FIELD OF THE INVENTION

The present invention relates to methods and apparatus for the volumetric fabrication of three-dimensional objects or articles from photoresponsive materials loaded with cells, biologic con tents or micro and nano-particles. In particular, the present invention is related, but not restricted, to manufacturing sys tems wherein the objects are generated by tomographic back- projections .

BACKGROUND

In conventional additive manufacturing, a three-dimensional ob ject is fabricated either by pointwise scanning of the object volume or in a layer-by-layer fashion. An example is stereo lithography (SLA) (see for example US-5,344,298), where the ob ject is formed one layer at a time by the solidification of a photocurable resist under light irradiation before application of a subsequent layer. The successive layers of the object can be defined for example by scanning a laser beam point-by-point, as suggested in US-5,344,29, or by digital light processing (DLP) technology, as described in US-6,500,378.

In these methods, the layer thickness typically ranges from 10 pm to 200 pm. Thus, the photocuring of a layer at a time with such a thickness can be achieved using highly absorbing or scat tering resins. Moreover, using highly absorbing inks is benefi cial in SLA and DLP as it prevents the exposure of an already processed layer by the next layer being formed, which could re sult in manufacturing artefacts, a phenomenon referred as over curing in additive manufacturing (T. Baldacchini, Three- Dimensional Microfabrication Using Two-Photon Polymerization, William Andrew, 2015).

As opposed to layer-wise additive manufacturing techniques such as SLA and DLP, in volumetric additive manufacturing (VAM), the entire volume of the object is solidified at once. An example of VAM (see for example WO 2019/043529) is tomographic volumetric additive manufacturing, in which a three-dimensional object is formed by irradiating a cylindrical volume of resin with a se quence of two-dimensional light patterns while synchronously ro tating the volume of resin. In this process, the irradiation of the resin build volume from multiple angles results in an accu mulation of light dose that locally overcomes the resin gelation threshold, thus forming the three-dimensional object. This local three-dimensional cumulative light dose deposited in the resin build volume is created by pre-computing the sequence of two- dimensional light patterns using an algorithm, such as a fil tered inverse Radon transform. With such volumetric additive manufacturing methods, addressing the entire cylindrical build volume of resin with each the two-dimensional light patterns is essential to accurately create the cumulative three-dimensional light dose distribution that leads to the object formation.

Hence, in VAM the use of resins with high transparency and low scattering properties is favored for the accurate fabrication of three-dimensional objects. The propagation of the two- dimensional light patterns through the entire volume is indeed affected by the resin scattering properties. In scattering or absorbing resins, the resulting light dose distribution in the resin build volume will be blurred or will present unwanted in tensity gradients that are detrimental to the object formation.

An example of the detrimental effect of scattering resins on the printing accuracy in VAM is the use of resins seeded with high concentrations of living cells for bioprinting purposes. A straightforward solution would be to reduce the cell concentra tion, however the differentiation of the printed living cell constructs into functional living units requires high cell con centration (>10 ⁷ cells/mL) in the host resin. At such cell con centrations, the scattering of the light patterns limits the achievable width of the prints to about 10 mm in VAM.

Similarly, composite resins may contain micro and/or nano parti cles, or fibrils, which contribute to light scattering. Thus, depending on the scattering properties of the resin, the VAM produces parts with low fidelity and resolution.

The volumetric fabrication of three-dimensional objects with photoresponsive material containing scattering particles is of paramount importance, for example in bioprinting applications, where the photoresponsive material can be seeded with living cells, or for composite material, such as ceramics, where the photoresponsive material can be loaded with ceramic precursor particles. Indeed, tomographic volumetric additive manufacturing enables the fabrication of objects with more design freedom and with a higher cell viability than other existing manufacturing techniques .

