Method for manufacturing microlens array

Abstract

A method for manufacturing a microlens array that irradiates a surface with a light beam having a predetermined wavelength, the method comprising the steps of: determining the amplitude distribution of light on the irradiation surface on the basis of the intensity distribution of target light on the irradiation surface; calculating the distribution of absolute values of the amplitude of the light of the surface of the microlens array from the amplitude distribution of the light of the irradiation surface; determining a shape of the surface of the microlens array from a distribution of absolute values of amplitudes of light of the surface of the microlens array; and calculating the amplitude distribution of the light passing through the microlens array on the irradiation surface. The step of calculating the distribution of the absolute value of the amplitude of the light on the surface of the microlens array and the subsequent step are repeated as necessary. The sum of the absolute value of the amplitude of the light at each position of the irradiation surface obtained by calculation and the difference between the absolute value of the amplitude of the light corresponding to the intensity of the target light at each position of the irradiation surface is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to a manufacturing method of a microlens array. BACKGROUND

[0002] In the case of a diffusion element configured by a microlens array that irradiates a surface with light of a prescribed wavelength, if a microlens array in which microlenses having a square, regular hexagonal, or the like as a base surface are arranged without gaps on a plane is used, it is not possible to avoid the influence of diffracted light caused by the periodic structure. Therefore, in order to avoid the influence of diffracted light, a microlens array in which the center position of the base surface and the shape of the base surface are randomly changed from the above-described arrangement and a manufacturing method of a microlens array have been developed (Patent Literature 1 and Patent Literature 2). However, with the above-described conventional manufacturing method, it is not possible to manufacture a microlens array that realizes the intensity distribution of light of various targets of the irradiation surface. Furthermore, it is necessary to consider measures for avoiding the influence of diffracted light caused by the periodic structure for each housing. So far, a manufacturing method of a microlens array that is capable of realizing the intensity distribution of light of various targets of the irradiation surface and does not need to consider measures for avoiding the influence of diffracted light caused by the periodic structure for each housing has not been developed. Therefore, there is a demand for a manufacturing method of a microlens array that is capable of realizing the intensity distribution of light of various targets of the irradiation surface and does not need to consider measures for avoiding the influence of diffracted light caused by the periodic structure for each housing.

[0003] Patent Literature 1: Japanese Patent Application Publication No. 2021-156914

[0004] Patent Literature 2: Japanese Patent Application Publication No. 2021-189394 SUMMARY

[0005] The present application relates to a manufacturing method of a microlens array.

[0006] In the manufacturing method of the microlens array of the present invention, the microlens array is irradiated with a light beam of a prescribed wavelength against a surface, wherein the manufacturing method of the microlens array comprises the steps of determining an amplitude distribution of light of the irradiation surface from an intensity distribution of light of the target of the irradiation surface, calculating a distribution of absolute values of amplitudes of light of the surface of the microlens array from the amplitude distribution of light of the irradiation surface, determining a shape of the surface of the microlens array from the distribution of absolute values of amplitudes of light of the surface of the microlens array, and calculating an amplitude distribution of light on the irradiation surface after passing through the microlens array. In the manufacturing method of the microlens array of the present invention, the step of calculating the distribution of absolute values of amplitudes of light of the surface of the microlens array and the subsequent steps are repeated as necessary to determine the shape of the surface of the microlens array so as to reduce the sum of the difference between the absolute value of the amplitude of light at each position of the irradiation surface calculated and the absolute value of the amplitude of light corresponding to the intensity of light of the target at each position of the irradiation surface.

[0007] According to the manufacturing method of the microlens array of the present invention, it is possible to manufacture a microlens array that realizes a variety of intensity distributions of light of a target of an irradiation surface without considering a countermeasure for avoiding the influence of diffracted light caused by a periodic structure for each housing.

[0008] In the manufacturing method of the microlens array of the first embodiment of the present invention, the surface of the microlens array is divided into a plurality of regions, and the shape of the surface of the microlens array is determined based on the shape obtained by arranging the reference shapes of the microlenses in the regions in which the absolute values of amplitudes of light are relatively large in a prescribed range.

