Lens, simulation method, and free-form surface shape specification method

Abstract

To provide a lens, a simulation method, and a free-form surface shape specification method, with which the intensities of rays of light can be made uniform, which are gathered from various focal positions different in the distance from the lens.SOLUTION: A lens comprises a plurality of lens segments. The plurality of lens segments gather rays of light different in the focal position from the lens on a focal surface separated by an appropriate distance from the lens. The plurality of lens segments have different numerical apertures so as to make equal the quantity of light gathered by the plurality of lens segments.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a lens, a simulation method, and a method for specifying the shape of a free curved surface. [Background technology]

[0002] Patent Document 1 discloses microlenses that are arranged two-dimensionally in a matrix and have the same curvature in both the vertical and horizontal directions. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2012-134261 A Summary of the Invention [Problem to be solved by the invention]

[0004] Such lenses have focal lengths adjusted to focus light on the surface of the image sensor. Because of this, the light rays collected from the focal plane tend to come from the same distance, so the light intensity is uniform. However, the light intensity coming from focal planes at different distances from the lens is stronger the closer the focal plane is to the lens, so the light intensity is not uniform.

[0005] The present invention has been made in consideration of the above circumstances, and has an object to provide a lens, a simulation method, and a method for specifying a free curved surface shape that can uniform the intensity of light collected from various focal positions that are different distances from the lens. [Means for solving the problem]

[0006] The present application includes multiple means for solving the above problems. One example is a lens having multiple lens segments, each of which focuses light having a different focal position from the lens onto a focal plane that is an appropriate distance away from the lens, and each of which has a different numerical aperture so that the amount of light focused by each of the multiple lens segments is equal. Effect of the Invention

[0007] According to the present invention, the intensity of light collected from various focal positions at different distances from the lens can be made uniform. [Brief description of the drawings]

[0008] [Figure 1] FIG. 2 is a diagram illustrating an example of a lens structure according to the present embodiment. [Diagram 2] FIG. 2 is a diagram illustrating an example of the structure of a lens of Comparative Example 1. [Diagram 3] FIG. 4 is a diagram illustrating an example of the structure of a lens of Comparative Example 2. [Figure 4] 5A to 5C are diagrams illustrating another example of the lens structure of the present embodiment. [Diagram 5] FIG. 2 is a diagram illustrating an example of a configuration of a simulator according to the present embodiment. [Figure 6] FIG. 13 is a diagram illustrating an example of an output result of a simulation. [Figure 7] FIG. 1 is a diagram showing the relationship between the thermal expansion coefficient and the amount of light that can be collected. [Figure 8] FIG. 2 is a diagram showing an example of a general arrangement of multiple lens segments according to the present embodiment. [Figure 9] FIG. 11 is a diagram showing an example of a processing procedure of a free curved surface shape specifying method. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] Hereinafter, the present invention will be described with reference to the drawings showing the embodiments. FIG. 1 is a diagram showing an example of the structure of a lens 10 according to the present embodiment. The lens 10 according to the present embodiment is a microlens array including a plurality of lens segments. In the example of FIG. 1, the lens 10 is circular (specifically, concentric) in plan view (as viewed from the light entrance surface or exit surface). A circular opening is formed in the center. The opening is not an essential component. The plurality of lens segments are represented by the reference symbols 1 to 6. For convenience, the number of lens segments is six, but the number of lens segments is not limited to six. In addition, in an actual lens, the number of lens segments may be greater. In the example of FIG. 1, the plurality of lens segments are arranged adjacent to each other, but the plurality of lens segments do not have to be arranged adjacent to each other.

