High dimensional volume additive manufacturing

Abstract

A three-dimensional (3D) printing apparatus includes: a light source including a plurality of pixels configured to emit a plurality of light beams toward an optical objective; an optical objective configured to diverge the plurality of light beams when the plurality of light beams exit the optical objective toward the resin volume; and one or more motors configured to translate the optical objective lens relative to the resin volume. The one or more motors are configured to translate the optical objective relative to the resin volume to apply the plurality of light beams to the plurality of voxels within the resin volume. Applying the plurality of light beams to the plurality of voxels solidifies the plurality of voxels. The optical objective applies a plurality of light beams such that each of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams.

Description

TECHNICAL FIELD

[0001] Embodiments described in this specification generally relate to apparatuses, systems, and methods for manufacturing three-dimensional (3D) objects. More specifically, embodiments described in this specification relate to apparatuses, systems, and methods that use exposure to cure a photosensitive resin to form 3D objects. BACKGROUND

[0002] Traditional volumetric additive manufacturing (VAM) printing uses three or fewer degrees of freedom (hereinafter “dimensions”) to manufacture objects. Examples of traditional VAM methods are computed axial lithography (CAL) and Xolography, both of which use three dimensions for printing. In CAL, two-dimensional images are typically exposed at a normal angle on a transparent cylinder containing resin that is rotated around one axis to achieve three total dimensions of exposure. Volumetric helical additive manufacturing is a variant of CAL that additionally translates the cylindrical vial along the axis of rotation using this additional translation to expand the effective size of the 2D image projector without gaining an independent degree of freedom, and can thus be classified as using the same dimensions as CAL. Xolography uses a linear translation in one dimension of a sheet of light of one color, projecting two-dimensional images sequentially from orthogonal dimensions. However, additional degrees of freedom can improve printing resolution, fidelity, and / or allow for printing of more complex structures. SUMMARY

[0003] This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is neither intended to identify key or essential features of the claimed subject matter nor is it used to determine or limit the scope of the claimed subject matter.

[0004] One or more embodiments described in this specification relate to a three-dimensional (3D) printing device. The 3D printing device includes a light source comprising a plurality of pixels configured to emit a plurality of light beams toward an optical objective, the optical objective configured to diverge the plurality of light beams as the plurality of light beams exit the optical objective toward a volume of resin, and one or more motors configured to translate the optical objective relative to the volume of resin. The one or more motors are configured to translate the optical objective relative to the volume of resin to apply the plurality of light beams to a plurality of voxels within the volume of resin. Applying the plurality of light beams to the plurality of voxels cures the plurality of voxels. The optical objective applies the plurality of light beams such that each voxel of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams. The at least two different light beams expose each voxel at two different times such that the at least two different light beams only spatially overlap in each voxel. A total exposure amount to cure the volume of resin in each voxel is at least equal to a sum of exposure amounts of the at least two different light beams at each voxel.

[0005] One or more embodiments described in this specification relate to a method for operating a 3D printing device. The method includes controlling a light source comprising a plurality of pixels to emit a plurality of light beams toward an optical objective, diverging the plurality of light beams via the optical objective as the plurality of light beams exit the optical objective toward a volume of resin, translating the optical objective relative to the volume of resin via one or more motors, applying the plurality of light beams to a plurality of voxels within the volume of resin by translating the optical objective relative to the volume of resin, curing the plurality of voxels by applying the plurality of light beams to the plurality of voxels, applying the plurality of light beams via the optical objective such that each voxel of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams, and exposing each voxel at two different times via the at least two different light beams such that the at least two different light beams only spatially overlap in the each voxel. A total exposure amount to cure the volume of resin in each voxel is at least equal to a sum of exposure amounts of the at least two different light beams at each voxel.

[0006] One or more embodiments described in this specification relate to a system for 3D printing. The system comprises: a light source comprising a plurality of pixels configured to emit a plurality of light beams toward an optical objective; the optical objective configured to diverge the plurality of light beams as they exit the optical objective toward a resin volume; one or more motors configured to translate the optical objective relative to the resin volume; a processor configured to control the one or more motors to thereby control translation of the optical objective relative to the resin volume; a memory storing instructions for translating the optical objective relative to the resin volume; wherein the processor controls translation of the optical objective relative to the resin volume based on the instructions to apply the plurality of light beams to a plurality of voxels within the resin volume. Applying the plurality of light beams to the plurality of voxels causes the plurality of voxels to solidify. The processor controls translation of the optical objective to apply the plurality of light beams such that each voxel of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams. The processor controls translation of the optical objective such that the at least two different light beams expose each voxel at two different times. The at least two different light beams at the two different times only spatially overlap in each voxel. A total amount of exposure to cause the resin volume in each voxel to solidify is at least equal to a sum of the exposure amounts of the at least two different light beams at each voxel.

[0007] Other aspects and advantages of the claimed subject matter will become apparent from the following description and accompanying claims. BRIEF DESCRIPTION OF DRAWINGS

[0008] Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying drawings. Like reference numerals can be used to identify like elements throughout the accompanying drawings. The size and relative positions of elements in the drawings accompanying this disclosure are not necessarily drawn to scale. For example, the shapes of various elements and angles are not necessarily drawn to scale, and can have been arbitrarily enlarged and positioned to improve drawing legibility. Further, the specific dimensions and other numerical details are not to be construed as limiting, but rather as exemplifying one way of implementing the application.

[0009] Figures 1A-1C Print dimensions (i.e., degrees of freedom) are shown relative to the angle of illumination.

[0010] Figure 2 Six print dimensions are shown using light from a single point on an image display chip to illuminate a resin volume, here labeled as a point spread function (PSF).

[0011] Figure 3AA 3D schematic of a 3D printer is shown in accordance with one or more embodiments of the present disclosure.

[0012] Figure 3B A 3D schematic of a 3D printer is shown in accordance with one or more embodiments of the present disclosure. Figure 3A A longitudinal cross-section of the schematic shown in

[0013] Figure 4A A longitudinal cross-section of the schematic shown in Figure 4B Operation of a 3D printer in accordance with one or more embodiments is shown.

[0014] Figures 5A-5C Discretization of an object model in accordance with one or more embodiments is shown.

[0015] Figure 6 A system for 3D printing in accordance with one or more embodiments is shown.

[0016] Figure 7 A flowchart of 3D printing in accordance with one or more embodiments is shown.

[0017] Figures 8A-8C 3D printing in a cylindrical coordinate system in accordance with one or more embodiments is shown.

[0018] Figures 9A-9D A target object, a computed intensity, a computed dose, and an error for 3D printing of a target object in a cylindrical coordinate system in accordance with one or more embodiments are shown.

[0019] Figure 10A A close-up view of a target object and a target object boundary in accordance with one or more embodiments is shown. Figure 10B A close-up view of a target object and a target object boundary in accordance with one or more embodiments is shown.

[0020] Figure 11 A dose target for a target object and a close-up view of the dose target in accordance with one or more embodiments is shown. Figure 10A A dose target for a target object and a close-up view of the dose target in accordance with one or more embodiments is shown.

[0021] Figure 12 An image set computed by forward projection of a dose target shown in Figure 11 An image set computed by forward projection of a dose target shown in

[0022] Figure 13 A computed error between an object of a back-projection and a dose target shown in Figure 11 A computed error between an object of a back-projection and a dose target shown in

[0023] Figures 14A-14C A forward projection of an error shown in Figure 13 A forward projection of an error shown in

[0024] Figure 15 An error with respect to the iteration is shown in accordance with one or more embodiments.

[0025] Figure 16 A final image set of the image set shown in Figures 14A-14C is modified based on the error shown in Figure 15 . Figure 12

[0026] Figure 17 A final object to be printed based on the final image set of Figure 16 is shown in accordance with one or more embodiments.

[0027] Figure 18A An error and a close-up view of the error between the final object of Figure 18B and the dose target of Figure 17 are shown in accordance with one or more embodiments. Figure 11

[0028] Figure 19 A flowchart of determining a final image set for 3D printing of an object in accordance with one or more embodiments is shown.

[0029] Figure 20 A computer system for 3D printing of an object in accordance with one or more embodiments is shown. DETAILED DESCRIPTION

[0030] In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure can be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.

[0031] Throughout the application, ordinal numbers (e.g., first, second, third, etc.) can be used as adjectives to refer to elements (i.e., any noun in the present application). The use of ordinal numbers does not imply or create any particular order to the elements, nor limit any element to only a single element, unless explicitly disclosed, e.g., using the terms “before,” “after,” “single,” and other such terms. Rather, the use of ordinal numbers is to distinguish between elements. As an example, a first element is distinct from a second element, a first element can contain more than one element and be ordered after (or before) a second element in an ordering of elements.

[0032] In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure can be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description. Figure 20 ​​In the description of embodiments set forth in the specification, any component described with reference to a drawing can be identical to one or more similarly named components described with reference to any other drawing. Descriptions of these components will not be repeated for every drawing for the sake of brevity. Thus, every embodiment of a component in each drawing is incorporated by reference within, and assumed to optionally exist within, every other drawing having one or more similarly named components. Additionally, any description of a component in one drawing is to be interpreted as an optional embodiment that can be implemented in addition to, in conjunction with, or in place of, the embodiments described with respect to the corresponding similarly named component in any other drawing, in accordance with the various embodiments disclosed in the specification.