Consequently, there is a need for systems and methods to enable the volumetric additive manufacturing of resins loaded with cells or particles for bioprinting applications or the pro cessing of composite resins. It was therefore the object of the present invention to provide a method and apparatus for generat ing three-dimensional objects from scattering photoresponsive materials with volumetric additive manufacturing methods with improved accuracy. SUMMARY OF THE INVENTION

In tomographic volumetric additive manufacturing, the scattering properties of the photoresponsive materials used to produce a three-dimensional article are critical to obtaining a high accu- racy and high resolution of the printed article with respect to its digital three-dimensional model. The present invention dis closes an apparatus and methods to carry out volumetric additive manufacturing with resins loaded with cells or particles for op timal print accuracy and resolution. In detail, the present invention is related to a method of fab ricating a three-dimensional article comprising the steps of: providing, in a transparent container of an apparatus for tomographic additive manufacturing, a photoresponsive mate rial, wherein said photoresponsive material contains scat tering particles, adjusting the refractive index of said photoresponsive ma terial so as to match the refractive index of said scatter ing particles; generating from a light source of said apparatus two- dimensional light-patterns based on computed tomographic projections of said three-dimensional article, and projecting two-dimensional light-patterns into said pho toresponsive material and defining a three-dimensional dose distribution, thereby creating a distribution of alterations in said photoresponsive material, and thereby creating said article.

The present invention is furthermore related to a method of fab ricating a three-dimensional article comprising the steps of: providing, in a transparent container of an apparatus for tomographic additive manufacturing, a photoresponsive mate rial, wherein said photoresponsive material preferably con tains scattering particles, generating from a light source of said apparatus two- dimensional light-patterns based on computed tomographic projections of said three-dimensional article, and projecting two-dimensional light-patterns into said pho toresponsive material and defining a three-dimensional dose distribution, thereby creating a distribution of alterations in said photoresponsive material, and thereby creating said article; characterized in that said two-dimensional light-patterns are projected into said photoresponsive material using a light source emitting light of a wavelength longer than 630 nm, pref erably in a range from 630 nm to 1000 nm, more preferably in a range from 650 nm to 900 nm.

The present invention is furthermore related to a system appa ratus for the fabrication of a three-dimensional article by com puted tomographic projections, preferably by a method according to any of the preceding claims, comprising a light source (10) for projecting dynamic two-dimensional light-patterns (11, 64) into a photoresponsive material (12) that is contained in a transparent vessel (13) of said apparatus, wherein said trans parent vessel (13) is provided on a rotation platform (14), characterized in that said light source (10) is capable of emit ting light of a wavelength longer than 630 nm, preferably in a range from 630 nm to 1050 nm, more preferably in a range from 650 nm to 900 nm.

The present invention is furthermore related to a method of fab- ricating a three-dimensional article comprising the steps of: providing, in a transparent container (13) of an apparatus for tomographic additive manufacturing, a photoresponsive material (12), wherein said photoresponsive material (12) contains scattering particles (13), generating from a light source (10) of said apparatus a first set of two-dimensional light-patterns (11; 64) based on computed tomographic projections of said three- dimensional article, and - generating a second set of two-dimensional light-patterns

(11; 64) obtained from said first set of two-dimensional light-patterns by applying a computed pre distortion to com pensate for the distortion effect caused by light propaga tion in said photoresponsive material (12),and - projecting said second set of two-dimensional light- patterns (11; 64) into said photoresponsive material (12) and defining a three-dimensional dose distribution, thereby creating a distribution of alterations (15) in said photore sponsive material (12), and thereby creating said article, characterized in that said second set og two-dimensional light-patterns (11; 64) are projected into said photore sponsive material (12) using a light source emitting light of a wavelength preferably in a range from 400 nm to 1050 nm. BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood through the detailed de scription of preferred embodiments and in reference to the draw ings, wherein Figure 1A is a perspective view of one example embodiment of a volumetric additive manufacturing apparatus suitable for the present invention;

Figure IB is a top view of the apparatus of Figure 1A;

Figures 2A-2B are schematic illustrations of fabrication using the volumetric additive manufacturing apparatus of Figure 1;

Figure 3 is a schematic illustration of the effect on the volu metric printing method of using a scattering photoresponsive ma terial.

