OPTICAL DETAILS

Abstract

The invention proposes an optical detail (10) in a scheme of the invention, including a first principal surface (11a) and a second principal surface (12a) facing each other, wherein the first principal surface (11a) has a first lens-like shape (11), the second principal surface (12a) has a second lens-like shape (12), the long axis (Y) of the first lens-like shape (11) is perpendicular to the long axis (X) of the second lens-like shape (12) or intersects with it to form an additional deviation angle of ±70 degrees with respect to the perpendicular direction, the first lens-like shape (11) has a curved surface shape with a conical constant kx of -2.4 or greater and -0.6 or less, and the second lens-like shape (12) has a curved surface shape with a conical constant ky of -0.9 or greater and -0.5 or less.

Description

Optical elements

[0001] The present invention relates to an optical element.

[0002] In recent years, head-up displays (hereinafter sometimes referred to as HUDs) that project driving assistance information such as navigation from an image display device onto the windshield of a moving object such as an automobile have been attracting attention. A head-up display device mainly includes an image display device, a diffuser plate on which the image projected from the image display device is formed as an intermediate image, and a magnifying glass that magnifies the intermediate image and guides it onto the windshield. A microlens array is widely used as the diffuser plate.

[0003] In order to achieve low power consumption in a head-up display device, a laser projector that uses a laser beam, which consumes little power, as the light source for the image display device is sometimes used. For example, Patent Document 1 proposes an image forming device as a head-up display device, which includes a laser projector that uses a laser beam as a light source and projects an image formed by an array of multiple pixels, a microlens array in which multiple microlenses are arranged, an optical system correction element, and an optical system magnification element.

[0004] Japanese Patent Application Publication No. 2010-145745

[0005] Microlens arrays can appropriately diffuse incident light, and their curved surface shapes can be freely designed depending on the desired light distribution characteristics and the optical properties of the material. However, when laser light is used as the light source, the spot diameter of the laser light is small, making it difficult to uniformize the brightness of the emitted light across the diffusion range. On the other hand, as the pitch size of the microlenses becomes smaller with the trend toward higher image quality, mold production becomes more complex, resulting in increased time and cost. The present invention has been made in consideration of the above circumstances, and aims to provide an optical element that emits light with a uniform brightness across the diffusion range and is suitable for mass production.

[0006] The inventor discovered that by using lenticular lenses on both the incident and exit sides of an optical element, arranging the long axis direction of the lenticular lens on the incident side and the long axis direction of the lenticular lens on the exit side so that they are perpendicular to each other, and controlling the curved shape of each lenticular lens, it is possible to make the brightness uniform over the diffusion range of the exiting light using a simple manufacturing process, and this led to the present invention.

[0007] That is, the present invention provides an optical element having opposing first and second principal surfaces, wherein the first principal surface has a first lenticular lens, the second principal surface has a second lenticular lens, the long axis direction of the first lenticular lens being perpendicular to the long axis direction of the second lenticular lens, or the long axis directions intersect with each other at an angle deviated from the perpendicular direction by an angle within a range of ±70 degrees, and the curved surface shape of the first lenticular lens being expressed by the following formula (1): [In formula (1), cx represents the curvature [1 / mm], x represents the distance [mm] from the central axis of the first lenticular lens in the x direction, and kx represents the conic constant, which is equal to or greater than -2.4 and equal to or less than -0.6.] The curved surface shape of the second lenticular lens is an optical element expressed by the following formula (2). [In formula (2), cy represents the curvature [1 / mm], y represents the distance [mm] from the central axis of the second lenticular lens in the y direction, and ky represents the conic constant, which is equal to or greater than -0.9 and equal to or less than -0.5.]

[0008] According to the optical element of the present invention, the brightness of the emitted light is uniform over the diffusion range, and an optical element suitable for mass production can be provided.

