Diffusion element and optical system including the diffusion element

Abstract

The present invention provides a diffusion element and an optical system including the diffusion element that can efficiently realize diffused light with a diffusion angle greater than 140 degrees in full width at half maximum. [Solution] The diffusion element has a plurality of microlenses, the curved surface of each microlens is continuous and smooth except for the boundary, and in a cross section perpendicular to the plane that includes a line passing through the projection point of the vertex of the microlens onto the plane and the distance between the two intersection points with the periphery of the base surface is maximized, the following equation is satisfied, where x' is the coordinate along the line, z' is the coordinate of the curved surface in the direction perpendicular to the plane, d is the maximum value of the first derivative of z' with respect to x', D0 is the value at the x' coordinate of the center of the absolute value of the second derivative of z' with respect to x', and D is the value at the x' coordinate of the end of the diagonal. TIFF2026108780000025.tif2241

Description

Technical Field

[0001] The present invention relates to a diffusion element and an optical system including the diffusion element.

Background Art

[0002] For example, there is a need for a diffusion element that can realize diffused light with a wide diffusion angle, such as diffused light with a diffusion angle of 140 degrees or more in terms of full width at half maximum. Patent Document 1 discloses a diffusion element that can realize diffused light with a relatively wide diffusion angle. However, the diffusion angle in terms of full width at half maximum is 90 degrees, and diffused light with a sufficiently wide diffusion angle has not been realized. Patent Document 2 discloses a diffusion element provided with a microlens array that can realize diffused light with a diffusion angle of 140 degrees in terms of full width at half maximum. However, the cross-sectional shape of the microlenses of the above-mentioned diffusion element is represented by a quadratic function, and considering Fresnel reflection, the luminous intensity cannot be sufficiently increased at a wide diffusion angle. Further, in the optical system disclosed in Patent Document 2, the microlens array is arranged on the main slope side of the diffusion element, and it is considered that the efficiency is lowered because each of the plurality of microlenses shields the emitted light of other microlenses.

[0003] As described above, a diffusion element and an optical system including the diffusion element that can realize diffused light with a diffusion angle of more than 140 degrees in terms of full width at half maximum with high efficiency have not been developed. Therefore, there is a need for a diffusion element and an optical system including the diffusion element that can realize diffused light with a diffusion angle of more than 140 degrees in terms of full width at half maximum with high efficiency.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] The technical problem of the present invention is to provide a diffusion element and an optical system including a diffusion element that can efficiently realize diffused light with a diffusion angle greater than 140 degrees in full width at half maximum. [Means for solving the problem]

[0006] A first aspect of the present invention provides a diffusion element comprising a microlens array including a plurality of microlenses whose bases are arranged on a plane. The curved surface of each microlens is continuous and smooth except for the boundary, and in each microlens, in a cross section perpendicular to the plane that includes a line passing through the projection point of the vertex of the microlens onto the plane and maximizing the distance between two intersection points with the periphery of the base, the coordinate along the line is x', the coordinate of the curved surface in the direction perpendicular to the plane is z', the maximum value of the first derivative of z' with respect to x' is d, the value at the x' coordinate of the center of the absolute value of the second derivative of z' with respect to x' is D0, and the value at the x' coordinate of the end of the diagonal is D.

number

number

[0007] The shape of the microlens of the diffusion element in this embodiment is configured to sufficiently enlarge the luminosity cloth over a wide diffusion angle. Therefore, the optical system including the light source and the diffusion element in this embodiment can realize diffused light with a diffusion angle of full width at half maximum greater than 140 degrees.

[0008] A diffusion element according to a first embodiment of a first aspect of the present invention is a diffusion element comprising a microlens array including a plurality of microlenses of the same shape, each having a congruent quadrilateral or congruent regular hexagon as its base, arranged without gaps on a plane. The curved surface of each microlens is continuous and smooth except for the boundary, and the projection points of the vertices of the microlens onto the plane coincide with the intersection of the diagonals of the quadrilateral or regular hexagon, and in a cross section perpendicular to the plane that includes the longest diagonal, the coordinate along the diagonal is x', the coordinate of the curved surface in the direction perpendicular to the plane is z', the maximum value of the first derivative of z' with respect to x' is d, the value at the x' coordinate of the center of the absolute value of the second derivative of z' with respect to x' is D0, and the value at the x' coordinate of the end of the diagonal is D.

number

number

[0009] In this embodiment, since microlenses of the same shape are arranged without gaps on a plane, a more favorable distribution of diffused light can be obtained. The quadrilateral may be a right quadrilateral, a rhombus, or a parallelogram. A regular hexagon can be replaced with a hexagon in which three pairs of opposite sides are parallel to each other (a modified parallel hexagon).

[0010] In the diffusion element of the second embodiment of the first aspect of the present invention, the curved surface is axially symmetric about an axis passing through the projection point and perpendicular to the plane.

[0011] In each microlens, the reference radius is the radius of the circle formed by the intersection of the curved surface and the plane, with the projection point as the center. Preferably, the bottom surface of each microlens includes a circular region with a radius of 50% of the reference radius, with the projection point as the center. More preferably, the bottom surface of each microlens includes a circular region with a radius of 70% of the reference radius, with the projection point as the center. Even more preferably, the bottom surface of each microlens includes a circular region with a radius of 80% of the reference radius, with the projection point as the center.

[0012] In the diffusion element of the third embodiment of the first aspect of the present invention, for each microlens

Number

[0013] Diffused light with a diffusion angle having a full width at half maximum greater than 150 degrees can be realized by an optical system including a light source and the diffusion element of the present embodiment.

