Diffusion plate

Abstract

To secure sufficient deflection performance even in the case of oblique incidence so as to be able to bend outgoing light at a large bend angle in a desired direction.SOLUTION: A microlens array type diffusion plate 1 includes: a base material 10; and a microlens array 20 consisting of a plurality of microlenses 21 which are irregularly arranged on an XY plane in at least one surface of the base material 10. A surface shape of each of the microlenses 21 is an aspheric shape expressed by an aspheric equation having at least a third-order term.SELECTED DRAWING: Figure 11

Description

[Technical field]

[0001] The present invention relates to a diffuser plate. [Background technology]

[0002] In order to change the diffusion characteristics of light, a diffuser plate that diffuses incident light in a desired direction is used. Diffuser plates are widely used in various devices, such as display devices such as displays, projection devices such as projectors, and various lighting devices. There is a type of diffuser plate that diffuses incident light at a desired diffusion angle by utilizing the refraction of light caused by the surface shape of the diffuser plate. As a diffuser plate of this type, a microlens array type diffuser plate in which a plurality of microlenses having a size of about several tens of μm are arranged is known.

[0003] In such a microlens array type diffuser, the wavefronts of the light from each microlens interfere with each other, resulting in diffracted waves due to the periodic structure of the microlens array, which causes unevenness in the intensity distribution of the diffused light. For this reason, a technology has been proposed to reduce unevenness in the intensity distribution of the diffused light caused by interference and diffraction by varying the arrangement of the microlenses, the shape of the lens surface, and the shape of the opening.

[0004] For example, Patent Document 1 discloses an irregular arrangement of multiple microlenses using a honeycomb structure as a basic pattern. In Patent Document 1, multiple microlenses are irregularly arranged on the surface of a diffuser plate such that the vertex positions of the surfaces of the microlenses are located within a predetermined circle centered on the vertex positions of the surfaces in the basic pattern.

[0005] In the conventional diffuser plate described in the above Patent Document 1, a plurality of microlenses are arranged at irregular positions on the surface of the diffuser plate (on the XY plane) or the vertex positions of the surface of each microlens are shifted to decenter the optical axis. However, in the conventional diffuser plate, the optical axis of each microlens extends in a direction perpendicular to the surface of the diffuser plate (normal direction: Z direction). Therefore, the direction of the chief ray of the outgoing light (diffused light) diffused by the diffuser plate is parallel to the direction of the chief ray of the incident light, so that the light flux of the outgoing light (diffused light) cannot be deflected in a desired direction with respect to the light flux of the incident light. For example, when collimated light is incident in a direction perpendicular to the surface of the conventional diffuser plate (normal direction: Z direction), the light flux of the outgoing light (diffused light) is diffused symmetrically with the normal direction (i.e., the optical axis direction of the microlens) as the central axis and is emitted. For this reason, the direction of the chief ray of the outgoing light (diffused light) is always the normal direction, so the light flux of the outgoing light cannot be tilted in a desired direction with respect to the normal direction and deflected with respect to the light flux of the incident light.

[0006] Of course, even with a conventional diffuser, the macroscopic emission direction of the entire outgoing light (diffused light) that passes through the diffuser and is diffused may be tilted in a direction different from that of the incident light due to the refraction action of the diffuser. However, as described above, the optical axis of the conventional microlens is parallel to the normal direction (Z direction) of the diffuser, so it is not possible to deflect the luminous flux of the outgoing light in a desired direction different from the normal refraction action of the diffuser.

[0007] Therefore, in the past, there was a demand for a diffuser plate equipped with a microlens array capable of deflecting the light beam of the exiting light in a desired direction, for example, in order to expand the design freedom in the optical axis direction of the incident light and exiting light relative to the diffuser plate and to miniaturize the optical equipment system.

[0008] Therefore, for example, Patent Document 2 discloses that the optical axis of a microlens is tilted with respect to the normal direction (Z direction) to the surface of a substrate while keeping the surface shape of the microlens symmetrical. By using a microlens with an inclined optical axis in this way, it is possible to bend the outgoing light with respect to the incident light, and to diffuse the outgoing light while deflecting it in a direction inclined with respect to the normal direction. [Prior art documents] [Patent documents]

[0009] [Patent Document 1] Patent No. 4981300 [Patent Document 2] JP 2023-044051 A Summary of the Invention [Problem to be solved by the invention]

[0010] In the technology of Patent Document 2, in the case of normal incidence where light is incident from the normal direction (Z direction) of the surface of the diffuser plate, it is possible to deflect the outgoing light in a desired direction. However, in the technology of Patent Document 2, in the case of oblique incidence where light is incident from a direction inclined to the normal direction, there is a problem that the deflection performance of the outgoing light is insufficient compared to the case of normal incidence. In particular, when the outgoing light is deflected by bending it in two-dimensional directions (X direction and Y direction) of the surface of the diffuser plate with respect to the incident light, it is difficult to increase the bending angle, and there is a problem that the deflection performance is insufficient.

[0011] Therefore, the present invention has been made in consideration of the above problems, and an object of the present invention is to provide a diffuser plate that can ensure sufficient deflection performance even in the case of oblique incidence, and can bend the exiting light in a desired direction at a large bending angle. [Means for solving the problem]

[0012] In order to solve the above problems, according to one aspect of the present invention, A microlens array type diffuser plate, A substrate; A microlens array including a plurality of microlenses irregularly arranged on an XY plane on at least one surface of the substrate; Equipped with There is provided a diffuser plate, wherein the surface shape of the microlenses is an aspheric shape represented by an aspheric equation having at least a third-order term.

[0013] The surface shape of the microlens may be an aspheric shape expressed by an aspheric equation having the third-order term and the fourth-order term.

[0014] The third-order term is a term for making the surface shape of the microlens asymmetric, The fourth-order term may be a term for correcting an inflection point of a cross-sectional shape of the surface of the microlens.

[0015] The aspheric surface formula may satisfy the following formula (10). A4 / A3>0 …(10) A3: Aspheric coefficient of the third-order term A4: Aspheric coefficient of the fourth-order term

[0016] The aspheric surface formula may satisfy the following formula (11). A4 / A3>0.03 (11)

[0017] The aspheric surface formula may satisfy the following formula (12). A4 / A3<0.5 (12)

[0018] the third-order term includes a third-order term in the X direction and a third-order term in the Y direction on the XY plane, the fourth-order term includes a fourth-order term in the X direction and a fourth-order term in the Y direction, The aspheric surface equation may satisfy the following equations (21) and (22). A 4x / A 3x>0 (21) A 4y / A 3y >0 (22) A 3x : the aspheric coefficient of the third-order term in the X direction A 4x : the aspheric coefficient of the fourth-order term in the X direction A 3y : the aspheric coefficient of the third-order term in the Y direction A 4y : the aspheric coefficient of the fourth-order term in the Y direction

[0019] The aspheric surface equation may satisfy the following equations (23) and (24). A 4x / A 3x >0.03 (23) A 4y / A 3y >0.03 (24)

[0020] The aspheric surface equation may satisfy the following equations (25) and (26). A 4x / A 3x <0.5 ···(25) A 4y / A 3y <0.5 ···(26)

[0021] the third-order term includes both a third-order term in the X direction and a third-order term in the Y direction on the XY plane, The surface shape of the microlens may be an aspheric shape that is distorted asymmetrically in both the X direction and the Y direction with respect to a reference surface shape having an axis of symmetry.

[0022] the third-order term includes either a third-order term in the X direction or a third-order term in the Y direction on the XY plane, The surface shape of the microlens may be asymmetrically distorted in either the X direction or the Y direction with respect to a reference surface shape having an axis of symmetry, and may be an aspheric shape that is symmetric in the other direction. Effect of the Invention

[0023] As described above, according to the present invention, even in the case of oblique incidence, sufficient deflection performance can be ensured, and the emitted light can be bent at a large bending angle in a desired direction. [Brief description of the drawings]

[0024] [Figure 1] 1A and 1B are a plan view and an enlarged view showing a schematic view of a diffusion plate according to one embodiment of the present invention. [Diagram 2] 3A and 3B are an enlarged plan view and an enlarged cross-sectional view illustrating a schematic configuration of a diffusion plate according to the embodiment. [Diagram 3] 4 is an enlarged cross-sectional view showing a schematic view of the vicinity of a boundary of a microlens according to the embodiment; FIG. [Figure 4] 2 is a plan view that illustrates a schematic planar shape (outer shape) of a microlens when the microlens is viewed in a direction perpendicular to the surface of a substrate according to the embodiment. FIG. [Diagram 5] FIG. 2 is an explanatory diagram showing a planar shape of a reference surface shape having an anamorphic shape. [Figure 6] FIG. 2 is a perspective view showing a three-dimensional shape of a reference surface shape having an anamorphic shape. [Figure 7] This is a graph based on equation (2), which includes a cubic term in the Y direction but does not include a cubic term in the X direction. [Figure 8] This is a graph based on equation (2), which includes a cubic term in the Y direction but does not include a cubic term in the X direction. [Figure 9] 9 is a graph based on Equation (3) when the inflection point shown in FIG. 8 is corrected. [Figure 10] 1 is a schematic diagram showing the diffusion function of transmitted light by a microlens having a reference surface shape. FIG. [Figure 11] 5A to 5C are schematic diagrams illustrating the diffusion and deflection functions of transmitted light of the microlens according to the embodiment. [Figure 12] 13 is a graph illustrating a change in the degree of bending due to a change in the aspheric coefficient A3 of the third order term. [Figure 13]13 is a flowchart showing a method for designing a microlens according to the embodiment. [Figure 14] 4 is a plan view showing the arrangement of lens center coordinates of the microlenses according to the embodiment. FIG. [Figure 15] 2 is a plan view showing an arrangement of microlenses having a rotationally asymmetric aspheric shape according to the embodiment. FIG. [Figure 16] 5 is a flowchart showing a method for manufacturing the diffusion plate according to the embodiment. [Figure 17] 1 is a graph showing design values ​​of the first embodiment. [Figure 18] 11 is an image showing a simulation result of a radiance distribution of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 1. [Figure 19] 11 is an image showing a simulation result of a radiance cross-sectional distribution in the X direction of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 1. [Figure 20] 11 is an image showing a simulation result of the radiance cross-sectional distribution in the Y direction of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 1. [Figure 21] 1 shows the angular distribution of radiance of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 1. [Figure 22] 11 is a graph showing design values ​​of the second embodiment. [Figure 23] 13 is an image showing a simulation result of the radiance distribution of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 2. [Figure 24] 13 is an image showing a simulation result of a radiance cross-sectional distribution in the X direction of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 2. [Diagram 25] 13 is an image showing a simulation result of the radiance cross-sectional distribution in the Y direction of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 2. [Figure 26]1 shows the angular distribution of radiance of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 2. [Figure 27] 13 is a graph showing design values ​​of the third embodiment. [Figure 28] 13 is an image showing a simulation result of a radiance distribution of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 3. [Figure 29] 13 is an image showing a simulation result of a radiance cross-sectional distribution in the X direction of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 3. [Diagram 30] 13 is an image showing a simulation result of the radiance cross-sectional distribution in the Y direction of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 3. [Diagram 31] 13 shows the angular distribution of radiance of diffused light projected onto a screen located 100 mm away from the diffuser plate of Example 3. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In this specification and the drawings, components having substantially the same functional configurations are designated by the same reference numerals, and duplicated explanations will be omitted.