[0009] 1 is a perspective view showing a portion of an optical element according to one embodiment of the present invention (first embodiment); FIG. 2 is a plan view showing a portion of an optical element according to one embodiment of the present invention; FIG. 3 is a plan view showing (a) a first main surface and (b) an X-X cross-sectional view of a portion of an optical element according to one embodiment of the present invention; FIG. 4 is a plan view showing (a) a second main surface and (b) a Y-Y cross-sectional view of a portion of an optical element according to one embodiment of the present invention; FIG. 5 is a schematic view showing an optical element according to one embodiment of the present invention (second embodiment); FIG. 6 is a schematic view showing a head-up display device using the optical element of the present invention; FIG. 7 is a photograph showing heat maps of Examples 1 to 5; FIG. 8 is a photograph showing heat maps of Examples 6 to 10; FIG. 9 is a photograph showing heat maps of Examples 11 to 15; FIG. 10 is a photograph showing heat maps of Examples 16 to 19; FIG. 11 is a photograph showing heat maps of Examples 20 to 23; FIG. 12 is a graph showing luminance versus diffusion angle of emitted light for Example 1; FIG. 13 is a graph showing luminance versus diffusion angle of emitted light for Example 11; FIG. 14 is a graph showing luminance versus diffusion angle of emitted light for Example 19; FIG. 15 is a graph showing luminance versus diffusion angle of emitted light for Example 20; Photographs showing heat maps of the diffusers of Examples 24, 25, 27, and 28. Graph showing the distribution of the radiant intensity (W / sr) of diffused light in the diffuser of Example 25. Graph showing the distribution of the radiant intensity (W / sr) of diffused light in the diffuser of Example 28. Graphs plotting the results of angular intensity uniformity for Examples 24 to 31 and Comparative Examples 1 and 2 by angle range. Heat maps for the diffuser of Example 28 (shifted at an angle of 40 degrees from perpendicular) are shown for angle ranges (1) to (3). Heat maps for the diffuser of Example 29 (shifted at an angle of 50 degrees from perpendicular) are shown for angle ranges (1) to (3).

[0010] [Optical Element (First Embodiment)] An optical element according to one embodiment of the present invention (first embodiment) will now be described with reference to the drawings. Fig. 1 is a perspective view showing a portion of the optical element according to this embodiment. Fig. 2 is a plan view showing a portion of the optical element according to one embodiment of the present invention. Fig. 3 is (a) a plan view of a first main surface and (b) an X-X cross-sectional view of a portion of the optical element according to this embodiment. Fig. 4 is (a) a plan view of a second main surface and (b) a Y-Y cross-sectional view of a portion of the optical element according to this embodiment.

[0011] As shown in FIG. 1 , the optical element of this embodiment is an optical element 10 having opposing first and second major surfaces 11a and 12a, with the first major surface 11a being the light-emitting side and the second major surface 12a being the light-incident side. The first major surface 11a has first lenticular lenses 11, and the second major surface 12a has second lenticular lenses 12, which are arranged so that the long axis direction (Y) of the first lenticular lenses 11 is perpendicular to the long axis direction (X) of the second lenticular lenses 12. As shown in FIG. 2 , the optical element 10 of this embodiment is arranged so that the long axis direction (Y) of the first lenticular lenses 11 and the long axis direction (X) of the second lenticular lenses 12 are perpendicular to each other, thereby forming individual microlenses 10a at the intersections of the lenses, and the optical element 10 as a whole is composed of a microlens array. Details of the first lenticular lenses 11 and the second lenticular lenses 12 will be described below.

[0012] (First Lenticular Lens) As shown in Fig. 3(a), the first lenticular lens 11 is formed by arranging a plurality of lenticular lenses in the X direction with the Y direction as the long axis direction. Fig. 3(b) shows an X-X cross section of (a). The curved shape of the first lenticular lens 11 is expressed by the following formula (1).

[0013]

[0014] In the formula (1), cx represents the curvature [1 / mm], and x represents the central axis L of the first lenticular lens 11. １１the distance [mm] in the X direction from the center axis L １１ The angle θ indicates the distance on the surface along the direction perpendicular to the θ axis (direction perpendicular to the θ axis). kx indicates the conic constant and is -2.4 or more and -0.6 or less. When the conic constant kx is -2.4 or more and -0.6 or less, in the spectrum showing the luminance characteristics with respect to the diffusion angle of the emitted light, it is possible to achieve a luminance of 80% or more of the maximum luminance within an angular range of 90% of the full width at half maximum (FWHM). Furthermore, the conic constant kx is preferably -2.0 or more and -1.0 or less, and within this range, it is possible to achieve a luminance of 90% or more of the maximum luminance within an angular range of 90% of the full width at half maximum (FWHM). A conic constant kx of -1.6 is particularly preferable. By reducing the angular dependency of luminance, the brightness of the displayed image viewed from any viewpoint position can be perceived as more balanced.

[0015] In formula (1), the distance x from the central axis of the first lenticular lens 11 in the X direction is preferably 0 or more and Px / 2 or less, where Px represents the pitch between the lenses of the first lenticular lens 11, as described below. When the distance x is within the above range, no flat portion is formed on the lenticular lens-shaped surface of the first main surface of the optical element, and a significant improvement in front brightness can be suppressed.

[0016] In the first lenticular lens 11, the pitch Px between the lenses is preferably 5 μm or more, and more preferably 25 μm or more. By setting the pitch Px in this manner, it is possible to prevent the difficulty in controlling the viewing angle due to the diffraction phenomenon. It is also possible to suppress the occurrence of interference fringes. Furthermore, the pitch Px between the lenses is preferably 500 μm or less, and more preferably 250 μm or less. By setting the pitch Px in this manner, it is possible to prevent the pixels of the head-up display image from becoming coarse.