[0033] It should be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a wellbore” includes reference to one or more of such wellbores.

[0034] Terms, such as “approximately,” “substantially,” and the like, refer to allowing a margin or variation (including, for example, tolerances, measurement errors, measurement accuracy limitations, and other factors known to those skilled in the art) to occur in an amount that does not exclude the effect the characteristic is intended to provide.

[0035] It should be understood that one or more of the steps shown in the flowcharts can be omitted, repeated, and / or executed in a different order than shown. Thus, the scope of the disclosure should not be considered limited to the particular arrangements of steps shown in the flowcharts.

[0036] Embodiments disclosed in the specification relate to three-dimensional (3D) printing of an object by irradiating light onto a resin. Throughout the text of the present disclosure, 3D printing is also referred to as volume additive manufacturing (VAM). To this end, an image set is created using a model of the object. The image set is then irradiated into the resin through an optical objective (hereinafter simply “objective lens”). Irradiation of the image set onto the resin causes the resin in a region corresponding to the model of the object to solidify. The solidified resin is then extracted from the resin, which is the printed object. To this end, the solidified resin can be put into a bath to wash away the non-solidified resin.

[0037] Embodiments disclosed in the specification describe a new class of VAM architectures. The classical VAM approach, computed axial lithography (CAL), projects 2D images into a volume rotating around a single axis, thus providing a 3D spatial projection (hereinafter simply “spatial addressing”) of light onto the resin. This arrangement is shown in Figure 1A Specifically, Figure 1AA digital micromirror device (DMD) 104 is shown projecting 2D images onto a resin 102. Note that the lens implementing the projection is not shown, but is well known to those skilled in the art. The resin 102 can be arranged in a liquid form in a cylindrical container. By rotating the cylindrical container about its axis of rotation (central axis), the DMD 104 can project images onto the resin in three dimensions, two of which are the two-dimensional array of pixels arranged on the DMD projection, and one is the rotational dimension of the resin 102. For example, by selecting appropriate pixels on the DMD 104 to turn on, Figure 1A a single voxel of the resin 102 in the image set can be uniquely addressed by having a light ray intersect that voxel, where one image from the image set illuminates the resin at one rotational angle of the resin.

[0038] Tilting the axis of rotation relative to the projection direction of the DMD 104 can be seen as reducing the dimensionality of the spatial addressing to less than 3, thereby reducing the printing capability. This reduction in spatial addressing is illustrated in Figure 1B and Figure 1C Specifically, if the images are projected parallel to the axis of rotation of the resin 102, as shown in Figure 1C , then 3D addressing is lost. This is because the rotation of the resin 102 does not provide any additional addressing of the resin 102 relative to the 2D illumination of the DMD 104. Thus, Figure 1C the configuration simplifies to a 2D printer, similar to conventional photolithography. Figure 1B The transition between Figure 1A and Figure 1C is shown. In Figure 1B , the angle between the optical projection of the DMD 104 and the axis of rotation of the resin 102 is between 0 and 90 degrees. Thus, in Figure 1B , the control of the printed structure varies between 3D corresponding to Figure 1A and 2D corresponding to Figure 1C . In other words, Figure 1B the configuration can be thought of as fractional dimensional addressing of the resin 102 between 2 and 3 independent dimensions. Thus, the configuration shown in Figures 1A-1C can be characterized as providing variable dimensional addressing of the resin 102, where the dimensionality ranges from 3 to 2.

[0039] As the dimensionality increases from 2 (in which case 3D printing is not possible) to 3 (similar to conventional CAL), various 3D printing metrics improve. These metrics include the minimum size of a 3D printed voxel, the complexity of a printable object, and the contrast between the optical dose deposited by the printer in the interior and exterior regions of the printed object. According to one or more embodiments, increasing the dimensionality of the written images can improve such printing quality metrics.

[0040] One or more embodiments describe a novel printing architecture that effectively prints in more than 3 dimensions. As Figure 2 illustrated, the intensity projected from a single pixel of a display device has a 3D shape, which is referred to as a point spread function (PSF). One common PSF is a Gaussian beam. Like a solid, the PSF has six degrees of freedom (often referred to as “rigid body modes”). Of the six degrees of freedom, three are translations 202 along Cartesian axes, and the remaining three are rotations 204 about the Cartesian axes. Typically, the PSF is rotationally symmetric about the axis of optical propagation. In the symmetric case, rotation about that axis does not change the light distribution in the resin, reducing the number of available modes to five. Furthermore, conventional CALs use a large focal depth “pencil beam” PSF, which is invariant to translation along the optical axis (e.g., along the longitudinal axis in the Cartesian axes illustrated in Figure 2 FIG. 1). This configuration reduces the number of effective modes to four. However, Gaussian beams with a focal depth smaller than the resin are well known in imaging tomography and have been explored for CALs.

[0041] As illustrated, conventional CALs use a DMD 104 to translate the PSF in two lateral dimensions corresponding to a two-dimensional grid of pixels. Furthermore, the resin 102 is rotated about an axis orthogonal to the direction of optical propagation. Thus, conventional CALs correspond to three of the possible six degrees of freedom illustrated in Figure 1A FIG. 1— two translations 202 along two Cartesian axes of the projected DMD pixels and one independent rotation of the resin relative to the projected image. However, Figure 2 it is shown that the projected light can be rotated and translated in up to six dimensions (i.e., degrees of freedom). Figure 2

[0042] ​According to one or more embodiments, in VAM printing, an optical image set must first be determined. Illumination of the optical image from outside the resin volume causes the resin to solidify into a shape approximating the desired 3D object. This is an inverse problem that needs to be solved. In tomographic imaging, this inverse problem can be more easily solved with the addition of "useful" additional images. A "useful" image is one that adds important information not present in the remainder of the image set. For example, increasing the density of images presented during a rotation can be useful, but only up to the limits known in tomographic imaging. In contrast, according to one or more embodiments, the quality of the inverse solution can be improved by adding images that are incident at a different position or angle than those in the original image set. This can be understood by considering the desired dose delivered to the resin volume as a set of constraints and the intensity of each pixel in the image set as a variable that can be used to satisfy the constraints. The intensity of each pixel sampled at each voxel in the resin volume forms a set of linear equations that relate the variables (pixel intensities) to the constraints (voxel dose). The more independent variables, the better the possible solution. In this context, "independent" is essentially the same as the "useful" concept introduced earlier. That is, adding an image set with a different PSF can improve the solution.

[0043] Figure 3A and Figure 3B and Figure 4A and Figure 4B A 3D printer (i.e., 3D printing device) according to one or more embodiments is shown. In one or more embodiments, the 3D printer is configured such that a plurality of independent light rays (i.e., beams) can pass through voxels in the resin at different angles. To this end, an image set providing a set of angles can be determined. A light source 402 comprising a plurality of pixels illuminates a plurality of beams 302 through an objective lens 306. When the plurality of pixels are on, a cone of light 408 is formed. The objective lens 306 causes the diverging beams 304 (out of the objective lens) to travel in the resin 310. By moving the objective lens 306 relative to the resin 310 and specifically selecting the images in the image set, the 3D printer is able to control the angle of illumination of the diverging beams 304 and the voxels in the resin 310 that the beams are illuminated in. Controlled application of the diverging beams 304 to the voxels causes the voxels to solidify and create an object.

[0044] In one or more embodiments, the divergence of the light beams can be between 30 degrees or more of half angle from the optical axis as measured in air. According to one or more embodiments, higher divergence of the light beams can improve the resolution of the final printed object. This is because higher divergence is able to cause individual beams illuminating individual voxels to have a greater angle of rotation, thereby more fully utilizing the relevant rotational degrees of freedom. Thus, as mentioned previously, higher divergence can improve the print quality metric.

[0045] According to one or more embodiments, the objective lens that diverges the light beams can be a single objective lens, or can be one or more optical components that diverge the light beams. For example, the objective lens can include one or more lenses, one or more mirrors, or any of one or more custom objective lenses or commercial objective lenses, which in combination can bend the light beams. Thus, the term "objective lens" as used herein refers to a set of optical components arranged to convert an array of pixels having modulated intensity into an array of point spread functions having a desired size, shape, and direction of propagation within the resin.

[0046] Throughout the text of the present disclosure, solidifying a voxel means that the viscosity of the resin in the voxel is increased via exposure to the point that the printed object can be extracted from the remaining resin. For example, in one or more embodiments, a solidified voxel can be in the form of a gel that is able to maintain its shape. Those skilled in the art of photochemistry will recognize that there are many materials and reactions that can satisfy this description, including photopolymerization and photoisomerization.