Figure 4 is a schematic illustration of the effect on the print- ed three-dimensional object of using a scattering photorespon sive material.

Figure 5 is a graph illustrating the effect of the present in vention of matching the refractive index of the photoresponsive material to the index of the scattering particles in suspension in the photoresponsive material.

Figure 6 is a schematic illustration of the scattering of the illumination patterns by the build volume without index-matching of the photoresponsive material and particles.

Figure 7 is a schematic illustration of the scattering of the illumination patterns by the build volume with index-matching of the photoresponsive material and particles according to the pre sent invention. Figure 8 is a flow chart illustrating an embodiment of the in dex-matching process of the present invention of the photore- sponsive material for accurate volumetric additive manufacturing of particle-seeded resins. Figure 9 is a graph illustrating the angular scattered power of a photoresponsive material with scattering particles for differ ent wavelengths.

Figure 10 is the absorption spectrum of a ruthenium-sodium per sulfate photoinitiator in phosphate buffered saline. Figure 11 is a schematic illustration of an embodiment of the present invention of using up-conversion nanoparticles for volu metric additive manufacturing.

DETAILED DESCRIPTION

In tomographic volumetric additive manufacturing, a volume of photoresponsive materials is illuminated from many directions with patterns of light. These patterns of light are computed with an algorithm similar to that used in X-ray computed tomog raphy, also known as medical CT scanners. These algorithms are known to the skilled person. An example of a possible embodiment of tomographic additive man ufacturing is illustrated in Figure 1A. An apparatus for tomo graphic additive manufacturing is described in detail in e.g. WO 2019/043529 A1.

A light source 10 is projecting dynamic two-dimensional light- patterns 11 into a photoresponsive material 12 that is contained in a transparent vessel 13. The light source may be, for exam ple, a laser, a plurality of laser, a LED or a LED array. The transparent vessel 13 is fully or essentially transparent for the light coming from the light source 12. The transparent vessel 13 and photoresponsive material 12 are set onto a rotation platform 14 that is concurrently rotating while the dynamic two-dimensional light-patterns 11 are dis played. The cumulative effect of illuminating the photorespon sive material with each of the light patterns from each corre sponding direction is to deposit a controlled three-dimensional distribution of light dose into the photoresponsive medium. As illustrated in Figure IB, this distribution of light dose leads to a distribution of alterations 15 in the photoresponsive medi um, which creates the three-dimensional object. For example, for a photoresponsive material that solidifies under exposure to light, the three-dimensional distribution of light dose causes the material to solidify in the desired three-dimensional ob ject. In this example of embodiment, all the mentioned compo nents are mounted on a fixed damping platform 16.

The photoresponsive material to be used in tomographic additive manufacturing is known, for example from WO 2019/043529 A1. Gen erally, the photoresponsive material comprises components that may undergo polymerization when irradiated. Suitable components may be monomers, reactive diluents, oligomers or prepolymers. In addition, a photoinitiator and optionally a photosynergist is present. The photoresponsive material may additionally comprise conventional suitable additives such as fillers, gellifying agents, plasticizers, colorants such as pigments or dyes, ex tenders, wax, or antioxidants.

Preferably, said photoresponsive material has a dynamic viscosi ty between 1000 and 50000 centipoises at a temperature of 25°C.

In a further preferred embodiment, said photoresponsive material comprises a concentration of said photo-initiator such that at most 90% of the intensity of said patterns of light is absorbed by the largest thickness of said volume of said photoresponsive material through which said patterns of light are propagating.

In a further preferred embodiment, said photoresponsive material comprises a two-stage photo-initiator, such that said photore sponsive material is locally altered upon local simultaneous or successive illumination with a first and second wavelength of light but not altered if locally illuminated with only one of the wavelengths of light.

