Microlens array and projection type image display device

Abstract

To provide a microlens array with less diffusion intensity variation.SOLUTION: In the microlens array, a plurality of microlenses are arranged in a matrix in plan view. Each of the plurality of microlenses is consist of four main sides in planar view, or four main sides and one or more sub-sides connecting two main sides of the four main sides. At least one of the four main sides is inclined with respect to a virtual row line parallel to a row direction or with respect to a virtual column line parallel to a column direction. The one main side has an inclination angle θ of a predetermined range with respect to the row virtual line or the column virtual line, and distribution of the inclination angle θ is -2.5°≤θ≤2.5 to -27.7°≤θ≤27.7°.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a microlens array and a projection type image display device. [Background technology]

[0002] A diffuser plate diffuses incident light in various directions. Diffuser plates are used in various applications, such as displays, projectors, and lighting. A microlens array can be used as a diffuser plate. A microlens array has a plurality of lens-like irregularities on its surface. Light incident on the microlens array is refracted and diffused by the irregularities on the surface.

[0003] For example, Patent Documents 1 and 2 disclose a diffusion plate using a microlens array. Patent Document 1 discloses a diffusion plate using a plurality of microlenses that have different cross-sectional shapes and no axis of symmetry. Patent Document 2 discloses a microlens array in which the positions of the vertices are shifted from the basic pattern. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2016 / 051785 [Patent Document 2] Patent No. 4845290 Summary of the Invention [Problem to be solved by the invention]

[0005] In a projector, light that passes through a diffuser plate is irradiated onto, for example, an integrator lens or an image display device. These components are rectangular, and if the diffused light is circular, the light utilization efficiency decreases. For this reason, a diffuser plate that diffuses light into a rectangular shape is required. On the other hand, when diffusing light into a rectangular shape, the lenses are arranged periodically. A diffuser plate with a periodic structure may generate diffracted light, making it difficult to diffuse light uniformly.

[0006] For example, the microlens arrays described in Patent Documents 1 and 2 have lenses arranged in a matrix, and can diffuse light in a quadrangle. However, as described in Patent Document 1, it is difficult to make the diffused light sufficiently uniform by simply making the cross-sectional shape of the lens non-uniform. Also, for example, as described in Patent Document 2, it is difficult to diffuse light uniformly by simply biasing the apex positions of the lenses.

[0007] The present invention has been made in consideration of the above problems, and has an object to provide a microlens array with less variation in diffusion intensity, a projection type image display device, a method for designing a microlens array, and a method for manufacturing a microlens array. [Means for solving the problem]

[0008] In order to solve the above problems, the present invention provides the following means.

[0009] The microlens array according to the first aspect is a microlens array in which a plurality of microlenses are arranged in a matrix in a planar view, and each of the plurality of microlenses has four main sides in a planar view, and each of the four main sides is inclined with respect to a row virtual line parallel to the row direction or a column virtual line parallel to the column direction.

[0010] In the microlens array according to the above aspect, each of the plurality of microlenses may have, in a plan view, one or more sub-sides connecting two of the four main sides.

[0011] In the microlens array according to the above aspect, an inclination angle θ of each of the four main sides with respect to the row virtual line or the column virtual line may be equal to or greater than 2.5° and equal to or less than 36°.

[0012] In the microlens array according to the above aspect, each of the plurality of microlenses may be a concave lens that is concave with respect to a reference surface.

[0013] The microlens array according to the above aspect may further include an anti-reflection film, which may be laminated on at least one of a first surface on which the multiple microlenses are arranged and a second surface opposite to the first surface.

[0014] A projection type image display device according to a second aspect has the microlens array according to the above aspect.

[0015] A design method for a microlens array according to the third aspect includes a first step of drawing a plurality of row virtual lines parallel to the row direction and a plurality of column virtual lines parallel to the column direction, and setting a basic pattern in which a plurality of microlenses are arranged in a matrix, each curved with a vertex being the center of a rectangle enclosed by the row virtual lines and the column virtual lines, and a second step of varying two or more of the spacing between the row virtual lines and the column virtual lines, the position of the vertex of each microlens, and the radius of curvature of each microlens, from the basic pattern.

[0016] In the second step of the method for designing a microlens array according to the above aspect, the spacing between the row virtual lines and the column virtual lines, the apex positions of each microlens, and the radius of curvature of each microlens may all be varied with respect to the basic pattern.

