Cutting method for mold of micro-lens array

Abstract

Provided is a cutting method for a mold of a micro-lens array provided with a plurality of micro-lenses having approximately the same shape and each having an optical axis in the same direction. When one surface of the mold corresponding to a surface of one micro-lens is cut, in a coordinate system which has the x-axis, y-axis, and z-axis orthogonal to one another and in which the z-axis is defined as the direction of a center axis corresponding to the optical axis of the micro-lens of the one surface, and an angle between a rotational axis of the tool and a straight line in the direction of the z-axis passing through a point on the rotational axis of the tool is defined as θ, and an angle around the straight line in a plane including the rotational axis of the tool and the straight line is defined as Φ, cutting is performed while changing the value of the angle θ and maintaining the value of the angle Φ at a fixed value, and the variance of the angle Φ is distributed so as to be a prescribed value or higher with respect to the plurality of surfaces of the mold when the plurality of surfaces of the mold corresponding to the surfaces of the plurality of micro-lenses are cut.

Description

Cutting method for forming mold of microlens array

[0001] The present invention relates to a cutting method for a molding die for a microlens array.

[0002] When machining a molding die for a microlens array using a machining device such as a multi-axis machining center, multiple surfaces of the molding die corresponding to the surfaces of multiple microlenses in the microlens array are machined sequentially (see, for example, Patent Document 1). When cutting the surfaces of the molding die using a tool that rotates around a central axis, such as a ball end mill, significant shape errors tend to occur, particularly in areas machined near the central axis of the tool, due to misalignment between the position of the central axis of the tool's shape and the position of the rotation axis caused by tool manufacturing errors and tool installation errors. For this reason, conventional cutting methods tend to produce significant shape errors at the same locations on the multiple surfaces of the molding die corresponding to the surfaces of multiple microlenses. Therefore, the shape errors at specific positions on the surfaces of multiple microlenses in a microlens array manufactured using the molding die tend to be large. As a result, when a microlens array is used as an optical element that increases the divergence angle of a light beam through refraction, the illuminance of the surface illuminated using the microlens array tends to increase due to the sum of illuminance variations caused by shape errors at specific positions on the surfaces of the multiple microlenses.

[0003] For this reason, conventional cutting methods for molding dies for microlens arrays have not been able to adequately address the effects of miniaturization of microlenses and increasing size of microlens arrays. In other words, no cutting method has been developed for molding dies for large-area microlens arrays that contain a large number of fine microlenses and have high optical performance. Therefore, there is a need for a cutting method for molding dies for large-area microlens arrays that contain a large number of microlenses and have high optical performance.

[0004] Japanese Patent Application Publication No. 2018-43444

[0005] An object of the present invention is to provide a cutting method for a molding die for a large-area microlens array containing a large number of microlenses and having high optical performance.

[0006] The first aspect of the present invention is a cutting method for a microlens array molding die, which cuts a microlens array molding die having a plurality of microlenses of approximately the same shape, each of which has an optical axis in the same direction, using a tool equipped with a blade that rotates around a rotation axis. When cutting one surface of the molding die corresponding to each microlens surface, in an (x, y, z) coordinate system having mutually orthogonal x, y, and z axes, with the direction of the central axis of the surface corresponding to the optical axis of the microlens being the z axis, θ is the angle between the rotation axis of the tool and a line in the direction of the z axis passing through a point on the rotation axis of the tool, and Φ is the angle around the line of a plane containing the rotation axis of the tool and this line, the value of angle Φ is kept constant, and cutting is performed by changing the (x, y, z) coordinates of the processing point while changing the value of angle θ, and when cutting multiple surfaces of the molding die corresponding to the surfaces of the multiple microlenses, the values ​​of angle Φ are distributed so that the variance of the values ​​of angle Φ for the multiple surfaces of the molding die is equal to or greater than a predetermined value, so that changes in illuminance occurring at positions corresponding to approximately the same positions in the multiple surfaces of the molding die when the value of angle Φ is the same for the multiple surfaces of the molding die are sufficiently small.

[0007] According to the cutting method for a microlens array molding die of this aspect, by distributing the values ​​of angle Φ so that the variance of the values ​​of angle Φ for the multiple surfaces of the molding die is equal to or greater than a predetermined value, it is possible to reduce illuminance changes due to tool-induced shape errors of the multiple microlenses in the illuminance distribution of the surface irradiated using the microlens array. Therefore, according to this aspect, it is possible to machine a molding die for a large-area microlens array with high optical performance that includes a large number of fine microlenses.

[0008] Also, by setting the angle θ to a small value at the periphery of one surface of the forming die, interference between the tool and that surface can be prevented.

[0009] In the method for cutting a molding die for a microlens array according to the first embodiment of the first aspect of the present invention, the maximum value of the angle θ when cutting one surface of the molding die is determined for each surface.