[0014] In the diffusion element of the fourth embodiment of the first aspect of the present invention, for each microlens

Number

[0019] According to this embodiment, interference between the tool used to process the mold for the diffusion element and the mold can be avoided, and sufficient optical performance of the microlens can be obtained.

[0020] In a diffusion element according to the ninth embodiment of the first aspect of the present invention, the surface opposite to the surface equipped with microlenses is a convex surface, and the absolute value of the radius of curvature of the convex surface is 100 times or more R, where R is the absolute value of the radius of curvature at the vertex of the curved surface of each microlens.

[0021] The efficiency of the optical system can be increased by setting the absolute value of the radius of curvature of the convex surface to an appropriate value of 100 times or more R.

[0022] An optical system according to a second aspect of the present invention includes any of the above-described diffusion elements and a light source.

[0023] The optical system of this embodiment can realize diffused light with a sufficiently large diffusion angle.

[0024] In the optical system of the first embodiment of a second aspect of the present invention, the microlens array is located on the side of the diffusion element facing the light source.

[0025] In the optical system of this embodiment, the efficiency of the optical system is relatively high because, unlike in the case of an optical system where the microlens array is a diffusing element and is located on the opposite side from the light source, each of the multiple microlenses does not block the light emitted by the other microlenses.

[0026] In the optical system of the first embodiment of the second aspect of the present invention, the light source is a divergent light source. [Brief explanation of the drawing]

[0027] [Figure 1] This is a side view (yz plane) of the diffusion element in Example 1. [Figure 2] This is a perspective view of the microlens of the diffusion element in Example 1. [Figure 3] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 1. [Figure 4] This is a side view (yz plane) of the microlens of the diffusion element in Example 1. [Figure 5] This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base of a microlens, where x' is the coordinate along the diagonal passing through the center of the square base of the microlens, and z' is the coordinate of the curved surface of the microlens perpendicular to the base. [Figure 6] This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base of a microlens, where x' is the coordinate along the diagonal passing through the center of the square base of the microlens and z' is the coordinate of the curved surface of the microlens perpendicular to the base. [Figure 7] This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 8] This is a side view (yz plane) of the diffusion element in Example 2. [Figure 9] This is a perspective view of the microlens of the diffusion element in Example 2. [Figure 10] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 2. [Figure 11] This is a side view (yz plane) of the microlens of the diffusion element in Example 2. [Figure 12] This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base of a microlens, where x' is the coordinate along the diagonal passing through the center of the square base of the microlens, and z' is the coordinate of the curved surface of the microlens perpendicular to the base. [Figure 13] This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base of a microlens, where x' is the coordinate along the diagonal passing through the center of the square base of the microlens and z' is the coordinate of the curved surface of the microlens perpendicular to the base. [Figure 14]This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 15] This is a side view (yz plane) of the diffusion element in Example 3. [Figure 16] This is a perspective view of the microlens of the diffusion element in Example 3. [Figure 17] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 3. [Figure 18] This is a side view (yz plane) of the microlens of the diffusion element in Example 3. [Figure 19] This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the rectangle of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 20] This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the rectangle of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 21] This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 22] This is a side view (yz plane) of the diffusion element in Example 4. [Figure 23] This is a perspective view of the microlens of the diffusion element in Example 4. [Figure 24] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 4. [Figure 25] This is a side view (yz plane) of the microlens of the diffusion element in Example 4. [Figure 26] This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 27]This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 28] This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 29] This is a side view (yz plane) of the diffusion element in Example 5. [Figure 30] This is a perspective view of the microlens of the diffusion element in Example 5. [Figure 31] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 5. [Figure 32] This is a side view (yz plane) of the microlens of the diffusion element in Example 5. [Figure 33] This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 34] This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 35] This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 36] This is a side view (yz plane) of the diffusion element in Example 6. [Figure 37] This is a perspective view of the microlens of the diffusion element in Example 6. [Figure 38] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 6. [Figure 39] This is a side view (yz plane) of the microlens of the diffusion element in Example 6. [Figure 40]This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 41] This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 42] This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 43] This is a side view (yz plane) of the diffusion element in Example 7. [Figure 44] This is a perspective view of the microlens of the diffusion element in Example 7. [Figure 45] This is a plan view (xy-plane) of the microlens of the diffusion element in Example 7. [Figure 46] This is a side view (yz plane) of the microlens of the diffusion element in Example 7. [Figure 47] This figure shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 48] This figure shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. [Figure 49] This figure shows the luminous intensity distribution of a beam diffused by a diffusion element. [Figure 50] This figure shows the arrangement of the square bases of the microlenses in Example 1-2. [Figure 51] This figure shows the arrangement of the rectangular bases of the microlens in Example 3. [Figure 52]This figure shows the arrangement of the hexagonal bases of the microlenses in Example 4-7. [Figure 53] This diagram shows a cross-section including the central axis of a beam emitted from a single light-emitting element. [Figure 54] This figure shows a cross-section including the central axis of the beams emitted from multiple light-emitting elements. [Figure 55] This diagram shows a cross-section including the central axis of the beam emitted from a light source, as observed from a position sufficiently far from the light source. [Modes for carrying out the invention]

[0028] The diffusion element of the present invention comprises a microlens array including a plurality of microlenses whose base surfaces are arranged on a plane. The curved surfaces of each microlens are continuous and smooth except for the boundaries.

[0029] The diffusion element of the present invention is designed such that the microlens array is positioned on the light source side of the diffusion element. When a beam is shone onto the diffusion element of the present invention from the side with the microlens array, the beam is diffused over a wide angle. If the microlens array is designed to be positioned on the output side of the diffusion element, the power of the diffused light is reduced because the widely spread light rays are shielded by the adjacent lenses in the arrangement.

