Patent Description:
Additive manufacturing (AM) fabrication methods are proliferating rapidly, with photopolymer-based approaches comprising some of the most prominent methods. These stereolithographic techniques provide a useful balance of resolution, build speed, process control, and capital cost. However, these system metrics typically must be traded off one against another. Resolving the speed limitations, surface roughness (stair-step artifacts), and requirements for support structures will provide the next major steps forward in the progress of these technologies.

As additive manufacturing (AM) technologies gain prominence and versatility, one constraint on nearly every AM approach is the reliance on serially repeating low-dimensional unit operations, building structures up voxel-by-voxel, or layer-by-layer. This can be an advantage, yielding significant process flexibility, but is often a shortcoming, imposing deficiencies in surface finish and dimensional limitations; for instance, it is impossible to produce smoothly curving geometries. A few approaches have demonstrated the capability to generate 3D structures without requiring planar slicing, notably Hughes Research Laboratories' fabrication of lattices via latticed light-beams (see, <NPL>) and photonic crystals produced by interference lithography (see, <NPL>. However, these approaches are limited to periodic structures, with one of the dimensions substantially smaller than two others. Even Carbon3D's "continuous" liquid interface process (see, <NPL>) still requires sequential fabrication based on 2D discretization.

Expanding the AM technology base to include fabrication by means of <NUM>-D unit operations, which generate 3D shapes with arbitrary geometry ("volume at once") is highly desirable. Such approaches are in their infancy: the first "volume-at-once" photopolymer-based fabrication was recently demonstrated as noted in <NPL>. This approach used a holographically-shaped light field generated by a phase-only liquid crystal on silicon (LCoS) spatial light modulator (SLM). The geometries achievable by the Shusteff et al. , approach are limited due to having constant cross-section along each of three orthogonal directions. This limitation arises largely from the small diffractive angles available from state of the art SLMs owing to their relatively large pixel size (minimum approximately <NUM>, but more typically <NUM> or larger).

The document <CIT> discloses an optical modelling apparatus that models a desired three-dimensional model using a photocurable resin that is cured by irradiation with light.

In one aspect the present invention relates to a method with the features of claim <NUM> of forming a three dimensional (3D) object.

In another aspect the present invention relates to a system with the features of claim <NUM> for forming a three dimensional (3D) object by providing a volume of photo-curable resin contained within an optically transparent resin container.

The approach described in the present invention disclosure accomplishes volumetric fabrication by applying computed tomography (CT) techniques in reverse, that is, by fabricating structures by exposing a photopolymer resin volume with a 3D light field from multiple angles, and updating the light field at each angle. The necessary light fields are spatially and/or temporally multiplexed, such that their summed energy dose in a target resin volume crosslinks the resin into a user-defined geometry. These light fields may be static or dynamic, and may be generated by any suitable mechanism, for example a spatial light modulator (SLM). The SLM controls either the phase or the amplitude of a light field, or possibly both, to provide the necessary intensity distribution. The light fields at each angle θ may be generated simultaneously or sequentially in time. In the sequential case, they may be generated in any order. The present disclosure significantly advances the process possibilities in this area, providing a means to generate a 3D radiation dose distribution within a given volume, allowing for nearly arbitrary structures in photopolymer curing.

This present disclosure is based on spatial and/or temporal multiplexing of three-dimensional (3D) optical light fields with respect to a photosensitive resin bath volume. Multiplexing can be accomplished in a number of ways including, but not limited to, those described in the specific embodiments and methods in the following paragraphs. Multiplexing may be implemented as to cure 3D user-designed geometries in situ in the photopolymer build volume by delivering a controlled exposure dose to selected regions of the resin.

Conceptually, the teachings of the present disclosure build upon the well-developed field of computed tomography (CT). CT generally refers to imaging of a 3D volume from multiple angles, most often by X- rays transmitted through the volume, where each image is sequentially generated by illumination from azimuthally-arrayed directions. The 3D volume is then reconstructed by various known computational techniques. Such known computational techniques may include Fourier-domain methods such as filtered back-projection (FBP) or iterative optimization-based techniques. See, e.g., <NPL>. With CT approaches being useful for capturing and recording 3D geometrical information, computed axial lithography (CAL) inverts the concept to generate a 3D geometry from exposures of a photopolymer from multiple angles. The embodiments described herein retain the "volume-at-once" capability, while significantly improving the geometric flexibility of the three beam holographic lithography approach (Shusteff et al. , supra), which eliminates conventional discretization "stairstep" artifacts.