[0009] According to the present embodiment, it is possible to determine the shape of the surface of the microlens array in a simple procedure.

[0010] In the manufacturing method of the microlens array of the second embodiment of the present invention, in the case where the reference shapes of the plurality of microlenses overlap, the shape of the surface of the microlens array is determined based on the reference shape having the highest height.

[0011] In the manufacturing method of the microlens array of the third embodiment of the present invention, the distribution of amplitudes of light of the irradiation surface is corrected based on the absolute values of amplitudes of light at each position of the irradiation surface calculated and the absolute values of amplitudes of light corresponding to the intensity of light of the target at each position of the irradiation surface, and the step of calculating the distribution of absolute values of amplitudes of light of the surface of the microlens array and the subsequent steps are repeated as necessary to determine the shape of the surface of the microlens array.

[0012] According to the present embodiment, the distribution of the amplitude of light of the irradiation surface is corrected and repeated calculation is performed according to the absolute value of the amplitude of light of each position of the irradiation surface calculated by calculation and the absolute value of the amplitude of light corresponding to the intensity of light of the target of each position of the irradiation surface, whereby the shape of the surface of the microlens array can be determined in a simple step.

[0013] In the manufacturing method of the microlens array of the fourth embodiment of the present application, the inverse Fourier transform is used in the step of calculating the distribution of the absolute value of the amplitude of light of the surface of the microlens array, and the Fourier transform is used in the step of calculating the amplitude distribution of light on the irradiation surface after passing through the microlens array.

[0014] In the present embodiment, the load of calculation can be reduced by using the Fourier transform and the inverse Fourier transform. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 is a diagram showing a microlens array functioning as a diffusion element configured to be irradiated with light of a prescribed wavelength.

[0016] Figure 2 is a photograph showing a plane of a microlens array of the related art.

[0017] Figure 3 is a sectional view of a microlens array of the related art.

[0018] Figure 4 is a flowchart showing a manufacturing method of a microlens array of one embodiment of the present application.

[0019] Figure 5 is a diagram showing a light beam irradiating an irradiation surface after passing through a microlens.

[0020] Figure 6 is an example of a plan view of a microlens array unit.

[0021] Figure 7 is a diagram showing a distribution of a target of a relative value of the amplitude (real number) of light on an irradiation surface.

[0022] Figure 8 is a diagram showing a distribution of a relative value of the amplitude (real number) of light on a surface of a unit.

[0023] Figure 9 is a diagram for explaining a position of a center axis of a microlens on a surface of a microlens array unit.

[0024] Figure 10 is a diagram showing a cross section of a plurality of reference shape microlenses on a surface of a microlens array unit.

[0025] Figure 11 is a diagram showing a cross section of the microlens perpendicular to the above-mentioned face on the face of the microlens array unit.

[0026] Figure 12 is a diagram for explaining the determination method of R.

[0027] Figure 13 is a diagram showing the intensity distribution of light in the irradiation face obtained by the second microlens array unit. Figure 4 is a diagram showing the distribution of the relative value of the amplitude (real number) of light on the face of the microlens array unit calculated by step S1030 of

[0028] Figure 14 is a diagram showing the shape of the microlens on the face of the microlens array unit determined by step S1040 of Figure 4

[0029] is a diagram showing the intensity distribution of light in the irradiation face obtained by the first microlens array unit. Figure 15

[0030] is a diagram showing the intensity distribution of light of the target of the irradiation face of the first microlens array unit. Figure 16

[0031] is a diagram showing the distribution of the relative value of the amplitude (real number) of light on the face of the microlens array unit calculated by step S1030 of Figure 17 Figure 4 is a diagram showing the shape of the microlens on the face of the microlens array unit determined by step S1040 of

[0032] Figure 18 Figure 4 is a diagram showing the intensity distribution of light in the irradiation face obtained by the second microlens array unit.

[0033] Figure 19 is a diagram showing the intensity distribution of light of the target of the irradiation face of the second microlens array unit.