[0017] The method for manufacturing a microlens array according to the above aspect includes the steps of applying a resist onto a substrate, exposing the resist through a grayscale mask to form a resist pattern on the surface of the resist based on the microlens array design method described in claim 7 or 8, and etching through the resist. Effect of the Invention

[0018] According to the microlens array of the above aspect, it is possible to suppress variations in the diffusion intensity of the diffused light. According to the projection type image display device of the above aspect, it is possible to improve the light utilization efficiency. According to the design method and manufacturing method of the microlens array of the above aspect, it is possible to obtain a microlens array with small variation in the diffusion intensity of diffused light. [Brief description of the drawings]

[0019] [Figure 1] 1 is a schematic diagram of a projection type image display device according to a first embodiment. [Diagram 2] FIG. 2 is a plan view of the microlens array according to the first embodiment. [Diagram 3] 1 is a cross-sectional view of a microlens array according to a first embodiment. [Figure 4] FIG. 2 is an enlarged plan view of a characteristic portion of the microlens array according to the first embodiment. [Diagram 5] FIG. 11 is a cross-sectional view of a microlens array according to a first modified example. [Figure 6] 2A to 2C are diagrams illustrating a manufacturing method of the microlens array according to the first embodiment. [Figure 7] 5A to 5C are diagrams for explaining a method of designing the microlens array according to the first embodiment. [Figure 8] 5A to 5C are diagrams for explaining a method of designing the microlens array according to the first embodiment. [Figure 9] FIG. 2 is a schematic diagram for explaining an evaluation method of the microlens arrays according to Examples 1 to 6 and Comparative Example 1. [Figure 10] 1 is a distribution diagram of the inclination angles of the main sides of the microlens arrays according to Examples 1 to 6 and Comparative Example 1 with respect to row virtual lines or column virtual lines. [Figure 11] 13 shows the diffusion characteristics of a microlens array according to Comparative Example 1. [Figure 12] 3 shows the diffusion characteristics of the microlens array according to the first embodiment. [Figure 13] 13 shows the diffusion characteristics of the microlens array according to the second embodiment. [Figure 14] 13 shows the diffusion characteristics of the microlens array according to Example 3. [Figure 15] 13 shows the diffusion characteristics of the microlens array according to Example 4. [Figure 16] 13 shows the diffusion characteristics of the microlens array according to the fifth embodiment. [Figure 17] 13 shows the diffusion characteristics of the microlens array according to Example 6. [Figure 18] 13 shows the diffusion characteristics of a microlens array according to Comparative Example 2. [Figure 19] 1 is a graph summarizing the results of the diffusion characteristics of Examples 1 to 6 and Comparative Examples 1 and 2. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] The present embodiment will be described in detail below with reference to the drawings as appropriate. The drawings used in the following description may show characteristic parts in an enlarged scale for the sake of convenience in order to make the characteristics easier to understand, and the dimensional ratios of each component may differ from the actual ones. The materials, dimensions, etc. exemplified in the following description are merely examples, and the present invention is not limited thereto. They may be modified as appropriate within the scope of the effects of the present invention.

[0021] "Projection type image display device" 1 is a schematic diagram of a projection type image display device PJ according to a first embodiment. The projection type image display device PJ is, for example, a projector. The projection type image display device PJ has, for example, a light source Ls, diffusers Dp1 and Dp2, an integrator lens IR, and a screen Sc.

[0022] The light source Ls is, for example, a lamp or a laser. As for the laser, blue, green, and red lasers may be prepared, or yellow, green, and red may be produced by irradiating a phosphor with a blue laser.

[0023] The diffusers Dp1 and Dp2 diffuse the light from the light source Ls. The diffusers Dp1 and Dp2 are, for example, diffusers in which a plurality of microlens arrays are arranged. Details of the microlens array will be described later. By providing two or more diffusers Dp1 and Dp2 between the light source Ls and the screen Sc, unevenness in the light projected onto the screen Sc is reduced. It is preferable that the shape of the integrator lens IR and the image projected onto the screen Sc are rectangular, and that the diffusers Dp1 and Dp2 diffuse the light into a rectangular shape.

[0024] The integrator lens IR is a lens that increases the uniformity of the illuminance on the irradiation surface. When light passes through the integrator lens IR, the accuracy of the image projected onto the screen Sc is improved.

[0025] "Microlens array" Fig. 2 is a plan view of the microlens array 100 according to the first embodiment. Fig. 3 is a cross-sectional view of the microlens array 100 according to the first embodiment. Fig. 3 is a cross-sectional view of the microlens array 100 taken along line AA in Fig. 2. For example, by regularly arranging a plurality of microlens arrays 100, the above-mentioned diffusers Dp1 and Dp2 are formed.

[0026] Here, the directions are defined. The plane on which the microlens array 100 spreads is the xy plane, one direction of the xy plane is the x direction, and the direction perpendicular to the x direction is the y direction. The x direction and the y direction are each a direction in which the microlenses 10 constituting the microlens array 100 are arranged. The x direction is an example of a row direction, and the y direction is an example of a column direction. The z direction is a direction perpendicular to the xy plane. The z direction is also the direction in which light is incident on the microlens array 100.

[0027] In the microlens array 100, a plurality of microlenses 10 are arranged in a matrix in plan view from the z direction. Arranged in a matrix means that the microlenses 10 are lined up in the x and y directions. The principal vector direction of the line connecting the vertices of adjacent microlenses 10 is the x or y direction. The size of one microlens 10 is, for example, about 100 μm.

