High-dimensional volumetric additive manufacturing

Abstract

The three-dimensional printing apparatus includes a light source including a plurality of pixels and configured to emit a plurality of beams toward an objective system, an objective system configured to diverge the plurality of beams as they pass through the objective system and are emitted toward a resin region, and one or more motors configured to move the objective system relative to the resin region. The one or more motors are configured to irradiate a plurality of voxels in the resin region with the plurality of beams by moving the objective system relative to the resin region. Irradiating the plurality of beams on the plurality of voxels hardens the plurality of voxels. The objective system irradiates the plurality of beams such that each of the plurality of voxels is exposed by at least two different beams of the plurality of beams.

Description

[Technical Field]

[0001] FIELD OF THE INVENTION The embodiments described herein generally relate to apparatus, systems, and methods for manufacturing three-dimensional (3D) objects. More specifically, the embodiments described herein relate to apparatus, systems, and methods for curing photosensitive resins with light irradiation to form 3D objects. [Background technology]

[0002] Conventional volume additive manufacturing (VAM) printing uses three or fewer degrees of freedom (hereafter referred to as "dimensions") to build objects. Examples of conventional VAM methods include computed axial lithography (CAL) and xolography, both of which use three dimensions for building. CAL projects a two-dimensional image onto a transparent cylindrical container containing resin, rotated around its axis, usually in the normal direction, for a total of three dimensions of light exposure. Volume helical additive manufacturing (VAM) is a variation of CAL in which the cylindrical container is both rotated and translated along its axis. This additional translation is used to expand the effective size of the two-dimensional image projector and does not provide an independent degree of freedom, so it is classified as a method using the same dimensions as CAL. Xolography uses a single-color sheet moving linearly in one direction to sequentially project two-dimensional images from orthogonal directions. However, adding more degrees of freedom makes it possible to improve modeling resolution and fidelity, or to model complex structures. Summary of the Invention

[0003] This Summary is provided to introduce some of the concepts that are described in more detail below. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter.

[0004] One or more embodiments described herein relate to a three-dimensional printing device. The three-dimensional printing device includes a light source including a plurality of pixels and configured to emit a plurality of beams toward an objective system; the objective system configured to diverge the plurality of beams as they pass through the objective system and are emitted toward a resin region; and one or more motors configured to move the objective system relative to the resin region. The one or more motors are configured to move the objective system relative to the resin region, thereby irradiating a plurality of voxels within the resin region with the plurality of beams. Irradiating the plurality of voxels with the plurality of beams hardens the plurality of voxels. The objective system irradiates the plurality of beams such that each of the plurality of voxels is exposed by at least two different beams from the plurality of beams. The at least two different beams expose each voxel at two different times such that the at least two different beams spatially overlap only within each voxel. The total exposure dose that hardens the resin region in each voxel is equal to or greater than the sum of the exposure doses of the at least two different beams in each voxel.

[0005] One or more embodiments described herein relate to a method of operating a three-dimensional printing apparatus, the method including: controlling a light source including a plurality of pixels and emitting a plurality of beams toward an objective system; diverging the plurality of beams as they pass through the objective system and exit toward a resin region through the objective system; moving the objective system relative to the resin region via one or more motors; irradiating a plurality of voxels in the resin region with the plurality of beams by moving the objective system relative to the resin region; irradiating the voxels with the plurality of beams to harden the voxels; irradiating the plurality of beams through the objective system such that each of the plurality of voxels is exposed by at least two different beams of the plurality of beams; and exposing each voxel at two different times such that the at least two different beams spatially overlap only within each voxel. The total exposure dose that hardens the resin region in each voxel is equal to or greater than the sum of the exposure doses of the at least two different beams in each voxel.

[0006] One or more embodiments described herein relate to a three-dimensional printing system. The three-dimensional printing system includes: a light source including a plurality of pixels and configured to emit a plurality of beams toward an objective; an objective configured to diverge the plurality of beams as they pass through the objective and toward a resin region; one or more motors configured to move the objective relative to the resin region; a processor configured to control the one or more motors to control the movement of the objective relative to the resin region; and a memory storing instructions for the processor to control the movement of the objective relative to the resin region, wherein the processor controls the movement of the objective relative to the resin region based on the instructions to irradiate a plurality of voxels within the resin region with the plurality of beams. The irradiation of the plurality of beams at the plurality of voxels hardens the plurality of voxels. The processor controls the movement of the objective such that each of the plurality of voxels is exposed by at least two different beams from the plurality of beams. The at least two different beams at two different times spatially overlap only within each voxel. The total exposure dose that hardens the resin region in each voxel is equal to or greater than the sum of the exposure doses of the at least two different beams in that voxel.

[0007] Other aspects and advantages of the present invention will become apparent from the following description and appended claims.

[0008] Specific embodiments of the disclosed technology will be described in detail with reference to the accompanying drawings. Identical elements in the various figures are labeled with the same reference numerals for consistency. The sizes and relative positions of elements in the figures are not necessarily drawn to scale. For example, the shapes and angles of each element are not necessarily drawn to scale, and some elements may be arbitrarily enlarged or positioned to enhance the readability of the drawings. Furthermore, the shapes of particular elements depicted in the figures are not intended to convey any information regarding the actual shape of the elements, but have been selected solely for ease of identification in the drawings. [Brief explanation of the drawings]

[0009] [Figure 1A] FIG. 1 illustrates the dimensions (or degrees of freedom) of printing with respect to illumination angle. [Figure 1B] FIG. 1 illustrates the dimensions (or degrees of freedom) of printing with respect to illumination angle. [Figure 1C] FIG. 1 illustrates the dimensions (or degrees of freedom) of printing with respect to illumination angle. [Figure 2] 1 illustrates the six printing dimensions for illumination of a resin area with light from a single point on an image display chip, here labeled as point spread functions (PSFs). [Figure 3A] FIG. 1 is a three-dimensional schematic diagram of a 3D printer in accordance with one or more embodiments. [Figure 3B] FIG. 3B is a longitudinal cross-sectional view of the schematic diagram shown in FIG. 3A. [Figure 4A] FIG. 1 illustrates the operation of a 3D printer in accordance with one or more embodiments. [Figure 4B] FIG. 1 illustrates the operation of a 3D printer in accordance with one or more embodiments. [Figure 5A] FIG. 1 illustrates a discretization of an object model in accordance with one or more embodiments. [Figure 5B] FIG. 1 illustrates a discretization of an object model in accordance with one or more embodiments. [Figure 5C] FIG. 1 illustrates a discretization of an object model in accordance with one or more embodiments. [Figure 6] FIG. 1 illustrates a system for 3D printing in accordance with one or more embodiments. [Figure 7] FIG. 1 illustrates a flowchart for 3D printing in accordance with one or more embodiments. [Figure 8A] FIG. 1 illustrates 3D printing in a cylindrical coordinate system in accordance with one or more embodiments. [Figure 8B] FIG. 1 illustrates 3D printing in a cylindrical coordinate system in accordance with one or more embodiments. [Figure 8C]FIG. 1 illustrates 3D printing in a cylindrical coordinate system in accordance with one or more embodiments. [Figure 9A] FIG. 2 is a diagram illustrating a target object in a cylindrical coordinate system in accordance with one or more embodiments. [Figure 9B] FIG. 10 illustrates calculated intensities in a cylindrical coordinate system according to one or more embodiments. [Figure 9C] FIG. 1 illustrates a calculated exposure dose in a cylindrical coordinate system according to one or more embodiments. [Figure 9D] FIG. 1 illustrates errors associated with 3D printing of a target object in a cylindrical coordinate system in accordance with one or more embodiments. [Figure 10A] FIG. 1 illustrates a target object in accordance with one or more embodiments. [Figure 10B] FIG. 10B shows a close-up view of the boundary of the target object shown in FIG. 10A. [Figure 11] FIG. 10B illustrates a target exposure and a close-up view of the target exposure of the target object of FIG. 10A in accordance with one or more embodiments. [Figure 12] FIG. 12 illustrates a set of images calculated by forward projecting the target exposure shown in FIG. 11 in accordance with one or more embodiments. [Figure 13] FIG. 12 illustrates a calculated error between the target exposure and the backprojected object shown in FIG. 11 in accordance with one or more embodiments. [Figure 14A] FIG. 14 illustrates forward projection of the error onto the object interior shown in FIG. 13 in accordance with one or more embodiments. [Figure 14B] FIG. 14 illustrates forward projection of the error onto the object exterior shown in FIG. 13 in accordance with one or more embodiments. [Figure 14C] FIG. 14C illustrates the final sum of the signed errors shown in FIGS. 14A and 14B in accordance with one or more embodiments. [Figure 15] FIG. 10 is a diagram illustrating error versus iteration in accordance with one or more embodiments. [Figure 16]FIG. 16 is a diagram showing a final image set obtained by correcting the image set shown in FIG. 12 based on the errors shown in FIGS. 14A to 14C and 15. [Figure 17] FIG. 17 illustrates a final object printed based on the final image set of FIG. 16 in accordance with one or more embodiments. [Figure 18A] 18 is a diagram illustrating the error between the final object of FIG. 17 and the target exposure of FIG. 11 in accordance with one or more embodiments. [Figure 18B] FIG. 18B is an enlarged view of the diagram showing the error shown in FIG. 18A. [Figure 19] FIG. 1 illustrates a flowchart for determining a final image set for 3D printing of an object in accordance with one or more embodiments. [Figure 20] FIG. 1 illustrates a computer system for 3D printing objects in accordance with one or more embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0010] In the following detailed description of embodiments of the present disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the present disclosure. However, it will be apparent to those skilled in the art that the present disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail in order to avoid unnecessarily complicating the description.