[0017] (Second Lenticular Lens) As shown in Fig. 4(a), the second lenticular lens 12 is composed of a plurality of lenticular lenses arranged with their major axes aligned in the X direction. Fig. 4(b) shows a Y-Y cross section of (a). The curved surface shape of the second lenticular lens is expressed by the following formula (2).

[0018]

[0019] In formula (2), cy represents the curvature [1 / mm], and y represents the central axis L of the second lenticular lens. １２ the distance [mm] in the Y direction from the center axis L １２ ky denotes the Conic constant, which is between -0.9 and -0.5.

[0020] By setting the conic constant ky to -0.9 or more and -0.5 or less, it is possible to achieve a luminance of 80% or more of the maximum luminance within an angular range of 90% of the full width at half maximum (FWHM) in a spectrum showing the luminance characteristics relative to the diffusion angle of the emitted light. Furthermore, the conic constant ky is preferably set to -0.8 or more and -0.6 or less, and within this range, it is possible to achieve a luminance of 90% or more of the maximum luminance within an angular range of 90% of the full width at half maximum (FWHM). A conic constant ky of -0.7 is particularly preferable. By reducing the angular dependency of luminance, the brightness of the displayed image viewed from any viewpoint position can be perceived as more balanced.

[0021] In formula (2), the distance y in the Y direction from the central axis of the first lenticular lens 11 is preferably 0 mm or more and Py / 2 or less, where Py represents the pitch between the lenses of the second lenticular lens 12, which will be described later. When the distance y is within the above range, no flat portion is formed on the lenticular lens-shaped surface of the first main surface of the optical element, and a significant improvement in front brightness can be suppressed.

[0022] In the second lenticular lens 12, the pitch Py between the lenses is preferably 5 μm or more, and more preferably 25 μm or more. By setting the pitch Py in this manner, it is possible to prevent the difficulty in controlling the viewing angle due to the diffraction phenomenon. It is also possible to suppress the occurrence of interference fringes. Furthermore, the pitch Py between the lenses is preferably 500 μm or less, and more preferably 250 μm or less. By setting the pitch Py in this manner, it is possible to prevent the pixels of the head-up display image from becoming coarse.

[0023] The material for forming the lenticular lens can be a radiation-curable resin or a thermoplastic resin. The refractive index of the resin is preferably 1.35 or more and 1.7 or less, and more preferably 1.45 or more and 1.66 or less. By using a resin with such a refractive index, it is possible to appropriately control the light entrance characteristics or light exit characteristics of the optical element. Examples of resins having such a refractive index include acrylic resin, polycarbonate, polyethylene terephthalate, polyvinyl chloride, polystyrene, etc. Using a radiation-curable resin or a thermoplastic resin, an optical element consisting of microlenses can be easily and reliably manufactured by manufacturing a mold corresponding to the above shape and performing injection molding, heat pressing, or UV transfer molding.

[0024] When a wider viewing angle or more uniform angular luminance is required, it is preferable that the curved surface shape of the first lenticular lens 11 is further adjusted according to the following formula (3).

[0025]

[0026] In equation (3), A represents a symmetric coefficient, and B represents an asymmetric coefficient, which is −1.

[0027] By adjusting the curved surface shape of the first lenticular lens 11 according to formula (3), it is possible to make the brightness uniform over a wide viewing angle.

[0028] When a wider viewing angle or more uniform angular luminance is required, it is preferable that the curved surface shape of the second lenticular lens 12 is further adjusted according to the following formula (4).

[0029]

[0030] In equation (4), A represents a symmetric coefficient, and B represents an asymmetric coefficient, which is 1.

[0031] By adjusting the curved surface shape of the second lenticular lens 12 according to equation (4), it is possible to make the luminance uniform over a wide viewing angle.

[0032] The optical element 10 of this embodiment has a rectangular diffusion shape. Furthermore, the optical element 10 can maintain a high luminance of 90% or more of the maximum luminance of the emitted light across a diffusion angle of the emitted light ranging from 40° in the horizontal direction H to 28° in the vertical direction V, thereby achieving a uniform luminance of the emitted light. Furthermore, the optical element 10 of this embodiment can maintain a high luminance of 98% or more of the maximum luminance of the emitted light across a diffusion angle of the emitted light ranging from 25.5° in the horizontal direction H to 19.5° in the vertical direction V, thereby achieving a uniform luminance of the emitted light. The light distribution shape (intensity distribution of the emitted light) in each direction can be a top-hat shape. Furthermore, the optical element 10 of this embodiment has an optimal configuration for achieving uniform luminance over a wide viewing angle, with respect to the shape and position (whether located on the entrance surface or the exit surface) of the lenticular lens, as the refractive index of incident light changes from small to large as it passes through the optical element from air. Furthermore, the optical element 10 of this embodiment achieves uniform brightness at the diffusion angle by providing lenticular lenses on both opposing surfaces, and is suitable for mass production because the mold processing process is significantly simplified compared to when similar optical characteristics are obtained by providing lenses on only one surface.