[0047] In particular, a 3D printer according to one or more embodiments includes a light source 402 that includes a plurality of pixels configured to emit a plurality of light beams 302 toward objective lenses 406-1, 406-2. The objective lenses 406-1, 406-2 are configured to diverge the plurality of light beams 404 as they exit the objective lenses 406-1, 406-2 toward a volume of resin 410. The resin 410 is contained in a container 412. The container 412 is configured so that the diverging light beams 404 can pass through the container 412 into the resin 410. For example, the container 412 can include a transparent top side so that the diverging light beams 404 are able to pass through to reach the resin 410. In one or more embodiments, the container 412 can not include a top side, and the resin 410 can be directly exposed to the diverging light beams 404. The objective lenses can be separated from the top side or the resin by air, or, as is known in the art, the intervening space can be filled with a material having a refractive index higher than air (i.e., higher than 1) in order to be able to achieve greater angles of propagation of the light beams within the resin. Such a coupling material can include oil, water, various elastomers, or can be the resin itself.

[0048] In one or more embodiments, the 3D printer includes one or more motors configured to translate the objective lens 406-1, 406-2 relative to the resin 410. The motors are configured to translate the objective lens 406-1, 406-2 relative to the resin 410 to apply the light beam 404 to a plurality of voxels within the resin 410. To this end, the motors are configured to translate the objective lens 406-1, 406-2 relative to the resin 410. For example, the motors can be coupled to and move the objective lens 406-1, 406-2. Alternatively, the motors can be coupled to and move the container 412, or both the objective lens 406-1, 406-2 and the container 412 to translate the objective lens 406-1, 406-2 and the resin 410 relative to each other. In one or more embodiments, the motors can be stepper motors, voice coil motors, piezoelectric motors, or combinations thereof. However, embodiments of the present invention are not limited to the type of motor.

[0049] In embodiments disclosed in this specification, moving the objective lens relative to the resin is not limited to moving only the objective lens, unless specifically stated. Moving the objective lens relative to the resin can be any of moving the objective lens, moving the resin, or moving both. Furthermore, these motors can move only a portion of the device including the objective lens, thereby moving or altering the light within the resin without moving the entire objective lens relative to the resin. For example, a turning mirror can be rotated to redirect or reposition the light directed at the resin. Other actuators known in the art include deformable mirrors and liquid lenses that can be used to alter the depth of focus or shape of the PSF. These actuators need not be mechanical, but can also use opto-electric processes (e.g. electro-optic, liquid crystal, or other well-known physical properties) to modify the function of the objective lens such that the PSF is modulated in a "useful" manner as defined previously.

[0050] In one or more embodiments, a motor moves objective lenses 406-1 and 406-2 to apply diverging light beams 404 such that each voxel in a plurality of voxels is exposed by at least two different light beams 404 from the plurality of light beams. To achieve this, two different light beams 404 expose a voxel at two different times, such that the two different light beams spatially overlap only within that voxel. Specifically, a motor moves objective lens 406-1 to position 1. In position 1, light source 402 illuminates image 1, wherein pixels of light source 402 illuminate light beams 404 such that the diverging light beams 404 exiting objective lens 406-1 pass through the voxel. Then, a motor moves the same objective lens in position 1 to position 2. The objective lens in position 2 is indicated by reference character "406-2." In position 2, light source 402 illuminates image 2, wherein pixels of light source 402 illuminate light beams 404 such that the diverging light beams 404 exiting objective lens 406-2 pass through the voxel at a different angle than the diverging light beams 404 corresponding to position 1. Thus, the voxel receives exposure from the beam 404 corresponding to position 1 and the beam 404 corresponding to position 2. In a similar manner, the 3D printer exposes multiple voxels with beams at different angles to cure the resin at those voxels to create the object.

[0051] According to one or more embodiments, the 3D printer can solidify the voxels by exposing the voxels with at least two light beams at different angles. Figure 4A An example of exposing a voxel with two light beams at different angles is shown in FIG. The total exposure amount for curing the resin 410 in the voxel is at least equal to the sum of the exposure amounts of the at least two different light beams 404 at the voxel.

[0052] In one or more embodiments, the image set or the movement of the objective lenses 406-1, 406-2 can be selected so that more than two beams from different angles are exposed to the voxel, thereby curing the resin at the voxel as desired. Figure 4A The objective lens shown in FIG can then be moved to position 3 and the voxel is illuminated at a third angle different from the angles corresponding to positions 1 and 2. According to one or more embodiments, the number of shots, the images in the image set, and the angle of illumination are calculated for each voxel in the print area so that: the voxels inside the object forming the object are exposed sufficiently to be cured; and the voxels outside the object are exposed sufficiently low to remain in their liquid form so that they can be separated from the object.

[0053] Calculate the necessary irradiation at each voxel as Figures 5A-5C Specifically, Figure 5A The object model 502 is discretized into a 3D grid of voxels 506. The voxels are then printed using a beam 504. Assume that in order to print a voxel, the beam 504 must be irradiated at a point (x0, y0, z0), such that Figure 5BAs shown. Figure 5C As shown, when the light beam 504 is irradiated on the voxel 508, the light beam 504 also passes through other voxels 510, 512 in the grid. Such irradiation on the other voxels 510, 512 can be considered as residual exposure. According to one or more embodiments, in order to determine the image set and the translation of the objective lens relative to the resin, the overall (total) exposure at each voxel can be calculated, including the residual exposure. In other words, the image set and the translation of the objective lens relative to the resin are determined so that the overall exposure at each voxel within the object model is high enough to cure the resin at that voxel. Conversely, the image set and the translation of the objective lens relative to the resin are determined so that the overall exposure at each voxel outside the object model is low enough so that the resin at that voxel will not cure.

[0054] also, Figure 4A In each of positions 1 and 2, only one pixel is shown turned on. This illustration is for the purpose of simply demonstrating the operation of a 3D printer according to one or more embodiments. However, at each position, the image corresponding to the position can be selected so that multiple pixels are turned on. In this way, multiple voxels can be addressed at each position of the objective lens relative to the resin. For example, Figure 4B A prototype according to one or more embodiments is shown, in which a light beam 414 is irradiated from an objective lens 406-1 in position 1 and an objective lens 406-2 in position 2 into a resin disposed in a container 412. According to one or more embodiments, the container 412 can be configured to contain the resin 410 such that the surface of the resin 410 into which the light beam 404 enters is flat and perpendicular to the axial direction (i.e., the optical axis) of the objective lenses 406-1, 406-2.

[0055] According to one or more embodiments, the light source 402 may include a DMD configured to reflect a plurality of light beams toward the resin 410 .

[0056] According to one or more embodiments, the light source 402 may include one or more lasers that generate a plurality of light beams. The light source 402 may include one or more mirrors or prisms that reflect the light beams toward the objective lenses 406-1, 406-2.

[0057] According to one or more embodiments, the 3D printer may collimate multiple light beams before entering the objective lens. For example, the 3D printer may include a collimator including one or more lenses, one or more prisms, or one or more reflectors before the objective lens. Figure 3B An example is shown in FIG, where the light beam 302 is collimated before entering the objective lens 306.

[0058] According to one or more embodiments, the objective lens can be an oil immersion objective lens. The output end of an oil immersion objective lens is immersed in, for example, a drop or film of oil, the resin itself, or an elastomeric solid. In one or more embodiments, immersing the objective lens in a medium with a refractive index greater than 1 enables the light beam to have a greater angular divergence within the resin with a refractive index greater than 1. This technique is used in various optical technologies including lithography and microscopy, and is known to include various coupling materials, including water or elastomers, and evanescent coupling across a thin air gap known as “solid immersion.”

[0059] According to one or more embodiments, the motor is configured to move the objective lens relative to the resin along at least two axes that are orthogonal to an axial direction of the objective lens. For example, in Figure 3A and Figure 4A the motor can move the objective lens 306, 406-1, 406-2 relative to the resin along two axes within a plane that is orthogonal to an axial direction of the objective lens. In Figure 3A and Figure 4A the axial direction of the objective lens 306, 406-1, 406-2 is a longitudinal axis along an illumination direction of the collimated light beam 302. According to one or more embodiments, the two axes within the plane can be orthogonal to each other.

[0060] In one or more embodiments, the motor can move the objective lens relative to the resin along an axial direction of the objective lens. This additional degree of movement enables shaping of the light beam size at the voxel.

[0061] Figure 6 A schematic diagram of a system 600 according to one or more embodiments is shown. The system 600 includes, for example, a buffer 602 and a 3D printer 606, examples of which are discussed above with reference to Figure 3A and Figure 3B and Figure 4A and Figure 4B The buffer 602 can be implemented in hardware (i.e., circuitry), software, or any combination thereof. The buffer 602 is configured to store a print object file 604. The print object file 604 can include an object model and instructions to print the object model using the printer 606. Based on the print object file 604, the printer 606 can print an object corresponding to the object model. To implement the printing function, the printer 606 includes one or more motors 608, a light source 610, an objective lens 612, and a container 614 containing a resin. Examples of the motors 608, the light source 610, the objective lens 612, and the container 614 are described above with reference to Figure 3A and Figure 3B and Figure 4A and Figure 4B As discussed below with reference to Figure 20Further described, the system 600 can include a processor that controls operation of the one or more motors 608 and the light source 610 for performing a printing function. For example, based on the print object file 604, the processor can control the light source 610 to project a set of images and control the translation of the objective lens 612 relative to the resin, as discussed above with reference to Figure 4A and Figure 4B .