[0028] The microlenses 10 are formed on one surface of the substrate S. Hereinafter, the surface of the substrate S on which the microlenses 10 are arranged is referred to as a first surface Sa, and the surface opposite to the first surface Sa is referred to as a second surface Sb. The substrate S is, for example, a substrate transparent to the wavelength band of the incident light. The substrate S is, for example, optical glass, quartz, sapphire, a resin plate, or a resin film. The optical glass is, for example, quartz glass, borosilicate glass, white plate glass, or the like. The resin is, for example, polymethyl methacrylate (PMMA), polyethylene terephthalate (PET), polycarbonate (PC), cyclic olefin copolymer (COC), or the like. The inorganic materials of optical glass, quartz, and sapphire have excellent light resistance. Furthermore, quartz and sapphire have excellent heat dissipation properties. The planar shape of the substrate S in the z direction does not matter.

[0029] Each of the multiple microlenses 10 is, for example, a concave lens that is concave with respect to a reference plane Rp. Each of the multiple microlenses 10 may be, for example, a convex lens that protrudes with respect to the reference plane Rp. The reference plane Rp is a plane parallel to the xy plane (for example, the second surface Sb) and is a surface that contacts the most protruding portion of the first surface Sa. The reference plane Rp is, for example, the surface of the substrate S before processing.

[0030] The surface of each microlens 10 is a curved surface 10a. The curved surface 10a refracts light, thereby diffusing the incident light. The radius of curvature of each curved surface 10a is, for example, different. The radius of curvature of each curved surface 10a is, for example, 50% or more and 150% or less of the average radius of curvature. The curvature of each curved surface 10a may be, for example, 70% or more and 130% or less of the average radius of curvature.

[0031] The maximum or minimum point of the curved surface 10a is called the vertex 10v. When the microlens 10 is a concave lens, the minimum point of the curved surface 10a is the vertex 10v, and when the microlens 10 is a convex lens, the maximum point of the curved surface 10a is the vertex 10v. The distance between the vertex 10v and the reference plane Rp of each microlens 10 is not constant, for example.

[0032] 4 is an enlarged plan view of a characteristic portion of the microlens array 100 according to the first embodiment. The microlenses 10 are arranged in the x and y directions along a basic pattern. The basic pattern is a pattern in which rectangles separated by a plurality of row virtual lines RL and a plurality of column virtual lines CL are arranged in the x and y directions. The row virtual lines RL are virtual lines parallel to the x direction, and the column virtual lines CL are virtual lines parallel to the y direction. The spacing G between each of the column virtual lines CL x is constant, and the interval G between each row imaginary line RL y is constant. The interval G x , G y are several μm to several tens of μm, for example, 1 μm to 100 μm. One microlens 10 is arranged in each quadrangle of the basic pattern. The quadrangles separated by the row virtual lines RL and the column virtual lines CL may be squares or rectangles.

[0033] The shape of each microlens 10 when viewed in a plan view from the z direction is a polygon having four main sides m1, m2, m3, and m4. The polygon is, for example, composed of four main sides m1, m2, m3, and m4 and one or more sub-sides s. The sub-sides s are connecting parts connecting two main sides. For example, the main side m1 and the main side m4 shown in FIG. 4 are connected by the sub-side s. The main sides m1, m2, m3, and m4 and the sub-side s are boundaries between adjacent microlenses 10, and are linear regions where the curvature of the microlenses 10 changes abruptly. When the microlenses 10 are concave lenses, the boundaries are ridges, and when the microlenses 10 are convex lenses, the boundaries are valleys. The main sides m1, m2, m3, and m4 and the sub-sides s may be curved in the z direction.

[0034] Of the four main sides m1, m2, m3, and m4, main sides m1 and m2 extend in the x direction, and main sides m3 and m4 extend in the y direction. In this specification, "extending in the x direction" means, for example, that the length in the x direction is longer than the length in the y direction in the xy plane. The lengths of main sides m1, m2, m3, and m4 are longer than the length of sub-side s. The length of main sides m1 and m2 is, for example, 50% to 150% of the interval Gx between adjacent column virtual lines CL, and the length of main sides m3 and m4 is, for example, 50% to 150% of the interval Gy between adjacent row virtual lines RL.

[0035] At least one of the four main sides m1, m2, m3, and m4 is inclined with respect to the row virtual line RL or the column virtual line CL. The four main sides m1, m2, m3, and m4 may be inclined with respect to the row virtual line RL or the column virtual line CL. The main sides m1 and m2 are inclined with respect to the row virtual line RL. The main side m1 is inclined, for example, at an inclination angle θ1 with respect to the row virtual line RL. The main side m2 is inclined, for example, at an inclination angle θ2 with respect to the row virtual line RL. The main sides m3 and m4 are inclined with respect to the column virtual line CL. The main side m3 is inclined, for example, at an inclination angle θ3 with respect to the column virtual line CL. The main side m4 is inclined, for example, at an inclination angle θ4 with respect to the column virtual line CL. The inclination angles θ1, θ2, θ3, and θ4 are different from each other.

[0036] At least one of the inclination angles θ1, θ2, θ3, and θ4 is 2.5° or more and 36° or less. The inclination angles θ1, θ2, θ3, and θ4 are, for example, 2.5° or more and 36° or less. The average value of the inclination angles θ1, θ2, θ3, and θ4 is, for example, 19.3°. When the inclination angles θ1, θ2, θ3, and θ4 are within the range, the variation in the diffusion intensity of the diffused light after passing through the microlens array 100 is reduced.