[0011] Throughout this specification, ordinal numbers (e.g., first, second, third, etc.) may be used as adjectives to refer to elements (i.e., any nouns herein). The use of such ordinal numbers is not intended to indicate a particular order of elements or to limit an element to a single one, unless expressly disclosed using terms such as "before," "after," "single," etc. Rather, ordinal numbers are used to distinguish elements. For example, a first element is a different element from a second element, a first element may include multiple elements, and a first element may be after (or before) a second element in the ordering of elements.

[0012] In the following description of Figures 1-20, any component described with respect to a figure of the various embodiments disclosed herein may be equivalent to one or more components of the same name described with respect to other figures. For the sake of brevity, the description of these components will not be repeated in each figure. Accordingly, any embodiment of a component in each figure is incorporated by reference into the other figures and is considered to be optionally present in each of the other figures with one or more components of the same name. Furthermore, in accordance with the various embodiments disclosed herein, the description of a component shown in the figures may be interpreted as any embodiment implemented in addition to, in combination with, or in place of, the embodiment described with respect to the corresponding component of the same name in the other figures.

[0013] Terms such as "almost" and "substantially" mean that it is not necessary to exactly achieve the stated characteristics, parameters, or values, and deviations and variations including other factors known to those skilled in the art, such as tolerances, measurement errors, and measurement accuracy limits, may occur, and are allowed to the extent that they do not interfere with the intended effect of the characteristics.

[0014] It should be understood that one or more steps shown in the flowcharts may be omitted, repeated, or performed in a different order than that shown in the flowcharts, and therefore the scope of what is disclosed herein is not limited to the particular arrangement of steps shown in the flowcharts.

[0015] Embodiments disclosed herein relate to three-dimensional (3D) printing of objects by irradiating resin with light. Throughout this specification, this 3D printing is also referred to as Volumetric Additive Manufacturing (VAM). For this purpose, an image set is created using an object model. The image set is then irradiated onto the resin through an optical objective (hereinafter referred to as the "objective"). The irradiation of this image set hardens the resin in areas corresponding to the object model. The hardened resin then becomes the printed 3D object and is removed from the resin. For this purpose, the hardened resin may be immersed in a liquid bath to wash away unhardened resin.

[0016] The embodiments disclosed herein describe a new type of architecture for VAM. Computed Axial Lithography (CAL), a conventional VAM method, projects a 2D image onto a region rotating around a single axis and spatially projects light onto the resin in three dimensions (hereinafter referred to as "spatial addressing"). This configuration is shown in FIG. 1A. Specifically, FIG. 1A shows a digital micromirror device (DMD) (104) projecting a 2D image onto the resin (102). Note that lenses that achieve this projection are not shown but are well known to those skilled in the art. The resin (102) is disposed within a cylindrical container, which may be in a liquid state. By rotating the cylindrical container around its central axis, the rotation axis, the DMD (104) can illuminate the resin with an image in three dimensions: two dimensions due to the two-dimensional pixel array disposed on the DMD and one dimension due to the rotation of the resin (102). For example, a single voxel of resin (102) shown in Figure 1A can be uniquely addressed by a ray of light intersecting the voxel by selecting and turning on the appropriate pixels on the DMD (104) in each image in a set of images in which the resin is illuminated at one rotational angle of the resin.

[0017] Tilting the rotation axis relative to the projection direction of the DMD (104) can be considered to reduce the spatial addressing dimension to less than three and thus reduce printing capabilities. This reduction in spatial addressing dimension is illustrated in Figures 1B and 1C. Specifically, when an image is projected parallel to the rotation axis of the resin (102), as shown in Figure 1C, three-dimensional addressing is lost. This is because the rotation of the resin (102) does not provide an additional dimension of spatial addressing relative to the two-dimensional illumination by the DMD (104). Therefore, the configuration of Figure 1C reduces to a 2D printer similar to conventional lithography. Figure 1B shows an intermediate state between Figures 1A and 1C. In Figure 1B, the angle between the projection direction of the DMD (104) and the rotation axis of the resin (102) is between 0 and 90 degrees. Therefore, the control of the printing structure in Figure 1B changes between three dimensions, corresponding to Figure 1A, and two dimensions, corresponding to Figure 1C. In other words, the configuration of Figure 1B can be considered to have fractional dimensional addressing between 2 and 3 independent dimensions. Thus, each of the configurations shown in Figures 1A-1C can be characterized as providing spatial addressing for the resin (102) that varies continuously from 3 to 2 dimensions.

[0018] Various metrics related to 3D printing improve as the dimension increases from 2 (3D printing is not possible) to 3 (similar to traditional CAL). These metrics include the minimum size of a 3D printed voxel, the complexity of the object that can be printed, and the contrast between the interior and exterior regions of the object in the amount of exposure deposited by the printer. According to one or more embodiments, increasing the dimensionality of the rendered image can improve these print quality metrics.

[0019] One or more embodiments describe a novel printing architecture with effective printing dimensions greater than three. As shown in Figure 2, the intensity projected from a single pixel of a display device has a three-dimensional shape, called a point spread function (PSF). A typical PSF is a Gaussian beam. Similar to a solid object, the PSF has six degrees of freedom, commonly referred to as "rigid body modes." Of the six degrees of freedom, three are translations along Cartesian coordinate axes (202) and the remaining three are rotations around Cartesian coordinate axes (204). Typically, the PSF has rotational symmetry around the optical axis. When symmetric, rotations around that axis do not change the light distribution within the resin, reducing the number of effective modes to five. Furthermore, conventional CAL uses a "pencil beam" PSF with a large depth focus that is invariant to translations along the optical axis (e.g., the vertical axis of the Cartesian coordinate system shown in Figure 2). This configuration reduces the number of effective modes to four. However, Gaussian beams with a depth focus smaller than the resin are well known in tomography and are being explored for CAL applications.

[0020] As shown in FIG. 1A, conventional CAL uses the DMD (104) to translate the PSF in two lateral dimensions corresponding to a two-dimensional grid of pixels. Additionally, the resin (102) is rotated about an axis orthogonal to the optical axis direction. Thus, conventional CAL accommodates three of the six possible degrees of freedom shown in FIG. 2: translation along two Cartesian coordinate axes (202) due to the projection of the DMD pixels, and one independent rotation of the resin relative to the projected image. However, FIG. 2 illustrates that the projected light can be rotated and translated in up to six dimensions (i.e., degrees of freedom).

[0021] According to one or more embodiments, VAM printing begins with determining a set of optical images. Illuminating these optical images from outside the resin region causes the resin to harden in a shape that approximates the shape of the desired 3D object. This is the inverse problem to be solved. In the field of tomographic imaging, adding additional “useful” images can facilitate this inverse problem. By “useful” images, we mean images that add important information not included in the image set. For example, increasing the density of images presented during rotation can be useful, but only up to the known limits of tomography. However, according to one or more embodiments, adding images that are incident from positions or angles distinctly different from the original image set can improve the accuracy of the solution to the inverse problem. This can be understood by considering the exposure dose to be applied to the resin region as a set of constraints, and the intensity of each pixel in the image set as a variable for satisfying the constraints. The pixel intensities sampled at each voxel in the resin region form a set of linear equations relating the variables (pixel intensities) to the constraints (voxel exposure doses). The more independent variables there are, the better the solution. "Independent" in this context is essentially synonymous with "useful" as mentioned above: the solution can be improved by adding image sets with different PSFs.

[0022] 3A-3B and 4A-4B illustrate a 3D printer (i.e., a 3D printing device) according to one or more embodiments. In one or more embodiments, the 3D printer is configured to allow multiple independent light rays (i.e., light beams) to pass through a single voxel in the resin at different angles. To this end, an image set providing a set of multiple angles may be determined. A light source (402) including multiple pixels projects multiple light beams (302) through an objective (306). When multiple pixels are turned on, a cone of light (408) is formed. The objective (306) diverges the output beams (304) that propagate through the resin (310). By moving the objective (306) relative to the resin (310) and selecting images within the image set, the 3D printer can control the angles of the diverging beams (304) and the voxels in the resin (310) that are illuminated by these beams. By controlling this divergent beam (304) and irradiating it onto voxels, the voxels are hardened and an object is generated.

[0023] According to one or more embodiments, the beam divergence may be equal to or greater than 30 degrees half angle from the optical axis, measured in air. According to one or more embodiments, a larger beam divergence can increase the resolution of the final printed object because the larger divergence allows the individual beams to illuminate each voxel through a larger rotation angle, fully utilizing the associated rotational degrees of freedom. As such, a larger divergence may improve the print quality metrics discussed above.

