Possibilities and limitations of the ART-Sample algorithm for reconstruction of 3D temperature fields and the influence of opaque obstacles

Abstract

The need for the measurement of complex, unsteady, three-dimensional (3D) temperature distributions arises in a variety of engineering applications, and tomographic techniques are applied to accomplish this goal. Holographic interferometry (HI), one of the optical methods used for visualizing temperature fields, combined with tomographic reconstruction techniques requires multi-directional interferometric data to recover the 3D information. However, the presence of opaque obstacles (such as solid objects in the flow field and heaters) in the measurement volume, prevents the probing light beams from traversing the entire measurement volume. As a consequence, information on the average value of the field variable will be lost in regions located in the shade of the obstacle. The capability of the ART-Sample tomographic reconstruction method to recover 3D temperature distributions both in unobstructed temperature fields and in the presence of opaque obstacles is discussed in this paper. A computer code for tomographic reconstruction of 3D temperature fields from 2D projections was developed. In the paper, the reconstruction accuracy is discussed quantitatively both without and with obstacles in the measurement volume for a set of phantom functions mimicking realistic temperature distributions. The reconstruction performance is optimized while minimizing the number of irradiation directions (experimental hardware requirements) and computational effort. For the smooth temperature field both with and without obstacles, the reconstructions produced by this algorithm are good, both visually and using quantitative criteria. The results suggest that the location and the size of the obstacle and the number of viewing directions will affect the reconstruction of the temperature field. When the best performance parameters of the ART-Sample algorithm identified in this paper are used to reconstruct the 3D temperature field, the 3D reconstructions with and without obstacle are both excellent, and the obstacle has little influence on the reconstruction. The results indicate that the ART-Sample algorithm can successfully recover instantaneous 3D temperature distributions in the presence of opaque obstacles with only 4 viewing directions.