[0030] In a cross-section perpendicular to a plane that includes a straight line passing through the projection point of the apex of the microlens onto the plane and having the maximum distance between two intersection points with the periphery of the bottom surface, with the coordinate along the straight line being x', the coordinate of the curved surface in the direction perpendicular to the plane being z', the maximum value of the first-order derivative of z' with respect to x' being d, the absolute value of the second-order derivative of z' with respect to x' at the x'-coordinate of the center being D0, and the value at the x'-coordinate of the boundary (the end of the diagonal) being D. According to the new findings of the inventors, in a light source including a light source and a diffusion element, by changing the value of D / D0, the diffusion angle of the diffused light can be changed. Here, the diffusion angle can be defined, for example, by the angle formed by the central axis of the beam with the region having a luminous intensity equal to half of the maximum luminous intensity at the central axis of the beam in a cross-section perpendicular to the traveling direction of the beam. The angle twice the angle formed by the central axis of the above beam is called the diffusion angle at half value full width. When D / D0 < 1 when d is 2 or more, the diffusion angle at half value full width can be made larger than 140 degrees. When D / D0 < 0.5 when d is 2 or more, the diffusion angle at half value full width can be made larger than 150 degrees. When D / D0 < 0.3 when d is 2 or more, the diffusion angle at half value full width can be made larger than 160 degrees.

[0031] On the other hand, the diffusion element including the above microlens array is usually manufactured by injection molding using a mold. Considering the optical performance of the microlens and the workability of the mold, with the length of the diagonal passing through the center of a right-angled quadrilateral or a regular hexagon being P and the radius of curvature at the apex of the curved surface being R, it is preferable that 1 < P / (2R) < 5.7 is satisfied. The lower limit of the above formula is determined by the focal length required for the microlens, and the upper limit is determined from the shape of the mold that can avoid interference with the tool used when processing the mold.

[0032] The exit surface of the diffusion element is a plane parallel to the bottom surface of the microlens or a convex surface with a relatively large radius of curvature. From the perspective of the efficiency of the optical system combining the light source and the diffusion element, the exit surface of the diffusion element is preferably a convex surface having a radius of curvature with an appropriate value of 100 times or more of R.

[0033] Embodiments of the present invention are described below. The embodiment includes a light source and a diffusion element equipped with a microlens array.

[0034] For an optical system including a light source and a diffusion element, the origin is defined at the center of the light source surface, and the x and y axes are defined in a plane parallel to the bottom surface of the microlens. A z axis is defined perpendicular to the x and y axes. The direction of the z axis is the direction of propagation of light traveling in the z-axis direction from the light source. The light source surface coincides with the xy plane and is perpendicular to the z axis. The diffusion element is positioned such that its center (center of the emission surface) lies on the z axis.

[0035] As an example, a light source is placed to the left of the diffusion element shown in Figure 1. Light emitted from the light source travels in the z-axis direction, enters the microlens array, passes through the diffusion element, and is then diffused as diffused light from the right-hand exit surface of the diffusion element.

[0036] For each microlens in the microlens array and the emission surface of the diffusion element, the vertex of the lens is defined as the origin, and the x and y axes are defined in a plane containing the origin and parallel to the base surface, and the z axis is defined perpendicular to the x and y axes. The direction of the z axis is the direction of propagation of light traveling in the z-axis direction from the light source.

[0037] The curved surface and emission surface of a microlens can be expressed by the following equations.

number

[0038] Example 1 Figure 1 is a side view (yz plane) of the diffusion element of Example 1.

[0039] Figure 2 is a perspective view of the microlens of the diffusion element in Example 1.

[0040] Figure 3 is a plan view (xy-plane) of the microlens of the diffusion element in Example 1.

[0041] Figure 4 is a side view (yz plane) of the microlens of the diffusion element in Example 1.

[0042] In the diagram, the pattern on the curved surface of the microlens is added to make the shape of the curved surface easier to understand.

[0043] The shape of the diffusion element in Example 1 in the xy plane is a square with sides of 1.48 millimeters.

[0044] The base of the microlens in Example 1 is square, and the square base is arranged without gaps on the xy-plane.

[0045] Figure 50 shows the arrangement of the square bases of the microlens in Example 1. In Figure 50, the x-axis distance dx between the centers of adjacent squares with sides in the y-axis direction and the y-axis distance dy between the centers of adjacent squares with sides in the x-axis direction are 0.07071 millimeters. The length P of the diagonal passing through the center of the square is 0.1 millimeters.

[0046] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 0.01795 mm k: -0.963 A2: 0 A4: 5.077762E+03 A6: 1.907324E+06 A8: -1.770637E+09 A10: 2.732180E+11 Based on the data above, the value of P / (2R) is 2.786.

[0047] The reference radius of the circle formed by the intersection of the curved surface of the microlens and the plane containing the base, centered at the intersection of the diagonals of the base square, is 0.1 / 2 = 0.05 millimeters. Furthermore, a circle with a radius of 0.07071 / 2 = 0.03536 millimeters, centered at the intersection of the diagonals of the base square, is included within the base. Therefore, the region of a circle with a radius of 70.7% of the reference radius, centered at the intersection of the diagonals of the base square, is included within the base.

[0048] The emission surface of the diffusion element is spherical, and the numerical data for equation (1) representing the emission surface is as follows. In this embodiment and the following embodiments, Rexit represents the radius of curvature of the emission surface, i.e., the radius of the sphere. Rexit: -15mm k: 0

[0049] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.0 millimeter.