[0010] When light from focal position F5, which has a focal length of L5 from the lens 10, enters the lens segment 5, the incident light is focused on the imaging surface as the focal plane and is condensed on the imaging surface. The angle between the focal position F5 and the two line segments connecting the upper and lower boundaries of the lens segment 5 is Ω5. When light from focal position F4, which has a focal length of L4 from the lens 10, enters the lens segment 4, the incident light is focused on the imaging surface and is condensed on the imaging surface. The angle between the focal position F4 and the two line segments connecting the upper and lower boundaries of the lens segment 4 is Ω4. When light from focal position F3, which has a focal length of L3 from the lens 10, enters the lens segment 3, the incident light is focused on the imaging surface and is condensed on the imaging surface. The angle between the focal position F3 and the two line segments connecting the upper and lower boundaries of the lens segment 3 is Ω3. The same applies to the other lens segments. The focal plane is not limited to the imaging surface.

[0011] Ω3, Ω4, and Ω5 are physical quantities equivalent to the numerical aperture, and correspond to the amount of light collected by each lens segment 3, 4, and 5, or the brightness on the imaging surface. The longer the distance to the focal position, the larger the area of ​​the lens segment that collects the light from that focal position. Conversely, the shorter the distance to the focal position, the smaller the area of ​​the lens segment that collects the light from that focal position. This makes it possible to prevent a large amount of light from entering the lens segment from a focal position that is closer to the lens, so that the amount of light collected by each of the multiple lens segments (or the brightness on the imaging surface) becomes equal (uniform). In the example of FIG. 1, Ω3=Ω4=Ω5. The same applies to the other lens segments.

[0012] That is, in the lens 10 of this embodiment, each of the multiple lens segments focuses light having a different focal position from the lens 10 onto an imaging surface that is an appropriate distance away from the lens 10, and the numerical aperture of each of the multiple lens segments is made different so that the amount of light focused by each of the multiple lens segments (or the brightness on the imaging surface) is equal (uniform).

[0013] As described above, in the lens 10 of the present embodiment, the areas of the light incident surfaces of the multiple lens segments are different, thereby making the numerical apertures different.

[0014] FIG. 2 is a diagram showing a schematic example of the structure of lens 100 of Comparative Example 1. Lens 100 of Comparative Example 1 is a convex lens with convex surfaces. Lens 100 is a fixed focal length lens. As shown in FIG. 2, light from focal position F4 is focused on the imaging surface. That is, only light from a certain focal length can be focused. Light from other focal positions F5 and F3 is not focused.

[0015] FIG. 3 is a diagram illustrating an example of the structure of lens 200 of Comparative Example 2. Lens 200 of Comparative Example 2 is a microlens array. Lens 200 has six lens segments 1 to 6, and the area of ​​each lens array is the same. As shown in FIG. 3, when light from focal position F5 enters lens segment 5, the incident light is focused on the imaging surface and collected on the imaging surface. When light from focal position F4 enters lens segment 4, the incident light is focused on the imaging surface and collected on the imaging surface. When light from focal position F3 enters lens segment 3, the incident light is focused on the imaging surface and collected on the imaging surface.

[0016] In the example of Fig. 3, since the areas of the lens segments are the same, the amount of light incident on the lens segment from a focal position that is farther away from lens 200 is small. Conversely, the amount of light incident on the lens segment from a focal position that is closer away from lens 200 is large. That is, in lens 200, Ω3>Ω4>Ω5, and the brightness (amount of light) of the imaging surface differs depending on the focal position.

[0017] 1, according to the lens 10 of this embodiment, the brightness (amount of light) on the imaging surface is the same (uniform) regardless of the focal position. This makes it possible to uniform the intensity of light collected from various focal positions at different distances from the lens 10.