[0024] According to one or more embodiments, the objective that diverges the beam may be a single objective lens or may include one or more optical components that diverge the beam. For example, the objective may include one or more lenses, one or more mirrors, or one or more customized or commercially available objectives, any combination of which may be used to bend the beam. Thus, as used herein, the term "objective" refers to a set of optical components arranged to convert an intensity-modulated array of pixels into an array of point spread functions having a desired size, shape, and direction of propagation within the resin.

[0025] Throughout this specification, curing a voxel means increasing the viscosity of the resin in that voxel upon exposure to light to the extent that the printed object can be removed from the remaining resin. For example, in one or more embodiments, the cured voxel may be in the form of a gel that can retain its shape. One of ordinary skill in the art of photochemistry will recognize that there are many materials and reactions that meet the description set forth herein, including photopolymerization and photoisomerization.

[0026] Specifically, a 3D printer according to one or more embodiments includes a light source (402) including a plurality of pixels configured to emit a plurality of beams (402) toward objectives (406-1, 406-2). The objectives (406-1, 406-2) are configured to diverge the plurality of beams (404) as they exit the objectives (406-1, 406-2) toward a region of resin (410). The resin (410) is contained within a container (412). The container (412) is configured to allow the diverging beams (404) to pass through the container (412) and enter the resin (410). For example, the container (412) may include a transparent top surface to allow the diverging beams (404) to pass through and reach the resin (410). In one or more embodiments, the container (412) may not include a top surface, in which case the resin (410) may be directly exposed to the diverging beam (404). The objective may be separated from the top surface or resin by air, and the intermediate space may be filled with a material having a refractive index higher than air (i.e., a refractive index of 1) to increase the angle of travel of the beam within the resin, as known to those skilled in the art. This bonding material may include oil, water, various elastomers, or the resin itself.

[0027] According to one or more embodiments, the 3D printer includes one or more motors configured to move the objectives (406-1, 406-2) relative to the resin (410). The motors are configured to move the objectives (406-1, 406-2) relative to the resin (410) to irradiate the beam (404) on a plurality of voxels. To this end, the motors are configured to move the objectives (406-1, 406-2) relative to the resin (410). For example, the motors may be connected to and move the objectives (406-1, 406-2). Alternatively, the motors may be connected to and move the container (412), or may be connected to both the objectives (406-1, 406-2) and the container (412) to move the objectives (406-1, 406-2) relative to the resin (410). In one or more embodiments, the motor may be a stepper motor, a voice coil motor, a piezoelectric motor, or a combination thereof, although the type of motor is not limited to embodiments of the present invention.

[0028] In the embodiments disclosed herein, unless otherwise specified, movement of the objective relative to the resin is not limited to moving only the objective. Movement of the objective relative to the resin may involve movement of the objective, movement of the resin, or both. Furthermore, these motors may not move the entire objective relative to the resin, but may move only a portion of the objective's components to move or alter the light within the resin. For example, a steering mirror may be rotated to change the direction or placement of the light directed toward the resin. Other actuators known to those skilled in the art include deformable mirrors and liquid lenses that can be used to change the depth of focus or the shape of the PSF. These actuators need not be mechanical; they may utilize optoelectronic processes, such as the photoelectric effect, liquid crystals, or other known physical processes, to alter the function of the objective and modulate the PSF in a "useful" manner as defined above.

[0029] In one or more embodiments, the motor irradiates the diverging beams (404) by moving the objectives (406-1, 406-2) so that each of the multiple voxels is exposed by at least two different beams (404) of the multiple beams (404). To achieve this, the two different beams (404) expose the voxel at two different times so that they spatially overlap only at the voxel. Specifically, the motor moves the objective (406-1) to Position 1. At Position 1, the light source (402) irradiates Image 1, and one pixel of the light source (402) emits a beam (404) so ​​that the diverging beam (404) emitted from the objective (406-1) passes through that voxel. The motor then moves the objective from Position 1 to Position 2. The objective at Position 2 is designated by the reference symbol "(406-2)." At position 2, the light source (402) emits image 2, where one pixel of the light source (402) emits a beam (404), and the divergent beam (404) emerging from the objective system (406-2) passes through that voxel at a different angle than the divergent beam (404) corresponding to position 1. Thus, that voxel is exposed by the beam (404) corresponding to position 1 and the beam (404) corresponding to position 2. Similarly, a 3D printer exposes multiple voxels with beams at different angles, hardening resin in those voxels to form an object.

[0030] According to one or more embodiments, a 3D printer may cure a voxel by exposing the voxel with at least two beams at different angles. An example of exposing a voxel with two beams at different angles is shown in Figure 4A. The total exposure dose to cure the resin (410) in the voxel is at least equal to the sum of the exposure doses of the at least two different beams (404) at that voxel.

[0031] In one or more embodiments, movement of the image set or objective (406-1, 406-2) may be selected to expose a voxel to beams at more than two different angles to desired harden the resin in that voxel. For example, the objective shown in FIG. 4A may move to position 3 to illuminate that voxel at a third angle different from the angles corresponding to positions 1 and 2. According to one or more embodiments, the number of exposures, images in the image set, and exposure angle are calculated for each voxel in the print area. That is, voxels inside the object that form the object are exposed to a sufficient amount to harden, while voxels outside the object are exposed to a low enough amount to remain liquid and separable from the object.

[0032] The calculation of the required exposure at each voxel is shown in Figures 5A-5C. Specifically, Figure 5A shows that an object model (502) is discretized onto a 3D grid (506) of voxels. The voxels are then printed using a beam (504). To print a voxel, the beam (504) must be illuminated at point (x0, y0, z0), as shown in Figure 5B. As shown in Figure 5C, when the beam (504) illuminates voxel (508), it also passes through other voxels (510, 512) in the grid. The illumination of these other voxels (510, 512) can be considered the residual exposure. According to one or more embodiments, the cumulative (total) exposure at each voxel, including the residual exposure, may be calculated to determine the movement of the objective relative to the image set and the resin. In other words, the movement of the objective relative to the image set and resin is determined so that the overall exposure at each voxel within the object model is high enough to cure the resin in that voxel, and conversely, the movement of the objective relative to the image set and resin is determined so that the overall exposure at each voxel outside the object model is low enough so as not to cure the resin in that voxel.

[0033] Furthermore, FIG. 4A shows that only one pixel is turned on at each of Position 1 and Position 2. This illustration is provided for the purpose of simplifying the operation of a 3D printer according to one or more embodiments. However, at each position, the image corresponding to that position may be selected such that multiple pixels are turned on. In this manner, multiple voxels may be addressed at each position of the objective relative to the resin. For example, FIG. 4B shows a prototype according to one or more embodiments, in which beams (414) emitted from the objective at Position 1 (406-1) and Position 2 (406-2) are directed into resin contained in a container (412). According to one or more embodiments, the container (412) may be configured to contain the resin (410) such that the surface of the resin (410) onto which the beam (404) is incident is flat and perpendicular to the axial direction (i.e., optical axis) of the objectives (406-1, 406-2).

[0034] According to one or more embodiments, the light source (402) may include a DMD configured to reflect multiple beams toward the resin (410).

[0035] According to one or more embodiments, the light source (402) may include one or more lasers that generate multiple beams, and the light source (402) may include one or more mirrors or prisms that reflect the beams toward the objectives (406-1, 406-2).

[0036] According to one or more embodiments, the 3D printer may collimate the beams before they enter the objective. For example, the 3D printer may include a collimator before the objective, the collimator including one or more lenses, one or more prisms, or one or more mirrors. In the example shown in FIG. 3B, the beam (302) is collimated before it enters the objective (306).

[0037] According to one or more embodiments, the objective may be an oil immersion objective. The output side of the oil immersion objective is immersed in, for example, a droplet or thin film of oil, the resin itself, or an elastic solid. According to one or more embodiments, immersing the objective in a medium with a refractive index greater than 1 allows for a larger angular dispersion of the beam in resins with a refractive index greater than 1. This technique is used in various optical technologies, such as lithography and microscopy, and is known for various coupling materials, including water and elastomers, as well as evanescent coupling through a thin air gap, known as "solid immersion."

[0038] According to one or more embodiments, the motor is configured to move the objective relative to the resin along at least two axes that are orthogonal to the axial direction of the objective. For example, in FIGS. 3A and 4A, the motor may move the objective relative to the resin along two in-plane axes that are orthogonal to the axial direction of the objective (306, 406-1, 406-2). The axial direction of the objective (306, 406-1, 406-2) in FIGS. 3A and 4A is a vertical axis that aligns with the irradiation direction of the collimated beam (302). According to one or more embodiments, these two in-plane axes may be orthogonal to each other.

[0039] According to one or more embodiments, a motor may move the objective relative to the resin along the axial direction of the objective, this additional degree of freedom allowing for adjustment of the beam size in the voxel.