[0034] Figure 20 is a diagram showing the intensity distribution of light in the irradiation face obtained by the second microlens array unit. DETAILED DESCRIPTION

[0035] Figure 1 is a diagram showing the microlens array 100 functioning as a diffusion element configured to irradiate a face with a light beam of a prescribed wavelength. The irradiation face 200 is irradiated with a light beam that has passed through the microlens array 100 having microlenses 111. The microlens array 100 is configured to, in a case where a light beam of a prescribed wavelength parallel to the central axis of the microlenses 111 is irradiated from one face, irradiate a prescribed range of the irradiation face.

[0036] ​​Figure 2 is a photograph showing a plane of a micro lens array of the related art.

[0037] Figure 3 is a cross-sectional view of a plurality of micro lenses of a micro lens array of the related art arranged in a row, including a central axis. Figure 3 The horizontal axis indicates the position of the micro lens. Figure 3 The vertical axis indicates the height of the micro lens from the substrate plane.

[0038] As shown in Figure 2 and Figure 3 , in a micro lens array of the related art, a plurality of micro lenses are arranged at constant intervals on a substrate plane.

[0039] Figure 4 is a flowchart showing a manufacturing method of a micro lens array of one embodiment of the present application.

[0040] In Figure 4 step S1010, the diameter on the surface of each micro lens and the focal distance and the size of the micro lens array unit are determined. The micro lens array unit is described later. Here, the surface of the micro lens is a spherical surface, and the diameter on the surface of the micro lens refers to the diameter of a circle that is the intersection of the spherical surface of the micro lens and the plane on which the micro lens is provided, i.e., the outer periphery of the base.

[0041] Figure 5 is a diagram showing a light beam that irradiates the irradiation plane 200 after passing through the micro lens 111. Let the diameter on the substrate plane of the micro lens 111 be D, the focal distance of the micro lens 111 be f, and the field of view angle be φ. The diameter on the substrate plane of the micro lens 111 is the diameter of a circle that is the intersection of the spherical surface of the micro lens 111 and the plane on which the micro lens 111 is provided, i.e., the outer periphery of the base. The distance from the substrate plane 150 to the irradiation plane 200 is L, and the size of the irradiated region is W, the following relationship holds.

[0042] D*(L-f) = W*f (1)

[0043] W = 2*(L-f)*tan(φ / 2) (2)

[0044] D = 2*f*tan(φ / 2) (3)

[0045] The diameter D on the substrate plane of the micro lens 111 and the focal distance f of the micro lens 111 can be determined using the above relationships, from the size W of the irradiated region, the distance L, and the field of view angle φ.

[0046] The numerical data of the example are as follows. In the example, a laser with a wavelength of 650 nm is used.

[0047] D = 300 μm

[0048] f = 1.7 mm

[0049] ​L = 100 mm

[0050]

[0051] W = 17.3 mm

[0052] Figure 6 is an example of a plan view of the microlens array 100 and the unit 110. The microlens array 100 is formed as a collection of a plurality of microlens array units 110. The microlens array unit 110 corresponds to a plurality of microlenses, and the plurality of microlens array units 110 have the same shape. The optical performance of the microlens array 100 is determined by the microlens array units 110 of the same shape. In the case where a plurality of units are repeatedly arranged, diffracted light caused by the periodic structure is generated. Let the size of the unit be Ω and the wavelength of the light be λ, then the diffraction angle θ of the diffracted light caused by the periodic structure in which a plurality of units are repeatedly arranged is expressed by the following equation.

[0053] sin θ = λ / Ω (4)

[0054] In order to reduce the influence of the diffracted light caused by the periodic structure, it is preferable to reduce the diffraction angle θ as much as possible, and for this purpose, it is preferable to increase the size Ω of the unit as much as possible.

[0055] On the other hand, in the embodiment, let the resolution of the irradiation surface be 0.05 mm, then the angle of the unit surface corresponding to the resolution dx' is as follows.

[0056] dx' / L = 0.05 / 100 (radian) = 0.0286 (degree)

[0057] The size Ω of the unit is determined by substituting this angle into the diffraction angle θ of equation (4) and setting the wavelength λ of the light to be 650 nm. The size Ω of the unit is 1.3 mm.

