Optical element

Abstract

A microlens array (1100) equipped with a plurality of microlenses and formed as the only component comprising a collimator lens (1200), wherein each microlens has: N sides (S) of a convex polygon, a microlens vertex (T) located from a face of the convex polygon, and N curved surfaces (CS) separated by lines connecting the microlens vertex (T) and the N vertices of the convex polygon, and where the straight line passing through the microlens vertex (T) and perpendicular to the face of the convex polygon is defined as the z-axis, the intersection point between the z-axis and the face of the convex polygon is defined as the origin (O), and the straight line in the face of the convex polygon passing through the origin (O) and perpendicular to a side (S) of the convex polygon is defined as the x-axis, the z-coordinate of the curved surface corresponding to the side (S) is represented by z = f ( x ) , where t is a distance from the origin (O) to the side (S), n is a refractive index of a microlens material, A is a non-negative constant, C is a positive constant, and g(x) is defined by g ( x ) = − x | x | ⋅ C x 2 + A n 1 + ( C x 2 + A ) 2 − 1 where each microlens is designed in such a way that g ( x ) − 0.035 ≤ df ( x ) dx ≤ g ( x ) + 0.035 for 0.25·t < |x| ≤ t.

Description

Technical field

[0001] The present invention relates to a microlens array for forming an illuminated area with a uniform illuminance distribution. background

[0002] Optical elements for modifying the light distribution from a light source, creating an illuminated area used as alignment marks or indicators for visual recognition in measuring devices, medical instruments, industrial robots, or similar applications, have been developed. Among these optical elements are those in which subdivided parts of a cylindrical lens are combined (Patent Document 1), and those shaped as a pyramid with lateral faces that have a cylindrical envelope (Patent Document 2).

[0003] However, an optical element designed in such a way that the distribution of light in an illuminated area formed on a surface becomes uniform to a satisfactory degree has not been conventionally developed. State-of-the-art documents, patent documents Patent document 1: JP 11 - 133 209 A Patent document 2: JP 2003 - 504 217 A (WO 01 / 03 892 A1)

[0004] Other exemplary microlens arrays are known from publications US 6 816 311 B1, US 2006 / 0 250 707 A1 and JP 2000 - 56 101 A. Brief description of the invention; Problem to be solved by the invention

[0005] Accordingly, there is a need for an optical element designed in such a way that the distribution of light in an illuminated area formed on a surface becomes sufficiently uniform. Measures to solve the problem

[0006] According to the present invention, a microlens array as defined in claim 1 is provided. Exemplary embodiments of the present invention are defined in the dependent claims.

[0007] An optical element according to one aspect of the present disclosure is equipped with a plurality of microlenses. Each microlens has N sides of a convex polygon, a microlens vertex located a distance from a plane of the convex polygon, and N curved surfaces subdivided by lines connecting the microlens vertex and the N vertices of the convex polygon. If the straight line passing through the microlens vertex and perpendicular to the plane is defined as the z-axis, the intersection point between the z-axis and the plane is defined as the origin, and the straight line in the plane passing through the origin and perpendicular to a side is defined as the x-axis, then a z-coordinate of the curved surface corresponding to the side is represented by z=f(x), where a distance from the origin to the side is represented as t, and a virtual curved surface at 0 ≤ |x| ≤ t is represented by z=F(x), where n is a refractive index of a microlens material, A represents a non-negative constant, C represents a positive constant, and g(x) is defined by g(x)=dF(x)dx=−x|x|⋅Cx2+An1+(Cx2+A)2−1, where each microlens is designed in such a way that g(x)−0.035≤df(x)dx≤g(x)+0.035 This condition is met for 0.25·t < |x| ≤ t.

[0008] Each curved surface of each microlens of the optical element according to the present aspect is formed such that the difference between a gradient of the curved surface of each microlens and a virtual curved surface, which renders a uniform illuminance distribution in an illuminated region formed by a uniform beam of parallel rays incident at a right angle to the plane of the polygon of each microlens on a plane perpendicular to the parallel beam, is 0.035 or less than 0.25·t < |x| ≤ t. Accordingly, an illuminance distribution in an illuminated region formed by a uniform beam of parallel rays incident at a right angle to the plane of the polygon of each microlens of the optical element according to the present aspect, on a plane perpendicular to the beam of parallel rays, becomes substantially uniform.Even if variations in the intensity of a bundle of parallel rays exist, the illuminance distribution in an illuminated area formed by the entire microlens array will be essentially uniform because the microlens array comprises a plurality of microlenses. Furthermore, because the region of any curved surface where 0.25·t < |x| ≤ t is satisfied is small, the gradient is not significant there.

[0009] In the optical element according to the first embodiment of the present disclosure, where an acute angle of the direction in which a ray, which strikes the plane perpendicularly and moves in the z-axis direction, moves after exiting the virtual curved surface is represented with the z-axis by θ, θ at x=0 is represented by θc, and θ at |x|=t is represented by θe, the following relationships apply. A=tan θc C=tan θe−tan θct2

[0010] In the optical element according to the second embodiment of the present disclosure, z=F(x) monotonically decreases for |x| within 0 ≤ |x| ≤ t.

