OPTICAL SYSTEM
Patent Information
- Application Number
- DE112015002502
- Authority / Receiving Office
- DE · DE
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2015-05-26
- Publication Date
- 2025-11-06
- Estimated Expiration
- 2035-05-26
Smart Images
Figure 00000000_0000_ABST
Abstract
Description
Technical field
[0001] The present invention relates to an optical system. background
[0002] A diffuser that creates a uniform intensity distribution profile of scattered light is needed for a wide range of applications, such as general lighting, including interior lighting, light sources for optical sensors for industrial purposes, and screens for visual displays.
[0003] A Gaussian diffuser, which achieves a Gaussian intensity distribution profile of scattered light by refracting incident light, is well known as a diffuser that achieves a uniform intensity distribution profile of scattered light. Gaussian diffusers have a rough surface that exhibits a perfectly random height distribution profile. Gaussian diffusers are known to include: one manufactured by a process in which a base material, such as glass, is sandblasted to create a shape with a rough surface, and the roughness of the shape is transferred to a plastic material; one manufactured by a process in which a base material is exposed to a so-called speckle pattern, which is a random light intensity pattern generated by the interference of light from coherent light sources to create a shape, and the shape is transferred to a plastic material; and similar designs.Such Gaussian diffusers provide a natural and uniform light intensity distribution profile. However, since the distribution profile does not significantly exceed Gaussian intensity profiles, design flexibility is limited, and transmissivity is reduced at wide light distribution angles (N). Furthermore, Gaussian diffusers tend to have a grainy texture on their surfaces, often resulting in a mottled pattern. Consequently, Gaussian diffusers are not suitable for applications like displays, where a uniform appearance and feel are essential.
[0004] In applications requiring higher transmissivity or a distribution profile exceeding Gaussian intensity profiles, many devices have been developed that utilize a microlens array instead of a Gaussian diffuser. With a microlens array, the intensity distribution profile of scattered light can be controlled by adjusting the shape of a microlens. Furthermore, higher transmissivity can be achieved compared to a rough surface. However, in a microlens array where microlenses are arranged at small intervals, wavefronts from the beams of the corresponding microlenses interfere with each other. Due to the periodic structure of the array, deflected waves, such as refracted or diffracted waves, are generated, resulting in a detrimental inconsistency in the light distribution.Furthermore, if the radius of curvature of a microlens becomes small, it becomes disadvantageous that a deflection, for example refraction and / or diffraction, at an aperture of the microlens itself causes an unevenness in the light intensity distribution of the scattered light.
[0005] Under these circumstances, microlens arrangements have been proposed in which arrangements, surface shapes, or aperture shapes are varied to reduce the unevenness of the light intensity distribution due to interference and deflection. For example, a focal plane plate for camera focusing was developed in which microlenses are arranged randomly to reduce the unevenness of scattered light intensity due to deflection, such as refraction and / or diffraction, caused by a periodic structure of a microlens arrangement (Patent Documents 1 and 2). Furthermore, a microlens arrangement was developed in which various features, such as arrangement, surface shape, and aperture shape, are provided randomly (Patent Document 3).
[0006] However, prior art documents, including those described above, fail to disclose how the arrangement and shapes can be varied to sufficiently reduce the unevenness of the light intensity distribution. Furthermore, in the case of a microlens with a small aperture radius, required to achieve a distribution with a large divergence angle, the problem arises from unevenness in the light intensity distribution due to deflection, such as refraction and / or diffraction, at the aperture of a single microlens, rather than from the periodic structure of the microlenses.However, a microlens arrangement in which the arrangement and shapes were varied to reduce the unevenness of the light intensity distribution, including taking into account the deflection at the aperture of a single microlens, and an optical system including such a microlens, were not developed. State-of-the-art documents Patent Document 1: JP S63 - 221 329 A; Patent Document 2: JP H03 - 192 232 A (JP 2 881 877 B2); Patent Document 3: JP 2006-500621 A.
[0007] Further optical systems are known from the publications JP 2005- 70 631 A and DE 10 2006 047 941 A. Brief description: Task of the invention
[0008] Accordingly, an optical system is required that has a microlens arrangement in which the arrangement and shapes are designed to reduce any unevenness in the light intensity distribution, including unevenness in the light intensity distribution due to deflection, for example refraction and / or diffraction, at the aperture of a single microlens. Means of solving the task
[0009] According to the present invention, an optical system according to claim 1 is provided.
[0010] A microlens arrangement according to a first aspect of the present disclosure is a microlens arrangement comprising N microlenses arranged in an XY plane. A projection of each vertex of the microlenses onto the XY plane is arranged in the XY plane adjacent to a grid point of a reference grating, wherein a grid spacing of the reference grating in a predetermined direction is D / M (in millimeters), where M is a positive integer, and, where a boundary between microlenses is referred to as a side of a lens, a distance between two sides facing each other is approximately equal to D, and a distance between a projection of a vertex of one of the lenses onto the XY plane and a projection of a side of the lens onto the XY plane is D / 2+εi σ2=∑i=1N(εi−ε¯)2N ε¯=∑i=1NεiN=0, and , if n represents the refractive index of the microlens material, R (in millimeters) represents the radius of curvature in the given direction near the center of the microlenses, and f (in millimeters) represents the focal length of the microlenses, then the conditions are 0.0042D <D2f=D(n−1)2R 0.0048f{1+(D2f)2}<σ<0.014f{1+(D2f)2} fulfilled.
[0011] In the microlens arrangement according to the present aspect, a non-uniformity of the light intensity distribution, including the non-uniformity of the light intensity distribution due to deflection, for example refraction and / or diffraction, at the aperture of a single microlens can be reduced by appropriately varying the distance between two sides facing each other, each side forming a boundary between the lenses.
[0012] In a microlens arrangement according to a first embodiment of the first aspect of the present disclosure, the reference grating is rectangular or hexagonal.
[0013] M = 1 if the reference grid is rectangular, and M = 2 if the reference grid is hexagonal.