[0018] FIG. 4 is a diagram showing a schematic diagram of another example of the structure of the lens 10 of this embodiment. The lens 10 shown in FIG. 4A is the same as the example in FIG. 1. As shown in FIG. 4A, the shape of each lens segment may be defined by two line segments extending in a radial direction from the center of the lens 100. The central angle enclosed by the two line segments defining the shape of each lens segment is different, thereby making the numerical aperture of each lens segment different. In the example of FIG. 4A, if the central angles of lens segments 1 to 6 are θ1 to θ6, then θ1<θ2<θ3<θ4<θ5<θ6, and if the areas of lens segments 1 to 6 are S1 to S6, then S1 <S2<S3<S4<S5<S6となっている。

[0019] Also, as shown in FIG. 4B, the shape of each lens segment may be defined by two concentric circles sharing the center of lens 10. By having different radial dimensions between the two concentric circles that define the shape of each lens segment, the numerical aperture of each lens segment is made different. In the example of FIG. 4B, if the radial dimensions of lens segments 1 to 6 are r1 to r6, then r1 < r2 < r3 < r4 < r5 < r6, and if the areas of lens segments 1 to 6 are S1 to S6, then S1 < S2 < S3 < S4 < S5 < S6.

[0020] Also, as shown in FIG. 4C, the shape of each lens segment may be defined by two line segments extending radially from the center of lens 100 and two concentric circles sharing the center of lens 10. For lens segment 1, the central angle is θ11 and the radial dimension is r11. For lens segment 2, the central angle is θ12 and the radial dimension is r11. For lens segment 3, the central angle is θ13 and the radial dimension is r11. For lens segment 4, the central angle is θ11 and the radial dimension is r12. For lens segment 5, the central angle is θ12 and the radial dimension is r12. For lens segment 6, the central angle is θ13 and the radial dimension is r12. For lens segment 7, the central angle is θ11 and the radial dimension is r13. For lens segment 8, the central angle is θ12 and the radial dimension is r13. For lens segment 9, the central angle is θ13 and the radial dimension is r13. If the areas of lens segments 1 to 9 are S1 to S9, then S1 < S4 < S7 < S2 < S5 < S8 < S3 < S6 < S9.

[0021] As shown in FIG. 4D, each lens segment has a rectangular shape, and at least one of the vertical and horizontal dimensions of the rectangular shape of each lens segment is different, thereby making the numerical aperture of each lens segment different. Lens segment 1 has a horizontal dimension of x1 and a vertical dimension of y1. Lens segment 2 has a horizontal dimension of x2 and a vertical dimension of y1. Lens segment 3 has a horizontal dimension of x3 and a vertical dimension of y1. Lens segment 4 has a horizontal dimension of x1 and a vertical dimension of y2. Lens segment 5 has a horizontal dimension of x2 and a vertical dimension of y2. Lens segment 6 has a horizontal dimension of x3 and a vertical dimension of y2. Lens segment 7 has a horizontal dimension of x1 and a vertical dimension of y3. Lens segment 8 has a horizontal dimension of x2 and a vertical dimension of y3. Lens segment 9 has a horizontal dimension of x3 and a vertical dimension of y3. If the areas of lens segments 1 to 9 are S1 to S9, then S1 <S2<S3<S4<S5<S6<S7<S8<S9となっている。

[0022] The lens 10 (microlens array) of this embodiment can be applied to a device that includes an imaging element and measures light. Such a device can, for example, collect light from a plurality of focal positions that are discretely different in distance from the lens 10 using a plurality of lens segments that correspond to the respective focal positions, and uniformly receive the light on the imaging surface. By increasing the number of lens segments, the number of focal positions can be increased, and a device that can receive uniform light over a wide range of focal lengths can be provided.

[0023] The free-form surface shape of each lens segment of the lens 10 can be calculated using a known method. For example, the method described in papers such as “Automated design of freeform imaging system”, Tong Yang, Guo-Fan Jin and Jun Zhu, Light: Science & Applications (2017) can be used. The free-form surface includes a flat surface, a spherical surface, an aspheric surface, and a free-form surface.

[0024] Next, a simulation method for topologically optimizing the layout of the lens segments of lens 10 will be described.

[0025] 5 is a diagram showing an example of the configuration of a simulator 50 according to this embodiment. The simulator 50 can be configured with a personal computer (PC) or the like. The simulator 50 includes a control unit 51 that controls the entire simulator, an input unit 52, a memory 53, an operation unit 54, a display unit 55, and a storage unit 56.