[0037] In addition, in a plan view from the z direction, the vertex 10v of each microlens 10 may be shifted from the center 10c of a rectangle defined by the row virtual lines RL and the column virtual lines CL. The shift amount of the vertex 10v from the center 10c in the x direction is, for example, within 50% of the interval Gx between adjacent column virtual lines CL, and may be within 30%. The shift amount of the vertex 10v from the center 10c in the y direction is, for example, within 50% of the interval Gy between adjacent row virtual lines RL, and may be within 30%.

[0038] In the microlens array 100 according to the first embodiment, each microlens 10 has four main sides m1, m2, m3, and m4, so that the shape of the diffused light becomes a rectangle. In addition, each of the main sides m1, m2, m3, and m4 is inclined with respect to the column virtual line CL or the row virtual line RL, so that the variation in the diffusion intensity of the diffused light can be suppressed.

[0039] Furthermore, since the microlens 10 has the minor side s, the shape of the diffused light can be maintained as a rectangle while the variation in the diffusion intensity can be further suppressed. When the microlens 10 has the minor side s, the position at which the microlens 10 is arranged does not deviate significantly from the rectangle of the basic pattern separated by the row virtual lines RL and the column virtual lines CL. Since the microlenses 10 maintain the arrangement of the basic pattern, the shape of the diffused light can be kept more rectangular, and since each side is inclined with respect to the column virtual lines CL or the row virtual lines RL that constitute the basic pattern, the variation in the diffusion intensity of the diffused light can be suppressed.

[0040] Although the first embodiment has been described above in detail, the present invention is not limited to this example, and various modifications and variations are possible within the scope of the gist of the present invention described in the claims.

[0041] For example, Fig. 5 is a cross-sectional view of a microlens array 101 according to a first modified example. The microlens array 101 differs from the microlens array 100 shown in Fig. 3 in that it has antireflection films 11 and 12. In the microlens array 101, the same components as those in the microlens array 100 shown in Fig. 3 are denoted by the same reference numerals and will not be described.

[0042] The antireflection coating 11 covers a first surface Sa of the substrate S. The antireflection coating 12 covers a second surface Sb of the substrate S.

[0043] The anti-reflection films 11 and 12 are, for example, a laminated film in which a low refractive index layer and a high refractive index layer are laminated. The low refractive index layer is, for example, SiO2, MgF2, or CaF2. The high refractive index layer is, for example, Nb2O5, TiO2, Ta2O5, Al2O3, HfO2, or ZrO2. SiO2, Nb2O5, and Ta2O5 have excellent light resistance and are not easily deteriorated even when irradiated with high-density light emitted by a high-output laser or the like.

[0044] 5 shows an example in which antireflection films 11 and 12 are provided on both sides of the substrate S, but an antireflection film may be provided on only one of the surfaces. The antireflection film may have a moth-eye structure in which minute projections and recesses are arranged with a pitch of several hundred nm.

[0045] The microlens array 101 according to the first modification has a similar configuration to the microlens array 100 according to the first embodiment, and therefore has the same effects as the microlens array 100 according to the first embodiment. In addition, by providing the antireflection films 11 and 12, it is possible to suppress interface reflection and thus suppress reflected stray light.

[0046] Although the microlens arrays 100 and 101 have been described so far as being used in a projection type image display device PJ, the microlens arrays 100 and 101 may be used for other purposes, such as in a lighting device.

[0047] "Method of manufacturing microlens array" 6A and 6B are diagrams for explaining the method for manufacturing the microlens array according to the first embodiment. The method for manufacturing the microlens array includes a resist application step, an exposure and development step, and an etching step.

[0048] First, in the resist coating step, resist R1 is coated on substrate S1. Substrate S1 is made of the same material as substrate S, since it will be processed to become substrate S. In the etching step described below, a fluorine-based etching gas (CF4, SF6, CHF3, etc.) may be used as the etching gas. Al2O3 and alkali metals may react with fluorine-based etching gas to become non-volatile substances. For example, when a glass substrate (e.g., Corning Eagle XG) that does not contain alkali metals but contains 27% Al2O3 is etched with a fluorine-based etching gas, Al2O3 that is difficult to etch remains, minute protrusions are generated on the surface, and the transmittance of the glass substrate decreases. Substrate S1 preferably contains 20% by mass or less of an alkali component, more preferably 10% by mass or less. Substrate S1 is preferably made of, for example, quartz glass or Tempax glass. A known resist R1 can be used.

[0049] Next, in the exposure process, the resist R1 is irradiated with light L1 through a grayscale mask Gm to expose the resist R1. For example, the exposure is performed by step-and-repeat exposure in which exposure is repeated while moving the grayscale mask. Depending on the positional accuracy of the stepping, a seam having a width of up to about several μm may be formed between the basic cells formed by one exposure. In order to avoid such a problem, it is preferable to expose the basic cells so that they overlap each other. When the basic cells are to be largely overlapped with each other, the exposure may be adjusted so that the desired amount of exposure is achieved by multiple exposures.

