CN113865958A - Method for producing three-dimensional structures - Google Patents
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- CN113865958A CN113865958A CN202111105699.4A CN202111105699A CN113865958A CN 113865958 A CN113865958 A CN 113865958A CN 202111105699 A CN202111105699 A CN 202111105699A CN 113865958 A CN113865958 A CN 113865958A
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Abstract
The invention discloses a method for manufacturing a three-dimensional structure, which comprises the following steps: drawing a three-dimensional model of the portion that needs to be removed and/or deposited from the blank in order to obtain the three-dimensional structure; slicing the three-dimensional model in slicing software, thereby decomposing the three-dimensional model into a plurality of sliced layers; and importing the data of the plurality of sliced layers into processing software, and removing and/or depositing the plurality of sliced layers on the blank layer by layer so as to obtain the three-dimensional structure. In the invention, the three-dimensional model is decomposed into a plurality of slice layers in a mode of slicing the three-dimensional model, and the slice layers are removed and/or deposited layer by layer to obtain the three-dimensional structure, so that the accurate three-dimensional structure can be manufactured in a simple and reliable mode.
Description
Technical Field
The invention relates to the technical field of optics and processing, in particular to a method for manufacturing a three-dimensional structure.
Background
Focused Ion Beam (FIB) is a device that uses a Focused Ion Beam (Ga +, He +, etc.) to act on a sample to perform etching and deposition processes on the surface of the sample. Because the focused ion beam has certain energy, when the focused ion beam bombards the surface of the sample, atoms on the surface of the sample obtain energy to escape from the surface, thereby realizing the function of etching the surface of the sample. When etching is carried out, because the ion beam is focused, etching processing can be carried out in a designed pattern in a designated area. When the ion beam acts on the surface of the sample and simultaneously has different chemical precursors, the particles (secondary electrons) excited by the ion beam react with the precursors to realize different materials (such as Pt, C and SiO)2W, Au, etc.).
Currently, a common focused ion beam apparatus has a dual beam structure, in which two energy beams form a certain angle. Further, there is a focused ion beam apparatus of a three-beam structure (e.g., three-beam ions of He, Ne, Ga).
The focused ion beam is a processing mode which acts on the surface of a sample vertically, and etched or deposited shape side walls of the focused ion beam are only vertical to the surface of the sample. Focused ion beams are difficult to achieve if one wants to process three-dimensional structures with non-vertical sidewalls, but in practice most three-dimensional structures have non-vertical sidewalls. Because focused ion beams are difficult to achieve for the processing of three-dimensional structures.
Disclosure of Invention
The present invention is based on the object of providing a method for producing a three-dimensional structure, which solves the above-mentioned problems of the prior art.
Embodiments of the present invention provide a method of fabricating a three-dimensional structure, the method comprising:
drawing a three-dimensional model of the portion that needs to be removed and/or deposited from the blank in order to obtain the three-dimensional structure,
slicing the three-dimensional model in slicing software to decompose the three-dimensional model into a plurality of sliced layers,
and importing the data of the plurality of sliced layers into processing software, and removing and/or depositing the plurality of sliced layers on the blank layer by layer so as to obtain the three-dimensional structure.
Optionally, the plurality of sliced layers is removed and/or deposited layer by layer on the stock material using an energy beam.
Optionally, the energy beam comprises at least one of: laser beams, electron beams, plasma, and ion beams.
Alternatively, the number of sliced layers can be adjusted.
Alternatively, the interval between every two adjacent sliced layers can be adjusted. That is, the interval between two adjacent sliced layers can be flexibly controlled as desired. If the intervals are set to be the same, it is advantageous that the processing parameters can be set in batch in the processing software. If the interval is set to be different, the number of repeated patterns of the same size can be reduced, and simultaneously, the processing software can set the processing parameters of the patterns respectively. In addition, for a drawn three-dimensional model, a part of slice layers of the three-dimensional model can be selected according to actual needs to be processed. Therefore, for the same three-dimensional model, after different sliced layers are processed, the obtained three-dimensional structures can be different.
Optionally, the sliced layer data is exported from the slicing software and imported into the machining software in the form of a vector file. The vector file has the advantages of small occupied storage space, good controllability in the processing process and suitability for processing complex shapes.