[0011] In the optical element according to the third embodiment of the present disclosure, the convex polygon is a regular polygon.

[0012] In the optical element according to the fourth embodiment of the present disclosure, the z-axis is defined such that it passes through the center of the regular polygon.

[0013] In the optical element according to the fifth embodiment of the present disclosure, N is 3, 4 or 6.

[0014] In the optical element according to the sixth embodiment of the present disclosure, each microlens is formed such that adjacent curved surfaces have a different shape.

[0015] For example, if curved surfaces corresponding to adjacent sides in the quadrilateral have different shapes, an illuminated area in the shape of a cross with a substantially uniform illuminance distribution may be formed, and the length of the arms of the cross in the direction of one of the adjacent sides will differ from that in the direction of the other of the adjacent sides.

[0016] The optical element according to the sixth embodiment of the present disclosure is integrated with a collimator lens to form a single component.

[0017] According to the present embodiment, a compact optical element can be achieved at a low price. Brief description of the drawings Fig. Figure 1 shows a microlens array, which is an optical element according to an embodiment of the present invention; Fig. Figure 2 shows a microlens, which is a component of the microlens array located in Fig. 1 is shown; Fig. Figure 3 shows an optical system comprising a light source, a collimator lens and a microlens array; Fig. 4 is the first drawing to illustrate the function of the microlens; Fig. 5 is the second drawing to illustrate the function of the microlens; Fig. Figure 6 shows an illuminance distribution in an illuminated area formed by the microlens array from Example 1 on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 7 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array from Example 1 on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 8 shows the gradient of the curved surface of the microlens from Example 1; Fig. Figure 9 shows an illuminance distribution in an illuminated area formed by the microlens array of the comparison example on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 10 shows the illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array of the comparison example on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 11 shows the gradient of the curved surface of the microlens of the comparison example; Fig. Figure 12 shows an illuminance distribution in an illuminated area formed by the microlens array from Example 2 on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 13 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array from Example 2 on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 14 shows the gradient of the curved surface of the microlens from Example 2; Fig. Figure 15 shows the microlens array from Example 3; Fig. Figure 16 shows an illuminance distribution in an illuminated area formed by the microlens array from Example 3 on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 17 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array from Example 2 on a plane which is 3.0 meters away from the center A1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 18 shows the gradient of the curved surface of the microlens of example 3; Fig. Figure 19 shows an optical system from Example 4; Fig. Figure 20 shows the shape of the optical element from Example 4; Fig. Figure 21 shows an illuminance distribution in an illuminated area formed by the microlens array from Example 4 on a plane which is 3.0 meters away from the center B1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 22 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array from Example 4 on a plane which is 3.0 meters away from the center B1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 23 shows an illuminance distribution in the perpendicular direction of an illuminated area formed by the microlens array from Example 4 on a plane which is 3.0 meters away from the center B1 of the light source in the direction of the optical axis, and which is arranged perpendicular to the optical axis; Fig. Figure 24 shows the gradient in the horizontal direction of the curved surface of the microlens from Example 4; and Fig. Figure 25 shows the gradient in the vertical direction of the curved surface of the microlens from Example 4. Description of the exemplary implementations

[0018] Fig. Figure 1 shows a microlens array, that is, an optical element according to an embodiment of the present invention. The microlens array comprises a plurality of microlenses of the same shape, which are arranged on a plane.

[0019] Fig. Figure 2 shows a microlens, which is a component of the microlens array located in Fig. Figure 1 shows the microlens having the microlens vertex T and four curved surfaces CS, which are defined by four sides S of a quadrilateral and curved lines connecting the microlens vertex T and the four vertices of the quadrilateral.

[0020] Fig. Figure 3 shows an optical system comprising a light source 310, a collimator lens 200, and a microlens array 100. Fig. Figure 3 shows the optical axis of the optical system, represented by a dashed line. The optical axis is defined such that it passes through the center point A1 of the emitting surface of the light source 310, is aligned with the principal axis of the collimator lens 200, and is orthogonal to the light source side surface of the microlens array 100. Light emitted by the light source 310 is converted by the collimator lens 200 into a beam of rays parallel to the optical axis and is shaped so that it strikes the light source side surface of the microlens array 100 perpendicularly. The beam of parallel rays entering the microlens array 100 is then directed by the microlenses in predetermined directions.