[0062] Figure 7 A flowchart of a method for operating a 3D printer is shown in accordance with one or more embodiments. In one or more embodiments, one or more steps shown in Figure 7 may be omitted, repeated, and / or performed in a different order than shown in Figure 7 . Accordingly, the scope of the application should not be considered limited to the specific arrangement of steps shown in Figure 7 . The steps 700-735 shown in Figure 7 are explained below.

[0063] In step 700, a light source comprising a plurality of pixels is controlled to emit a plurality of light beams toward an objective lens. Examples of this step are shown above with reference to Figure 3A and Figure 3B , Figure 4A and Figure 4B , and Figure 6 . For example, the processor can control the light source 402 shown in Figure 4A to project a set of images.

[0064] In step 705, the plurality of light beams are diverged via the objective lens as the plurality of light beams exit the objective lens toward a resin volume. Examples of this step are shown above with reference to Figure 3A and Figure 3B , and Figure 4A and Figure 4B . For example, the objective lens 306 shown in Figure 3B diverges the light beams 304 before the light beams 304 enter the resin 310.

[0065] In step 710, one or more motors translate the objective lens relative to the resin.

[0066] In step 715, the plurality of light beams are applied to a plurality of voxels within the resin volume by translating the optical objective lens.

[0067] In step 720, the plurality of voxels are solidified by applying the plurality of light beams to the plurality of voxels.

[0068] In step 725, the optical objective lens applies the plurality of light beams such that each voxel of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams.

[0069] In step 730, at least two different light beams expose each voxel at two different times such that the at least two different light beams spatially overlap only in each voxel.

[0070] In step 735, a total exposure amount that cures a resin volume in each voxel is determined to be at least equal to a sum of exposure amounts of the at least two different light beams at each voxel.

[0071] Examples of steps 710-735 are also shown above with reference to Figure 4A and Figure 4B and Figure 6 .

[0072] Based on the embodiments disclosed in the present specification, the method can include one or more steps. For example, according to one or more embodiments, the application of the at least two light beams can be such that the at least two different light beams have different angles from each other. According to one or more embodiments, the method can include reflecting the plurality of light beams toward the resin volume. According to one or more embodiments, the method can include collimating the plurality of light beams before the plurality of light beams enter the optical objective. According to one or more embodiments, the method can include translating the objective along at least two axes that are orthogonal to an axial direction of the optical objective.

[0073] A 3D printer according to one or more embodiments can be advantageous compared to conventional VAMs. For example, unlike CAL, in which a resin sample is rotated in front of the projected light (e.g., in a cylindrical container), one or more embodiments disclosed in the present specification can provide more angular diversity. Furthermore, a 3D printer according to one or more embodiments will free the resin to be packaged into almost any geometry, such as Figure 3A and Figure 3B and Figure 4A and Figure 4B shown. Due to the higher degrees of freedom, e.g., four or more degrees of freedom according to one or more embodiments, more complex patterns with higher resolution can potentially be printed. To elaborate, according to one or more embodiments, a single voxel can experience light tilted along two orthogonal axes (at different times), rather than just one. According to one or more embodiments, unlike conventional VAMs, the translation of the light beams relative to the resin is not limited; a motor can potentially translate the objective to any position scaled in commercial units.

[0074] In conventional VAMs, the bundle of light corresponding to each pixel must pass through the thickness of the resin approximately aligned, performing a minimum bundle diameter due to the physical properties of diffraction. On the other hand, in a 3D printer according to one or more embodiments, the thickness of the resin and the lateral dimensions of the translation of the objective are not coupled.

[0075] One or more embodiments disclosed in this specification relate to a method and system for printing a 3D object based on an object model. In particular, one or more embodiments relate to a method and system for generating a set of images to be projected by a light source. Reference is made above to Figure 4A An example of a set of images projected by a light source 402 is shown. The set of images must be selected / computed in accordance with the translation of the objective lens to achieve the desired 3D object. To this end, the intensity must be selected for each pixel at each angle to make the 2D slices of the 3D part. According to one or more embodiments, the 3D object model is addressed by the images in four effective dimensions (degrees of freedom); pixel row + pixel column = 2D, then translation through two dimensions = two more dimensions. These translations are independent dimensions because the multiple beams of light emanating from the objective lens diverge at two angles. If the multiple beams of light are parallel or near parallel, then the translation will not impose a "useful" change in illumination, as described previously and as Figure 2 shown.

[0076] To determine the set of images and their translation to the object, the inverse (image to object) and forward (object to image) projections must be determined. In this disclosure, the inverse projection is also referred to as "back projection". The inverse projection can be defined as a matrix B that converts the intensities of the images in the image space (i.e., the space in which the set of images exists) to the dose deposited in the object in the object space (i.e., the space in which the object and object model exist). Conversely, the forward projection can be defined as a matrix F that converts the quantities (e.g., dose or error of the desired dose with respect to the target) defined throughout the object or object model in the object space to the images in the image space. The B and F matrices can be determined by the optical system of the 3D printer projecting the light and then determining the refraction of the light through the resin, and / or via simulations or calculations corresponding to the physical properties of refraction, diffraction, lens aberrations, scattering, or other relevant optical and material physical properties.

[0077] Turning to the explanation of the method of determining the set of images and converting the set of images to the object space, for simplicity, the method is explained in a cylindrical coordinate system, for example as Figures 8A-8C shown in FIG. 8A according to one or more embodiments. However, the embodiments are not limited to describing the object in a cylindrical coordinate system, but other coordinate systems can be used, for example a Cartesian coordinate system, examples of which are described above with reference to Figure 4A FIG. 7.

[0078] Figure 8A A 3D printing of an object described in a cylindrical coordinate system according to one or more embodiments is shown. In particular, in Figure 8A FIG. 8A, a 2D array of pixels S 802 irradiates beams of light into a cylinder containing resin. Similar to a conventional VAM, by rotating the cylinder and projecting a set of images through the array of pixels associated with the rotation of the cylinder, a 3D object can be printed.Figure 8B A slice of the print region is shown for angle Θ = 0 only. Figure 8C A slice of the print region is shown for angle Θ = 0 only. Figure 8B A close-up view of the slice shown above as a horizontal cut. In Figures 8A-8C In the middle, the “x” and “z” coordinates are along the plane of the pixel array S and perpendicular to “y”. Figure 8B In the middle, the “x” and “z” coordinates are along the plane of the pixel array S and perpendicular to “y”. Figure 8C The intensity levels to the right of the slice show the dose intensity in the spatial region shown in the graph. Throughout the text of this disclosure, dose intensity is also referred to as object intensity, dose intensity, or object dose.

[0079] According to one or more embodiments, an advantage of a cylindrical coordinate system can be that for rotationally symmetric objects, only a single angle can need to be computed. All other angles can be computed by a cyclic shift (i.e., incrementing Θ) because the motion trajectory and the representation of the object are in the same coordinate system. For example, for a typical VAM system using 1° angular intervals, rotational symmetry can save 360 times the computation time and possibly storage. Similarly, for systems in which the motion of the objective lens relative to the resin is most easily described as a translation in a Cartesian coordinate system, it can be advantageous to describe the object in a Cartesian coordinate system. In general, the choice of coordinate system for describing the object can exploit the symmetry of the printer to reduce storage or other computational resources.

[0080] According to one or more embodiments, the relationship of object dose to image intensity is considered to be linear. That is, the back-projection operation can be represented as a matrix vector multiplication B x I = O, where I is a vector of all image pixels (at all locations s and all angles) and O is a vector of all object voxels (here at all radii “r” and all angles Θ). B is a matrix with equal to the number of all image pixels and the number of all object voxels. As previously mentioned, this can be too large to actually generate or store. However, according to one or more embodiments, the computation can be reduced by computing sub-matrices of B for only the pixel array S and all object voxels at one location of the motion system (e.g., at Θ for a rotating printer like CAL). Based on the fact that the motion trajectory is a circle, the sub-matrices can be cyclically shifted (i.e., incremented by Θ) to compute the matrix for all angles. For example, the matrix for Θ = 0 can be computed, and then the matrix for Θ = 1° can be computed by cyclically shifting the matrix for Θ = 0 by 1°. This process can be repeated for all angles. Figure 8BThe sub-matrices of B can be quite sparse, as the number of zero values shown (most of the slices in the figure are black (i.e. no dose intensity)). Thus, the sub-matrices of B can be represented numerically using "sparse matrices" that store only non-zero values. Storage and mathematical manipulation of such "sparse matrices" is standard in modern computing languages such as MATLAB. For typical problems, the sparse matrices can be less than 1% of the full matrix size. Furthermore, computation at only one motion position (e.g. one angle) and matrix sparsity can reduce memory usage and time requirements by 4 to 5 orders of magnitude. While a typical cylindrical coordinate system for CAL is shown, where the cylindrical resin vial is rotated about its axis, this discussion applies broadly to any volumetric printer where the motion of the objective relative to the resin can be chosen as the axes of the coordinate system. Thus, Figure 4A and Figure 4B Translation motion as shown in FIGS. 1 1 and 12 can be most efficiently represented in a Cartesian coordinate system, which can result in storage savings for the projection matrix as described above if this Cartesian coordinate system is used to represent the object.

