Method for manufacturing microlens array

Abstract

This method for manufacturing a microlens array for irradiating a surface with a light flux having a prescribed wavelength includes: a step for determining the amplitude distribution of light on the surface to be irradiated from a target intensity distribution for light on the surface to be irradiated; a step for calculating the distribution of the absolute values of the amplitudes of light on a surface of the microlens array from the amplitude distribution of light on the surface to be irradiated; a step for determining the shape of the surface of the microlens array according to the distribution of the absolute values of the amplitudes of light on the surface of the microlens array; and a step for calculating the amplitude distribution of light that has passed through the microlens array on the surface to be irradiated. The step for calculating the distribution of the absolute values of the amplitudes of light on the surface of the microlens array, as well as the subsequent steps, are repeated, as needed, to reduce the sum of the respective differences between the absolute value of the amplitude of light at each position on the surface to be irradiated, obtained through calculation, and the absolute value of the amplitude of light corresponding to the target intensity of light at that position on the surface to be irradiated.

Description

Microlens array manufacturing method

[0001] The present invention relates to a method for manufacturing a microlens array.

[0002] When a diffusion element that illuminates a surface with light of a predetermined wavelength is constructed using a microlens array, if the microlens array uses microlenses with square, regular hexagonal, or other bases tightly arranged on a flat surface, the effects of diffracted light due to the periodic structure are unavoidable. Therefore, to avoid the effects of diffracted light, microlens arrays and methods for manufacturing microlens arrays have been developed in which the center positions and shapes of the bases are randomly changed from the above arrangement (Patent Documents 1 and 2). However, the above-mentioned conventional manufacturing methods cannot manufacture microlens arrays that can achieve various target light intensity distributions on the irradiated surface. Furthermore, measures must be taken to avoid the effects of diffracted light due to the periodic structure for each case. Until now, no method has been developed for manufacturing a microlens array that can achieve various target light intensity distributions on the irradiated surface without requiring measures to avoid the effects of diffracted light due to the periodic structure for each case. Therefore, there is a need for a method for manufacturing a microlens array that can achieve various target light intensity distributions on the irradiated surface without requiring measures to avoid the effects of diffracted light due to the periodic structure for each case.

[0003] Patent Document 1: JP 2021-156914 A Patent Document 1: JP 2021-189394 A

[0004] The object of the present invention is to provide a method for manufacturing a microlens array that can realize various target light intensity distributions on the irradiation surface and does not require consideration of measures to avoid the influence of diffracted light caused by the periodic structure in each case.

[0005] The method for manufacturing a microlens array of the present invention is a method for manufacturing a microlens array in which a surface is illuminated with a light beam of a predetermined wavelength, and includes the steps of determining the light amplitude distribution of the illumination surface from the target light intensity distribution of the illumination surface, calculating the distribution of absolute values ​​of light amplitude on the surface of the microlens array from the light amplitude distribution of the illumination surface, determining the shape of the surface of the microlens array in accordance with the distribution of absolute values ​​of light amplitude on the surface of the microlens array, and calculating the amplitude distribution on the illumination surface of light that has passed through the microlens array.In the method for manufacturing a microlens array of the present invention, the step of calculating the distribution of absolute values ​​of light amplitude on the surface of the microlens array and 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 differences between the calculated absolute values ​​of light amplitude at each position on the illumination surface and the absolute values ​​of light amplitude corresponding to the target light intensity at each position on the illumination surface.

[0006] According to the microlens array manufacturing method of the present invention, it is possible to manufacture microlens arrays that realize various target light intensity distributions on the irradiation surface, and there is no need to consider measures to avoid the effects of diffracted light caused by the periodic structure in each case.

[0007] In a manufacturing method of a microlens array according to a first embodiment of the present invention, the surface of the microlens array is divided into a plurality of regions, and a reference shape of a microlens is placed in each of the regions of a predetermined range in which the absolute value of the amplitude of light in the region is relatively large, and the shape of the surface of the microlens array is determined based on the shape obtained.

[0008] According to this embodiment, the surface shape of the microlens array can be determined by a simple procedure.

[0009] In the method for manufacturing a microlens array according to the second embodiment of the present invention, when the reference shapes of the arranged multiple microlenses overlap, the surface shape of the microlens array is determined by the reference shape with the highest height.