[0014] In a microlens arrangement according to a second embodiment of the first aspect of the present disclosure, a vertex of a lens is oriented in the specified direction by η i to the corresponding lattice point, such that the aperture of the corresponding microlens, which is formed by boundaries between adjacent microlenses, is shifted by ε i has changed and the relationships εi≅ηi+ηi+12 ση=∑i=1N(ηi−η¯)2N=2σ η¯=∑i=1NηiN apply.
[0015] According to the present embodiment, if the microlenses are axially symmetric, a boundary between adjacent microlenses is the perpendicular bisector of the line connecting the vertices of the adjacent microlenses, and no step is created at the boundaries between the surfaces of the adjacent microlenses.
[0016] In a microlens arrangement according to a third embodiment of the first aspect of the present disclosure, the reference grating in the XY plane is perpendicular, the grating spacing in the X direction is Dx and the grating spacing in the Y direction is Dy, and each projection of one of the vertices of the lenses of the microlens onto the XY plane is by (η xi , η yi ) offset from the corresponding grid position.
[0017] In a microlens arrangement according to a fourth embodiment of the first aspect of the present disclosure, the reference grating is perpendicular in the XY plane, the points are arranged in the X and Y directions, and adjacent to the centers of the microlenses is the radius of curvature in the X direction Rx (millimeters) and the radius of curvature in the Y direction Ry (millimeters).
[0018] In a microlens arrangement according to a fifth embodiment of the first aspect of the present disclosure, the relationship is further 0.047D <D2f=D(n−1)2R fulfilled.
[0019] In a microlens arrangement according to a sixth embodiment of the first aspect of the present disclosure, the relationship is further 0.0064f{1+(D2f)2}<σ<0.014f{1+(D2f)2} fulfilled.
[0020] In a microlens arrangement according to a seventh embodiment of the first aspect of the present disclosure, the vertex positions of the microlenses are uniformly distributed in the direction perpendicular to the XY plane in the range of 0 to 0.55 / (n-1) (micrometers).
[0021] According to the present embodiment, a so-called dark spot can be attenuated by shifting the phases of the light from several microlenses by offsetting the vertices of the majority of the microlenses relative to each other in the direction that is perpendicular to the XY plane, i.e. the grating plane.
[0022] In a microlens arrangement according to an eighth embodiment of the first aspect of the present disclosure, when a maximum value of the absolute value of ε i by |ε i | max The condition is marked as follows: |εi|max<3σ fulfilled.
[0023] An optical system according to a second aspect of the present disclosure is an optical system comprising a light source that emits light, wherein a minimum wavelength of the light λ (in micrometers) is, and a microlens arrangement configured to deflect the light from the light source, for example, to widen it. The microlens arrangement comprises N microlenses arranged in an XY plane.Projections of the vertices of the microlenses onto the XY plane are each adjacent to grid points of a reference grating in the XY plane, wherein a grid spacing of the reference grating in a given direction is D / M (in millimeters), where M is a positive integer, and, if a boundary between microlenses is called a side of the lenses, a distance between two sides facing each other is approximately equal to D and a distance between a projection of the vertex of a lens onto the XY plane and a projection of a side of the lens onto the XY plane. D / 2+εi σ2=∑i=1N(εi−ε¯)2N ε¯=∑i=1NεiN=0 is, and , where n represents the refractive index of the microlens material, R (in millimeters) represents the radius of curvature in the given direction near the center of the microlenses, and f (in millimeters) represents the focal length of the microlenses, the conditions are 0.0072λD <D2f=D(n−1)2R 0.0062λf{1+(D2f)2}<σ<0.019λf{1+(D2f)2} fulfilled.
[0024] In the optical system according to the present aspect, a non-uniformity of the light intensity distribution, including a non-uniformity of the light intensity distribution due to deflection, for example refraction and / or diffraction, at the aperture of a single microlens can be reduced by appropriately varying the distance between two sides facing each other, each side forming a boundary between the lenses.
[0025] In an optical system of a first embodiment of the second aspect of the present disclosure, the following relationship is further observed for the microlenses of the microlens arrangement: 0.080λD <D2f=D(n−1)2R fulfilled.
[0026] In an optical system of a second embodiment of the second aspect of the present disclosure, the following relationship is further observed for the microlenses of the microlens arrangement: 0.0083λf{1+(D2f)2}<σ<0.019λf{1+(D2f)2} fulfilled.
[0027] In an optical system of a third embodiment of the second aspect of the present disclosure, the vertex positions of the microlenses in the direction perpendicular to the XY plane are uniformly distributed in a range from zero to λ / (n-1) (in micrometers).
[0028] According to the present embodiment, a so-called dark spot can be attenuated by shifting the phases of the light from several microlenses by offsetting the vertices of the several microlenses relative to each other in the direction perpendicular to the XY plane, i.e., the grating plane.