[0010] In the method for cutting a molding die for a microlens array according to the second embodiment of the first aspect of the present invention, the maximum value of the angle θ when cutting one surface of the molding die is 3 degrees or greater for 50% or more of the total number of surfaces of the molding die that correspond to the surfaces of the microlenses.

[0011] Considering all surfaces of the molding die that correspond to the surfaces of the microlenses, it is preferable to change the position at which shape errors occur by setting the maximum value of the angle θ to 3 degrees or more on surfaces that make up 50 percent or more of the total number of surfaces of the molding die that correspond to the surfaces of the microlenses.

[0012] In the method for cutting a molding die for a microlens array according to the third embodiment of the first aspect of the present invention, when cutting one surface of the molding die, cutting is performed while changing the value of the angle θ in areas where the distance from the central axis of the processing point is greater than a predetermined value, and cutting is performed with the value of the angle θ fixed in areas where the distance is equal to or less than the predetermined value.

[0013] According to the cutting method for a microlens array molding die of this embodiment, the angle θ is set to a small value at the periphery of one surface of the molding die to prevent interference between the tool and the surface, and the angle θ is fixed in the region close to the central axis of the surface during cutting. The predetermined value of the distance from the central axis of the machining point is, for example, 30 percent of the distance from the central axis to the periphery of the surface.

[0014] In the fourth embodiment of the first aspect of the present invention, in the cutting method for a molding die for a microlens array, when cutting one surface of the molding die, the rate of change when increasing the value of the angle θ is determined so that the positioning accuracy of the tool in all movement directions is below a predetermined value.

[0015] According to the cutting method for the molding die for the microlens array of this embodiment, cutting can be performed with high precision while increasing the value of the angle θ.

[0016] In the method for cutting a molding die for a microlens array according to the fifth embodiment of the first aspect of the present invention, when cutting one surface of the molding die, the locus of the processing point is spiral around the central axis.

[0017] In the method for cutting a molding die for a microlens array according to the sixth embodiment of the first aspect of the present invention, when cutting the multiple surfaces of the molding die corresponding to the surfaces of the multiple microlenses, the multiple surfaces are divided into one or more groups, and the values ​​of the angles Φ of the individual surfaces in each group are determined so as to be distributed uniformly or at equal intervals.

[0018] According to the cutting method of the microlens array molding die of this embodiment, the variance in the values ​​of the angles Φ of the multiple surfaces can be easily increased, and therefore the illuminance change due to shape errors caused by the tool of the multiple microlenses can be reduced.

[0019] In the cutting method for a molding die for a microlens array according to the seventh embodiment of the first aspect of the present invention, a five-axis machining center is used, and machining is performed by making the x-axis, y-axis, and z-axis correspond to the three linear axes of the five-axis machining center, and making the angles θ and Φ correspond to the angles around the two rotation axes of the multi-axis machining center.

[0020] According to this embodiment, the molding die for the microlens array can be easily machined using a five-axis machining device.

[0021] In the method for cutting a molding die for a microlens array according to the eighth embodiment of the first aspect of the present invention, when cutting one surface of the molding die, the value of the angle θ is changed so that the value of the angle θ increases as the distance from the central axis of the processing point decreases.

[0022] According to this embodiment, the value of angle θ is set to a small value at the peripheral portion of the surface to prevent interference between the side of the tool and the surface, and the value of angle θ is set to a large value near the central axis of the surface, and the values ​​of angle Φ are distributed so that the variance of the values ​​of angle Φ for the multiple surfaces of the mold is equal to or greater than a predetermined value, thereby making it possible to reduce illuminance changes due to shape errors caused by the multiple microlens tools in the illuminance distribution of the surface illuminated using a microlens array.

[0023] In the cutting method for a molding die for a microlens array according to the ninth embodiment of the first aspect of the present invention, when cutting one surface of the molding die, the value of the angle θ is changed according to the shape of the surface so that the side of the cutting tool does not interfere with the surface. According to this embodiment, interference between the side of the tool and the surface can be prevented even when the shape of a cross section including the center axis of the surface is complex.

[0024] The method for producing a microlens array according to the second aspect of the present invention uses a molding die processed by any of the above-described cutting methods for a molding die for a microlens array.

[0025] According to the manufacturing method of the microlens array of this aspect, a large-area microlens array containing a large number of microlenses and having high optical performance can be obtained.