[0050] The light source surface is square, with dimensions of 0.8 millimeters in the x and y directions. The distance in the z direction between the light source and the diffusion element is 1.0 millimeter. In this embodiment, a beam of the same size as the light source is irradiated onto the diffusion element. The luminous intensity within the beam is uniform. The power of the light source is 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at this wavelength is 1.63852.

[0051] Figure 5 shows the first derivative of z' with respect to x' in a cross-section perpendicular to the base surface, including a diagonal passing through the center of the square base surface of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base surface are z'. The horizontal axis of Figure 5 represents the coordinates x' along the diagonal. The coordinate of the center of the square is set to 0, and the unit of length is millimeters. The vertical axis of Figure 5 represents the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent line to the curved surface in the above cross-section makes with the x' axis direction. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.686, which corresponds to 74.8 degrees on the vertical axis of Figure 5.

[0052] Figure 6 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the square base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. The horizontal axis of Figure 6 shows the coordinate x' along the diagonal. The coordinate of the center of the square is set to 0, and the unit of length is millimeters. The vertical axis of Figure 6 shows the absolute value of the second derivative of z' with respect to x'. If D0 is the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the square, and D is the value at the x' coordinate of the end of the diagonal of the square, then D0 is 55.719, D is 13.914, and D / D0 is 0.250.

[0053] The line parallel to the diagonal defining coordinate x' and intersecting the z-axis of the optical system is called the x' axis of the optical system.

[0054] Figure 7 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 7 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes of the optical system. The unit of angle is degrees. The vertical axis of Figure 7 represents the luminous intensity of the ray in a cross-section containing the x' and z axes of the optical system. The unit of luminous intensity is watts / steradians.

[0055] The efficiency of the optical system, including the light source and the diffusion element, is 73.2%. In this embodiment and the following embodiments, the efficiency of the optical system is the ratio of the power of the diffused light to the power of the light source (1 watt).

[0056] Example 2 Figure 8 is a side view (yz plane) of the diffusion element in Example 2.

[0057] Figure 9 is a perspective view of the microlens of the diffusion element in Example 2.

[0058] Figure 10 is a plan view (xy-plane) of the microlens of the diffusion element in Example 2.

[0059] Figure 11 is a side view (yz plane) of the microlens of the diffusion element in Example 2.

[0060] The shape of the diffusion element in Example 2 is a square with sides of 1.26 millimeters in the xy plane.

[0061] The base of the microlens in Example 2 is square, and the square base is arranged without gaps on the xy-plane.

[0062] Figure 50 shows the arrangement of the square bases of the microlens in Example 2. In Figure 50, the distance dx in the x-axis direction between the centers of adjacent squares along the y-axis direction and the distance dy in the y-axis direction between the centers of adjacent squares along the x-axis direction are 0.06 millimeters. The length P of the diagonal passing through the center of the square is 0.08485 millimeters.

[0063] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 0.01795 mm k: -0.963 A2: 0 A4: 5.077762E+03 A6: 1.907324E+06 A8: -1.770637E+09 A10: 2.732180E+11 Based on the data above, the value of P / (2R) is 2.364.

[0064] The emission surface of the diffusion element is spherical, and the numerical data for equation (1) representing the emission surface is as follows. Rexit: -15mm k: 0

[0065] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.0 millimeter.

[0066] The light source surface is square, with dimensions of 0.8 millimeters in the x and y directions. The distance in the z direction between the light source and the diffusion element is 1.0 millimeter. In this embodiment, a beam of the same size as the light source is irradiated onto the diffusion element. The luminous intensity within the beam is uniform. The power of the light source is 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at this wavelength is 1.63852.

[0067] Figure 12 shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface, including a diagonal passing through the center of the square base surface of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base surface are z'. The horizontal axis of Figure 12 represents the coordinates x' along the diagonal. The coordinate of the center of the square is set to 0, and the unit of length is millimeters. The vertical axis of Figure 12 shows the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent line to the curved surface in the above cross section makes with the x' axis direction. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.491, which corresponds to 74.0 degrees on the vertical axis of Figure 12.

[0068] Figure 13 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the square base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. The horizontal axis of Figure 13 shows the coordinate x' along the diagonal. The coordinate of the center of the square is set to 0, and the unit of length is millimeters. The vertical axis of Figure 13 shows the absolute value of the second derivative of z' with respect to x'. If D0 is the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the square, and D is the value at the x' coordinate of the end of the diagonal of the square, then D0 is 55.719, D is 53.879, and D / D0 is 0.967.

[0069] The line parallel to the diagonal defining coordinate x' and intersecting the z-axis of the optical system is called the x' axis of the optical system.

[0070] Figure 14 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 14 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes of the optical system. The unit of angle is degrees. The vertical axis of Figure 14 represents the luminous intensity of the ray in a cross-section containing the x' and z axes of the optical system. The unit of luminous intensity is watts / steradians.

[0071] The efficiency of the optical system, including the light source and diffusion element, is 78.8%.

[0072] Example 3 Figure 15 is a side view (yz plane) of the diffusion element in Example 3.

[0073] Figure 16 is a perspective view of the microlens of the diffusion element in Example 3.

[0074] Figure 17 is a plan view (xy-plane) of the microlens of the diffusion element in Example 3.

[0075] Figure 18 is a side view (yz plane) of the microlens of the diffusion element in Example 3.

[0076] The shape of the diffusion element in Example 3 in the xy plane is a square with sides of 1.65 millimeters.

[0077] The base of the microlens in Example 3 is rectangular, and the rectangular base is arranged without gaps on the xy-plane.