[0021] Fig. Figure 4 is the first diagram illustrating the function of the microlens. The base B of the microlens is parallel to the four sides S of the quadrilateral. The straight line perpendicular to base B and passing through the vertex T of the microlens is defined as the z-axis. The intersection of the z-axis with the quadrilateral is defined as the origin O, and in the plane containing the quadrilateral, the straight line passing through the origin O is parallel to two sides of the quadrilateral and orthogonal to the other two sides, defined as the x-axis. Fig. Figure 4 shows a cross-section of the microlens, which has the z-axis and the x-axis. A curved surface CS, which has one side of the quadrilateral perpendicular to the x-axis, is shaped such that the z-coordinate of the curved surface is solely a function of the x-coordinate. That is, the curved surface CS is represented by the following expression. z=f(x)

[0022] In cross-section, which in Fig. As shown in Figure 4, a ray R, striking the base B of the microlens perpendicularly, strikes the curved surface at an angle φ, and its exit direction is at an angle θ with respect to the z-axis. That is, the angle θ is an acute angle between the direction of propagation of the ray emanating from the curved surface CS and the z-axis. With respect to the angle θ and the angle of incidence φ, an angle measured clockwise from the z-axis is defined as positive, and an angle measured counterclockwise from the z-axis is defined as negative. As is clear in Fig. As shown in Figure 4, the angle θ is positive and the angle of incidence φ is negative in the region where x is positive, and the angle θ is negative and the angle of incidence φ is positive in the region where x is negative. The bundle of parallel rays striking the ground B at a right angle is transformed into a bundle of rays that diverges only in a zx-plane after passing through the curved surface CS, which has one side of the quadrilateral perpendicular to the x-axis. Accordingly, the shape of the illuminated region formed on a plane perpendicular to the z-axis is a line of predetermined length in the x-axis direction.Furthermore, the shape of the illuminated area, formed on a plane perpendicular to the z-axis by means of a bundle of parallel rays that strikes the ground B at a right angle and passes through a curved surface CS, which has one side of the quadrilateral parallel to the x-axis, is a line of predetermined length in the direction perpendicular to the x-axis. Accordingly, the illuminated area formed on a plane perpendicular to the z-axis is defined as a line of predetermined length in the x-axis direction and in the direction perpendicular to the x-axis.

[0023] Fig. Figure 5 is the second drawing illustrating the function of the microlens. The right part of Fig. Figure 5 shows a cross-section of the microlens, where the cross-section has the z-axis and the x-axis. The left part of Fig. Figure 5 shows a top view of the microlens. Two rays striking the base B of the microlens at right angles are represented by R1 and R2. Inside the microlens, the x-coordinate of ray R1 is x1, and the x-coordinate of ray R2 is x2. The ratio x1 < x2 is satisfied. Ray R1 moves in the direction forming an angle θ1 with the z-axis, and ray R2 moves in the direction forming an angle θ2 with the z-axis.

[0024] As in Fig. Figure 5 shows an infinitesimal region near the coordinate x through which a light stream passes, represented by the following expression. ΔS=2Δx⋅x

[0025] Accordingly, assuming that the luminous flux density of an incoming luminous flux is constant, the luminous flux passing through ΔS1 i near x = x1, which is closer to the center of the microlens and is refracted in the direction forming an angle θ1 with the z-axis, is smaller than the luminous flux passing through ΔS2 near x = x2. Provided that a distance L from the microlens to a plane perpendicular to the z-axis, on which an illuminance distribution is estimated, is significantly greater than the size of the microlens, a ray refracted in the direction forming an angle θ1 with the z-axis is considered to be projected onto a position of the plane where the position Ltanθ is a distance from the optical axis. Accordingly, a condition for uniform illumination is represented by the following expression: ddx(tan θ)=2C⋅x where C is a positive constant.

[0026] A virtual curved surface of the microlens that makes illumination uniform on a plane sufficiently far from the microlens and perpendicular to the z-axis is represented by the following expression: z=F(x)

[0027] If the angle of inclination of z = F(x) with respect to the x-axis is represented as φ, the following expression applies: dF(x)dx=tan ϕ

[0028] If the refractive index of the microlens is represented as n, the following expression applies according to Snell's law: sin(−ϕ+θ)=nsin(−ϕ)

[0029] To achieve uniform lighting, expressions (1) to (3) should be satisfied simultaneously. A large number of variables will be reduced below. The following expression can be obtained by taking a definite integral of expression (1): tan θ=Cx2+A=X where A is a non-negative constant.

[0030] Assuming that the distance from the origin to a side of the quadrilateral is t, the following expression can be obtained by substituting x=0 and x=t into expression (4). tanθT=A tanθS=Ct2+A where θτ is an acute angle between the direction in which a ray leaving the curved surface CS at the vertex of the microlens moves, and the z-axis, and θ S is an acute angle between the direction in which a ray leaving the curved surface CS on one side of the quadrilateral moves and the z-axis. The following expression results from the expressions described above: C=tanθS−tanθrt2

[0031] The following expressions can be obtained by modifying expression (4). In the case of X ≥ 0 sin θ=X21+X2

[0032] In the case of X < 0 sin θ=X21+X2 cos θ=11+X2

[0033] On the other hand, the following expression can be obtained by modifying expression (3). sinθcosϕ−cosθsinϕ=−nsinϕ

[0034] Furthermore, the following expression can be obtained: tanϕ=−sinθn−cosθ

[0035] The following expressions can be obtained by ordering expressions (2), (5a), (6) and (7).