[0058] As described above, the optical performance of the microlens array 100 is determined by the microlens array units 110 of the same shape, and therefore the microlens array unit 110 will be described below.

[0059] Here, the basic technical idea of the present application will be described. It is well known that, with respect to light of a prescribed wavelength, under prescribed conditions, the complex amplitude of the Fraunhofer diffraction image of a rectangular aperture is proportional to the Fourier transform of the amplitude transmittance of the object. Therefore, it is expected that the complex amplitude of the aperture which realizes the desired complex amplitude of the Fraunhofer diffraction image can be obtained by performing the inverse Fourier transform of the desired complex amplitude of the Fraunhofer diffraction image.

[0060] Let Φ(x, y) represent the complex amplitude distribution of the surface of the unit 110, and let Φ'(x', y') represent the complex amplitude distribution of the irradiation surface 200, then

[0061] Φ(x, y) = A(x, y) * exp(iφ(x, y)) (5)

[0062] |Φ(x, y)| = A(x, y)

[0063] Φ'(x', y') = B(x', y') * exp(iξ(x', y')) (6)

[0064] |Φ'(x', y')| = B(x', y'),

[0065] (x, y) is a coordinate on the face of the unit 110, and the origin is the center of the face of the unit 110. (x', y') is a coordinate on the irradiation plane 200. The x' axis is parallel to the x axis, and the y' axis is parallel to the y axis. Also, the origin of the (x', y') coordinate is the intersection point of a straight line passing through the origin of the (x, y) coordinate and perpendicular to the unit 110 and the irradiation plane 200 and the irradiation plane 200. A(x, y) and B(x', y') respectively represent the amplitudes at each coordinate of the face of the unit 110 and the irradiation plane 200, and ξ(x', y') respectively represent the phases at each coordinate of the face of the unit 110 and the irradiation plane 200.

[0066] On the other hand, the relationship between the complex amplitude distribution Φ(x, y) of the face of the unit 110 and the complex amplitude distribution Φ'(x', y') of the irradiation plane 200 is expressed, for example, using the Fourier transform FT and the inverse Fourier transform IFT as follows.

[0067] Φ'(x', y') ~ FT[Φ(x, y)] (7)

[0068] Φ(x, y) ~ IFT[Φ'(x', y')] (8)

[0069] Equation (7) is referred to as a forward transform, and equation (8) is referred to as an inverse transform. The forward transform and the inverse transform are described later.

[0070] wherein the known parameters and the unknown parameters are as follows.

[0071] Known parameters: B(x', y')

[0072] Unknown parameters: A(x, y), ξ(x', y')

[0073] The phase ξ(x', y') is a dependent processing variable for maintaining the optical wave property. Also, the phase is determined by the lens shape.

[0074] Therefore, in the present application, the arbitrary variable ξ(x', y') is a non-constant value, and the amplitude distribution A(x, y) of the face of the lens array unit 110 and the lens shape are calculated by the calculation unit 110 in such a way that |Φ'(x', y')| = B(x', y') achieves the target intensity distribution

[0075] In step S1020 of the process of FIG. 10, the amplitude distribution of the irradiation plane 200 is determined from the intensity distribution of the light of the target of the irradiation plane 200. Figure 4

[0076] In step S1030 of the process of FIG. 11, the amplitude distribution Φ(x, y) of the face of the lens array unit 110 shown in equation (5) is calculated from the amplitude distribution Φ'(x', y') of the irradiation plane 200 by inverse transformation of equation (8). Figure 4

[0077] The method of calculating A(x, y) of equation (5) is described.

[0078] The amplitude A(x, y) of the face of the unit 110 is expressed by the product of the ratio I0(x, y) of the absolute value of the amplitude distribution of the light beam incident to the unit 110 to the maximum value and the ratio Aorg(x, y) of the absolute value of the complex amplitude obtained by inverse transformation from the irradiation plane to the maximum value.

[0079] A(x, y) = I0(x, y) * Aorg(x, y)

[0080] wherein the amplitude distribution of the light beam incident to the unit 110 is set to, for example, a Gaussian distribution or a flat plane light (I0(x, y) = 1), and the value of I0(x, y) is not changed in the repeated calculation described later.

