Study On Calibration Of Light Field Camera And Reconstruction Of 3D Temperature Field Of Flame

Combustion is widely applied in industries such as metallurgy,aerospace and steel.The temperature of flames is a vital parameter to investigate the nature of combustion chemistry.Therefore,the temperature measurement of flames is crucial and valuable for basic research of combustion process,development of new combustion devices,and investigating the economics,clean,safty and stability of combustion.The existing measurement methods and systems of flame temperature are limited in accuracy and industrial application.This paper proposes a three-dimensional(3-D)temperature measurement method of the flame based on the light field imaging technique.Calibration technique of light field camera and reconstruction of flame temperature are carried out theoretically and experimentally.The mathematical model of radiative light field imaging of flame was developed by combining the models of light field imaging and flame radiative transfer.The LSQR(least squares via QR factorization)and Tikhonov regularization algorithms are introduced to solve radiative transfer equations.Considering the unknown absorption coefficients in real flames,a novel hybrid algorithm of Tikhonov–LMBC(Tikhonov–Levenberg–Marquardt method with Boundary Constraint)is then proposed.Numerical simulations of 3-D temperature reconstruction are carried out to compare the performance of Tikhonov regularization and LSQR algorithms,and to validate Tikhonov-LMBC algorithm.The results have demonstrated that the Tikhonov regularization algorithm has better accuracy and is more stable than LSQR algorithm.The maximum relative errors of the reconstructed temperature and absorption coefficient by Tikhonov-LMBC are below 3% and 2.5% respectively.It is indicated that the Tikhonov-LMBC hybrid algorithm can reconstruct flame temperature and absorption coefficient with good accuracy and robustness.A novel calibration method is proposed for the focused light field camera.The calibration model of the focused light field camera is developed based on the raw light field images.The calibration model is solved by Levenberg-Marquardt algorithm,and the specific parameters of the light field camera are further calculated according to the characteristic of the matching F-numbers.In order to verify the accuracy of the proposed calibration method,experiment was performed.The calibration results illustrated that the reprojection errors of virtual image points of raw light field images and total focused images are below 17 and 13 pixels,respectively.The reprojection errors of image points of raw light field images are below 3 pixels.Therefore,the proposed method is proved to be feasibale and reliable for the calibration of the focused light field camera.The radiation intensity calibration of the focused light field camera was carried out by using the blackbody furnace.To elimilate the effect of vignetting,the effective calibration region is determined for each sub-image.The fitting relationship between the gray value of Red(R),G(Green)and B(Blue)channels and the radiation intensity is then obtained.The experiments for asymmetric ethylene laminar diffusion flames are carried out in a co-flow burner and the 3-D temperature measurement system based on light field imaging.The reconstructed flame temperature of the hybrid Tikhonov-LMBC algorithm are validated by the thermocouple.Results by the Tikhonov-LMBC and the thermocouple have good agreement.Threrefore the Tikhonov-LMBC algorithm is accurate and reliable to reconstruct the 3-D temperature of the flame based on light field imaging.