[0081] According to one or more embodiments, generating the full B matrix can be accomplished by indexing the sub-matrices of B (at one position of the objective, e.g. at 0). This can save storage, as sparse matrices can make computation and storage of B feasible. As mentioned above, in the case of rotational symmetry of the object in a cylindrical coordinate system, computation can only need to be done once for one angle. Similar logic applies to the matrix F that performs the forward projection, which relies on the same computation and can be written using the same sparse matrix represented as O x F = I.

[0082] According to one or more embodiments, by using sparse matrices, the forward and inverse projections can be performed faster than traditional methods. According to one or more embodiments, a single sub-matrix can be computed, which can then be matrix multiplied with the object O or intensity I vector, and then summed over motion (e.g. rotation angles) with appropriate indexing to represent the motion. This approach can replace one dimension of the operations done by the full B and F matrices with an iterative sum (e.g. a "for" loop), thus saving storage.

[0083] Thus, by choosing a coordinate system that remains constant for the motion of the object relative to the image, the discretization of the object can be significantly improved in terms of storage or speed of mathematical operations. According to one or more embodiments, for translation motion, a grid can be chosen that remains constant for one dimension (for one-dimensional translation) or two dimensions (for two-dimensional translation). This can include a Cartesian grid, but other choices are possible. For example, a 2D translation layout can not need to be translated as a 2D Cartesian raster, but can be moved in a cylindrical coordinate system.

[0084] There are three general approaches (1)-(3) that can be used to compute the image set for projection.

[0085] (1) Filtered Back Projection (FBP) (known from computed tomography techniques) - This approach produces negative intensities that do not make physical sense. The negative intensities are truncated to the minimum value of zero. This approach can result in poor print fidelity.

[0086] (2) Gradient Descent (GD) in image space - This approach uses traditional optimization methods to improve the object. It is computationally expensive and requires knowledge of the derivative of the merit function representing the quality of the object at each pixel. The computation of these gradients is expensive and not always accurate, resulting in poor convergence.

[0087] (3) Object Space Model Optimization (OSMO) - This approach applies the FBP method to an "object model" in object space that is allowed to not make physical sense (e.g., allowed to use negative values). However, the back projection of this model generates the optimal object. This approach attempts to force the interior of the (to be solidified) object to be above the upper threshold dose intensity D 上 , and force the exterior of the (must remain liquid) object to be below the lower threshold dose intensity D 下 .

[0088] The method described below according to one or more embodiments can provide at least the following advantages. One advantage of the method is that feedback can be derived from a simple comparison of the object to two target dose thresholds (D 上 and D 下 ). In contrast, gradient descent in image space requires estimation of the derivative of some error metric at each pixel intensity. Another advantage is that the error metric can be derived from the object. The error metric, which will be described further below according to one or more embodiments, can make it simple and natural to include material physics that occurs within the object. The material physics can include inhibition, non-linear response, or diffusion. These physical properties can be more difficult to include when using gradient descent of images.

[0089] According to one or more embodiments, the following new methods are described: 1) direct matrix solution and 2) forward projection of the object error.

[0090] 1) Direct Matrix Solution

[0091] According to one or more embodiments, when the entire object is known (i.e., a dose value is given, rather than an inequality), the above-mentioned back-projection matrix B can be used to find a least squares optimal solution. That is, if B has a sufficient rank, the linear system B×I=O can be solved for I. It is well known in the field of linear algebra that the solution does not require inverting the matrix B, but rather the system can be solved by matrix decomposition (e.g., QR decomposition). These solution methods minimize the error between the realized object O=B×I and the target object. An example according to one or more embodiments is shown in FIG9 . In FIG9 , a photograph of a female face is selected as an exemplary object, where the dose of the entire part is known.

[0092] This method does not guarantee that the non-negativity constraint is satisfied. That is, negative intensities are allowed. However, this constraint can be satisfied by reducing contrast and smoothing the object. Figure 9A The target object, i.e. the printed target, is shown. Figure 9A In , the minimum dose is set to 0.9 and a low-pass filter is also used for smoothing to reduce contrast and smooth the image. As the contrast is reduced and / or the object is smoothed, the minimum intensity is increased and the intensity range is reduced. Figure 9A In , the intensity ranges from 0.9 to 1. Therefore, the target object can be modified to satisfy the minimum intensity constraint and the maximum intensity constraint.

[0093] Figure 9B The image intensity I (in image space) is shown with respect to the pixel array S and the rotation angle θ according to one or more embodiments. Figure 9A The target object shown in FIG is forward projected to calculate the image intensity representing the image set relative to various angles. Specifically, O×F=I.

[0094] Figure 9C FIG. 4 shows the dose intensity (in object space) of a slice in object space with respect to a Cartesian coordinate system according to one or more embodiments. Figure 9B The dose in object space corresponding to the image intensity shown in is calculated by back-projecting the image intensity I using the back-projection matrix B. Specifically, as described above, B×I=O.

[0095] Figure 9D The error is shown, i.e. Figure 9A The target object shown in Figure 9C In other words, Figure 9D Shown Figure 9C The dose strengths shown in Figure 9A One or more embodiments described below provide methods for reducing errors.

[0096] 2) Forward projection of object error

[0097] According to one or more embodiments, the method can be applied to a more typical VAM process for printing a 3D object that is solid within a target region, with the outer region of the target remaining liquid. Since the intensity constraints in image space are coupled to the dose constraints in object space by back-projection, iterations between these two spaces can be performed. The OSMO method uses forward projection (object to image) to create an “intermediate” model that is responsive to the error in the object (unmet constraints) in order to find an improved image set. Here, in one or more embodiments, the model is eliminated by computing the error in the object space and directly forward propagating the error to the image space to compute a new image set.

[0098] The following describes, in alphabetical order, a number of steps corresponding to forward projection of object error. The presentation in alphabetical order is merely for ease of understanding the embodiments disclosed in this specification and is not meant to limit the invention to only this particular order or steps.

[0099] A) According to one or more embodiments, the target object that one wishes to print is first discretized onto a voxel grid. An example of this step is shown in Figure 10A and Figure 10B . Figure 10A A target object 1006 within a print region 1008 in cylindrical coordinates is shown. The white regions of the target object 1006 are intended to be solidified (printed), while the darker regions 1008 outside of the target object are intended to remain liquid. Figure 10B The edges 1004 of the object when the target object 1006 is discretized onto a voxel grid are shown. Figure 10B The difference between the edges 1002 of the target object and the edges 1004 of the discretized object is shown in. According to one or more embodiments, the fractional area of each voxel that overlaps the target object can be computed, or a binary representation can be used in which voxels are classified as being either entirely inside the object (e.g., 1) or entirely outside the object (e.g., 0).

[0100] B) According to one or more embodiments, three quantities can be specified in addition to the target object to be printed (step A). These three quantities are described below.

[0101] The first quantity is D 上 . D 上 is the minimum desired object dose inside the target. In other words, D 上 is the minimum object dose for voxels that are intended to be solidified to form the object. This quantity can be chosen from rheological tests that determine the minimum dose sufficient to harden the material for post-processing, which includes removal from the printer and solvent washing.

[0102] The second quantity is D 下 . D 下 is the maximum desired object dose outside the target. In other words, D 下 is the maximum object dose of voxels that are intended to remain liquid or have low viscosity so that the resin outside can be separated from the printed / solidified object. This quantity can be chosen from a photorheology test that determines the maximum dose at which the resin remains liquid. This maximum dose is often referred to as the gelation dose.

[0103] The third quantity is Δ. Δ is the desired printing resolution. This quantity is determined by the characteristics of the printer (e.g., the diffraction limit of the optical projection) and the characteristics of the resin (e.g., the characteristic length scale of the various species to diffuse in the printing time). These limits can enforce a minimum feature size that can be physically printed. As the target resolution is relaxed (the minimum feature size is decreased), the set of feasible solutions expands. Thus, the optimal design can be one that matches but does not exceed the printer resolution. That is, the same design resolution and printer / material resolution can be chosen.

[0104] According to one or more embodiments, the three quantities described above can be used to create a target dose distribution, where D 上 inside the target, 下 outside the target. The target dose can then be spatially filtered by a low-pass filter (e.g., a Gaussian or moving average filter) to set the resolution based on Δ. Figure 11 An example of this filtering according to one or more embodiments is shown in FIG. 11. In particular, Figure 11 The interior 1106 of the object that is intended to be printed and the exterior 1108 of the object that is not intended to be printed are shown. The boundary 1110 between the interior 1106 and the exterior 1108 of the object is smoothed based on Δ. Figure 11 The close-up view in FIG. 11 shows the smoothed region at the boundary 1110.