[0081] As the initial value of the relative value (ratio to the maximum value) of the absolute value of the complex amplitude obtained by inverse transformation from the irradiation plane, Aorg(x, y) = 1 is set, and the relative value of the calculation result is substituted into Aorg(x, y).

[0082] The function of equation (5) is a function that expresses the shape of the microlens by the phase.

[0083] Figure 7 is a graph showing the distribution of the target of the relative value of the amplitude (real number) of the light of the irradiation plane 200. Figure 7 The horizontal axis of FIG. 12 indicates the angle formed by the central axis of the microlens and the light ray after passing through the unit 110. The maximum value of the absolute value of the angle is 5 degrees, which is Figure 5 The horizontal axis of FIG. 12 indicates the angle formed by the central axis of the microlens and the light ray after passing through the unit 110. The maximum value of the absolute value of the angle is 5 degrees, which is is 1 / 2. As Figure 1 ​​As shown, parallel light beams in the direction of the central axis of the microlens enter the microlens array 100 . Figure 7 The vertical axis represents the relative value of the amplitude (real number) of the light irradiating the surface 200. The amplitude (real number) of the light irradiating the surface 200 corresponds to the above-mentioned |Φ'(x',y')|=B1(x',y'). Figure 7 In the case shown, the irradiation surface 200 Figure 5 The light intensity is uniform in an area of ​​size W.

[0084] Figure 8 3 is a diagram showing the distribution of relative values ​​of the amplitude (real number) of light on the surface of the cell 110 . Figure 8 The horizontal axis represents the x-coordinate, that is, the position in the x-axis direction. Figure 8 The vertical axis represents the relative value of the amplitude (real number) of the light on the surface of the unit 110. The amplitude (real number) of the light on the surface of the unit 110 corresponds to the above-mentioned |Φ(x,y)|=A(x,y). Φ(x,y) is obtained using the formula (8) of the inverse Fourier transform IFT. Here, the phase distribution ξ(x',y') of the irradiated surface 200 is assumed to be a non-uniform random value. According to Figure 8 , |Φ(x,y)|=A(x,y) has a periodicity of 0.65 mm, which is half the size of the unit cell 110 , 1.3 mm.

[0085] exist Figure 4 In step S1040 , the shape of the surface of the microlens array unit 110 is determined according to the amplitude distribution Φ(x, y) of the surface of the microlens array unit 110 .

[0086] First, the surface of the microlens array unit 110 is divided into square regions each having a side of Ω / N. N is 2048. One side of the square is Ω / N = 1.3 / 2048 (mm) = 0.635 (μm).

[0087] Next, the following mathematical formula is determined based on |Φ(x,y)|.

[0088]

[0089] Armin≤Ar≤Armax (10)

[0090] Armin∈[0.5,0.95],Armax=1 (11)

[0091] In the embodiment, Armax=1, Armin=0.85. Figure 8 In FIG, Armax=1 and Armin=0.85 are shown by dashed lines.

[0092] The center axis of the reference shape micro lens is arranged at the center of the region of the square which satisfies the equation (10) (the intersection of the diagonals of the square). The micro lens having the reference shape will be described later.

[0093] Figure 9 is a diagram for explaining the position of the center axis of the micro lens on the face of the micro lens array unit 110. Figure 9 The horizontal axis of indicates the x coordinate, that is, the position in the x axis direction. The position of the center axis of the micro lens is indicated by the coordinates x1, x2, x3. The interval between the coordinates x1 and x2 is Ω / N = 1.3 / 2048 (mm) = 0.635 (μm). Figure 9 The vertical axis of indicates the amplitude (real number) of light on the face of the unit 110.

[0094] Figure 10 is a diagram showing the cross section of the plurality of reference shape micro lenses on the face of the micro lens array unit. Figure 10 The horizontal axis of indicates the x coordinate, that is, the position in the x axis direction. Figure 10 The vertical axis of indicates the height of the reference shape micro lens. In Figure 10 In the cross section shown in, the shape of the micro lens array unit is determined by the profile formed by the plurality of reference shape micro lenses. That is, in the case where the reference shape micro lenses overlap, the shape of the micro lens array unit is determined from the highest position of the plurality of shapes.