[0036] In the case of X ≥ 0 dF(x)dx=Xn1+X2−1=−Cx2+An1+(Cx2+A)2−1

[0037] Furthermore, the following expressions can be obtained by arranging expressions (2), (5b), (6) and (7).

[0038] In the case of X < 0 dF(x)dx=Xn1+X2−1=Cx2+An1+(Cx2+A)2−1

[0039] Accordingly, a microlens with a cross-section satisfying expressions (8a) and (8b) makes illumination uniform on a surface that is sufficiently far from the microlens and perpendicular to the z-axis.

[0040] Even if uniformity of luminous flux density of an incoming radiant flux is not guaranteed, the entire illumination distribution, which is formed as a combination of distributions caused by a plurality of microlenses, will be made uniform, provided that the number of microlenses is large enough.

[0041] Expressions (8a) and (8b) can be represented by the following expression: g(x)=dF(x)dx=−x|n|⋅Cx2+An1+(Cx2+A)2−1

[0042] In general, the condition that a curved surface f(x) of a microlens achieves such a uniform illumination distribution as is sufficient for various applications can be represented by the following expression. g(x)−0.035≤df(x)dx≤g(x)+0.035

[0043] Furthermore, since the contribution to an illumination distribution is approximately proportional to an area of ​​the optical surface, the overall illumination distribution is not significantly affected, and the function will not deteriorate, even if expression (10) is not satisfied in a limited region near the optical axis. For example, the area of ​​the region where the distance t from the optical axis is 25% or less covers approximately 6%, and therefore an almost uniform radial illumination distribution can be obtained even if expression (10) is not satisfied in this case but is satisfied in the other expression (10).

[0044] Examples and a comparative example are described below. Optical systems of examples 1-2 and comparative example

[0045] The optical systems of examples 1-2 and the comparison example are those in Fig. Figure 3 shows the specifications of the 200 collimator lenses used in Examples 1-2 and the comparison example. These specifications are described below. Position (relative to the center of the light source): Z = 30 [mm] Material: BK7 (refractive index: n = 1.519) Thickness: 4.0 [mm] Radius of curvature at the center of the entrance surface: 130.7 [mm] Radius of curvature at the center of the exit surface: -19.38 [mm]

[0046] The position of the collimator lens 200 means the position of the intersection point between the entrance surface of the collimator lens 200 and the optical axis, that is, the position that is in Fig. 3 is labelled A2. Z = 30 [mm] means that the distance between the center point A1 of the light source and A2 is 30 millimeters. Thickness of the collimator lens 200 means the center thickness along the optical axis.

[0047] The specifications of the microlenses used in Examples 1-2 and the comparison example are common to all of them, except for the shape of the curved surface CS, and are described below. That is to say, the microlens arrays of Example 2 and the comparison example are essentially the same as the microlens array from Example 1, which is shown in Example 1. Position (relative to the center of the light source): Z = 40 [mm] Material: Polycarbonate (refractive index: n = 1.590) Thickness: 1.0 [mm] Polygon: Square Size of the square: Square with sides, each 2.0 millimeters long. The position of the microlens array 100 means the position of the intersection point between the surface without lenses, that is, the base of the microlens array 100, and the optical axis, that is, the position that is in Fig. 3 is marked with A3. Z = 40 [mm] means that the distance between the center A1 of the light source and A3 is 40 millimeters. The thickness of the microlens array 100 means the distance from the bottom to the vertex of a microlens, the distance from B to T in Fig. 4. Microlens from Example 1

[0048] The curved surface of the microlens from Example 1 can be represented by the following expression: z=f(x)=∑n=110(x|x|)nanxn

[0049] Table 1 shows coefficients of expression (11), which represents the curved surface of the microlens from Example 1. Table 1 a 1 a 2 a 3 a 4 a 5 -0,050 -0,003 -0,406 0,044 -0,185 a 6 a 7 a 8 a 9 a 10 0,396 -0,159 0,000 0,000 0,000

[0050] Fig. Figure 6 shows an illuminance distribution in an illuminated area formed by the microlens array from Example 1 on a surface located 3.0 meters away from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. Fig. Figure 3, which shows Example 1, represents the optical axis in the horizontal direction. Each microlens is arranged such that two sides of the microlens's quadrilateral face horizontally and the other two sides face vertically. Accordingly, as shown in Fig. Figure 6 shows an illuminated area with a lighting distribution shaped like lines of predetermined length in the horizontal and vertical directions.