[0010] In the manufacturing method of a microlens array according to the third embodiment of the present invention, the distribution of the light amplitude of the irradiation surface is corrected based on the absolute value of the light amplitude at each position on the irradiation surface obtained by calculation and the absolute value of the light amplitude corresponding to the target light intensity at each position on the irradiation surface, and the shape of the surface of the microlens array is determined by repeating the steps of calculating the distribution of the absolute value of the light amplitude of the surface of the microlens array as necessary and the subsequent steps.

[0011] According to this embodiment, the surface shape of the microlens array can be determined in a simple procedure by correcting the distribution of the light amplitude of the irradiation surface based on the absolute value of the light amplitude at each position on the irradiation surface obtained by calculation and the absolute value of the light amplitude corresponding to the target light intensity at each position on the irradiation surface and performing repeated calculations.

[0012] In the method for manufacturing a microlens array according to the fourth embodiment of the present invention, an inverse Fourier transform is used in the step of calculating the distribution of the absolute value of the amplitude of light on the surface of the microlens array, and a Fourier transform is used in the step of calculating the amplitude distribution on the irradiation surface of light that has passed through the microlens array.

[0013] In this embodiment, the calculation load can be reduced by using a Fourier transform and an inverse Fourier transform.

[0014] 4. FIG. 5 is a diagram showing a microlens array functioning as a diffusing element configured to illuminate a surface with light of a predetermined wavelength. FIG. 6 is a photograph showing a plan view of a microlens array of the prior art. FIG. 7 is a cross-sectional view of a microlens array of the prior art. FIG. 8 is a flow chart showing a method for manufacturing a microlens array according to an embodiment of the present invention. FIG. 9 is a diagram showing a light beam irradiating an illumination surface after passing through a microlens. FIG. 10 is an example of a plan view of a microlens array and a unit. FIG. 11 is a diagram showing a target distribution of relative values ​​of light amplitude (real numbers) on an illumination surface. FIG. 12 is a diagram showing a distribution of relative values ​​of light amplitude (real numbers) on the surface of a unit. FIG. 13 is a diagram for explaining the position of the central axis of a microlens on the surface of a microlens array unit. FIG. 14 is a diagram showing cross sections of microlenses of multiple reference shapes on the surface of a microlens array unit. FIG. 15 is a diagram showing cross sections of microlenses on the surface of a microlens array unit perpendicular to the surface. FIG. 16 is a diagram for explaining how to determine R. FIG. 17 is a diagram showing the distribution of relative values ​​of light amplitude (real numbers) on the surface of a microlens array unit determined by step S1030 of FIG. 17. FIG. 18 is a diagram showing the shape of a microlens on the surface of a microlens array unit determined by step S1040 of FIG. 18. 4. A diagram showing the light intensity distribution on the irradiation surface obtained by the first microlens array unit. A diagram showing the target light intensity distribution on the irradiation surface of the first microlens array unit. A diagram showing the distribution of relative values ​​of light amplitude (real numbers) on the surface of the microlens array unit determined by step S1030 of Figure 4. A diagram showing the shape of microlenses on the surface of the microlens array unit determined by step S1040 of Figure 4. A diagram showing the light intensity distribution on the irradiation surface obtained by the second microlens array unit. A diagram showing the target light intensity distribution on the irradiation surface of the second microlens array unit.

[0015] 1 shows a microlens array 100 functioning as a diffusing element configured to illuminate a surface with a light beam of a predetermined wavelength. The light beam passes through the microlens array 100, which includes microlenses 111, and illuminates an illumination surface 200. The microlens array 100 is configured to illuminate a predetermined area of ​​the illumination surface when a light beam of a predetermined wavelength parallel to the central axis of the microlens 111 is irradiated from one surface of the microlens array 100.

[0016] FIG. 2 is a photograph showing a plan view of a prior art microlens array.

[0017] Fig. 3 is a cross-sectional view of a conventional microlens array including the central axis of a plurality of microlenses arranged in a row. The horizontal axis of Fig. 3 represents the position of the microlens. The vertical axis of Fig. 3 represents the height of the microlens from the substrate surface.

[0018] As shown in FIGS. 2 and 3, in the conventional microlens array, a plurality of microlenses are arranged at regular intervals on the surface of a substrate.

[0019] FIG. 4 is a flow chart illustrating a method for manufacturing a microlens array according to one embodiment of the present invention.

