Acoustic computer tomographic pyrometry for two-dimensional measurementof gases taking into account the effect of refraction of sound wavepaths

Abstract

The algorithm which takes into account the effect of refraction ofsound wave paths for acoustic computer tomography (CT) is developed.Incorporating the algorithm of refraction into ordinary CT algorithms whichare based on Fourier transformation is very difficult. In this paper, theleast-squares method, which is capable of considering the refraction effect,is employed to reconstruct the two-dimensional temperature distribution. Therefraction effect is solved by writing a set of differential equations whichis derived from Fermat's theorem and the calculus of variations. It isimpossible to carry out refraction analysis and the reconstruction oftemperature distribution simultaneously, so the problem is solved using theiteration method. The measurement field is assumed to take the shape of acircle and 16 speakers, also serving as the receivers, are set around itisometrically. The algorithm is checked through computer simulation withvarious kinds of temperature distributions. It is shown that the presentmethod which takes into account the algorithm of the refraction effect canreconstruct temperature distributions with much greater accuracy than canmethods which do not include the refraction effect.