[0095] The reference shape of the micro lens will be described. The micro lens of the embodiment is a spherical lens, and the radius of curvature, that is, the radius Rc of the sphere is determined by the following equation.

[0096] Rc = (n - 1) * f

[0097] n is the refractive index of the micro lens, and in the embodiment, n = 1.5. f is the focal length of the micro lens, and as described above, f = 1.7 mm. Therefore, Rc = 0.85 (mm). The reference shape of the micro lens is determined in accordance with the focal length f.

[0098] Figure 11 is a diagram showing the cross section of the reference shape micro lens on the face of the micro lens array unit perpendicular to the above-mentioned face. The height of the micro lens on the face is indicated by h, and the radius of the circle formed by the intersection line of the curved surface of the reference shape micro lens and the face of the micro lens array unit is indicated by R. As shown in Figure 11 , the following relationship holds.

[0099]

[0100] Figure 12 is a diagram for explaining the determination method of R. Considering the case where the adjacent reference shape micro lenses overlap, it is set as follows.

[0101]

[0102] D=300 (μm), Rc=0.85 (mm), and therefore the maximum height h of the microlens of the reference shape is as follows.

[0103]

[0104] exist Figure 4 In step S1050, the forward transformation of equations (5) and (7) is used to calculate the amplitude distribution Φ'(x', y') of the light on the illumination surface after passing through the microlens array.

[0105] exist Figure 4 In step S1060, a determination is made as to whether the calculated difference between the amplitude distribution of the light on the illuminated surface and the amplitude distribution of the target light on the illuminated surface is within a specified value. If the difference is within the specified value, the process ends. If the difference is greater than the specified value, the process proceeds to step S1070 and repeats. Alternatively, the number of repetitions in step S1060 may be limited, and the shape of the microlens on the surface of unit 110 may be determined for each repetition in which the difference is minimized.

[0106] The calculated complex amplitude distribution of the irradiated surface 200 is expressed by the following equation.

[0107] Φ'(x',y')=B(x',y')*exp(iξ(x',y'))

[0108] The complex amplitude distribution of the target image is expressed by the following formula.

[0109] Φtarget(x',y')=C(x',y')*exp(iξtarget(x',y'))

[0110] The above difference is determined by the following formula.

[0111] ∑||Φtarget(x',y')|-|Φ'(x',y')||

[0112] That is, the difference is the sum of the difference between the absolute value of the amplitude of light at each position on the irradiation surface and the absolute value of the amplitude of light corresponding to the intensity of the target light at each position on the irradiation surface.

[0113] exist Figure 4 In step S1070, the amplitude distribution of the irradiated surface is corrected according to the above difference. As an example, assuming

[0114] P=∑|Φtarget(x',y')|*|Φ'(x',y')|

[0115] Q = ∑Φtarget(x', y')|^2

[0116] R = P / Q,

[0117] The amplitude distribution of the irradiation surface is corrected by the following equation.

[0118] Φ'(x', y') = R * |Φtarget(x', y')| * exp(iξ(x', y'))

[0119] After the amplitude distribution of the irradiation surface is corrected, the process returns to step S1030, and the process is repeated.

[0120] Further, in step S1040 of the process of the embodiment, the value of the focal distance f is randomly changed each time the process is repeated, and the value of f is used. As an example, the value of the focal distance f can be randomly changed within the range of the following equation. Figure 4

[0121] 0.5 * Amin / {Amin + (Amax - Amin) / 2} * f ≤ f ≤ 1.5 * Amax / {Amin + (Amax - Amin) / 2} * f

[0122] The microlens array unit obtained by the manufacturing method of the embodiment will be described below.