[0040] FIG. 6 shows a schematic diagram of a system (600) according to one or more embodiments. The system (600) includes, for example, a buffer (602) and a 3D printer (606), examples of which are described above with reference to FIGS. 3A-3B and 4A-4B. The buffer (602) may be implemented in hardware (i.e., circuitry), software, or a combination thereof. The buffer (602) is configured to store a print object file (604). The print object file (604) may include an object model and instructions for printing by a printer (606) using the object model. The printer (606) can print an object corresponding to the object model based on the print object file (604). To perform the printing function, the printer (606) includes one or more motors (608), a light source (610), an objective (612), and a container (614) for containing resin. Examples of the motor (608), light source (610), objective (612), and container (614) are described above with reference to Figures 3A-3B and 4A-4B. As described further below with reference to Figure 20, the system (600) may include a processor that controls the operation of one or more motors (608) and light source (610) to perform a printing function. For example, the processor may control the light source (610) to project an image set and control the movement of the objective (612) relative to the resin, as described above with reference to Figures 4A-4B, based on the print object file (604).

[0041] 7 illustrates a flowchart of a method of operating a 3D printer according to one or more embodiments. In one or more embodiments, one or more steps illustrated in FIG. 7 may be omitted, repeated, or performed in a different order than that illustrated in FIG. 7. Thus, the scope of the present invention is not limited to the specific order of steps illustrated in FIG. 7. Steps 700 through 735 illustrated in FIG. 7 are described below.

[0042] In step 700, a light source including a plurality of pixels is controlled to emit a plurality of beams toward an objective system. Examples of this step are provided above with reference to Figures 3A-3B, 4A-4B, and 6. For example, the processor may control the light source (402) shown in Figure 4A to project a set of images.

[0043] In step 705, the beams are diverged through the objective as they are emitted from the objective toward the resin region. Examples of this step are shown above with reference to Figures 3A-3B and 4A-4B. For example, the objective (306) shown in Figure 3B diverges the beam (304) before it enters the resin (310).

[0044] In step 710, one or more motors move the objective relative to the resin.

[0045] In step 715, the objective is moved so that multiple beams irradiate multiple voxels within the region of the resin.

[0046] In step 720, the voxels are hardened by irradiating the voxels with the beams.

[0047] In step 725, the objective emits a plurality of beams such that each of the plurality of voxels is exposed by at least two different beams of the plurality of beams.

[0048] In step 730, each voxel is exposed at two different times with at least two different beams such that the at least two different beams spatially overlap only within each voxel.

[0049] In step 735, the total exposure dose to cure the resin in each voxel is determined to be greater than or equal to the sum of the exposure doses of at least two different beams in each voxel.

[0050] Examples of steps 710 through 735 are also shown above with reference to FIGS. 4A-4B and 6.

[0051] According to embodiments disclosed herein, the method may include one or more steps. For example, according to one or more embodiments, the irradiation of at least two beams may be performed such that the at least two different beams are oriented at different angles relative to each other. According to one or more embodiments, the method may include reflecting the beams toward the resin portion. According to one or more embodiments, the method may include collimating the beams before they enter the objective system. According to one or more embodiments, the method may include moving the objective system along at least two axes orthogonal to an axial direction of the objective system.

[0052] 3D printers according to one or more embodiments may offer advantages over conventional VAMs. For example, whereas in CALs, a resin sample is rotated in front of a projection light, e.g., within a cylindrical container, one or more embodiments disclosed herein can provide multiple angles. Furthermore, 3D printers according to one or more embodiments allow resin to be filled into virtually any shape, such as the planar packages shown in FIGS. 3A-3B and 4A-4B. In one or more embodiments, more degrees of freedom, e.g., four or more degrees of freedom, may enable printing of more complex and higher-resolution patterns. Specifically, in one or more embodiments, a single voxel may receive light tilted about two orthogonal axes (at different times) rather than a single one. Also, in one or more embodiments, unlike conventional VAMs, the beam movement relative to the resin is not restricted, and motors can move the objective to any position defined by a commercially available unit.

[0053] In a conventional VAM, the beam corresponding to each pixel must be nearly collimated throughout the entire thickness of the resin, and physical diffraction limits the minimum beam diameter. In contrast, in one or more embodiments, in a 3D printer, the thickness of the resin is not linked to the lateral movement of the objective.

[0054] One or more embodiments disclosed herein relate to methods and systems for printing 3D objects based on an object model. Specifically, one or more embodiments relate to methods and systems for generating a set of images projected by a light source. An example of an image set projected by a light source (402) is described above with reference to FIG. 4A. The image set must be selected / calculated as a function of the objective system's movement to achieve the desired 3D object. To this end, the intensity of each pixel at each angle must be selected to create 2D slices of the 3D part. According to one or more embodiments, the 3D object model is represented by an image with four effective dimensions (degrees of freedom): pixel row + pixel column = two dimensions, followed by two-dimensional movement, i.e., two more dimensions. These movements are independent because the beams emitted from the objective system diverge at two angles. If the beams were parallel or nearly parallel, the movement would not produce a "useful" change in illumination, as described above and shown in FIG. 2.

[0055] To determine the image set and its transformation to the object, the reverse (image to object) and forward (object to image) projections must be determined. Back projection is also referred to herein as "back projection." Back projection can be defined as a matrix (B) that transforms the intensity of an image in image space (i.e., the space in which the image set resides) into the exposure dose imparted to the object in object space (i.e., the space in which the object and object model reside). Conversely, forward projection can be defined as a matrix (F) that transforms a quantity defined over an object or object model in object space (e.g., the exposure dose or the error of the desired exposure dose relative to the target) into an image in image space. The B and F matrices are determined by projecting light through the optics of the 3D printer and then determining the refraction of the light through the resin through simulations or calculations that account for refraction, diffraction, lens aberrations, scattering, and other relevant optical and material physics.

[0056] We now turn to a method for determining the image set and transforming the image set into object space. For simplicity, this method will be described using the cylindrical coordinate system shown in Figures 8A-8C in accordance with one or more embodiments. However, these embodiments are not limited to describing objects in a cylindrical coordinate system; other coordinate systems, such as the Cartesian coordinate system described in Figure 4A, can also be used.

[0057] FIG. 8A illustrates 3D printing of an object described in a cylindrical coordinate system, according to one or more embodiments. Specifically, in FIG. 8A, a 2D pixel array (S) (802) projects a beam into a cylinder containing resin. Similar to a conventional VAM, a 3D object can be printed by rotating the cylinder and projecting a set of images with the pixel array coordinated with the rotation of the cylinder. FIG. 8B shows a cross-section of the printed area only when angle θ=0. FIG. 8C shows a magnified horizontal cross-section of the cross-section shown in FIG. 8B. In FIGS. 8A-8C, the "x" and "z" coordinates are along the plane of the pixel array (S) and perpendicular to "y." The intensity levels shown on the right side of FIGS. 8B and 8C indicate the intensity of the light quantity in the spatial region indicated in the figure. Throughout this specification, exposure intensity is also referred to as object intensity, light quantity intensity, or object light quantity.

[0058] According to one or more embodiments, an advantage of a cylindrical coordinate system is that for rotationally symmetric objects, only a single angle needs to be calculated. Because the trajectory and the object representation are in the same coordinate system, all other angles can be calculated by a circumferential shift (i.e., increasing θ). For example, in a typical VAM system with one-degree angular intervals, rotational symmetry can potentially reduce computation time and, in some cases, memory usage by a factor of 360. Similarly, in systems where the object's motion relative to the resin can most easily be described as a translation in a Cartesian coordinate system, describing the object in a Cartesian coordinate system is advantageous. In general, the choice of coordinate system for describing the object can take advantage of the printer's symmetry to reduce memory and other computational resources.

[0059] According to one or more embodiments, the relationship between object light intensity and image intensity is considered to be linear. That is, the backprojection process can be expressed as a matrix-vector product B × I = O, where I is the vector of all image pixels at all positions s and all angles, and O is now the vector of all object voxels at all radii "r" and all angles θ. B is a matrix whose rows and columns are equal to the total number of image pixels and object voxels. As previously mentioned, this can be impractically large to generate or store. However, according to one or more embodiments, it is possible to reduce computation by calculating a submatrix of B for the pixel array S at θ and all object voxels at one position of the motion system, e.g., a rotary printer such as CAL. As shown in FIG. 8B, the submatrix of B can be nearly sparse because most of the cross section is black (i.e., no exposure intensity) and many values ​​are zero. Therefore, the submatrix of B may be represented as a "sparse matrix" that stores only non-zero values. Storing and computing such "sparse matrices" is standard in modern computing languages ​​such as MATLAB. For a typical problem, the size of the sparse matrix can be less than 1% of the full matrix size. Furthermore, sparseness of calculations and matrices at a single motion position, such as an angle, typically reduces memory usage and time requirements by 4–5 orders of magnitude. While this has been described for a typical cylindrical coordinate system in CAL, where a cylindrical resin container is rotated on its axis, this discussion applies broadly to any volume printer where the motion of the object relative to the resin can be selected as the axis of the coordinate system. Therefore, the translational motion shown in Figures 4A and 4B can be most efficiently represented in a Cartesian coordinate system, and using this Cartesian coordinate system to represent the object saves memory in the projection matrix, as discussed above.