[0026] <1. Overview of the diffuser plate> First, an overview of a diffusion plate 1 according to one embodiment of the present invention will be described with reference to FIGS.

[0027] As shown in Fig. 1 to Fig. 4, the diffuser plate 1 according to this embodiment is a microlens array type diffuser plate having a function of diffusing light uniformly. The diffuser plate 1 has a substrate 10 and a microlens array 20 formed on an XY plane on at least one surface (principal surface) of the substrate 10. The microlens array 20 is composed of a plurality of microlenses 21 irregularly arranged and developed on the XY plane. The microlenses 21 have a convex structure (convex lens) or a concave structure (concave lens) having a light diffusing function, and have, for example, aperture widths Dx, Dy (also referred to as lens diameter or aperture diameter) of about several tens of µm and curvature radii Rx, Ry of about several tens of µm.

[0028] In the diffuser 1 according to this embodiment, the surface shape (three-dimensional shape) of each microlens 21 has an aspheric shape, and each microlens 21 is an aspheric lens. Furthermore, the surface shape of each microlens 21 has an aspheric shape that is asymmetrically distorted in either or both of the X direction and the Y direction with respect to a predetermined reference surface shape.

[0029] As a result, even if the incident direction (incident angle θin) of the incident light to the diffuser 1 is the normal direction (Z direction) to the surface (XY surface) of the flat base material 10 of the diffuser 1 (normal incidence) or is inclined to the Z direction (oblique incidence), the outgoing light (diffused light) that passes through the diffuser 1 and is diffused can be deflected in a direction different from the normal refraction action of the diffuser 1. Due to the deflection action of the diffuser 1, even if the incident light is normal incidence or oblique incidence, sufficient deflection performance can be ensured and the outgoing light can be bent at a large bending angle in a desired direction. Therefore, the degree of freedom of the incident direction of the incident light to the diffuser 1 and the degree of freedom of the outgoing direction of the outgoing light (outgoing angle θout) can be improved. Therefore, the degree of freedom of design of the optical axis direction of the incident light and outgoing light to the diffuser 1 can be expanded, and the optical device system in which the diffuser 1 is mounted can be made smaller.

[0030] Furthermore, according to this embodiment, the microlenses 21 are arranged at irregular positions on the XY plane of the substrate 10 of the diffusion plate 1. For example, the microlenses 21 may be arranged at irregular positions while overlapping each other so that the overlap amount Ov between adjacent microlenses 21 on the XY plane is within a predetermined allowable range. Furthermore, as shown in FIG. 2, the microlenses 21 are arranged without gaps between each other on the XY plane of the substrate 10, and it is preferable that no flat portion exists at the boundary between adjacent microlenses 21.

[0031] As a result, the surface of the diffuser 1 is occupied by the uneven structure of the multiple irregularly arranged microlenses 21, and no flat portion exists. Therefore, the light incident on the diffuser 1 is refracted by being transmitted through or reflected by the lens surface of one of the microlenses 21, so that the zero-order transmitted light component that is transmitted through the flat portion of the base material 10 without being refracted can be suppressed. Therefore, by imparting an irregular phase difference to the diffused light emitted from the multiple microlenses 21, it is possible to suppress the generation of unnecessary diffracted light, while also preventing the generation of light that is transmitted through the diffuser 1 without being refracted.

[0032] Furthermore, the aperture widths Dx, Dy and the radii of curvature Rx, Ry of each microlens 21 may vary irregularly so that the aperture widths Dx, Dy (lens diameters) and the radii of curvature Rx, Ry of the multiple microlenses 21 are different from one another. In this case, the aperture widths Dx, Dy of each microlens 21 may vary irregularly within a range of a predetermined variation rate δDx, δDy based on a predetermined reference aperture width Dxk, Dyk (Dx [μm] = Dxk [μm] ± δDx [%], Dy [μm] = Dyk [μm] ± δDy [%]). Similarly, the curvature radii Rx and Ry of each microlens 21 may vary irregularly within a range of a predetermined variation rate δRx and δRy with respect to a predetermined reference curvature radii Rxk and Ryk (Rx [μm] = Rxk [μm] ± δRx [%], Ry [μm] = Ryk [μm] ± δRy [%]). Here, the reference opening widths Dxk and Dyk are the opening widths of the reference surface shape of the microlens 21, and the reference curvature radii Rxk and Ryk are the curvature radii of the reference surface shape of the microlens 21. The reference surface shape is a lens surface shape that is a reference for designing the microlens 21. This allows the surface shapes of the multiple microlenses 21 to be randomly varied with respect to the reference surface shape, to be irregular shapes that are different from each other.

[0033] In this manner, in this embodiment, the arrangement of the multiple microlenses 21, the aperture widths Dx and Dy, the radii of curvature Rx and Ry, etc. may be varied irregularly. As a result, the surface shapes of the multiple microlenses 21 arranged and developed on the XY plane vary irregularly and become different shapes from one another.

[0034] This allows realization of a highly irregular three-dimensional surface structure of the microlens array 20, making it possible to control the overlapping state of the phases of the diffused light emitted from each microlens 21. This makes it possible to reduce unevenness in the intensity distribution of the diffused light due to interference and diffraction of the diffused light emitted from the multiple microlenses 21, and to distribute the diffused light uniformly. As a result, it is possible to control the cutoff property of the intensity distribution of the diffused light while having high transmittance luminance characteristics and satisfying the uniformity of the light distribution of the diffused light.

[0035] The diffusion plate 1 according to this embodiment having the above-mentioned characteristics will be described in detail below.

[0036] <2. Overall structure of the diffusion plate> Next, the overall configuration of a diffuser plate 1 according to one embodiment of the present invention and a layout pattern of microlenses will be described with reference to Fig. 1. Fig. 1 is a plan view and an enlarged view showing a schematic view of the diffuser plate 1 according to one embodiment of the present invention.

[0037] The diffuser 1 according to this embodiment is a microlens array type diffuser in which a microlens array 20 consisting of a plurality of microlenses 21 (single lenses) is arranged on a substrate 10. As shown in FIG. 1, the microlens array of the diffuser 1 is composed of a plurality of unit cells 3. The unit cells 3 are a basic arrangement pattern of the microlenses 21. On the surface of each unit cell 3, a plurality of microlenses 21 are arranged in a predetermined layout pattern (arrangement pattern).

[0038] 1 shows an example in which the shape of the unit cells 3 constituting the microlens array 20 of the diffuser 1 is rectangular, particularly square. However, the shape of the unit cells 3 is not limited to the example shown in Fig. 1, and may be any shape, such as an equilateral triangle or a regular hexagon, as long as it can fill the surface (XY plane) of the diffuser 1 without gaps.

[0039] When the surface of the microlens array 20 of the diffuser 1 is divided into a plurality of unit regions, the unit cells 3 correspond to each of the unit regions. In the example of FIG. 1, a plurality of square unit cells 3 are repeatedly arranged vertically and horizontally on the surface of the diffuser 1. The number of unit cells 3 constituting the diffuser 1 is not particularly limited, and the diffuser 1 may be composed of one unit cell 3, or may be composed of a plurality of unit cells 3. In the diffuser 1, unit cells 3 having different surface structures may be repeatedly arranged, or unit cells 3 having the same surface structure may be repeatedly arranged.

[0040] As shown in the enlarged view on the right side of FIG. 1, the layout pattern (arrangement pattern) of the microlenses 21 provided in the unit cell 3 is continuous between the adjacent unit cells 3 in the arrangement direction of the unit cells 3 (in other words, the array arrangement direction). The microlens array 20 is formed by arranging the unit cells 3 without gaps while maintaining the continuity of the surface shape of the microlenses 21 at the boundary between the adjacent unit cells 3. Here, the continuity of the surface shape of the microlenses 21 means that the microlenses 21 located on the outer edge of one unit cell 3 and the microlenses 21 located on the outer edge of the other unit cell 3 of two adjacent unit cells 3, 3 are continuously connected without any misalignment in planar shape or step in height direction.

[0041] As described above, in the diffuser 1 according to this embodiment, the unit cells 3 (basic structure) of the microlens array 20 are arranged without gaps while maintaining the continuity of the boundaries to form the microlens array 20. This makes it possible to prevent unintended problems such as diffraction, reflection, and scattering of light at the boundaries between adjacent unit cells 3, 3, and obtain the desired light distribution characteristics of the diffuser 1. Furthermore, by forming the microlens array 20 into a structure in which the unit cells 3 are repeated, the design efficiency and productivity of the microlens array 20 can be improved.

[0042] <3. Structure of the diffusion plate> Next, the configuration of the diffuser plate 1 according to this embodiment will be described in more detail with reference to Fig. 2 to Fig. 4. Fig. 2 is an enlarged plan view and an enlarged cross-sectional view that typically show the configuration of the diffuser plate 1 according to this embodiment. Fig. 3 is an enlarged cross-sectional view that typically shows the vicinity of the boundary of a microlens 21 according to this embodiment. Fig. 4 is a plan view that typically shows the planar shape (outer shape) of a microlens 21 when the microlens 21 is viewed in plan from a direction perpendicular to the surface of a substrate 10 according to this embodiment.

[0043] As shown in FIG. 2, the diffuser plate 1 according to this embodiment includes a base material 10 and a microlens array 20 formed on the surface of the base material 10.

[0044] First, the substrate 10 will be described. The substrate 10 is a substrate for supporting the microlens array 20. The substrate 10 may be in the form of a film or a plate. The substrate 10 may be in the form of a flat plate or a curved plate. The substrate 10 shown in FIG. 2 has, for example, a rectangular flat plate shape, but is not limited to this example. The shape and thickness of the substrate 10 may be any shape and thickness depending on the shape, configuration, etc. of the device in which the diffusion plate 1 is mounted.

[0045] The substrate 10 is a transparent substrate capable of transmitting light. The substrate 10 is made of a material that can be regarded as transparent in the wavelength band of light incident on the diffusion plate 1. For example, the substrate 10 may be made of a material having a light transmittance of 70% or more in the wavelength band of visible light.

[0046] The substrate 10 may be formed of a known resin such as polymethyl methacrylate (PMMA), polyethylene terephthalate (PET), polycarbonate (PC), cycloolefin copolymer (COC), cycloolefin polymer (COP), triacetylcellulose (TAC), etc. Alternatively, the substrate 10 may be formed of a known optical glass such as quartz glass, borosilicate glass, white plate glass, etc.

[0047] Next, the microlens array 20 will be described. The microlens array 20 is provided on at least one surface (principal surface) of the substrate 10. The microlens array 20 is a collection of a plurality of microlenses 21 (single lenses) arranged on the surface of the substrate 10. In this embodiment, as shown in FIG. 2, the microlens array 20 is formed on one surface (principal surface) of the substrate 10. However, this is not limited to such an example, and the microlens array 20 may be formed on both principal surfaces (front and back surfaces) of the substrate 10.

[0048] The surface of the substrate 10 on which the microlens array 20 is provided may be, for example, a flat surface. Hereinafter, the flat surface of the substrate 10 may also be referred to as an XY plane. The X and Y directions in the XY plane are parallel to the surface of the substrate 10. The X and Y directions are perpendicular to each other. The Z direction is perpendicular to the surface of the substrate 10 (i.e., the normal direction) and corresponds to the thickness direction of the diffuser plate 1. The Z direction is perpendicular to the XY plane, the X direction, and the Y direction.