In a preferred embodiment of the present invention, the photore sponsive material 12 may form a hydrogel upon irradiation, in which cells may grow. Such hydrogels are known in the art, e.g. from WO 2014/180970 A1.

The basic principle of tomographic volumetric additive manufac turing is illustrated in Figures 2A- 2J to better appreciate the impact of scattering resins on this fabrication method. In Fig ure 2A, a section of the photoresponsive material 12 and its container (transparent vessel) 13 are shown. The container 13 can be rotated (as indicated by the arrow). A beam of light rep resenting two-dimensional light-patterns 11 is directed inside the container 13. Hence, a certain dose of light is deposited inside the photoresponsive material 12. This dose is represented by a grey shaded area in Figure 2B. The projection of light is interrupted after a short time, such that the photoresponsive material 12 is not yet converted to its alternate form. For ex ample, if the photoresponsive material 12 is a photopolymer ma terial that polymerizes under illumination by a radiation, the projection is halted at an illumination dose that is well below the polymerization threshold. The sample of photoresponsive ma terial 12 is then rotated as shown in Figure 2C. The volume that was previously illuminated has now changed orientation with re spect to the direction of illumination, as shown in Figure 2D. The photoresponsive material 12 is then illuminated from a dif- ferent direction, as shown in Figure 2E. In doing so, it is pos sible to expose certain volumes of the photoresponsive material 12 again (represented with a darker shading in Figure 2E), while other volumes of the photoresponsive material 12 receive only a single, low exposure dose (lighter shading in Figure 2E). After the second exposure, the process can be repeated by rotating the sample more, as shown in Figure 2F and Figure 2G, and illuminat ing the photoresponsive material 12 from a new orientation, as shown in Figure 2H. The accumulation of all the projections from all the different orientations determines which parts of the photoresponsive material 12 received enough illumination to be converted to an alternate form, as exemplified by the dark shad ed area in Figure 21, and which parts are insufficiently exposed to be converted, as exemplified by the lighter shaded areas in Figure 21. It is understood that the process explained here may also be done with smaller steps of rotation, or even with a con tinuous rotating motion. After development of the photorespon sive material 12, a structure can be extracted from the photore sponsive material 12 as illustrated in Figure 2J. By modulating the light beam representing two-dimensional light-patterns 11 in an appropriate fashion while the photoresponsive material 12 ro tates, a controlled distribution of light dose is applied to the photoresponsive material 12.

While Figure 2A to Figure 2J illustrate only one section of the photoresponsive material 12 for clarity, it is understood that this process may be carried out concurrently for several layers of the photoresponsive material 12. The distribution of the il lumination dose can be controlled independently in each layer, thereby allowing three-dimensional structures to be created.

It is understood from Figure 2A to Figure 2J that the light pat terns should propagate through the photoresponsive material 12 without modifications or alterations in order to accurately de- fine the dose distribution that eventually leads to the object formation .

As illustrated in Figure 3, the presence of scattering particles 30 in the photoresponsive material 12 will affect the shape of each light patterns displayed in the photoresponsive material 12 and will eventually smear out the dose deposited 31 in the pho toresponsive material 12, thus leading to an inaccurate fabrica tion of the object after development, as illustrated in Figure 4.

It has been surprisingly found that the scattering of the light patterns by particles loaded in the photoresponsive material can be dramatically reduced by matching the refractive index of the photoresponsive material with the refractive index of the parti cles. This is illustrated in Figure 5 where the power scattered by a lO-pm spherical particle in suspension in the photorespon sive material (resin) is several orders of magnitude lower if the refractive index of the resin is closely matched to that of the particle (see dashed line) than if there is a large mismatch of refractive index (see thick line).

The photoresponsive material and scattering particles used in Figure 5 for the thick curve were respectively a solution of 10% (v/v) of gelatin methacrylate in phosphate buffered saline and human colon cancer cells (HT29). For the dashed curve of Figure 5, the same human colon cancer cells were used as scattering particles whereas the photoresponsive material was modelled as a solution index-matched to the scattering particles, in accord ance with the present invention.