[0033] [Optical Element (Second Embodiment)] An optical element according to one embodiment of the present invention (second embodiment) will now be described with reference to the drawings. Fig. 5 is a schematic diagram showing an optical element 10' according to the second embodiment.

[0034] 5, the optical element 10′ of this embodiment is a plate-like optical element having a first main surface 11′a and a second main surface 12′a that is the back surface of the first main surface 11′a, where the first main surface 11′a is the surface on the light-emitting side and the second main surface 12′a is the surface on the light-incident side. The first main surface 11′a has first lenticular lenses 11′, and the second main surface 12′a has second lenticular lenses 12′, and the major axis direction of the first lenticular lenses 11′ is arranged on the X-Y plane such that the major axis direction of the second lenticular lenses 12′ is offset by an angle θ within a range of ±70 degrees from being perpendicular to the major axis direction of the second lenticular lenses 12′. By forming a shift angle θ between the first and second lenticular lenses in this manner, the pitch direction, which was parallel to the X-axis direction of the first lenticular lens 11' in the first embodiment, is arranged so that a shift angle within the range of ±70 degrees is generated on the X-Y plane with respect to the pitch direction, which is parallel to the Y-axis direction of the second lenticular lens 12'.

[0035] The optical element 10' is arranged such that the major axis direction of the first lenticular lenses 11' is offset by an angle θ within a range of ±70° from the orthogonal direction with respect to the major axis direction of the second lenticular lenses 12', which are arranged parallel to the X-axis direction. This results in individual microlenses 10'a being formed at the intersections of the lenses, and the optical element 10' as a whole is made up of a microlens array. Here, the microlenses 10'a are formed such that the pitch direction of the first lenticular lenses 11' and the pitch direction of the second lenticular lenses 12' form an offset angle θ.

[0036] The first lenticular lens 11′ of the optical element 10′ is the same as the first lenticular lens 11 of the first embodiment except that it is arranged to form a misalignment angle θ. The second main surface 12′a and second lenticular lens 12′ of the optical element 10′, and the materials constituting the first and second lenticular lenses are the same as those of the first embodiment, and therefore description thereof will be omitted.

[0037] As shown in FIG. 5 , the first lenticular lens 11′ is preferably arranged on the X-Y plane so as to form a misalignment angle θ with respect to the Y axis within a range of ±70 degrees. The misalignment angle θ is more preferably within a range of ±40 degrees, and most preferably within a range of ±10 degrees. Within these ranges, a smaller misalignment angle θ can further enhance the uniformity of the luminance of the emitted light. The misalignment angle θ of the first lenticular lens 11′ can be adjusted according to the angular range of the diffusion angle of the emitted light. More specifically, by setting the misalignment angle θ of each lenticular lens within a range of ±70 degrees, the optical element 10′ can maintain a high luminance of 98% or more of the maximum luminance of the emitted light within a diffusion angle range of 0 to 26 degrees in the horizontal direction H and 0 to 12 degrees in the vertical direction V, thereby achieving uniform luminance of the emitted light. Furthermore, the light distribution pattern (intensity distribution of the emitted light) in each direction can be a top hat shape. Furthermore, although not limited thereto, the optical element 10' can be used with the brightness of the emitted light being uniform within a diffusion angle range of 0 to 13 degrees in the horizontal direction H and 0 to 12 degrees in the vertical direction V.

[0038] The curved shape of the first lenticular lens 11' is preferably expressed by the above-mentioned formula (1) in a cross section perpendicular to the long axis direction of the first lenticular lens 11', and the conic constant ky is preferably -2.4 or more and -0.6 or less. By having the conic constant kx in a cross section perpendicular to the long axis direction of the first lenticular lens 11', i.e., a cross section cut parallel to the pitch direction, be -2.4 or more and -0.6 or less, similar to the first embodiment, a luminance of 80% or more of the maximum luminance can be achieved within an angular range of 90% of the full width at half maximum (FWHM) in the spectrum showing the luminance characteristics versus the diffusion angle of the emitted light. Furthermore, similar to the first embodiment, the conic constant kx is preferably -2.0 or more and -1.0 or less, and within this range, a luminance of 90% or more of the maximum luminance can be achieved within an angular range of 90% of the full width at half maximum (FWHM). As in the first embodiment, the conic constant kx is particularly preferably −1.6, which reduces the angular dependency of brightness, making the brightness of the displayed image seen from any viewpoint appear more balanced. Furthermore, the preferred ranges of the distance x from the central axis in the X direction and the pitch Px between the lenses, which are defined in the above formula (1), are the same as in the first embodiment, and therefore will not be described here.