[0026] The control unit 51 may be configured by incorporating a required number of central processing units (CPUs), micro-processing units (MPUs), graphics processing units (GPUs), etc. The control unit 51 may also be configured by combining digital signal processors (DSPs), field-programmable gate arrays (FPGAs), etc.

[0027] Input data used in the simulation is input to the input unit 52. The input unit 52 also accepts input data necessary for the simulator 50 to process.

[0028] The display unit 55 can be configured with a liquid crystal panel, an organic EL (Electro Luminescence) display, or the like.

[0029] The operation unit 54 is configured with a touch panel or the like, and can accept operations on the information displayed on the display unit 55. The operation unit 54 may be configured with a keyboard, a mouse, a touch pad, or the like.

[0030] The storage unit 56 can be configured, for example, by a hard disk or a semiconductor memory, and stores computer programs (program products) 61 and 62 and required information. The computer program 61 is for executing a process for topologically optimizing the layout of the lens segments of the lens 10. The computer program 62 will be described later.

[0031] The memory 53 can be configured with a semiconductor memory such as a static random access memory (SRAM), a dynamic random access memory (DRAM), a flash memory, etc. Computer programs 61 and 62 can be loaded into the memory 53, and the control unit 51 can execute the computer programs 61 and 62.

[0032] In order to perform a simulation for topologically optimizing the layout of the lens segments of the lens 10 using the simulator 50, input data including an initial pattern having a plurality of regions and a thermal expansion coefficient assigned to each of the plurality of regions is input to the input unit 52. By utilizing thermal expansion, it is possible to create an internal stress inside an elastic material. In the elastic simulation, the internal stress can be specified via an initial stress tensor matrix. Note that the thermal simulation (thermal expansion) is one example of a method for creating an internal stress inside an elastic material, and the method is not limited to the thermal simulation as long as it is a method that can create an internal stress inside an elastic material.

[0033] FIG. 6 is a diagram showing an example of the output result of the simulation. The output result shown in FIG. 6 is displayed on the display unit 55. FIG. 6A shows a state in which an initial pattern is set. The initial pattern is a pattern in which the lens segment layout of the lens 10 is determined according to a target illumination pattern. The initial pattern has a plurality of regions 1 to 7. The shape and arrangement of each of the regions 1 to 7 differ according to the target illumination pattern. A required thermal expansion coefficient is assigned to each of the regions 1 to 7. The thermal expansion coefficient may be different for each region, or the same thermal expansion coefficient may be assigned to multiple regions. The value of the thermal expansion coefficient assigned according to the simulation result may be changed as appropriate. The circle in the figure indicates the boundary of the lens 10. The boundary is assumed to be geometrically fixed and not deformed even if the set temperature is changed. A thermal expansion coefficient smaller than the thermal expansion coefficient assigned to the multiple regions is assigned to the region other than the initial pattern within the boundary.

[0034] When the set temperature is increased in the state of Fig. 6A, the regions 1-7 thermally expand within their boundaries in accordance with the thermal expansion coefficients of the regions 1-7 as shown in Fig. 6B, and the areas of the regions 1-7 increase in plan view. The change in the areas of the regions 1-7 is determined by the thermal expansion coefficients of the regions 1-7.

[0035] When the set temperature is increased in the state of Fig. 6B, the regions 1-7 further thermally expand within their boundaries in accordance with the thermal expansion coefficients of the regions 1-7 as shown in Fig. 6C, and the area of ​​each of the regions 1-7 increases in plan view. Eventually, the total area of ​​the regions 1-7 approaches the area of ​​the boundaries. In other words, in the method of topologically optimizing the layout of the lens segments of lens 10, the lens segments can occupy nearly 100% of the surface area of ​​the lens.