[0026] FIG. 1 is a diagram showing a five-axis processing machine as an example of a processing device used in the cutting method of the present invention. FIG. 2 is a diagram showing an example of a processing path S of the tool when processing a surface of a molding die corresponding to a lens surface using a five-axis processing machine. FIG. 3 is a diagram showing a cross section including the rotation axis of the tool. FIG. 4 is a diagram showing a cross section including the rotation axis of the tool. FIG. 5 is a diagram showing a cross section including the rotation axis of the tool and the central axis of the surface. FIG. 6 is a diagram showing a cross section of the tool including the central axis AX' and rotation axis AX when the central axis AX' of the tool shape does not coincide with the rotation axis AX due to a manufacturing error of the tool. FIG. 7 is a diagram showing a cross section of the tool including the central axis AX' and rotation axis AX when the central axis AX' of the tool shape does not coincide with the rotation axis AX due to an attachment error. FIG. 8 is a conceptual diagram showing a shape error of the surface of the molding die corresponding to the lens surface to be processed. FIG. 9 is a diagram for explaining the inclination of the tool. FIG. 10 is a diagram showing the positional relationship between the tool and the processing path of the tool when the angle (acute angle) formed between the z axis of the tool and the rotation axis of the tool is θ. FIG. 11 is a diagram for explaining how to determine the maximum value of the angle (acute angle) θ formed between the z axis of the tool and the rotation axis of the tool. 19A and 19B are diagrams for explaining the angle (acute angle) Φ formed by the y-axis and the rotation axis of the tool and a plane including a straight line in the z-axis direction passing through the rotation axis of the tool. FIG. 20A is a diagram for explaining the cutting method of the present invention. FIG. 20B is a diagram for explaining a cutting method of another embodiment of the present invention. FIG. 21C is a conceptual diagram showing the shape error of a surface 210 obtained by a conventional cutting method in which the angle Φ is constant and the angle θ is 0. FIG. 21D is a conceptual diagram showing the shape error of a surface obtained by the cutting method of the present invention in which the angle Φ is constant and the angle θ increases as the distance from the central axis of the surface to the processing point decreases. FIG. 21E is a diagram showing the actual shape error of a surface cut by the cutting method described in FIG. 15. FIG. 21F is a diagram showing the actual shape error of a surface cut by the cutting method described in FIG. 16. FIG. 21F is a diagram showing the shape error of the x-z cross section of the surface of a forming mold. FIG. 21C is a diagram showing the illuminance on a surface in the absence of a shape error. FIG. 21D is a diagram showing the x-z cross section of the illuminance distribution shown in FIG. 20A. FIG. 21E is a diagram showing the illuminance on a surface in the presence of the shape error shown in FIG. 19. FIG. 21F is a diagram showing the x-z cross section of the illuminance distribution shown in FIG. 21A. This figure shows the average illuminance distribution obtained by simulating the illuminance distribution on the surface of a microlens cut from a molding die with an angle Φ of 360 / 7, 360x2 / 7, 360x3 / 7, ..., 360 degrees and an angle θ of 0 to 15 degrees.22A shows an xz cross section of the illuminance distribution shown in FIG. 22B. This figure shows the average illuminance obtained by simulating the illuminance distribution on the surface of a microlens cut by a mold with an angle Φ of 360 / 61, 360x2 / 61, 360x3 / 61, ..., 360 degrees, and varying the angle θ from 0 to 15 degrees in each case. This figure shows the xz cross section of the illuminance distribution shown in FIG. 23A. This figure shows the average illuminance distribution obtained by simulating the illuminance distribution on the surface of a microlens cut by a mold with an angle Φ of 360 / 127, 360x2 / 127, 360x3 / 127, ..., 360 degrees, and varying the angle θ from 0 to 15 degrees in each case. This figure shows the xz cross section of the illuminance distribution shown in FIG. 24A. This figure shows the actual shape error of the mold surface corresponding to one microlens surface cut by the conventional cutting method described in FIG. 15. 29A is a diagram showing the actual shape error of the surface of a molding die corresponding to another microlens surface cut by the conventional cutting method described in Figure 15. FIG. 30B is a diagram showing the actual shape error of the surface of a molding die corresponding to one microlens surface cut by the cutting method of the present invention described in Figure 16. FIG. 30C is a diagram showing the actual shape error of the surface of a molding die corresponding to another microlens surface cut by the cutting method of the present invention described in Figure 16. FIG. 30D is a diagram showing the illuminance on a surface by a microlens array manufactured using a molding die cut by the cutting method described in Figure 15. FIG. 30E is a diagram showing the xz cross section of the illuminance distribution shown in Figure 29A. FIG. 30F is a diagram showing the illuminance on a surface by a microlens array manufactured using a molding die cut by the cutting method described in Figure 16.

[0027] 1 is a diagram showing a five-axis machining device 100 as an example of a machining device used in the cutting method of the present invention. The five-axis machining device 100 has three linear axes (X, Y, Z) and two rotary axes (B, C). A workpiece 200 is machined by a tool 110. One example of the tool 110 is a ball end mill.

[0028] 2 is a diagram showing the tool 110. The tool 110 has a cutting edge 115, and cuts a workpiece 200 by rotating about a rotation axis. The cutting edge 115 has an arc-shaped profile in a cross section including the rotation axis of the tool 110.