[0029] In an optical system of a fourth embodiment of the second aspect of the present disclosure, the optical system comprises light sources n of different wavelengths λ1, λ2, ...λn, and, if λmulti represents a constant determined such that, if Remi represents the remainder when λmulti is divided by λi, the condition Remi<(λi / 10) or Remi>(λi / 10) For all i, the vertex positions of the microlenses in the direction perpendicular to the XY plane are uniformly distributed in a range from zero to λmulti / (n-1). Brief description of the drawings Fig. Figure 1 shows a microlens arrangement according to an embodiment of the present invention; Fig. Figure 2 shows a cross-section of a prior art microlens arrangement; Fig. Figure 3A shows a light intensity distribution obtained when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.07 mm and diverges; Fig. 3B is an enlarged drawing of a section of Fig. 3A in a range of angle θ from -11 to -7 degrees; Fig. Figure 4A shows an illuminated area when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.05 mm and diverges; Fig. Figure 4B shows a light intensity distribution obtained when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.05 mm and diverges; Fig. Figure 5A shows an illuminated area when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.1 mm and diverges; Fig. Figure 5B shows a light intensity distribution obtained when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.1 mm and diverges; Fig. Figure 6A shows an illuminated area when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.15 mm and D = 0.1 mm and diverges; Fig. Figure 6B shows a light intensity distribution obtained when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.15 mm and D = 0.1 mm and diverges. Fig. Figure 7 shows a relationship between a curvature at the center of a microlens and a period α; Fig. Figure 8 shows a relationship between an aperture width D of a microlens and a period α; Fig. Figure 9 shows a relationship between a difference in the refractive index of the material of a microlens and that of the material surrounding it and a period α; Fig. Figure 10 shows a relationship between the wavelength λ of the incident beam and a period α; Fig. Figure 11 shows a cross-section of a microlens arrangement; Fig. Figure 12 shows regions where an aperture width D and an angle θ of divergence satisfy equations (17) and (19). Fig. Figure 13 shows a state in which the vertices of microlenses are fixed at grating positions of the reference grating, which is a square grating, and the aperture values are varied. Fig. Figure 14A shows a state in which first vertices of a plurality of microlenses are fixed at grid positions of the reference grid, which is a rectangular grid, and then the vertices of the plurality of microlenses are offset from the grid points in the grid plane; Fig. Figure 14B shows a state in which first vertices of a plurality of microlenses are fixed at lattice points of the reference lattice, which is a rectangular lattice, and then the vertices of the plurality of microlenses are offset from the lattice points in the lattice plane; Fig. 14C is an enlarged view of the circled area in Fig. 14B; Fig. Figure 15 shows a light intensity distribution obtained when a light beam of wavelength 0.5876 µm is normally incident on the underside of the microlens arrangement of Example 1 and diverges; Fig. Figure 16 shows an arrangement of the optical system of Example 2; Fig. Figure 17A shows a light intensity distribution in the direction of the X-axis (the horizontal direction) obtained using the optical system according to Example 2; Fig. Figure 17B shows a light intensity distribution in the direction of the Y-axis (the vertical direction) obtained using the optical system according to Example 2; Fig. Figure 18A shows an arrangement of the optical system according to Example 3; and Fig. Figure 18B shows an arrangement of the light source optical system. Description of the embodiments
[0030] Fig. Figure 1 shows a microlens arrangement according to an embodiment of the present invention. The microlens arrangement comprises a plurality of microlenses that are essentially identical in shape and arranged in a plane. The structural features of the microlens arrangement according to the present invention are described below.
[0031] Fig. Figure 2 shows a cross-section of a prior art microlens arrangement 100A. Light rays normal, for example perpendicular, to a plane on the left side of Fig. The two incident wavelengths are deflected, for example refracted, by means of the convex surface of the microlens 1000A. The plane on the left side of Fig. Figure 2 is designated as the bottom surface of the microlens assembly 100A. The straight line passing through the vertex of the microlens 1000A and perpendicular to the bottom surface is defined as the Z-axis. The direction in which the light propagates is defined as the positive direction of the Z-axis. In the plane containing the vertex of the microlens 1000A and perpendicular to the Z-axis, the X-axis and Y-axis, which are orthogonal to each other, are defined. Fig. Figure 2 shows a cross-sectional view containing the Z-axis of the 1000A microlens. Fig. 2 is the Z-axis, labeled OP.
[0032] The convex surface of the microlens 1000A can be described, for example, by the following equation. z=cr21+1−(1+k)c2r2+∑nαnr2n
[0033] In the equation, r represents the distance from the Z-axis and c represents the curvature at the center of the lens. The following relationship holds between c and the radius of curvature R. α n represents a coefficient. r=x2+y2c=1R
[0034] Furthermore, as another example, the convex surface of the microlens 1000A can be described using the following equations. z=cr21+1−(1+k)c2r2+∑n∑mαnmxnym
[0035] In the equation, r represents the distance from the Z-axis. r=x2+y2 c represents the curvature at the center of the axisymmetric term. The radius of curvature Rx at the center in the direction of the x-axis and the radius of curvature Ry at the center in the direction of the y-axis are described by the following equations, also taking into account the second-order coefficients. c+2α20=1Rx c+2α02=1Ry
[0036] In Fig. 2. Light rays L1 and L2 are incident normally, for example perpendicularly and / or at a right angle, onto the underside of the microlens assembly 100A and pass through the periphery of the microlens 1000A. The angle that L1 forms with the Z-axis is identical to the angle that L2 forms with the Z-axis. This angle is called the divergence angle and is denoted by θ. If the focal length of the microlens 1000A is denoted by f and the aperture width of the microlens 1000A is denoted by D, the angle θ can be described by the following equations. tan θ=D2fθ=arctan(D2f)
[0037] Furthermore, the focal length of the microlens 1000A is described by the following equation, where the refractive index of a material of the microlens arrangement is denoted by n and the curvature in the center is denoted by R. f=Rn−1
[0038] It is known that when a light beam diverges due to a prior art microlens arrangement, a non-uniformity in the light intensity distribution of the diverging light is generated. This non-uniformity is caused by deflection, for example refraction and / or diffraction, at the arrangement of the majority of microlenses and by deflection, for example refraction and / or diffraction, at the aperture of a single microlens. This non-uniformity in the light intensity distribution becomes particularly evident when a coherent light source, such as a laser diode, is used.
[0039] Fig. Figure 3A shows a light intensity distribution obtained when a light beam of wavelength 550 nm is incident and diverges normally, for example perpendicularly and / or at right angles, on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm, and D = 0.07 mm.
[0040] Fig. 3B is an enlarged view of a section from Fig. 3A in the range of the angle θ from -11 degrees to -7 degrees.
[0041] The horizontal axes of the Fig. 3A and Fig. 3B represent the angle θ of divergence and the vertical axes of the Fig. 3A and Fig. 3B represents relative values of light intensity. The unit of angle θ is degrees.