[0049] The microlens 21 is a minute optical lens of, for example, the order of several tens of μm. The microlens 21 constitutes a single lens of the microlens array 20. The microlens 21 may have a concave structure (concave lens) formed so as to be recessed in the thickness direction of the diffusion plate 1, or may have a convex structure (convex lens) formed so as to protrude in the thickness direction of the diffusion plate 1. In this embodiment, an example in which the microlens 21 has a convex structure (convex lens) as shown in FIG. 2 will be described, but the present invention is not limited to such an example. Depending on the desired optical characteristics of the diffusion plate 1, the microlens 21 may have a concave structure (concave lens).

[0050] The surface shape of the microlens 21 has an aspheric shape. The surface shape of the microlens 21 according to this embodiment is an aspheric shape that is distorted asymmetrically in either one or both of the X direction and the Y direction with respect to a reference surface shape having an axis of symmetry. The surface shape of the microlens 21 according to this embodiment will be described later.

[0051] As shown in FIG. 2, the microlenses 21 are preferably arranged densely so as to be adjacent to each other without gaps. In other words, the microlenses 21 are preferably arranged continuously so as to overlap each other so that there are no gaps (flat parts) at the boundary parts between the adjacent microlenses 21, 21. In this way, the microlenses 21 are preferably arranged without gaps on the surface (XY plane) of the substrate 10. In other words, the microlenses 21 are preferably arranged so that the filling rate of the microlenses 21 on the surface of the substrate 10 is 100%. This makes it possible to suppress the component of the incident light that is not scattered on the surface of the diffusion plate 1 and is transmitted as it is (hereinafter also referred to as the "zeroth order transmitted light component"). As a result, the microlens array 20 in which the microlenses 21 are arranged adjacent to each other without gaps can further improve the diffusion performance.

[0052] In order to suppress the zero-order transmitted light component, the filling rate of the microlenses 21 on the substrate 10 is preferably 90% or more, and more preferably 100%. Here, the filling rate refers to the ratio of the area of ​​the portion on the surface (XY plane) of the substrate 10 that is occupied by the multiple microlenses 21. If the filling rate is 100%, the surface of the microlens array 20 is formed of curved surface components and contains almost no flat surface components.

[0053] However, in the actual manufacture of the microlens array 20, the curved surfaces of the multiple microlenses 21 are continuously connected, so that the vicinity of the inflection point at the boundary between the adjacent microlenses 21 may become substantially flat. In such a case, the width of the substantially flat region near the inflection point at the boundary between the microlenses 21 (the width of the boundary line 24 between the microlenses 21 shown in FIG. 3 and FIG. 4) is preferably 1 μm or less. This allows the zero-order transmitted light component to be sufficiently suppressed.

[0054] In the microlens array 20 according to this embodiment, the microlenses 21 are irregularly (randomly) arranged on the XY plane. Here, "irregular" means that there is no substantial regularity in the arrangement of the microlenses 21 in any region of the microlens array 20. However, even if there is some regularity in the arrangement of the microlenses 21 in a small region, the arrangement of the microlenses without regularity in the entire region is considered to be included in "irregular". Note that a method of irregularly arranging the microlenses 21 in the microlens array 20 according to this embodiment will be described later.

[0055] Furthermore, lens parameters such as the aperture widths Dx, Dy, and the radii of curvature Rx, Ry that determine the surface shape of each microlens 21 may vary irregularly for each microlens 21. In other words, the aperture widths Dx, Dy and the radii of curvature Rx, Ry of each microlens 21 may be irregularly varying values ​​rather than predetermined fixed values. The aperture width Dx is the width of the aperture of the microlens 21 in the X direction, and the aperture width Dy is the width of the aperture of the microlens 21 in the Y direction (see, for example, FIG. 5), and corresponds to the lens diameter of the microlens 21. The radius of curvature Rx is the radius of curvature in the X direction of the curved shape of the microlens 21. The radius of curvature Ry is the radius of curvature in the Y direction of the curved shape of the microlens 21.

[0056] For example, the aperture widths Dx, Dy of each microlens 21 may vary irregularly within a range of predetermined variation rates δDx, δDy with respect to a predetermined reference aperture width Dxk, Dyk (Dx=Dxk±δDx%, Dy=Dyk±δDy%). Similarly, the curvature radii Rx, Ry of each microlens may vary irregularly within a range of predetermined variation rates δRx, δRy with respect to a predetermined reference curvature radii Rxk, Ryk (Rx=Rxk±δRx%, Ry=Ryk±δRy%). This allows the aperture widths Dx, Dy and the curvature radii Rx, Ry to vary appropriately with respect to the predetermined reference aperture widths Dxk, Dyk and the reference curvature radii Rxk, Ryk. Therefore, while maintaining the desired optical characteristics (diffusion performance) of the diffuser 1, unevenness in the intensity distribution of the diffused light (uneven brightness, uneven color, etc.) caused by interference and diffraction of the diffused light from each microlens 21 can be reduced.

[0057] Thus, in the microlens array 20 according to this embodiment, the radii of curvature Rx, Ry and the aperture widths Dx, Dy of each microlens 21 vary irregularly within a predetermined range around the reference radii of curvature Rxk, Ryk and the reference aperture widths Dxk, Dyk. The phase distribution of the optical aperture of each microlens 21 differs depending on the orientation. Furthermore, on the surface of the substrate 10 (on the XY plane), a plurality of microlenses 21 are densely and continuously arranged so as to overlap each other, and each microlens 21 is arranged at an irregular position on the XY plane.

[0058] As a result, the surface shape (three-dimensional curved shape) and planar shape (shape projected onto the XY plane of the substrate 10) of each microlens 21 vary irregularly with respect to a predetermined reference shape. As a result, the surface shapes and planar shapes of each microlens 21 are different from one another. Therefore, the multiple microlenses 21 have various planar shapes, as shown typically in FIG. 2, and many of them are not symmetrical.

[0059] As a result, for example, as shown in FIG. 3, the radius of curvature of the microlens 21A is Rx AOn the other hand, the radius of curvature of the microlens 21B adjacent to the microlens 21A is Rx B (≠Rx A The radius of curvature Rx of the adjacent microlenses 21A and 21B is A , Rx B are different from each other, the boundary line 24 between the microlenses 21A and 21B is not formed only by straight lines, but is formed to include at least a part of a curve.

[0060] Specifically, as shown in Fig. 4, consider a case where the microlens 21 is viewed in plan from a normal direction (Z direction) perpendicular to the surface of the base material 10. In this case, the outline of the planar shape of the microlens 21 (boundary line 24 between the microlens 21 and other adjacent microlenses 21) is composed of multiple curved lines with different curvatures. In this way, when the boundary line 24 between adjacent microlenses 21, 21 includes multiple curved lines with different curvatures, the regularity of the boundary between the microlenses 21, 21 is further broken, and the diffraction component of the diffused light can be further reduced.

[0061] <4. Surface shape of microlenses and their function of deflecting diffused light> <4.1. Surface shape of microlenses> Next, the surface shape of the microlens 21 according to this embodiment will be described. The surface shape of the microlens 21 according to this embodiment is an aspheric shape that is distorted asymmetrically in either one or both of the X direction and the Y direction with respect to a reference surface shape having an axis of symmetry. Here, first, the reference surface shape will be described, and then the surface shape of the microlens 21 according to this embodiment will be described.

[0062] The reference surface shape according to this embodiment is an anamorphic shape that is rotationally asymmetric with respect to the normal direction (Z direction) perpendicular to the surface of the base material 10 and is an aspheric shape having anisotropy.

[0063] A reference surface shape having an anamorphic shape will be described with reference to Fig. 5 and Fig. 6. Fig. 5 is an explanatory diagram showing a planar shape of the reference surface shape having an anamorphic shape. Fig. 6 is a perspective view showing a three-dimensional shape of the reference surface shape having an anamorphic shape.

[0064] The reference surface shape shown in Fig. 5 and Fig. 6 is an aspheric shape including a curved surface of an anamorphic shape. As shown in Fig. 5, the planar shape of the reference surface shape is an elliptical shape having anisotropy. The major axis of the elliptical shape in the Y-axis direction is Dy, and the minor axis of the elliptical shape in the X-axis direction is Dx. These Dx and Dy correspond to the aperture diameters of the microlens 21 in the X-axis direction and the Y-axis direction. As shown in Fig. 6, the reference surface shape is composed of an aspheric curved surface having predetermined radii of curvature Rx and Ry in the major axis direction and the minor axis direction of the elliptical shape, respectively. The reference surface shape is an aspheric shape having anisotropy in the Y-axis direction.

[0065] Here, a method for setting a reference surface shape having an anamorphic shape will be described with reference to Fig. 6 and the following formula (1). The curved surface (aspheric surface) of the anamorphic shape shown in Fig. 6 is expressed by the following formula (1). The following formula (1) is an example of a formula expressing a curved surface (aspheric surface) of an anamorphic shape.

[0066]

number

[0067] In the formula (1), the parameters are as follows: Cx=1 / Rx Cy=1 / Ry Rx: Radius of curvature in the X direction Ry: Radius of curvature in the Y direction Kx: Conic constant in the X direction Ky: Conic constant in the Y direction

[0068] As shown in Fig. 6, a curved surface is cut out from the curved surface of the anamorphic shape defined by the above formula (1) so that the minor axis in the X direction of the ellipse shape on the XY plane is Dx and the major axis in the Y direction is Dy. The shape of the curved surface of this cut out part is set as the reference surface shape (anamorphic shape) of the microlens 21. Here, the major axis Dy, minor axis Dx, radius of curvature Ry in the Y direction (major axis direction), and radius of curvature Rx in the X direction (minor axis direction) of the ellipse shape are irregularly varied within a range of a predetermined variation rate δ for each microlens 21 to cause variation. This makes it possible to set the reference surface shapes of the multiple microlenses 21 having mutually different anamorphic shapes.

[0069] Next, a description will be given of the surface shape of the microlens 21 according to this embodiment. The surface shape of the microlens 21 according to this embodiment is an aspheric shape expressed by an aspheric equation having at least a third-order term, as shown in the following mathematical expression (2).

[0070]

number

[0071] In the formula (2), the parameters are as follows: Cx=1 / Rx Cy=1 / Ry Rx: Radius of curvature in the X direction Ry: Radius of curvature in the Y direction Kx: Conic constant in the X direction Ky: Conic constant in the Y direction A 3x : Aspheric coefficient of the third order term in the X direction A 3y : Aspheric coefficient of the third order term in the Y direction

[0072] The third-order term is a term of the variable "x" or the variable "y" included in the aspheric surface formula, in which the degree of the variable "x" or the variable "y" is "3". In other words, the third-order term is "A 3x x 3 " and "A 3y y 3The aspheric coefficient is the coefficient of the third order term "A 3x " and "A 3y "

[0073] In addition, the fact that the aspheric equation contains a third-order term means that the aspheric coefficient "A 3x " or "A 3y " means that one or both of the aspheric coefficients "A" in the X direction are not zero. 3x Even if " is zero (A 3x =0), Y-direction aspheric coefficient "A 3x If " is not zero, then (A 3y ≠0), the aspheric equation is a cubic term (i.e., the cubic term in the Y direction "A 3y y 3 Similarly, the aspheric coefficient "A 3y Even if " is zero (A 3y =0), and the aspheric coefficient in the X direction "A 3x If " is not zero, then (A 3x ≠0), the aspheric equation is a cubic term (i.e., the cubic term in the X direction "A 3x x 3 On the other hand, the third-order aspheric coefficient "A 3x " and "A 3y " are both zero (A 3x =0 and A 3y =0), the aspheric equation does not contain any third-order terms.