[0050] Next, in the development process, the exposed resist pattern is developed. Part of the resist R1 is removed by development, resulting in resist R2 having a resist pattern on its surface. A resist pattern similar to the desired microlens array is formed on the surface of the resist R2. The method of designing the resist pattern into the desired microlens array pattern will be described in detail later.

[0051] Next, in the etching process, the substrate S1 is dry-etched through the resist R2. The dry etching is performed using, for example, reactive gas G. The gas G is, for example, the above-mentioned fluorine-based etching gas. The pattern of the microlens array formed on the surface of the resist R2 by dry etching is transferred to the substrate S1. The substrate S1 becomes a substrate S having a microlens array formed on a first surface Sa.

[0052] 5, thereafter, anti-reflection films 11 and 12 are formed. The anti-reflection films 11 and 12 are formed by, for example, deposition, sputtering, or the like.

[0053] "Design method for microlens array" The design method of a microlens array is divided into a first step, a second step, and a third step. The first step is a step of setting a basic pattern. The second step is a step of setting a pattern in which various conditions are varied for the basic pattern. The third step is a step of selecting etching conditions. Each step will be described below with reference to Figs. 7 and 8. Figs. 7 and 8 are diagrams for explaining the design method of a microlens array according to the first embodiment.

[0054] First, in the first step, a basic pattern is set as shown in Fig. 7. First, a plurality of row virtual lines RL and column virtual lines CL are drawn to set an array pattern in which rectangles surrounded by the row virtual lines RL and column virtual lines CL are arranged. Next, as shown in Fig. 8, the radius of curvature R of the microlenses is determined according to the diffusion angle θd required for the microlens array. The radius of curvature R and the diffusion angle θd satisfy the following relationship. θd=2sin -1 {(p(n-1) / 2R) In the above formula, p is the interval Gx between adjacent column virtual lines CL or the interval Gy between adjacent row virtual lines RL, and n is the refractive index of the substrate S.

[0055] Next, the center c of each square in the array pattern is set to be the vertex v of the microlens. In this manner, a basic pattern is set in which microlenses with a predetermined curvature are arranged in a matrix. Figures 7 and 8 show an example of the set basic pattern.

[0056] Next, in the second step, some parameters are varied based on the basic pattern set in the first step. The parameters to be varied with respect to the basic pattern are the interval G between the row virtual lines RL and the column virtual lines CL, x , G y , the position of the apex of each microlens, and the radius of curvature of each microlens. All of these parameters may be shifted.

[0057] Distance G between adjacent column virtual lines CL x The spacing Gx between the column virtual lines CL in the basic pattern is used as a reference. y ' is the spacing G between the row imaginary lines RL in the basic pattern y The interval G between adjacent virtual column lines CL is used as a reference. x and the distance G between adjacent row virtual lines RL y When the length of each side of the rectangle in the shift pattern varies with respect to the length of each side of the rectangle in the basic pattern, the length of each side of the rectangle in the shift pattern varies with respect to the length of each side of the rectangle in the basic pattern.

[0058] Distance G between adjacent column virtual lines CL x ' satisfies the following relationship: g x is the degree of variation, and g x ≧0% and 0% <g x It is preferable that the ratio satisfies ≦50%. G x '=G x ±G x ×g x

[0059] Also, the interval G between adjacent virtual row lines CL y ' satisfies the following relationship: g y is the degree of variation, and g y ≧0% and 0% <gy Preferably, it satisfies ≤ 50%. G y ’ = G y ±G y ×g y

[0060] The position of the vertex v of each microlens is varied with respect to the position of the center c of each square of the basic pattern. The amount of variation in the x direction of the vertex v of the microlens with respect to the center c of each square of the basic pattern is G x ×T x and is represented by, and the amount of variation in the y direction is G y ×T y and is represented by. T x and T y are the degrees of variation, and 0% ≤ T x , T y ≤ 50% is satisfied, and preferably 0% < T x , T y ≤ 50% is satisfied.

[0061] The radius of curvature of each microlens is varied with reference to the radius of curvature R of the microlens set in the basic pattern. The amount of variation in the radius of curvature is represented by R × r. r is the degree of variation, and 0% ≤ r ≤ 50% is satisfied, and preferably 0% < r ≤ 50% is satisfied.

[0062] In the above procedure, a shift pattern in which various parameters are varied within the above ranges with respect to the basic pattern is laid out. The layout is performed based on a known lens arrangement calculation algorithm. Next, it is determined whether the laid out shift pattern satisfies the planar view pattern of the desired microlens array. The planar view pattern of the desired microlens array is a microlens array pattern that satisfies the above-mentioned configuration. If it is determined that the shift pattern satisfies the planar view pattern of the desired microlens array, proceed to the third step. If it is determined that the shift pattern does not satisfy the planar view pattern of the desired microlens array, return to the second step again to adjust the amount of variation in various parameters. As a result, the planar view pattern of the microlens array is determined by the first and second steps.

[0063] Next, in the third step, the etching conditions are selected. The etching conditions to be set are the ratio of the etching rate of the substrate S1 to the etching rate of the resist R2 in the etching step ("etching rate of the substrate S1" / "etching rate of the resist R2"). Hereinafter, the ratio of the etching rate of the substrate S1 to the etching rate of the resist R2 is referred to as the etching selectivity. The etching selectivity is adjusted, for example, by the flow rate ratio of multiple etching gases used in etching.