[0042] In the Fig. 3A and Fig. 3B The thin line represents the light intensity, and the thick line represents the average light intensity within one degree. For example, the value of the thick line at -9.0 degrees represents the average of the values of the thin line in the range from -8.5 degrees to -9.5 degrees. According to Fig. 3B shows that the light intensity has a component with a period of approximately 0.5 degrees, represented by the thin line, and a component with a period of several degrees, represented by the thick line. The component with a period of approximately 0.5 degrees, represented by the thin line, is caused by deflection, such as refraction and / or diffraction, due to the arrangement of the majority of microlenses. The component with a period of several degrees, represented by the thick line, is caused by deflection, such as refraction and / or diffraction, at the aperture of a single microlens. In the case where the aperture width of a microlens is tens of micrometers, in other words, several tens of micrometers (in English, 1 / 2000), the component with a period of several degrees is caused by deflection, such as refraction and / or diffraction, at the aperture of a single microlens.: several tens of micrometers), or similarly, as in the present example, the component caused by the aperture of a microlens becomes larger.
[0043] According to Fig. 3A, in the range from approximately -12 degrees to approximately +12 degrees, the intensity represented by the thick line is 0.3 or greater. A peak-trough difference in intensity shows a maximum value between the extreme maximum, which is the maximum with the largest absolute value of the angle within the previously described range, and the trough adjacent to the extreme maximum and within the range. The difference in angle between the maximum with the largest absolute value of the angle and the maximum with the second largest absolute value of the angle is defined as the period α, which is used as a parameter of the intensity of the light diverging due to a microlensing arrangement.The difference in angle between the maximum with the largest absolute value of the angle and the maximum with the second largest absolute value of the angle can be determined, for example, by performing a least-squares fitting of a combination of two Gaussian functions and obtaining the interval between the maxima of the two Gaussian functions.
[0044] How the component described above, which has a period of a few degrees and is represented by the thick line, is influenced by the shape of a microlens is described below.
[0045] Fig. Figure 4A shows an illuminated area when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.05 mm and diverges.
[0046] Fig. Figure 4B shows a light intensity distribution obtained when a light beam with a wavelength of 550 nm is normally incident on the underside of a microlens array comprising microlenses with n = 1.5, R = 0.075 mm and D = 0.05 mm and diverges. The horizontal axis of the Fig. 4B represents the angle θ of divergence and the vertical axis of the Fig. 4B represents a relative value of light intensity. The unit of angle θ is degrees.
[0047] Fig. Figure 5A shows an illuminated area when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.075 mm and D = 0.1 mm and diverges.
[0048] Fig. Figure 5B shows a light intensity distribution obtained when a light beam with a wavelength of 550 nm is normally incident on the underside of a microlens array comprising microlenses with n = 1.5, R = 0.075 mm and D = 0.1 mm and diverges. The horizontal axis of the Fig. 5B represents the angle θ of divergence and the vertical axis of the Fig. 5B represents a relative value of light intensity. The unit of angle θ is degrees.
[0049] Fig. Figure 6A shows an illuminated area when a light beam of wavelength 550 nm is normally incident on the underside of a microlens arrangement having microlenses with n = 1.5, R = 0.15 mm and D = 0.1 mm and diverges.
[0050] Fig. Figure 6B shows a light intensity distribution obtained when a light beam with a wavelength of 550 nm is incident normally on the underside of a microlens array comprising microlenses with n = 1.5, R = 0.15 mm, and D = 0.1 mm, and diverges. The horizontal axis of the Fig. 6B represents the angle θ of divergence and the vertical axis of the Fig. 6B represents a relative value of light intensity. The unit of angle θ is degrees.
[0051] The microlenses according to Fig. 4B and according to Fig. 5B differ from each other with respect to their aperture width D. The region of the angle θ of divergence, in which the light intensity is greater than 0.2, extends in Fig. 4B from approximately -10 degrees to approximately +10 degrees and in Fig. 5B from approximately -17 degrees to approximately +17 degrees. The period α is the same in both cases. Fig. 4B and Fig. 5B approximately 3 degrees.
[0052] The microlenses according to Fig. 5B and according to Fig. 6B differ from each other with respect to the radius of curvature R at the center. The region of the angle θ of divergence, in which the light intensity is greater than 0.2, extends from approximately -17 degrees to approximately +17 degrees. Fig. 5B and from approximately -9 degrees to approximately +9 degrees in Fig. 6B. The period α is approximately 3 degrees in Fig. 5B and approximately 2 degrees in Fig. 6B.
[0053] Fig. Figure 7 shows a relationship between the curvature at the center of a microlens and the period α. The horizontal axis of the Fig. 7 represents the curvature at the center (1 / R) of a microlens and the vertical axis of the Fig. 7 represents the period α. The unit of the horizontal axis is 1 / millimeter and the unit of the vertical axis is degrees. Furthermore, the dashed line in Fig. 7 the curve obtained by fitting the following equation to measurement points and which shows the relationship between the curvature at the center (1 / R) and the period α. α=a11R
[0054] Therefore, a square of period α and a curvature at the center (1 / R) are proportional to each other.
[0055] Fig. Figure 8 shows a relationship between the aperture width D of a microlens and the period α. The horizontal axis of the Fig. 8 represents the aperture width D of a microlens and the vertical axis of the Fig. 8 represents the period α. The unit of the horizontal axis is millimeters and the unit of the vertical axis is degrees. According to Fig. 8. No significant correlation is found between period α and aperture width.
[0056] Fig. Figure 9 shows a relationship between the difference in refractive index between the material of a microlens and the medium surrounding it, and the period α. The horizontal axis of the Fig. 9 represents a difference in refractive index (n-1) between the material of a microlens and the medium surrounding it, and the vertical axis of the Fig. 9 represents the period α. The unit of the vertical axis is degrees. Furthermore, the dashed line in Fig. 9 the curve obtained by fitting the following equation to measurement points and which shows the relationship between the difference in refractive index (n-1) between the material of a microlens and the medium surrounding it and the period α. α=an−1
[0057] Thus, the square of the period α and the difference in refractive index (n-1) between the material of a microlens and the medium surrounding it are proportional to each other.