Optionally, if the three-dimensional structure is a hemispherical groove, the method specifically includes:
drawing a three-dimensional model of the hemispherical concave groove,
slicing in slicing software along a direction perpendicular to an axis of symmetry of the three-dimensional model, thereby decomposing the three-dimensional model into a plurality of circular sliced layers having different diameters,
and removing the plurality of circular sliced layers on the blank layer by using an energy beam so as to obtain the hemispherical groove.
Optionally, the three-dimensional structure is a hemisphere formed in the frustum-conical groove, and the method specifically includes:
drawing a hemisphere and a truncated cone which takes the bottom surface of the hemisphere as a small circle and the distance from the bottom surface to the vertex of the hemisphere as high, wherein the part of the truncated cone which is not overlapped with the hemisphere is a three-dimensional model of the part which needs to be removed from a blank material,
slicing in slicing software along a direction perpendicular to the axis of symmetry of the three-dimensional model, thereby decomposing the three-dimensional model into a plurality of concentric circular sliced layers having different inner and outer diameters, wherein the outer diameter of each sliced layer gradually decreases from a maximum value, the inner diameter of each sliced layer gradually increases from substantially 0 until the outer and inner diameters of the last sliced layer are substantially equal to the diameter of a hemisphere,
removing the plurality of concentric circular sliced layers layer by layer on the blank by using an energy beam, thereby obtaining a hemisphere formed in the frustum-conical groove.
Embodiments of the present invention also provide a hemispherical recess manufactured by the above-described method according to the present invention.
Embodiments of the present invention also provide a hemisphere formed in a frustoconical recess, the hemisphere formed in the frustoconical recess being manufactured by the above method according to the present invention.
Embodiments of the present invention also provide a cone manufactured by the above method according to the present invention.
Embodiments of the present invention also provide an irregularly shaped frustum pillar manufactured by the above-described method according to the present invention.
Embodiments of the present invention also provide a spherical cap structure formed in a hemispherical recess, which is manufactured by the above-described method according to the present invention.
Embodiments of the present invention also provide a microlens manufactured by the method according to the present invention, the specific form of the microlens including at least one of: a hemispherical recess, a hemisphere formed in a frustoconical recess, a cone, an irregularly shaped frustum, a spherical cap structure formed in a hemispherical recess, and two or more hemispheres formed in a cylindrical recess, a frustoconical recess, or a hemispherical recess.
Embodiments of the present invention also provide a method of manufacturing a spherical cap structure formed in a hemispherical recess, the method including:
slicing is performed in slicing software along a direction perpendicular to a symmetry axis of the three-dimensional model, so that the three-dimensional model is decomposed into a plurality of concentric circular sliced layers with different inner and outer diameters, wherein the outer diameter of each sliced layer is gradually reduced from a maximum value, the inner diameter of each sliced layer is gradually increased from substantially 0 until the outer diameter and the inner diameter of the last sliced layer are substantially equal to the diameter of the bottom surface of the spherical crown, and the plurality of concentric circular sliced layers are removed on the blank layer by using an energy beam, so that the spherical crown structure formed in the hemispherical concave groove is obtained.
Embodiments of the present invention also provide two or more hemispheres formed in a cylindrical recess, a frustoconical recess, or a hemispherical recess, different hemispheres having the same radius or different radii, the two or more hemispheres formed in the cylindrical recess, the frustoconical recess, or the hemispherical recess being manufactured by the above-described method according to the present invention.
The method of manufacturing a three-dimensional structure of an embodiment of the present invention has at least the following advantages:
in the invention, the three-dimensional model is decomposed into a plurality of slice layers in a mode of slicing the three-dimensional model, and the slice layers are removed and/or deposited layer by layer to obtain the three-dimensional structure, so that the accurate three-dimensional structure can be manufactured in a simple and reliable mode.
Drawings
Further details and advantages of the present invention will become apparent from the detailed description provided hereinafter. It is to be understood that the following drawings are merely illustrative and not drawn to scale and are not to be considered limiting of the application, the detailed description being made with reference to the accompanying drawings, in which:
FIG. 1 shows a flow chart of a method of fabricating a three-dimensional structure according to an embodiment of the present invention.
Fig. 2A shows a perspective view of a three-dimensional model of hemispherical indentations created by mapping software according to another embodiment of the present invention.