[0060] According to one or more embodiments, generating the complete B matrix can be achieved by appropriately indexing sub-matrices of B (e.g., those corresponding to one position of the objective at angle θ). This makes it practical to compute and store B using a sparse matrix, thereby conserving memory. As mentioned above, if the object has rotational symmetry in a cylindrical coordinate system, the computation only needs to be done once per angle. Similar logic applies to matrices performing a forward projection (F), which relies on the same computations and can be written with the same sparse matrix indexing as O × F = I.

[0061] According to one or more embodiments, forward and back projections can be performed faster than traditional approaches by using sparse matrices. According to one or more embodiments, after computing a sub-matrix, a matrix product of this sub-matrix with an object vector (O) or an intensity vector (I) can be performed, and then a sum of the motions (e.g., rotation angles) with appropriate indexing can be performed to represent the motion. This method can replace one dimension of the operations performed by the full B and F matrices with an iterative summation (e.g., a "for" loop), thereby saving memory.

[0062] Thus, by discretizing an object by selecting a coordinate system that is invariant to the object and its motion relative to the image, dramatic memory or speed improvements can be realized in mathematical operations. For translational motion, according to one or more embodiments, a grid that is invariant to one-dimensional translation (1D translation) or a grid that is invariant to two-dimensional translation (2D translation) may be selected. This includes a Cartesian coordinate grid, although other options are contemplated. For example, a two-dimensional translational layout need not be translated as a two-dimensional Cartesian raster, but could instead be translated in a cylindrical coordinate system.

[0063] Methods that can be used to calculate an image set for projection are roughly divided into the following three types (1) to (3). (1) Filtered back projection (FBP) (known in computed tomography) - This method produces unphysical negative intensities. Negative intensities are truncated to a minimum value of 0. This method may result in poor printing fidelity. (2) Gradient Descent (GD) in Image Space - This method uses traditional optimization techniques to refine the object. This method is computationally expensive and requires knowledge of the derivatives of an evaluation function that represents the quality of the object at each pixel. These gradients are expensive to compute and not necessarily accurate, resulting in poor convergence. (3) Object Space Model Optimization (OSMO) - This method applies the FBP method to an "object model" in object space, which is allowed to be non-physical (e.g., negative values ​​are allowed). Back-projection of this model yields the optimal object. This method is based on the assumption that the interior of the object (the part to be cured) is within the upper critical exposure intensity D upper The outside of the object (the part that remains liquid) is exposed to the lower critical exposure intensity D lower We try to force the following:

[0064] The method according to one or more embodiments described below may provide at least the following advantages: One advantage of the method is that the object is exposed to two target exposure thresholds (D upper and D lower ) to derive feedback. In contrast, gradient descent in image space requires estimating the derivative of some error metric for each pixel intensity. Another advantage of the present method is that the error metric can be derived from the object. The error metric, as described further below in accordance with one or more embodiments, allows for a simple and natural capture of material physics occurring within the object. This material physics may include inhibitory effects, nonlinear responses, or diffusion. These physical phenomena may be difficult to capture using image gradient descent.

[0065] Below, we describe, in one or more embodiments, new methods for 1) direct matrix solution and 2) forward projection of object error. 1) Direct matrix solution method

[0066] According to one or more embodiments, when the entire object is known (i.e., exposure values ​​are given, not inequalities), a least-squares optimal solution can be found using the backprojection matrix (B) described above. That is, if matrix B has sufficient rank, a system of linear equations B×I=O can be solved for I. It is well known in the field of linear algebra that this solution does not require inverting matrix B, but can instead be solved by matrix decomposition, such as QR decomposition. These solutions 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 FIG. 9. In FIG. 9, a photograph of a woman's face is chosen as the object, as an example of an object where the exposure across the entire portion is known.

[0067] This technique does not guarantee that the non-negativity constraint is satisfied; that is, negative intensities are allowed. However, this constraint can be satisfied by reducing the contrast and smoothing the object. FIG. 9A shows a target object targeted for printing. In FIG. 9A, the minimum exposure is set to 0.9, and the object may be further smoothed using a low-pass filter to reduce and smooth the contrast of the image. As the contrast is reduced and / or the object is smoothed, the minimum intensity increases and the range of intensity decreases. In FIG. 9A, the range of intensity is between 0.9 and 1. Thus, the target object may be modified to satisfy the minimum and maximum intensity constraints.

[0068] 9B illustrates image intensity (I) (in image space) versus pixel array (S) and rotation angle (θ) in accordance with one or more embodiments. The image intensity represents a set of images corresponding to various angles and is calculated by forward projecting the object of interest shown in FIG. 9A using a forward projection matrix (F). Specifically, O×F=I.

[0069] Figure 9C, in one or more embodiments, illustrates the exposure intensity (in object space) in a Cartesian coordinate system for a slice in object space. This exposure intensity represents the exposure amount in object space that corresponds to the image intensities shown in Figure 9B. This exposure intensity is calculated by backprojecting the image intensity (I) using the backprojection matrix (B). Specifically, as previously discussed, B x I = O.

[0070] Figure 9D shows an error, which is the difference between the target object shown in Figure 9A and the exposure intensity shown in Figure 9C. In other words, Figure 9D shows the deviation of the exposure intensity shown in Figure 9C from the target object shown in Figure 9A. One or more embodiments described below provide ways to reduce this error. 2) Forward projection of object error

[0071] According to one or more embodiments, this method may be applied to more typical VAM processes for printing 3D objects where the target area is hardened while the area outside the target remains liquid. The intensity constraints in image space are combined with the exposure constraints in object space through back projection, so that an iterative process can be performed between these two spaces. The OSMO method uses forward projection (from object to image) to create an "intermediate" model that corresponds to the errors in the object (unsatisfied constraints) and finds an improved image set. Here, according to one or more embodiments, the model is rejected by calculating the error in object space and propagating the error directly forward to image space, and a new image set is calculated.

[0072] The steps corresponding to the forward projection of object error are listed below in alphabetical order, which is provided solely for ease of understanding the embodiments disclosed herein and is not intended to limit the invention to this particular order or steps.

[0073] A) According to one or more embodiments, a target object to be printed is first discretized onto a voxel grid. An example of this step is shown in FIGS. 10A-10B. FIG. 10A shows a target object (1006) within a print area in a cylindrical coordinate system. The white areas of the target object (1006) are intended to be cured (printed), while the dark areas (1008) outside the target object are intended to remain liquid. FIG. 10B shows the edge (1004) of the target object (1006) when it is discretized onto a voxel grid. FIG. 10B illustrates the difference between the boundary (1002) of the target object and the edge (1004) of the discretized object. According to one or more embodiments, the fractional area of ​​each voxel that overlaps with the target object may be calculated, or a binary representation may be used in which the voxel is classified as being completely inside (e.g., 1) or completely outside (e.g., 0) the object.

[0074] B) According to one or more embodiments, in addition to the target object to be printed (step A), three quantities may be defined. These three quantities are described below.

[0075] The first quantity is D upper D upper is the minimum amount of desired object exposure within the target. In other words, D upper is the minimum object exposure dose for voxels intended to be cured to form the object. This amount may be selected from photorheological testing to determine the minimum exposure dose that will cure the material sufficiently for post-processing, including removal from the printer and solvent washing.

[0076] The second quantity is D lower D lower is the maximum desired object exposure outside the target. In other words, D lower is the maximum object exposure for a voxel that is intended to remain liquid or have low viscosity, allowing the outer resin to separate from the printed / cured object. This amount may be selected from photorheological testing to determine the maximum exposure at which the resin remains liquid. This maximum exposure is sometimes referred to as the gel exposure.

[0077] The third quantity is Δ, which is the desired print resolution. This quantity is determined from printer properties, such as the diffraction limit of optical projection, and resin properties, such as the characteristic scale of component diffusion at print time. These limits may dictate the smallest feature size that can be physically printed. As the target resolution is relaxed (i.e., the minimum feature size is reduced), the set of feasible solutions expands. Therefore, the optimal design is one that matches and does not exceed the printer resolution. That is, the design resolution and the printer / material resolution may be chosen to be the same.

[0078] According to one or more embodiments, the three amounts mentioned above are D upper , D outside the target lower This target exposure may then be spatially filtered with a low-pass filter, such as a Gaussian or moving average, to set the resolution based on Δ. An example of this filtering process, in one or more embodiments, is shown in FIG. 11. Specifically, FIG. 11 shows the interior (1106) of the object, which is intended to be printed, and the exterior (1108) of the object, which is intended not to be printed. The boundary (1110) between the interior (1106) and exterior (1108) of the object is smoothed based on Δ. The expanded view of FIG. 11 shows the area where the boundary (1110) has been smoothed.