[0051] Fig. Figure 7 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array from Example 1 on a surface located 3.0 meters from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. The horizontal axis of Fig. 7 represents a position on the surface in the horizontal direction. The position where the optical axis intersects the plane corresponds to the position of the coordinate 0,0 on the horizontal axis. The vertical axis of Fig. 7 represents a relative illuminance. A relative illuminance of 1 corresponds to the maximum value.

[0052] Fig. Figure 8 shows the gradient of the curved surface of the microlens from Example 1. The horizontal axis of Fig. 8 represents an x-axis coordinate of the microlens, and the vertical axis of Fig. Figure 8 represents the gradient of the curved surface of the microlens Example 1 df(x)dx and the gradient of the virtual curved surface g(x)=dF(x)dx which makes the illuminance distribution uniform. The gradient of the curved surface of the microlens from Example 1 satisfies expression (10) over the entire range of x. Microlens of the comparison example

[0053] The microlens of the comparison example is shaped as a circular segment, and the radius of curvature at the center is 1.66 millimeters.

[0054] Fig. Figure 9 shows an illuminance distribution in an illuminated area formed by the microlens array of the comparison example on a surface located 3.0 meters away from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. Fig. Figure 3, which shows a comparative example, has the optical axis in the horizontal direction. Each microlens is arranged such that two sides of the microlens's quadrilateral face horizontally and the other two sides face vertically. Accordingly, as shown in Fig. Figure 9 shows an illuminated area having a lighting distribution shaped like lines of predetermined length in the horizontal and vertical directions.

[0055] Fig. Figure 10 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens of a comparative example on a surface located 3.0 meters away from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. The horizontal axis of Fig. 10 represents a position on the surface in the horizontal direction. The position where the optical axis intersects the surface corresponds to the position of the coordinate 0,0 on the horizontal axis. The vertical axis of Fig. 10 represents a relative illuminance. A relative illuminance of 1 corresponds to the maximum value.

[0056] Fig. Figure 11 shows the gradient of the curved surface of the microlens in the comparison example. The horizontal axis of Fig. 11 represents the x-axis coordinate of the microlens, and the vertical axis of Fig. 11 represents the gradient of the curved surface of the microlens of the comparison example. df(x)dx and the gradient of the virtual curved surface g(x)=dF(x)dx which makes an illuminance distribution uniform. The gradient of the curved surface of the microlens in the comparison example does not satisfy expression (10) in 70% or more of the entire range of x. Microlens from example 2

[0057] The curved surface of the microlens from Example 2 can be represented by the following expression: z=f(x)=∑n=110(x|x|)nanxn

[0058] Table 2 shows coefficients of expression (11) which represent the curved surface of the microlens of Example 2. Table 2 a 1 a 2 a 3 a 4 a 5 0,000 -0,600 1,912 -4,604 5,088 a 6 a 7 a 8 a 9 a 10 -2,754 0,604 0,000 0,000 0,000

[0059] Fig. Figure 12 shows an illuminance distribution in an illuminated area formed by the microlens array of Example 2 on a surface located 3.0 meters away from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. Fig. 3, which shows Example 2, is the optical axis in the horizontal direction. Each microlens is arranged such that two sides of the microlens's quadrilateral are in the horizontal direction and the other two sides are in the vertical direction. Accordingly, as shown in Fig. Figure 12 shows an illuminated area which has a lighting distribution shaped like lines of a predetermined length in the horizontal direction and in the vertical direction.

[0060] Fig. Figure 13 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens of Example 2 on a surface located 3.0 meters from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. The horizontal axis of Fig. 13 represents a position on the surface in the horizontal direction. The position where the optical axis intersects the plane corresponds to the position of the coordinate 0,0 on the horizontal axis. The vertical axis of Fig. 13 represents a relative illuminance. A relative illuminance of 1 corresponds to the maximum value.

[0061] Fig. Figure 14 shows the gradient of the curved surface of the microlens from Example 2. The horizontal axis of Fig. 14 represents a coordinate of the x-axis of the microlens, and the vertical axis of Fig. 14 represents the gradient of the curved surface of the microlens from Example 2 df(x)dx and the gradient of the virtual curved surface g(x)=dF(x)dx which makes the illuminance distribution uniform. The gradient of the curved surface of the microlens from Example 2 satisfies expression (10), except for the region where x < 0.1. Optical system and microlens from Example 3

[0062] The optical system of Example 3 is the one which is in Fig. Figure 3 is shown. The specifications of the collimator lens 200 used in Example 3 are described below. Position (relative to the center of the light source): Z = 30 [mm] Material: BK7 (refractive index: n = 1.519) Thickness: 4.0 [mm] Radius of curvature at the center of the entrance surface: 130.7 [mm] Radius of curvature at the center of the exit surface: -19.38 [mm]

[0063] The position of the collimator lens 200 means the position of the intersection point between the entrance surface of the collimator lens 200 and the optical axis, that is, the position that is in Fig. 3 is marked with A2. Z = 30 [mm] means that the distance between the center point A1 of the light source and A2 is 30 millimeters. Thickness of the collimator lens 200 means the center thickness along the optical axis.