This method of reducing the scattering of particle-loaded resins for volumetric additive manufacturing is further illustrated in Figures 6 and 7. In figure 6, an example of tomographic volumet ric additive manufacturing with a scattering photoresponsive ma- terial in which there is a mismatch between the refractive index of the particles and the photoresponsive material is illustrat ed. A rotation platform 14holds the photoresponsive material build volume 12 in which scattering particles 30 are loaded. An input light beam representing two-dimensional light-patterns 11, such as the two-dimensional pattern 64, is projected into the build volume. Owing to the scattering particles 30 contained in the photoresponsive material 12, the propagating light beam 65 is scattered and the two-dimensional light pattern 66 is smeared out, which will negatively impact the volumetric printing accu racy.

In order to obtain well-defined spatial dose distributions with tomographic volumetric additive manufacturing, it is important to match the refractive index of the photoresponsive material with the refractive index of the particles. Figure 7 shows a preferred of embodiment of the present invention, in which a tomographic volumetric additive manufacturing apparatus is used with a scattering photoresponsive material 12 in which there is a refractive index-matching of the particles 30 and the photore sponsive material 12. A rotation platform 14 holds the photore sponsive material build volume 12 in which scattering particles 30 are loaded. An input light beam representing two-dimensional light-patterns 11, such as the two-dimensional pattern 64 is projected into the build volume. Owing to matching of the re fractive index of the photoresponsive material 12 with the re fractive index of the loaded scattering particles 30, the propa gating light beam 75 is not scattered and the two-dimensional light pattern 76 is accurately displayed through the entire build volume 12 thus ensuring and optimal volumetric printing accuracy .

Methods and devices for determining the refractive index of a material are known and do not have to be discussed here in de- tail. Reference may be made, for example, to refractometers, spectrometers, interferometers, or microscopes.

According to the present invention, the average refractive index of the scattering particles 30 is the statistical mean of the refractive indices of the individual particles.

Adjustment of the refractive index of the photoresponsive mate rial 12 may be achieved according to the present invention by mixing said photoresponsive material 12 with a medium having a different refractive index that will act as a tunable refractive index medium. By mixing said photoresponsive material 12 with said medium having a different refractive index in varying amounts, a desired refractive index (i.e. a refractive index that matches the refractive index of the loaded scattering par ticles 30) can be obtained. Mixing can be performed by any known method, e.g. combining the components and stirring them until a homogeneous blend of the components has been obtained.

According to the present invention, any material can be used as medium having a different refractive index that does not ad versely affect the creation of the desired three-dimensional ar ticle and that (in the case of biological material such as cells) has no toxic effect.

An example of tunable refractive index medium for bioprinting applications in volumetric additive manufacturing include, but are not limited to, iodixanol or glycerin. Examples of tunable refractive index medium for organic photoresponsive materials include, but are not limited to: Ethoxylated (4) Bisphenol A Di methacrylate (BPA4EODMA), Ethoxylated (10) Bisphenol A Dimethac rylate (BPA10EODMA), Ethoxylated (2) Bisphenol A Dimethacrylate (BPA2EODMA), Ethoxylated (3) Bisphenol A Dimethacrylate (BPA3EODMA), 2-Phenoxyethyl Methacrylate, Tricyclodecanedimetha- nol Diacrylate, Ethoxylated (10) Bisphenol A Diacrylate (BPAIOEODA), Ethoxylated (4) Bisphenol A Diacrylate (BPA4EODA), Ethoxylated (3) Bisphenol A Diacrylate (BPA3EODA), Ethoxylated 4 Phenyl Acrylate (P(4E0)A), 2-Phenoxyethyl Acrylate (2-PEA), and combinations thereof.