[0079] Without the smoothing step, even in ideal binary image projections and in the absence of chemical species diffusion, the dose distribution is continuous, so that for binary objects, D upper and D lower It may be impossible or difficult to find a solution that maximizes separation of . Conventional solutions that report optimal results with a finite gap (called a "process window") may be erroneous. The reported gap may be an artifact due to discrete sampling of the object. If the sampling is fine enough, the gap will disappear. Therefore, a smoothing step with a finite resolution Δ, as described in one or more embodiments, may improve the calculation.

[0080] Therefore, according to one or more embodiments, two exposure dose constraints (D upper and D lower ) is set. Then, the image intensity constraints (e.g., non-negative) are satisfied and the associated object exposure is determined to be within the object exposure constraints (e.g., D upper and D lower ) is found / determined. In regions such as smoothed boundary regions (e.g., smoothed boundary (1110) in FIG. 11), the exposure constraint within the boundary of interest is D upper and D lower The goal is to reduce the exposure in the outer regions, e.g., the far outside of the object, to D lower and the exposure at the smoothed boundary of the object is kept below D upper and D lower The exposure amount inside the object is calculated by D upper The goal is to exceed this.

[0081] According to one or more embodiments, image intensity constraints may be explicitly satisfied and object exposure constraints may be attempted to be satisfied, but the optimal solution may not always achieve those metrics.

[0082] According to one or more embodiments, boundary smoothing can facilitate finding a solution for an image set and object exposure with some error, where "error" in this paragraph means that some part of the object (e.g., near the edge) does not satisfy the exposure constraint.

[0083] According to one or more embodiments, an iterative process refines the initial guess to find an optimal set of images based on the target exposure.

[0084] C) According to one or more embodiments, an initial guess for the image set is calculated. This guess may be all ones, all zeros, or random. A forward projection of the target object (e.g., using matrix F) may be a good guess, as shown in Figure 12. In the field of computed tomography, this transform is sometimes called the Radon transform or a "sinogram" of the object. Figure 12 shows a forward projection of the smoothed target exposure shown in Figure 11.

[0085] D) According to one or more embodiments, the image set calculated in step C is backprojected into object space (eg, using matrix B) to calculate the expected exposure distribution over the object.

[0086] E) According to one or more embodiments, the predicted exposure calculated in step D is used to calculate an error function for each voxel. The error function is calculated by comparing the predicted exposure calculated in step D with the target object determined in step B. To calculate the error, for each voxel within the object, the predicted exposure is multiplied by the upper exposure limit D upper The difference between the predicted exposure in the inner region calculated in step D and the predicted exposure in the inner region calculated in step D is calculated as D upper If it is greater than D, the error is zero. Otherwise, the error is the difference between the expected exposure in the interior region calculated in step D, for example, and D upper Similarly, for each voxel outside the object, the expected exposure calculated in step D is calculated as the square of the difference between the lower exposure limit Dlower The predicted exposure in the outer region calculated in step D is compared with D lower If it is smaller than D, the error is zero. Otherwise, the error is the difference between the expected exposure in the outer region calculated in step D, for example, and D lower It is calculated as the square of the difference between

[0087] Figure 13 shows an example of the error calculation performed in step E in one or more embodiments. Specifically, in Figure 13, the shading in the object interior region (1306) is calculated based on the predicted exposure D upper and the expected exposure in the interior voxels is less than D upper Similarly, the shading in the object exterior area (1308) indicates the difference between the predicted exposure and the lower Expected exposure in outer voxels above D lower 13 shows the RMS of the error, which is the difference between the internal and external shadows. The close-up on the right side of FIG. 13 shows a close-up of the internal and external shadows. According to one or more embodiments, the error calculation in step E may ignore the boundary (1310) of the object since there is no shadow at the boundary (1310), as shown in the close-up of FIG. 13. Instead, the exposure at the boundary (1310) is calculated by upper and D lower may be treated as a smooth curve between

[0088] F) According to one or more embodiments, the error distribution across the object may be forward projected into image space. Specifically, the interior error and the exterior error may be forward projected separately. This process calculates two RMS errors for each voxel illuminated by each pixel: one error representing underexposure in the interior region of the object, and one error representing overexposure in the exterior region of the object. Each of these is calculated for each pixel in the image set.

[0089] 14A-14C illustrate an example of step F. As shown in FIG. 14A, errors corresponding to the object's interior regions (final signed RMS interior errors) are forward projected into image space. The errors shown in FIG. 14A have negative signs because they occur only when the interior exposure is too low. Similarly, as shown in FIG. 14B, errors corresponding to the object's exterior regions (final signed RMS exterior errors) are forward projected into image space. The errors shown in FIG. 14B have positive signs because they occur only when the exterior exposure is too high. The forward projection may be performed using a forward projection matrix F. FIG. 14C illustrates the final signed RMS error, which is the sum of the forward projection errors shown in FIGS. 14A and 14B. Because some of the forward projection errors shown in FIGS. 14A and 14B cancel each other out, the sum shown in FIG. 14C has a smaller magnitude than the forward projection errors shown in FIGS. 14A and 14B. In other words, the magnitude is adjusted to balance the interior and exterior errors, so the sum can be close to zero for most pixels.

[0090] G) According to one or more embodiments, the sum of two signed forward projection errors (e.g., as shown in FIG. 14C) at each pixel may provide a signed error function that determines how pixel intensities should be updated in image space. For example, by taking the square root of the two mean squared errors to generate a root-mean-square (RMS) error, the sum of the two signed forward projection errors may be added to the pixel intensity to update its value. For example, the sum of errors shown in FIG. 14C may be applied to the pixel intensities of pixel array S to modify the image set. According to one or more embodiments, an acceleration technique that takes a larger step size may be used to converge in fewer iterations.

[0091] H) According to one or more embodiments, after each update, the image set is constrained to be positive and (optionally) less than a desired maximum value. If the intensity constraint is met, the error function is not used to further update the image. In other words, the iterative process may stop if the error for this pixel no longer decreases and the solution is not feasible. For example, the iterative process may continue to improve all errors, producing an optimal design for the given input, but a finite error remains and feasibility is rejected.

[0092] I) According to one or more embodiments, the image set may further be discretized (e.g., to 8 bits) to match the resolution of the light source (e.g., image projection chip such as a DMD) used in the printer, which may reduce physical printing errors caused by discretizing a continuous numerical solution to a projector with a finite discrete resolution.

[0093] J) According to one or more embodiments, steps D-G may be repeated until a termination condition is reached. The termination condition may be, for example, reaching an upper limit on the number of iterations or slowing down of improvement in error reduction.

[0094] K) According to one or more embodiments, if the intensity constraints are not met, the magnitude and final slope of the error function may be evaluated to determine the feasibility of the solution within a certain error tolerance. Possible intensity constraints are as described above, including non-negativity, upper intensity limits, and discretization into a finite number of values, such as 256. For example, in FIG. 15, the total RMS error (1506) decreases by a factor of 1000 from the initial estimate and continues to decrease with further iterations. This solution may be defined as feasible within a predetermined tolerance for the total object error or maximum object error. In FIG. 15, the RMS of the internal error (1504) and the RMS of the external error (1502) continuously converge, and the total RMS error (1506) continues to decrease.

[0095] According to one or more embodiments, at the end of the image correction process, a final image set is obtained, as shown in Figure 16. The intensities of the final image set are constrained to be in the range 0 to 1, and at each step, they are discretized to a number of bits that matches, for example, the resolution of a typical DMD projector chip (e.g., 8 bits).

[0096] According to one or more embodiments, the final object exposure is D upper and in the outer region, lower For example, in Figure 17, D upper and D lower are 0.4 and 0.35, respectively, and the final object exposure is close to these values ​​in the interior and exterior regions of the object, respectively.

[0097] 18A and 18B show the final error, i.e., D upper and D lower This shows that the exposure that does not satisfy the condition is concentrated around the boundary of the object. The final error is calculated by backprojecting the final image set and upper (inside the object) and D lower (outside the object). Figure 18B shows an enlarged view of Figure 18A.

[0098] According to one or more embodiments, the method described with reference to steps A-K and FIGS. 8A-18B may provide one or more of the following advantages: The use of sparse matrix multiplication in the optimal coordinate system described above (e.g., cylindrical coordinate system in CAL) may reduce the number of iterations compared to conventional methods. By selecting an appropriate error function, the error may converge continuously and quickly. By accessing both object space and image space, it may be possible to prevent divergence by including object space physics and image space constraints. There is flexibility in choosing an error function in object space that directly generates gradients in image space. The simplicity, memory efficiency, and speed of the method presented here for 2D telecentric geometry may allow for the method to be extended to more complex multidimensional structures.

[0099] Although the methods described above with reference to steps A-K and Figures 8A-18B are described with reference to a cylindrical coordinate system, these methods can be extended to a Cartesian coordinate system.

[0100] Figure 19 illustrates a flowchart of a method for determining an image set, in one or more embodiments. In one or more embodiments, one or more steps illustrated in Figure 19 may be omitted, repeated, or performed in a different order than that illustrated in Figure 19. Thus, the scope of the present invention should not be limited to the particular order of steps illustrated in Figure 19. Steps 1900 through 1940 illustrated in Figure 19 are described below.