[0029] FIG. 3 is a diagram showing an example of a machining path S indicating the position of the machining point of the tool 110 when machining a mold surface 210 corresponding to a lens surface using the five-axis machining device 100. The lens surface and surface 210 may be spherical, aspherical, free-form, or the like. As shown in FIG. 3 , the machining path is, for example, a spiral around the central axis of the mold surface 210, and the machining point approaches the central axis from the periphery of the surface 210 along the machining path. Generally, machining is preferably performed so that the machining point of the tool is located on a continuous, non-intersecting line on the mold surface 210. The position of the machining point of the tool 110 is controlled by the linear axes (X, Y, Z) of the five-axis machining device 100.

[0030] FIG. 4 is a cross-sectional view including the rotation axis of the tool 110.

[0031] Figure 5 is an enlarged view of the portion surrounded by the dotted line in Figure 4. In the cross section of Figure 5, the design arc of the contour of the cutting edge 115 is indicated by C, and the center of arc C is indicated by O. Center O is located on the rotation axis. In Figure 5, the position of point P on the cutting edge 115 is indicated by the angle (acute angle) α formed between the rotation axis and the line connecting point O and point P.

[0032] Fig. 6 is a diagram showing a cross section including the rotation axis of tool 110 and the central axis of surface 210. When cutting is performed in a state in which the rotation axis of tool 110 and the central axis of surface 210 are parallel to each other as shown in Fig. 6, the angle between the central axis of surface 210 and the straight line indicating the tangent plane of surface 210 at point P' on surface 210 cut by point P on the blade of tool 110 is (90-α) degrees. In this way, the position on surface 210 cut by the point on the blade of tool 110 is determined by angle α.

[0033] Figure 7 is a diagram showing a cross section of a tool including the central axis AX' and the rotation axis AX when the central axis AX' of the tool shape does not coincide with the rotation axis AX due to a manufacturing error of the tool. In Figure 7, the arc representing the blade of an ideal tool is represented by C'. The central axis of the ideal tool shape coincides with the rotation axis AX. On the other hand, when the central axis AX' of the tool shape does not coincide with the rotation axis AX due to a manufacturing error, the arc of the blade of an actual tool is represented by C. In this case, the shape around the rotation axis of the tool becomes approximately flat.

[0034] FIG. 8 is a diagram showing a cross section of a tool including the central axis AX' and the rotation axis AX when the central axis AX' of the tool shape does not coincide with the rotation axis AX due to an attachment error.

[0035] Figure 9 is a conceptual diagram showing the shape error of surface 210 of the molding die corresponding to the lens surface of workpiece 200. The horizontal axis of Figure 9 represents the coordinate in the direction of a line perpendicular to the central axis of surface 210, and the vertical axis of Figure 9 represents the shape error. When cutting is performed in the state shown in Figure 6, the shape error that occurs near the central axis of surface 210 cut when the tool blade is in the position of α=0 tends to be greatest due to the manufacturing error described in Figure 7 and the installation error described in Figure 8.

[0036] FIG. 10 is a diagram for explaining the inclination of the tool 110. A point on the rotation axis of the tool 110 is set as the origin, and a straight line passing through the origin and parallel to the central axis of the surface 210 corresponding to the optical axis of the microlens surface is set as the z axis of the tool. The x and y axes of the tool, which are perpendicular to each other, are set within a plane perpendicular to the z axis of the tool. How to set the x and y axes of the tool will be explained later. The angle (acute angle) formed by the z axis of the tool and the rotation axis of the tool is set as θ. The angle (acute angle) formed by the y axis of the tool and a plane including the z axis of the tool and the rotation axis of the tool is set as Φ.

[0037] 11 is a diagram showing the positional relationship between the tool and the machining path of the tool when the angle (acute angle) formed between the z axis of the tool and the rotation axis of the tool is θ. In the case of the conventional cutting method described using FIG. 6, the angle (acute angle) formed between the z axis and the rotation axis of the tool 110 is 0.

[0038] 12 is a diagram for explaining how to determine the maximum value of the angle (acute angle) θ formed between the z axis of the tool and the rotation axis of the tool. Fig. 12 shows a cross section including the central axis of the tool 110 and the central axis of the surface 210. The maximum value of the angle θ is determined so that the side surface of the tool and the surface 210 do not interfere with each other.

[0039] FIG. 13 is a diagram illustrating the angle (acute angle) Φ formed between the y-axis of the tool and a plane including the tool rotation axis and a line in the z-axis direction passing through the tool rotation axis. In FIG. 13, the z-axis of the surface coincides with the central axis of the mold surface 210 corresponding to the microlens surface. The x-axis and y-axis of the surface are defined as being perpendicular to each other in a plane perpendicular to the z-axis of the surface. Note that for multiple mold surfaces corresponding to multiple microlens surfaces, the x-axis, y-axis, and z-axis of the surface are defined as being parallel to each other. The x-axis and y-axis of the tool are defined as being parallel to the x-axis and y-axis of the surface, respectively. The angle Φ corresponds to the angle around the central axis of the surface 210. In FIG. 13, the angle Φ is an angle measured counterclockwise with respect to the y-axis. The plane including the z-axis of the surface and forming an angle Φ with the plane including the y-axis and z-axis of the surface is indicated as PL. In the case of the conventional cutting method described using FIG. 6, the tool angle Φ is constant during machining of the surface 210 corresponding to one lens surface.