For cancer therapeutic purposes, CT optimization has been used to deliver intensity-modulated radiation therapy (IMRT), which delivers a targeted 3D distribution of radiation doses to specific regions within a patient's physiology, while minimizing the dose in non-target areas. See, e.g.,<NPL>. The constraints of 3D lithographic fabrication are typically less stringent, suggesting that a similarly-specified 3D dose distribution of radiation can be used to cross-link a photosensitive resin.

To understand the relationship between the target 3D part geometry, and the computed projections, consider <FIG>, as well as the coordinate system designations in <FIG>. For the following discussion, it is convenient to adopt a global Cartesian coordinate system (x,y,z) to refer to the 3D build volume and a rotated Cartesian coordinate system (x',y',z') whose orientation depends on the angle θ of the projection being considered. In these coordinate systems, z is the axis for azimuthal arraying of exposures at angles θ around volume <NUM>. For each angle θ, a projection is computed. At a particular angle θ, we define a projection as a two-dimensional function Pe(y',z) which fully determines a three-dimensional intensity map lθ(x,y,z) generated in the target volume (note that Pe depends on the angle θ but will be referred to as a two-dimensional function as it has two spatial dimensions). In the simplest case the projection can be thought of as a two dimensional image in the (y',z) domain which propagates through the resin volume in the x' direction. In this idealized case, the 3D intensity profile generated by the projection looks like the (y',z) domain image extruded through the target volume in the x' direction. This approximation holds well physically if the illuminating projections are collimated. In medical imaging applications, this is analogous to parallel beam tomography. For the present disclosure, this is a sufficiently good approximation whenever the optical configuration has a long depth of focus (particularly relevant for the small diffraction angles available with current SLM technology). In the general case, an optical propagation and attenuation model describes the 3D intensity map generated from a 2D projection function at a particular angle. In this description and in <FIG> we consider the idealized case for simplicity in describing the method.

The objective of the tomographic image computation is to design a set P(y',z,θ) of 2D projection images from a range of angles θ such that the 3D intensity map generated from the superposition of the 3D light fields generated from each projection closely or exactly approximates a target 3D intensity map. From a known target 3D intensity map we now consider design of the projections. To further simplify the explanation, we reduce the problem of generating a set of 2D projections for a 3D intensity map to that of generating a set of 1D projections P(y',θ) for a 2D intensity map I(x,y). Again, in this case, 1D refers to the one spatial dimension y'. In the physical (x,y,z) resin volume system, we can think of the 2D intensity map as a horizontal constant z slice of the true 3D intensity map. Ultimately, the 2D projection Pθ(y',z) at a give angle θ can then be generated by stacking of each of the computed 1D projections at each z-plane for that particular angle.

Among the many ways to accomplish CT image reconstruction, two major approaches that lend themselves readily to dose-optimization for fabrication are filtered back-projection (FBP) and iterative optimization-based algorithms. Here we first consider the FBP approach and its limitations, and describe how it may be used to provide useful starting parameters for an optimization algorithm.

The FBP approach for reconstructing a 2D optical density distribution within an (x,y) plane for a given value of z starts with computing a mathematical 1D projection at each of M angular samples (θ = θ<NUM>, θ<NUM>,. These projections taken together comprise the Radon transform of the 2D image. From the projection slice theorem, as discussed in<NPL> and <NPL>, it is known that the Fourier transform of each 1D projection at a particular angle θ is exactly equal to a 1D sample of the Fourier transform of the original 2D density distribution. This 1D sample lies along a line through the origin in the Fourier domain and is sloped at an angle θ. This is depicted in <FIG>. Sufficiently dense sampling in the Fourier domain is required for an accurate CT image reconstruction. To appropriately choose the number of samples M in the Fourier domain, one possible conservative heuristic is to ensure that the maximum distance between slices is no greater than the separation of N sample points in the radial direction. This leads to πN/<NUM> angular samples within <NUM> degrees of angular range.

The lithographic fabrication of each 2D z plane can follow an algorithmic time reversal of the CT imaging process. The target 2D Intensity map for the slice Iz(x,y) is transformed into the Fourier domain, then sampled along each of the M azimuthal angles, generating M 1D intensity distributions, or projections Pe(y'), one for each angle θ<NUM>, θ<NUM>,. Each of these distributions is used to expose the target plane with its respective pattern from its specific angle, which corresponds to building up the sample in the Fourier domain from slices through the origin. FBP for CT reconstruction relies on high-pass spatial filtering before back-projection in order to deemphasize the low frequency oversampling inherent to the central slicing approach. An equivalent way to describe this would be as a radially increasing ramp filter. This filter typically leads to negative excursions in the back-projected images that are unphysical for lithography. Some heuristic approaches to eliminate negative values, producing images suitable for lithography, include imposed positivity constraints or offsetting the calculated image. The results of such heuristics impose trade-offs between the contrast and resolution of calculated dose distributions; however, they can be used as initial dose estimates for a constrained optimization procedure.

