JP2022019243A - Microlens array and microlens array fabrication method - Google Patents

Abstract

To provide an easily designable microlens array that does not cause excessive Moire at a location by a prescribed distance away from a light source, and to provide a microlens array fabrication method.SOLUTION: A microlens array (3) has: a rectangular contour; and an incidence surface of light and emitting surface thereof, and forms a light beam having a prescribed intensity distribution in an irradiation region in which an aspect ratio is 1:τ. On one surface of the emitting surface or incidence surface, the microlens array has a plurality of tightly packed unit cells with the unit cell overlapped with each other. Respective unit cells include: one center lenslet; and four peripheral lenslets arranged along four sides of the center lenslet. All contours of the center lenslet and peripheral lenslet have a rectangle. An angle θ (θ is equal to or more than 0° and equal to or less than 90° ) that is made by a least square straight line passing through a center of a plurality of adjacent peripheral lenslets and the contour of the microlens array form is Tan-1 (0.466τ) or more and Tan-1(0.933τ) or less.SELECTED DRAWING: Figure 3

Description

The present invention relates to a microlens array and a method for manufacturing a microlens array.

A microlens array in which microlenses are arranged in an array may be used in order to uniformly illuminate a position (long-distance field) away from the light source by a laser beam or the like emitted from the light source. However, when the microlenses are arranged regularly, a moire pattern occurs and uniform illumination is not achieved.

Therefore, in order to form a uniform intensity distribution in the long-distance field scattering pattern, a plurality of circular microlenses that are randomly arranged, whose outer shape is randomly changed, and whose surface shape is randomly changed are placed on the substrate. A microlens array formed in is known (see, for example, Patent Document 1).

Special Table 2006-500621

However, in the microlens array described in Patent Document 1, it depends on the irradiation of light by the region where the circular microlens is formed (compatible region) and the region of the substrate portion where the circular microlens is not formed (non-compatible region). Irradiation of light will occur. Therefore, it is necessary to consider the behavior of light in the compatible region and the non-compatible region, and it is not easy to design a microlens array that does not cause excessive moire at a position separated from the light source by a predetermined distance.

Therefore, an object of the present invention is to provide a microlens array and a method for manufacturing a microlens array, which can be easily designed and does not cause excessive moire at a position separated from a light source by a predetermined distance.

In order to solve the above-mentioned problems, the present invention has, as one aspect, a rectangular outer shape, an incident surface and an emitted surface of light, and a light beam having a predetermined intensity distribution in an irradiation region having an aspect ratio of 1: τ. It is a microlens array forming a lens array having a plurality of unit cells spread without gaps on one surface of an exit surface or an incident surface while overlapping with each other, and each unit cell has one central lenslet. , 4 peripheral lenslets arranged along the 4 sides of the central lenslet, and all outer shapes of the central lenslet and the peripheral lenslet have a rectangular shape, and the 4 sides of the central lenslet and the above 4 sides. Each one side of the peripheral lenslet is arranged side by side on a straight line, and the four sides of the central lenslet and the other one side of the four peripheral lenslets are arranged so as to face each other, and the four peripheral lenslets are arranged. The other side is longer than the side of the central lenslet facing each other, and the four vertices of the central lenslet and one of the four peripheral lenslets are co-located and included in the microlens array. The center positions of the plurality of peripheral lenslets are randomly set, and the angle θ (θ is 0 ° or more, 90) formed by the minimum squared straight line passing through the centers of the plurality of adjacent peripheral lenslets and one side of the peripheral lenslets. ° or less) provides a microlens array characterized by Tan ^-1 (0.466τ) or more and Tan ^-1 (0.933τ) or less.

In the above microlens array, it is preferable that one of the unit cells and one of the other unit cells adjacent to the unit cell are arranged so as to share two peripheral lenslets.

In the above microlens array, the surface shape z of the central lenslet and the peripheral lenslet is represented by the following equation (1) when the width of the central lenslet and the peripheral lenslet is W and the height is H. It is a surface, where the width of the rectangular initial lens lenslet is L, the height is τL, the radius of curvature is r, and the cornic coefficient is k, rx = (W / L) r, ry = (H / τL). It is preferable that r, kx = k, and ky = k.