FIG. 2B shows a cross-sectional view along the axis of symmetry of a three-dimensional model of a hemispherical groove of another embodiment of the present invention.
Figure 2C shows a schematic view of slicing a three-dimensional model of a hemispherical recess, in accordance with another embodiment of the present invention.
Figure 2D shows another embodiment of the present invention of a hemispherical indentation made by the method of the present invention.
Fig. 3A shows a perspective view of a three-dimensional model of a hemisphere formed in a frustoconical recess drawn by mapping software according to yet another embodiment of the present invention.
FIG. 3B shows a cross-sectional view of a three-dimensional model of yet another embodiment of the present invention, with portions that need to be removed shown in phantom.
FIG. 3C shows a schematic view of slicing a three-dimensional model according to yet another embodiment of the present invention.
Fig. 3D shows the trend of the slice layers of the concentric circular ring shape according to still another embodiment of the present invention.
Fig. 4 shows a perspective view of a three-dimensional model of a cone produced by deposition by means of the method according to the invention.
Fig. 5A shows a perspective view of a three-dimensional model of an irregularly shaped frustum of a column produced by means of deposition by means of the method of the invention.
Fig. 5B shows a cross-sectional view of a three-dimensional model of an irregularly shaped frustum of a column produced by means of deposition by means of the method of the invention.
Fig. 6 shows a cross-sectional view of a three-dimensional model of a spherical cap structure in a hemispherical recess manufactured by means of the method of the invention.
Fig. 7 shows a cross-sectional view of a three-dimensional model of two hemispheres in a cylindrical groove made by means of the method of the invention, wherein the two hemispheres have the same radius.
Fig. 8 shows a cross-sectional view of a three-dimensional model of two hemispheres in a cylindrical groove made by means of the method of the present invention, wherein the two hemispheres have different radii.
Detailed Description
Embodiments of the present invention are described below with reference to the drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of, and enabling description for, those skilled in the art. It will be apparent, however, to one skilled in the art that the present invention may be practiced without some of these specific details. Furthermore, it should be understood that the invention is not limited to the specific embodiments described. Rather, any combination of the features and elements described below is contemplated as carrying out the invention, whether or not they relate to different embodiments. Thus, the following aspects, features, embodiments and advantages are merely illustrative and are not considered elements or limitations of the claims except where explicitly recited in a claim.
Referring now to FIG. 1, a flow diagram of a method of fabricating a three-dimensional structure is shown, in accordance with an embodiment of the present invention. As shown in fig. 1, the method includes:
step S101, a three-dimensional model of a portion that needs to be removed and/or deposited from the blank material in order to obtain a three-dimensional structure is rendered.
The three-dimensional model can be drawn using existing drawing software, such as AutoCAD, SolidWork, 3D Fusion, CST, and Zemax simulation software. The rendered three-dimensional model may be derived in (. stl) format. For example, if the manufactured three-dimensional structure is a hemispherical recess, a three-dimensional model of the hemispherical recess is drawn using drawing software, and fig. 2A and 2B show a perspective view and a sectional view along a symmetry axis of the three-dimensional model of the hemispherical recess, respectively.
Step S102, slicing the three-dimensional model in slicing software, so as to decompose the three-dimensional model into a plurality of slicing layers.
Also taking the fabrication of the hemispherical recess as an example, as shown in fig. 2C, slicing is performed in slicing software along a direction perpendicular to the symmetry axis of the three-dimensional model of the hemispherical recess (i.e., Z-axis in fig. 2C), thereby decomposing the three-dimensional model into a plurality of circular sliced layers having different diameters. Each slice layer may be considered approximately as a two-dimensional circle. Continuing with fig. 2C, assuming a hemispherical indentation with a radius of 30, the spacing between each two adjacent sliced layers can be the same for ease of processing. The interval between every two adjacent slicing layers can be set to be 0.1, so that 301 slicing layers are obtained, and the coordinates of each slicing layer on the Z axis are respectively 0, -0.1, -0.2, -0.3, -0.4, … -29.8, -29.9 and-30. The number of sliced layers (i.e., the spacing between adjacent sliced layers) can also be adjusted, with the more sliced layers, the more accurate the hemispherical depressions can be made.
And step S103, importing the data of the plurality of sliced layers into processing software, and removing and/or depositing the plurality of sliced layers on the blank layer by layer so as to obtain a three-dimensional structure.
