The increasing use of colored materials in 3D printing enables the creation of complex structures with realistic color appearances. Ensuring that the printed colors match the design requires advanced rendering methods to accurately predict the final product. We use a fully optical property-based pipeline for rendering the physically correct color of 3D-printed objects, achieving results nearly indistinguishable compared to the final printed samples. Our approach is based entirely on the intrinsic optical properties of the printing materials: the reduced scattering coefficient, absorption coefficient, refractive index, and scattering anisotropy factor. First, we employed an integrating sphere setup to measure the spectrally resolved absorption and reduced scattering coefficients of the base materials. This method was extended to handle both highly scattering and nearly non-scattering materials with precision. Next, a spectral Monte Carlo path tracing simulation was used to compute light transfer through the printed object, fully modeling the physics of light propagation in heterogeneous turbid media. Our results achieved CIE Δ E ₂₀₀₀ values below 2.0, with renderings accurately reproducing the colors of the specially designed validation samples printed using a Stratasys PolyJet system. This pipeline provides a robust tool for predicting and optimizing the color appearance of 3D-printed objects. It offers broad applicability across various printing systems and material compositions while eliminating the need for time- and cost-intensive trial-and-error test prints.

Context. The size of dust grains in the interstellar medium follows a distribution where most of the dust mass is made up of smaller grains. However, the redistribution from larger grains towards smaller sizes, especially by means of rotational disruption, is still poorly understood. Aims. We aim to study the dynamics of porous grain aggregates undergoing an accelerated rotation, namely, a spin-up process that rapidly increases the angular velocity of the aggregate. In particular, we aim to determine the deformation of the grains and the maximal angular velocity up to the rotational disruption event by caused by centrifugal forces. Methods. We precalculated the porous grain aggregate by means of ballistic aggregation analogous to the interstellar dust as input for subsequent numerical simulations. We performed three-dimensional (3D) N-body simulations, mimicking the radiative torque spin-up process up to the point where the grain aggregates become rotationally disrupted. Results. Our simulations results are in agreement with theoretical models predicting a characteristic angular velocity, ω_disr, on the order of 10⁸–10⁹ rad s⁻¹, where grains become rotationally disrupted. In contrast to theoretical predictions, we show that for large porous grain aggregates (⪆300 nm), the ω_disr values do not strictly decline. Instead, they reach a lower asymptotic value. Hence, such grains can withstand an accelerated rotation more efficiently up to a factor of 10 because the displacement of mass by centrifugal forces and the subsequent mechanical deformation supports the buildup of new connections within the aggregate. Furthermore, we report that the rapid rotation of grains deforms an ensemble with initially 50:50 prolate and oblate shapes, respectively, preferentially into oblate shapes. Finally, we present a best-fit formula to predict the average rotational disruption of an ensemble of porous dust aggregates dependent on the internal grain structure, total number of monomers, and applied material properties.

This study introduces a physics-based inverse rendering method for determining the reduced scattering and absorption coefficients of turbid materials with arbitrary shapes, using a single image as input. The approach enables fully spectrally-resolved reconstruction of the wavelength-dependent behaviour of the optical properties while also circumventing the specialised sample preparation required by established measurement techniques. Our approach employs a numerical solution of the Radiative Transfer Equation based on an inverse Monte Carlo framework, utilising an improved Levenberg–Marquardt algorithm. By rendering the edge effects accurately, particularly translucency, it becomes possible to differentiate between scattering and absorption from just one image. Importantly, the errors induced by only approximate prior knowledge of the phase function and refractive index of the material were quantified. The method was validated through theoretical studies on three materials spanning a range of optical parameters, initially using a simple cube geometry and later extended to more complex shapes. Evaluated via the CIE $\Delta E_{2000}$ colour difference, forward renderings based on the recovered properties were indistinguishable from those preset, which were obtained from integrating sphere measurements on real materials. The recovered optical properties showed less than 4% difference relative to these measurements. This work demonstrates a versatile approach for optical material characterisation, with significant potential for digital twin creation and soft-proofing in manufacturing.