[0058] Fig. Figure 10 shows a relationship between the wavelength λ of the incident beam and the period α. The horizontal axis of the Fig. 10 represents the wavelength λ of the incident beam and the vertical axis of the Fig. 10 represents the period α. The unit of the horizontal axis is micrometer and the unit of the vertical axis is degrees. Furthermore, the dashed line in Fig. 10 the curve obtained by fitting the following equation to measurement points and which shows the relationship between the wavelength λ of the incident beam and the period α. α=a3λ
[0059] Thus, the square of the period α and the wavelength λ of the incident ray are proportional to each other.
[0060] The following equation can be derived from equation (2) and the results described above. α≈1.43λ(n−1)R=1.43λf
[0061] The following describes how shifting a boundary between the surfaces of the microlenses that define the aperture of a microlens affects the angle of divergence.
[0062] Fig. Figure 11 shows a cross-section of a microlens arrangement 100. Light directed onto the underside of the microlens arrangement 100 according to Fig. 11 is reflected by the convex surface of the microlens 1000 according to Fig. 11. The straight line passing through the vertex of the microlens 1000 and perpendicular to its underside is defined as the Z-axis. The direction in which the light propagates is defined as the positive direction of the Z-axis. In the plane containing the vertex of the microlens 1000, which is perpendicular to the Z-axis, the X-axis and the Y-axis, which are orthogonal to each other, are defined. Fig. Figure 11 shows a cross-section that includes the Z-axis of the microlens 1000. Fig. 11 is the Z-axis, labeled OP.
[0063] As in Fig. As shown in Figure 11, shifting the boundaries between the surfaces of the lenses by ε changes the angle θ of the divergence by Δθ. Using equation (1), the relationship between ε and Δθ can be expressed by the following equations. tan(θ−Δθ)=D−2ε2f tanθ−tanΔθ1+tanθtanΔθ=D−2ε2f tanΔθ=4εf4f2+D2=ε{1+(D2f)2}f
[0064] Since Δθ is sufficiently small, the following relationship holds. Δθ≈3602πtanΔθ=360ε2π{1+(D2f)2}f
[0065] If the difference Δθ of the divergence angle between two randomly selected microlenses is half the period α, the component produced at the aperture of one microlens due to deflection (e.g., refraction and / or diffraction) and the component produced at the aperture of the other microlens due to deflection (e.g., refraction and / or diffraction) cancel each other out and are reduced. In other words, the components produced at the apertures due to deflection (e.g., refraction and / or diffraction) cancel each other out and are reduced if the following relationship holds. Δθ2−Δθ1=α2
[0066] By substituting equations (3) and (4) into equation (5) the following equation can be obtained. 360(ε2−ε1)2π{1+(D2f)2}f=1.432λfε2−ε1=0.0125λf{1+(D2f)2}
[0067] In the entire microlens array, which comprises a plurality of microlenses, the offset ε of the boundaries between the lens surfaces is varied to reduce components generated at the apertures of the plurality of microlenses due to deflection, such as refraction and / or diffraction. When the variance of the offset ε of the boundaries between the lens surfaces is determined by σ 2 Given the given equation, the following equation is satisfied. 0.0060λf{1+(D2f)2}<σ<0.019λf{1+(D2f)2}
[0068] The following relationship applies. σ2=∑i=1N(εi−ε¯)2N ε¯=∑i=1NεiN=0
[0069] Assuming the wavelength of the light from the light source is 0.5876 µm of the d line, the following relationship should preferably be satisfied. 0.0048f{1+(D2f)2}<σ<0.014f{1+(D2f)2}
[0070] If the value in equations (7) or (8) reaches the lower limit, the components generated at the apertures due to deflection, for example refraction and / or diffraction, cannot be sufficiently reduced. Furthermore, if the value in equations (7) or (8) exceeds the upper limit, the uniformity of the intensity distribution of the propagating light deteriorates, and the tangential angle of a microlens becomes so steep that its fabrication becomes difficult.
[0071] Furthermore, the following relationships should preferably be fulfilled. 0.0083λf{1+(D2f)2}<σ<0.019λf{1+(D2f)2} 0.0064f{1+(D2f)2}<σ<0.014f{1+(D2f)2}
[0072] Furthermore, the following relationships should preferably be fulfilled. 0.0113λf{1+(D2f)2}<σ<0.0113λf{1+(D2f)2} 0.0086f{1+(D2f)2}<σ<0.0106f{1+(D2f)2}
[0073] If |ε| maxThe maximum value of an offset ε of the boundaries between two surfaces should preferably be satisfied by the following relationship. |ε|max<3σ
[0074] Furthermore, the following relationship should preferably be fulfilled. |ε|max<2.5σ
[0075] The period β of the component generated due to deflection, for example refraction and / or diffraction, caused by the arrangement of the majority of microlenses and which is in the Fig. 3A and Fig. The representation of 3B by the thin lines is examined below. If the period of the arrangement, i.e., the aperture width of a microlens, is denoted by D (in millimeters) and the wavelength of the light is denoted by λ (in micrometers), then β can be represented by the deflection equation as follows. β≈sinβ=3602πλ1000 D
[0076] If a ratio of the period α of the component produced due to the deflection, for example refraction and / or diffraction, at the aperture of a single microlens to the period β of the component caused by the deflection, for example refraction and / or diffraction, due to the arrangement of the plurality of microlenses is called M, then M can be represented using equations (3) and (15) as follows. M=αβ=25Dλf
[0077] The following equations can be obtained using equation (1). M=252D tan θλ 8.0E−4M2λD=tan θ
[0078] α must be significantly larger than β and M should be greater than 3. Therefore, the following relationship should preferably hold true. 0.0072λD <tan θ
[0079] Assuming that the wavelength of the light from the light source is 0.5876 µm of the d line, the following relationship should preferably be satisfied. 0.0042D <tan θ
[0080] Furthermore, M should be greater than 10. Accordingly, the following conditions should preferably be met. 0.080λD <tan θ 0.047D <tan θ
[0081] Fig. Figure 12 shows regions where the aperture width D and the angle θ of divergence satisfy equations (17) and (19), respectively. The horizontal axis of the Fig. 12 represents the aperture width D and the vertical axis of the Fig. Figure 12 represents the angle θ of divergence. The unit of the horizontal axis is millimeters and that of the vertical axis is degrees. It can be seen that the present embodiment is particularly effective in the case of a large angle θ of divergence, even if the aperture width D of a microlens is on the order of a few tens of micrometers.