[0020] In step S1010 of Fig. 4, the diameter and focal length of each microlens on its surface and the size of the microlens array unit are determined. The microlens array unit will be described later. Here, the microlens surface is assumed to be spherical, and the diameter of the microlens on its surface refers to the diameter of the circle that forms the intersection between the spherical surface of the microlens and the surface on which the microlens is installed, i.e., the diameter of the circle on the periphery of the bottom surface.

[0021] 5 is a diagram showing a light beam that passes through the microlens 111 and then illuminates the irradiation surface 200. If the diameter of the microlens 111 on the substrate surface is D, the focal length of the microlens 111 is f, the angle of view is φ, the distance from the substrate surface 150 to the irradiation surface 200 is L, and the size of the illuminated area is W, the following relationships hold: D*(Lf) = W*f (1) W = 2*(Lf)* tan(φ / 2) (2) D = 2*f* tan(φ / 2) (3) Using the above relationships, the diameter D of the microlens 111 on the substrate surface and the focal length f of the microlens 111 can be determined from the size w of the illuminated area, the distance L, and the angle of view φ.

[0022] The numerical data of the embodiment are as follows: In the embodiment, a laser beam with a wavelength of 650 nanometers is used. D = 300 μm f = 1.7 mm L = 100 mm φ = 10 degrees w = 17.3 mm

[0023] FIG. 6 is an example of a plan view of the microlens array 100 and the units 110. The microlens array 100 is formed as a collection of multiple microlens array units 110. Each microlens array unit 110 corresponds to multiple microlenses, and the multiple microlens array units 110 have the same shape. The optical performance of the microlens array 100 is determined by the microlens array units 110 having the same shape. When multiple units are arranged repeatedly, diffracted light occurs due to the periodic structure. If the unit size is Ω and the light wavelength is λ, the diffraction angle θ of diffracted light caused by the periodic structure in which multiple units are arranged repeatedly can be expressed by the following equation: sin θ=λ / Ω (4) To minimize the influence of diffracted light caused by the periodic structure, it is desirable to make the diffraction angle θ as small as possible, and to achieve this, it is desirable to make the unit size Ω as large as possible.

[0024] On the other hand, in this example, if the resolution on the irradiation surface is 0.05 millimeters, the angle on the unit surface corresponding to the resolution dx' is dx' / L = 0.05 / 100 (radian) = 0.0286 (degrees). Substituting this angle for the diffraction angle θ in equation (4), and setting the wavelength λ of light to 650 nanometers, the unit size Ω is determined. The unit size Ω is 1.3 millimeters.

[0025] As described above, the optical performance of the microlens array 100 is determined by the microlens array unit 110 having the same shape, so the microlens array unit 110 will be described below.

[0026] The basic technical concept of the present invention will now be explained. As is well known, for light of a given wavelength and under given conditions, the complex amplitude of a Fraunhofer diffraction pattern of a rectangular aperture is proportional to the Fourier transform of the amplitude transmittance of an object. Therefore, it can be expected that by performing an inverse Fourier transform on a desired complex amplitude corresponding to a Fraunhofer diffraction pattern, it is possible to obtain the complex amplitude of an aperture that realizes the desired complex amplitude corresponding to the Fraunhofer diffraction pattern.

[0027] If the complex amplitude distribution on the surface of the unit 110 is represented by Φ(x, y), and the complex amplitude distribution on the irradiation surface 200 is represented by Φ'(x', y'), then Φ(x, y)=A(x, y)*exp(iφ(x, y)) (5) |Φ(x, y)|=A(x, y) Φ'(x', y')=B(x', y')*exp(iξ(x', y')) (6) |Φ'(x', y')|=B(x', y') where (x, y) are coordinates on the surface of the unit 110, and the origin is the center of the surface of the unit 110. (x', y') are coordinates on the irradiation surface 200. The x'-axis is parallel to the x-axis, and the y'-axis is parallel to the y-axis. The origin of the (x', y') coordinates is the intersection of the irradiation surface 200 and a line that passes through the origin of the (x, y) coordinates and is perpendicular to the unit 110 and the irradiation surface 200. A(x, y) and B(x', y') represent the amplitude at each coordinate on the surface of the unit 110 and the irradiation surface 200, respectively, and φ(x, y) and ξ(x', y') represent the phase at each coordinate on the surface of the unit 110 and the irradiation surface 200, respectively.