[0039] When a wider viewing angle or more uniform angular luminance is required, it is preferable that the curved surface shape of the first lenticular lens 11' is adjusted according to the above-mentioned formula (3).

[0040] From the maximum and minimum values ​​of the radiation intensity (W / sr), the angular intensity uniformity calculated based on the following formula can be set to 60% or more, more preferably 80% or more: Angular intensity uniformity = ((minimum radiation intensity) / (maximum radiation intensity)) × 100% This allows the optical element 10' to achieve uniform brightness over a wide viewing angle.

[0041] [Head-up display device] Next, an embodiment of a head-up display device using the optical element of the present invention will be described with reference to the drawings. FIG. 6 is a schematic diagram showing the head-up display device of this embodiment. The head-up display device of this embodiment is a head-up display device for a vehicle, and uses a laser projector using laser light as a light source as an image forming device. The laser projector can use a semiconductor laser with low power consumption as a light source, thereby realizing low power consumption of the entire head-up display device. In this embodiment, the optical element of the present invention is used as a diffuser plate that diffuses an image or video emitted from the laser projector and projects it onto a primary mirror.

[0042] 6, the head-up display device 100 includes a laser projector 101 as an image forming device, a diffuser 102 arranged on the emission side of the laser projector 101, a primary mirror 103, a secondary mirror 104, and a transmissive reflector 105. In the head-up display device 100 for a vehicle, the transmissive reflector 105 serves as the windshield.

[0043] The image projected from the laser projector 101 is incident as perpendicular incident light on the second main surface (second lenticular lens 12) side of the diffuser plate 102, and is formed as an intermediate image on the first main surface (first lenticular lens 11) side. A condenser lens or the like may be disposed between the laser projector 101 and the diffuser plate 102 to correct the angle of incidence of the laser light so that it falls within the aperture angle of the microlenses of the diffuser plate 102.

[0044] When the optical element 10' is used as the diffuser 102, the angle of the second principal surface (second lenticular lens 12') of the optical element 10' is adjusted to the optimization angle when the optical element 10' is parallel to a plane perpendicular to the incident light between the laser projector 101 and the primary mirror 103 (concave mirror). Setting of the optimization angle will be described in detail in the Examples section.

[0045] In the head-up display device 100, the size and the like of the diffuser 102 may be designed depending on the size of the laser projector 101 as a light source and its arrangement relative to the diffuser 102. In other words, the size of the optical element of the present invention, the shape of each of the lenticular lenses on its first and second principal surfaces, and the shape of the microlenses formed by these lenticular lenses may be designed taking into consideration the size of the light source and its arrangement relative to the light source.

[0046] The intermediate image formed by the diffuser 102 is magnified by the primary mirror 103 (concave mirror), passes through the secondary mirror 104, and is reflected by the transmissive reflector 105 (windshield) before being directed to the driver's eyes. The laser light emitted from the laser projector 101 is reflected by the transmissive reflector 105 and enters the driver's eyes, and at this time, the image displayed as the intermediate image appears to the driver as if it were located in front of the transmissive reflector 105.

[0047] In this embodiment, an optical correction system including a primary mirror 103 and a secondary mirror 104 is used, but the present invention is not limited to this configuration, and other optical correction systems can be used.

[0048] In this embodiment, a laser projector is used as the image forming device, thereby enabling the realization of high-resolution images or videos. Furthermore, an optical element using the microlenses of the present invention is used as the diffuser, thereby enabling the brightness of the emitted light to be uniform throughout the diffusion range, thereby enabling the realization of high-brightness, higher-quality images or videos. The optical element of the present invention preferably has a thickness of 10 mm or less, more preferably 5 mm or less, since this allows the head-up display device to be made thinner. On the other hand, the optical element of the present invention preferably has a thickness of 0.5 mm or more, and may have a thickness of 1 mm or more, from the viewpoint of ensuring the strength of the optical element. The thickness of the optical element of the present invention is not limited, and the optical element may be in the form of a film or sheet having a thickness of 0.5 mm or less, or more preferably 0.2 mm or less. Forming the optical element in the form of a film or sheet has the advantage of enabling the size of the device incorporating the optical element to be reduced.