[0078] Figure 51 shows the arrangement of the rectangular bases of the microlens in Example 3. In Figure 51, the x-axis distance dx between the centers of adjacent rectangles with sides in the y-axis direction is 0.0455 millimeters, and the y-axis distance dy between the centers of adjacent rectangles with sides in the x-axis direction is 0.0788 millimeters. The length P of the diagonal passing through the center of each rectangle is 0.091 millimeters.

[0079] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 0.01795 mm k: -0.963 A2: 0 A4: 5.077762E+03 A6: 1.907324E+06 A8: -1.770637E+09 A10: 2.732180E+11 Based on the data above, the value of P / (2R) is 2.535.

[0080] The reference radius of the circle formed by the intersection of the curved surface of the microlens and the plane containing the base, centered at the intersection of the diagonals of the base rectangle, is 0.091 / 2 = 0.0455 millimeters. Furthermore, a circle with a radius of 0.0455 / 2 = 0.02275 millimeters, centered at the intersection of the diagonals of the base rectangle, is included within the base. Therefore, the region of a circle with a radius of 50% of the reference radius, centered at the intersection of the diagonals of the base rectangle, is included within the base.

[0081] The emission surface of the diffusion element is spherical, and the numerical data for equation (1) representing the emission surface is as follows. Rexit: -15mm k: 0

[0082] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.0 millimeter.

[0083] The light source surface is square, with dimensions of 0.8 millimeters in the x and y directions. The distance in the z direction between the light source and the diffusion element is 1.0 millimeter. In this embodiment, a beam of the same size as the light source is irradiated onto the diffusion element. The luminous intensity within the beam is uniform. The power of the light source is 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at this wavelength is 1.63852.

[0084] Figure 19 shows the first derivative of z' with respect to x' in a cross section perpendicular to the base surface, including a diagonal line passing through the center of the rectangle on the base surface of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base surface are z'. The horizontal axis of Figure 19 represents the coordinates x' along the diagonal. The coordinate of the center of the rectangle is set to 0, and the unit of length is millimeters. The vertical axis of Figure 19 represents the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent line to the curved surface in the above cross section makes with the x' axis direction. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.615, which corresponds to 74.5 degrees on the vertical axis of Figure 19.

[0085] Figure 20 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the rectangle of the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. The horizontal axis of Figure 20 shows the coordinate x' along the diagonal. The coordinate of the center of the rectangle is set to 0, and the unit of length is millimeters. The vertical axis of Figure 20 shows the absolute value of the second derivative of z' with respect to x'. If D0 is the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the rectangle, and D is the value at the x' coordinate of the end of the diagonal of the rectangle, then D0 is 55.719, D is 27.116, and D / D0 is 0.487.

[0086] The line parallel to the diagonal defining coordinate x', intersecting the z-axis of the optical system (55.719), and where D is (27.116), is called the x' axis of the optical system.

[0087] Figure 21 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 21 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes. The unit of angle is degrees. The vertical axis of Figure 21 represents the luminous intensity of the ray in a cross-section containing the x' and z axes. The unit of luminous intensity is watts / steradians.

[0088] The efficiency of the optical system, including the light source and diffusion element, is 74.2%.

[0089] Example 4 Figure 22 is a side view (yz plane) of the diffusion element in Example 4.

[0090] Figure 23 is a perspective view of the microlens of the diffusion element in Example 4.

[0091] Figure 24 is a plan view (xy-plane) of the microlens of the diffusion element in Example 4.

[0092] Figure 25 is a side view (yz plane) of the microlens of the diffusion element in Example 4.

[0093] The shape of the diffusion element in Example 4 in the xy plane is a square with sides of 5 millimeters.

[0094] The base of the microlens in Example 4 is a regular hexagon, and the hexagonal base is arranged without gaps on the xy-plane.

[0095] Figure 52 shows the arrangement of the bases of the regular hexagons of the microlens in Example 4. In Figure 52, the distance dx in the x-axis direction between the centers of adjacent regular hexagons is 0.225 millimeters, and the distance dy in the y-axis direction between the centers of adjacent regular hexagons is 0.260 millimeters. The length P of the diagonal passing through the center of each regular hexagon is 0.3 millimeters.

[0096] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 0.056 mm k: -0.956 A2: 0 A4: 8.348E+001 A6: 2.382E+004 A8: -3.014E+006 A10: 2.078E+008 A12: -9.608E+009 A14: 2.518E+011 A16: -2.726E+012 Based on the data above, the value of P / (2R) is 2.685.

[0097] The reference radius of the circle formed by the intersection of the curved surface of the microlens and the plane containing the base, centered at the intersection of the diagonals of the regular hexagon of the base, is 0.3 / 2 = 0.15 millimeters. Additionally, a circle with a radius of 0.260 / 2 = 0.13 millimeters, centered at the intersection of the diagonals of the regular hexagon of the base, is included within the base. Therefore, the area of ​​a circle with a radius of 86.7% of the reference radius, centered at the intersection of the diagonals of the square of the base, is included within the base.

[0098] The emission surface of the diffusion element is spherical, and the numerical data for equation (1) representing the emission surface is as follows. Rexit: -50mm k: 0

[0099] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.45 millimeters.

[0100] The light source surface is rectangular, with dimensions of 0.85 millimeters in the x-axis direction and 0.65 millimeters in the y-axis direction, respectively. The distance in the z-axis direction between the light source and the diffusion element is 2.0 millimeters.

[0101] The light source in Example 4 is a light source with a divergence angle.

[0102] Figures 53-55 illustrate the light source of Embodiment 4, which has a divergence angle. A large number of light-emitting elements are arranged on the light-emitting surface of the light source.

