Retrieval of temperature and extinction coefficient from modulated absorption emission technique: Effects of practical light collection, self-absorption, in-scattering, and finite spatial resolution

Light extinction and emission measurements in soot-laden flames have extensive application for axisymmetric fields where Abel inversion can de-convolve the radial field. The simplified treatment of the radiative transfer equation typically ignores the contributions from signal trapping, in-scattering, physical light collection systems, and finite spatial resolution. A backward Monte Carlo ray tracing methodology is implemented to gauge the validity of these assumptions for high pressure counterflow diffusion flames (CDFs) modelled as an axisymmetric, non-homogeneous, anisotropic, attenuating, and emitting media. Results show that the practical light collection angle is an important parameter with $cot\theta =\alpha <107$ resulting in errors larger than 5% whereas the optical design in terms of telecentric and non-telecentric system has nominal effects. The in-scattering contributions are noted to be large for high pressure CDFs with measured extinction coefficients close to absorption coefficients at smaller wavelengths. Signal trapping is also larger for such flames and can cause $\sim 50\text{\%}$ reduction in recovered absolute radiance for $\lambda =\text{650}\text{nm}$. A correction methodology for signal trapping is proposed and is noted to recover the unattenuated signal, albeit with slight over-predictions. The temperature estimates using uncorrected radiance can under-predict actual temperatures by $\sim \text{150}\text{K}$ for the highly sooting flame while the corrected radiance over-predicts it by $\sim \text{25}\text{K}$. Finite spatial resolution is also noted to cause a 23% reduction in peak extinction coefficients at $\lambda =\text{900}\text{nm}$, the error in which reduces with improved spatial resolution. Spectral disparity in spatial resolution also causes errors in temperature gradients and can over-predict the measured temperatures by $\sim \text{50}\text{K}$.