Stereo imaging camera model for 3D shape reconstruction of complex crystals and estimation of facet growth kinetics

Abstract

The principle that the 3D shape of crystals that grow from a solution can be characterised in real-time using stereo imaging has been demonstrated previously. It uses the 2D images of a crystal that are obtained from two or more cameras arranged in defined angles as well as a mathematical reconstruction algorithm. Here attention is given to the development of a new and more robust 3D shape reconstruction method for complicated crystal structures. The proposed stereo imaging camera model for 3D crystal shape reconstruction firstly rotates a digitised crystal in the three-dimensional space and varies the size dimensions in all face directions. At each size and orientation, 2D projections of the crystal, according to the angles between the 2D cameras, are recorded. The contour information of the 2D images is processed to calculate Fourier descriptors and radius-based signature that are stored in a database. When the stereo imaging instrument mounted on a crystalliser captures 2D images, the images are segmented to obtain the contour information and processed to obtain Fourier descriptors and radius-based information. The calculated Fourier descriptors and radius-based signature are used to find the best matching in the database. The corresponding 3D crystal shape is thus found. Potash alum crystals that each has 26 habit faces were used as a case study. The result shows that the new approach for 3D shape reconstruction is more accurate and significantly robust than previous methods. In addition, the growth rates of {111}, {110} and {100} faces were correlated with relative supersaturation to derive models of facet growth kinetics.