According to the present invention, by a "match" of the reactive indices of the photoresponsive material 12 and the scattering particles 30 loaded therein it is meant that the refractive in dices of the photoresponsive material 12 and of the scattering particles 30 differ from each other by not more than 2%, prefer ably 0 to 2%, more preferably 0,01 to 1,5%, even more preferably 0,01 to 1% and especially preferred 0,01 to 0,2%.

The ratio in which the photoresponsive material 12 and the medi um having a different refractive index are mixed with each other depends on the degree of match one wants to obtain. Different volume ratios V _m , including, but not limited to, 0:100, 20:80,

40:60, 60:40, 80:20 and 100:0 (v/v) may be used.

The flowchart in Figure 8 further describes a method of the pre sent invention to formulate a photoresponsive material 12 whose refractive index matches the refractive index of the loaded scattering particles 30 in order to enable the processing of the scattering photoresponsive material 12 with a tomographic volu metric additive manufacturing method:

• The average refractive index <n _part > of the scattering parti cles 30 is first measured, for example with a refractometer or a digital holographic microscope (step 80).

• Provided that initially a photoresponsive material 12 hav ing a known certain refractive index was used in the tomo graphic volumetric additive manufacturing apparatus, this photoresponsive material 12 is mixed with another medium of different refractive index that will act as a tunable re fractive index medium. The photoresponsive material 12 is mixed with the tunable refractive index medium in different volume ratios V _m , in cluding, but not limited to, 0:100, 20:80, 40:60, 60:40,

80:20 and 100:0 (v/v), and the refractive index n _mixt of each of the mixtures is measured (step 81 in Figure 8).

• The measurements of n _mixt for different volume ratios V _m made in Step 81 are interpolated (step 82) so that the optimal volume ratio V _opt of the photoresponsive material 12 and the tunable refractive index medium can be derived to yield a mixture of refractive index n _miXt( V _opt) = <n _part > (step 83).

• The photoresponsive material 12 and the tunable refractive index medium are mixed in said volume ratio V _opt (step 84)

• The refractive index n _mixt ,2 of the subsequent mixture is measured, for example with a refractometer (step 85)

• If the difference between the refractive index of the mix ture n _miXt ,2 and the average refractive index of the parti cles <n _part > is more than a certain threshold (i.e. the re fractive indices do not match), including, but not limited to 0.1%, 1% or 2% the user should start over the procedure again from step 81.

• If the refractive index matching is within the selected threshold (i.e. the refractive indices match), the scatter ing particles 30 can be loaded in the mixture of original photoresponsive material 12 and tunable refractive index medium (step 87 in Figure 8).

• The resulting mixture is processed with a tomographic volu metric additive manufacturing apparatus to form a three- dimensional object (step 88).

In another preferred embodiment of the present invention, more than one tunable refractive index medium can be added to the original photoresponsive material. Most photoresponsive materials used in existing additive manu facturing apparatus are sensitive to ultraviolet or blue light i.e. wavelengths in the range 365-450 nm. This is due to the conventionally used photoinitiators that exhibit an absorption maximum in said range of the electromagnetic spectrum.

However, as illustrated in Figure 9, it has been surprisingly found that it would be beneficial to use a light source in the red part of the visible spectrum. As shown in Figure 9, for small scattering angles, where scattering is predominant, the scattered power of an incident lW/m ² light beam is 16 times high er at a wavelength of 400 nm (thick line) than at a wavelength of 800 nm (dashed line), considering the same refractive index mismatch between a photosensitive material and a 10-pm spherical particle in both cases.

Thus, in a preferred embodiment of the present invention, the two-dimensional light patterns 11 in Figure 1A, are produced us ing a light source at a wavelength longer than 630 nm, i.e. in the red or infrared region of the electromagnetic spectrum, preferably in a range from 630 nm to 1050 nm, more preferably in a range from 650 nm to 900 nm, in order to dramatically reduce the scattering. Indeed, using illumination wavelengths longer than 630 nm allows for the accurate volumetric fabrication of objects 4 times to 16 times wider than when using the conven tional 350 nm to 450 nm range.

