Estimating Crystal Growth Rates using Computed Tomography

It has been observed that sugar crystals growing in solution do not all grow at the same rate, due to internal lattice imperfections within crystals. This report will consider the problem of estimating the distribution of growth rates in a batch of crystals, given only samples of their sizes at a number of fixed points in time. The problem can be expressed as a tomographic image reconstruction problem, in which we try to reconstruct the joint density of initial size and growth, from a set of marginal densities obtained by integrating the joint density in a number of different directions. 1 Crystal growth Sugar refineries grow batches of sugar crystals is supersaturated solution (molasses) , and are interested in controlling the speed and quality of crystals grown. Crystals are grown from a quantity of small seed crystals, usually obtained by milling larger crystals grown in a previous batch. Mostly, each seed grows to give a single crystal in the final batch, though there may also be ..