[0049] The optical element of the present invention is used as a diffuser plate and can be suitably used in a head-up display device in which the diffusion angle of light incident on the first main surface and exiting from the second main surface is set in the range of 0 to 26 degrees in the horizontal direction H and 0 to 12 degrees in the vertical direction V. Therefore, a head-up display device including the optical element of the present invention also falls within the scope of the present invention.

[0050] [Summary] An optical element according to Aspect 1 of the present invention is an optical element having a first principal surface and a second principal surface opposing each other, wherein the first principal surface has a first lenticular lens, the second principal surface has a second lenticular lens, the long axis direction of the first lenticular lens is perpendicular to the long axis direction of the second lenticular lens or intersects with the long axis direction of the second lenticular lens at an angle deviated from the perpendicular direction by an angle within a range of ±70 degrees, and the curved surface shape of the first lenticular lens is expressed by the following formula (1): [In formula (1), cx represents the curvature [1 / mm], x represents the distance [mm] from the central axis of the first lenticular lens in the x direction, and kx represents the conic constant, which is equal to or greater than -2.4 and equal to or less than -0.6.] The curved surface shape of the second lenticular lens is an optical element expressed by the following formula (2). [In formula (2), cy represents the curvature [1 / mm], y represents the distance [mm] from the central axis of the second lenticular lens in the y direction, and ky represents the conic constant, which is equal to or greater than -0.9 and equal to or less than -0.5.]

[0051] In the optical element according to Aspect 2 of the present invention, in Aspect 1, kx is preferably −2.0 or more and −1.0 or less.

[0052] In the optical element according to Aspect 3 of the present invention, in Aspect 1 or 2, ky is preferably −0.8 or more and −0.6 or less.

[0053] The optical element according to Aspect 4 of the present invention, in any one of Aspects 1 to 3, is preferably made of a resin having a refractive index of 1.35 or more and 1.7 or less.

[0054] In the optical element according to Aspect 5 of the present invention, in any one of Aspects 1 to 4, it is preferable that the angular intensity uniformity is 60% or more.

[0055] In the optical element according to Aspect 6 of the present invention, in any one of Aspects 1 to 5, it is preferable that the luminance is 80% or more of the maximum luminance in an angular range of 90% of the full width at half maximum (FWHM).

[0056] The optical element according to Aspect 7 of the present invention is preferably a diffusion plate in any one of Aspects 1 to 6 above.

[0057] In the optical element according to Aspect 8 of the present invention, in any one of Aspects 1 to 7, it is preferable that the curved surface shape of the first lenticular lens is further adjusted according to the following formula (3). [In formula (3), A represents a symmetric coefficient. B represents an asymmetric coefficient, which is −1.]

[0058] In the optical element according to Aspect 9 of the present invention, in any one of Aspects 1 to 8, it is preferable that the curved surface shape of the second lenticular lens is further adjusted according to the following formula (4). [In formula (4), A represents a symmetry coefficient. B represents an asymmetry coefficient, which is 1.]

[0059] In the optical element according to Aspect 10 of the present invention, in any one of Aspects 1 to 9, the diffusion plate is preferably used in a head-up display device.

[0060] In the optical element according to Aspect 11 of the present invention, in any one of Aspects 1 to 10, it is preferable that the image forming device in the head-up display device is a laser projector that uses laser light as a light source.

[0061] The optical element according to Aspect 12 of the present invention is preferably used in any one of Aspects 1 to 11 above such that the diffusion angle of light incident on the first principal surface and exiting from the second principal surface is in the range of 0 to 26 degrees in the horizontal direction H and 0 to 12 degrees in the vertical direction V.

[0062] The present invention will now be described in more detail with reference to examples.

[0063] [Examples 1 to 23] (Microlens Design) As an optical element of the examples, a diffusion plate consisting of a microlens array with a first lenticular lens on the opposing first principal surface and a second lenticular lens on the opposing second principal surface was used for simulation with the following design items. <Design Items> - The refractive index of the diffusion plate was set to 1.49, which is the refractive index of acrylic resin. - The diffusion shape of the emitted light was rectangular, and the diffusion angle of the emitted light with respect to perpendicular incident light was set to 26° in the horizontal direction H and 12° in the vertical direction V, and the light distribution shape in each direction was set to a top hat shape. - The curvature cx was set to 27 mm. －１ The curvature cy is 60 mm －１ The pitch Px of the first lenticular lenses in the X direction was set to 30±2 μm. The pitch Py of the second lenticular lenses in the Y direction was set to 30±2 μm. In the above formulas (1) and (2), the conic constants kx and ky were set as shown in Table 1.