[0064] Fig. Figure 15 shows the microlens array from Example 3.

[0065] The specifications of the microlenses used in Example 3 are described below. Position (relative to the center of the light source): Z = 40 [mm] Material: Polycarbonate (refractive index: n = 1.590) Thickness: 1.0 [mm] Polygon: Regular hexagon Size of the regular hexagon: Regular hexagon in which the distance between opposite sides (horizontal length) is 2.0 millimeters and the distance between opposite vertices (vertical length) is 2.309 millimeters.

[0066] The position of the microlens array 100 means the position of the intersection point between the surface without lenses, that is, the base of the microlens array 100, and the optical axis, that is, the position that is in Fig. 3 is marked with A3. Z = 40 [mm] means that the distance between the center A1 of the light source and A3 is 40 millimeters. The thickness of the microlens array, 100, means the distance from the base to the apex of the microlens, that is, the distance from B to T. Fig. 4.

[0067] The curved surface of the microlens from Example 3 can be represented by the following expression: z=f(x)=∑n=110(x|x|)nanxn

[0068] Table 3 shows coefficients of expression (11) which represent the curved surface of the microlens of Example 3. Table 3 a 1 a 2 a 3 a 4 a 5 -0,100 -0,002 -0,210 0,014 -0,035 a 6 a 7 a 8 a 9 a 10 0,066 0,000 0,000 0,000 0,000

[0069] Fig. Figure 16 shows an illuminance distribution in an illuminated area formed by the microlens array of Example 3 on a surface located 3.0 meters away from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. Fig. Figure 3, which shows Example 3, represents the optical axis in the horizontal direction. The microlens is positioned such that two sides of the regular hexagon of the microlens are aligned horizontally. Accordingly, as shown in Fig. Figure 16 shows an illuminated area which has a lighting distribution shaped like six lines.

[0070] Fig. Figure 17 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens of Example 3 on a surface located 3.0 meters from the center A1 of the light source in the direction of the optical axis and perpendicular to the optical axis. The horizontal axis of Fig. 17 represents a position on the plane in the horizontal direction. The position where the optical axis intersects the plane corresponds to the position of the coordinate 0,0 on the horizontal axis. The vertical axis of Fig. 17 represents a relative illuminance. A relative illuminance of 1 corresponds to the maximum value.

[0071] Fig. Figure 18 shows the gradient of the curved surface of the microlens from Example 3. The horizontal axis of Fig. 18 represents the x-axis coordinate of the microlens, and the vertical axis of Fig. 18 represents the gradient of the curved surface of the microlens from Example 3 df(x)dx and the gradient of the virtual curved surface g(x)=dF(x)dx which makes the illuminance distribution uniform. The gradient of the curved surface of the microlens from Example 3 satisfies expression (10) over the entire range of x. However, in the range of 0.5 < x < 0.8, the gradient of the curved surface is essentially equal to the upper limit of expression (10). Optical system and optical element of Example 4

[0072] Fig. Figure 19 shows an optical system from Example 4. The optical system of Example 4 comprises a light source 320, a collimator lens 1200, and a microlens array 1100. The collimator lens 1200 and the microlens array 1100 are formed as a single component. The collimator lens 1200 has a transmitting surface 1201 and a reflecting surface 1203. Light rays emitted by the light source 320 and passing through the transmitting surface 1201 or being reflected by the reflecting surface 1203 form a bundle of parallel rays and enter the microlens array 1100. The arrangement is designed such that the principal axis of the collimator lens 1200 is aligned with the optical axis, and the optical axis passes through the center of the light source 320. Fig. 19 the optical axis is arranged in the horizontal direction.

[0073] Fig. Figure 20 shows the shape of the optical element of Example 4. The optical element of Example 4 comprises the collimator lens 1200 and the microlens array 1100 provided at the output side of the collimator lens 1200. The optical element is arranged such that two adjacent sides of the quadrilateral of each microlens are aligned horizontally and vertically, respectively. The material of the optical element is polycarbonate (refractive index: n = 1.590). The transmitting surface 1201 of the collimator lens 1200 is convex towards the light source side and is aspherical. If a distance from the optical axis is represented by r, the shape of the surface is defined by the following expression: z(r)=1R⋅r21+1−(1+k)1R2⋅r2

[0074] In this expression, z represents a distance from the vertex of the transmitting surface 1201, located on the optical axis, to a point on the surface in the z-axis direction, and r represents a distance from the optical axis to the point on the surface. The parameters defining the transmitting surface 1201 are described below. Position (relative to the center of the light source): z = 2.25 [mm] The transmitting area: R = 1.327 [mm] Conic constant: k = -2.527

[0075] The position of the transmitting surface 1201 of the collimator lens means the position of the intersection of the transmitting surface 1201 and the optical axis, that is, the position that is in Fig. 19 is marked with B2. The position of B2 is that of the vertex of the transmitting surface 1201 described above. Z = 2.25 [mm] means that the distance between the center point B1 of the light source and B2 is 2.25 millimeters.