Accurate knowledge of the intrinsic optical properties of 3D printing materials, i.e., spectral absorption and scattering coefficients, phase function, and refractive index, is essential for simulating the appearance of translucent prints on displays (softproofing) or optimizing material arrangements to achieve desired optical effects in multi-material 3D prints. This information is also critical for designing printing materials that mimic the optical characteristics of other materials, a key requirement in applications like dental restorations. Current methods for measuring these properties rely on specialized laboratory equipment and expert knowledge. In this paper, we propose an approach that uses a commercial reflectance/transmittance spectrophotometer to determine the spectral absorption and scattering coefficients and refractive index of 3D printing materials. We model the light path of this device to simulate reflectance and transmittance measurements via a Monte Carlo path tracer. We then predict measurements for a large set of random but plausible intrinsic optical material properties for three different sample thicknesses. With these data, we train machine learning models to infer the intrinsic properties from phenomenological reflectance/transmittance measurements, considering a priori knowledge of smoothness as a regularization constraint. We validate our method by comparing results for real printing materials with accurate laboratory measurements and provide the trained machine learning models to the community.

This work presents an experimental validation of a physics-based inverse rendering method for determining the reduced scattering and absorption coefficients of turbid materials in arbitrary shape from a single image per wavelength. Based on our previously published theoretical inverse rendering framework, we constructed and experimentally characterised a wavelength-selective measurement setup to realise and validate the method under real acquisition conditions. By accurately modelling the spectral behaviour and angle-dependent transmission of the employed bandpass filters, we ensured a close correspondence between captured and simulated reflectance. The method was evaluated on three silicone materials, beginning with simple cube geometries and later extending to a complex Einstein bust. Relative to integrating-sphere reference data, the recovered optical properties exhibit maximum absolute errors of approximately 4–10% for reduced scattering and 5–10% for absorption for the cubes, and 16–19% and 16–22%, respectively, for the bust. Forward renderings based on the recovered coefficients achieve CIE $\Delta E_{2000}$ values below 1 for the cube and below 2 for the complex geometry when compared with photographs. Additionally, we demonstrated that the approach can be applied using a common commercially available RGB camera, recovering optical parameters from each RGB channel, albeit with increased errors due to the camera’s broad spectral channels. Overall, our method enables the recovery of optical properties and the creation of accurate digital twins for objects of arbitrary shape using comparatively simple hardware, including common commercially available RGB cameras. This broadens its applicability to practical scenarios such as process monitoring and digital twinning when appearance, rather than precise material parameters, is the primary focus.

Accurate colour reproduction remains a challenge in manufactured dental restorations because tooth appearance depends on wavelength-dependent absorption and scattering, geometry, illumination, and viewing conditions. We present a measurement- and simulation-based workflow for determining 3D-printable multi-material compositions. We demonstrate our workflow by reproducing the appearance of the 16 VITA classical A1–D4 shade guide colours with a set of six Stratasys Vero and VeroUltra photopolymers. Each reference tooth was recorded in a photobox using a camera with six narrow-band spectral filters spanning 450 nm to 700 nm. A physics-based, GPU-accelerated Monte Carlo light transport simulation was then used inversely to recover the six material concentrations that minimised the CIE $\Delta E_{2000}$ colour difference between the measured and simulated appearance considering all six wavelength bands. Additionally, we compared four colour optimisation strategies for determining material compositions. We further investigated metamerism in the colour optimisation by independently the illuminant and comparing a single- and double-light-source setup. These variations produced substantial changes in the resulting colour differences. With the given material set, the resulting mixtures reproduced all 16 teeth across the shade guide with a mean colour difference of CIE $\Delta E_{2000}=2.76\pm 0.88$ over the evaluated tooth regions. Crucially, the printing materials require optical characterisation only once, after which new target teeth need only be spectrally measured to determine their printable compositions. More broadly, the framework provides a general route from spectral measurements to physically realisable multi-material reproductions, extending beyond dental applications.