Three-Dimensional Temperature Distribution Reconstruction via an Ellipsoidal Reflector: Algorithm Development and Numerical Validation

Accurate measurement of three-dimensional flame temperature distribution is crucial for combustion diagnosis. Traditional optical methods rely on observation windows or multi-camera arrays, which can be difficult to deploy in environments with restricted optical access, such as aviation engine burners. This paper proposes a passive radiation temperature measurement method based on ellipsoidal reflector (ER). By using the confocal characteristics of the ER, the radiation inside the flame is collected through a single aperture at one focus and guided to the Charge-Coupled Device (CCD) at another focus. A complete measurement model has been developed, combining the ray tracing of each detector element through the ER with the discretized Radiative Transfer Equation (RTE) under the pure absorption approximation. Temperature reconstruction is performed using the Least Squares QR (LSQR) algorithm. The method is validated numerically on a cylindrical flame under three configurations with identical grid and detection settings, differing only in the temperature field and absorption coefficient: symmetric with uniform absorption, asymmetric with uniform absorption, and asymmetric with non-uniform absorption. Gaussian noise (0–5%) is added to the simulated measurements. Noise-free reconstruction converges to near machine precision. Under 5% noise, the mean relative errors are 3.1%, 8.7%, and 6.1% for the three cases, with errors concentrated at the flame periphery while the core remains accurately reconstructed. The proposed method provides a practical solution for temperature monitoring where optical access is severely limited.