[0082] If θ is eliminated from equations (16) to (19) using equation (1), equations (20) to (23) are obtained. 0.0072λD <D2f=D(n−1)2R 0.0042D <D2f=D(n−1)2R 0.080λD <D2f=D(n−1)2R 0.047D <D2f=D(n−1)2R
[0083] How the aperture width D can be varied over the majority of microlenses so that equation (7) is satisfied is described by way of example.
[0084] Fig. Figure 13 shows a state in which the vertices of the microlenses are fixed at grid points of the reference grating, which is a square grating, and the aperture values are varied. In this case, a non-uniform step is created at a boundary between adjacent microlenses. Such a step can cause unwanted scattered light or can negatively contribute to parts of a mold separating from each other during an injection molding process.
[0085] Fig. Figure 14A shows a state in which the first vertices of a plurality of microlenses are fixed at the points of the reference grating, which is a rectangular grating, with grating spacings Dx and Dy being the same values, and then the vertices of the plurality of microlenses are offset from the grating points in the grating plane. In this case, a boundary between adjacent microlenses is the perpendicular bisector of the line connecting the vertices of adjacent microlenses, and no step is created at the boundary between the surfaces of the adjacent microlenses if the microlenses are axially symmetric. If the microlenses are not axially symmetric, an offset from the perpendicular bisector is created. However, the offset can be neglected, provided that components of ε orthogonal to the grating are sufficiently small compared to the grating spacings Dx or Dy. A boundary between the microlenses is called a side.In the case of a reference grid that is a rectangular grid, the distance between two sides facing each other is approximately equal to Dx or Dy.
[0086] In this case, the following relationship applies, assuming that an offset in the direction of the grating of the microlens arrangement is provided by η i , η i+1 , ... is marked. “i” denotes an integer that identifies the grid cells. εi≅ηi+ηi+12 ση=∑i=1N(ηi−η¯)2N=2σ η¯=∑i=1NηiN
[0087] Accordingly, it can be understood that a suitable variance of the aperture offset can be obtained if a variance σ η The offset of the lens vertex by the square root of 2 times is greater than the required variance of the aperture offset.
[0088] Fig. Figure 14B shows a state in which, first, the vertices of the majority of the microlenses are fixed at grid points of the reference grating, which is a hexagonal grating, and then the vertices of the majority of the microlenses are offset from the grid points in the grating plane. If the grating directions are denoted by l, m, and n, the three values of the grating spacings can be expressed as Dl / 2, Dm / 2, and Dn / 2. In this case, a distance between two facing sides is equal to Dl, Dm, or Dn.
[0089] Fig. 14C is an enlarged view of the circled area in Fig. 14B.
[0090] The surface shape of a microlens can be a so-called freeform surface. In this case, the magnitude of the aperture variance can be determined by calculating the curvature of a microlens profile in each reference direction of the arrangement, where the lenses are periodically arranged.
[0091] Even if the inconsistency in intensity distribution due to deflection, such as refraction and / or diffraction, at the aperture of a microlens is eliminated, the inconsistency in intensity distribution due to interference caused by the periodic structure of the microlens array remains. If the vertices of the microlenses are offset from the grating points of the reference grating in the grating plane, the periodic structure of the microlens array itself is disturbed, thereby reducing the inconsistency in intensity distribution caused by the periodic structure. However, the offset in the grating plane alone does not effectively change the shape of an extreme value of the interference of scattered light, and consequently, a dark spot with very low intensity around 0 degrees can be produced.To reduce such a dark spot, it is effective to shift the phases of the light from the majority of the microlenses by also offsetting the vertices of the majority of the microlenses relative to each other in the direction of the optical axis, i.e., in a direction perpendicular to the grating plane.
[0092] To eliminate the inconsistency of the intensity distribution due to interference, it is desirable that the phase shifts be uniformly distributed in the range of 2π. For a uniform distribution of phase shifts for a light source of wavelength λ, the values of the microlens offsets along the optical axis should be in the range 0 ≤ η. zi < mλ / (n-1) be uniformly distributed, where m is an integer greater than or equal to 1. For the manufacturing process and the control of the light, a small value of η is required. z It is advantageous, and therefore desirable, that the values be in the range 0 ≤ η zi< λ / (n-1) are uniformly distributed.
[0093] Examples of the present revelation are described below. Example 1
[0094] As in Fig. As shown in Figure 1, Example 1 is a microlens array in which spherical microlens surfaces are arranged in accordance with a square grid as a reference grid. Specifications of the microlens array according to Example 1 are given below. Radius of curvature at the center of a microlens surface: 0.095 mm Grating spacing D of the reference grating: 0.082 mm Component thickness: 1.0 mm Refractive index of a material (acrylic): 1.492
[0095] The component thickness of a microlens refers to the distance between the apex and the underside.
[0096] If two orthogonal directions of the square grid are designated as the X-direction and Y-direction, the vertices of the lenses of the microlenses are uniformly distributed with respect to the points of the reference grid in the X-direction in the range of ±7.6 µm and in the Y-direction in the range of ±7.6 µm.
[0097] In this case, the relationship D applies. 2 / 2f = 0.0174 and therefore equations (21) and (23) are satisfied. Furthermore, the following equations hold: σ=0.0076 / 6=0.031mm and σf{1+(D / 2f)2}=0.0068 and therefore equations (8) and (9) are satisfied.