[0103] Figure 53 shows a cross-section including the central axis of a beam emitted from a single light-emitting element. The luminous intensity in the cross-section including the central axis of the beam emitted from the light source in this embodiment follows a Gaussian distribution, and the luminous intensity within the beam is proportional to the luminous intensity of 1 at the center of the beam.

number

[0104] Figure 54 shows a cross-section including the central axis of the beams emitted from multiple light-emitting elements.

[0105] Figure 55 shows a cross-section including the central axis of the beam emitted from a light source, as observed from a position sufficiently far from the light source.

[0106] The light source has a power of 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at the above wavelength is 1.6296.

[0107] Figure 26 shows the first derivative of z' with respect to x' in a cross-section perpendicular to the base of a regular hexagon that includes the diagonal passing through the center of the base of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base are z'. The horizontal axis of Figure 26 represents the coordinates x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 26 represents the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent to the curved surface in the above cross-section makes with the x' axis. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.691, which corresponds to 74.8 degrees on the vertical axis of Figure 26.

[0108] Figure 27 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon at the base surface of the microlens. The coordinate along the diagonal is x', and the coordinate of the curved surface of the microlens perpendicular to the base surface is z'. The horizontal axis of Figure 27 shows the coordinate x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 27 shows the absolute value of the second derivative of z' with respect to x'. If D0 is the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the regular hexagon, and D is the value at the x' coordinate of the end of the diagonal of the regular hexagon, then D0 is 17.900, D is 8.901, and D / D0 is 0.497.

[0109] The line parallel to the diagonal defining coordinate x' and intersecting the z-axis of the optical system is called the x' axis of the optical system.

[0110] Figure 28 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 28 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes. The unit of angle is degrees. The vertical axis of Figure 28 represents the luminous intensity of the ray in a cross-section containing the x' and z axes. The unit of luminous intensity is watts / steradians.

[0111] The efficiency of the optical system, including the light source and diffusion element, is 81.8%.

[0112] Example 5 Figure 29 is a side view (yz plane) of the diffusion element in Example 5.

[0113] Figure 30 is a perspective view of the microlens of the diffusion element in Example 5.

[0114] Figure 31 is a plan view (xy-plane) of the microlens of the diffusion element in Example 5.

[0115] Figure 32 is a side view (yz plane) of the microlens of the diffusion element in Example 5.

[0116] The shape of the diffusion element in Example 5 in the xy plane is a square with sides of 5 millimeters.

[0117] The base of the microlens in Example 5 is a regular hexagon, and the hexagonal bases are arranged without gaps on the xy-plane.

[0118] Figure 52 shows the arrangement of the bases of the regular hexagons of the microlens in Example 5. In Figure 52, the x-axis distance dx between the centers of adjacent regular hexagons is 0.225 millimeters, and the y-axis distance dy between the centers of adjacent regular hexagons is 0.260 millimeters. The length P of the diagonal passing through the center of each regular hexagon is 0.3 millimeters.

[0119] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 0.045m k: -6.134 A2: 0 A4: 1.422+03 A6: -1.573E+05 A8: 1.358E+07 A10: -7.198+08 A12: 1.994+10 A14: -2.216+11 Based on the data above, the value of P / (2R) is 3.333.

[0120] The emission surface of the diffusion element is planar, and the numerical data for equation (1) representing the emission surface is as follows. Rexit: Infinity k: 0

[0121] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.25 millimeters.

[0122] The light source surface is square, with dimensions of 1.0 millimeter in the x and y directions. The distance in the z direction between the light source and the diffusion element is 2.0 millimeters.

[0123] The light source in this embodiment, like the light source in Embodiment 4, is a light source with a divergence angle. The luminous intensity in a cross-section including the central axis of the beam emitted from the light source in this embodiment follows a Gaussian distribution, and the position where the luminous intensity within the beam is 1 / 2 of the luminous intensity of 1 at the center of the beam is at an angle of 10 degrees with respect to the z-axis axis passing through the center of the light source.

[0124] The light source has a power of 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at the above wavelength is 1.6296.

[0125] Figure 33 shows the first derivative of z' with respect to x' in a cross-section perpendicular to the base of a regular hexagon that includes the diagonal passing through the center of the base of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base are z'. The horizontal axis of Figure 33 represents the coordinates x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 33 represents the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent to the curved surface in the above cross-section makes with the x' axis. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.464, which corresponds to 73.9 degrees on the vertical axis of Figure 33.

[0126] Figure 34 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon at the base surface of the microlens. The coordinate along the diagonal is x', and the coordinate of the curved surface of the microlens perpendicular to the base surface is z'. The horizontal axis of Figure 34 shows the coordinate x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 34 shows the absolute value of the second derivative of z' with respect to x'. If the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the regular hexagon is D0, and the value at the x' coordinate of the end of the diagonal of the regular hexagon is D, then D0 is 22.222, D is 0.505, and D / D0 is 0.023.

[0127] The line parallel to the diagonal defining coordinate x' and intersecting the z-axis of the optical system is called the x' axis of the optical system.

[0128] Figure 35 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 35 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes. The unit of angle is degrees. The vertical axis of Figure 35 represents the luminous intensity of the ray in a cross-section containing the x' and z axes. The unit of luminous intensity is watts / steradians.

[0129] The efficiency of the optical system, including the light source and diffusion element, is 67.8%.

[0130] Example 6 Figure 36 is a side view (yz plane) of the diffusion element of Example 6.

[0131] Figure 37 is a perspective view of the microlens of the diffusion element in Example 6.

[0132] Figure 38 is a plan view (xy plane) of the microlens of the diffusion element in Example 6.

[0133] Figure 39 is a side view (yz plane) of the microlens of the diffusion element in Example 6.