In order to solve the above-mentioned problems, the present invention has, as one aspect, a unit cell including one central lenslet and four peripheral lenslets arranged along four sides of the central lenslet. A method for manufacturing a microlens array, which has an emission surface or an incident surface that are overlapped and spread without gaps, and forms a light beam having a predetermined intensity distribution in an irradiation region having an aspect ratio of 1: τ. 1: Based on the size of the initial lenslet of τ and the tilt angle θ of the initial lenslet, the angle formed by the line segment passing through the centers of the plurality of initial peripheral lenslets and a predetermined side of the initial peripheral lenslet is the tilt. An initial lattice consisting of a plurality of rectangular initial peripheral lenslets is generated so as to have an angle θ, and the positions of the plurality of initial peripheral lenslets are randomly shifted to generate a plurality of intermediate peripheral lenslets, and a plurality of intermediate peripherals are generated. By changing the outer shape of the lenslet and multiple central lenslets, the four sides of the central lenslet and one side of each of the four peripheral lenslets are arranged side by side on a straight line, respectively, and the four sides and four of the central lenslet are arranged. Each other side of one peripheral lenslet is arranged to face each other, and the other side of the four peripheral lenslets is longer than the side of the central lenslet facing each other, and the four sides of the central lenslet The apex and one apex of each of the four peripheral lenslets form a surface in which unit cells arranged at the same position overlap each other and are spread without gaps, and all lenslets including the central lenslet and the peripheral lenslet. Provided is a method for manufacturing a microlens array, which is characterized by calculating a sag amount and outputting design data of a surface in which unit cells are spread without gaps while overlapping each other using the calculated sag amount. ..

INDUSTRIAL APPLICABILITY According to the present invention, it is possible to provide a microlens array and a method for manufacturing a microlens array that do not cause excessive moire at a position separated from a light source that can be easily designed.

It is a schematic diagram for demonstrating the irradiation area when the microlens array which concerns on this invention is used. (A) is a plan view showing the incident surface side of the microlens array 3, and (B) is a diagram showing an example of the illuminance distribution by the light beam formed by the microlens array 3 in the irradiation region 4. It is an enlarged view which expanded the area 12 of FIG. 2 (A). (A) is an exploded view of five lenslets included in the unit cell 51, and (B) is a detailed view of the unit cell 51. It is a figure for demonstrating the unit cell 51. It is a figure for demonstrating the overlap of unit cells. It is a figure for demonstrating the shape of the sag of a lens let. It is a figure for demonstrating the relationship between the tilt angle, the moire suppression effect, and the clarity of an illumination range when the aspect ratio of an initial lens let is 1: 1 in the microlens array which concerns on this invention. To explain the relationship between the tilt angle, the moire suppressing effect, and the clarity of the illumination range when the aspect ratio of the initial lenslet is 16: 9 (1: 9/16) in the microlens array according to the present invention. It is a figure. To explain the relationship between the tilt angle, the moire suppressing effect, and the clarity of the illumination range when the aspect ratio of the initial lenslet is 4: 3 (1: 3/4) in the microlens array according to the present invention. It is a figure. It is a flowchart which shows an example of the manufacturing method of the microlens array which concerns on this invention. It is a figure for demonstrating the generation of an initial lattice. It is a figure for demonstrating the rotation of an initial lattice. It is a figure for demonstrating the generation of the position variation of a peripheral lens let. It is a figure for demonstrating the matching of the position and size of a lens let. It is a figure for demonstrating the microlens array which completed the design. It is a schematic block diagram of the design apparatus which designs the microlens array which concerns on this invention.

Hereinafter, various embodiments of the present invention will be described with reference to the drawings. However, it should be noted that the technical scope of the present invention is not limited to those embodiments but extends to the inventions described in the claims and their equivalents. Further, those having the same or equivalent functions in each figure may be designated by the same reference numerals, and the description thereof may be omitted or simplified.

(Composition of microlens array)
The general usage of the microlens array will be described below with reference to FIG.

As shown in FIG. 1, the light emitted from the light source 2 arranged on the substrate 1 and having one or a plurality of light emitting elements emitting light is incident on the microlens array 3. The microlens array 3 has a rectangular outer shape, an incident surface and an emitted surface of light, and forms a light beam having a predetermined intensity portion in an irradiation region 4 separated by a predetermined distance. As the light source 2 used together with the microlens array 3, it is possible to use a vertical cavity surface emitting laser light source, an end surface emitting laser light source, an LED light source, or the like, which is also called a VCSEL (Vertical Cavity Surface Emitting LASER). be.

Using FIGS. 2A and 2B, the illuminance distribution due to the light beam formed in the irradiation region 4 by the microlens array 3 will be described below.

As shown in FIG. 2A, a plurality of minute lenslets are arranged without gaps on the incident surface side of the microlens array 3. Each of the lenslets is a microlens having a predetermined curved surface shape only on the incident surface side as shown in FIG. The exit surface side of the microlens array 3 has a planar shape (not shown). However, it is also possible to have a plurality of minute lenslets only on the exit surface side of the microlens array and to have a planar shape on the incident surface side.

The first direction and the second direction shown in FIG. 2A indicate directions parallel to the vertical or horizontal sides of the microlens array 3 having a rectangular outer shape. The same applies to FIGS. 2B, 3, 4 and 9 to 12 in the first direction and the second direction. Further, the center of a part of the minute lenslet is arranged in the vicinity of a straight line inclined by a predetermined side forming the outer shape of the lenslet and an angle θ, which will be described in detail later.

