High dimensionality volumetric additive manufacturing (Invited Paper)

Computed axial lithography (CAL) is mathematically founded on the Radon transform which is the 1:1 invertible linear transform between 3D object space (x,y,z) and 3D image space (row,column,theta). However, this cannot be applied in the presence of the nonlinear constraint of non-negative image intensity, motivating the current practice of image-set optimization to meet image intensity and object dose constraints. The optimal solution can be improved by providing more linearly independent degrees of freedom in image space. These additional degrees of freedom include the six rigid body transformations of the projector point-spread function of which axial rotation used in CAL is just one. We demonstrate efficient image generation algorithms able to solve the optimization between 3D object and 4D and 5D image spaces. A specific VAM architecture that enables these high dimensional image projections is shown and its properties are discussed.