[0105] Without the smoothing step, it can not be possible or difficult to find a solution for D 上 and D 下 that maximally separates the binary target, even with ideal binary image projection and no chemical diffusion, because the dose distribution is continuous. The solution reported by conventional reporting of optimal results with a finite gap (called the “process window”) can be incorrect. The reported gap can be an artifact of the discrete sampling of the object. If the sampling is fine enough, the gap disappears. Thus, the smoothing step with finite resolution Δ described in one or more embodiments can improve the calculation.

[0106] Thus, according to one or more embodiments, two dose limits (D 上 and D下 ). Then, the image set that satisfies the image intensity constraints (e.g., non-negativity) and the associated object dose that satisfies the object dose constraints (e.g., D 上 and D 下 ) are found / determined. In regions where the image edges have been smoothed by the filtering operation (e.g., smooth boundary 1110 in Figure 11 ), the dose constraint within the target boundary is between D 上 and D 下 . The goal is to reduce the dose in the outer region (e.g., away from the object exterior) to below D 下 , to have the smooth boundary of the object between D 上 and D 下 , and to have the interior of the object greater than D 上 .

[0107] According to one or more embodiments, the constraints on the image intensity can be explicitly satisfied while the object dose constraints can be attempted to be satisfied, but the optimal solution can not always achieve these metrics.

[0108] According to one or more embodiments, the smoothing of the boundary can facilitate finding a solution for the image set and the object dose in the presence of some error. The error in this paragraph means that a portion of the object (e.g., near the edge) does not satisfy the dose constraint.

[0109] According to one or more embodiments, the initial guess is iteratively refined to find the optimal image set based on the dose objectives.

[0110] C) According to one or more embodiments, an initial guess of the image set is computed. This can be all ones, all zeros, or random. One guess that can often yield good results is the forward projection of the target object (e.g., using matrix F), as shown in Figure 12 In the language of computed tomography, this transform can be referred to as the Radon transform or "sinogram" of the object. Figure 12 shows the forward projection of the smooth dose objective shown in Figure 11 .

[0111] D) According to one or more embodiments, the image set computed in step C is back (inverse) projected (e.g., using matrix B) to the object space to compute the expected dose distribution throughout the object.

[0112] E) According to one or more embodiments, the expected dose computed in step D is used to compute an error function for each voxel. The error function is computed by comparing the expected dose computed in step D with the target object determined in step B. To compute the error, for each voxel within the object, the expected dose and the upper limit D 上If the expected dose in the inner region calculated in step D is greater than D 上 , then the error is zero. Otherwise, for example, the error is calculated as the difference between the expected dose in the inner region calculated in step D and the D in the inner region. 上 Similarly, for each external voxel, the expected dose calculated in step D is compared with the lower limit D 下 If the expected dose in the outer region calculated in step D is lower than D 下 , then the error is zero. Otherwise, the error is calculated as the expected dose in the outer region calculated in step D and D 下 The square of the difference.

[0113] Figure 13 An example of the error calculation performed in step E according to one or more embodiments is shown. Specifically, Figure 13 The shading in the inner region 1306 of the object shows the root mean square (RMS) of the error, which is the error when the expected dose is less than D 上 The expected dose in the internal voxel and D 上 Similarly, the shading in the area outside the object 1308 shows the RMS of the error that is expected to be higher than D 下 The expected dose in the external voxels and D 下 The difference between. Figure 13 The close-up view on the right shows a magnified view of the inner shadow and the outer shadow. According to one or more embodiments, the error calculation in step E can ignore the boundary 1310 of the object, such as Figure 13 As shown in the close-up view in FIG, there is no shadow in the boundary 1310. Instead, the exposure on the boundary 1310 can be considered as D 上 and D 下 A smooth curve between .

[0114] F) According to one or more embodiments, the error distribution across the object can be forward-projected into image space. Specifically, the internal and external errors can be forward-projected separately. This process yields two RMS errors for each voxel illuminated by each pixel. One error indicates underdose in the object's interior regions, while the other error indicates overdose in the object's exterior regions. Each of these errors is calculated for each pixel in the image set.

[0115] Figures 14A-14C An example of step F is shown. Figure 14A As shown, the error corresponding to the interior region of the object (the final signed RMS interior error) is forward projected into the image space. Figure 14A The error shown has a negative sign because it occurs if and only if the internal dose is too low.Figure 14B The error corresponding to the exterior region of the object (the final signed RMS exterior error) is forward projected into image space as shown. Figure 14B The error shown has a positive sign because the error occurs if and only if the exterior dose is too high. The forward projection can be performed by using the forward projection matrix F. Figure 14C The final sum of signed RMS errors is shown, which is Figure 14A and Figure 14B the sum of the forward projection errors presented in Figure 14A and Figure 14B Some of the forward projection errors presented in Figure 14A and Figure 14B cancel each other out, so the sum shown in Figure 14C includes less intensity than the forward projection errors presented in

[0116] G) According to one or more embodiments, the sum of the two signed forward projection errors at each pixel (e.g., as shown in Figure 14C ) can provide a signed error function that determines how the pixel intensity should be updated in image space. For example, the sum of the two signed forward projection errors can be added to the pixel intensity to update its value, e.g., by taking the square root of the two mean squared errors to produce a root mean square (RMS) error. For example, the total error shown in Figure 14C can be applied to the pixel intensities of the pixel array S to modify the image set. According to one or more embodiments, acceleration techniques can be used to take larger steps, resulting in convergence with fewer iterations.

[0117] H) According to one or more embodiments, after each update, the image set is bounded to be positive and (optionally) below some desired maximum value. If the intensity bounds are met, the error function is not used to further update the image. In other words, if the solution is infeasible because the error for that image pixel will no longer decrease, the iteration process can be stopped. For example, the iteration process can continue to improve the total error, generating an optimal design for a given input, but the finite error will remain and the feasibility has been rejected.

[0118] I) According to one or more embodiments, additionally, the image set can be discretized (e.g., to 8 bits) to match the resolution of the light source used in the printer (e.g., the light source of an image projection chip like a DMD). This can reduce the error introduced in the physical print by discretizing the continuous numerical solution to a projector with finite discrete resolution.

[0119] J) According to one or more embodiments, steps DG may be repeated until an exit condition is reached, such as a maximum number of iterations or a slowdown in the improvement of the error reduction.

[0120] K) According to one or more embodiments, if the strength constraint has not been reached, the magnitude and final slope of the error function may be evaluated to determine feasibility within a certain error tolerance. Possible strength constraints are described above, including non-negativity, an upper limit on the strength, and discretization to a finite number of values ​​(e.g., 256). For example, in Figure 15 In , the total RMS error 1506 is reduced by a factor of 1000 from the initial guess and continues to decrease with further iterations. The solution can be defined as feasible within a given tolerance of the total object error or the maximum object error. Figure 15 , the internal RMS error 1504 and the external RMS error 1502 continuously converge, and the total RMS error 1506 continuously decreases.

[0121] According to one or more embodiments, at the end of the image correction process, a final image set is obtained, such as Figure 16 The intensity of the final image set is bounded to lie between 0 and 1 and has been discretized at each step to a number of bits (e.g. 8 bits) that matches the resolution of a typical DMD projector chip.

[0122] According to one or more embodiments, the resulting object dose is closer to D in the interior region of the object. 上 , closer to D in the area outside the object 下 For example, in Figure 17 In, D 上 and D 下 are 0.4 and 0.35, respectively, and the final object doses are close to these numbers in the inner and outer regions of the object, respectively.

[0123] Figure 18A and Figure 18B The final error (i.e., not meeting D 上 and D 下 The final error is calculated by comparing the back projection of the final image set with D 上 (for the interior of the object) and D 下 The error calculated by comparison (with respect to the exterior of an object). Figure 18B Shown Figure 18A Magnified view of .

[0124] According to one or more embodiments, referring to steps AK and Figures 8A-18BThe described methods can provide one or more of the following advantages. Using sparse matrix multiplication in the optimal coordinate system described above (e.g., cylindrical coordinates for CAL) can provide fewer iterations than traditional methods. Using a properly chosen error function, the error can converge continuously and rapidly. By accessing both object space and image space, object space physical properties and image space boundaries can be included to prevent divergence. The choice of error function in object space can have flexibility, with the error function directly generating gradients in image space. The simplicity, memory efficiency, and speed of the methods shown here for 2D epi-geometry can make it possible to extend the methods to more challenging multi-dimensional architectures.

[0125] While reference is made to steps A-K and Figures 8A-18B The described methods above are described with reference to a cylindrical coordinate system, but these methods can be extended to Cartesian coordinates.

[0126] Figure 19 A flowchart of a method for determining a set of images is shown in accordance with one or more embodiments. In one or more embodiments, one or more steps shown in Figure 19 may be omitted, repeated, and / or performed in a different order than shown in Figure 19 . Accordingly, the scope of the present invention should not be considered limited to the particular arrangement of steps shown in Figure 19 . The steps shown in Figure 19 are explained below.