[0098] Fig. Figure 15 shows a light intensity distribution obtained when a light beam with a wavelength of 0.5876 µm is normally incident on a bottom surface of the microlens arrangement according to Example 1 and diverges. The horizontal axis of the Fig. 15 represents an angle θ of divergence and the vertical axis of the Fig. 15 represents relative values of light intensity. The unit of angle θ is degrees. In Fig. 15 The thin line represents the intensity of the light and the thick line represents the average light intensity within one degree.
[0099] If the intensity distribution, which in Fig. 15 is represented by the thick line, with the intensity distribution shown in Fig. 3A, represented by the thick line, is compared to the section that is in Fig. 3A is designated by α and in which a large difference in intensity is generated, in Fig. 15 is not present. Accordingly, the microlens arrangement according to Example 1 provides an illumination distribution that is more uniform than that obtained using a conventional microlens arrangement. Example 2
[0100] Fig. Figure 16 shows an arrangement of the optical system according to Example 2. The optical system according to Example 2 comprises a laser diode light source 200, a collimating lens 300, and a microlens arrangement 102. The wavelength of the laser of the laser diode light source 200 is 780 nm.
[0101] The collimation lens 300 is an aspherical lens made of BK7 material. The entrance and exit surfaces can be described by the following equations, where the straight line connecting the centers of curvature of the entrance and exit surfaces is called the Z-axis and the distance from the Z-axis is given by r. z=cr21+1−(1+k)c2r2 c=1R
[0102] The parameters of the entrance area are given below. R=2.462mm, k=−1 The parameters of the exit surface are specified below. R=−0.979mm, k=−1
[0103] The other specifications of the 300 collimation lens are given below. Distance from the light source to the entrance surface: 1.0 mm Component thickness: 1.0 mm Refractive index of the material: 1.511
[0104] The component thickness refers to the thickness of the collimation lens 300 at the center.
[0105] In the microlens arrangement 102, the surfaces of the microlenses, which are freeform surfaces, are arranged in accordance with a square grid that is used as a reference grid.
[0106] If the straight line passing through the vertices of the lenses and perpendicular to the underside of the microlens arrangement 102 is called the Z-axis, and the two directions of the square grid in a plane perpendicular to the Z-axis are called the X-axis and Y-axis, a microlens surface can be expressed by the following equation. z=cr21+1−(1+k)c2r2+∑n∑mαnmxnym
[0107] In the equation, r represents the distance from the Z-axis. r=x2+y2 “c” represents the curvature at the center of the asymmetric term. The radius of curvature Rx at the center in the direction of the x-axis and the radius of curvature Ry at the center in the direction of the y-axis can be described by the following equations, taking into account the second-order coefficients. c+2α20=1Rx c+2α02=1Ry
[0108] The coefficients that define the freeform surface are given below. 1 / c=0,k=0 α20=2.0, α02=1.5
[0109] The other coefficients α nm are zero.
[0110] Taking into account the second-order coefficients, the radius of curvature at the center of the microlens surface differs in the direction of the X-axis from that in the direction of the Y-axis as follows. Rx: 0.25 mm Ry: 0.33 mm
[0111] The other specification data for the microlens assembly 102 are as follows. Grid spacing D of the reference grid: 0.2 mm Component thickness: 0.5 mm Refractive index of the material (acrylic): 1.486 (λ = 780 nm or 0.78 µm)
[0112] The component thickness of a microlens refers to the distance between the vertex and the underside.
[0113] The lens vertices of the microlenses, which are ellipses, each with its center at one of the reference grid points, a radius of 13.3 µm in the X direction and a radius of 50.0 µm in the Y direction, are uniformly distributed.
[0114] In this case, if fx denotes the focal length in the XY plane and fy denotes the focal length in the YZ plane, the following relationships apply. D2 / (2 fxλ)=0.056 and D2 / (2 fyλ)=0.044 Therefore, equation (20) is satisfied. Furthermore, the following equations hold: σx=0.00133 / 8=0.0047mm and σxλfx{1+(D / 2fx)2}=0.0077 Therefore, equation (7) is satisfied. Furthermore, the following equations hold: σy=0.0053mm and σyλfy{1+(D / 2fy)2}=0.0077 and therefore equation (7) applies.
[0115] Fig. Figure 17A shows a light intensity distribution along the X-axis (in the horizontal direction) obtained using the optical system according to Example 2. The horizontal axis of the Fig. 17A represents the angle θ of divergence and the vertical axis of the Fig. 17A represents the relative value of the light intensity. The unit of angle θ is degrees. In Fig. 17A the thin line represents the light intensity and the thick line represents the average light intensity over 1 degree.
[0116] Fig. Figure 17B shows a light intensity distribution along the Y-axis (the vertical direction) obtained using the optical system according to Example 2. The horizontal axis of the Fig. 17B represents the angle θ of divergence and the vertical axis of the Fig. 17B represents relative values of light intensity. The unit of angle θ is degrees. In Fig. 17B the thin line represents the light intensity and the thick line represents the average light intensity over 1 degree.
[0117] If the intensity distributions that are in the Fig. 17A and Fig. 17B are represented by the thick lines, with the intensity distribution shown in Fig. 3A, represented by the thick line, can be compared to the one in Fig. 3A marked area α, in which a large difference in intensity is generated, in the Fig. 17A and Fig. 17B is not present. Accordingly, the illumination distribution obtained using the microlens arrangement according to Example 2 is more uniform than that obtained using a conventional microlens arrangement. Example 3
[0118] Fig. Figure 18A shows an arrangement of the optical system according to Example 3. The optical system according to Example 3 comprises a light source optical system 2100, a screen 103 which is a microlens arrangement, a freeform surface mirror 2200 and a curved screen 2300.
[0119] Fig.Figure 18B shows an arrangement of the light source optical system 2100. The light source optical system 2100 includes laser diodes 200A, 200B and 200C, collimation lenses 300A, 300B and 300C, a dichroic mirror 400, a mirror 500 and a MEMS mirror 600.