[0028] On the other hand, the relationship between the complex amplitude distribution Φ(x, y) on the surface of the unit 110 and the complex amplitude distribution Φ'(x', y') on the irradiation surface 200 can be expressed as follows using, for example, a Fourier transform FT and an inverse Fourier transform IFT: Φ'(x', y')~FT[Φ(x, y)] (7) Φ(x, y)~IFT[Φ'(x', y')] (8) Equation (7) is called the forward transform, and equation (8) is called the inverse transform. Forward transform and inverse transform will be explained later.

[0029] Here, the known and unknown parameters are as follows: Known parameters: B(x', y') Unknown parameters: A(x, y), φ(x, y), ξ(x', y') The phase ξ(x', y') is a dependent processing variable that maintains the optical wave property. The phase φ(x, y) is determined by the lens shape.

[0030] Therefore, in the present invention, ξ(x', y') is an arbitrary variable that is not a constant value, and the amplitude distribution A(x, y) on the surface of unit 110 and the lens shape φ(x, y) are determined so that |Φ'(x', y')| = B(x', y') realizes the target intensity distribution.

[0031] In step S1020 of FIG. 4, the amplitude distribution of the irradiation surface 200 is determined from the target light intensity distribution of the irradiation surface 200.

[0032] In step S1030 of FIG. 4, the amplitude distribution Φ(x, y) on the surface of the microlens array unit 110, which can be expressed by equation (5), is calculated from the amplitude distribution Φ'(x', y') on the irradiation surface 200 by inverse transformation of equation (8).

[0033] The method for determining A(x, y) in equation (5) will now be described.

[0034] The amplitude A(x, y) of the surface of unit 110 is expressed as the product of the ratio I0(x, y) of the absolute value of the amplitude distribution of the light beam incident on unit 110 to the maximum value and the ratio Aorg(x, y) of the absolute value of the complex amplitude inversely transformed from the irradiation surface to the maximum value: A(x, y)=I0(x, y)*Aorg(x, y) Here, the amplitude distribution of the light beam incident on unit 110 is set to, for example, a Gaussian distribution or flat planar light (I0(x, y)=1), and the value of I0(x, y) is not changed during the iterative calculations described later.

[0035] The relative value (ratio to the maximum value) Aorg(x, y) of the absolute value of the complex amplitude inversely transformed from the irradiated surface is set to Aorg(x, y) = 1 as the initial value, and the relative value of the calculation result is substituted for Aorg(x, y).

[0036] In equation (5), φ(x, y) is a function that represents the shape of the microlens in terms of phase.

[0037] FIG. 7 is a diagram showing the target distribution of the relative value of the light amplitude (real number) on the irradiation surface 200. The horizontal axis of FIG. 7 indicates the angle between the light ray passing through the unit 110 and the central axis of the microlens. The maximum absolute value of the angle, 5 degrees, is 1 / 2 of φ in FIG. 5. As shown in FIG. 1, a parallel light beam is incident on the microlens array 100 in the direction of the central axis of the microlens. The vertical axis of FIG. 7 indicates the relative value of the light amplitude (real number) on the irradiation surface 200. The light amplitude (real number) on the irradiation surface 200 corresponds to |Φ'(x', y')| = B1(x', y') described above. In the case shown in FIG. 7, the light intensity in the area of ​​size w in FIG. 5 on the irradiation surface 200 is uniform.

[0038] FIG. 8 is a diagram showing the distribution of the relative values ​​of the light amplitude (real number) on the surface of the unit 110. The horizontal axis of FIG. 8 represents the x-coordinate, i.e., the position in the x-axis direction. The vertical axis of FIG. 8 represents the relative values ​​of the light amplitude (real number) on the surface of the unit 110. The light amplitude (real number) on the surface of the unit 110 corresponds to |Φ(x, y)|=A(x, y) described above. Φ(x, y) is calculated using equation (8) of the inverse Fourier transform (IFT). Here, the phase distribution ξ(x', y') on the irradiated surface 200 is assumed to be a non-uniform random value. According to FIG. 8, |Φ(x, y)|=A(x, y) has a periodicity of 0.65 millimeters, which is half the size of the unit 110, 1.3 millimeters.

[0039] In step S1040 of FIG. 4, the shape of the surface of the microlens array unit 110 is determined according to the amplitude distribution Φ(x, y) on the surface of the microlens array unit 110.

