Dr.TVAM: Inverse-Design Platform for TVAM

• Dr.TVAM is an open-source inverse-design and forward-modeling platform for tomographic volumetric additive manufacturing that integrates differentiable optimization with realistic physics models.
• It employs ray-optical and wave-optical models to accurately simulate and optimize projection patterns, effectively handling refraction, scattering, and diffraction effects.
• Its chemistry-aware extension compensates for oxygen diffusion and photochemical dynamics, ensuring defect-free bioprinting and high-fidelity volumetric prints.

Dr.TVAM is an open-source inverse-design and forward-modeling platform for tomographic volumetric additive manufacturing (TVAM). In its core formulation, it treats volumetric printing as a differentiable optimization problem: 2D projection patterns are optimized so that a rotating vial of photosensitive resin accumulates a 3D dose field that polymerizes a target geometry while suppressing curing elsewhere. Across the recent literature, Dr.TVAM appears not as a single static algorithm but as a platform-level framework that has evolved from physically based ray-optical inverse rendering for non-ideal TVAM scenes to wave-optical forward modeling for micron-scale fidelity, and further to coupled ray-optical, photochemical, and diffusion-aware optimization for oxygen-inhibited bioprinting (Wechsler et al., 18 Jul 2025, Wechsler et al., 2024, Rizzo et al., 7 Apr 2026).

1. Platform definition and conceptual scope

Dr.TVAM is described as an existing open-source framework for TVAM pattern optimization, and more specifically as an inverse-design and forward-modeling platform that uses differentiable, physically based optics to compute projection sequences for rotating-resin volumetric printing (Wechsler et al., 18 Jul 2025). In the overprinting literature it is explicitly situated as a differentiable physically based simulation software for TVAM, introduced previously by Nicolet et al. and built on Mitsuba 3; in the bioprinting literature it is described as an in-house, open source optical framework that has been expanded with advanced polymerization modeling capabilities (Wechsler et al., 18 Jul 2025, Rizzo et al., 7 Apr 2026).

The platform’s defining feature is that existing scene structure is part of the forward model rather than an afterthought. A target object is optimized jointly with the resin, vial, projector, and any pre-existing inserts or occlusions already present in the printable volume. This distinguishes Dr.TVAM from inverse-Radon or attenuation-corrected ray models that assume simple straight-ray propagation and treat the resin volume as optically uncomplicated. In Dr.TVAM, arbitrary scene geometry and optical material parameters are used directly in the forward model, which allows optimization in the presence of refraction, reflection, scattering, attenuation, index mismatch, and non-telecentric illumination (Wechsler et al., 18 Jul 2025).

This scope is broader than standard tomographic reconstruction. TVAM does not seek a linear reconstruction of attenuation coefficients; it seeks projection patterns whose cumulative nonlinear exposure yields a manufacturable binary object after thresholding. That distinction becomes explicit in both the wave-optical and chemistry-aware extensions, where the optimization variable is still the set of projected patterns, but the physically relevant state may be a coherent field, a dose field, an oxygen field, or a coupled chemical state rather than a single static tomographic image (Wechsler et al., 2024, Rizzo et al., 7 Apr 2026).

2. Ray-optical inverse design and overprinting workflows

In its ray-optical form, Dr.TVAM models how projector pixels emit rays into a scene containing the optical setup, vial geometry, resin, target object region, and embedded or pre-existing structures. Those rays are refracted or reflected at interfaces, attenuated in absorbing media, and ultimately contribute absorbed intensity $I_v$ in each voxel of a discretized object space. Because the renderer is differentiable, gradients of the optimization objective with respect to the projected grayscale patterns can be computed and used in gradient-based optimization (Wechsler et al., 18 Jul 2025).

The overprinting formulation uses a loss with four terms: forcing polymerization inside the object, preventing polymerization outside it, penalizing over-polymerization inside the object, and regularizing pattern sparsity,

$$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$

Here $I_v$ is the absorbed intensity accumulated in voxel $v$, $P_j$ is a pattern pixel value, and $t_u$ and $t_l$ are the upper and lower thresholds used to separate object and void regions (Wechsler et al., 18 Jul 2025).

A central feature of this formulation is that embedded objects are modeled through the forward optics rather than by ad hoc masking. Black SLA-printed adapters are treated as fully absorbing occlusions, glass spheres as reflective and refractive occlusions, a polished steel rod as a rough scattering reflector with a Beckmann microfacet distribution, and LED or glass-tube assemblies as refractive scene elements inside the printable domain (Wechsler et al., 18 Jul 2025).

The overprinting demonstrations define the practical meaning of Dr.TVAM in current TVAM research.

