluorescence decay data of adenosine monophosphate in aqueous solution obtained by femtosecond fluorescence upconversion (excited at 267 nm, observed at 310 nm; T. Gustavsson and Á. Bányász, unpublished data). time domain results frequency domain results - - signal processing Model functionused to testtransient fluorescence: biexponential decay with τ1= 100 fs, τ2= 500 fs spread:310 fs fwhm Gaussian Kinetic response function (F): Conclusion and Perspectives • Contrarylytomodel-free deconvolution via time-domain iterative methods2 and inverse filtering in the frequency domain2-4, use ofgenetic algorithms results in a distortion-free deconvolved kinetic signal that • does not have low-frequencywavy behaviour • correctly reproduces sudden steplike features of kinetic functions • efficiently damps experimental error without signal distortion • fully recovers the whole frequency spectrum of the undistorted kinetic function • Experience shows that there isless systematic distortionif nonparametric (model-free) deconvolutionis applied, even in the case if an established photophysical and kinetic model is known and used to performstatistical inference. • The procedure can efficiently be applied to both synthetic andreal-life experimental data. • Further workconcentrates on improving the quality of deconvolution by applying a genetic algorithm to create the initial population, deconvolving more real-life experimental data, and developing auser-friendly graphical interface to perform the deconvolution. time domain results frequency domain results Acknowledgement References Thomas Gustavsson and Ákos Bányász for detailed experimental data Balaton exchange project 11038YM OTKA project T 048 725 1E.Keszei:J. 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