[0127] In step 1900, an initial object model O in object space is determined by discretizing the object onto a voxel grid. One or more examples of this step are described above with reference to step A and Figure 10A and Figure 10B . In accordance with one or more embodiments, an upper dose D 上 may be defined as the minimum dose inside the object. In accordance with one or more embodiments, a lower dose D 下 may be defined as the maximum dose outside the object. In accordance with one or more embodiments, a print resolution Δ can be defined as the minimum printable feature size. In accordance with one or more embodiments, a low-pass spatial filter with a cutoff of Δ can be applied to the smoothed boundary of the object. The dose inside the smoothed boundary of the object can be smoothed between D 上 and D 下 .

[0128] In step 1905, a set of images I in image space is determined by forward projecting O using a forward projection matrix F. One or more examples of this step are described above with reference to step C and Figure 12 .

[0129] In step 1910 , the expected dose distribution D in object space is determined by back-projecting I using the back-projection matrix B. One or more examples of this step are described above with reference to step D.

[0130] In step 1915, an error set E corresponding to D is determined. One or more examples of this step are described above with reference to steps E and Figure 13 According to one or more embodiments, the D and D of the internal voxels of the object can be determined. 上 If the expected dose of the internal voxel (expressed in D) is not less than D 上 , then the error corresponding to the internal voxel is determined to be zero. If the expected dose of the internal voxel is less than D 上 , then based on the expected dose of the internal voxels and D 上 According to one or more embodiments, the error corresponding to the internal voxel D and D of the external voxel of the object can be determined. 下 If the expected dose to the external voxel (expressed in D) is not greater than D 下 , then the error corresponding to the external voxel is determined to be zero. If the expected dose of the external voxel is greater than D 下 , then based on the expected dose of the external voxels and D 下 The error corresponding to the external voxel is determined by the difference between them.

[0131] In step 1920, forward project E using F. One or more examples of this step are described above with reference to steps F and Figures 14A-14C and Figure 15 Described.

[0132] In step 1925, I is modified based on the forward projection of E. One or more examples of this step are described above with reference to steps GH and Figure 16 According to one or more embodiments, the modified I is compared with a predetermined intensity limit to determine whether the modified I is within the intensity limit.

[0133] In step 1930, the modified I is forward projected using F to determine D. One or more examples of this step are described above with reference to steps HK and Figure 17 Described.

[0134] In step 1935, the modification of I is continuously performed until a predetermined condition occurs. One or more examples of this step are described above with reference to steps JK and Figure 15 、 Figure 17 and Figure 18A and Figure 18Bare described above with reference to steps J-K and

[0135] In step 1940, the object is printed using the final I corresponding to the predetermined condition. One or more examples of this step are described above with reference to steps J-K and Figure 15 、 Figure 16 and Figure 18A and Figure 18B are described above.

[0136] According to one or more embodiments, error determination is not performed on the boundaries of the object.

[0137] According to one or more embodiments, the errors corresponding to the interior voxels and the errors corresponding to the exterior voxels are forward projected separately.

[0138] One or more embodiments of the operations for a 3D printer disclosed in this specification (e.g., with reference to Figures 3A-19 ) can be implemented on virtually any type of computer system, regardless of the platform being used. The computer system can have a program or algorithm in place, controlling the functions / operations of the measurements described in the above embodiments. For example, the computer system can be one or more mobile devices (e.g., a laptop computer, a smart phone, a personal digital assistant, a tablet computer, or other mobile device), a desktop computer, a server, a blade in a server chassis, or any other type of computer system that at least includes the minimum processing ability, memory, and input and output devices for performing one or more embodiments of the present invention.

[0139] Examples of computer systems according to one or more embodiments are described with reference to Figure 20 Figure 20 ​is a block diagram of a computer system for providing computing functionality in accordance with an embodiment, which computing functionality is associated with algorithms, methods, functions, processes, flows, and procedures as described in this disclosure. The computer 2002 shown in the computer system is intended to encompass any computing device such as a server, desktop computer, laptop / notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing devices including physical or virtual instances of the computing device (or both). Additionally, the computer 2002 can include an input device such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer 2002, including digital data, visual information, or audio information (or a combination of information), or a GUI.

[0140] In one or more embodiments, the 3D printer described in the above embodiments can include, be in the form of, or be implemented on the computer 2002 such that the computer 2002 performs the processing and calculations described above with reference to Figures 3A-19 the processing and calculations described above with reference to the 3D printer. For example, the computer 2002 implementing the 3D printer includes tools for performing processing related to 3D printing and determining the final image set described in the above embodiments.

[0141] The computer 2002 can function in the role of a client, a network component, a server, a database or other persistent device, or any other component (or combination of roles) in a computer system for performing the subject matter described in this disclosure. The computer 2002 shown is communicably coupled with a network 2030. In some embodiments, one or more components of the computer 2002 can be configured to operate within an environment including a cloud computing-based environment, a local environment, a global environment, or other environment (or combination of environments).

[0142] At a high level, the computer 2002 is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some embodiments, the computer 2002 can also include, be, or be communicably coupled with an application server, an email server, a web server, a cache server, a streaming data server, a business intelligence (BI) server, or other server (or combination of servers).

[0143] The computer 2002 can receive requests from a client application (for example, a client application executing on another computer 2002) via the network 2030 and respond to the requests by processing the received requests in an appropriate software application. Additionally, requests can also be sent to the computer 2002 from internal users (for example, from a command console or through other appropriate access methods), external or third parties, other automated applications, and any other appropriate entities, individuals, systems, or computers.

[0144] Each of the components of the computer 2002 can communicate using the system bus 2003. In some embodiments, any or all of the components of the computer 2002 (hardware or software (or combination of hardware and software)) can interact with each other (or the interface 2004 (or a combination of the two)) using the application programming interface (API) 2012 or the service layer 2013 (or a combination of the API 2012 and the service layer 2013) on the system bus 2003. The API 2012 can include specifications for routines, data structures, and object classes. The API 2012 can be either computer language independent or dependent and refer to either a complete interface, a single function, or even a group of APIs. The service layer 2013 provides software services to the computer 2002 or other components (whether illustrated or not) that are communicably coupled to the computer 2002. Functions of the computer 2002 can be accessible through the service layer 2013 by all service consumers using that service layer 2013. Software services provided by the service layer 2013 (for example, using the API 2012) provide re-usable

[0145] The computer 2002 includes the interface 2004. Although illustrated as a separate element in the computer 2002, the interface 2004 can be incorporated as part of the system bus 2003 or other elements of the computer 2002. Figure 20The interface 2004 is shown as a single interface 2004, but two or more interfaces 2004 can be used according to particular needs, desires, or particular implementations of the computer 2002. The interface 2004 is used by the computer 2002 for communicating with other systems that are connected to the network 2030 in a distributed environment. Generally, the interface 2004 includes logic encoded in software or hardware (or a combination of software and hardware) and is operable to communicate with the network 2030. More specifically, the interface 2004 can include software supporting one or more communication protocols associated with communicating with the network 2030 or one or more other systems. As such, the interface 2004 is operable to receive and

[0146] The computer 2002 includes at least one computer processor 2005. Although shown as a single computer processor 2005, two or more computer processors 2005 can be used according to particular needs, desires, or particular implementations of the computer 2002. Generally, the computer processor 2005 executes instructions and manipulates data to operate the computer 2002 and to implement the algorithms, methods, functions, processes, flows, and procedures as described in this disclosure. Figure 20

[0147] The computer 2002 also includes memory 2006 that retains instructions for executing operations, as well as temporary variable instructions, by the computer 2002 or other components that can be connected to the network 2030 (or a combination of both). For example, the memory 2006 can be a database that stores data consistent with this disclosure. In one example, the memory 2006 can store programs or algorithms for controlling the process for 3D printing and determining the final image set described in the above embodiments. Although shown as a single memory 2006, two or more memories 2006 can be used according to particular needs, desires, or particular implementations of the computer 2002 and the described functionality. While the memory 2006 is illustrated as an integral component of the computer 2002, in alternative embodiments, the memory 2006 can be external to the computer 2002. Figure 20

[0148] The application 2007 is an algorithmic software engine that provides functionality according to particular needs, desires, or particular implementations of the computer 2002, particularly with respect to the functionality described in this disclosure. For example, the application 2007 can be used as one or more components, modules, applications, etc. In one example, the application 2007 can include programs or algorithms for controlling the operation of a 3D printer and determining the final image set described in the above embodiments. More specifically, in this example, the programs or algorithms can control 3D printing and determine the final image set described with reference to the above embodiments. Figures 3A-19 ​​The final image set is described. In addition, although shown as a single application 2007, the application 2007 can be implemented as multiple applications 2007 on the computer 2002. Further, although shown as integral with the computer 2002, in alternative embodiments, the application 2007 can be external to the computer 2002. In one example, reference is made to Figure 7 and Figure 19 The method described can be implemented by the application 2007.

[0149] There can be any number of computers 2002 associated with or external to a computer system containing the computer 2002, with each computer 2002 communicating over the network 2030. Further, the terms "client," "user," and other appropriate terminology can be used interchangeably as appropriate, without departing from the scope of the present disclosure. Moreover, the present disclosure contemplates that many users can use one computer 2002, or that one user can use multiple computers 2002. Further, in one or more embodiments, the computer 2002 is a non-transitory computer readable medium (CRM).