Scenario	Modeled optical conditions	Reported result
Square-cuvette perfusion channels	Angle-dependent refraction, black absorbing adapters, frosted-corner exclusion	Best IoU $=0.9972$
Channels around embedded spheres	Refractive and reflective glass spheres, fast low-fidelity optimization	Best IoU $=0.9951$
Gear on polished steel rod	Beckmann rough-surface reflection with estimated $\alpha=0.04$	IoU $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$0 with reflective model; $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$1 with absorptive mismatch
Engraving and lens on LED	Non-telecentric LED projection, multiple refractions and absorptions	Successful print and image projection
Microlenses on water-filled glass tube	Nested refractive interfaces across vial, resin, glass, and water	Successful qualitative imaging demonstration

These examples show that Dr.TVAM is not limited to canonical telecentric, unobstructed TVAM. It is used for printing inside preassembled square cuvettes, around arbitrarily located embedded spheres, onto reflective metal, onto a commercial LED, and onto a water-filled glass tube under LED-based non-telecentric projection (Wechsler et al., 18 Jul 2025).

The computational trade-off is explicit. High-fidelity pattern sets are optimized in minutes, while lower-quality but still useful solutions can be obtained in seconds. Reported optimization times range from $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$2 for a fast sphere-connection case to $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$3 for LEDTVAM lens optimization, whereas experimental print times remain below one minute (Wechsler et al., 18 Jul 2025).

3. Wave-optical extension and the resolution question

A major development directly relevant to Dr.TVAM is the replacement of the straight-ray forward model by a rigorous wave-based optical amplitude optimization scheme for TVAM (Wechsler et al., 2024). The motivating claim is precise: the resolution limits commonly associated with current TVAM optimization are not fundamental to the printing concept itself, but largely arise from the ray-optical assumptions built into prior pattern-design methods. In simulation, ray-optics-based pattern design begins to produce artifacts when desired features are $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$4 and below, while wave-optical optimization predicts micrometer-scale features for amplitude-modulated TVAM across the full volume (Wechsler et al., 2024).

The critical physical distinction is that TVAM accumulates intensity incoherently across projection angles, because patterns are projected sequentially, but each projected 2D field propagates coherently through the volume before its intensity is added to the dose. Ray optics misses this intra-pattern diffraction structure. The wave model instead treats the projected field as a complex scalar field propagated by the angular spectrum method,

$$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$5

with transfer function

$$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$6

The reported implementation fixes phase to zero and optimizes only real nonnegative amplitudes, using $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$7 and $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$8 (Wechsler et al., 2024).

The dose-shaping objective is also threshold-based rather than reconstruction-based. It penalizes object voxels that do not reach an upper polymerization threshold $$\mathcal{L} = w_\text{in}\sum_{v\in \text{object}} \mathrm{ReLU}(t_u-I_v)^2 + w_\text{out}\sum_{v\notin \text{object}} \mathrm{ReLU}(I_v-t_l)^2 + w_\text{o}\sum_{v\in \text{object}} \mathrm{ReLU}(I_v-1)^2 + w_\text{sparsity}\sum_{j\in \text{patterns}} |P_j|^D .$$9, void voxels that exceed a lower threshold $I_v$0, and object voxels that exceed normalized intensity $I_v$1, thereby introducing an explicit overexposure penalty. Typical values are $I_v$2 with exponent $I_v$3, and optimization is performed with L-BFGS, which is reported to require around 50 iterations to obtain a well-separated intensity histogram (Wechsler et al., 2024).

The numerical results are scale dependent. For a $I_v$4 volume, wave-optical and ray-optical optimization produce nearly identical results under the wave model. At $I_v$5, the difference remains small but a ray-optimized pattern already fails on one small feature. At $I_v$6, ray-optimized patterns “misprint the object significantly” when evaluated with the wave model, whereas wave-optimized patterns still produce a perfect print after thresholding, with reported IoU $I_v$7 for the wave-optimized cases shown. The ray-optical IoU degradation becomes especially strong for $I_v$8, and the authors infer from the Benchy target that wave effects start to matter significantly below roughly $I_v$9 feature size (Wechsler et al., 2024).

This line of work directly challenges a common misconception that present TVAM resolution limits are solely chemical or hardware-imposed. The simulations support a more specific interpretation: a substantial part of the observed $v$0 plateau is attributable to inverse design based on an incorrect forward model. The stated implication is that Dr.TVAM can move beyond Radon-style pattern generation toward physically rigorous wave-based inverse design, and that doing so appears necessary if TVAM is to push toward truly micron-scale volumetric printing (Wechsler et al., 2024).