Suitable light sources that emit in this range of the electro magnetic spectrum are known. For example, lasers emitting at wavelenghts longer than 630 nm are known and commercially avail able (e.g. http://www.roithner-laser.com/lasersystems/laser sys tems 671.html) .

Owing to the lack of available photo-initiators for photorespon- sive materials that have an absorption maximum in this wave- length range, in this embodiment of the present invention, a light source at a wavelength longer than 630 nm, preferably in a range from 630 nm to 1050 nm, more preferably in a range from 650 nm to 900 nm, is combined with a conventional photo initiator whose absorption band is predominantly in the 365 nm to 450 nm range, but at least to a slight extent expands into the red region of the electromagnetic spectrum (i.e. to wave- lenghts longer than 630 nm) to process a photoresponsive materi al 12 loaded with scattering particles 30. Indeed, according to the present invention it could be demonstrated that a suffi ciently strong illumination, for example above 50 mW/cm ² , at a wavelength distinct from the absorption spectrum of a photo initiator can activate the photo-initiator to alter the phase of the photoresponsive material.

Suitable photoinitiators whose absorption band is predominantly in the 365 nm to 450 nm range, but at least to a slight extent expands into the red region of the electromagnetic spectrum (i.e. to wavelenghts longer than 630 nm), are commercially available and known from the literature. An example of a suita ble photoinitiator is a ruthenium-sodium persulfate system, such as a combination of ruthenium II trisbipyridyl chloride ([RuII(bpy ₃ )] ²⁺ ) and sodium persulfate (SPS) (e.g. Bjork et al. Biomaterials 2011; 32(10): 2479-2488).

An example of said preferred embodiment is a volumetric additive manufacturing apparatus, as the one illustrated in Figure 1, in which the light source is a laser emitting light at a wavelength of 671 nm, a three-dimensional object or article is formed with the volumetric additive manufacturing apparatus out of a photo responsive material 12 loaded with scattering particles 30 and in which Ruthenium/sodium persulfate is used as a photo initiator. Interestingly, this photo-initiator is mostly sensi tive in the 300 nm to 500 nm region, as illustrated by the ab- sorption spectrum in Figure 10, yet the authors of the present invention demonstrated that a strong illumination at 671 nm can activate the photo-initiator to form a three-dimensional object or article.

It has been found according to the present invention that the method of fabricating a three-dimensional article is improved even if the two-dimensional light patterns 11 are produced using a light source at a wavelength longer than 630 nm, preferably in a range from 630 nm to 1050 nm, more preferably in a range from 650 nm to 900 nm, without adjusting the refractive index of the photoresponsive material (12) so as to match the refractive in dex of said scattering particles (30). Thus, while the most ben eficial effects of the present invention are obtained by both adjusting the refractive index of the photoresponsive material (12) so as to match the refractive index of said scattering par ticles (30), and producing the two-dimensional light patterns 11 using a light source at a wavelength longer than 630 nm, prefer ably in a range from 630 nm to 1050 nm, more preferably in a range from 650 nm to 900 nm, in the same method, the present in vention covers also methods employing only one of these steps.

In another preferred variant of this embodiment of the present invention, up-conversion nanoparticles are included in the scat tering photoresponsive material in order to allow for its pro cessing with a volumetric additive manufacturing apparatus.

Up-conversion particles (or up-converting) particles are known in the art. They are characterized by the fact that they absorb light of a longer wavelength and emit light of a shorter wave length.

Examples of up-conversion nanoparticles that can be used in this embodiment include, but are not limited to, a core-shell nano particle composed of a core of sodium yttrium fluoride doped with neodymium and a shell composed of sodium yttrium fluoride doped with ytterbium, a core-shell nanoparticle composed of a core of sodium yttrium fluoride doped with neodymium and a shell composed of sodium yttrium fluoride doped with ytterbium, erbium and neodymium.

