Reconstruction of 3D crystal growth from transmission optical microscopy images

Abstract Variations in the 3D shapes of crystalline materials can greatly affect their physical chemical properties, influencing the downstream processes required for their formulation, precision manufacturing and transportation. Under different growth conditions, identical compounds can produce a wide variety of particle shapes and sizes, yet a comprehensive understanding of the relationship between crystallisation conditions and final product properties is severely lacking. In part, this reflects the technical challenges associated with accurately recovering 3D crystal shape information during their growth. Here, we present a novel method for reconstructing the evolving 3D polyhedral shape of a single crystal in a growth cell from a sequence of transmission optical microscopy images. Our approach combines deep learning with synthetic image generation based on theoretically grounded crystallography together with accurate simulation of the refraction of light at the crystal faces, yielding robust estimates of the dynamics of the crystal shape evolution during the crystallisation process. We demonstrate our approach by tracking the 3D growth and shape development of the polyhedral α form of l-glutamic acid and validate our results against manual measurements collected using a purpose-built interactive software tool. We observe changes in the relative areas of crystal faces, characterising not just the size but also the shape changes during growth. This approach offers a new framework for in situ monitoring of crystal growth and may support future advances in the precision manufacturing of crystalline particles through the improved digital design and control of crystallisation processes.