4. Photochemical and diffusion-aware extension for oxygen-inhibited bioprinting

A second major extension transforms Dr.TVAM from a primarily optical optimization tool into a coupled ray-optical, photochemical, and diffusion-aware solver (Rizzo et al., 7 Apr 2026). The motivating failure mode is the “Pandoro effect,” a recurrent truncated-cone distortion in thermoreversible gelatin-based resins, where the bottom polymerizes prematurely and the top remains inhibited and undercured. The work identifies the cause as a vertical oxygen gradient created by thermal hysteresis during resin preparation: heating depletes dissolved oxygen, cooling raises equilibrium solubility, and subsequent re-oxygenation occurs only from the air–resin interface by diffusion (Rizzo et al., 7 Apr 2026).

The oxygen-gradient model is one-dimensional along height $v$1, governed by Fick’s second law,

$v$2

with $v$3, initial concentration $v$4, and upper boundary concentration $v$5 in a $v$6 vial. The simulations predict a substantial gradient beginning around 30 min and peaking around 90 min, with the ratio $v$7 falling below 0.6 at maximum effect (Rizzo et al., 7 Apr 2026).

Within Dr.TVAM, this phenomenon is handled by augmenting the forward model with two chemical state variables during exposure: oxygen concentration and polymerization dose. The surrogate reaction logic is explicitly simplified but differentiable: absorbed photons generate radicals, radicals are immediately quenched by local inhibitor, and only after local inhibitor depletion does the remaining radical budget contribute to polymerization. Oxygen diffusion during printing is modeled with an FFT-convolution kernel based on the Green’s function of the diffusion equation, and the entire forward process remains differentiable so that automatic differentiation and L-BFGS can optimize the projection patterns (Rizzo et al., 7 Apr 2026).

The chemistry-aware loss moves beyond static thresholding by depending explicitly on local oxygen and polymerization dose. The thresholds are stated as $v$8, $v$9, and $P_j$0, with $P_j$1. The interpretation is that object voxels must exceed a polymerization threshold plus the local oxygen burden, while void voxels must remain sufficiently oxygen-dominated to preserve inhibition. In the normalized initialization, $P_j$2 immediately after preparation and approaches $P_j$3 after long equilibration, corresponding to the ratio $P_j$4 (Rizzo et al., 7 Apr 2026).

Experimentally and in simulation, the gradient-aware Dr.TVAM formulation corrects the defect. Without correction, object height decreases with increasing storage time because uniform illumination cannot overcome the oxygen-rich top region. With correction, optimized patterns assign more light near the top and produce defect-free prints at 60 and 120 min. The paper also validates two process-level alternatives—removing the air–resin interface and controlling headspace atmosphere with 99% argon—but the computational extension is significant because it lets Dr.TVAM compensate predictively for a heterogeneous chemical state rather than merely reacting to it (Rizzo et al., 7 Apr 2026).

The relevance to bioprinting is reinforced by cell-laden validation. Using GelMA with $P_j$5, the non-mitigated condition fails after 30 min, while all three mitigation strategies, including the Dr.TVAM gradient-aware optimization, yield defect-free prints close to target geometry. Reported viability remains $P_j$6 at day 0, $P_j$7 at day 2, and $P_j$8 at day 5, with no significant differences from control (Rizzo et al., 7 Apr 2026).

5. Computational architecture, software stack, and optimization machinery

Dr.TVAM is best understood as a differentiable process-simulation stack rather than a single solver. In the overprinting work, the platform is built on Mitsuba 3 and uses differentiable physically based ray optics. In the chemistry-aware extension, the same optical backbone is layered with stateful oxygen and polymerization dynamics. In the wave-optical work directly relevant to Dr.TVAM, the forward model is replaced by an angular-spectrum wave propagator with custom adjoints and checkpointing (Wechsler et al., 18 Jul 2025, Rizzo et al., 7 Apr 2026, Wechsler et al., 2024).

The ray-optical branch is scene-centric. Inputs include target geometry, projector configuration, vial geometry, refractive indices, attenuation coefficients, and existing objects. The output is a set of optimized TVAM patterns together with simulated dose fields. LaserTVAM and LEDTVAM are both supported: telecentric laser projection is modeled with parallel ray optics, whereas LEDTVAM requires a non-telecentric projector model in which each DMD pixel emits a finite cone. In the LED setup, Dr.TVAM parameterizes the optics by horizontal field of view, aperture, and the distance between the aperture and the focal distance, and these parameters are calibrated against experimentally visualized light paths (Wechsler et al., 18 Jul 2025).