[0040] 1 is used for machining, the angle θ corresponds to the angle indicated by C, and the angle Φ corresponds to the angle indicated by B. In the case of a conventional cutting method, the angles indicated by B and C are constant during machining, and the angle indicated by C is determined so that the rotation axis of the tool 110 is vertical. In this case, the angle θ is 0.

[0041] Figure 14A is a diagram illustrating a cutting method according to one embodiment of the present invention. According to the cutting method of this embodiment, angle Φ is kept constant while machining mold surface 210 corresponding to one lens surface, and angle θ increases as the distance from the central axis of surface 210 to the machining point decreases. The surfaces shown at (1), (2), and (3) in Figure 14A correspond to surface PL described in Figure 13. In Figure 14A, angle θ is 0 when cutting the periphery of surface 210 shown at (1). As the distance from the central axis of surface 210 at the cutting position decreases, angle θ increases and reaches a maximum at the position of the central axis of surface 210 shown at (3). The maximum value of angle θ is 3 degrees or greater.

[0042] In the cutting method of this embodiment, the angle B is kept constant during machining, while the angle C is changed so that the angle θ increases as the distance from the central axis of the machining point to the surface 210 decreases.

[0043] It is preferable that the angle θ continuously and monotonically increase as the distance from the central axis of the surface 210 decreases. The rate at which the angle θ is changed is determined so that the positioning accuracy of all moving axes of the processing machine is equal to or less than a predetermined value. The predetermined value is, for example, 10 nanometers.

[0044] FIG. 14B is a diagram illustrating a cutting method according to another embodiment of the present invention. FIG. 14B shows a cross section including the central axis of surface 210. According to the cutting method of this embodiment, angle Φ is kept constant while machining mold surface 210 corresponding to one lens surface, and angle θ is changed according to the shape of surface 210. In (1) of FIG. 14B, angle θ is 0, and there is no interference between the side surface of tool 110 and surface 210. In (2), (3), and (4) of FIG. 14B, angle θ is set so that there is no interference between the side surface of tool 110 and surface 210. The maximum value of angle θ is 3 degrees or greater.

[0045] FIG. 15 is a conceptual diagram showing the shape error of the surface 210 produced by a conventional cutting method in which the angle Φ is constant and the angle θ is zero. The left diagram in FIG. 15 shows the shape error of the surface 210 in the cross section of the surface PL described in FIG. 13. The horizontal axis of the left diagram represents the coordinate of the direction of a line perpendicular to the central axis of the surface 210, and the vertical axis of the left diagram represents the shape error. The right diagram is a plan view of the surface 210. The position of a point on the cutting edge of the tool is represented by the angle (acute angle) formed between the rotation axis and the line connecting points O and P. If a tool shape error exists at angles α0, α1, α2, and α3, shape errors will occur at positions E0, E1, E2, and E3 of the surface 210 cut at the cutting edge angles α0, α1, α2, and α3, respectively. α0 is zero. In FIG. 15, the position E0 where the maximum shape error occurs is near the central axis of the surface 210. Note that the shape shown in FIG. 15 is symmetrical with respect to the z-axis of the surface.

[0046] FIG. 16 is a conceptual diagram showing the shape error of the surface 210 produced by the cutting method of the present invention, in which the angle Φ is kept constant and the angle θ increases as the distance from the center axis of the surface 210 to the machining point decreases. The left diagram in FIG. 16 shows the shape error of the surface 210 in the cross section of the surface PL described in FIG. 14A. The horizontal axis of the left diagram indicates the coordinate of the direction of a line perpendicular to the center axis of the surface 210, and the vertical axis of the left diagram indicates the shape error. The right diagram is a plan view of the surface 210. The position of a point on the tool blade is represented by the angle (acute angle) formed by the rotation axis and the line connecting points O and P. If a tool shape error exists at angles α0, α1, α2, and α3, shape errors will occur at positions E0', E1', E2', and E3' of the surface 210 cut at the blade angles α0, α1, α2, and α3, respectively. α0 is 0. In FIG. 16, the position E0′ where the maximum shape error occurs is to the left of the central axis of the surface 210.

[0047] Figure 17 is a diagram showing the actual shape error of a surface 210 cut by the cutting method described in Figure 15. In Figures 17 and 18, the central axis of the surface 210 is defined as the z-axis, and the intersection of the surface 210 and the central axis is defined as the origin, with the x-axis and y-axis perpendicular to each other. The scale intervals on the x-axis and y-axis are 200 micrometers, and the scale interval on the z-axis is 0.5 micrometers. The surface shown in the left diagram of Figure 15 corresponds to the xz plane in Figure 17. In Figure 17, the position where the maximum shape error occurs is near the origin.