[0134] The shape of the diffusion element in Example 6 in the xy plane is a square with sides of 5 millimeters.

[0135] The base of the microlens in Example 6 is a regular hexagon, and the hexagonal base is arranged without gaps on the xy-plane.

[0136] Figure 52 shows the arrangement of the bases of the regular hexagons of the microlens in Example 6. In Figure 52, the distance dx in the x-axis direction between the centers of adjacent regular hexagons is 0.225 millimeters, and the distance dy in the y-axis direction between the centers of adjacent regular hexagons is 0.260 millimeters. The length P of the diagonal passing through the center of each regular hexagon is 0.3 millimeters.

[0137] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 0.042m k: -0.956 A2: 0 A4: 3.517E+02 A6: -2.282E+04 A8: 2.737E+05 Based on the data above, the value of P / (2R) is 3.571.

[0138] The emission surface of the diffusion element is planar, and the numerical data for equation (1) representing the emission surface is as follows. Rexit: Infinity k: 0

[0139] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.50 millimeters.

[0140] The light source surface is square, with dimensions of 1.0 millimeter in the x and y directions. The distance in the z direction between the light source and the diffusion element is 2.0 millimeters. In this embodiment, a beam of the same size as the light source is irradiated onto the diffusion element. The luminous intensity within the beam is uniform. The power of the light source is 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at this wavelength is 1.6296.

[0141] Figure 40 shows the first derivative of z' with respect to x' in a cross-section perpendicular to the base of a regular hexagon that includes the diagonal passing through the center of the base of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base are z'. The horizontal axis of Figure 40 represents the coordinates x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 40 represents the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent to the curved surface in the above cross-section makes with the x' axis. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.483, which corresponds to 74.0 degrees on the vertical axis of Figure 40.

[0142] Figure 41 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon at the base surface of the microlens, where x' is the coordinate along the diagonal and z' is the coordinate of the curved surface of the microlens perpendicular to the base surface. The horizontal axis of Figure 41 shows the coordinate x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 41 shows the absolute value of the second derivative of z' with respect to x'. If D0 is the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the regular hexagon, and D is the value at the x' coordinate of the end of the diagonal of the regular hexagon, then D0 is 23.810, D is 4.886, and D / D0 is 0.205.

[0143] The line parallel to the diagonal defining coordinate x' and intersecting the z-axis of the optical system is called the x' axis of the optical system.

[0144] Figure 42 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 42 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes. The unit of angle is degrees. The vertical axis of Figure 42 represents the luminous intensity of the ray in a cross-section containing the x' and z axes. The unit of luminous intensity is watts / steradians.

[0145] The efficiency of the optical system, including the light source and diffusion element, is 63.1%.

[0146] Example 7 Figure 43 is a side view (yz plane) of the diffusion element in Example 7.

[0147] Figure 44 is a perspective view of the microlens of the diffusion element in Example 7.

[0148] Figure 45 is a plan view (xy plane) of the microlens of the diffusion element in Example 7.

[0149] Figure 46 is a side view (yz plane) of the microlens of the diffusion element in Example 7.

[0150] The shape of the diffusion element in Example 7 is a square with sides of 5 millimeters in the xy plane.

[0151] The base of the microlens in Example 7 is a regular hexagon, and the hexagonal bases are arranged without gaps on the xy-plane.

[0152] Figure 52 shows the arrangement of the bases of the regular hexagons of the microlens in Example 7. In Figure 52, the distance in the x-axis direction between the centers of adjacent regular hexagons is 0.225 millimeters, and the distance in the y-axis direction between the centers of adjacent regular hexagons is 0.260 millimeters. The length P of the diagonal passing through the center of each regular hexagon is 0.3 millimeters.

[0153] The numerical data for equation (1), which represents the curved surface of the microlens, is as follows: R: 5.384E-02 mm k: -0.963 A2: 0 A4: 1.881E+02 A6: 7.849E+03 A8: -8.096E+05 A10: 1.388E+07 Based on the data above, the value of P / (2R) is 3.686.

[0154] The emission surface of the diffusion element is spherical, and the numerical data for equation (1) representing the emission surface is as follows. Rexit: -50mm k: 0

[0155] The thickness of the diffusion element, i.e., the distance in the z-axis direction between the vertex of the microlens and the vertex of the emission surface, is 1.45 millimeters.

[0156] The light source surface is rectangular, with dimensions of 0.85 millimeters in the x-axis direction and 0.65 millimeters in the y-axis direction, respectively. The distance in the z-axis direction between the light source and the diffusion element is 2.0 millimeters.

[0157] The light source in this embodiment, like the light source in Embodiment 4, is a light source with a divergence angle. The luminous intensity in the cross-section including the central axis of the beam emitted from the light source in this embodiment is Gaussian, and the luminous intensity within the beam is equal to the luminous intensity of 1 at the center of the beam.

number

[0158] The light source has a power of 1 watt. The wavelength of the light is 850 nanometers, and the refractive index of the diffusion element at the above wavelength is 1.6296.

[0159] Figure 47 shows the first derivative of z' with respect to x' in a cross-section perpendicular to the base of a regular hexagon that includes the diagonal passing through the center of the base of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base are z'. The horizontal axis of Figure 47 represents the coordinates x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 47 represents the tangent angle corresponding to the first derivative of z' with respect to x'. The tangent angle is the angle (acute angle) that the tangent to the curved surface in the above cross-section makes with the x' axis. An angle measured clockwise is represented as positive, and an angle measured counterclockwise is represented as negative. The maximum value of the first derivative of z' with respect to x' is 3.686, which corresponds to 74.8 degrees on the vertical axis of Figure 47.

