Systematic Analysis of Penalty-Optimised Illumination Design for Tomographic Volumetric Additive Manufacturing via the Extendable Framework TVAM AID Using the Core Imaging Library

TL;DR

Tomographic Volumetric Additive Manufacturing (TVAM) designs illumination plans by shaping the energy-dose distribution with a back-projection model $\mathbf{f}=\mathbf{A}^{\mathrm{T}}\mathbf{g}$ to match a binary target, under a non-negativity constraint on $\mathbf{g}$. The authors introduce TVAM AID, a modular framework built on the Core Imaging Library, to compare penalty functions that govern voxel doses via $p_{\mathrm{in}}$ and $p_{\mathrm{out}}$ and to explore threshold design using $\tau_{\mathrm{lower}}$ and $\tau_{\mathrm{upper}}$. Four penalty families are analyzed: L2N, OSP, and two variants of OSP with penalties on high doses (OSPW), with solution via FISTA. Across 2D geometries and a 3D gyroid, OSPW with $w=0.0$ generally delivers the best balance of a wide process window (PW) and small in-part dose range (IPDR), while a threshold-sweep approach yields practical default values; the TVAM AID framework demonstrates reproducibility and extensibility via CIL, and the work points to further improvements through regularisation and slice-wise customization. The results establish a principled, penalty-driven path toward robust, high-fidelity TVAM printing with clear directions for future enhancements and 3D applicability.

Abstract

Tomographic Volumetric Additive Manufacturing(TVAM) is a novel manufacturing method that allows for the fast creation of objects of complex geometry in layerless fashion. The process is based on the solidification of photopolymer that occurs when a sufficient threshold dose of light-energy is absorbed. In order to create complex shapes, an illumination plan must be designed to force solidification in some desired areas while leaving other regions liquid. Determining an illumination plan can be considered as an optimisation problem where a variety of objective functionals (penalties) can be used. This work considers a selection of penalty functions and their impact on selected printing metrics; linking the shape of penalty functions to ranges of light-energy dose levels in in-part regions that should be printed and out-of-part regions that should remain liquid. Further, the threshold parameters that are typically used to demarcate minimum light-energy for in-part regions and maximum light-energy for out-of-part regions are investigated systematically as design parameters on both existing and new methods. This enables the characterisation of their effects on some selected printing metrics as well as informed selection for default values. This work is underpinned by a reproducible and extensible framework, TVAM Adaptive Illumination Design(TVAM AID), which makes use of the open-source Core Imaging Library(CIL) that is designed for tomographic imaging with an emphasis on reconstruction. The foundation of TVAM AID which is presented here can hence be easily enhanced by existing functionality in CIL thus lowering the barrier to entry and encouraging use of strategies that already exist for reconstruction optimisation.

Figures (19)

• Figure 1: Decomposition of slice $\Omega$, a continuous domain, into the solidified in-part $\Omega_\mathrm{in}$ (white) and liquid out-of-part $\Omega_\mathrm{out}$ (black) regions. Note the circular shape of $\Omega$ mimicking a cylindrical cuvette.
• Figure 2: The discrete $n=40$ voxel formulation of the domain shown in Figure \ref{['Fig_illustration_in_and_out']}, visualised as an image. Due to the $n\times n$ shape of the discretised domain, there is an additional region $I_\mathrm{ext}$ (grey) that falls outside of the circular printing region.
• Figure 3: Penalties on the out-of-part (red) and of the in-part (blue) for a) L2N which uses L2-norm penalties fitted to a specific target, b) OSP that uses one-sided penalties, c) $\mathrm{OSPW}(w>0.0)$ which uses one-sided penalties with a penalty on energy dose values greater than $\tau_\mathrm{upper} + w$ to voxels in the in-part region, d) $\mathrm{OSPW}(w=0.0)$ is a special case of $\mathrm{OSPW}(w>0.0)$ which could be considered as using a one-sided penalty for voxels in the out-of-part region and an L2-norm penalty for voxels in the in-part region. An energy dose value achieved through an illumination plan will incur a penalty dependent on the specific value. In L2N, any deviation from the target energy values is punished with increasing cost, whereas in OSP, only deviation from below the target for the in-part region and above the target for the out-of-part region are punished. In $\mathrm{OSPW}(w>0.0)$, the penalties of OSP are used with an additional penalty if values exceed a given dose value which could be considered as a disjoint L2-norm penalty function with a no-penalty region of width $w$. $\mathrm{OSPW}(w=0.0)$ thus reduces the no-penalty region and therefore takes a combination of L2-norm penalties in in-part and OSP in out-of-part. The total cost of an illumination plan is the sum of the costs incurred by all voxels.
• Figure 4: A comparison of achieved dose profiles (right) and their respective histograms (left) created by each of the four approaches with 1000 iterations. Thresholds are fixed at $\tau_\mathrm{lower} = 0.70$ and $\tau_\mathrm{upper} = 0.90$ and indicated by the black triangular markers.
• Figure 5: Summary of $\mathrm{IPDR}$ and $\mathrm{PW}$ for different approaches compared in Section \ref{['section_comparison_proposed_methods']}.