[0076] The reflecting surface 1203 of the collimator lens has a shape that is convex towards the light source side and is expressed by terms of even order. If a distance from the optical axis is represented by r, the shape of the surface is defined by the following expression. z(r)=a2r2+a4r4+a6r6

[0077] In this expression, z represents a distance from a point z(0) located on the optical axis to a point on the surface in the z-axis direction, and r represents a distance from the optical axis to the point on the surface. The point z(0) is described later. The parameters that define the reflecting surface 1203 of the collimator lens are described below. Position (relative to the center of the light source): z = -0.455 [mm] Aspheric coefficient a2: 3.44E-1 Aspheric coefficient a4: -5.56E-3 Aspheric coefficient a6: 7.68E-5

[0078] The position of the reflecting surface 1203 of the collimator lens is the position on the optical axis corresponding to the value of z(0) in the expression described above, which represents the reflecting surface 1203. Z = -0.45 mm means that the position on the optical axis corresponding to the value of z(0) is on the opposite side of the center B1 of the light source from the microlens array 1100 and 0.455 millimeters away from the center B1 of the light source.

[0079] The parameters that define the microlens array are described below. Position (relative to the center of the light source): z = 6.0 [mm] Segment size: 2.0 (horizontal direction) x 1.5 (vertical direction) [mm] 2 ]

[0080] The position of the microlens array 1100 means the position of the intersection point between the surface without lenses, that is, the base of the microlens array 1100, and the optical axis, that is, the position that is in Fig. 19 is marked with B3. z = 6.0 [mm] means that the distance between the center point B1 of the light source and B3 is 6.0 millimeters. The thickness of the microlens array 1100 is 2.0 millimeters.

[0081] The curved surface of the microlens from Example 4 can be represented by the following expression: z=f(x)=∑n=110(x|x|)nanxn

[0082] Table 4 shows coefficients of expression (11), which represents the curved surface of the microlens of Example 4, arranged in the horizontal direction (the curved surface which has sides in the horizontal direction of the quadrilateral). Table 4 a 1 a 2 a 3 a 4 a 5 -0,100 0,002 -0,210 0,014 -0,035 a 6 a 7 a 8 a 9 a 10 0,066 -0,020 0,000 0,000 0,000

[0083] Table 5 shows coefficients of expression (11) which represents the curved surface of the microlens of Example 4, arranged in the vertical direction (the curved surface which has sides in the vertical direction of the quadrilateral). Table 5 a 1 a 2 a 3 a 4 a 5 -0,100 -0,001 -0,266 0,009 -0,023 a 6 a 7 a 8 a 9 a 10 0,077 -0,020 0,000 0,000 0,000

[0084] Fig. Figure 21 shows an illuminance distribution in an illuminated area formed by the microlens array of Example 4 on a surface located 3.0 meters from the center B1 of the light source in the direction of the optical axis and perpendicular to the optical axis. Each microlens is arranged such that two sides of the microlens's quadrilateral face horizontally and the other two sides face vertically. Accordingly, as shown in Figure 21, the illuminance distribution appears as follows: Fig. Figure 21 shows an illuminated area having a lighting distribution shaped like lines of predetermined length in the horizontal and vertical directions.

[0085] Fig. Figure 22 shows an illuminance distribution in the horizontal direction of an illuminated area formed by the microlens array of Example 4 on a surface located 3.0 meters from the center point B1 of the light source in the direction of the optical axis and perpendicular to the optical axis. The horizontal axis of Fig. 22 represents a position on the surface in the horizontal direction. The position where the optical axis intersects the surface corresponds to the position of coordinate 0,0 on the horizontal axis. The vertical axis of Fig. 22 represents a relative illuminance. A relative illuminance of 1 corresponds to the maximum value.

[0086] Fig. Figure 23 shows an illuminance distribution in the vertical direction of an illuminated area formed by the microlens array of Example 4 on a surface located 3.0 meters from the center point B1 of the light source in the direction of the optical axis and perpendicular to the optical axis. The horizontal axis of Fig. 23 represents a position on the surface in the vertical direction. The position where the optical axis intersects the surface corresponds to the position of coordinate 0,0 on the horizontal axis. The vertical axis of Fig. 23 represents a relative illuminance. A relative illuminance of 1 corresponds to the maximum value.

[0087] Fig. Figure 24 shows the gradient in the horizontal direction of the curved surface of the microlens from Example 4. The horizontal axis of Fig. 24 represents a coordinate of the x-axis of the microlens, and the vertical axis of Fig. 24 represents the gradient in the horizontal direction of the curved surface of the microlens from Example 4. dfH(x)dx and the gradient of the virtual curved surface g(x)=dF(x)dx which makes the illuminance distribution uniform. The gradient in the horizontal direction of the curved surface of the microlens from Example 4 satisfies expression (10) over the entire range of x.