[0040] First, the surface of the microlens array unit 110 is divided into square regions with a side length of Ω / N, where N is set to 2048. The side length of the square is Ω / N=1.3 / 2048 (mm) =0.635 (μm).

[0041] Next, the following formula is determined from |Φ(x, y)|. Armin≦Ar≦Armax (10) Arminε[0.5, 0.95], Armax=1 (11) In the embodiment, Armax=1 and Armin=0.85 are set. In Fig. 8, Armax=1 and Armin=0.85 are indicated by dashed lines.

[0042] A microlens having a standard shape is arranged so that its central axis passes through the center of a square area (the intersection of the diagonals of the square) that satisfies formula (10). The microlens having the standard shape will be described later.

[0043] FIG. 9 is a diagram illustrating the position of the central axes of the microlenses on the surface of the microlens array unit 110. The horizontal axis of FIG. 9 represents the x-coordinate, i.e., the position in the x-axis direction. The positions of the central axes of the microlenses are indicated by coordinates x1, x2, and x3. The spacing between coordinates x1 and x2 is Ω / N=1.3 / 2048 (mm) =0.635 (μm). The vertical axis of FIG. 9 represents the amplitude (real number) of light on the surface of the unit 110.

[0044] Fig. 10 is a diagram showing a cross section of microlenses of multiple reference shapes on the surface of a microlens array unit. The horizontal axis of Fig. 10 indicates the x-coordinate, i.e., the position in the x-axis direction. The vertical axis of Fig. 10 indicates the height of the microlenses of the reference shapes. In the cross section shown in Fig. 10, the shape of the microlens array unit is determined by the outline formed by the microlenses of the multiple reference shapes. In other words, when microlenses of the reference shapes overlap, the shape of the microlens array unit is determined by the highest position of the multiple shapes.

[0045] The reference shape of the microlens will now be described. The microlens in this embodiment is a spherical lens, and the radius of curvature, i.e., the radius of the sphere, Rc, is determined by the following formula: Rc=(n-1)*fn is the refractive index of the microlens, and in this embodiment, n=1.5. f is the focal length of the microlens, and as mentioned above, f=1.7 mm. Therefore, Rc=0.85 (mm). The reference shape of the microlens is determined based on the focal length f.

[0046] 11 is a diagram showing a cross section of a microlens of a reference shape on the surface of a microlens array unit, taken perpendicular to the surface. The height of the microlens on the surface is represented by h, and the radius of the circle formed by the intersection of the curved surface of the microlens of the reference shape and the surface of the microlens array unit is represented by R. As shown in FIG. 11, the following relationship holds:

[0047] FIG. 12 is a diagram for explaining how to determine R. Taking into consideration that adjacent microlenses of the standard shape overlap, Since D = 300 (μm) and Rc = 0.85 (mm), the maximum height h of the microlens of the standard shape is is.

[0048] In step S1050 of FIG. 4, the amplitude distribution Φ'(x', y') on the illumination surface of the light that has passed through the microlens array is calculated using the forward transformation of equations (5) and (7).

[0049] In step S1060 of Fig. 4, it is determined whether the difference between the calculated light amplitude distribution on the irradiation surface and the target light amplitude distribution on the irradiation surface is within a predetermined value. If the difference is within the predetermined value, the process ends. If the difference is greater than the predetermined value, the process proceeds to step S1070 and is repeated. The number of repetitions in step S1060 may be limited, and the shape of the microlens on the surface of unit 110 when the difference is minimized during the repetitions may be determined.

[0050] The calculated complex amplitude distribution of the irradiation surface 200 is represented by Φ'(x', y')=B(x', y')*exp(iξ(x', y')), and the complex amplitude distribution of the target image is represented by Φtarget(x', y')=C(x', y')*exp(iξtarget(x', y')). The above difference is determined by the following equation: Σ||Φtarget(x', y')|- |Φ'(x', y')|| In other words, the above difference is the sum of the differences between the absolute value of the light amplitude at each position on the irradiation surface and the absolute value of the light amplitude corresponding to the target light intensity at each position on the irradiation surface.

[0051] In step S1070 of Fig. 4, the amplitude distribution of the irradiation surface is corrected according to the above difference. As an example, P = Σ|Φtarget(x', y')|*|Φ'(x', y')| Q = Σ|Φtarget(x', y')|^2 R = P / Q, and the amplitude distribution of the irradiation surface is corrected by the following formula: Φ'(x', y') = R * |Φtarget(x', y')|*exp(iξ(x', y')) After the amplitude distribution of the irradiation surface has been corrected, the process returns to step S1030 and repeats.