[0074] For example, in formula (2), the third-order term in the X-direction on the XY plane, "A 3x x 3 " or the cubic term in the Y direction "A 3y y 3 In the case where the microlens 21 includes either one of the three-dimensional term "A" and the three-dimensional term "B" in the X direction, the surface shape of the microlens 21 is distorted asymmetrically in either the X direction or the Y direction with respect to a reference surface shape having a symmetry axis, and has a symmetric aspheric shape in the other direction. 3x x 3 " and the cubic term "A 3y y 3In the case where the third-order term "A" in the Y direction is not included, the surface shape of the microlens 21 is distorted asymmetrically in the X direction with respect to the reference surface shape, and has an aspheric shape that is symmetrical in the Y direction. 3y y 3 " and the third order term in the X direction, "A 3x x 3 " is not included, the surface shape of the microlens 21 is distorted asymmetrically in the Y direction with respect to the reference surface shape, and has an aspheric shape that is symmetrical in the X direction.

[0075] Various specific examples of lens surface shapes expressed by the aspheric formula (2) and the following formula (3) will be described below with reference to Figs. 7 to 9. Figs. 7 to 8 are graphs showing specific examples of lens surface shapes expressed by the aspheric formula (2). The graphs in Figs. 7 to 8 show the cross-sectional shapes in the X and Y directions of the lens surface expressed by the aspheric formula (2). Fig. 9 is a graph showing a specific example of lens surface shapes expressed by the aspheric formula (3). The graph in Fig. 9 shows the cross-sectional shapes in the X and Y directions of the lens surface expressed by the aspheric formula (3). In Figs. 7 to 9, the distance [μm] in the Z direction on the vertical axis of the graphs is the relative height [μm] in the Z direction at each position on the surface of the microlens 21 when the height of the apex of the microlens 21 is taken as the reference (height zero). Additionally, the distance [μm] from the center on the horizontal axis of the graph represents the distance [μm] in the X or Y direction of each position on the surface of the microlens 21 when the lens center point 30 (see FIG. 11) is used as the reference (the origin on the XY plane).

[0076] Figure 7 shows the third order term "A 3y y 3 " (A 3y ≠0), the third order term in the X direction, "A 3x x 3 If " is not included (A 3x 7 shows the cross-sectional shapes of the lens surface in the X and Y directions at A = 0. 3x =0, A 3y =0.001, Rx=23mm, Ry=23mm, Kx=0.5, and Ky=0.5.

[0077] As shown in FIG. 7, in formula (2), A 3y ≠ 0, and the cubic term in the Y direction, "A 3y y 3 By including ", the lens surface shape can be made aspheric, distorted asymmetrically in the Y direction with respect to the reference surface shape. 3x = 0, and the cubic term in the X direction, "A 3x x 3 " can be made to have an aspheric shape that is symmetric in the X direction with respect to the reference surface shape. This makes it possible to bend the outgoing light in the Y direction with respect to the incident light, and deflect the outgoing light in a desired direction.

[0078] Similarly, in formula (2), A 3x ≠0, and the cubic term in the X direction, "A 3x x 3 By including ", it is possible to obtain an aspheric shape that is distorted asymmetrically in the X direction with respect to the reference surface shape. 3y = 0, and the cubic term in the Y direction, "A 3y y 3 " can be made to have an aspheric shape that is symmetric in the Y direction with respect to the reference surface shape. This makes it possible to bend the outgoing light in the X direction with respect to the incident light, and deflect the outgoing light in a desired direction.

[0079] Furthermore, in formula (2), A 3x ≠0, A 3y ≠0, and the cubic term in the X direction, "A 3x x 3 " and the cubic term in the Y direction "A 3y y 3 ", it is possible to create an aspheric shape that is distorted asymmetrically in both the X and Y directions with respect to the reference surface shape. This makes it possible to deflect the outgoing light with respect to the incident light by bending it in two-dimensional directions (X and Y directions) on the surface of the diffuser plate 1, and to deflect the outgoing light in a desired direction.

[0080] By the way, the aspheric coefficient of the third order term, "A 3x ","A 3y If " is too large, an inflection point where the curvature direction changes may be formed in the cross-sectional shape of the surface of the microlens 21 in the X or Y direction. If an inflection point exists in the cross-sectional shape of the surface of the microlens 21, there is a problem that the diffusion characteristics are not smooth. For this reason, it is preferable that the cross-sectional shape of the surface of the microlens 21 does not include an inflection point.

[0081] Therefore, when an inflection point is included in the aspheric shape expressed by the aspheric formula shown in formula (2), it is preferable to use formula (3) which has a fourth-order term in addition to the third-order term, to eliminate the inflection point caused by the third-order term.

[0082] That is, the surface shape of the microlens 21 according to this embodiment may be an aspheric shape expressed by an aspheric equation having a third-order term and a fourth-order term, as shown in the following mathematical expression (3).

[0083]

number

[0084] In the formula (3), the parameters are as follows: Cx=1 / Rx Cy=1 / Ry Rx: Radius of curvature in the X direction Ry: Radius of curvature in the Y direction Kx: Conic constant in the X direction Ky: Conic constant in the Y direction A 3x : Aspheric coefficient of the third order term in the X direction A 4x : Aspheric coefficient of the fourth order term in the X direction A 3y : Aspheric coefficient of the third order term in the Y direction A 4y : Aspheric coefficient of the fourth order term in the Y direction

[0085] The third-order term is a term of the variable "x" or the variable "y" included in the aspheric formula, in which the degree of the variable "x" or the variable "y" is "3". In other words, the third-order term is "A 3x x 3 " and "A 3y y 3 The aspheric coefficient is the coefficient of the third order term "A 3x " and "A 3y "

[0086] In addition, the fact that the aspheric equation contains a third-order term means that the aspheric coefficient "A 3x " or "A 3y " means that one or both of the aspheric coefficients "A" in the X direction are not zero. 3x Even if " is zero (A 3x =0), Y-direction aspheric coefficient "A 3x If " is not zero, then (A 3y ≠0), the aspheric equation is a cubic term (i.e., the cubic term in the Y direction "A 3y y 3 Similarly, the aspheric coefficient "A 3y Even if " is zero (A 3y =0), and the aspheric coefficient in the X direction "A 3x If " is not zero, then (A 3x ≠0), the aspheric formula is a cubic term (i.e., the cubic term in the X direction "A 3x x 3 On the other hand, the third-order aspheric coefficient "A 3x " and "A 3y " are both zero (A 3x =0 and A 3y =0), the aspheric equation does not contain any third-order terms.

[0087] The fourth-order term is a term of the variable "x" or the variable "y" included in the aspheric formula, in which the degree of the variable "x" or the variable "y" is "4". In other words, the fourth-order term is "A 4x x 4 " and "A 4y y 4The aspheric coefficient is the fourth-order coefficient "A 4x " and "A 4y "

[0088] In addition, the inclusion of a fourth-order term in the aspheric equation means that the coefficient of the fourth-order term, the aspheric coefficient "A 4x " or "A 4y " means that one or both of the aspheric coefficients "A" in the X direction are not zero. 4x Even if " is zero (A 4x =0), Y-direction aspheric coefficient "A 4x If " is not zero, then (A 4y ≠0), the aspheric equation has a fourth-order term (i.e., the fourth-order term in the Y direction, "A 4y y 4 Similarly, the aspheric coefficient "A 4y Even if " is zero (A 4y =0), and the aspheric coefficient in the X direction "A 4x If " is not zero, then (A 4x ≠0), the aspheric formula is a fourth-order term (i.e., the fourth-order term in the X direction, "A 4x x 4 On the other hand, the fourth-order aspheric coefficient "A 4x " and "A 4y " are both zero (A 4x =0 and A 4y =0), the aspheric equation does not contain any fourth-order terms.

[0089] Figure 8 shows the third order term "A 3y y 3 " (A 3y ≠0), the third order term in the X direction, "A 3x x 3 If " is not included (A 3x The formula (2) corresponding to FIG. 8 shows the cross-sectional shapes of the lens surface in the X and Y directions at A = 0. 3x =0, A 3y =0.002, Rx=23mm, Ry=23mm, Kx=0.5, and Ky=0.5.

[0090] As shown in Figure 8, the aspheric coefficient of the third order term in the Y direction, “A 3y If " is too large, an inflection point IP where the sign of curvature switches will be formed in the cross-sectional shape of the lens surface in the Y direction. The inflection point IP is the point where the cross-sectional shape of the lens surface changes from concave to convex, or from convex to concave. In FIG. 8, to the right of the inflection point IP, the cross-sectional shape of the lens surface in the Y direction is convex downward, and to the left of the inflection point IP, the cross-sectional shape of the lens surface in the Y direction is convex upward.

[0091] In this way, when the cross-sectional shape of the lens surface includes an inflection point IP, the emitted light is bent in an unintended direction. This hinders the bending of the emitted light. For this reason, it is preferable that the cross-sectional shape of the lens surface does not include an inflection point IP.

[0092] Therefore, in the aspheric shape expressed by formula (2) including a cubic term, when either or both of the cross-sectional shapes in the X direction and the Y direction include an inflection point IP, it is preferable to make the surface shape of the microlens 21 an aspheric shape expressed by formula (3) to which a quartic term in the direction including the inflection point IP is added. That is, in formula (3), the cubic term is a term for making the surface shape of the microlens asymmetric, and the quartic term is a term for correcting the inflection point IP of the cross-sectional shape of the surface of the microlens. By making it an aspheric shape expressed by formula (3), it is possible to eliminate the inflection point IP from the cross-sectional shape of the surface of the microlens 21.

[0093] Figure 9 shows the third order term "A 3y y 3 " (A 3y ≠0), the fourth order term in the Y direction, "A 4y y 4 " (A 4y ≠0), the third order term in the X direction, "A 3x x 3 " (A 3x =0), the fourth order term in the X direction, "A 4x x 4 " does not include (A 4x9 shows the cross-sectional shapes of the lens surface in the X and Y directions when A = 0. 3x =0, A 4x =0, A 3y =0.002, A 4y =0.0001, Rx=23mm, Ry=23mm, Kx=0.5, and Ky=0.5.

[0094] As shown in FIG. 9, in formula (3), the third-order term in the Y direction, “A 3y y 3 " In addition to the fourth order term in the Y direction, "A 4y y 4 8, it is possible to eliminate the inflection point IP in the cross-sectional shape of the lens surface in the Y direction.

[0095] Therefore, by making the surface shape of the microlens 21 aspheric, which is expressed by an aspheric equation having a cubic term and a quartic term as shown in formula (3), it is possible to eliminate the inflection point IP in the cross-sectional shape of the surface of the microlens 21. This makes it possible to prevent emitted light from bending in an unintended direction.

[0096] Furthermore, when manufacturing the microlens 21, a curved surface may be cut out within the effective range ER shown in Fig. 9. The effective range ER is the pitch of the lenses, or the range that is the boundary when the lenses are overlapped.

[0097] <4.2. Deflection of emitted light> Here, the deflection function of the emitted light (diffused light) by the microlens 21 according to this embodiment will be described in more detail with reference to Figs. 10 and 11. Fig. 10 is a schematic diagram showing the diffusion function of the transmitted light by the microlens 21 having a reference surface shape. Fig. 11 is a schematic diagram showing the diffusion function and deflection function of the transmitted light by the microlens 21 according to this embodiment. The upper diagram in Fig. 10 (Fig. 10A) shows the diffusion function of the transmitted light by the microlens 21 in the XZ cross section. The lower diagram in Fig. 10 (Fig. 10B) shows the diffusion function of the transmitted light by the microlens 21 in the YZ cross section. The upper diagram in Fig. 11 (Fig. 11A) shows the diffusion function and deflection function of the transmitted light by the microlens 21 in the XZ cross section. The lower diagram in Fig. 11 (Fig. 11B) shows the diffusion function and deflection function of the transmitted light by the microlens 21 in the YZ cross section.