The data of the sliced layer obtained in the slicing software is preferably exported from the slicing software and imported to the machining software in a format (e.g., format. ely) that can be directly opened by the machining software (e.g., SmartFIB). Preferably, the sliced layer data is exported from the slicing software in the form of a vector file and imported into the machining software. Thereafter, a plurality of circular sliced layers are removed layer by layer on a blank (e.g., a square solid blank) using an energy beam (e.g., a focused ion beam or a laser beam) to obtain hemispherical grooves, and fig. 2D schematically illustrates the hemispherical grooves manufactured by the method of the present invention.
Using the principles of the method of the present invention, three-dimensional structures of arbitrary shape can be fabricated without limitation to the hemispherical recesses mentioned above. For example, hemispheres formed in frustoconical recesses may also be fabricated using the methods of the present invention. First, a three-dimensional model is drawn in which a hemisphere and a truncated cone having a small bottom surface and a high radius are drawn, and a portion where the truncated cone and the hemisphere do not overlap each other is a portion to be removed from a material. Fig. 3A and 3B show a perspective view of a three-dimensional model of a hemisphere formed in a frustum-conical recess and a sectional view along a symmetry axis of the three-dimensional model, respectively, drawn. In fig. 3B, portions to be removed are shown in hatched lines. Next, as shown in fig. 3C, slicing is performed in the slicing software in a direction perpendicular to the symmetry axis of the three-dimensional model, thereby decomposing the three-dimensional model into a plurality of concentric circular sliced layers having different inner and outer diameters. Fig. 3D shows the trend of the slice layers of the concentric circular rings. As shown in FIG. 3D, the outer diameter D1 of each slice layer gradually decreases from a maximum value and the inner diameter D2 of each slice layer gradually increases from substantially 0 until the outer diameter D1 and the inner diameter D2 of the last slice layer are both substantially equal to the diameter of the hemisphere. Finally, a plurality of concentric circular sliced layers are removed layer by layer on a blank (e.g., a square solid blank) using an energy beam (e.g., a focused ion beam or a laser beam) to obtain hemispheres formed in the frustoconical grooves.
In the above-described embodiment of the present invention, the three-dimensional model is decomposed into a plurality of sliced layers by slicing the three-dimensional model, and the sliced layers are removed layer by layer to obtain the three-dimensional structure, so that the precise three-dimensional structure can be manufactured in a simple and reliable manner.
The hemispherical recess and the hemisphere formed in the truncated conical recess manufactured by the method of the present invention can be used as a microlens for processing a micrometer scale in the photoelectric field, and can also be used as a micro device in the electronic semiconductor field, and the like.
In the field of optoelectronic research, how to improve the optical signal detection efficiency of luminescent materials is a very important issue. By machining a micro-curved structure (i.e., a microlens) on the material, the optical signal collection efficiency at the machined location can be improved. The method can obtain the accurate micro lens by directly converting the three-dimensional model obtained by theory into the vector file which can be directly processed.
When the material has single photon emission performance (such as negatively charged nitrogen vacancies in diamond), the material can be applied to quantum storage, magnetic sensors, single photon emission sources and the like because the material has local electrons and nuclear spins with long spin coherence time suitable for quantum storage at room temperature. And the micro lens can enhance the detection efficiency of single photons and improve the application of the micro lens in the fields.
The micro lens is processed in the silicon waveguide material, so that the edge coupling effect of the silicon optical integrated circuit can be enhanced, and the utilization efficiency of the silicon waveguide is improved.
In addition, the applicant wishes to point out that the method of manufacturing three-dimensional structures to which the invention relates is not limited to material removal processing, but can also be used for three-dimensional structure processing for additive manufacturing (i.e. deposition of different materials). For example, the materials are heated and bonded using a laser beam, electron beam, plasma, and/or ion beam as a heat source to produce a three-dimensional structure. Material removal processing and additive manufacturing can also be used in conjunction to produce complex three-dimensional structures. Therefore, the method for manufacturing the three-dimensional structure of the present invention can manufacture not only the three-dimensional structure with the symmetrical central axis but also various asymmetrical three-dimensional structures and complex three-dimensional structures. In addition, different three-dimensional structures can be obtained by adjusting the included angle between the surface of the sample and the energy beam and combining slicing or deposition technology. For example, during machining, a plurality of different three-dimensional models may be rendered, sliced, and combined to achieve machining of a complex three-dimensional structure. A plurality of same three-dimensional models can be drawn, and a plurality of same three-dimensional structures can be processed at different positions of the same sample, so that array processing of the three-dimensional structures is realized.