[0064]

[0065] [Light Source and Light Receiver] In Examples 1 to 23, the conditions for the light source and light receiver were as follows: Light source size: 1 mm square Light source position: -1 mm behind the seat (-Z direction) Number of tracking rays: 10,000,000 Fixed light receiver size: 20 mm square Fixed light receiver position: 0.01 mm in front of the seat (Z direction)

[0066] (Brightness versus Diffusion Angle of Emitted Light) For Examples 1 to 23, the brightness versus diffusion angle of the emitted light was calculated using geometric optics simulation software LightTools (Synopsys). An optical element was placed on a surface parallel to the X and Y axes, and a lenticular shape was created so that the pitch direction of the first lenticular shape corresponding to the emission surface was the X direction and the pitch direction of the second lenticular shape corresponding to the incidence surface was the Y direction. A light source was set to irradiate collimated light from the incidence surface side of the optical element so that it was parallel to the Z axis, and angular brightness distribution information was obtained for the light after passing through the optical element. The geometric optics simulation software LightTools (Synopsys) used in these Examples is simulation software that is used in research and development in the field of optical materials, including the field to which the present invention belongs, and is widely known for its proven track record. For example, International Publication WO2023 / 053643 compares simulation results with optical sheets molded based on the simulation results, and the reliability of the simulation results is confirmed. Figures 7 to 11 show heat maps, and Figures 12 to 16 show graphs.

[0067] As shown in FIGS. 7 to 16, it was found that the optical element of the present invention can achieve a brightness of 80% or more of the maximum brightness at a diffusion angle of 26° in the horizontal direction H and 12° in the vertical direction V.

[0068] [Examples 24 to 31, Comparative Examples 1 and 2] (Microlens Design) As the optical element of Examples 24 to 31 and Comparative Examples 1 and 2, a diffuser plate consisting of a microlens array with a first lenticular lens on the first main surface and a second lenticular lens on the second main surface was used, and a simulation was carried out using the above-mentioned LightTools with the following design items. <Design Items> [Diffuser Plate] The refractive index of the diffuser plate was 1.49, the same as in Examples 1 to 23. The thickness of the diffuser plate was 2 mm in the Z-axis direction (surface normal direction), and the sheet size was 50 mm square. The curvature cx was 27 mm. －１ The curvature cy is 60 mm －１- The pitch Px of the first lenticular lens in the X direction was set to 30±2 μm. - The pitch Py of the second lenticular lens in the Y direction was set to 30±2 μm. - In the above formulas (1) and (2), the conic constants kx and ky were set to -1.6 and -0.7, respectively. - The deviation angle θ from the perpendicularity on the xy plane of the first lenticular lens and the second lenticular lens is as shown below.

[0069] [Light source and receiver] The conditions for the light source and receiver were as follows: Light source size: 45 mm square Light source position: -100 mm behind the seat (-Z direction) Number of tracking rays: 10,000,000 Fixed receiver size: 100 mm square Fixed receiver position: 3 mm in front of the seat (Z direction)

[0070] Fig. 17 shows heat maps of the diffusers of Examples 24, 25, 27, and 28, among Examples 24 to 31, evaluated by simulation based on the above conditions. Fig. 18 shows the distribution of the radiant intensity (W / sr) of diffused light for the diffuser of Example 25, and Fig. 19 shows the distribution of the radiant intensity (W / sr) for the diffuser of Example 28. In each of Figs. 18 and 19, the graph shown in the upper part shows the distribution of the radiant intensity (W / sr) along the X-axis direction of the diffuser, and the graph shown in the lower part shows the distribution of the radiant intensity (W / sr) along the Y-axis direction of the diffuser. From each of Figs. 18 and 19, it can be confirmed that a top-hat radiant intensity can be obtained when the deviation angle is in the range of 10 to 40 degrees.

[0071] Next, in order to match the change in the misalignment angle θ for each of the diffusers of Examples 24 to 31 and Comparative Examples 1 and 2, the optimized angles of the angle-adjustable receivers based on the fixed receiver were set as shown in Table 2. The optimized angles in Table 2 were set so that the aforementioned angular intensity uniformity (= (minimum radiant intensity) / (maximum radiant intensity) × 100%), which is an index of angular intensity uniformity, was maximized within the angle range ((1) to (3) described below).

[0072] Next, the diffusion shape of the emitted light for the angle-adjusted receiver adjusted to the optimized angle was set to a rectangle, and the diffusion angle of the emitted light for perpendicular incident light was set to the following angle ranges (1) to (3) in each of the horizontal direction H and vertical direction V.

[0073] The reference starting point of the angle range is the point where the center line of the incident light (for example, perpendicular incident light) intersects with the optical element (diffuser plate).