In FIG. 2B, the graph on the right side of the two-dimensional image of the illuminance distribution arranged in the center shows the light intensity measured along AA'parallel to the second direction, and the two-dimensional image of the illuminance distribution in the center. The lower graph shows the light intensity measured along BB'parallel to the first direction. As described above, the illuminance distribution by the light beam formed by the microlens array 3 has a substantially uniform light intensity in the irradiation region 4 in a rectangular shape similar to the boundary shape of the initial lenslet of the microlens array 3.

When moire occurs due to interference unevenness due to a plurality of lenslets, the amplitude of the portion of the region C becomes large in the light intensity distribution shown in FIG. 2 (B). However, as shown in the graphs on the lower side and the left side of FIG. 2B, since the light intensity distribution is almost flat in the irradiation region, it can be said that the microlens array 3 has a moire suppressing effect.

Further, in the light intensity distribution shown in FIG. 2B, when the portion of the region D gradually decreases, the clarity in the illuminance region decreases. However, as shown in the graphs on the lower and right sides of FIG. 2B, the light intensity distribution is sharply reduced around the irradiation region, so that the microlens array 3 has clarity. I can say.

FIG. 3 is an enlarged view of the region 12 of FIG. 2 (A), and FIGS. 4 (A), 4 (B) and FIG. 5 are views for explaining the unit cell 51. The lenslets included in the microlens array 3 will be described below with reference to FIGS. 3 to 5.

In FIG. 3, each rectangular shape shows the outer shape of a minute lenslet as seen from the incident surface side. Further, the outer shape of all the lenslets included in the microlens array 3 when viewed from the incident surface side is rectangular, and all four sides of the rectangular shape are arranged in parallel with the vertical or horizontal sides of the microlens array 3. ing. Further, in the microlens array 3, the unit cells 51 including the five lenslets are arranged without gaps so as to overlap each other.

In FIG. 3, shaded portions indicate one unit cell 51 and include one central lenslet 31 and four peripheral lenslets 24, 25, 29 and 30. The four peripheral lenslets 24, 25, 29 and 30 are arranged without gaps along the four sides of the central lenslet 31.

In FIG. 4A, the five lenslets included in the unit cell 51 are decomposed and shown for convenience, but the central lenslet 31 has four vertices 31-1, 31-2, 31-3 and 31-4. And has four sides 31a, 31b, 31c and 31d. Similarly, peripheral lenslets 24, 25, 29 and 30 also have four vertices and four sides.

As shown in FIG. 4B, the side 29d of the peripheral lenslet 29 and the side 31d of the central lenslet 31 are arranged side by side on a straight line, and the apex 29-3 and the central lenslet at the lower right of the peripheral lenslet 29 are arranged side by side. The upper right vertex 31-4 of 31 is arranged at the same position. Further, the side 29c of the peripheral lens let 29 is arranged so as to face the side 31a of the central lens let 31, and is longer than the side 31a.

The side 24a of the peripheral lenslet 24 and the side 31a of the central lenslet 31 are arranged side by side on a straight line, and the apex 24-4 on the upper right of the peripheral lenslet 24 and the apex 31-1 on the upper left of the central lenslet 31 are at the same position. Is located in. Further, the side 24d of the peripheral lens let 24 is arranged so as to face the side 31b of the central lens let 31, and is longer than the side 31b.

The side 25b of the peripheral lenslet 25 and the side 31b of the central lenslet 31 are arranged side by side on a straight line, and the upper left vertex 25-1 of the peripheral lenslet 25 and the lower left vertex 31-2 of the central lenslet 31 are at the same position. Is located in. Further, the side 25a of the peripheral lens let 25 is arranged so as to face the side 31c of the central lens let 31, and is longer than the side 31c.

The side 30c of the peripheral lenslet 30 and the side 31c of the central lenslet 31 are arranged side by side on a straight line, and the apex 30-2 at the lower left of the peripheral lenslet 30 and the apex 31-3 at the lower right of the central lenslet 31 are the same. It is placed in a position. Further, the side 30b of the peripheral lens let 30 is arranged so as to face the side 31d of the central lens let 31, and is longer than the side 31d.

As shown in FIGS. 4B and 5, each of the four peripheral lenslets has one side arranged in a straight line with any side of the center lenslet, and the center lenslet has one side. It has vertices arranged at the same position as any of the vertices. Also, each of the four peripheral lenslets has another side arranged to face one side of any one of the central lenslets, and the other side of the four peripheral lenslets, respectively. It is set to be longer than the sides of the facing central lenslets.