[0098] As shown in FIGS. 10 and 11, a case will be considered in which incident light 40 on the diffuser 1 is obliquely incident collimated light from a direction inclined with respect to the normal direction (Z direction) of the surface of the diffuser 1.

[0099] In the case of oblique incidence, for example, if the incident angle θinx of incident light 40 in the XZ cross section is αx [°] (αx ≠ 0°), the angle between the direction 42 of the chief ray 41 of incident light 40 and the Z direction is also αx. When collimated light is obliquely incident on the diffuser 1, the light passing through the diffuser 1 is diffused by the microlenses 21, and the outgoing light 50 becomes diffused light.

[0100] Here, as shown in FIG. 10A, when the surface shape of the microlens 21 is the reference surface shape, the surface shape of the microlens 21 is symmetrical with respect to the optical axis 25 passing through the vertex 28 and the center point 30 of the microlens 21 in the XZ cross section. Therefore, the light passing through the microlens 21 having the reference surface shape is diffused symmetrically with respect to the direction 42 of the principal ray 41 of the incident light 40. In detail, due to natural bending (Snell's law) caused by the difference in refractive index between the substrate 10 and the outside air, the principal ray 51 of the emitted light 50 is bent by a natural bending angle S with respect to the direction 42 of the principal ray 41 of the incident light 40. Therefore, the emitted light 50 becomes diffused light that is diffused symmetrically with respect to the direction 42 of the principal ray 41 of the incident light 40, the bent principal ray 51 being the natural bending angle S. As a result, the exit angle θoutx of the chief ray 51 of the exit light 50 in the XZ cross section is αx+S, and the angle between the direction of the chief ray 51 of the exit light 50 and the optical axis 25 is also αx+S.

[0101] Similarly, for example, if the incident angle θiny of incident light 40 on the YZ cross section is αy [°] (αy ≠ 0°), the angle between the direction 42 of the chief ray 41 of incident light 40 and the Z direction is also αy. When collimated light is obliquely incident on the diffuser 1, the light passing through the diffuser 1 is diffused by the microlenses 21, and the outgoing light 50 becomes diffused light.

[0102] 10B, when the surface shape of the microlens 21 is the reference surface shape, the surface shape of the microlens 21 in the YZ cross section is symmetrical with respect to the optical axis 25 passing through the vertex 28 and the center point 30 of the microlens 21. Therefore, the light passing through the microlens 21 having the reference surface shape is diffused symmetrically with respect to the direction 42 of the chief ray 41 of the incident light 40. In detail, due to natural bending, the chief ray 51 of the emitted light 50 is bent by the natural bending angle S with respect to the direction 42 of the chief ray 41 of the incident light 40. Therefore, the emitted light 50 becomes diffused light that is diffused symmetrically with respect to the direction 42 of the chief ray 41 of the incident light 40, with respect to the natural bending angle S, with respect to the direction 42 of the chief ray 41 of the incident light 40. As a result, the exit angle θouty of the chief ray 51 of the exit light 50 in the YZ cross section is αy+S, and the angle between the direction of the chief ray 51 of the exit light 50 and the optical axis 25 is also αy+S.

[0103] On the other hand, as shown in FIG. 11, when the surface shape of the microlens 21 is an aspheric shape that is distorted asymmetrically with respect to the reference surface shape, the chief ray 51 of the outgoing light 50 emerging from the diffuser 1 is deflected with respect to the chief ray 41 of the incident light 40.

[0104] 11A, when the surface shape of the microlens 21 is an aspheric shape distorted asymmetrically in the X direction with respect to the reference surface shape, the light passing through the diffuser 1 is diffused approximately symmetrically about a deflection direction different from the direction 42 of the chief ray 41 of the incident light 40. This deflection direction is the direction in which the chief ray 51 of the emitted light 50 is bent with respect to the chief ray 41 of the incident light 40, and is represented by a deflection angle βx. As shown in FIG. 11A, when the incident light 40 is obliquely incident on the diffuser 1 (θinx=αx (αx≠0)), the deflection direction of the chief ray 51 of the emitted light 50 is, for example, a direction in which the angle with the Z direction is larger than the direction 42 of the chief ray 41 of the incident light 40. Depending on the surface shape of the microlens 21, the deflection direction of the chief ray 51 of the outgoing light 50 may be a direction in which the angle it forms with the Z direction is smaller than the direction 42 of the chief ray 41 of the incident light 40. The deflection angle βx, which represents this deflection direction, is determined by the surface shape of the microlens 21. The deflection angle βx is determined by the radius of curvature Rx, the aspheric coefficient A 3x, aspheric coefficient A 4x , the conic constant Kx, and the pitch of the lens.

[0105] In this way, when the surface shape of the microlens 21 is an aspheric shape distorted asymmetrically in the X direction with respect to the reference surface shape, the light flux of the outgoing light 50 is deflected in a deflection direction (a direction represented by a deflection angle βx) with respect to the light flux of the incident light 40, and becomes a diffuse light that is diffused approximately symmetrically around the deflection direction. As a result, the emission angle θoutx of the chief ray 51 of the outgoing light 50 becomes αx+S+βx, and the direction of the chief ray 51 of the outgoing light 50 becomes a direction inclined by the deflection angle βx+natural bending angle S with respect to the direction 42 of the chief ray 41 of the incident light 40.

[0106] Similarly, as shown in FIG. 11B, when the surface shape of the microlens 21 is an aspheric shape distorted asymmetrically in the Y direction with respect to the reference surface shape, the light passing through the diffuser 1 is diffused almost symmetrically around a deflection direction different from the direction 42 of the chief ray 41 of the incident light 40. This deflection direction is the direction in which the chief ray 51 of the emitted light 50 is bent with respect to the chief ray 41 of the incident light 40, and is represented by a deflection angle βy. As shown in FIG. 11B, when the incident light 40 is obliquely incident on the diffuser 1 (θiny=αy (αy≠0)), the deflection direction of the chief ray 51 of the emitted light 50 is, for example, a direction in which the angle with the Z direction is larger than the direction 42 of the chief ray 41 of the incident light 40. Note that, depending on the surface shape of the microlens 21, the deflection direction of the chief ray 51 of the emitted light 50 may be a direction in which the angle with the Z direction is smaller than the direction 42 of the chief ray 41 of the incident light 40. The deflection angle βy, which represents the deflection direction, is determined by the surface shape of the microlens 21. The deflection angle βy is determined by the radius of curvature Ry, the aspheric coefficient A 3y , aspheric coefficient A 4y , the conic constant Ky, and the pitch of the lens.

[0107] In this way, when the surface shape of the microlens 21 is an aspheric shape distorted asymmetrically in the Y direction with respect to the reference surface shape, the light flux of the outgoing light 50 is deflected in a deflection direction (a direction represented by a deflection angle βy) with respect to the light flux of the incident light 40, and becomes a diffuse light that is diffused approximately symmetrically around the deflection direction. As a result, the exit angle θouty of the chief ray 51 of the outgoing light 50 becomes αy+S+βy, and the direction of the chief ray 51 of the outgoing light 50 becomes a direction inclined by the deflection angle βy+natural bending angle S with respect to the direction 42 of the chief ray 41 of the incident light 40.

[0108] As described above, according to this embodiment, the surface shape of each microlens 21 constituting the microlens array 20 is an aspheric shape expressed by an aspheric equation having at least a third-order term. That is, the surface shape of each microlens 21 constituting the microlens array 20 according to this embodiment is an aspheric shape distorted in either one or both of the X direction and the Y direction with respect to the reference surface shape. This makes it possible to bend the direction of the outgoing light 50 with respect to the direction of the incident light 40, and to deflect the outgoing light 50 in a desired direction. Therefore, according to this embodiment, the outgoing light 50 can be deflected in a direction different from the refraction direction due to the normal refraction action of the diffusion plate 1.

[0109] In particular, according to this embodiment, whether the incidence is normal or oblique, the bending angle of the outgoing light with respect to the incident light can be increased, thereby improving the deflection performance.

[0110] Moreover, by making the surface shape of each microlens 21 constituting the microlens array 20 according to this embodiment an aspheric shape distorted in the X direction with respect to a reference surface shape, it is possible to bend the direction of the outgoing light 50 in the XZ cross section with respect to the direction of the incident light 40. Moreover, by making the surface shape of each microlens 21 constituting the microlens array 20 according to this embodiment an aspheric shape distorted in the Y direction with respect to a reference surface shape, it is possible to bend the direction of the outgoing light 50 in the YZ cross section with respect to the direction of the incident light 40.

[0111] Furthermore, by making the surface shape of each microlens 21 constituting the microlens array 20 according to this embodiment aspheric in shape distorted in the X and Y directions with respect to a reference surface shape, it is possible to bend the direction of the outgoing light 50 with respect to the direction of the incident light 40 in both the XZ cross section and the YZ cross section. In other words, it is possible to bend and deflect the outgoing light 50 with respect to the incident light 40 in two-dimensional directions (X and Y directions) on the surface of the diffuser 1.

[0112] Furthermore, the surface shape of the microlens 21 according to this embodiment is an aspheric shape distorted in either or both of the X and Y directions with respect to a reference surface shape. This allows the surface shape of the microlens 21 to be significantly curved, and the deflection angle can be made larger compared to a technique in which the optical axis of the microlens is tilted with respect to the Z direction while keeping the surface shape of the microlens symmetrical.

[0113] Incidentally, the incident light incident on the diffusion plate 1 according to this embodiment may be, for example, collimated light collimated by an optical system, diffused light incident from one point light source, or diffused or collimated light incident from a plurality of light sources arranged in the same direction with respect to the diffusion plate 1. The microlens array 20 according to this embodiment is capable of suitably deflecting such incident light.

[0114] <4.3.3 Preferred range of aspheric coefficient A3> Fig. 12 is a graph for explaining the change in the degree of bending due to the change in the aspheric coefficient A3 of the third-order term. In Fig. 12, the vertical axis indicates the bending angle [°], and the horizontal axis indicates the aspheric coefficient of the third-order term. The upper graph in Fig. 12 shows the change in the degree of bending due to the change in the aspheric coefficient A3 of the third-order term in the X direction. 3x The figure below shows the change in the aspheric coefficient A of the third order term in the Y direction. 3y Shows the change in.

[0115] As shown in FIG. 12, the aspheric coefficient A3 of the third order term (A 3x ,A 3y) is preferably -0.00075 or more and +0.00075 or less. If the aspherical coefficient A3 of the cubic term is less than -0.00075, a problem occurs in that an inflection point may occur. Also, if the aspherical coefficient A3 of the cubic term is more than +0.00075, a problem occurs in that an inflection point may occur.