[0052] 4, the value of the focal length f may be randomly changed for each repetition, and the new value of f may be used. As an example, the value of the focal length f may be randomly changed within the range of the following formula: 0.5*Amin / {Amin+(Amax-Amin) / 2}*f≦f≦1.5*Amax / {Amin+(Amax-Amin) / 2}*f

[0053] The microlens array unit obtained by the manufacturing method of the embodiment will be described below.

[0054] The target light intensity distribution on the illumination surface of the first microlens array unit is a uniform light intensity distribution within a rectangular area as shown in FIG. 16, which will be described later.

[0055] Fig. 13 is a diagram showing the distribution of relative values ​​of the amplitude (real number) of light on the surface of the microlens array unit obtained in step S1030 of Fig. 4. In Fig. 13, the relative values ​​of the amplitude (real number) of light are shown as density. Fig. 8 corresponds to the amplitude distribution of one cross section in the horizontal direction (x-axis direction) of Fig. 13.

[0056] FIG. 14 is a diagram showing the shape of the surface of the microlens array unit determined by step S1040 in FIG. 4. In FIG. 14, the height of the shape is shown by density. The maximum height is 22.682 micrometers. The shape shown in FIG. 14 is obtained when the number of repetitions in the process shown in FIG. 4 is limited to 100. FIG. 14 shows that there is no regularity in the shape and arrangement of the microlenses.

[0057] 15 is a diagram showing the light intensity distribution on the illumination surface obtained by the first microlens array unit, in which the relative value of the light intensity is shown as density.

[0058] 16 is a diagram showing the target light intensity distribution on the illumination surface of the first microlens array unit, in which the relative value of the light intensity is shown as density.

[0059] As shown in FIG. 15, the first microlens array unit provides a uniform light intensity distribution within the rectangular area shown in FIG. 16, similar to the uniform light intensity distribution.

[0060] The target light intensity distribution on the illumination surface of the second microlens array unit is a uniform light intensity distribution within a triangular region as shown in FIG. 20, which will be described later.

[0061] Fig. 17 is a diagram showing the distribution of relative values ​​of the amplitude (real number) of light on the surface of the microlens array unit obtained in step S1030 of Fig. 4. In Fig. 17, the relative values ​​of the amplitude (real number) of light are shown as density.

[0062] FIG. 18 is a diagram showing the shape of the surface of the microlens array unit determined by step S1040 in FIG. 4. In FIG. 18, the height of the shape is shown by density. The maximum height is 22.682 micrometers. The shape shown in FIG. 18 is obtained when the number of repetitions in the process shown in FIG. 4 is limited to 100. According to FIG. 18, no regularity is observed in the shape and arrangement of the microlenses.

[0063] 19 is a diagram showing the light intensity distribution on the illumination surface obtained by the second microlens array unit, in which the relative value of the light intensity is shown as density.

[0064] 20 is a diagram showing the target light intensity distribution on the illumination surface of the second microlens array unit, in which the relative value of the light intensity is shown as density.

[0065] As shown in FIG. 19, the first microlens array unit provides a uniform light intensity distribution within the triangular region shown in FIG. 20, similar to the uniform light intensity distribution.

[0066] 15-16 and 19-20 show the light intensity distribution on the illumination surface by a single microlens array unit. The light intensity on the illumination surface can be increased by increasing the number of microlens array units. As mentioned above, a microlens array is a collection of microlens arrays that have the same shape and optical performance.

[0067] The above description has been given for the case where the target light intensity distribution on the irradiation surface is uniform. For example, when a sensor surface is illuminated by a microlens array, the sensitivity of the sensor decreases as the angle of incidence of the light rays increases. Therefore, in this case, it is desirable to not make the light intensity distribution on the irradiation surface uniform, but to relatively increase the intensity on the irradiation surface of light rays that form a large angle between the light rays that have passed through the microlens and the central axis of the microlens. According to the manufacturing method of the present invention, it is possible to manufacture a microlens array that achieves any target intensity distribution on the irradiation surface of the light rays.

[0068] In the above description, the microlenses are spherical lenses, but they may also be aspherical lenses.