[0064] For example, when CF4, Ar, and O2 are used as etching gases, the etching selectivity changes from 1.0 to 1.7 when the ratio of the flow rate of CF4 gas to the flow rate of Ar gas ("CF4 gas flow rate" / "Ar gas flow rate") is changed from 0.25 to 4.0. In addition, when O2 gas is added in the range of 3% to 10% in this state, the etching selectivity decreases to 0.7 or more and 1.0 or less. In other words, the etching selectivity can be set in the range of 0.7 or more and 1.7 or less. In this case, the radius of curvature of the microlens array formed on the substrate S can be adjusted in the range of 70% or more and 170% or less with respect to the radius of curvature of the resist pattern formed on the surface of the resist R2.

[0065] As described above, by changing the etching selectivity, the processing depth of the substrate S1 in dry etching can be changed. If the etching selectivity is η and the planned microlens depth is S, the depth of the actually formed microlens is approximated to η×S. Also, if the curvature radius of the resist pattern is Rr, the curvature radius of the actually formed microlens is Rr / η. In the third step, the etching conditions are selected based on the above relationship.

[0066] By going through the above procedure, a desired microlens array can be manufactured. That is, according to the method for designing and manufacturing a microlens array according to the present embodiment, a microlens array with small variation in the diffusion intensity of diffused light can be obtained. EXAMPLES

[0067] In the following Examples 1 to 6 and Comparative Examples 1 and 2, a microlens array was designed under predetermined conditions, and the diffusion characteristics of the obtained microlens array were obtained by simulation. The simulation was performed using OpticStudio by Zemax. The diffusion characteristics are the intensity distribution of the diffused light in a detector with a side length of 150 mm that is installed 200 mm away from the center of the fabricated microlens array, with incident light having an intensity of 1 W and a spot diameter of 0.6 mm. The incident light is a coherent parallel light with a wavelength of 450 nm. The diffusion characteristics were obtained in each of the x direction and the xy direction, as shown in FIG. 9. The xy direction is a direction inclined at 45° with respect to each of the x direction and the y direction. FIG. 9 is a schematic diagram for explaining an evaluation method of the microlens array according to Examples 1 to 6 and Comparative Example 1.

[0068] "Comparative Example 1" In Comparative Example 1, a microlens array with a basic pattern was designed. Each microlens was a square concave lens with a side length of 80 μm. The radius of curvature of the microlens was 150 μm, and the refractive index of the substrate for light with a wavelength of 450 nm was 1.47. Ten of these microlenses were arranged in the x and y directions to produce a microlens array with a matrix arrangement.

[0069] The planar shape of the microlens is a square, and is composed of only main sides. Each main side is parallel to a row virtual line or a column virtual line, and the inclination angles θ1, θ2, θ3, and θ4 with respect to the row virtual line or the column virtual line are 0°. Fig. 10(a) is a distribution diagram of the inclination angles of the main sides of the microlens array according to Comparative Example 1 with respect to the row virtual line or the column virtual line.

[0070] Fig. 11 shows the diffusion characteristics of the microlens array according to Comparative Example 1. Fig. 11(a) shows the diffusion characteristics in the x direction, and Fig. 11(b) shows the diffusion characteristics in the x and xy directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x and xy directions x , σ xy are both 0.039W / cm 2 The 10% angular width of the diffused light was also calculated. The 10% angular width is the range of angles where the intensity is 10% or more of the maximum intensity in the fitting curve when the intensity distribution is fitted with a Gaussian function. The 10% angular width in the x direction was 15.6°, and the 10% angular width in the xy direction was 22.9°. The ratio of the 10% angular width in the x direction to the 10% angular width in the xy direction was 0.68.

[0071] "Examples 1 to 6" In Examples 1 to 6, the intervals between the row virtual lines RL and the column virtual lines CL, the apex positions of each microlens, and the radius of curvature of each microlens were all varied based on the basic pattern. The refractive index of the substrate for light with a wavelength of 450 nm was set to 1.47, the same as in Comparative Example 1. Examples 1 to 6 had different degrees of variation. All of the microlenses in Examples 1 to 6 were polygonal in plan view, consisting of four main sides and four minor sides.

[0072] In the first embodiment, the degree of variation of the column virtual lines and row virtual lines g x , g y 5%, and the degree of variation in the vertex positions in the x and y directions T x , T ywas set to 5%, and the degree of variation in the radius of curvature of the microlens, r, was set to 5%.

[0073] 10(b) is a distribution diagram of the inclination angles of the main sides with respect to the row virtual lines or column virtual lines of the microlens array according to Example 1. In Example 1, the inclination angles θ1, θ2, θ3, and θ4 of the main sides with respect to the row virtual lines or column virtual lines were in the range of −3.7° or more and 3.7° or less.