51a, 51b, 51c and 51d shown in FIG. 5 indicate a line segment extended from each side of the central lens let 31. Each lenslet can be modified in size to fit other lenslets arranged around it, within a range that satisfies the above conditions. For example, the peripheral lenslet 29 is transformed into a lenslet 29'expanded from the current size, a lenslet 29'reduced from the current size, etc. within the range partitioned by the line segments 51a and 51b. can do. The other peripheral lenslets 25, 24 and 30 can be similarly deformed (see FIG. 5). Deformation of the shape of the peripheral lenslet according to other lenslets arranged around it will be described later. For convenience of explanation, in FIG. 5, the outer shape of the central lenslet 31 is fixed, but as will be described later, the outer shape of the central lenslet 31 changes in the manufacturing process of the microlens array 3. In some cases.

In the unit cell 51 in FIGS. 3 to 5, the right side 31d of the central lenslet 31 and the side 29d of the peripheral lenslet 29 arranged on a straight line are on the upper side in the drawing, and the left side of the central lenslet 31. The side 25b of the peripheral lens let 25 arranged in a straight line with 31b is on the lower side in the drawing. However, the arrangement of the unit cells 51 may be reversed left and right.

The overlap between unit cells will be described below with reference to FIG.

As shown in FIG. 6, another unit cell 52 is arranged diagonally to the upper left of the unit cell 51 shaded by diagonal lines, another unit cell 53 is arranged diagonally to the lower left, and another unit is arranged diagonally to the lower right. The spore 54 is arranged, and another unit spore 55 is arranged diagonally to the upper right. The unit cell 52 includes a central lenslet 33 and peripheral lenslets 23, 24, 32, 29, and a unit cell 53 includes a central lenslet 39 and peripheral lenslets 24, 25, 37, 38. Further, the unit cell 54 includes a central lenslet 41 and peripheral lenslets 25, 26, 30, 40, and the unit cell 55 includes a central lenslet 36 and peripheral lenslets 29, 30, 34, 35. Considering the unit cell 51 shaded by diagonal lines as the center, the peripheral lenslets 24 and 29 overlap each other in the unit cell 51 and the unit cell 52, and the unit cell 51 and the unit cell 53 are the peripheral lenslet 24 and 25 overlap each other. Similarly, the peripheral lenslets 25 and 30 overlap each other in the unit cell 51 and the unit cell 54, and the peripheral lenslets 29 and 30 overlap each other in the unit cell 51 and the unit cell 55. In this way, one unit cell and the other unit cells diagonally above and below the unit cell are arranged so that the two peripheral lenslets always overlap each other. The peripheral lenslet located at the peripheral edge of the microlens array 3 is not limited to this, and is formed along a straight line parallel to the outer shape of the microlens array 3.

In FIG. 3, the dotted line 10 which is the reference line represents a straight line parallel to a predetermined side forming the outer shape of the lens let. Since the four sides of all the lenslets face the same direction, any predetermined one side of the reference lenslet may be determined. In FIG. 3, the dotted line 10 is described so as to be parallel to the side 30a (see FIG. 4A) of the peripheral lens let 30. Points 21a to 28a are the centers of the other peripheral lenslets 21 to 28, respectively, which are close to each other in one diagonal direction. The dotted line 11 represents the least squares straight line close to the center points of all the peripheral lenslets that continue diagonally to the upper left and diagonally lower right of the peripheral lenslets 21 to 28 in the entire microlens array 3. In the microlens array 3, a minimum squared straight line (dotted line 11) passing close to the center point of a plurality of adjacent peripheral lenslets and a line parallel to a predetermined side forming the outer shape of the lenslet (dotted line 10) are formed. The angle θ (referred to as “tilt angle”) is configured to be within a predetermined range. 2 to 6 show an example in which θ is 35 °. For example, when the reference line for defining the tilt angle is a line parallel to the sides 30a or 30c of the peripheral lens let 30 (see FIG. 4 (A)), the value of the tilt angle θ does not change, but the tilt is tilted. When the reference line for defining the angle is a line parallel to the side 30b or 30d of the peripheral lens let 30 (see FIG. 4A), the inclination angle is (90 ° −θ).

The surface shape of each lens let will be described below with reference to FIG. 7.

In the microlens array 3 shown in FIG. 2, the boundary of the irradiation region 4 is a square. Since the boundary shape of the irradiation region and the shape of the initial lenslet are similar to each other, the shape of the initial lenslet of the microlens array 3 is square. However, as will be described later, the shape of the lenslet included in the completed microlens array 3 is deformed from the square of the initial lenslet (when the aspect ratio is 1: 1), and has a width as shown in FIG. 7. It has a rectangular shape with a height of W μm and a height of H μm. Note that FIG. 7 is a schematic perspective view of one lens let included in the microlens array 3.