[0123] The intensity distribution of the light of the target of the irradiation surface of the first microlens array unit is as shown in FIG. 10B, which is a uniform intensity distribution of light within a rectangular region. Figure 16

[0124] FIG. 12 is a graph showing the distribution of the relative values of the amplitude (real number) of the light of the surface of the microlens array unit calculated by step S1030 of the process of the embodiment. In FIG. 12, the relative values of the amplitude (real number) of the light are shown by concentration. Figure 13 Figure 4 Figure 13 corresponds to the amplitude distribution of one cross section in the horizontal direction (x-axis direction). Figure 8 Figure 13

[0125] Figure 14 FIG. 14 is a graph showing the shape of the surface of the microlens array unit determined by step S1040 of the process of the embodiment. In FIG. 14, the height of the shape is shown by concentration. The maximum height is 22.682 micrometers. Figure 4 Figure 14 Figure 14 The shape shown in FIG. 14 is the shape in the case where the number of repetitions is limited to 100 times in the process shown in FIG. 13. According to the embodiment, the shape and the arrangement of the microlenses have no regularity. Figure 4 Figure 14

[0126] Figure 15 ​​​​​​​​​is a graph showing the intensity distribution of light of the irradiation surface obtained by the first microlens array unit. In Figure 15 the relative value of the intensity of light is shown by the concentration.

[0127] Figure 16 is a graph showing the intensity distribution of light of the target of the irradiation surface of the first microlens array unit. In Figure 16 the relative value of the intensity of light is shown by the concentration.

[0128] As Figure 15 indicated, the same intensity distribution of light as that shown in Figure 16 in the rectangular region is obtained by the first microlens array unit.

[0129] The intensity distribution of light of the target of the irradiation surface of the second microlens array unit is the intensity distribution of light in the triangular region as shown in Figure 20 later described.

[0130] Figure 17 is a graph showing the distribution of the relative value of the amplitude (real number) of light of the face of the microlens array unit calculated by the step S1030 of Figure 4 In Figure 17 the relative value of the amplitude (real number) of light is shown by the concentration.

[0131] Figure 18 is a graph showing the shape of the face of the microlens array unit determined by the step S1040 of Figure 4 In Figure 18 the height of the shape is shown by the concentration. The maximum height is 22.682 micrometers. Figure 18 The shape shown in Figure 4 is the shape in the case where the number of repetitions is limited to 100 times in the process shown in Figure 18 According to , the shape and arrangement of the microlenses have no regularity.

[0132] Figure 19 is a graph showing the intensity distribution of light of the irradiation surface obtained by the second microlens array unit. In Figure 19 the relative value of the intensity of light is shown by the concentration.

[0133] Figure 20 is a graph showing the intensity distribution of light of the target of the irradiation surface of the second microlens array unit. In Figure 20 the relative value of the intensity of light is shown by the concentration.

[0134] As Figure 19 indicated, the same intensity distribution of light as that shown in Figure 20 in the triangular region is obtained by the second microlens array unit.

[0135] Figures 15 to 16 and Figures 19 to 20 The intensity distribution of light on the irradiation surface based on a single microlens array unit is shown. By increasing the number of microlens array units, the intensity of light on the irradiation surface can be increased. As described above, the microlens array is a collection of microlens array units having the same shape and the same optical performance.

[0136] In the above description, the case where the intensity distribution of light on the target of the irradiation surface is uniform is described. For example, in the case where the sensor surface is irradiated with the microlens array, if the incident angle of the light ray increases, the sensitivity of the sensor decreases. Therefore, in this case, it is preferable that the intensity distribution of light on the irradiation surface is not uniform, but the intensity of the light ray on the irradiation surface is relatively large for the light ray having a large angle with the central axis of the microlens after passing through the microlens. According to the manufacturing method of the present application, regardless of the intensity distribution of light on the target of the irradiation surface, a microlens array that realizes the distribution can be manufactured.

[0137] Also, in the above description, the microlens is a spherical lens, but can be an aspherical lens.

[0138] In the above description, the case where the diffraction based on the opening is regarded as Fraunhofer diffraction is described.

[0139] In the case where the diffraction based on the opening is regarded as Fraunhofer diffraction, the forward transform of equation (7), that is, the Fourier transform FT is expressed by the following equation. In the following equation, the coefficient other than the integral is omitted. Also, in the following equation, Φ(x, y) represents the complex amplitude of the surface of the unit, Φ'(x', y') represents the complex amplitude of the irradiation surface, and L represents the distance between the surface of the unit and the irradiation surface.