The wave-optical branch is memory-critical. Naive reverse-mode automatic differentiation through the full wave operator would store every propagated 3D field for every angle, leading to $P_j$9 memory. The custom adjoint instead recomputes propagated fields during the backward pass, avoiding that storage cost. This is the enabling mechanism for reported optimizations at $t_u$0 voxels with 600 angles on a single NVIDIA A100 GPU. The implementation uses Julia, ChainRules.jl for custom adjoints, CUDA acceleration, and a differentiable bilinear image rotation implemented via KernelAbstractions.jl; the reported runtime is about 6 hours for wave-optical optimization versus around 10 minutes for ray-tracing optimization (Wechsler et al., 2024).

The chemistry-aware branch is time-resolved. Its workflow is: simulate the pre-print oxygen profile from vial history; initialize the oxygen field $t_u$1; compute absorbed dose via Dr.TVAM optics; step the chemistry and diffusion model through exposure; evaluate the loss; update patterns with L-BFGS; and repeat. The paper reports optimization on an NVIDIA L40S GPU or NVIDIA RTX 3060 12 GB, and gives a supplementary example with 40 L-BFGS iterations for a 1 h storage condition (Rizzo et al., 7 Apr 2026).

These branches are computationally heterogeneous but conceptually unified. Each defines a differentiable forward operator that maps projected patterns to a physically meaningful volumetric state—absorbed dose, coherent wave intensity, or oxygen-conditioned polymerization dose—and then optimizes the patterns against threshold-aware manufacturability criteria.

6. Position in the TVAM literature, limitations, and prospective directions

Dr.TVAM occupies a distinct methodological position within TVAM research. It differs from inverse-Radon and attenuation-corrected methods by using scene-level differentiable forward models rather than idealized straight-ray assumptions. It differs from standard tomographic reconstruction because the optimization target is a thresholded polymerization outcome rather than a linear image estimate. And, in its chemistry-aware form, it differs from conventional threshold-based dose optimization by using a stateful forward model with explicit oxygen and polymer variables (Wechsler et al., 18 Jul 2025, Rizzo et al., 7 Apr 2026).

Its relation to adjacent optimization frameworks is also explicit. The TVAM AID framework analyzes penalty-optimized illumination design and cites Wechsler et al.’s Dr.TVAM-related formulation as inspiration for dual-threshold penalties with explicit over-polymerization control. TVAM AID’s mixed penalty $t_u$2 is presented as conceptually linked to that line of work while embedding it in a CIL-based framework and making the high-dose band width $t_u$3 tunable rather than implicitly normalized. In that study, the recommended defaults for the favored mixed penalty are $t_u$4 and $t_u$5, and the framework consistently outperforms OSMO on $t_u$6 and $t_u$7 across tested 2D geometries (Pellizzon et al., 12 Feb 2026). This suggests that Dr.TVAM has already influenced how dose-threshold penalties are formalized beyond its own codebase.

The limitations of Dr.TVAM are stated with similar clarity. The wave-optical model is scalar rather than full-vectorial, assumes homogeneous refractive index, ignores polymerization-induced index changes, neglects vial refraction and index-matching-bath effects, sets absorption to zero in the reported simulations, omits chemical effects such as inhibitor diffusion, and has not yet been experimentally validated (Wechsler et al., 2024). The ray-optical overprinting framework assumes that optical material parameters are known and can be calibrated accurately; the reflective-rod example shows that mismatched BSDF assumptions can materially degrade fine-feature fidelity (Wechsler et al., 18 Jul 2025). The chemistry-aware extension still uses a simplified surrogate rather than a full mechanistic kinetic network, and its threshold parameters are explicitly heuristic (Rizzo et al., 7 Apr 2026).

The forward-looking research directions are correspondingly concrete. For wave-optical Dr.TVAM, the next steps are experimental demonstration, inclusion of vial refraction, digital and mechanical stabilization of the rotating vial, and likely coupling to chemical diffusion models (Wechsler et al., 2024). For the chemistry-aware solver, future extensions may need to model oxygen consumption by encapsulated cells and more detailed kinetic effects (Rizzo et al., 7 Apr 2026). More broadly, related hardware work in holographic TVAM using a MEMS phase-only light modulator reports a pattern light efficiency of $t_u$8 versus $t_u$9 for DMD amplitude projection, which suggests a plausible future interface between physically richer Dr.TVAM-style optimization and more efficient coherent projection hardware (Álvarez-Castaño et al., 3 Jun 2025).

Taken together, these strands define Dr.TVAM as a platform whose central idea is not a single optical model but a differentiable inverse-design architecture for volumetric printing under increasingly realistic physics. In the current literature, that architecture spans physically based ray optics for overprinting, angular-spectrum wave optics for micron-scale resolution analysis, and oxygen-aware photochemical modeling for reproducible volumetric bioprinting (Wechsler et al., 18 Jul 2025, Wechsler et al., 2024, Rizzo et al., 7 Apr 2026).