[0160] Figure 48 shows the absolute value of the second derivative of z' with respect to x' in a cross section perpendicular to the base surface that includes a diagonal passing through the center of the regular hexagon at the base surface of the microlens. The coordinates along the diagonal are x', and the coordinates of the curved surface of the microlens perpendicular to the base surface are z'. The horizontal axis of Figure 48 shows the coordinates x' along the diagonal. The coordinate of the center of the regular hexagon is set to 0, and the unit of length is millimeters. The vertical axis of Figure 48 shows the absolute value of the second derivative of z' with respect to x'. If D0 is the value of the absolute value of the second derivative of z' with respect to x' at the x' coordinate of the center of the regular hexagon, and D is the value at the x' coordinate of the end of the diagonal of the regular hexagon, then D0 is 18.573, D is 4.638, and D / D0 is 0.250.

[0161] The line parallel to the diagonal defining coordinate x' and intersecting the z-axis of the optical system is called the x' axis of the optical system.

[0162] Figure 49 shows the luminous intensity distribution of a beam diffused by a diffusion element. The horizontal axis of Figure 49 represents the angle of the ray with respect to the z axis in a cross-section containing the x' and z axes. The unit of angle is degrees. The vertical axis of Figure 49 represents the luminous intensity of the ray in a cross-section containing the x' and z axes. The unit of luminous intensity is watts / steradians.

[0163] The efficiency of the optical system, including the light source and diffusion element, is 78.6%.

[0164] Table 1 shows the characteristics of the curved surface and emission surface of the microlens of the diffusion elements in Examples 1-7. [Table 1]

[0165] Table 2 shows the characteristics of the optical system including the light source and one of the diffusion elements from Examples 1-7. [Table 2]

[0166] According to Tables 1 and 2, each microlens in all embodiments has a d of 2 or greater, satisfies D / D0 < 1, and the diffusion angle of the full width at half maximum of the optical system including the diffusion element in each embodiment is greater than 140 degrees. Each microlens in Embodiment 1 and Embodiments 3-7 has a d of 2 or greater, satisfies D / D0 < 0.5, and the diffusion angle of the full width at half maximum of the optical system including the diffusion element in each embodiment is greater than 150 degrees. Each microlens in Embodiment 1 and Embodiments 5-7 has a d of 2 or greater, satisfies D / D0 < 0.3, and the diffusion angle of the full width at half maximum of the optical system including the diffusion element in each embodiment is greater than 160 degrees.

[0167] According to Tables 1 and 2, the efficiency of the optical systems in all examples is 60% or higher. The efficiency of the optical systems in Examples 1-4 and 7 is 70% or higher. The efficiency of the optical systems in Examples 2, 4 and 7 is 75% or higher.

Claims

1. A diffusion element comprising a microlens array including a plurality of microlenses whose bases are arranged on a plane, wherein the curved surface of each microlens is continuous and smooth except for the boundary, and in each microlens, in a cross section perpendicular to the plane that includes a line passing through the projection point of the vertex of the microlens onto the plane and maximizing the distance between two intersection points with the periphery of the base, the coordinate along the line is x', the coordinate of the curved surface in the direction perpendicular to the plane is z', the maximum value of the first derivative of z' with respect to x' is d, the value of the absolute value of the second derivative of z' with respect to x' at the center in x' coordinate is D0, and the value of the value of the end of the diagonal in x' coordinate is D. [Math 1] and 【Number 2】 A diffusion element that satisfies the following conditions.

2. A diffusion element comprising a microlens array containing multiple microlenses of the same shape, each having a congruent quadrilateral or congruent regular hexagon as its base, arranged without gaps on a plane, wherein the curved surface of each microlens is continuous and smooth except for the boundary, the projection points of the vertices of the microlenses onto the plane coincide with the intersection of the diagonals of the quadrilateral or regular hexagon, and in a cross section perpendicular to the plane that includes the longest diagonal, the coordinate along the diagonal is x', the coordinate of the curved surface perpendicular to the plane is z', the maximum value of the first derivative of z' with respect to x' is d, the value at the x' coordinate of the center of the absolute value of the second derivative of z' with respect to x' is D0, and the value at the x' coordinate of the end of the diagonal is D. [Math 3] and [Math 4] A diffusion element according to claim 1, wherein the condition is met.

3. The diffusion element according to claim 1 or 2, wherein the curved surface is an aspherical surface that is axially symmetric about an axis passing through the projection point and perpendicular to the plane.

4. About each microlens [Math 5] A diffusion element according to any one of claims 1 to 3, wherein the following conditions are met.

5. About each microlens [Math 6] A diffusion element according to any one of claims 1 to 4, wherein the following conditions are met.

6. About each microlens [Number 7] A diffusion element according to any one of claims 1 to 5, wherein the following conditions are met.

7. About each microlens [Number 8] A diffusion element according to any one of claims 1 to 6, wherein the following conditions are met.

8. For each microlens, let P be the length of the diagonal passing through the center of the right quadrilateral or regular hexagon, and R be the radius of curvature at the vertex of the curved surface. [Number 9] A diffusion element according to any one of claims 1 to 7, wherein the following conditions are met.

9. A diffusion element according to any one of claims 1 to 8, wherein the surface opposite to the surface equipped with microlenses is a convex surface, and the absolute value of the radius of curvature of the convex surface is 100 times or more R, where R is the absolute value of the radius of curvature at the vertex of the curved surface of each microlens.

10. An optical system comprising a diffusion element and a light source according to any one of claims 1 to 9.

11. The optical system according to claim 10, wherein the microlens array is located on the side of the diffusion element facing the light source.

12. The optical system according to claim 10 or 11, wherein the light source is a divergent light source.

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