Image-based analytical crystal shape computation exemplified for potassium dihydrogen phosphate (KDP)

The evolution of the shape of growing crystals is a process that depends on various factors including crystalline material and process conditions. Toward the objective to control not only the size of crystals but also their shape, it is necessary to observe its evolution process as a basis for understanding and modeling the underlying growth kinetics. Online microscopy provides 2D projections of 3D crystal shapes. In this paper, we present a technique to reconstruct the original 3D shapes from measured 2D projections of KDP crystals. The algorithm requires the projection to be bounded by a convex polygon with six or eight vertices. Numerical results are presented both for synthetic data as well as for experimental data. They show a good agreement between true and estimated values both for highly accurate as well as perturbed projections.