[0048] Fig. 18 is a diagram showing the actual shape error of a surface cut by the cutting method described in Fig. 16. The surface shown in the diagram on the left side of Fig. 16 corresponds to the xz plane in Fig. 18, i.e., plane PL described in Fig. 13. In Fig. 18, the position where the maximum shape error occurs is the position on the x-axis where the x coordinate is negative. In the case of Fig. 18, plane PL is the plane that includes the z-axis of the surface and the x-axis of the surface.

[0049] In this way, by performing cutting using the cutting method described with reference to FIG. 16, the position where the shape error occurs can be moved within the plane PL.

[0050] 12 occurs on the periphery of mold surface 210, i.e., in the region at a large distance from the central axis of mold surface 210. Therefore, when cutting the periphery of mold surface 210, angle θ is set to 0, for example, and the angle θ is increased as the distance from the central axis of the processing point decreases, thereby avoiding the above-described interference.

[0051] Furthermore, in areas where the distance from the central axis is greater than a predetermined value, cutting may be performed while increasing the value of angle θ as the distance from the central axis decreases, and in areas where the distance from the central axis is equal to or less than the predetermined value, cutting may be performed while fixing the value of angle θ regardless of the distance from the central axis.

[0052] Generally, it is not necessary to change the value of angle θ when machining all of the mold surfaces corresponding to the microlens surfaces. The value of angle θ may be fixed when machining one or more mold surfaces. Furthermore, the maximum value of angle θ may be varied for each surface. When considering all of the mold surfaces corresponding to the microlens surfaces, it is preferable to change the position at which shape errors occur by setting the maximum value of angle θ to 3 degrees or more for at least 50 percent of the total number of mold surfaces corresponding to the microlens surfaces.

[0053] Next, we will explain the effect that shape errors in the mold surface have on the performance of the microlens array manufactured using that mold.We performed a simulation in which a microlens array consisting of spherical microlenses with a radius of 0.3 millimeters was used to irradiate a parallel beam of light onto a plane perpendicular to its direction of travel.

[0054] Figure 19 is a diagram showing the shape error in the x-z cross section of surface 210 of the forming mold. The horizontal axis of Figure 19 represents the position in the x-axis direction. The unit of length is millimeters. The vertical axis of Figure 19 represents the shape error. The unit of length is micrometers. Figure 19 shows the shape error when cutting is performed using the cutting method described in Figure 15, and for simplicity, it is assumed that the shape error occurs only near the central axis of surface 210.

[0055] As described above, the position where a shape error occurs can be moved along surface PL by cutting using the cutting method described in Figure 16. When the angle θ is changed from 0 degrees to 15 degrees depending on the distance from the central axis as the processing point moves from the periphery of surface 210 toward the central axis, surface 210 is cut at blade angle α0 when angle θ is 11 degrees, which is the position -0.06 millimeters on the horizontal axis in Figure 19. Therefore, a simulation was performed assuming that a shape error similar to the shape error shown in Figure 19 occurs at the -0.06 millimeter position when cutting using the cutting method described in Figure 16.

[0056] For the surfaces of the multiple molds corresponding to the multiple microlenses, by changing the angle Φ of the surface PL and cutting using the cutting method described in Figure 16, the position where shape errors occur can be moved in the direction of the surface PL corresponding to the angle Φ.

[0057] Figure 20A shows the illuminance distribution on a surface when there is no shape error. The horizontal axis of Figure 20A represents the angle between the z-axis and a line obtained by projecting the light rays from the microlens array onto the x-z plane and reaching the illuminated surface. The vertical axis of Figure 20A represents the angle between the z-axis and a line obtained by projecting the light rays from the microlens array onto the y-z plane and reaching the illuminated surface. Here, the z-axis is defined as a line passing through the center of the microlens array and parallel to the central axis of each microlens, and the x-axis and y-axis are defined as lines perpendicular to each other in a plane perpendicular to the z-axis. The horizontal and vertical axes of Figures 21A, 22A, 23A, 24A, 29A, and 30A also represent the above angles.

[0058] Fig. 20B is a diagram showing the xz cross section of the illuminance distribution shown in Fig. 20A. The horizontal axis of Fig. 20B represents the angle between the z axis and a straight line formed by projecting the light rays reaching the irradiation surface from the microlens array onto the xz plane, and the vertical axis of Fig. 20B represents the relative value of illuminance. The horizontal axes of Fig. 21B, Fig. 22B, Fig. 23B, Fig. 24B, Fig. 29B, and Fig. 30B also represent the above angle, and the vertical axes of Fig. 21B, Fig. 22B, Fig. 23B, Fig. 24B, Fig. 29B, and Fig. 30B also represent the relative value of illuminance.

[0059] FIG. 21A is a diagram showing the illuminance distribution on a surface when there is the shape error shown in FIG.

[0060] Fig. 21B is a diagram showing the xz cross section of the illuminance distribution shown in Fig. 21A. As shown in Fig. 21B, there is a large change in illuminance when x is near 0.

