A reconstruction method for volumetric tomography within two parallel transparent plates

•Refraction and reflection are integrated into the calibration and imaging model for volumetric measurement.•Synthetic calibration is designed to show the significance of refraction.•Simulation and experiment are conducted to prove the superiority of the proposed method. Flame emission tomography is a powerful tool for spatially-resolved combustion diagnostics. Modalities for measuring both open and confined flames have been developed and found in extensive applications. However, the available methods for confined space are restricted to cylindrical enclosures. There is another common confinement, i.e., rectangular enclosure. The key characteristic of this confinement is two pairs of parallel transparent plates. The light will be refracted when passing through the plates, causing projection distortion. Another key point is the reflection of the plates, which will induce secondary projections. However, reflection is seldomly discussed in the literature. The existing methods for rectangular enclosure are all based on Zhang’s model [Seventh IEEE International Conference on Computer Vision (ICCV) (IEEE, 1999), Vol. 661, pp. 666–673], which ignores the refraction and reflection of the enclosure. As a result, this work proposes a modified calibration model, i.e., refraction-reflection model for volumetric tomography, which for the first time incorporates both the refraction and reflection processes. The synthetic calibration shows refraction of the plate can not only shift the projection but also rotate it. The simulation and experiment show that the imaging model based on Zhang’s model will not only wrongly estimate the position of the target, but also have a low accuracy. Nevertheless, the imaging model based on the refraction-reflection model can successfully resolve the above problems and show its superiority to the imaging model based on Zhang’s model.