Estimation of speed distribution of particles moving in an optically turbid multiple scattering medium by decomposition of laser-Doppler spectrum

International audienceA novel method for estimation of speed distribution of particles moving in an optically turbid multiple scattering medium by decomposition of laser-Doppler spectrum is presented. In the proposed method Doppler shift probability distributions (DSPD) are utilized. These distributions depend only on anisotropy of medium under investigation. An analytical form of DSPD was proposed which allows to avoid much slower DSPD generation with the use of Monte Carlo code. Method of analytical calculation of DSPDs and laser-Doppler spectra are validated by comparison with results of Monte Carlo simulations. Decomposition of the laser-Doppler spectrum is based on solution of a system of linear equations with constraints. In case of multiple Doppler scattering the decomposition is difficult because of strong dependence of DSPDs generated for various combinations of speeds and number of scattering events. We proposed an approximation based on analysis of multiple Doppler scattering events which occur on particles moving with the same speeds. It was shown that the approximated model gives good results and can be used for analysis of laser-Doppler spectra. The solution of the system of linear equation is based on interior point method, which allows to transform system of linear equations with constraints to minimization problem without constraints using logarithmic barrier functions. The proposed decomposition procedure was verified for different speed distributions with spectra generated by superposition of DSPDs obtained by analytical forms and by use of Monte Carlo simulations