[0069] In the above description, the diffraction due to the aperture is considered to be Fraunhofer diffraction.

[0070] When diffraction by an aperture is considered to be Fraunhofer diffraction, the Fourier transform FT, which is the forward transform of equation (7), is expressed by the following equation. In the following equation, coefficients outside the integral are omitted. In addition, in the following equation, the complex amplitude of the unit surface is expressed as Φ(x, y), the complex amplitude of the irradiation surface is expressed as Φ'(x', y'), and the distance between the unit surface and the irradiation surface is expressed as L. On the other hand, the inverse transformation of equation (8) is the inverse Fourier transform IFT, and is therefore expressed by the following equation: For the above Fourier transform FT and inverse Fourier transform IFT, a fast Fourier transform (FFT) can be used.

[0071] The present invention is also applicable to the case where the diffraction caused by the aperture is regarded as diffraction other than the Fraunhofer diffraction.

[0072] When diffraction by an aperture is regarded as Fresnel diffraction, the forward transform of equation (7) for an image that diffuses into the distance can be expressed as follows using a Fourier transform: On the other hand, the inverse transformation of equation (8) can also be expressed as follows: In this way, FFT can be used for Fresnel diffraction under the condition that the image is diffused into the distance.

[0073] When diffraction by an aperture is considered as Rayleigh-Sommerfeld diffraction, the forward transform of equation (7) can be written as follows using Fourier transform and convolution integral, provided that the irradiation surface is very close to the unit. On the other hand, the inverse transformation of equation (8) can also be expressed as follows: Here, the variables kx and ky are the wavenumber components in the x-axis and y-axis directions on each plane, and can be expressed as follows: kx=sin(θx) / λ ky=sin(θy) / λ θx and θy are the angles of travel of the ray in the x-axis and y-axis directions, respectively, and are in the range of [-π / 2, π / 2]. When θx=θy=0, the direction of travel of the ray is perpendicular to each plane.

[0074] Generally, for diffraction images that are diffused over a long distance, calculations are performed using either the Fraunhofer diffraction (Fourier transform) or Fresnel diffraction methods described above.

[0075] The method for manufacturing a microlens array of the present invention can be realized by processing a substrate or a molding die for injection molding or the like using well-known lithography techniques, electroforming techniques, and laser processing techniques, either alone or in combination.

Claims

1. 1. A method for manufacturing a microlens array in which a surface is illuminated with a light beam of a predetermined wavelength, comprising: determining a light amplitude distribution on the illumination surface from a target light intensity distribution on the illumination surface; calculating a distribution of absolute values ​​of the amplitude of light on the surface of the microlens array from the amplitude distribution of light on the illumination surface; determining a shape of the surface of the microlens array in accordance with a distribution of absolute values ​​of amplitudes of light on the surface of the microlens array; calculating an amplitude distribution of the light that has passed through the microlens array on the illumination surface; a step of calculating a distribution of absolute values ​​of light amplitudes on the surface of the microlens array as necessary, and a subsequent step are repeated to determine the shape of the surface of the microlens array, so as to reduce the sum of the differences between the absolute values ​​of light amplitudes at each position on the irradiation surface determined by calculation and the absolute values ​​of light amplitudes corresponding to target light intensities at each position on the irradiation surface; A method for manufacturing a microlens array in which 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 placing a reference shape of a microlens in each of the regions of a predetermined range where the absolute value of the amplitude of light in the region is relatively large.

2. The method for manufacturing a microlens array according to claim 1, wherein when the reference shapes of the arranged plurality of microlenses overlap, the surface shape of the microlens array is determined by the reference shape with the highest height.

3. 2. The method for manufacturing a microlens array according to claim 1, wherein the shape of the surface of the microlens array is determined by repeating a step of correcting the distribution of the amplitude of light on the irradiation surface based on the absolute value of the amplitude of light at each position on the irradiation surface obtained by calculation and the absolute value of the amplitude of light corresponding to the target light intensity at each position on the irradiation surface, and calculating the distribution of the absolute value of the amplitude of light on the surface of the microlens array, and the subsequent steps.

4. 2. The method for manufacturing a microlens array according to claim 1, wherein an inverse Fourier transform is used in the step of calculating the distribution of the absolute value of the amplitude of light on the surface of the microlens array, and a Fourier transform is used in the step of calculating the amplitude distribution on the irradiation surface of light that has passed through the microlens array.