ここで、正方形である初期レンズレットの１辺の長さをＬμｍ、曲率半径をｒμｍ、及び、コーニック係数をｋとする。その場合、式（１）中で、ｒ_x＝（Ｗ／Ｌ）ｒ、ｒ_y＝（Ｈ／Ｌ）ｒ、ｋ_x＝ｋ、ｋ_y＝ｋとすることによって、各レンズレットの面形状を設計することが可能となる。 Even with a rectangular lenslet as shown in FIG. 7, since it is necessary to finally align the beam with the irradiation area of a square (aspect ratio of 1: 1), the surface shape of each lenslet The profile (sag amount) z is a biconic surface represented by the following equation (1).

Here, let the length of one side of the initial lenslet, which is a square, be Lμm, the radius of curvature be rμm, and the conic coefficient be k. In that case, the surface shape of each lenslet is formed by setting r _x = (W / L) r, r _y = (H / L) r, k _x = k, and _ky = k in the equation (1). Can be designed.

In the above, the case where the initial lenslet is square (when the aspect ratio is 1: 1) has been described, but when the irradiation area of the microlens array is a rectangle which is not a square (when the aspect ratio is not 1: 1). There is. In such a case, it is necessary to make the initial lenslet a rectangle that matches the irradiation area of the desired aspect ratio (1: τ). Let the width of the rectangular initial lenslet be Lμm, the height be τLμm, the radius of curvature be rμm, and the conic coefficient be k. In that case, the surface shape of each lenslet is formed by setting r _x = (W / L) r, r _y = (H / τL) r, k _x = k, and k _y = k in the equation (1). Can be designed.

The relationship between the tilt angle, the microlens array moire suppression effect, and the clarity of the illumination range will be described below with reference to FIGS. 8 to 10.

A plurality of microlens arrays are created by changing the tilt angle, the illuminance distribution in the irradiation region 4 at the same predetermined distance is measured according to the configuration as shown in FIG. 1, and the moire suppression effect and the clarity in the irradiation region 4 are observed. Was done. For the moire suppressing effect and the clarity in the irradiation region 4, refer to the explanation in FIG. FIG. 8 is an example in which the moire suppressing effect and the clarity of the irradiation region are measured for a plurality of types of θ when the aspect ratio is 1: 1. Further, FIG. 9 is an example of performing the same measurement in the case of an aspect ratio of 16: 9, and FIG. 10 is an example of performing the same measurement in the case of an aspect ratio of 4: 3. In FIGS. 8 to 10, the uppermost stage θ indicates the above-mentioned tilt angle, and the lower stage shows the arrangement of the lenslets at each θ. If the moire suppression effect is high, add a "double circle", if a certain effect is obtained, add "○", and if the suppression effect is not sufficient and moire is noticeable, add an "x". There is. Further, when the clarity in the irradiation area 4 is large, a "double circle" is attached, when a certain effect can be obtained, an "○" is attached, and when the clarity is not sufficiently obtained, an "x" is attached. ing.

From FIG. 8, regarding the effect of suppressing moiré, good results were obtained when the inclination angle θ was 20 ° to 43 °, while the effect of suppressing moiré was obtained when the inclination angle was 43 ° <θ≤45 °. I couldn't. Regarding the clarity of the irradiation region 4, good results were obtained when the tilt angle θ was 25 ° to 45 °, while when the tilt angle θ <25 °, light scattering occurred due to the small central lenslet. , The blur became large at the boundary of the illumination range, and the boundary became unclear. Therefore, in order to obtain good results for both the moire suppression effect and the clarity of the illumination range, the inclination angle θ is configured to be 25 ° or more and 43 ° or less when the aspect ratio is 1: 1. preferable.

Considering the case where the aspect ratio is 1: τ from the result of FIG. 8, when the aspect ratio of the initial lenslet is 1: τ, the inclination angle θ is Tan ^-1 (tan (25 °) × τ) ≈ Good results are obtained when Tan ^-1 (0.466τ) or more and Tan ^-1 (tan (43 °) × τ) ≈ Tan ^-1 (0.933τ) or less.

When the aspect ratio is 16: 9, that is, 1: 9/16, the range of good θ according to the above is 14 ° or more and 27 ° or less. From FIG. 9, at θ = 10 ° below the good range, the central lenslet becomes too small and the irradiation area is blurred, and at θ = 29 ° above the good range, the lenslets are almost lined up in a row. The result was that moire occurred.

When the aspect ratio is 4: 3, that is, 1: 3/4, the range of good θ according to the above is 19 ° or more and 35 ° or less. From FIG. 10, at θ = 15 ° below the good range, the central lenslet becomes too small and the irradiation area is blurred, and at θ = 36 ° above the good range, the lenslets are almost lined up in a row. The result was that moire occurred.

From FIGS. 8 to 10, when the aspect ratio is 1: τ, the inclination angle θ is preferably configured to be Tan ^-1 (0.466τ) or more and Tan ^-1 (0.933τ) or less. I was able to confirm that.

(Manufacturing method of microlens array)
A method for manufacturing a microlens array will be described below with reference to FIG.