The following lists a few examples of three-dimensional structures produced according to the method of the invention:
fig. 4 shows a perspective view of a three-dimensional model of a cone produced by means of the method according to the invention. The cone may be produced by means of material removal or deposition.
Fig. 5A and 5B show a three-dimensional model of an irregularly shaped frustum of a column manufactured by means of the method of the invention. Wherein fig. 5A shows a perspective view of the three-dimensional model of the irregularly-shaped frustum and fig. 5B shows a cross-sectional view of the three-dimensional model of the irregularly-shaped frustum. The irregularly shaped frustum pillar may be fabricated by means of material removal or deposition.
Fig. 6 shows a cross-sectional view of a three-dimensional model of a spherical cap structure in a hemispherical recess manufactured by means of the method of the invention. To fabricate the three-dimensional structure, the hemispherical recesses may be first fabricated by material removal, for example using the method of the present invention as described in fig. 2A-2D, and then the spherical cap structures may be deposited in the hemispherical recesses by additive manufacturing. Alternatively, the spherical cap structure in the hemispherical recess can also be produced by means of the method according to the invention in the following manner: first, slicing is performed in slicing software along a direction perpendicular to a symmetry axis of a three-dimensional model, thereby decomposing the three-dimensional model into a plurality of concentric circular-ring-shaped sliced layers having different inner and outer diameters, wherein the outer diameter of each sliced layer is gradually decreased from a maximum value, and the inner diameter of each sliced layer is gradually increased from substantially 0 until the outer diameter and the inner diameter of the last sliced layer are both substantially equal to the diameter of the bottom surface of the spherical crown, and then the plurality of concentric circular-ring-shaped sliced layers are removed layer by layer on the blank using an energy beam, thereby obtaining the spherical crown structure formed in the hemispherical recess.
Figure 7 shows a cross-sectional view of a three-dimensional model of two hemispheres in a cylindrical recess made by means of the method of the invention. Wherein the two hemispheres have the same radius. To produce the three-dimensional structure, it is possible, for example, to first produce a cylindrical recess by means of material removal using the method according to the invention and then to deposit two hemispheres having the same radius in the cylindrical recess by means of additive manufacturing.
Fig. 8 shows a cross-sectional view of a three-dimensional model of two hemispheres in a cylindrical recess made by means of the method of the invention. Wherein the two hemispheres have different radii. To produce the three-dimensional structure, it is possible, for example, first to produce a cylindrical recess by means of material removal using the method according to the invention and then to deposit two hemispheres having different radii in the cylindrical recess by means of additive manufacturing.
It should be noted that the above description is only an example and not a limitation of the present invention. In other embodiments of the invention, the method may have more, fewer, or different steps, and the order, inclusion, or functional relationship between the steps may be different from that described and illustrated. For example, in general, multiple steps may be combined into a single step, or a single step may be split into multiple steps. For a person skilled in the art, the sequence of the steps is not changed without creative efforts and is within the protection scope of the invention.
The technical solution of the present invention may be substantially implemented or partially implemented in the prior art, or all or part of the technical solution may be implemented in a software product, which is stored in a storage medium and includes several instructions to enable a computer device (which may be a personal computer, a server, or a network device) or a processor or a microcontroller to execute all or part of the steps of the method according to the embodiments of the present invention.
Those of ordinary skill in the art will understand that: all or a portion of the steps of implementing the above-described method embodiments may be performed by hardware associated with program instructions. The program may be stored in a computer-readable storage medium. When executed, the program performs steps comprising the method embodiments described above; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
Although the present invention has been described with reference to the preferred embodiments, it is not to be limited thereto. Various changes and modifications within the spirit and scope of the present invention will become apparent to those skilled in the art from this disclosure, and it is intended that the scope of the present invention be defined by the appended claims.