[0088] Fig. Figure 25 shows the gradient in the vertical direction of the curved surface of the microlens from Example 4. The horizontal axis of Fig. 25 represents a coordinate of the x-axis of the microlens, and the vertical axis of Fig. 25 represents the gradient in the horizontal direction of the curved surface of the microlens from Example 4. dfH(x)dx and the gradient of the virtual curved surface g(x)=dF(x)dx which makes the illuminance distribution uniform. The gradient in the horizontal direction of the curved surface of the microlens from Example 4 satisfies expression (10) over the entire range of x. Comparison between the illuminance distributions of the examples and the illuminance distributions of the comparison example.

[0089] According to Fig. 7. In the illuminance distribution from Example 1, the relative illuminance is 0.95 or more in the range of 0.2 ≤ |x| ≤ 2.2. On the other hand, according to Fig. 10, in the illuminance distribution of the comparison example, the relative illuminance is less than 0.8, except in the range of 0.3 ≤|x| ≤ 1.2. Consequently, the illuminance distribution of example 1 is more uniform than that of the comparison example.

[0090] According to Fig. In the illuminance distribution from Example 2, the relative illuminance is 0.9 or more in the range of 0.3 ≤ |x| ≤ 2.0. On the other hand, according to Fig. 10, in the illuminance distribution of the comparison example, the relative illuminance is less than 0.8, except in the range of 0.3 ≤ |x| ≤ 1.2. Consequently, the illuminance distribution of Example 2 is more uniform than that of the comparison example. Although the gradient of the curved surface of the microlens of Example 2 does not satisfy expression (10) in the range of x < 0.1, as described above, a uniform illuminance distribution is achieved.

[0091] According to Fig. In the illuminance distribution from Example 3, the relative illuminance is 0.8 or more in the range of 0.2 ≤ |x| ≤ 1.3 and 0.6 or more in the range of 0.2 ≤ |x| ≤ 2.0. On the other hand, according to Fig. 10. In the illuminance distribution of the comparison example, the relative illuminance is less than 0.6 except in the range of 0.2 ≤ |x| ≤ 1.6. Consequently, the illuminance distribution of example 3 is more uniform than that of the comparison example. According to Fig. 18. The gradient of the curved surface of the microlens from Example 3 satisfies expression (10) over the entire range of x. However, in the range 0.5 < x < 0.8, the gradient of the curved surface is essentially equal to the upper limit of expression (10). If the difference between the gradient of the curved surface of the microlens and the gradient of the virtual curved surface becomes larger than in the present example, the superiority with respect to the uniformity of an illuminance distribution is lost.

[0092] According to Fig. 22 In the horizontal illuminance distribution of Example 4, the relative illuminance is 0.8 or more in the range of 0.3 ≤ |x| ≤ 1.1. According to Fig. 23. In the illuminance distribution in the vertical direction of Example 4, the relative illuminance is 0.8 or more in the range of 0.3 ≤ |x| ≤ 0.8. Although a direct comparison with a reference example equipped with a different optical system is not appropriate, an illuminated area with a relatively uniform illuminance distribution has been achieved.

Claims

[1] A microlens array (1100) equipped with a plurality of microlenses and comprising a collimator lens (1200) as the only component, wherein each microlens has: N sides (S) of a convex polygon, a microlens vertex (T) located from a face of the convex polygon, and N curved surfaces (CS) separated by lines connecting the microlens vertex (T) and the N vertices of the convex polygon, and where the straight line passing through the microlens vertex (T) and perpendicular to the face of the convex polygon is defined as the z-axis, the intersection point between the z-axis and the face of the convex polygon is defined as the origin (O), and the straight line in the face of the convex polygon passing through the origin (O) and perpendicular to a side (S) of the convex polygon is defined as the x-axis, the z-coordinate of the curved surface corresponding to the side (S) is represented by z=f(x), where t is a distance from the origin (O) to the side (S), n is a refractive index of a microlens material, A is a non-negative constant, C is a positive constant, and g(x) is defined by g(x)=−x|x|⋅Cx2+An1+(Cx2+A)2−1 where each microlens is designed in such a way that g(x)−0.035≤df(x)dx≤g(x)+0.035 for 0.25·t < |x| ≤ t. [2] A microlens array (1100) according to claim 1, wherein the convex polygon is a regular polygon. [3] A microlens array (1100) according to claim 2, wherein the z-axis is defined such that it passes through the center of the regular polygon. [4] A microlens array (1100) according to any one of claims 1 to 3, wherein N is 3, 4 or 6. [5] A microlens array (1100) according to any one of claims 1 to 4, wherein each microlens is formed such that adjacent curved surfaces (CS) have a different shape. [6] A microlens array (1100) according to claim 1, wherein the curved surface (CS) of the microlens is represented by z=f(x)=∑n=110(x|x|)nanxn where n represents a positive integer and a n represents a constant.

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