First, the shape of the illuminance region is assumed in consideration of the desired microlens array, and the size L and the angle θ of the initial peripheral lens let are determined (step S1). Here, assuming a square illuminance region, a square initial lenslet size L × L is used, and the angle θ will be described assuming that 35 ° is selected as in FIG. Hereinafter, a method for manufacturing a microlens array corresponding to an irradiation region having an aspect ratio of 1: 1 will be described. However, if the tilt angle θ according to the aspect ratio is selected and the sag amount of each lenslet is calculated according to the aspect ratio, the microlens array corresponding to the irradiation region having an aspect ratio of 1: τ. Can be manufactured.

初期中心レンズレットのサイズＡＬは、初期レンズレットサイズＬ及び角度θから、以下の式（３）によって求められる。

Next, the pitch P of the initial grid and the initial center lenslet size AL are calculated (step S2). The pitch P of the initial grid is obtained from the initial lenslet size L and the angle θ by the following equation (2).

The size AL of the initial center lenslet is obtained from the initial lenslet size L and the angle θ by the following equation (3).

In FIG. 12, using the calculated pitch P of the initial grid, the initial grids 91 and 92 are drawn at intervals P in the vertical and horizontal directions by the alternate long and short dash line, and a square having one side having a length L at the intersection 93 of the initial grid. An example in which the center of a certain initial peripheral lenslet is arranged is shown. At this time, in the region 98 surrounded by the four initial peripheral lenslets, an area corresponding to the initial center lenslet, which is a square having a length AL on one side, is secured.

Next, the initial grids 91 and 92 are rotated in the direction of the arrow X by an angle θ (step S3). In this state, each side of the outer shape of the initial peripheral lenslet and the initial center lenslet was rotated and arranged so as to be parallel to the side forming the outer shape of the finally formed microlens array 3. Become. By omitting the step shown in step S3, the microlens array 3 is cut out from the state of FIG. 12 so that the sides forming the outer shape of the microlens array 3 and each side of the initial peripheral lens let are parallel to each other. Is also good.

FIG. 13 shows a state in which the initial peripheral lenslet and the initial center lenslet shown in FIG. 12 are rotated by an angle θ = 35 ° in the direction of the arrow X in FIG. In FIG. 13, the first direction and the second direction are the same as the relationship shown in FIG.

Next, random positional variation is given to all the initial peripheral lenslets (step S4). As an example, it is conceivable to randomly shift the center point of the initial peripheral lenslet and shift the outer shape position of the initial peripheral lenslet according to the shifted center point. However, another method is used to shift the outer shape of the initial peripheral lenslet. You may shift the position.

FIG. 14 shows an example in which the external positions of the initial peripheral lenslets are randomly shifted. In FIG. 14, the dotted line shows the position of the initial lens let shown in FIG. 13, and the solid line shows the external position of the peripheral lens let after shifting.

For example, the Xj—Yj coordinates are introduced into the j-th initial peripheral lenslet as shown in the lower left of FIG. 14, and the deviation amount is set to (Δxj, Δyj). Further, Δxj is a range larger than − (L-AL) / 2 and smaller than (L-AL) / 2, and Δyj is a range larger than − (L-AL) / 2 and smaller than (L-AL) / 2. Then, if Δxj and Δyj are randomly selected using an arbitrary probability distribution function, the center position of the j-th initial peripheral lenslet is randomly shifted. For example, the center position 93 of the initial peripheral lenslet 94 is shifted to the center position 96 by the above method, whereby the external position of the initial peripheral lenslet 94 is shifted to the intermediate peripheral lenslet 97.

At this point, as shown in FIG. 14, some intermediate peripheral lenslets are overlapped with each other, and some intermediate peripheral lenslets are separated from each other. Since the total number of initial peripheral lenslets is sufficiently large and the center position of each initial peripheral lenslet is randomly shifted by an arbitrary probability distribution function, the mean square line drawn between the center positions of the intermediate lenslets is It corresponds to the angle θ of the initial lattice.

Next, the outer shape of the lens let is determined (step S5). Specifically, the lens is arranged so that the four intermediate peripheral lenslets are arranged around the central lenslet so that the entire incident surface of the microlens array 3 is filled with the peripheral lenslet and the central lenslet. Determine the outer shape of the lens.

FIG. 15 is a diagram for explaining matching of the position and size of the lens let by step S5. In the following, the matching of the position and size of the lenslet will be described by paying attention to one intermediate peripheral lenslet 25'. The intermediate peripheral lenslet 25'is moved from the arrangement of the initial peripheral lenslet (not shown) by step S4, and has a right side 25a', an upper side 25b', a left side 25c', and a lower side 25d' in the figure. , The outline is shown by the dotted line.