[0061] Figure 22A shows the average illuminance distribution obtained by simulating the illuminance distribution on the surface of a microlens cut from a molding die with an angle Φ of 360 / 7, 360x2 / 7, 360x3 / 7, ..., 360 degrees and an angle θ of 0 to 15 degrees.

[0062] FIG. 22B is a diagram showing the xz cross section of the illuminance distribution shown in FIG. 22A.

[0063] By averaging the illumination intensity from microlenses manufactured using multiple molds cut at multiple values ​​of angle Φ, the illumination change near x=0 is smaller than the illumination change shown in Figures 20A and 20B.

[0064] Figure 23A shows the average illuminance obtained by simulating the illuminance distribution on the surface of a microlens cut from a molding die with an angle Φ of 360 / 61, 360x2 / 61, 360x3 / 61, ..., 360 degrees and an angle θ of 0 to 15 degrees.

[0065] FIG. 23B is a diagram showing the xz cross section of the illuminance distribution shown in FIG. 23A.

[0066] Figure 24A shows the average illuminance distribution obtained by simulating the illuminance distribution on the surface of a microlens cut from a molding die with an angle Φ of 360 / 127, 360x2 / 127, 360x3 / 127, ..., 360 degrees and an angle θ of 0 to 15 degrees.

[0067] FIG. 24B is a diagram showing the xz cross section of the illuminance distribution shown in FIG. 24A.

[0068] Comparing Figures 21B to 24B, the more values ​​of the angle Φ there are, the smaller the change in illuminance when x is near 0 becomes.

[0069] The dispersion of angle Φ will be explained. For simplicity, the number of microlenses is assumed to be six. When the angle Φ of the surfaces 210 corresponding to all microlenses is 0, the dispersion of angle Φ is 0. If the microlenses are divided into three groups of two, and the angles Φ of the surfaces 210 corresponding to two microlenses in each group are set to 0 and 180 degrees, the dispersion is 9720. In this case, there are three surfaces that use the same angle Φ. If the microlenses are divided into two groups of three, and the angles Φ of the surfaces 210 corresponding to three microlenses in each group are set to 0, 120, and 240 degrees, the dispersion is 11520. In this case, there are two surfaces that use the same angle Φ. If the microlenses are divided into one group of six, and the angles Φ of the surfaces 210 corresponding to the six microlenses are set to 0, 60, 120, 180, 240, and 300 degrees, the dispersion is 12600. In this case, the angles Φ used for all surfaces are different. In each group, the angle Φ is set at equal intervals. The smaller the number of faces that use the same angle Φ, the greater the dispersion.

[0070] Generally, in a microlens array with a fixed number of microlenses, the greater the dispersion of the values ​​of the angle Φ of the surface 210 corresponding to each microlens, the smaller the change in illuminance when x is near 0.

[0071] To determine the values ​​of the angles Φ of the multiple faces so as to increase the variance, the values ​​of the angles Φ of the individual faces may be determined so as to be uniformly or equally spaced apart as described above, or the multiple faces may be divided into multiple groups and the values ​​of the angles Φ of the individual faces may be determined so as to be uniformly or equally spaced apart for each group. If there are a large number of multiple faces, the values ​​of the angles Φ of the multiple faces may be determined using pseudo-random numbers or the like.

[0072] Therefore, an appropriate distribution of angle Φ can be determined by finding the illuminance distribution on the surfaces while changing the value of angle Φ on the surfaces of multiple molds so as to increase the variance of angle Φ and comparing the illuminance distributions.

[0073] The results of actually processing a microlens array are shown below. The microlens array consists of 421 spherical microlenses with a radius of 0.1 mm.

[0074] Fig. 25 is a diagram showing the actual shape error of the surface of the molding die corresponding to one microlens surface cut by the conventional cutting method described in Fig. 15. In Fig. 25 to Fig. 28, the central axis of surface 210 is set as the z-axis, and the intersection of surface 210 and the central axis is set as the origin, with the x-axis and y-axis being orthogonal to each other.

[0075] FIG. 26 is a diagram showing the actual shape error of the surface of the molding die corresponding to another microlens surface cut by the conventional cutting method described with reference to FIG.

[0076] According to FIGS. 25 and 26, the maximum shape error occurs near the central axis in both cases.

[0077] FIG. 27 is a diagram showing the actual shape error of the surface of the molding die corresponding to one microlens surface cut by the cutting method of the present invention explained in FIG.

[0078] FIG. 28 is a diagram showing the actual shape error of the surface of the molding die corresponding to another microlens surface cut by the cutting method of the present invention explained in FIG.

[0079] 27 and 28, the maximum shape error occurs at different positions. Specifically, the maximum shape error occurs in the quadrant where the x and y coordinates are positive in the case of Fig. 27, and in the quadrant where the x and y coordinates are negative in the case of Fig. 28. The position where the maximum shape error occurs is determined by the value of the angle Φ.