[0074] 12 shows the diffusion characteristics of the microlens array according to the first embodiment. FIG. 12(a) shows the diffusion characteristics in the x direction, and FIG. 12(b) shows the diffusion characteristics in the xy directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x direction x is 0.025W / cm 2 and the standard deviation of the diffusion intensity in the x direction is σ xy is 0.028W / cm 2 The 10% angle width in the x direction was 16.2°, and the 10% angle width in the xy direction was 22.7°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 0.71.

[0075] In the second embodiment, the degree of variation of the column virtual lines and row virtual lines g x , g y 10%, and the degree of variation in the x and y directions of the vertex positions T x , T y was set to 10%, and the degree of variation in the radius of curvature of the microlens, r, was set to 10%.

[0076] 10(c) is a distribution diagram of the inclination angles of the main sides of the microlens array according to Example 2 relative to the row virtual lines or column virtual lines. In Example 2, the inclination angles θ1, θ2, θ3, and θ4 of the main sides relative to the row virtual lines or column virtual lines were in the range of −11.7° or more and 11.7° or less.

[0077] 13 shows the diffusion characteristics of the microlens array according to the second embodiment. FIG. 13(a) shows the diffusion characteristics in the x direction, and FIG. 13(b) shows the diffusion characteristics in the x and y directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x direction x is 0.023W / cm 2 and the standard deviation of the diffusion intensity in the x direction is σ xy is 0.027W / cm 2 The 10% angle width in the x direction was 16.6°, and the 10% angle width in the xy direction was 22.0°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 0.75.

[0078] In the third embodiment, the degree of variation of the column virtual lines and row virtual lines g x , g y 20%, and the degree of variation in the x and y directions of the vertex positions T x , T y was set to 20%, and the degree of variation in the radius of curvature of the microlens, r, was set to 20%.

[0079] 10(d) is a distribution diagram of the inclination angles of the main sides of the microlens array according to Example 3 relative to the row virtual lines or column virtual lines. In Example 3, the inclination angles θ1, θ2, θ3, and θ4 of the main sides relative to the row virtual lines or column virtual lines were in the range of −12.5° or more and 12.5° or less.

[0080] FIG. 14 shows the diffusion characteristics of the microlens array according to the third embodiment. FIG. 14(a) shows the diffusion characteristics in the x direction, and FIG. 14(b) shows the diffusion characteristics in the x and y directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x direction x is 0.022 W / cm 2 and the standard deviation of the diffusion intensity in the x direction is σ xy is 0.024 W / cm 2 The 10% angle width in the x direction was 18.0°, and the 10% angle width in the xy direction was 22.0°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 0.82.

[0081] In the fourth embodiment, the degree of variation of the column virtual lines and row virtual lines g x , g y 30%, and the degree of variation in the x and y directions of the vertex positions T x , T y was set to 30%, and the degree of variation in the radius of curvature of the microlens, r, was set to 30%.

[0082] 10(e) is a distribution diagram of the inclination angles of the main sides of the microlens array according to Example 4 relative to the row virtual lines or column virtual lines. In Example 4, the inclination angles θ1, θ2, θ3, and θ4 of the main sides relative to the row virtual lines or column virtual lines were in the range of -19.3° or more and 19.3° or less.

[0083] FIG. 15 shows the diffusion characteristics of the microlens array according to the fourth embodiment. FIG. 15(a) shows the diffusion characteristics in the x direction, and FIG. 15(b) shows the diffusion characteristics in the x and y directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x direction x is 0.019W / cm 2 and the standard deviation of the diffusion intensity in the x direction is σ xy is 0.024 W / cm 2 The 10% angle width in the x direction was 18.5°, and the 10% angle width in the xy direction was 23.2°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 0.80.

[0084] In the fifth embodiment, the degree of variation of the column virtual lines and row virtual lines g x , g y 40%, and the degree of variation in the x and y directions of the vertex positions T x , T y was set to 40%, and the degree of variation in the radius of curvature of the microlens, r, was set to 40%.

[0085] 10(f) is a distribution diagram of the inclination angles of the main sides of the microlens array according to Example 5 relative to the row virtual lines or column virtual lines. In Example 5, the inclination angles θ1, θ2, θ3, and θ4 of the main sides relative to the row virtual lines or column virtual lines were in the range of −27.7° or more and 27.7° or less.

[0086] FIG. 16 shows the diffusion characteristics of the microlens array according to the fifth embodiment. FIG. 16(a) shows the diffusion characteristics in the x direction, and FIG. 16(b) shows the diffusion characteristics in the x and y directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x direction x is 0.020W / cm 2 and the standard deviation of the diffusion intensity in the x direction is σ xy is 0.027W / cm 2 The 10% angle width in the x direction was 19.4°, and the 10% angle width in the xy direction was 22.0°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 0.88.

[0087] In Example 6, the degree of variation of the column virtual lines and row virtual lines g x , g y 50%, and the degree of variation in the x and y directions of the vertex positions T x , T y was set to 50%, and the degree of variation in the radius of curvature of the microlens, r, was set to 50%.

[0088] 10(g) is a distribution diagram of the inclination angles of the main sides of the microlens array according to Example 6 relative to the row virtual lines or column virtual lines. In Example 6, the inclination angles θ1, θ2, θ3, and θ4 of the main sides relative to the row virtual lines or column virtual lines were in the range of −35.9° or more and 35.9° or less.