[0120] The optical system according to Example 3 is a head-mounted display that uses lasers 200A, 200B, and 200C as light sources, each with three different emission wavelengths: 0.45 µm, 0.53 µm, and 0.65 µm, respectively. The light emitted by the three laser diodes 200A, 200B, and 200C is collimated by collimating lenses 300A, 300B, and 300C, respectively, and then focused by the dichroic mirror 400 to form a single beam. The focused beam is deflected by the MEMS mirror 600 to scan the microlens array 103. The laser diodes 200A, 200B and 200C are modulated in synchronization with the MEMS mirror 600, so that an intermediate image is displayed on the microlens arrangement 103.After the angle of divergence for the intermediate image is increased by means of the microlens arrangement 103, the light is reflected by means of the freeform surface mirror 2200 and the curved screen 2300, so that a virtual image 2400 is generated. If there is an inconsistency in the intensity of the light propagating across the microlens arrangement 103, it is disadvantageous that the inconsistency is also generated in the virtual image and the brightness of the virtual image varies due to a change in the position of the viewing point.
[0121] The microlens array 103, used as a screen, is a microlens array for which a rectangular grating with Dx = 0.1 mm and Dy = 0.05 mm is used as the reference grating. The vertices of the majority of the microlenses, which are ellipses arranged around a reference grating point, have a radius of 12.3 µm in the X-axis direction and a radius of 12.8 µm in the Y-axis direction. These vertices are uniformly distributed along the Z-axis in the range up to 2.65 µm.
[0122] The microlens surface is an axially symmetric and aspherical surface and can be described by the following equations, where the straight line passing through the vertex of the lens and perpendicular to the bottom is called the Z-axis and the distance from the Z-axis is represented by r. z=cr21+1−(1+k)c2r2 c=1R
[0123] The parameters of the lens surfaces are as follows. Radius of curvature at the center of the lens surface: 0.1 mm conic constant k: -1.0
[0124] The other specification data for the microlens assembly 103 are as follows. Component thickness: 1.0 mm Refractive index of the material (acrylic): 1.492
[0125] In this case, the relationships apply Dx2 / 2f / 0.45=0.055 Dx2 / 2f / 0.53=0.046 Dx2 / 2f / 0.65=0.038 Dy2 / 2f / 0.45=0.055 Dy2 / 2f / 0.53=0.046 Dy2 / 2f / 0.65=0038 and each of them satisfies equation (20).
[0126] Furthermore, the following equations apply: σ x = 0.00435 mm and σ y = 0.00417 mm and therefore the equations apply σx0.53⋅f{1+(Dx / 2f)2}=0.0125 and σy0.53⋅f{1+(Dy / 2f)2}=0.0125
[0127] Therefore, equations (7), (9) and (11) are satisfied for λ = 0.53 micrometers. Furthermore, equation (7) is satisfied for λ = 0.45 micrometers and λ = 0.65 micrometers.
[0128] Furthermore, the relationships apply 2.66 / 0.45=0.45×5+0.41 2.66 / 0.53=0.53×5+0.01 2.66 / 0.65=0.65×4+0.06 and the remainders obtained when 2.66 is divided by the wavelength values are 0.41, 0.01 and 0.06. Therefore, the following relationships are satisfied. 0.41 / 0.45>0.9 0.01 / 0.53<0.1 0.06 / 0.65<0.1
[0129] In summary, the positions of the vertices of the majority of the microlenses in the direction perpendicular to the grating plane are uniformly distributed in the range from 0 to 2.66 µm, and therefore the phases of the light from the majority of the microlenses are offset from each other for each of the three wavelengths, so that a so-called dark spot phenomenon can be attenuated.
[0130] In the head-mounted display according to Example 3, the unevenness of the intensity distribution of the light spreading across the microlens arrangement is low, and the unevenness of the brightness of the virtual image is reduced.
Claims
[1] Optical system comprising a light source emitting light of a wavelength λ and a microlens arrangement (100, 102, 103) configured to widen the light from the light source, wherein the microlens arrangement (100, 102, 103) comprises N microlenses (1000) arranged in a predetermined direction in an XY plane, wherein a projection of a vertex of a lens of the microlenses (1000) onto the XY plane is arranged adjacent to a grid point of a reference grating in the XY plane, wherein the grid spacing of the reference grating in the specified direction is D and, if a boundary between the microlenses (1000) is referred to as a side of a lens, a distance between two sides facing each other is approximately equal to D, and where a distance between a projection of a lens vertex i onto the XY plane and a projection of one side between the lens vertexi and a lens parting i+1 to the XY plane D / 2+εi is and for the N microlenses σ2=∑i=1N(εi−ε¯)N ε¯=∑i=1NεiN=0 holds true, and, if n represents the refractive index of the material of the microlenses (1000), R represents the radius of curvature in the given direction near the center of the microlenses (1000), and f represents the focal length of the microlenses (1000), the relationships 0.0072λD <D2f=D(n−1)2R 0.0062λf{1+(D2f)2}<σ<0.019λf{1+(D2f)2} are satisfied, where the unit of wavelength λ is micrometer, the unit of grating spacing D is millimeter, the unit of radius of curvature R is millimeter, and the unit of focal length f is millimeter. [2] Optical system according to claim 1, wherein a boundary between the lens vertex is formed in the XY plane i and the lens vertex i+1, which are adjacent to each other in the given direction, the perpendicular bisector of the line that forms the lens vertex is i and the lens parting i+1 connects, or an offset of the boundary from the perpendicular bisector can be neglected. [3] Optical system according to claim 1 or 2, wherein the microlenses (1000) of the microlens arrangement (100, 102, 103) furthermore the relationship 0.080λD <d2f=d(n−1)2ris fulfilled. [4] Optical system according to one of claims 1 to 3, wherein the microlenses (1000) of the microlens arrangement (100, 102, 103) further the relationship 0,0083λf{1+(D2f)2} <σ<0,019λf{1+(d2f)2}is fulfilled.< / σ<0,019λf{1+(d2f)2}
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