[0150] While only a few exemplary embodiments have been described in detail above, those skilled in the art will readily comprehend many modifications. Thus, the scope of the disclosure should be determined not with reference to the above description, but should instead be determined with reference to the appended claims, along with their full scope of equivalents.

[0151] In addition, one or more embodiments are described below with respect to determining an image set.

[0152] According to one or more embodiments, a method of 3D printing an object includes: determining an initial object model O in an object space by discretizing the object onto a voxel grid; determining an image set I by forward projecting O using a forward projection matrix F; determining an expected dose distribution D in the object space by back projecting I using a back projection matrix B; determining an error set E corresponding to D; forward projecting E using F; modifying I based on the forward projection of E; determining D using F to forward project the modified I; continuously performing the modification of I until a predetermined condition occurs; and printing the object using a final I corresponding to the predetermined condition.

[0153] According to one or more embodiments, determining O includes: defining an upper dose D 上 as a minimum dose inside the object; defining a lower dose D 下 as a maximum dose outside the object; defining a print resolution Δ as a minimum printable feature size; and applying a low pass spatial filter with a cutoff value of Δ to smooth the boundaries of the object, wherein the dose inside the smoothed boundaries of the object is between D 上 and D下 Smooth between.

[0154] According to one or more embodiments, determining E includes determining D and D of the internal voxels of the object. 上 If the expected dose of the internal voxel (expressed in D) is not less than D 上 , the error corresponding to the internal voxel is determined to be zero; if the expected dose of the internal voxel is less than D 上 , then based on the expected dose of the internal voxels and D 上 The error corresponding to the internal voxel is determined by the difference between D and D for the external voxel of the object; the error corresponding to the external voxel is determined to be zero if the expected dose (expressed in D) for the external voxel is not greater than D; and the error corresponding to the external voxel is determined to be zero if the expected dose for the external voxel is greater than D. 下 , then based on the expected dose of the external voxels and D 下 The error corresponding to the external voxel is determined by the difference between them.

[0155] According to one or more embodiments, the method further comprises comparing the modified I with a predetermined intensity limit such that the modified I is within the intensity limit.

[0156] According to one or more embodiments, in the method, the predetermined condition is that E becomes smaller than a first threshold.

[0157] According to one or more embodiments, the predetermined condition is reaching a maximum number of iterations.

[0158] According to one or more embodiments, the predetermined condition is that the difference between E of one iteration step and E of an immediately preceding iteration step is less than a second threshold.

[0159] According to one or more embodiments, the method further includes discretizing I to match a resolution of a projection chip used to project the final I.

[0160] According to one or more embodiments, in the method, no error determination is performed on the boundaries of the object.

[0161] According to one or more embodiments, in the method, errors corresponding to internal voxels and errors corresponding to external voxels are forward projected separately.

[0162] According to one or more embodiments, a system for 3D printing of an object includes an optical objective; one or more motors that move the optical objective relative to a resin; a light source coupled to the optical objective; and a processor. The processor is configured to: determine an initial object model O in an object space by discretizing the object onto a voxel grid; determine a set of images I in an image space by forward projecting O using a forward projection matrix F; determine an expected dose distribution D in the object space by back projecting I using a back projection matrix B; determine a set of errors E corresponding to D; forward project E using F; modify I based on the forward projection of E; determine D using F to forward project the modified I; continuously perform the modification of I until a predetermined condition occurs; use a final I corresponding to the predetermined condition for projecting light from the light source; and instruct the one or more motors to move the optical objective relative to the resin.

[0163] According to one or more embodiments, a non-transitory computer readable medium (CRM) stores instructions for performing a 3D printing operation. The operations include: determining an initial object model O in an object space by discretizing the object onto a voxel grid; determining a set of images I in an image space by forward projecting O using a forward projection matrix F; determining an expected dose distribution D in the object space by back projecting I using a back projection matrix B; determining a set of errors E corresponding to D; forward projecting E using F; modifying I based on the forward projection of E; determining D using F to forward project the modified I; continuously performing the modification of I until a predetermined condition occurs; and printing the object using a final I corresponding to the predetermined condition.

Claims

1. A three-dimensional (3D) printing apparatus, comprising: a light source comprising a plurality of pixels configured to emit a plurality of light beams toward an optical objective; the optical objective, the optical objective configured to diverge the plurality of light beams as the plurality of light beams exit the optical objective toward a resin volume; and one or more motors configured to translate the optical objective relative to the resin volume; wherein the one or more motors are configured to translate the optical objective relative to the resin volume to apply the plurality of light beams to a plurality of voxels within the resin volume, wherein applying the plurality of light beams to the plurality of voxels cures the plurality of voxels, wherein the optical objective applies the plurality of light beams such that each of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams, wherein the at least two different light beams expose the each of the plurality of voxels at two different times such that the at least two different light beams spatially overlap only in the each of the plurality of voxels, and wherein a total exposure amount to cure the resin volume in the each of the plurality of voxels is at least equal to a sum of exposure amounts of the at least two different light beams at the each of the plurality of voxels. the at least two different light beams propagate at different angles from each other.

2. The 3D printing device of claim 1, wherein, the light source comprises a digital micromirror device (DMD) configured to reflect the plurality of light beams toward the resin volume.

3. The 3D printing device of claim 1, wherein, the light source comprises one or more lasers configured to generate the plurality of light beams.

4. The 3D printing device of claim 1, wherein, the one or more motors translate the optical objective relative to the resin volume along an axial direction of the optical objective.

5. The 3D printing device of claim 1, wherein, the optical objective is coupled to the resin with an index matching material having an index of refraction greater than 1.

6. The 3D printing device of claim 1, wherein, the one or more motors are configured to translate the optical objective along at least two axes orthogonal to an axial direction of the optical objective.

7. The 3D printing device of claim 1, wherein, to translate the objective relative to the resin, the one or more motors move both the optical objective and the resin.

8. The 3D printing device of claim 1, wherein, the apparatus comprises a container that houses the resin volume.

9. The 3D printing device of claim 1, wherein, the container is configured to house the resin volume such that a surface of the resin volume that the plurality of light beams enter is planar and perpendicular to an axial direction of the optical objective.

10. The 3D printing device of claim 9, wherein, 11. A method for operating a three-dimensional (3D) printing apparatus, the method comprising: controlling a light source comprising a plurality of pixels to emit a plurality of light beams toward an optical objective; diverging, via the optical objective, the plurality of light beams as the plurality of light beams exit the optical objective toward a resin volume; translating, via one or more motors, the optical objective relative to the resin volume; applying, by translating the optical objective relative to the resin volume, the plurality of light beams to a plurality of voxels within the resin volume; curing the plurality of voxels by applying the plurality of light beams to the plurality of voxels; applying, via the optical objective, the plurality of light beams such that each of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams; and ​ ​ exposing each of the voxels by the at least two different light beams at two different times such that the at least two different light beams spatially overlap only in the each of the voxels, wherein a total exposure amount to cure the resin volume in the each of the voxels is at least equal to a sum of exposure amounts of the at least two different light beams at the each of the voxels.

12. The method of claim 11, wherein, application of the at least two light beams causes the at least two different light beams to propagate at different angles from each other.

13. The method of claim 11, further comprising translating the optical objective along an axial direction of the optical objective relative to the resin volume.

14. The method of claim 11, further comprising coupling the optical objective to the resin with an index matching material having an index of refraction greater than 1.

15. The method of claim 11, wherein, the translation of the optical objective is along at least two axes that are orthogonal to an axial direction of the optical objective.

16. A system for three-dimensional (3D) printing, comprising: a light source comprising a plurality of pixels configured to emit a plurality of light beams toward an optical objective; the optical objective configured to cause the plurality of light beams to diverge as the plurality of light beams exit the optical objective toward a resin volume; one or more motors configured to translate the optical objective relative to the resin volume; a processor configured to control the one or more motors to thereby control the translation of the optical objective relative to the resin volume; a memory storing instructions for translating the optical objective relative to the resin volume; wherein the processor controls the translation of the optical objective relative to the resin volume based on the instructions to apply the plurality of light beams to a plurality of voxels within the resin volume, wherein applying the plurality of light beams to the plurality of voxels causes the plurality of voxels to cure, wherein the processor controls the translation of the optical objective to apply the plurality of light beams such that each of the plurality of voxels is exposed by at least two different light beams of the plurality of light beams, wherein the processor controls the translation of the optical objective such that the at least two different light beams expose each of the voxels at two different times, wherein the at least two different light beams at the two different times spatially overlap only in the each of the voxels, and wherein a total exposure amount to cure the resin volume in the each of the voxels is at least equal to a sum of exposure amounts of the at least two different light beams at the each of the voxels.

17. The system of claim 16, wherein, the at least two different light beams propagate at different angles from each other.

18. The system of claim 16, wherein, the light source comprises a digital micromirror device (DMD) configured to reflect the plurality of light beams toward the resin volume.

19. The system of claim 16, wherein, the light source comprises one or more lasers configured to generate the plurality of light beams.

20. The system of claim 16, wherein, the one or more motors translate the optical objective along an axial direction of the optical objective relative to the resin volume.

Images