We are developing a 3D printing method based on volumetric solidification, as opposed to the layer-by-layer processes used by most current 3D printers. The volumetric 3D printing method is based on the Radon transform, which is the same principle that is used by tomographic CT-scanners in medical imaging. The Radon transform and its inverse relate the cross-sectional shape of an object with projections of the object as seen from outside. In 3D printing, this allows generating well-defined three-dimensional distributions of light dose inside a volume of photopolymer simply by irradiating the volume from outside with the calculated projections from many directions. Inside a photosensitive polymer, this three-dimensional distribution of light dose then leads to local solidification of the resin, which creates the 3D object.
In theory, the Radon algorithm leads to a perfect reconstruction of the object inside the build volume. In practice, the transform requires us to send both positive as well as negative patterns of light to obtain a perfect reconstruction. Since “subtracting” light dose is physically impossible, we currently only display the positive parts of the patterns. This approximation leads to artefacts, which we would like to reduce or eliminate.
The objective of the project is to write an efficient algorithm that can calculate optimized patterns of light under the constraint of positivity. The work includes modeling the light rays that enter and get absorbed in the cylindrical build volume, formulating the problem in sparse matrix form, and developing an efficient way to solve the inverse problem of finding the optimal projections that yield the desired object.
The project is intimately related with the problem of intensity-modulated radiation therapy in medicine, where doctors maximize the dose of X-rays applied to a tumor while at the same time minimizing the dose received by healthy tissue.
The candidate is expected to have very good mathematical and coding skills, and interest for numerical algorithms and 3D printing.