[0116] <4.4.Preferable range of the fourth-order aspheric coefficient A4 / third-order aspheric coefficient A3> It is preferable that the aspheric equation having the above third-order and fourth-order terms satisfies the following equation (10). A4 / A3>0 …(10)

[0117] In addition, in an aspheric equation having a third-order term and a fourth-order term, it is more preferable to satisfy the following equation (11), and it is even more preferable to satisfy the following equation (12). A4 / A3>0.03 (11) A4 / A3<0.5 (12)

[0118] Specifically, it is preferable that the following expressions (21) and (22) be satisfied in the formula (3). A 4x / A 3x >0 (21) A 4y / A 3y >0 (22)

[0119] In addition, in formula (3), the third-order term in the Y direction, "A 3y y 3 If " is not included (A 3y =0), it is preferable to satisfy formula (21). In addition, in formula (3), the third-order term in the X direction, "A 3x x 3 If " is not included (A 3x =0), it is desirable to satisfy formula (22). Also, in formula (3), the third-order term in the X direction, "A 3x x 3 " (A 3x ≠0), and the cubic term in the Y direction, "A 3y y 3 " (A 3y≠0), it is preferable to satisfy equations (21) and (22).

[0120] Moreover, in formula (3), it is more preferable to satisfy the following formulas (23) and (24), and it is even more preferable to satisfy the following formulas (25) and (26). A 4x / A 3x >0.03 (23) A 4y / A 3y >0.03 (24) A 4x / A 3x <0.5 ···(25) A 4y / A 3y <0.5 ···(26)

[0121] In addition, in formula (3), the third-order term in the Y direction, "A 3y y 3 If " is not included (A 3y =0), it is preferable to satisfy formula (23). In addition, in formula (3), the third-order term in the X direction, "A 3x x 3 If " is not included (A 3x =0), it is desirable to satisfy formula (24). In addition, in formula (3), the third-order term in the X direction, "A 3x x 3 " (A 3x ≠0), and the cubic term in the Y direction, "A 3y y 3 " (A 3y ≠0), it is preferable to satisfy equations (23) and (24).

[0122] In addition, in formula (3), the third-order term in the Y direction, "A 3y y 3 If " is not included (A 3y =0), it is desirable to satisfy formula (25). Also, in formula (3), the third-order term in the X direction, "A 3x x 3 If " is not included (A 3x =0), it is desirable to satisfy formula (26). In addition, in formula (3), the third-order term in the X direction, "A 3x x 3" (A 3x ≠0), and the cubic term in the Y direction, "A 3y y 3 " (A 3y ≠0), it is preferable to satisfy equations (25) and (26).

[0123] By satisfying formula (10), it is possible to eliminate the inflection point IP in the cross-sectional shape of the surface of the microlens 21. Similarly, by satisfying either one or both of formulas (21) and (22), it is possible to eliminate the inflection point IP in the cross-sectional shape of the surface of the microlens 21.

[0124] Furthermore, by satisfying formula (11), it is possible to eliminate inflection points in the cross-sectional shape of the surface of the microlens 21. By satisfying formulas (23) and (24), it is possible to eliminate inflection points in the cross-sectional shape of the surface of the microlens 21.

[0125] Furthermore, by satisfying formula (12), it is possible to prevent the height of the apex of the microlens 21 from becoming too large. By satisfying formulas (25) and (26), it is possible to prevent the height of the apex of the microlens 21 from becoming too large.

[0126] <5. Microlens design method> Next, a method for designing a microlens according to this embodiment will be described with reference to Fig. 13 to Fig. 15. Fig. 13 is a flowchart showing the method for designing a microlens according to this embodiment.

[0127] (S10) Setting the lens center coordinates 13, first, the lens center coordinate pn of each microlens 21 is set on the surface (XY plane) of the microlens array 20. The lens center coordinate pn is the coordinate on the XY plane of the center point 30 (see FIG. 11) of each microlens 21. When setting the lens center coordinate pn, it is preferable that the lens center coordinates pn are set at irregular positions so that the intervals between the lens center coordinates pn on the XY plane are distributed within a preset range.

[0128] Specifically, as shown in Fig. 14, a plurality of lens center coordinates pn (xpn, ypn) are set irregularly on the XY plane of a unit cell 3 of a microlens array 20 whose size is set in advance. Note that n is the number of installed microlenses 21 (n = 1, 2, 3, ...). The plurality of lens center coordinates pn (xpn, ypn) are irregularly arranged on the XY plane so that the intervals between the plurality of lens center coordinates pn are within a preset range.

[0129] 15, an adjustment process may be performed on the overlap amount Ov between adjacent microlenses 21, 21. By this adjustment process, the lens center coordinates pn of the multiple microlenses 21 are irregularly arranged by adjusting the lens center coordinates pn so that the overlap amount Ov between adjacent microlenses 21, 21 on the XY plane falls within a preset allowable range (for example, equal to or less than a preset value).

[0130] 15, first, the x and y coordinates of the lens center coordinate pn of a newly placed microlens 21, the distance dx in the X direction from the lens center coordinate pn on the XY plane, and the distance dy in the Y direction are determined by random numbers. Next, the overlap amount Ov between the planar shape of each microlens 21 already placed and the planar shape of the newly placed microlens 21 is calculated. The overlap amount Ov is the overlap width between the planar shapes of two adjacent microlenses 21, 21.

[0131] In this way, when a new microlens 21 is arranged on the XY plane, the overlap amount Ov with the microlens 21 already arranged is calculated, and if the overlap amount Ov is within a preset allowable range, the new microlens 21 is arranged. Conversely, if the calculated overlap amount Ov is outside the allowable range (for example, if it exceeds the upper limit of the allowable range or is less than the lower limit of the allowable range), the new microlens 21 is not arranged. It is preferable to determine the allowable range in advance according to the optical characteristics required for the microlens array 20, etc.

[0132] In this manner, as shown in FIG. 15, the lens center coordinates pn of the microlenses 21 may be irregularly arranged on the XY plane, while the overlap amount Ov may be adjusted within the allowable range. This allows the microlenses 21 to be arranged at irregular positions on the XY plane, while overlapping each other with an appropriate overlap amount Ov. Therefore, the occurrence of flat parts that do not become lens surfaces between the adjacent microlenses 21, 21 can be suppressed, and the occurrence of zero-order diffracted light that passes through the flat parts of the diffusion plate 1 can be suppressed. In addition, the unevenness of the intensity distribution of the diffused light due to interference and diffraction of the diffused light emitted from the multiple microlenses 21 can be reduced. Furthermore, since the microlenses 21, 21 do not overlap each other excessively, the moldability and feasibility of the microlens array structure are not impaired.

[0133] (S12) Lens parameter setting Next, lens parameters of each microlens 21 are set as shown in Fig. 13. The lens parameters are parameters that determine the surface shape (lens surface shape) of the microlens 21. It is preferable that the lens parameters are set irregularly within a preset variation range.

[0134] Specifically, the parameters of formula (2) are set as lens parameters. Also, by varying the parameters of formula (2) irregularly, the lens surface shapes (rotationally asymmetric aspheric shapes) of the multiple microlenses 21 can be varied to set them to different aspheric shapes.

[0135] In the lens parameter setting S12, instead of the formula (2), the aspheric coefficient A4 of the fourth order term in the formula (3) may be set to 0, and the other parameters may be set as the lens parameters.

[0136] The planar shape of the microlens 21 is, for example, an ellipse or a shape that is close to an ellipse as shown in FIG.

[0137] (S14) Determining the inflection point 13, in the lens parameter setting S12, it is determined whether or not there is an inflection point IP in the graph based on each formula (2) in which each parameter is set. As a result, if it is determined that there is a graph with an inflection point IP (YES in S14), the process proceeds to correction of the inflection point IP S16. On the other hand, if it is determined that there is no graph with an inflection point IP (NO in S14), the process proceeds to determination of the lens surface shape S18.

[0138] (S16) Inflection point correction 13, for a graph having an inflection point IP, the parameters set in formula (2) are set in formula (3), and further, the aspheric coefficient A4 of the fourth order term is set to a value other than zero. This makes it possible to perform a correction to eliminate the inflection point IP in the graph based on each formula (3) in which each parameter is set.

[0139] (S18) Determining the lens surface shape Next, the lens surface shape of each micro lens 21 is determined based on the lens parameters set in S12 or S16. Specifically, the Z coordinate position representing the surface shape of each micro lens 21 is calculated based on the lens parameters set above, and the lens surface shape of the micro lens 21 is set. Then, the height position in the Z direction of the set lens surface shape is adjusted so that the size (e.g., aperture width Dx, Dy) of the set lens surface shape on the XY plane matches the size of the parameters set in S12 (e.g., aperture width Dx, Dy set in S12 above). Then, the horizontal cross section of the lens surface shape in the XY plane after the height position adjustment is set as a cross section at the position z=0.

[0140] As described above, according to the design method of the microlens 21 of the present embodiment, the surface shape of each microlens 21 constituting the microlens array 20 is an aspheric shape expressed by an aspheric equation having at least a third-order term. That is, the surface shape of each microlens 21 constituting the microlens array 20 of the present embodiment is an aspheric shape distorted in either or both of the X direction and the Y direction with respect to the reference surface shape. As a result, as shown in FIG. 11, even in the case of oblique incidence, sufficient deflection performance can be ensured, and the outgoing light 50 can be bent and deflected at a large bending angle in a desired direction with respect to the incoming light 40 entering the microlens 21.

[0141] Furthermore, according to the design method of the microlens 21 of this embodiment, parameters (e.g., aperture widths Dx, Dy, radii of curvature Rx, Ry, etc.) that define the lens surface shape are irregularly varied. Furthermore, it is preferable that the multiple microlenses 21 are arranged so as to overlap each other without gaps, and that there is no flat portion at the boundary between the adjacent microlenses 21. This makes it possible to provide each microlens 21 with different diffusion characteristics while continuously arranging the multiple microlens arrays 20 on the XY plane without gaps. The microlens array 20 configured in this way has small macro light amount fluctuations that depend on the lens surface structure and small light amount changes due to diffracted light, and has a variety of light distribution controllability with high uniformity.

[0142] 6. Microlens manufacturing method Next, a method for manufacturing the diffuser plate 1 according to this embodiment will be described with reference to Fig. 16. Fig. 16 is a flowchart showing the method for manufacturing the diffuser plate 1 according to this embodiment.

[0143] 16, in the manufacturing method of the diffusion plate 1 according to this embodiment, first, the substrate (substrate of the master or substrate 10 of the diffusion plate 1) is cleaned (step S101). The substrate may be, for example, a roll-shaped substrate such as a glass roll, or a flat substrate such as a glass wafer or a silicon wafer.

[0144] Next, a resist is formed on the surface of the substrate after cleaning (step S103). For example, a resist layer can be formed by using a resist made of a metal oxide. Specifically, a resist layer can be formed on a roll-shaped substrate by spraying or dipping the resist. On the other hand, a resist layer can be formed on a flat substrate by subjecting the resist to various coating processes. As the resist, a positive photoreactive resist or a negative photoreactive resist can be used. A coupling agent can be used to increase the adhesion between the substrate and the resist.

[0145] Furthermore, the resist layer is exposed using a pattern corresponding to the shape of the microlens array 20 (step S105). For this exposure process, a known exposure method may be appropriately applied, such as exposure using a grayscale mask, multiple exposure by overlapping a plurality of grayscale masks, or laser exposure using a picosecond pulse laser or a femtosecond pulse laser.

[0146] Thereafter, the exposed resist layer is developed (S107). A pattern is formed in the resist layer by this development process. The development process can be carried out by using an appropriate developer depending on the material of the resist layer. For example, when the resist layer is formed of a resist using a metal oxide, the resist layer can be alkaline developed by using an inorganic or organic alkaline solution.