[0074] The angle ranges in Table 3 were set using the optimization function of LightTools, based on the conditions in angle range (3). The optimization conditions were as follows: Number of rays traced: 100,000 rays Result output: 2-degree intervals Smoothing: 3 cells Analysis coordinate system: IES Type B Photoreceiver filter: Only rays that passed through the shapes of the front and back of the diffuser were tallied.

[0075] Under the conditions of each of Examples 24 to 31 and Comparative Examples 1 and 2, the angular intensity uniformity was calculated from the maximum and minimum values ​​of the radiation intensity (W / sr) based on the following formula: Angular intensity uniformity = ((minimum radiation intensity) / (maximum radiation intensity)) × 100% The minimum radiation intensity and maximum radiation intensity were the minimum and maximum values ​​of the radiation intensity when optimized within the angle ranges (1) to (3).

[0076] Fig. 20 shows a graph plotting the results of angular intensity uniformity for each of Examples 24 to 31 and Comparative Examples 1 and 2. The angle ranges (1) to (3) shown in Fig. 20 correspond to the angle ranges shown in Table 3. Fig. 20 shows that in all of the angle ranges (1) to (3), the angular intensity uniformity tends to increase when the deviation angle from perpendicular is less than 70 degrees, and that the angular intensity uniformity increases more significantly when the deviation angle from perpendicular is 40 degrees or less.

[0077] Fig. 21 shows heat maps for each of the angle ranges (1) to (3) for the diffuser plate of Example 28 (shift angle 40 degrees), and Fig. 22 shows heat maps for each of the angle ranges (1) to (3) for the diffuser plate of Example 29 (shift angle 50 degrees). From the heat maps for the angle range conditions shown in Fig. 21 and Fig. 22, it can be seen that the radiant intensity tends to be more uniform and the brightness higher when the shift angle from perpendicular in the lenticular lens is 40 degrees rather than 50 degrees.

[0078] 10, 10' Optical element 10a, 10'a Microlens 11a First main surface 11 First lenticular lens L １１ Central axis (first lenticular lens) 12a, 12'a Second principal surface 12 Second lenticular lens L １２ Central axis (second lenticular lens) 100 Head-up display device 101 Laser projector 102 Diffuser (optical element) 103 Primary mirror 104 Secondary mirror 105 Transmissive reflector

Claims

1. An optical element having opposing first and second principal surfaces, wherein the first principal surface has a first lenticular lens, and the second principal surface has a second lenticular lens, the long axis direction of the first lenticular lens is perpendicular to the long axis direction of the second lenticular lens or intersects with the long axis direction of the second lenticular lens at an angle within a range of ±70 degrees from the perpendicular direction, and the curved shape of the first lenticular lens is expressed by the following formula (1): [In formula (1), cx represents a curvature [1 / mm], x represents a distance [mm] from the central axis of the first lenticular lens in the X direction, and kx represents a conic constant, which is equal to or greater than −2.4 and equal to or less than −0.6.] An optical element in which the curved shape of the second lenticular lens is expressed by the following formula (2): [In formula (2), cy represents a curvature [1 / mm], y represents a distance [mm] from the central axis of the second lenticular lens in the Y direction, and ky represents a conic constant, which is −0.9 or more and −0.5 or less.] 2. The optical element according to claim 1, wherein said kx is not less than -2.0 and not more than -1.

0.

3. The optical element according to claim 1, wherein said ky is not less than -0.8 and not more than -0.

6.

4. The optical element according to claim 1, wherein said optical element is made of a resin having a refractive index of 1.35 or more and 1.7 or less.

5. The optical element according to claim 1, wherein said optical element has an angular intensity uniformity of 60% or greater.

6. The optical element according to claim 1, wherein the optical element has a brightness of 80% or more of the maximum brightness over an angular range of 90% of the full width at half maximum (FWHM).

7. The optical element according to claim 1, wherein said optical element is a diffuser plate.

8. The optical element according to claim 1, wherein the curved surface shape of the first lenticular lens is further adjusted according to the following formula (3): [In formula (3), A represents a symmetric coefficient. B represents an asymmetric coefficient, which is −1.] 9. The optical element according to claim 1, wherein the curved surface shape of the second lenticular lens is further adjusted according to the following formula (4): [In formula (4), A represents a symmetric coefficient. B represents an asymmetric coefficient, which is equal to 1.] 10. The optical element according to claim 7, wherein the diffusion plate is used in a head-up display device.

11. The optical element according to claim 10, wherein the image forming device in the head-up display device is a laser projector that uses laser light as a light source.

12. An optical element according to any one of claims 1 to 11, wherein the diffusion angle of light incident on the first main surface and exiting from the second main surface is in the range of 0 to 26 degrees in the horizontal direction H and 0 to 12 degrees in the vertical direction V.

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