[0101] 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 Figures 10A and 10B. According to one or more embodiments, an upper exposure limit (D) is determined, which is the minimum exposure inside the object. upper ) may be defined. According to one or more embodiments, a lower exposure limit (D lower) may be defined. According to one or more embodiments, a printing resolution (Δ) may be defined, which is the smallest feature size that can be printed. According to one or more embodiments, a low-pass spatial filter with a cutoff of Δ may be applied to smooth the boundaries of the object. The exposure within the smoothed boundaries may be calculated as D upper and D lower may be smoothed between

[0102] 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 FIG. 12.

[0103] In step 1910, the expected exposure distribution in object space (D) is determined by backprojecting I using the backprojection matrix (B). One or more examples of this step are described above with reference to step D.

[0104] 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 step E and FIG. 13. According to one or more embodiments, for interior voxels of the object, D and D upper If the expected exposure of an interior voxel at D is greater than D, then the difference between upper If the expected exposure of the interior voxel is not less than D, the error corresponding to that interior voxel is determined to be zero. upper If the error corresponding to the interior voxel is less than the expected exposure, then the error is upper According to one or more embodiments, for the exterior voxels of the object, the difference between D and D lower The difference between the expected exposure of the outer voxels at D and D may be determined. lower If the expected exposure of the exterior voxel does not exceed D, the error corresponding to that exterior voxel is determined to be zero. lower If the error corresponding to the outer voxel is greater than the expected exposure, then the error is lowerIt is determined based on the difference between

[0105] In step 1920, E is forward projected using F. One or more examples of this step are described above with reference to step F and FIGS. 14A-14C and 15.

[0106] 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 G-H and Figure 16. According to one or more embodiments, the modified I may be compared to a predetermined intensity constraint to determine whether the modified I is within the intensity constraint.

[0107] 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 FIG.

[0108] In step 1935, the modification of I is performed sequentially until a predetermined condition occurs. One or more examples of this step are described above with reference to steps J-K and Figures 15, 17, and 18A-18B. According to one or more embodiments, the predetermined condition may be that E is less than a first threshold. According to one or more embodiments, the predetermined condition may be that a maximum number of iterations is reached. According to one or more embodiments, the predetermined condition may be that the difference between E of an iteration step and E of a immediately preceding iteration step is less than a second threshold.

[0109] In step 1940, the final I corresponding to the predetermined conditions is used to print the object. One or more examples of this step are described above with reference to steps J-K and Figures 15, 16, and 18A-18B.

[0110] According to one or more embodiments, no error determination is made relative to the boundary of the object.

[0111] 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.

[0112] For example, one or more embodiments relating to the operation of a 3D printer disclosed with reference to Figures 3A-19 can be implemented on virtually any type of computer system, regardless of the platform used. The computer system may include programs or algorithms that control the operations / functions described in the above-described embodiments. For example, the computer system may be one or more mobile devices (e.g., laptop computers, smartphones, personal digital assistants, tablet computers, or other mobile devices), desktop computers, servers, blades in a server chassis, or any other type of computer system that includes at least the minimum processing power, memory, and input / output devices to execute one or more embodiments of the present invention.

[0113] An example of a computer system according to one or more embodiments is described with reference to FIG. 20. FIG. 20 is a block diagram of a computer system that may be used to provide computational functionality related to the algorithms, methods, functions, processes, flows, and procedures described in this disclosure. The illustrated computer (2002) of the computer system is intended to encompass a server, desktop computer, laptop / notebook computer, wireless data port, smartphone, personal digital assistant (PDA), tablet computing device, one or more processors within these devices, or other suitable processing device, and may include physical or virtual instances (or both) of such processing devices. Additionally, the computer (2002) may include input devices such as a keypad, keyboard, touchscreen, or other device capable of accepting user information, and may also include output devices that communicate information related to the operation of the computer (2002). The output devices may include digital data, visual or audio information (or a combination thereof), or a GUI.

[0114] In one or more embodiments, the 3D printer described in the above embodiments may include, be in the form of, or be implemented on a computer (2002) that performs the processes and calculations described above with reference to Figures 3A-19. For example, the computer (2002) on which the 3D printer is implemented may include tools for performing processes related to 3D printing and determining the final image set described in the above embodiments.

[0115] The computer (2002) may function as a client, a network component, a server, a database or other persistent storage, or any other component (or a combination of these roles) for implementing the subject matter described herein. The illustrated computer (2002) is communicatively coupled to a network (2030). In some embodiments, one or more components of the computer (2002) may be configured to operate within an environment, including a cloud computing-based, local, global, or other environment (or a combination thereof).

[0116] Broadly speaking, the computer (2002) is an electronic computing device capable of receiving, transmitting, processing, storing, or managing data and information related to the described subject matter. According to some embodiments, the computer (2002) may include or be communicatively connected to an application server, email server, web server, caching server, streaming data server, business intelligence (BI) server, or other server (or combination thereof).

[0117] The computer 2002 can receive requests from client applications (e.g., those running on other computers 2002) over the network 2030 and respond to the received requests by processing the requests in an appropriate software application. Additionally, requests may also be sent to the computer 2002 from internal users (e.g., from a command console or other suitable access method), external or third-party applications, other automated applications, and other suitable entities, individuals, systems, or computers.

[0118] The components of the computer (2002) can communicate using a system bus (2003). In some embodiments, any or all of the components of the computer (2002), whether hardware or software (or a combination thereof), can connect to each other or to the interface (2004) (or both) over the system bus (2003) using an application programming interface (API) (2012) or a service layer (2013) (or a combination of the API (2012) and the service layer (2013)). The API (2012) may include specifications for routines, data structures, and object classes. The API (2012) may be computer language independent or language dependent and may refer to a complete interface, a single function, or a collection of APIs. The service layer (2013) provides software services to the computer (2002) or other components (whether shown or not) communicatively connected to the computer (2002). The functionality of the computer (2002) is accessible by all service consumers using this service layer (2013). The software services provided by the service layer (2013) provide reusable, predefined business functions through a defined interface. For example, this interface may be software written in Java, C++, Python, or another suitable language and providing data in Extensible Markup Language (XML) format or another suitable format. While shown as an integrated component of the computer (2002), in alternative embodiments, the API (2012) or service layer (2013) may be shown as a standalone component in conjunction with other components of the computer (2002) (whether or not shown). Furthermore, any or all portions of the API (2012) or service layer (2013) may be implemented as a child module or submodule of another software module, enterprise application, or hardware module.

[0119] The computer 2002 includes an interface 2004. While one interface 2004 is shown in FIG. 20, two or more interfaces 2004 may be used depending on the particular needs, requirements, or implementation of the computer 2002. The interface 2004 allows the computer 2002 to communicate with other systems in a distributed environment connected to a network 2030. Generally, the interface 2004 includes logic encoded in software or hardware (or a combination thereof) that can communicate with the network 2030. More specifically, the interface 2004 may include software supporting one or more communication protocols associated with the communication, thereby enabling the network 2030 or interface hardware to communicate physical signals within and outside the illustrated computer 2002.

[0120] The computer (2002) includes at least one computer processor (2005). While shown in Figure 20 as a single computer processor (2005), two or more processors may be used depending on the particular needs, desires, or particular implementation of the computer (2002). Generally, the computer processor (2005) executes instructions and manipulates data to perform the operation of the computer (2002) and the algorithms, methods, functions, processes, flows, and procedures described in this disclosure.

[0121] The computer (2002) also includes a memory (2006) or other components (or both) that hold data for the computer (2002) and are connectable to a network (2030). For example, the memory (2006) may be a database that stores data consistent with the present disclosure. As one example, the memory (2006) may store a program or algorithm for controlling the 3D printing process and determining the final image set described in the above-described embodiments. While a single memory (2006) is illustrated in FIG. 20 , two or more memories may be used depending on the specific needs, desires, or specific implementation of the computer (2002) and the described functionality. While the memory (2006) is illustrated as an integral component of the computer (2002), in other embodiments, the memory (2006) may be external to the computer (2002).

[0122] The application (2007) is an algorithmic software engine that provides functionality according to the specific needs, desires, or specific implementation of the computer (2002), particularly related to the functionality described in this disclosure. For example, the application (2007) may function as one or more components, modules, applications, etc. As an example, the application (2007) may include a program or algorithm for controlling the operation of a 3D printer and determining the final image set described in the above-described embodiments. More specifically, in this example, the program or algorithm may control 3D printing and determining the final image set described in the above-described embodiments with reference to FIGS. 3A-19. Furthermore, while the application (2007) is illustrated as a single application (2007), it may be implemented as multiple applications (2007) on the computer (2002). Also, while the application (2007) is illustrated as an integral component of the computer (2002), it may be implemented external to the computer (2002) in alternative embodiments. As an example, the methods described with reference to FIGS. 7 and 19 may be implemented by the application (2007).

