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

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.

💡 Research Summary

This paper addresses the core planning problem of tomographic volumetric additive manufacturing (TVAM), namely how to design illumination patterns that selectively cure a photopolymer in desired regions (in‑part) while keeping other regions (out‑of‑part) liquid. The authors formulate the problem as a non‑negative least‑squares optimization: find a sinogram g ≥ 0 such that the back‑projection Aᵀg (the accumulated dose image f) matches a binary target t (1 in‑part, 0 out‑of‑part). By introducing two scalar penalty functions p_in and p_out that encode the desired dose behavior for each region, the framework becomes modular: any combination of penalties can be plugged in to shape the dose distribution.

The work builds a reproducible, extensible software platform called TVAM AID on top of the open‑source Core Imaging Library (CIL), which already provides tomographic operators, forward/back‑projection, and iterative solvers such as FISTA. Within this platform the authors implement several penalty strategies: (1) a simple L₂‑norm penalty on both regions, (2) a dual‑threshold (upper and lower) penalty that penalises doses above a user‑defined upper bound in the out‑of‑part region and below a lower bound in the in‑part region, and (3) the previously published Object Space Model Optimisation (OSMO) approach, which uses binary thresholds but is recast in the same optimisation language. All problems are convex and solved with FISTA via CIL’s implementation.

To evaluate the quality of the resulting dose images, three metrics are adopted from Rackson et al.: Process Window (PW) = min(f_in) − max(f_out), In‑Part Dose‑Range (IPDR) = max(f_in) − min(f_in), and Voxel Error Rate (VER) = (number of voxels where f_out > min(f_in)) / total printable voxels. PW measures the separation between solid and liquid dose levels (larger is better), IPDR quantifies the spread of dose within the solid region (smaller is better, as it leads to more uniform cure times), and VER captures any overlap that would prevent a single threshold τ from perfectly binarising the dose image (zero is ideal). The authors also introduce outlier‑robust versions of these metrics by trimming a small percentage of extreme values.

Experimental studies are performed on a 2‑D circular slice and a 3‑D composite geometry. A systematic sweep of upper and lower threshold parameters is carried out for both the dual‑threshold penalty and OSMO. Results show that OSMO generally yields a large PW and low VER, but its IPDR remains relatively high, indicating a broad dose spread within the part. In contrast, the proposed dual‑threshold penalty can dramatically reduce IPDR while maintaining PW and VER comparable to OSMO, especially when the upper bound is set low (to suppress over‑curing in out‑of‑part) and the lower bound is set high (to concentrate dose in in‑part). The parameter sweep provides practical guidance for selecting default threshold values that balance these competing objectives.

Because TVAM AID is built on CIL, any existing CT reconstruction technique (e.g., total variation regularisation, SIRT, filtered back‑projection) can be swapped in as a pre‑ or post‑processor, facilitating rapid prototyping of new illumination‑planning strategies. All code and data are released publicly, ensuring reproducibility and encouraging community contributions.

In summary, the paper rigorously reformulates TVAM illumination planning as a constrained least‑squares problem, introduces a flexible penalty‑based framework, systematically investigates how penalty shape and threshold choices affect key printing metrics, and delivers an open‑source toolchain that lowers the barrier for future research in volumetric additive manufacturing. The findings suggest that carefully tuned dual‑threshold penalties can achieve more uniform cure times without sacrificing part fidelity, offering a promising direction for scaling TVAM to industrial‑level production.