[0080] In this example according to the present invention, the angles Φ of the 421 mold surfaces corresponding to the 421 microlenses were determined by pseudo-random numbers.

[0081] FIG. 29A is a diagram showing the illuminance distribution on the surface of a microlens array manufactured using a molding die cut by the cutting method described with reference to FIG.

[0082] FIG. 29B is a diagram showing the xz cross section of the illuminance distribution shown in FIG. 29A.

[0083] When cutting is performed using the cutting method described in Figure 15, the position where the maximum shape error occurs on the surfaces of the multiple forming dies is near the central axis, as shown in Figures 25 and 26. Therefore, in Figures 29A and 29B, a ring-shaped pattern caused by the difference in illuminance can be seen near the center.

[0084] FIG. 30A is a diagram showing the illuminance distribution on the surface of a microlens array manufactured using a molding die cut by the cutting method described with reference to FIG.

[0085] FIG. 30B is a diagram showing the xz cross section of the illuminance distribution shown in FIG. 30A.

[0086] When cutting is performed using the cutting method described in Figure 16, the positions at which the maximum shape error occurs on the surfaces of the multiple forming dies can be varied, as shown in Figures 27 and 28. Therefore, no annular pattern due to differences in illuminance is seen near the center in Figures 30A and 30B.

Claims

1. A cutting method for cutting a molding die for a microlens array, the molding die having a plurality of microlenses of substantially the same shape and each having an optical axis in the same direction, by a tool having a blade that rotates around a rotation axis, wherein, for one surface of the molding die corresponding to each surface of the microlens, the direction of the central axis of the surface corresponding to the optical axis of the microlens is defined as the z-axis, and the (x, y, z) coordinate system having mutually orthogonal x-, y- and z-axes is defined as an angle between the rotation axis of the tool and a line in the direction of the z-axis that passes through a point on the rotation axis of the tool, θ, and an angle around the line of a plane including the rotation axis of the tool and the line, and Φ, the (x, y, z) coordinate system for a plurality of surfaces of the molding die corresponding to the surfaces of the plurality of microlenses is defined such that the x-axes of the plurality of surfaces are parallel to each other and the y-axes of the plurality of surfaces are parallel to each other, When cutting one surface of the mold, the value of the angle Φ is kept constant, and when cutting at least one surface of the mold, the value of the angle θ is changed; A cutting method for a molding die for a microlens array, in which, when cutting a plurality of surfaces of the molding die corresponding to the surfaces of the plurality of microlenses, the value of angle Φ is distributed so that the variance of the value of angle Φ for the plurality of surfaces of the molding die is equal to or greater than a predetermined value, so that the change in illuminance on the surface irradiated using the microlens array molded by the molding die is sufficiently small.

2. 2. The method for cutting a molding die for a microlens array according to claim 1, wherein a maximum value of the angle .theta. when cutting one surface of the molding die is determined for each surface.

3. 2. The method for cutting a microlens array molding die as described in claim 1, wherein the maximum value of angle θ when cutting one surface of the molding die is 3 degrees or more for 50% or more of the total number of surfaces of the molding die that correspond to the surfaces of the microlenses.

4. 2. A cutting method for a microlens array molding die as described in claim 1, wherein, when cutting one surface of the molding die, cutting is performed while changing the value of the angle θ in an area where the distance of the processing point from the central axis is greater than a predetermined value, and cutting is performed while fixing the value of the angle θ in an area where the distance is equal to or less than the predetermined value.

5. 2. A method for cutting a microlens array mold as described in claim 1, wherein the rate of change in the value of the angle θ when cutting one surface of the mold is determined so that the positioning accuracy in all moving directions of the tool is below a predetermined value.

6. 2. The method for cutting a molding die for a microlens array according to claim 1, wherein when cutting one surface of the molding die, the locus of the processing point is in a spiral shape around the central axis.

7. 2. The method for cutting a molding die for a microlens array as described in claim 1, wherein, when cutting the multiple surfaces of the molding die corresponding to the surfaces of the multiple microlenses, the multiple surfaces are divided into one or multiple groups, and the values ​​of the angles Φ of the individual surfaces for each group are determined so as to be distributed uniformly or at equal intervals.

8. 2. The cutting method for a microlens array mold according to claim 1, wherein a five-axis machining center is used, the x-axis, the y-axis, and the z-axis correspond to the three linear axes of the five-axis machining center, and the angles θ and Φ correspond to the angles around the two rotation axes of the multi-axis machining center, to perform machining.

9. 2. A cutting method for a microlens array molding die as described in claim 1, wherein when cutting one surface of the molding die, the value of the angle θ is changed so that the value of the angle θ increases as the distance of the processing point from the central axis decreases.

10. 2. A method for cutting a microlens array mold as described in claim 1, wherein when cutting one surface of the mold, the value of the angle θ is changed according to the shape of the surface so that the side of the cutting tool does not interfere with the surface.

11. A method for manufacturing a microlens array, which uses a molding die machined by the machining method according to claim 1.