According to the present invention, it has been surprisingly found that if at least one up-converting material is included into the photoresponsive material to be processed in a method of fabricating a three-dimensional article, the embodiment of the present invention using a light source at a wavelength longer than 630 nm, preferably in a range from 630 nm to 1050 nm, more preferably in a range from 650 nm to 850 nm can be performed even more efficiently. The up-conversion particles absorb the light emitted from the light source, and within the photorespon sive material locally and isotropically emit light of a shorter wavelength, i.e. light in the range of the absorption band of conventional photoinitiators. Thus, even though the light emit ted from the light source is not optimal for the employed con ventional photoinitiators, within the photoresponsive material itself light of a suitable wavelength is generated, thereby pro moting the desired alteration of the photoresponsive material.

According to the present invention, the up-conversion particles should be nanoparticles, so as to minimize any adverse scatter ing. According to the present invention, a nanoparticle is a particle having an average particle size of 1-1000 nm, prefera bly 5-500 nm and most preferably 10-100 nm.

According to the present invention, the up-conversion particles should be used in the photoresponsive material in a concentra tion of 0,1-10 wt.-%, preferably 0,5-5 wt.-%, based on the weight of the entire photoresponsive material that is used in the method. An example of this further embodiment of the present invention is illustrated in Figure 11. A rotation platform 14 holds a build volume of photoresponsive material 12. The photoresponsive material 12 is loaded with up-conversion nanoparticles 112 sen sitive to long wavelengths, including, but not limited to, the range of 700 nm to 900 nm. The photoresponsive material 12 may additionally contain scattering particles 30 that prevent the accurate formation of three-dimensional object with a volumetric additive manufacturing apparatus. The photoresponsive material 12 additionally contains a photo-initiator sensitive to a range of wavelengths including, but not limited to, 350 nm to 500 nm. The build volume of photoresponsive material 12 is illuminated with a light source 10 with a wavelength in a range including, but not limited to, 700 nm to 900 nm. Dynamic two-dimensional light patterns 64 are formed out of the light source 10 to de posit a light dose in the photoresponsive material 12. Upon ab sorption of the light patterns 64 by the up-conversion nanopar ticles 116 located in the propagation path of the light patterns 64 in the photoresponsive material 12, a light with a wavelength in a range of, but not limited to, 350 nm to 500 nm, is isotrop ically locally emitted and triggers the photo-initiator to lo cally alter the phase of the photoresponsive material 12 and form a three-dimensional object or article.

This embodiment effectively takes advantage of the reduced scat tering of light of long wavelengths by particles to accurately form three-dimensional objects or articles with a volumetric ad ditive manufacturing apparatus.

In another embodiment of the present invention, the projected patterns, corresponding to projections in VAM, are pre-distorted by a spatial light modulator such that upon propagation into the scattering medium (i.e. the photoresponsive material loaded with scattered particles), a more accurate representation of the ob- ject projection is obtained. An embodiment to implement such a distortion compensation is to measure the transmission matrix of the scattering medium. For example, the transmission matrix can obtained according to the method described in "Measuring the Transmission Matrix in Optics: An Approach to the Study and Con trol of Light Propagation in Disordered Media", S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan Phys. Rev. Lett. 104, 100601 -2010).

Considering that the 2D image at the output of the scattering medium is represented by a one dimensional vector Y, the linear transformation of the scattering medium is represented by a ma trix A and the input image (e.g. on the spatial light modulator) described by a one dimensional vector X. There exists invariant spatial modes upon propagation. An estimate of these invariant modes can be obtained by the eigen-vectors of the matrix via for example performing a well know singular value decomposition. As a linear combination of invariant modes is also an invariant mode, the initial projected patterns obtained with VAM are de composed into in the invariant modes. The new pre-distorted pat- terns are then patterns which have been obtained by the proper linear combination of the invariant modes.