[0147] Next, the developed resist layer is used for sputtering or etching (S109), completing a master master on whose surface the shape of the microlens array 20 is formed (S111). Specifically, a glass master can be manufactured by glass etching a glass substrate using the resist layer on which the pattern is formed as a mask. Alternatively, a metal master can be manufactured by performing Ni sputtering or nickel plating (NED processing) on ​​the resist layer on which the pattern is formed, forming a nickel layer on which the pattern is transferred, and then peeling off the substrate. For example, a metal master master can be manufactured by forming a nickel layer on which the resist pattern is transferred by Ni sputtering with a film thickness of about 50 nm, or nickel plating (for example, Ni sulfamate bath) with a film thickness of 100 μm to 200 μm, or the like.

[0148] Furthermore, the master master (e.g., a glass master master, a metal master master) completed in S111 above is used to transfer (imprint) a pattern onto a resin film or the like, thereby creating a soft mold having an inverted shape of the microlens array 20 formed on its surface (S113).

[0149] Then, using a soft mold, the pattern of the microlens array 20 is transferred to a glass substrate or a film substrate or the like (S115), and further, a protective film, an anti-reflection film, etc. are formed as necessary (S117) to manufacture the diffuser plate 1 of this embodiment.

[0150] In the above, an example has been described in which a soft mold is manufactured (S113) using a master (S111), and then the diffusion plate 1 is manufactured (S115) by transfer using the soft mold. However, the present invention is not limited to this example, and a master (e.g., an inorganic glass master) on which an inverted shape of the microlens array 20 is formed may be manufactured, and the diffusion plate 1 may be manufactured by imprinting using the master. For example, the diffusion plate 1 can be manufactured by applying an acrylic photocurable resin to a base material made of PET (PolyEthylene Terephthalate) or PC (PolyCarbonate), transferring the pattern of the master to the applied acrylic photocurable resin, and curing the acrylic photocurable resin with UV light.

[0151] On the other hand, in the case of manufacturing the diffusion plate 1 by directly processing the glass substrate itself, following the development process in step S107, a dry etching process is performed on the substrate 10 using a known compound such as CF4 (S119), and then a protective film, an anti-reflection film, etc. are formed as necessary (S121), thereby manufacturing the diffusion plate 1 of this embodiment.

[0152] It should be noted that the manufacturing method shown in FIG. 16 is merely one example, and the manufacturing method of the diffusion plate is not limited to the above example.

[0153] <7. Examples of Diffusion Plate Applications> Next, application examples of the diffusion plate 1 according to this embodiment will be described.

[0154] The diffusion plate 1 as described above can be appropriately mounted on various devices that need to diffuse light in order to realize their functions. Examples of such devices include display devices such as various displays (e.g., LED and organic EL displays), projection devices such as projectors, and various lighting devices.

[0155] For example, the diffusion plate 1 can be applied to a backlight of a liquid crystal display device, a lens integrated with a diffusion plate, and the like, and can also be applied to light shaping applications. The diffusion plate 1 can also be applied to a transmissive screen, a Fresnel lens, a reflective screen, and the like of a projection device. The diffusion plate 1 can also be applied to various lighting devices used for spot lighting, base lighting, and the like, various special lighting, and various screens such as intermediate screens and final screens. Furthermore, the diffusion plate 1 can also be applied to applications such as diffusion control of light from a light source in an optical device, and can also be applied to light distribution control of an LED light source device, light distribution control of a laser light source device, and light distribution control of light incident on various light valve systems.

[0156] The device to which the diffuser plate 1 is applied is not limited to the above-mentioned application examples, and the diffuser plate 1 can be applied to any known device that utilizes light diffusion. For example, the diffuser plate 1 according to this embodiment can be mounted on optical devices such as various illumination optical systems, image projection optical systems, and measurement, detection, and sensing optical systems.

[0157] <8. Summary> The above has described the diffuser 1 including the microlens array 20 according to this embodiment. According to this embodiment, the surface shape of the microlenses 21 is an aspheric shape expressed by an aspheric equation having at least a third-order term.

[0158] Furthermore, the microlenses 21 are arranged at irregular positions on the surface of the substrate 10 (XY plane).

[0159] Furthermore, the lens parameters (e.g., aperture widths Dx, Dy, radii of curvature Rx, Ry) that determine the aspheric shape of each microlens 21 vary irregularly at a predetermined variation rate (e.g., variation rates δDx, δDy, δRx, δRy) with respect to a predetermined reference value (e.g., reference aperture widths Dxk, Dyk, reference radii of curvature Rxk, Ryk). As a result, the aspheric shape of each microlens 21 varies with respect to the reference shape, and the aspheric shapes of the multiple microlenses 21 are different from one another.

[0160] The microlens array 20 according to this embodiment has, as its minimum structural unit, a microlens 21 having an aspheric surface shape expressed by an aspheric equation having at least a third-order term as described above. A plurality of microlenses 21 having different aspheric shapes are densely and irregularly arranged within the surface of the microlens array 20.

[0161] With a microlens array 20 configured as described above, in both normal incidence and oblique incidence, the outgoing light 50 (diffused light) that passes through the diffuser 1 and is emitted can be bent at a large bending angle in the desired direction, and the light beam of the outgoing light 50 (diffused light) can be largely deflected in the desired direction relative to the incident light 40.

[0162] In this regard, in a conventional general diffuser plate, the macroscopic overall transmitted optical axis is determined by the action of transmission and refraction of the diffuser plate. In contrast, according to the diffuser plate 1 of the present embodiment, the optical axis 25 of the microlens 21 itself is tilted at an inclination angle α, and the aspheric shape is rotated, so that the light flux of the output light 50 can be deflected in a direction different from that of the normal action of transmission and refraction. This deflection action can expand the degree of freedom in designing the optical axis direction of the input light 40 and the output light 50 with respect to the diffuser plate 1, and can also reduce the size of the optical device system in which the diffuser plate 1 is mounted, and optimize optical functions such as visibility.

[0163] Furthermore, the microlens array 20 of this embodiment can achieve a larger deflection angle while preventing the creation of inflection points, compared to a technique in which the optical axis of the microlens is tilted with respect to the Z direction while keeping the surface shape of the microlens symmetrical.

[0164] The surface shape of the microlens 21 according to this embodiment may be an aspheric shape expressed by an aspheric equation having a third-order term and a fourth-order term. In the aspheric equation, the third-order term may be a term for making the surface shape of the microlens 21 asymmetric, and the fourth-order term may be a term for correcting an inflection point of the cross-sectional shape of the surface of the microlens. This makes it possible to eliminate the inflection point IP in the cross-sectional shape of the surface of the microlens 21. This makes it possible to prevent the emergent light from bending in an unintended direction.

[0165] Moreover, the aspheric surface equation according to this embodiment preferably satisfies the above equation (10), and more specifically, the above equations (21) and (22). This makes it possible to eliminate the inflection point IP in the cross-sectional shape of the surface of the microlens 21.

[0166] Moreover, the aspheric surface equation according to this embodiment preferably satisfies the above equation (11), and more specifically, the above equations (23) and (24). This makes it possible to eliminate inflection points in the cross-sectional shape of the surface of the microlens 21.

[0167] Moreover, the aspheric surface equation according to this embodiment preferably satisfies the above equation (12), and more specifically, the above equations (25) and (26). This makes it possible to prevent the height of the apex of the microlens 21 from becoming too large.

[0168] Moreover, the third-order term includes both the third-order term in the X direction and the third-order term in the Y direction in the XY plane, and the surface shape of the microlens is preferably an aspheric shape that is distorted asymmetrically in both the X direction and the Y direction with respect to a reference surface shape having an axis of symmetry. This makes it possible to bend the direction of the outgoing light 50 with respect to the direction of the incident light 40 in both the XZ cross section and the YZ cross section. In other words, it becomes possible to bend and deflect the outgoing light 50 with respect to the incident light 40 in two-dimensional directions (X direction and Y direction) on the surface of the diffusion plate 1.

[0169] The third-order term may include either a third-order term in the X direction or a third-order term in the Y direction in the XY plane, and the surface shape of the microlens may be asymmetrically distorted in either the X direction or the Y direction with respect to a reference surface shape having an axis of symmetry, and may be an aspheric shape that is symmetric in the other direction. This allows the direction of the outgoing light 50 to be bent at a large bending angle with respect to the direction of the incoming light 40.

[0170] The deflection direction of the emitted light 50 by the multiple microlenses 21 may be the same throughout the microlens array 20, or may be different for each region of the microlenses 21. Similarly, the deflection angles βx, βy of the emitted light 50 by the multiple microlenses 21 may be the same throughout the microlens array 20, or may be different for each region of the microlenses 21.

[0171] If the deflection direction and deflection angles βx, βy are the same, the microlens array 20 as a whole can deflect the light flux of the output light 50 in the same deflection direction and at the same deflection angles βx, βy. On the other hand, if the deflection direction and deflection angles βx, βy are different for each region of the microlens array 20, the light flux of the output light 50 can be deflected in different deflection directions and deflection angles βx, βy by each region of the microlens array 20. In this way, if a plurality of regions with mutually different deflection directions and deflection angles βx, βy are included in the same surface of the microlens array 20, and the deflection direction and deflection angles βx, βy are different for each region, the output light can be deflected in various deflection modes by one microlens array 20. This makes it possible, for example, to efficiently utilize the light flux of diffused light over a wide range, or to improve the visibility of the projected image by controlling the chief ray in the optical projection system.

[0172] In addition, the diffusion plate 1 having the microlenses 21 having the inclined aspheric shape according to this embodiment can be manufactured, for example, by imprint processing using a master having the uneven structure of the microlenses 21. The master can be manufactured by highly precise drawing exposure or stepper exposure using a laser beam or a controlled light source, and photolithography techniques such as etching. For example, the master can be manufactured by transferring a structure surface formed by lithography by electroforming, and can also be manufactured as an inorganic device by glass etching. Alternatively, the master can be manufactured by precision machining techniques.

[0173] The product of the diffusion plate 1 according to this embodiment may be provided as an inorganic device by, for example, glass etching. The diffusion plate 1 may also be provided as an organic imprint film replicated from a master. In this way, the product of the diffusion plate 1 can be provided as a transfer film product or a member surface transfer product. When manufacturing a transfer product of the diffusion plate 1, a flat master or a roll-shaped master can be used to utilize injection molding, melt transfer, or UV resin transfer by a photopolymerization method. EXAMPLES

[0174] Next, a diffusion plate according to an embodiment of the present invention will be described. Note that the following embodiment is merely an example for illustrating the effect and feasibility of the diffusion plate according to the present invention, and the present invention is not limited to the following embodiment.

[0175] The diffusers according to Examples 1 to 3 were designed under the design conditions described below while changing the surface structure of the microlens array.

[0176] The microlens arrays according to Examples 1 to 3 were designed with the surface of each microlens being an aspheric shape expressed by the mathematical formula (3). A simulation was performed on the state of diffuse light distribution by the microlens array when incident light was obliquely incident on this microlens array.

[0177] Simulation results of Examples 1 to 3 will be described below with reference to Fig. 17 to Fig. 31. Fig. 17 to Fig. 21 show the simulation results of Example 1, Fig. 22 to Fig. 26 show the simulation results of Example 2, and Fig. 27 to Fig. 31 show the simulation results of Example 3.

