Flame tomography is a compelling approach for extracting large amounts of data from experiments via 3-D thermochemical reconstruction. Recent efforts employing neural-network flame representations have suggested improved reconstruction quality compared with classical tomography approaches, but a rigorous quantitative comparison with the same algorithm using a voxel-grid representation has not been conducted. Here, we compare a classical voxel-grid representation with varying regularizers to a continuous neural representation for tomographic reconstruction of a simulated pool fire. The representations are constructed to give temperature and composition as a function of location, and a subsequent ray-tracing step is used to solve the radiative transfer equation to determine the spectral intensity incident on hyperspectral infrared cameras, which is then convolved with an instrument lineshape function. We demonstrate that the voxel-grid approach with a total-variation regularizer reproduces the ground-truth synthetic flame with the highest accuracy for reduced memory intensity and runtime. Future work will explore more representations and under experimental configurations.
Figures & tables
Figure 1: The tomographic process is conducted iteratively. (1) Temperature and composition are obtained by sampling the 3-D representation. We test continuous (Neural Network) and discrete (voxel) representations. (2) The radiative transfer equation is solved along each ray for spectral intensity Iη(s) , where s is the path length, η is the wavenumber, κη(T,X) is the temperature- and composition-dependent spectral absorption coefficient, and Ib,η(T) is the blackbody emission. (3) The Michelson spectral ILS (triangular apodization) is applied to the incident spectra. (4) The loss function is evaluated, (5) gradients with respect to representation parameters are computed, and (6) parameters are updated via gradient descent. This procedure is repeated until the predicted measurement g^ matches the ground truth g .
Figure 2: Cutaway plots of 3-D reconstructions from the DR pipeline against the ground truth. Isocontours of temperature are shown for intervals of 100 K between 500 and 1500 K.
Method
Epoch Time [ms]
Mem. [MB]
MSE T
MSE CO2
MSE H2O
VG/NR
430
3.0
0.0295
0.0436
0.0416
VG/Tikh.
432
3.0
0.0203
0.0391
0.0384
VG/TV
431
3.0
0.0121
0.0219
0.0197
NN/NR
479
65.0
0.0571
0.0871
0.2569
NN/Tikh.
489
66.0
0.0268
0.0705
0.0946
NN/TV
493
66.0
0.0754
0.1427
0.4356
Table 1: Performance comparison of different 3-D representations for the 3-D pool fire.
Utah State University, Department of Mathematics & Statistics, Logan, UT USA · Los Alamos National Laboratory, Intelligence and Space Research Division, Los Alamos, NM USA