Briefly, an optimization procedure takes as its starting point a forward process model that relates resin monomer crosslinking to the received light energy dose. Various 2D versions of such models, such as discussed at <NPL>, available, with limited progress toward 3D analogs. Comparing the modeled degree of cure (induced by the summed dose distribution from all angles), to the desired part geometry, an error function is generated, which is reverse-transformed and used to modify the initial dose estimate. This cycle is iterated for a number of cycles sufficient to meet a particular error criterion, such as edge sharpness, contrast, or total error over the build volume. The optimization procedure provides a means for process non-linearities such as intensity absorption to be accurately modeled and accounted for in the image generation. This is a significant benefit in terms of feature quality. The extension from 2D planes into 3D is straightforward, with the 1D intensity patterns from each z plane assembled into a 2D y'-z image for projection at every angle θ corresponding to the particular x' propagation direction. Effectively, this is a physical projection of the computed Radon transforms for all z planes at each angle θ to reconstruct the desired 3D dose volume.

One specific embodiment, which is not covered by the claims, but which implements the above described method is system <NUM> shown in <FIG>. The system <NUM> may include a plurality of optical subsystems <NUM> arranged such that a set of optical projections P(y',z,θ) at specific selected angles θ<NUM>, θ<NUM>,. is generated around a target volume of resin <NUM> contained within an optically transparent container 29a. One possible design of the optical subsystems <NUM> may include an OLED array <NUM> covered by microlenses <NUM> surrounding the 3D target volume of resin <NUM>. The OLED arrays <NUM> may be controlled in part by a controller 26a. Different groups of the optical subsystems <NUM> simultaneously generate projections Pθ(y',z) and corresponding 3D intensity maps le(x,y,z) <NUM><NUM>, <NUM><NUM>, <NUM><NUM>, etc., at different angles θ<NUM>, θ<NUM>, θ<NUM>, respectively, etc., that project through the target resin volume <NUM>, as shown in <FIG>. The projections Pθ(y',z) and Intensity maps Iθ(x,y,z) are analogous to those described in section [<NUM>]. <FIG> illustrates the 2D nature of each of the optical projections <NUM><NUM>, <NUM><NUM>, <NUM><NUM>. The projections <NUM><NUM>, <NUM><NUM>, <NUM><NUM> are delivered to the target resin volume <NUM> contained within the resin container 29a simultaneously from M different angles θ (i.e., two or more) about the z-axis (<FIG>). The simultaneous superposition of the 3D intensity fields <NUM><NUM>, <NUM><NUM>, <NUM><NUM>, etc., from all angles around the full <NUM> degree circumference of the target resin volume <NUM>, as indicated in <FIG>, generates a 3D intensity function I(x,y,z) in space. This intensity function acts over a fixed temporal exposure period. During exposure, regions where material formation is desired receive a sufficient optical energy dose to cause solidification due to photocuring, while regions where formation (i.e., curing) is not desired receive an insufficient dose. After the exposure period, the resin container 29a may be rinsed to remove uncured resin from regions of the 3D part which have received an insufficient dose of optical energy to achieve photocuring.

Further underlying information on light field photography and 3D displays may be found in <NPL>) and <NPL>. This information is relevant to the possibility of creating the necessary optical subsystems from arrays of LEDs covered by microlenses. The system <NUM> thus forms a means of simultaneously generating images from many viewpoints and simultaneously exposing the entire target volume of resin <NUM> to the projections <NUM><NUM>, <NUM><NUM>, <NUM><NUM> from each angle θ. Because each projection <NUM><NUM>, <NUM><NUM>, <NUM><NUM> acts on the volume simultaneously, the final 3D part can be printed in a single step.

By printing in a single step and avoiding serial layer-by-layer printing, a number of potential issues which may arise in existing AM methods can be addressed. These include difficulties in printing overhang geometries as well as avoiding layering artifacts such as poor surface finish and mechanical anisotropies. An additional benefit of this approach is that the structure being built does not move relative to the fluid medium, enabling fabrication of very compliant or fragile components such as low-volume fraction hydrogel scaffolds (combined with suitable rinsing/drying approaches, such as solvent exchange followed by supercritical CO2 drying).