First select one of the intermediate peripheral lenslets (eg, top left or rightmost of the area forming the lenslet in one plane of the microlens array). Assuming that the outer shape of the selected intermediate peripheral lenslet is fixed, the outer shape of the intermediate peripheral lenslet and the initial center lenslet around the intermediate peripheral lenslet is sequentially deformed based on the method described later. In FIG. 15, it is assumed that the outer shapes of the peripheral lenslets 23, 24, 29, 30, 32, 34, and 35 and the outer shapes of the central lenslets 33 and 36 have already been determined.

First, the upper side 25b'of the intermediate peripheral lens let 25'is aligned with the lower side in the figure of the peripheral lens let 30 so as not to overlap or separate from the outer shape of the peripheral lens let 30 that has already been determined. Shift. Next, the left side 25c'of the intermediate peripheral lens let 25'is aligned with the right side in the drawing of the peripheral lens let 24 so as not to overlap or separate from the outer shape of the peripheral lens let 24 that has already been determined. Shift to. As a result, the final positions of the upper side 25b and the left side 25c of the peripheral lens let 25 are determined. Further, as the right side and the lower side in the figure of the peripheral lens let 25, a part of the right side 25a'and the lower side 25d' of the intermediate peripheral lens let 25'is used as it is. As a result, the outer shape of the peripheral lens let 25 is fixed.

By determining the outer shape of the peripheral lenslet 25, the outer shape of the central lenslet 31 arranged above the peripheral lenslet in the drawing is also determined. By determining the outer shapes of the peripheral lens let 25 and the central lens let 31, the unit cell 51 described with reference to FIGS. 3 to 5 is completed. The positions of the other peripheral lenslets and the central lenslet can be determined in the same manner, and finally the outer shapes of all the lenslets included in the microlens array 3 can be determined.

FIG. 16 shows only the periphery of the unit cell 51 whose position has been determined by step S5 in the microlens array 3, and FIG. 16 will be used to describe the microlens array in which the lenslet design is completed.

By the process described with reference to FIG. 14, the center position of the initial peripheral lenslet is randomly displaced. However, by the outer shape fixing process described with reference to FIG. 15, the outer shape is finally fixed in order to be fitted so as not to create a gap between the lenslet and the other lenslets whose outer shape has already been fixed. The outer shapes of the peripheral lenslet and the central lenslet are not randomly determined. If the outer shapes of the peripheral lenslet and the central lenslet are randomly changed, a gap will be created between the lenslets, and the efficiency of light utilization in the entire microlens array 3 will be reduced. In addition, the behavior of light in the portions formed between the lenslets must be considered, which complicates the design. That is, it is important that the center position of the lens let is randomly shifted, but the outer shape is not randomly changed.

Next, the sag amount of each of the peripheral lens let and the central lens let is calculated (step S6). Specifically, the sag amount is calculated by the method described with reference to FIG. 7. The initial peripheral lenslet may be a square with a side of Lμm, and the initial center lenslet may be a square with an ALμm side.

Based on the above-mentioned S1 to S6, the outer shapes of the plurality of peripheral lenslets and the central lenslet, and the sag amount of each lenslet are obtained (step S7). As a result, it becomes possible to output the design data of the entrance surface or the exit surface in which the unit cells overlap each other and are spread without gaps in the microlens array 3, and it becomes possible to manufacture the microlens array 3. ..

FIG. 17 is a block diagram of a design device 100 for designing the microlens array 3.

The design device 100 is a general computer such as a desktop computer, a workstation, and a notebook computer. The design device 100 includes an input unit 101, a display unit 102, a communication unit 103, a storage unit 104, a processing unit 105, a data bus 106, and the like.

The input unit 101 has an input device (keyboard, mouse, etc.) and an interface circuit for acquiring a signal from the input device, and receives an input operation from an operator who operates the design device 100.

The display unit 102 has a display such as a liquid crystal display or an organic EL (Electro-Luminence) and an interface circuit for outputting image data to the display, and displays various information on the display.

The communication unit 103 has, for example, a communication interface circuit compliant with TCP / IP or the like, and connects to a communication network such as the Internet. The communication unit 103 outputs the data received from the communication network to the processing unit 105, and transmits the data input from the processing unit 105 to the communication network.

The storage unit 104 is an example of a storage means, and includes a semiconductor memory such as a ROM and a RAM, an optical disk drive such as a magnetic disk or a CD-ROM, and a DVD-ROM, and a recording medium thereof. Further, the storage unit 104 stores a computer program for controlling the design device 100 and various data, and inputs and outputs these information to and from the processing unit 105. The computer program may be installed in the storage unit 104 from a computer-readable portable recording medium such as a CD-ROM or a DVD-ROM using a known setup program or the like.

The processing unit 105 has a processor such as a CPU and an MPU, a memory such as a ROM and a RAM, and a peripheral circuit thereof, and executes various signal processing of the design device 100. A DSP, LSI, ASIC, FPGA, or the like may be used as the processing unit 105. The processing unit 105 includes an initial value acquisition unit 111, an initial grid generation unit 112, a variation generation unit 113, a determination unit 114, a lens sag calculation unit 115, an output unit 116, and the like.

