Deducing three dimensions from two

Reconstructing the 3d shape distribution of grains or other objects randomly packed together with access only to 2d slices through them.

Slurries are fluids full of solid particles, like lava and ice cream. Their solid forms are made up of randomly oriented crystalline grains. Determining such materials’ 3D structures is tricky, requiring costly and tedious imaging techniques. One approach is x-ray tomography, where the structure is deduced by merging multiple 2D x-ray images taken at different angles. Another is an iterative imaging process, where a thin layer at the surface of a sample is repeatedly sliced off, and an image is acquired after each cut.

In this project we develop a mathematical formalism for capturing the 3D structure of a material’s grains in a single shot. It allows for the quick measurement of the size and shape distribution of grains using just one 2D image and electron diffraction data. We verify our method on simulated materials consisting of randomly oriented ellipsoids and blocks, and test it on minerals.

Our approach is applicable to any isotropic polycrystalline material, and will help geologists and materials scientists determine 3D structures at a fraction of the cost of current methods. It could shed light on fundamental processes of rock formation, help optimize oil extraction, and better connect percolation theory with geological percolation.

Deducing three dimensions from two

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