[0178] 17, 22, and 27 are graphs showing specific examples of lens surface shapes expressed by aspheric expressions. In Fig. 17, 22, and 27, the Z-direction distance [μm] on the vertical axis of the graph is the relative height [μm] in the Z direction at each position on the surface of the microlens 21 when the height of the apex of the microlens 21 is set as the reference (height zero). Also, the distance [μm] from the center on the horizontal axis of the graph is the X-direction or Y-direction distance [μm] at each position on the surface of the microlens 21 when the lens center point 30 (see Fig. 11) is set as the reference (origin on the XY plane).

[0179] Figures 18, 23, and 28 are images showing the simulation results of the radiance distribution of diffused light projected onto a screen located 100 mm away from the diffuser. In Figures 18, 23, and 28, the vertical axis of the graph indicates the vertical coordinate position on the screen [mm], and the horizontal axis of the graph indicates the horizontal coordinate position on the screen [mm].

[0180] Figures 19, 24, and 29 are images showing the simulation results of the cross-sectional distribution of radiance in the X direction of diffused light projected onto a screen located 100 mm away from the diffuser. In Figures 19, 24, and 29, the vertical axis of the graph indicates radiance (angular space), and the horizontal axis of the graph indicates the coordinate position [mm] in the horizontal direction of the screen.

[0181] Figures 20, 25, and 30 are images showing the simulation results of the cross-sectional distribution of radiance in the Y direction of diffused light projected onto a screen located 100 mm away from the diffuser. In Figures 20, 25, and 30, the vertical axis of the graph indicates radiance (angular space), and the horizontal axis of the graph indicates the coordinate position [mm] in the vertical direction of the screen.

[0182] Figures 21, 26, and 31 show the angular distribution of radiance of diffused light projected onto a screen located 100 mm away from the diffuser. In Figures 21, 26, and 31, 0° indicates the X direction, and 90° indicates the Y direction.

[0183] <Example 1> In the first embodiment, in the formula (3), A 3x =0, A 4x =0, A 3y =0.003, A 4y = 0.001, Rx = 23 mm, Ry = 23 mm, Kx = 0.5, and Ky = 0.5. That is, A 4y / A 3y It was set to ≒0.33.

[0184] As shown in FIG. 17, in the first embodiment, in the formula (3), the third-order term “A 3y y 3 ", that is, A3y By setting ≠ 0, the aspheric shape is distorted asymmetrically in the Y direction with respect to the reference surface shape. On the other hand, in the formula (3), the third-order term "A 3x x 3 ", that is, A 3x By setting =0, the surface shape becomes aspheric and symmetrical in the X direction with respect to the reference surface shape.

[0185] In the first embodiment, in the formula (3), the fourth-order term in the Y direction, “A 4y y 4 ", that is, A 4y By setting ≠ 0, it is possible to avoid a situation in which an inflection point IP is formed in the Y direction.

[0186] In addition, a simulation was performed on the state of diffused light distribution by the microlens array when incident light was obliquely incident on the microlens array designed as the first embodiment.

[0187] In Example 1, the simulation was performed with the angles of incidence of the incident light being X=0° and Y=30°. That is, the simulation was performed using incident light that is normally incident in the X direction and obliquely incident in the Y direction.

[0188] As shown in Figures 18 and 19, it was confirmed that the radiance of the light diffused by the diffuser plate of Example 1 had a distribution shape that was symmetrical with respect to the peak in the X direction. On the other hand, as shown in Figures 18 and 20, it was confirmed that the radiance of the light diffused by the diffuser plate of Example 1 had a distribution shape that was shifted in the negative direction with respect to the peak in the Y direction. In other words, it was found that the diffuser plate of Example 1 can bend the diffused light only in the Y direction.

[0189] 21, the radiance of the diffused light diffused by the diffusion plate of Example 1 peaks near 0° in the X direction and near -1° in the Y direction. As described above, in Example 1, the incident angle of the incident light was set to X=0° and Y=30°. Therefore, considering that the natural bending (Snell's law) caused by the difference in refractive index between the substrate 10 and the outside air is about -6°, it was confirmed that the diffusion plate of Example 1 can bend the emitted light (diffused light) by about 5°.

[0190] <Example 2> In the second embodiment, in the formula (3), A 3x =0.0006, A 4x =0, A 3y =0.0005, A 4y = 0, Rx = 23 mm, Ry = 23 mm, Kx = 0.5, and Ky = 0.5. In other words, in formula (2), A 3x =0.0006, A 3y =0.0005, Rx=23mm, Ry=23mm, Kx=0.5, and Ky=0.5 were set.

[0191] As shown in FIG. 22, in the second embodiment, in the formula (3), the third-order term “A 3x x 3 " and the cubic term in the Y direction "A 3y y 3 ", that is, A 3x ≠0, A 3y By setting ≠0, the surface shape becomes aspheric, distorted asymmetrically in both the X and Y directions with respect to the reference surface shape.

[0192] In addition, a simulation was performed on the state of diffused light distribution by the microlens array when incident light was obliquely incident on the microlens array designed as the second embodiment.

[0193] In Example 2, the simulation was performed with the angles of incidence of the incident light set to X=0° and Y=30°. That is, the simulation was performed using incident light that is normally incident in the X direction and obliquely incident in the Y direction.

[0194] As shown in Figures 23 and 24, it was confirmed that the radiance of the light diffused by the diffuser plate of Example 2 had a distribution shape that was shifted in the negative direction from the peak in the X direction. Also, as shown in Figures 23 and 25, it was confirmed that the radiance of the light diffused by the diffuser plate of Example 2 had a distribution shape that was shifted in the negative direction from the peak in the Y direction. In other words, it was found that the diffuser plate of Example 2 can bend the diffused light two-dimensionally in the X and Y directions.

[0195] 26, the radiance of the diffused light diffused by the diffuser plate of Example 2 peaks near -3.4° in the X direction and near -5° in the Y direction. As described above, in Example 2, the incident angle of the incident light was set to X=0° and Y=30°. Therefore, considering the natural bending to be about -6°, it was confirmed that the diffuser plate of Example 2 can bend the emitted light (diffused light) by about 1°.

[0196] <Example 3> In the third embodiment, in the formula (3), A 3x =0.001, A 4x =0.0001, A 3y =0.001, A 4y = 0.0001, Rx = 23 mm, Ry = 23 mm, Kx = 0.5, and Ky = 0.5. That is, A 4y / A 3y =0.1.

[0197] As shown in FIG. 27, in the third embodiment, in the formula (3), the third-order term “A 3x x 3 " and the cubic term in the Y direction "A 3y y 3 ", that is, A 3x ≠0, A 3y By setting ≠ 0, an aspheric surface shape is obtained that is distorted asymmetrically in both the X and Y directions with respect to the reference surface shape.

[0198] In the third embodiment, in the formula (3), the fourth-order term in the X direction, “A 4x x 4 " and the fourth order term in the Y direction, "A 4y y 4 ", that is, A 4x ≠0, A 4y By setting ≠ 0, it is possible to avoid a situation in which an inflection point is formed in both the X direction and the Y direction.

[0199] In addition, a simulation was performed on the state of diffused light distribution by the microlens array when incident light was obliquely incident on the microlens array designed as the third embodiment.

[0200] In Example 3, the simulation was performed with the incidence angles of the incident light set to X=20° and Y=20°. That is, the simulation was performed using incident light that was obliquely incident in both the X direction and the Y direction.

[0201] As shown in Figures 28 and 29, it was confirmed that the radiance of the light diffused by the diffuser plate of Example 3 had a distribution shape that was shifted in the negative direction from the peak in the X direction. Also, as shown in Figures 28 and 30, it was confirmed that the radiance of the light diffused by the diffuser plate of Example 3 had a distribution shape that was shifted in the negative direction from the peak in the Y direction. In other words, it was found that the diffuser plate of Example 3 can bend the diffused light two-dimensionally in both the X direction and the Y direction.

[0202] 31, the radiance of the diffused light diffused by the diffuser plate of Example 3 peaks near -3.4° in the X direction and near -5° in the Y direction. As described above, in Example 3, the incident angles of the incident light were set to X=20° and Y=20°. Therefore, considering the natural bending to be about -6°, it was confirmed that the diffuser plate of Example 3 can bend the emitted light (diffused light) by about 1°.

[0203] Although the preferred embodiment of the present invention has been described in detail above with reference to the accompanying drawings, the present invention is not limited to such an example. It is clear that a person having ordinary knowledge in the technical field to which the present invention pertains can conceive of various modified or altered examples within the scope of the technical ideas described in the claims, and it is understood that these also naturally belong to the technical scope of the present invention. [Explanation of symbols]

[0204] 1 Diffuser 10 Base material 20 Microlens Array 21 Microlens

Claims

1. A microlens array type diffuser plate, A substrate; A microlens array including a plurality of microlenses irregularly arranged on an XY plane on at least one surface of the substrate; Equipped with A diffusion plate, wherein the surface shape of the microlenses is an aspheric shape expressed by an aspheric equation having at least a third-order term.

2. The diffuser plate according to claim 1 , wherein the surface shape of the microlenses is an aspheric shape expressed by an aspheric equation having a third-order term and a fourth-order term.

3. The third-order term is a term for making the surface shape of the microlens asymmetric, The diffuser plate according to claim 2 , wherein the fourth-order term is a term for correcting an inflection point of a cross-sectional shape of the surface of the microlens.

4. The diffusion plate according to claim 2 , wherein the aspheric surface formula satisfies the following formula (10): A ４ / A ３ >0 …(10) A ３ : Aspheric coefficient of the third-order term A ４ : Aspheric coefficient of the fourth-order term

5. The diffuser plate according to claim 4 , wherein the aspheric surface equation satisfies the following equation (11): A ４ / A ３ >0.03 ・・・(11)

6. The diffuser plate according to claim 4 , wherein the aspheric surface equation satisfies the following equation (12): A ４ / A ３ <0.5 ・・・(12)

7. the third-order term includes a third-order term in the X direction and a third-order term in the Y direction on the XY plane, the fourth-order term includes a fourth-order term in the X direction and a fourth-order term in the Y direction, The diffuser plate according to claim 4 , wherein the aspheric surface equation satisfies the following equations (21) and (22). A ４ｘ / A ３ｘ >0 ・・・(21) A ４ｙ / A ３ｙ >0 ・・・(22) A ３ｘ :The aspheric coefficient of the third-order term in the X direction A ４ｘ :The aspheric coefficient of the fourth-order term in the X direction A ３ｙ :Aspheric coefficient of the third-order term in the Y direction A ４ｙ : the aspheric coefficient of the fourth-order term in the Y direction

8. The diffuser plate according to claim 7 , wherein the aspheric surface equation satisfies the following equations (23) and (24). A ４ｘ / A ３ｘ >0.03 ・・・(23) A ４ｙ / A ３ｙ >0.03 ・・・(24)

9. The diffuser plate according to claim 7 , wherein the aspheric surface equation satisfies the following equations (25) and (26). A ４ｘ / A ３ｘ <0.5 ・・・(25) A ４ｙ / A ３ｙ <0.5 ・・・(26)

10. The third-order term includes both a third-order term in the X direction and a third-order term in the Y direction on the XY plane, 4. The diffusion plate according to claim 1, wherein the surface shape of the microlenses is an aspheric shape that is distorted asymmetrically in both the X direction and the Y direction with respect to a reference surface shape having an axis of symmetry.

11. the third-order term includes either a third-order term in the X direction or a third-order term in the Y direction on the XY plane, 4. The diffusion plate according to claim 1, wherein the surface shape of the microlens is asymmetrically distorted in either the X direction or the Y direction with respect to a reference surface shape having an axis of symmetry, and is an aspheric shape that is symmetric in the other direction.

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