Referring to <FIG>, a system <NUM> is shown which generates a 3D exposure dose distribution over a fixed time interval by physical rotation of a target volume of resin <NUM> about a z axis <NUM>, synchronized via a controller <NUM> with temporal manipulation of a single 2D optical projection from a digital light processing (DLP) projector or other image generation optical system <NUM>. In the implementation as described previously herein, the image generation optical system <NUM> produces a collimated optical image or projection <NUM> from a single direction along an axis x' <NUM> that impinges on the target volume of resin <NUM>. It will be appreciated that the images could also have some divergence (i.e., not collimated) and the algorithm to design them could be updated accordingly.

The relative angle θ between the incident light of the projection <NUM> and the target volume of resin <NUM> is changed in time as different (y',z) plane images are sequentially projected. Following the coordinate system convention described earlier and depicted in <FIG>, the (x,y,z) system rotates about the z axis as the target volume of resin <NUM> rotates and the (x',y',z) system remains fixed in space. Thus, as the target volume of resin <NUM> rotates, the angle θ between the x-axis and x'-axis changes. In one example, a resin containment vessel <NUM> that holds the target volume of resin <NUM> is mounted on a rotating mount or stage <NUM>. The rotating stage rotates about z axis <NUM> and operation of the DLP projector <NUM> is synchronized with rotation of the mount <NUM> by the controller <NUM>. The containment vessel <NUM> may be submerged within a second containment vessel <NUM> which contains a fluid <NUM> with the same (or similar) refractive index as the resin <NUM>. This provides a flat interface where the refractive index changes and mitigates lensing effects which would arise at a curved interface of mismatched refractive index. Note that in the description of the above system, the coordinate notation is such that the x'-axis is stationary while the (x,y,z) coordinate system rotates with the resin containment vessel <NUM>.

Another embodiment of the system <NUM> shown in <FIG> may involve the use of a plurality of DLP projectors <NUM> (i.e., a plurality of optical subsystems) positioned to face each of the four vertical sides of the second containment vessel <NUM>, to generate the plurality of optical 2D projections. Still another embodiment may involve a modification to the system <NUM> shown in <FIG> in which the containment vessel <NUM> and the second containment vessel <NUM> are both held stationary, while the DLP projector <NUM> (i.e., the optical subsystem) is rotated on a doughnut shaped support 34a around the full circumference of the containment vessel <NUM> to produce the plurality of optical 2D projections.

Still another variation of the embodiment shown in <FIG> may involve using photo-degradable (i.e., photo-responsive) material instead of a resin. This variation of the embodiment is not covered by the claims. For example, one might start with a solid 3D block of photo-degradable material and use optical 2D projections as described herein to remove only certain portions of the solid 3D block to produce a desired 3D part. Such materials are used, for example, in tissue engineering.

Referring to <FIG>, a system <NUM> in accordance with another embodiment of the present disclosure is shown. With the system <NUM>, a resin volume <NUM> is contained within a stationary container <NUM>. A secondary container <NUM> may be used to hold an additional quantity of fluid 55a which has the same (or similar) refractive index as the resin volume <NUM>. An optical subsystem <NUM>, produces an optical projection <NUM> along and x axis (fixed relative to the stationary target volume). The 3D intensity map generated by the projection is rotated around the resin volume <NUM> (i.e., about z axis <NUM>, and propagating along a rotating x'-axis <NUM>) via a rotating arm assembly 50a. A stationary mirror <NUM> receives the projection <NUM> and feeds it to a collection of mirrors <NUM>-<NUM> contained within the rotating arm assembly 50a. The mirrors <NUM>-<NUM> direct the projection <NUM> to illuminate the resin volume. As the arm rotates, y'-z plane images are projected at many angles θ about the full circumference. As is the case with the other embodiments, the net exposure dose from the sum of the 3D intensity distributions generated from all of the projections over one rotation is such that regions where material formation is desired receive a sufficient dose to photo crosslink the resin while other regions receive an insufficient dose. Spatial and temporal modulation of the projections (i.e., modulation of image intensity of the 2D (y'-z) images being projected) <NUM> at each angle θ is controlled in the same way as described above for <FIG>, for example, by means of a spatial light modulator (SLM) <NUM> or DLP projector. The system <NUM> allows for potentially much faster rotation speeds compared to the methodology described in connection with <FIG>, as fluid motion considerations are eliminated. Compared to the methodology described in connection with <FIG>, the system <NUM> offers the advantage of a simpler optical system based in prior art. The proposed configuration shown in <FIG> can be applied with one or more simultaneously rotating optical projections. Similarly to the methodology described in connection with <FIG> the resin container <NUM> does not move relative to the fluid during fabrication, so the formation of more fragile, delicate or compliant structures is possible.