[0123] The computer system may include any number of computers (2002) associated with or external to the computer (2002), and each computer (2002) communicates via a network (2030). Furthermore, the terms "client," "user," and other appropriate terms may be used interchangeably, as appropriate, without departing from the scope of this disclosure. This disclosure may also contemplate multiple users using one computer (2002), or one user using multiple computers (2002). Furthermore, in one or more embodiments, the computer (2002) is a non-transitory computer-readable medium (CRM).

[0124] While only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many changes can be made in the illustrated embodiments without substantially departing from the invention, and all such modifications are intended to be included within the scope of this disclosure as defined by the following claims.

[0125] Further, one or more embodiments relating to determining the image set are described below.

[0126] According to one or more embodiments, a method for 3D printing an object includes: determining an initial object model (O) in object space by discretizing the object onto a voxel grid; determining an image set (I) in image space by forward projecting O using a forward projection matrix (F); determining an expected exposure distribution (D) in object space by backprojecting I using a backprojection matrix (B); determining an error set (E) corresponding to D; forward projecting E using F; modifying I based on the forward projection of E; forward projecting the modified I using F to determine D; sequentially performing the modifications of I until a predetermined condition occurs; and printing the object using the final I corresponding to the predetermined condition.

[0127] According to one or more embodiments, determining O includes: determining an upper exposure limit (D upper ) to define the minimum exposure limit (D lower ) and define the print resolution (Δ), which is the smallest feature size that can be printed. Then, apply a low-pass spatial filter with a cutoff of Δ to smooth the boundaries of the object, and the exposure within the smoothed boundaries of the object is calculated as D upper and D lower The difference is smoothed between the two.

[0128] According to one or more embodiments, determining E includes: for interior voxels of the object, determining D and D upper Determine the difference between the expected exposure of the interior voxel at D and D upper If the predicted exposure of the interior voxel is not less than D, determine the error corresponding to that interior voxel as zero. upper If the error is less than 1 / 2, the error corresponding to the interior voxel is calculated by dividing the expected exposure of the interior voxel by D upper For voxels outside the object, the decision is based on the difference between D and D lower Determine the difference between the expected exposure of the outer voxels at D and Dlower If the expected exposure of the outer voxel does not exceed D, the error corresponding to that outer voxel shall be determined to be zero. lower If the error exceeds D, the error corresponding to the exterior voxel is calculated by dividing the expected exposure of the exterior voxel by D. lower The decision shall be based on the difference between

[0129] According to one or more embodiments, the method further includes comparing the modified / to a predetermined intensity constraint, and ensuring that the modified / is within the intensity constraint.

[0130] According to one or more embodiments, in the method, the predetermined condition is that E is less than a first threshold.

[0131] According to one or more embodiments, the predetermined condition is reaching a maximum number of iterations.

[0132] According to one or more embodiments, the predetermined condition is that the difference between E of an iterative step and E of the immediately preceding iterative step is less than a second threshold.

[0133] According to one or more embodiments, the method further includes discretizing / to match the resolution of the projector chip used to project the final / .

[0134] According to one or more embodiments, in the method, no error determination is performed on the boundary of the object.

[0135] According to one or more embodiments, in the method, the errors corresponding to the interior voxels and the errors corresponding to the exterior voxels are forward projected separately.

[0136] According to one or more embodiments, an apparatus for 3D printing an object includes an optical objective, one or more motors for moving the objective relative to a resin, a light source coupled to the objective, and a processor that determines an initial object model (O) in object space by discretizing the object onto a voxel grid, determines an image set (I) in image space by forward projecting O using a forward projection matrix (F), determines an expected exposure dose distribution (D) in object space by backprojecting I using a backprojection matrix (B), determines an error set (E) corresponding to D, forward projects E using F, modifies I based on the forward projection of E, forward projects the modified I using F to determine D, sequentially modifies I until a predetermined condition occurs, projects light from the light source using a final I corresponding to the predetermined condition, and directs the one or more motors to move the objective relative to the resin.

[0137] According to one or more embodiments, a non-transitory computer-readable medium (CRM) stores instructions for performing a process for 3D printing, including determining an initial object model (O) in object space by discretizing the object onto a voxel grid, determining an image set (I) in image space by forward projecting O using a forward projection matrix (F), determining an expected exposure dose distribution (D) in object space by backprojecting I using a backprojection matrix (B), determining an error set (E) corresponding to D, forward projecting E using F, modifying I based on the forward projection of E, forward projecting the modified I using F to determine D, iteratively modifying I until a predetermined condition occurs, and printing the object using a final I corresponding to the predetermined condition.

Claims

1. a light source including a plurality of pixels and configured to emit a plurality of beams toward an objective; the objective configured to diverge the plurality of beams when passing through the plurality of beams from the light source and exiting toward a resin region; one or more motors configured to move the objective relative to the resin region; Equipped with the one or more motors are configured to move the objective relative to the resin region to irradiate the beams onto a plurality of voxels within the resin region; irradiating the plurality of beams onto the plurality of voxels hardens the plurality of voxels; the objective system irradiates the plurality of beams such that each of the plurality of voxels is exposed by at least two different beams of the plurality of beams; exposing each voxel with the at least two different beams at two different times such that the beams spatially overlap only within each voxel; a total exposure dose for hardening the resin region in each voxel is equal to or greater than a sum of the exposure doses of the at least two different beams in each voxel; A three-dimensional printing device.

2. the at least two different beams propagate at different angles relative to one another; The three-dimensional printing device according to claim 1 .

3. the light source includes a digital micromirror device configured to reflect the plurality of beams toward the resin region. The three-dimensional printing device according to claim 1 .

4. the light source includes one or more lasers that generate the plurality of beams; The three-dimensional printing device according to claim 1 .

5. the one or more motors move the objective system relative to the resin region along an axial direction of the objective system. The three-dimensional printing device according to claim 1 .

6. the objective system is coupled to the resin via a refractive index matching material having a refractive index greater than 1; The three-dimensional printing device according to claim 1 .

7. the one or more motors are configured to move the objective along at least two axes orthogonal to an axial direction of the objective. The three-dimensional printing device according to claim 1 .

8. the one or more motors move both the objective system and the resin to move the objective system relative to the resin; The three-dimensional printing device according to claim 1 .

9. a container for containing the resin region; The three-dimensional printing device according to claim 1 .

10. the container accommodates the resin region such that a surface of the resin region onto which the plurality of beams are incident is flat and perpendicular to an axial direction of the objective system.

10. The three-dimensional printing device according to claim 9.

11. controlling a light source including a plurality of pixels to emit a plurality of beams toward the objective; diverging the plurality of beams through the objective system as they pass through the objective system and exit toward a resin region; moving the objective relative to the resin region via one or more motors; moving the objective relative to the resin region to irradiate the beams onto a plurality of voxels within the resin region; curing the voxels by irradiating the voxels with the beams; illuminating the plurality of beams through the objective such that each of the plurality of voxels is exposed by at least two different ones of the plurality of beams; exposing each voxel at two different times such that the at least two different beams spatially overlap only within each voxel; Including, a total exposure dose for hardening the resin region in each voxel is equal to or greater than a sum of the exposure doses of the at least two different beams in each voxel; A method of operating a three-dimensional printing device.

12. The irradiation of the at least two beams is performed such that the at least two different beams propagate at different angles relative to each other.

12. The method according to claim 11 .

13. the objective system is moved relative to the resin region along an axial direction of the objective system; 12. The method according to claim 11 .

14. the objective system is coupled to the resin via a refractive index matching material having a refractive index greater than 1; 12. The method according to claim 11 .

15. the objective system is moved relative to the resin region along at least two axes perpendicular to an axial direction of the objective system; 12. The method according to claim 11 .

16. a light source including a plurality of pixels and configured to emit a plurality of beams toward the objective; an objective configured to diverge the plurality of beams as they pass through the objective and exit toward a resin region; one or more motors configured to move the objective relative to the resin region; a processor configured to control the one or more motors to control movement of the objective relative to the resin region; a memory storing instructions for the processor to control movement of the objective relative to the resin region; Equipped with the processor controls, based on the instructions, movement of the objective system relative to the resin region to irradiate the beams onto a plurality of voxels within the resin region; irradiating the plurality of voxels with the plurality of beams hardens the plurality of voxels; the processor controls movement of the objective system that irradiates the plurality of beams such that each of the plurality of voxels is exposed by at least two different beams of the plurality of beams; the processor controls movement of the objective system such that the at least two different beams expose each voxel at two different times; the at least two different beams at the two different times spatially overlap only within each voxel; a total exposure dose for hardening the resin region in each voxel is equal to or greater than a sum of the exposure doses of the at least two different beams in each voxel; A three-dimensional printing system.

17. the at least two different beams propagate at different angles relative to one another; 17. The three-dimensional printing system of claim 16.

18. the light source includes a digital micromirror device configured to reflect the plurality of beams toward the resin region.

17. The three-dimensional printing system of claim 16.

19. the light source includes one or more lasers that generate the plurality of beams; 17. The three-dimensional printing system of claim 16.

20. the one or more motors move the objective system relative to the resin region along an axial direction of the objective system; 17. The three-dimensional printing system of claim 16.

Images