It is also possible to automatically perform the flow shown in FIG. 11 using the design device 100 shown in FIG. For example, the user inputs the size L and the angle θ of the initial peripheral lens let by the initial value acquisition means 111. After that, the initial grid generation means 112 executes the process corresponding to steps S2 and S3, the variation generation means 113 executes the process corresponding to step S4, and the determination means 114 executes the process corresponding to step S5. Further, the lens sag calculation means 115 executes the process corresponding to step S6, and the output means 116 outputs the data of the finally designed microlens array 3 (step S7), and ends the predetermined process.

A mold is created based on the design data generated by the design device 100, and the microlens array is finally manufactured. The microlens array may be manufactured by a 3D printer by directly using the design data.

For example, by setting the external dimensions of the microlens array to 5 mm × 5 mm, setting the lenslet forming range to 4.4 mm × 4.4 mm inside the external shape, and setting L = 50 μm and θ = 35 °, the micro shown in FIG. 2 The lens array 3 can be designed and manufactured. It is preferable that L is 10 to 100 μm and the total number of lenslets is 1000 to 10000.

3 Microlens Array, 4 Irradiation Area, 24, 25, 29, 30 Peripheral Lenslet, 31 Center Lenslet

Claims (4)

A microlens array having a rectangular outer shape, an incident surface and an emitted surface of light, and forming a light beam having a predetermined intensity distribution in an irradiation region having an aspect ratio of 1: τ.
It has a plurality of unit cells spread without gaps while overlapping with each other on one surface of the exit surface or the entrance surface.
Each of the unit cells comprises one central lenslet and four peripheral lenslets arranged along the four sides of the central lenslet.
All outer shapes of the central lenslet and the peripheral lenslet have a rectangular shape and have a rectangular shape.
The four sides of the central lenslet and one side of each of the four peripheral lenslets are arranged side by side on a straight line, and the four sides of the central lenslet and the other one side of the four peripheral lenslets are arranged side by side. Are arranged to face each other, the other side of the four peripheral lenslets is longer than the sides of the central lenslet facing each other, and the four vertices of the central lenslet and the four peripheral lenslets are facing each other. Each one of the vertices is placed in the same position,
The center positions of the plurality of peripheral lenslets included in the microlens array are randomly set.
The angle θ (θ is 0 ° or more and 90 ° or less) formed by the minimum squared straight line passing through the center of a plurality of adjacent peripheral lenslets and one side of the peripheral lenslet is Tan ^-1 (0.466 τ) or more. And it is less than Tan ^-1 (0.933 τ),
A microlens array characterized by that. The microlens array according to claim 1, wherein one of the unit cells and one of the other unit cells adjacent to the unit cell are arranged so as to share two peripheral lenslets. The sag amount z of the central lenslet and the peripheral lenslet is a biconic surface represented by the following equation (1) when the width of the central lenslet and the peripheral lenslet is W and the height is H. ,
Here, letting the width of the rectangular initial lens lenslet be L, the height being τL, the radius of curvature being r, and the conic coefficient being k, rx = (W / L) r, ry = (H / τL) r, kx = The microlens array according to claim 1 or 2, wherein k and ky = k.

A unit cell including one central lenslet and four peripheral lenslets arranged along the four sides of the central lenslet has an exit surface or an incident surface that are spread without gaps while overlapping each other. A method for manufacturing a microlens array that forms a light beam having a predetermined intensity distribution in an irradiation region having an aspect ratio of 1: τ.
Based on the size of the initial lenslet with an aspect ratio of 1: τ and the tilt angle θ of the initial lenslet, the angle formed by a line segment passing through the center of a plurality of initial peripheral lenslets and a predetermined side of the initial peripheral lenslet is An initial lattice consisting of a plurality of rectangular initial peripheral lenslets is generated so as to have the inclination angle θ.
A plurality of intermediate peripheral lenslets are generated by randomly shifting the positions of the plurality of initial peripheral lenslets.
By changing the outer shape of the plurality of intermediate peripheral lenslets and the plurality of central lenslets, the four sides of the central lenslet and one side of each of the four peripheral lenslets are arranged side by side on a straight line. The four sides of the central lenslet and the other one side of the four peripheral lenslets are arranged so as to face each other, and the other one side of the four peripheral lenslets faces each other. The four apex of the central lenslet and one apex of each of the four peripheral lenslets, which are longer than the sides of the lenslet, form a surface in which the unit cells arranged at the same position overlap each other and are spread without gaps. death,
The sag amount was calculated for all the lenslets including the central lenslet and the peripheral lenslet.
Using the calculated sag amount, the design data of the surface in which the unit cells are spread without gaps while overlapping with each other is output.
A method for manufacturing a microlens array.

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