[0140]

[0141] On the other hand, the inverse transform of equation (8) is the inverse Fourier transform IFT, and is therefore expressed by the following equation.

[0142]

[0143] As for the Fourier transform FT and the inverse Fourier transform IFT described above, a high-speed Fourier transform (FFT) can be used.

[0144] The present application can also be applied to the case where the diffraction based on the opening is regarded as diffraction other than Fraunhofer diffraction.

[0145] In the case where the diffraction based on the opening is regarded as Fresnel diffraction, for the image that is diffused to the far field, the forward transform of equation (7) can be expressed by the following equation using the Fourier transform.

[0146]

[0147] On the other hand, the inverse transform of formula (8) can also be expressed as follows.

[0148]

[0149] Thus, for Fresnel diffraction, under the condition of an image spreading to the far field, FFT can also be used.

[0150] In the case where the diffraction based on the opening is considered as Rayleigh-Sommerfeld diffraction, only under the condition that the irradiation surface is extremely close to the unit, the forward transform of formula (7) can be expressed by using Fourier transform and convolution integral with the following formula.

[0151]

[0152] On the other hand, the inverse transform of formula (8) can also be expressed as follows.

[0153]

[0154] wherein the variables kx, ky are the wave number components in the x-axis and y-axis directions of each plane, and are expressed by the following formulas.

[0155] kx = sin(θx) / λ

[0156] ky = sin(θy) / λ

[0157] θx, θy are the traveling angles of the light rays in the x-axis and y-axis directions, respectively, and are in the range of [-π / 2, π / 2]. In the case of θx = θy = 0, the traveling direction of the light ray is perpendicular to each plane.

[0158] Generally, for a diffraction image spreading to the far field, any method in the above Fraunhofer diffraction (Fourier transform) or Fresnel diffraction is used for calculation.

[0159] The manufacturing method of the microlens array of the present application can be realized by machining a base material or a molding die for injection molding, etc. by using known photolithography technology, electroforming machining technology, laser machining technology, alone or in combination.

Claims

1. A manufacturing method of a microlens array which irradiates a surface with a light beam of a prescribed wavelength, wherein the manufacturing method of the microlens array comprises the steps of: determining an amplitude distribution of light of the surface from an intensity distribution of light of an object of the surface; calculating a distribution of absolute values of amplitudes of light of the surface of the microlens array from the amplitude distribution of light of the surface; determining a shape of the surface of the microlens array from the distribution of absolute values of amplitudes of light of the surface of the microlens array; and calculating an amplitude distribution of light on the surface after passing through the microlens array, the step of calculating the distribution of absolute values of amplitudes of light of the surface of the microlens array and the subsequent steps being repeated as necessary to determine the shape of the surface of the microlens array so as to reduce a sum of differences between the absolute values of amplitudes of light at each position of the surface calculated by the calculation and the absolute values of amplitudes of light corresponding to the intensity of light of the object at each position of the surface.

2. The manufacturing method of the microlens array according to claim 1, wherein the shape of the surface of the microlens array is determined based on shapes obtained by arranging reference shapes of microlenses in each region of a region of a prescribed range in which the absolute values of amplitudes of light are relatively large in the region.

3. The manufacturing method of the microlens array according to claim 2, wherein in a case where the reference shapes of the plurality of microlenses overlap, the shape of the surface of the microlens array is determined based on the reference shape having the highest height.

4. The manufacturing method of the microlens array according to claim 1, wherein the amplitude distribution of light of the surface is corrected based on the absolute values of amplitudes of light at each position of the surface calculated by the calculation and the absolute values of amplitudes of light corresponding to the intensity of light of the object at each position of the surface, and the step of calculating the distribution of absolute values of amplitudes of light of the surface of the microlens array and the subsequent steps are repeated as necessary to determine the shape of the surface of the microlens array.

5. The manufacturing method of the microlens array according to claim 1, wherein an inverse Fourier transform is used in the step of calculating the distribution of absolute values of amplitudes of light of the surface of the microlens array, and a Fourier transform is used in the step of calculating the amplitude distribution of light on the surface after passing through the microlens array. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​

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