Claims (16)
1. A method of fabricating a three-dimensional structure, the method comprising:
drawing a three-dimensional model of the portion that needs to be removed and/or deposited from the blank in order to obtain the three-dimensional structure,
slicing the three-dimensional model in slicing software to decompose the three-dimensional model into a plurality of sliced layers,
and importing the data of the plurality of sliced layers into processing software, and removing and/or depositing the plurality of sliced layers on the blank layer by layer so as to obtain the three-dimensional structure.
2. The method of claim 1, wherein the plurality of sliced layers are removed and/or deposited layer by layer on the billet using an energy beam.
3. The method of claim 1, wherein the energy beam comprises at least one of: laser beams, electron beams, plasma, and ion beams.
4. The method of claim 1, wherein the number of sliced layers can be adjusted.
5. The method of claim 1, wherein the spacing between each two adjacent sliced layers can be adjusted.
6. The method of claim 1, wherein the sliced layer of data is exported from the slicing software and imported into the machining software in the form of a vector file.
7. The method according to any of claims 1-6, wherein the three-dimensional structure is a hemispherical indentation, the method comprising in particular:
drawing a three-dimensional model of the hemispherical concave groove,
slicing in slicing software along a direction perpendicular to an axis of symmetry of the three-dimensional model, thereby decomposing the three-dimensional model into a plurality of circular sliced layers having different diameters,
and removing the plurality of circular sliced layers on the blank layer by using an energy beam so as to obtain the hemispherical groove.
8. The method according to any of claims 1-6, wherein the three-dimensional structure is a hemisphere formed in a frustoconical recess, the method in particular comprising:
drawing a hemisphere and a truncated cone which takes the bottom surface of the hemisphere as a small circle and the distance from the bottom surface to the vertex of the hemisphere as high, wherein the part of the truncated cone which is not overlapped with the hemisphere is a three-dimensional model of the part which needs to be removed from a blank material,
slicing in slicing software along a direction perpendicular to the axis of symmetry of the three-dimensional model, thereby decomposing the three-dimensional model into a plurality of concentric circular sliced layers having different inner and outer diameters, wherein the outer diameter of each sliced layer gradually decreases from a maximum value, the inner diameter of each sliced layer gradually increases from substantially 0 until the outer and inner diameters of the last sliced layer are substantially equal to the diameter of a hemisphere,
removing the plurality of concentric circular sliced layers layer by layer on the blank by using an energy beam, thereby obtaining a hemisphere formed in the frustum-conical groove.
9. A hemispherical recess wherein said hemispherical recess is manufactured by the method of claim 7.
10. A hemisphere formed in a frustoconical recess, characterized in that the hemisphere formed in the frustoconical recess is manufactured by a method according to claim 8.
11. A cone, characterized in that it is manufactured by a method according to any one of claims 1-6.
12. An irregularly shaped frustum of a column, characterized in that it is manufactured by a method according to any of claims 1-6.
13. A spherical cap structure formed in a hemispherical recess, characterized in that the spherical cap structure formed in a hemispherical recess is manufactured by the method according to any one of claims 1 to 6.
14. A method of manufacturing the spherical cap structure of claim 13 formed in a hemispherical recess, the method comprising:
slicing is performed in slicing software along a direction perpendicular to a symmetry axis of the three-dimensional model, so that the three-dimensional model is decomposed into a plurality of concentric circular sliced layers with different inner and outer diameters, wherein the outer diameter of each sliced layer is gradually reduced from a maximum value, the inner diameter of each sliced layer is gradually increased from substantially 0 until the outer diameter and the inner diameter of the last sliced layer are substantially equal to the diameter of the bottom surface of the spherical crown, and the plurality of concentric circular sliced layers are removed on the blank layer by using an energy beam, so that the spherical crown structure formed in the hemispherical concave groove is obtained.
15. Two or more hemispheres formed in a cylindrical recess, a frustoconical recess or a hemispherical recess, the different hemispheres having the same radius or different radii, wherein the two or more hemispheres formed in a cylindrical recess, a frustoconical recess or a hemispherical recess are manufactured by the method according to any one of claims 1 to 6.
16. A microlens manufactured by the method according to any one of claims 1 to 6, wherein the specific form of the microlens includes at least one of: a hemispherical recess, a hemisphere formed in a frustoconical recess, a cone, an irregularly shaped frustum, a spherical cap structure formed in a hemispherical recess, and two or more hemispheres formed in a cylindrical recess, a frustoconical recess, or a hemispherical recess.
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