Finally, the optical signal multiplexing necessary to achieve Computed Axial Lithography could be performed by systems which share features of any or all of the embodiments described above. As one example, a light field projection display (<FIG>) which does not span a full <NUM>° of angular projection could be combined with a rotating vial, similar to what is used with system <NUM> of <FIG>, in order to expand the angular range. For example, consider the use of a curved display such as shown in <FIG>, which instead of having a cylindrical shape looks like a half-cylinder or a smaller angular section of a cylinder. It still projects images from multiple angles simultaneously but the range of angles spans less than <NUM> degrees (in the half cylinder case it's <NUM> degrees). However if that display is rotated about the resin volume and the projections are updated in time, then it is possible to span a full <NUM> degrees, even faster than what could likely be achievable in the embodiment shown in <FIG>. Such an embodiment would likely not print as fast as the <FIG> embodiment but it may be easier to fabricate. Similarly, target volume of resin could remain static while the < <NUM> degree projection display is rotated about the volume.

The system and method of the present disclosure surpasses recently reported volumetric aperiodic three-dimensional (3D) structure fabrication using holographic light fields in its geometric flexibility. Similarly, the inherently volume-based approach of the present disclosure provides an order of magnitude improvement in fabrication speed over conventional layer-by-layer "<NUM><NUM>/2D" printing techniques. Finally, the surface roughness problems imposed by layer-by-layer fabrication are substantially reduced if not removed entirely.

The system and method of the present disclosure is expected to find utility in a number of applications. For example, the system and method of the present disclosure provides an improvement to photopolymer-based additive manufacturing in a number of important aspects, such as more rapid part generation, improved surface quality (e.g., no "stair step" artifacts from layering), and a reduction of geometric constraints that arise from 2D layer slicing and simplified post-processing. Potential applications of the various embodiments and methods described herein may involve AM generated optics with high quality surface finish; hollow or overhanging structures; large dynamic range mesoscale AM structures; printing/fabrication on a previously fabricated 3D structure immersed in a resin; and processing soft, flexible or brittle polymers and geometrically delicate/fragile structures (as there is no relative structure/fluid motion during printing).

Claim 1:
A method of forming a three dimensional object, comprising:
providing a volume of photo-curable resin (<NUM>;<NUM>) contained within an optically transparent resin container (<NUM>;<NUM>), a z axis (<NUM>;<NUM>) extending through the volume of photo-curable resin (<NUM>;<NUM>) and an x' axis (<NUM>;<NUM>) extending normal to the z axis (<NUM>;<NUM>);
using an optical subsystem (<NUM>;<NUM>) to generate an optical two dimensional projection (<NUM>;<NUM>);
causing the optical two dimensional projection or the resin container (<NUM>;<NUM>) to rotate relative to the other to receive the optical two dimensional projection (<NUM>;<NUM>) around a complete circumference of the volume of photo-curable resin (<NUM>;<NUM>) while maintaining the optical two dimensional projection (<NUM>;<NUM>) directed through the volume of photo-curable resin (<NUM>;<NUM>),
wherein rotating the two dimensional projection or the resin container (<NUM>;<NUM>) to move relative to the other comprises
a) mounting the resin container (<NUM>) on a rotating mount or stage (<NUM>) and physical rotation of the resin container (<NUM>) about the z axis (<NUM>), or
b) rotating the optical subsystem (<NUM>) circumferentially about the resin container (<NUM>) to direct the optical two dimensional projections toward the volume of photo-curable resin (<NUM>) from the plurality of angles while the resin container (<NUM>) is held stationary, or
c) using a rotating arm assembly (50a) having a plurality of mirrors (<NUM>,<NUM>,<NUM>) configured to direct the optical two dimensional projections toward the volume of photo-curable resin (<NUM>) while the resin container (<NUM>) and the optical subsystem (<NUM>) are both held stationary,
and
wherein a two dimensional projection function of the optical two dimensional projection (<NUM>;<NUM>) is controlled at each angle θ to deliver a controlled three dimensional exposure dose over a fixed temporal exposure period, and where a plurality of two dimensional projections is generated from a plurality of angles θ, and where the plurality of two dimensional projections are summed to produce a three dimensional exposure dose in the volume of photo-curable resin (<NUM>;<NUM>) which is sufficient to cause photocuring in desired regions, while being insufficient to cause photocuring in undesired regions.