[0089] FIG. 17 shows the diffusion characteristics of the microlens array according to Example 6. FIG. 17(a) shows the diffusion characteristics in the x direction, and FIG. 17(b) shows the diffusion characteristics in the xy directions. The horizontal axis shows the angle with respect to the incident light, and the vertical axis shows the intensity of the diffused light. The standard deviation σ of the diffusion intensity in the x direction x is 0.018W / cm 2 and the standard deviation of the diffusion intensity in the x direction is σ xy is 0.023W / cm 2 The 10% angle width in the x direction was 23.2°, and the 10% angle width in the xy direction was 23.2°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 1.00.

[0090] "Comparative Example 2" Comparative Example 2 differs from Comparative Example 1 in that the microlenses were not arranged but randomly arranged. The average vertex interval of adjacent microlenses was 80 μm, and the average radius of curvature of the microlenses was 150 μm. The refractive index of the substrate for light with a wavelength of 450 nm was 1.47, the same as in Comparative Example 1. Since the microlenses were not arranged, the diffused light was circular.

[0091] Fig. 18 shows the diffusion characteristics of the microlens array according to Comparative Example 2. Fig. 18 shows the diffusion characteristics in an arbitrary position direction (for example, the x direction). Since the diffused light is circular, the diffusion characteristics are approximately the same in any direction. The horizontal axis is the angle with respect to the incident light, and the vertical axis is the intensity of the diffused light. The standard deviation σ of the diffusion intensity is 0.031 W / cm 2 The 10% angle width in the x direction was 22.5°, and the 10% angle width in the xy direction was 22.4°. The ratio of the 10% angle width in the x direction to the 10% angle width in the xy direction was 1.00.

[0092] The above manufacturing conditions are summarized in Table 1, and the characteristics of the manufactured microlens array are summarized in Table 2.

[0093] [Table 1]

[0094] [Table 2]

[0095] When one side of a square is 1, the length of the diagonal is about 1.414. That is, the ratio of the length in the x direction divided by the length in the x and y directions is about 0.70. That is, the closer the ratio of the angular width in the x direction to the angular width in the x and y directions in the diffused light of the microlens array is to 0.70, the more rectangular the shape of the diffused light becomes. It can be said that the diffused light in Examples 1 to 5 is closer to a rectangle than that in Comparative Example 2. In Example 6, the shape of the diffused light is closer to a circle, but the standard deviation of the intensity is smaller than that in Comparative Example 2, and it can be said that the uniformity of the intensity of the diffused light is improved.

[0096] Fig. 19 summarizes the results of the optical characteristics of Examples 1 to 6, Comparative Example 1, and Comparative Example 2. The circular dots in Fig. 19 are the results of plotting x / xy for Examples 1 to 6 and Comparative Example 1, the triangular dots are the results of plotting the standard deviation σxy of the intensity in the x and y directions for Examples 1 to 6 and Comparative Example 1, and the square dots are the results of plotting the standard deviation σx of the intensity in the x direction for Examples 1 to 6 and Comparative Example 1. The standard deviation of the microlens array of Comparative Example 2 was 0.031 W / cm 2 The microlens arrays of Examples 1 to 6 all had standard deviations σ x , σ xy However, all of these values ​​are smaller than the standard deviation of the microlens array of Comparative Example 2, which indicates that the light diffused from the microlens arrays of Examples 1 to 6 is uniform. [Explanation of symbols]

[0097] 10 Microlenses 10a Curved Surface 10c, c center 10v Vertex 11, 12 Anti-reflection coating 100, 101 Microlens array CL column virtual line RL Row Imaginary Line m1, m2, m3, m4 main side s subside PJ projection type image display device

Claims

1. A microlens array in which a plurality of microlenses are arranged in a matrix in a plan view, Each of the plurality of microlenses includes, in a plan view, four main sides, or the four main sides and one or more sub-sides connecting two of the four main sides; At least one of the four main sides is inclined with respect to a row virtual line parallel to the row direction or a column virtual line parallel to the column direction, A microlens array in which, in terms of the light intensity of diffused light, the ratio of the 10% angular width in the x direction to the 10% angular width (°) in the xy directions is in the range of 0.71 to 0.

88.

2. The standard deviation σ of the diffuse intensity in the x direction of the diffuse light ｘ , but 0.019 W / cm ２ 0.025W / cm or more ２ 2. The microlens array of claim 1 , wherein:

3. The standard deviation σ of the diffusion intensity in the x and y directions of the diffused light ｘｙ , but 0.024 W / cm ２ 0.028W / cm or more ２ 3. The microlens array according to claim 1, wherein:

4. At least one of the four main sides has an inclination angle θ within a predetermined range with respect to a row virtual line or a column virtual line, 4. The microlens array according to claim 1, wherein the distribution of the angle range of the tilt angle θ is from -3.7°≦θ≦3.7° to -27.7°≦θ≦27.7°.

5. A projection type image display device comprising the microlens array according to claim 1 .

Images