[0036] As described above, in the simulation method of the present embodiment, an initial pattern having a plurality of regions within the boundary of a lens is set, a required thermal expansion coefficient is assigned to each of the plurality of regions, the temperature within the boundary of the lens is changed to thermally expand the plurality of regions within the boundary, and a plurality of lens segment layouts can be determined based on the plurality of thermally expanded regions. By determining the layout, the area of ​​each lens segment can also be determined.

[0037] Next, the fact that the amount of light that can be collected in each of the multiple regions can be adjusted by changing the thermal expansion coefficients assigned to the multiple regions will be described.

[0038] FIG. 7 is a diagram showing the relationship between the thermal expansion coefficient and the amount of light that can be collected. FIG. 7A shows a target illumination pattern. In FIG. 7A, for convenience, a pattern resembling a dragonfly is used, but the target illumination pattern is not limited to the example in FIG. 7. For convenience, the target illumination pattern is composed of seven regions 1 to 7. Using an initial pattern (composed of seven regions 1 to 7) previously set according to the target illumination pattern, the results obtained by the method shown in FIG. 6 are shown in FIGS. 7B to 7D.

[0039] In Fig. 7B, attention is focused on region 4. The thermal expansion coefficient assigned to region 4 is smaller than those in Fig. 7C and Fig. 7D. As a result, the amount of light that can be collected by the entire lens segment included in region 4 is equivalent to the other regions 1 to 3 and 5 to 7.

[0040] In Fig. 7C, attention is focused on region 4. The thermal expansion coefficient assigned to region 4 is larger than that in Fig. 7B and smaller than that in Fig. 7D. This allows the amount of light that can be collected by the entire lens segment included in region 4 to be 1.25 times that in Fig. 7B. In Fig. 7C, it can be seen that region 4 of the illumination pattern corresponding to region 4 is brighter than that in Fig. 7B.

[0041] In Fig. 7D, attention is focused on region 4. The thermal expansion coefficient assigned to region 4 is larger than that in Fig. 7B and Fig. 7C. This allows the amount of light that can be collected by the entire lens segment included in region 4 to be 1.5 times that in Fig. 7B. In Fig. 7D, it can be seen that region 4 of the illumination pattern corresponding to region 4 is brighter than that in Fig. 7C.

[0042] After the areas of the lens segments are determined by the simulation method exemplified in FIG. 6, the free curved surface shape of each lens segment of lens 10 can be calculated using the known method described above.

[0043] The illumination pattern described above can be a pattern on the surface of various materials, such as a film, a screen, a plate, a wafer, etc. More specifically, it can be applied to (1) a film having a filter function containing water containing a photoresponsive polymer, in which when the film is irradiated with UV light, the irradiated polymer becomes highly viscous, and when the film is irradiated with visible blue light, the irradiated polymer becomes less viscous, and the water containing the polymer can flow, (2) a screen that can display various characters, figures, patterns, and textures depending on the wavelength and intensity of light, (3) a plate on which a focal pattern is formed to generate Marangoni convection on a gold film on a glass surface, (4) a semiconductor lithography technology that transfers an ultrafine circuit pattern (nano pattern) onto a wafer, (5) a plate for generating a polarization map on an optical material, etc.

[0044] FIG. 8 is a diagram showing an example of a general arrangement of a plurality of lens segments according to this embodiment. The lens shown in FIG. 8 includes a plurality of lens segments #1 to #10. The plurality of lens segments #1 to #10 can be combined without contacting each other. The plurality of lens segments do not need to be arranged adjacent to each other, but may be arranged partially adjacent to each other. The lens segments #1 to #5 are shaped like a rectangle, and a predetermined portion (e.g., a center or a corner) of the lens segment is arranged at a coordinate position indicated by Var1 and Var2, and have vertical and horizontal dimensions indicated by Var3 and Var4. The lens segments #6 to #9 are shaped like a hexagon, and Var1 to Var4 are the same as the lens segments #1 to #5. The lens segments #10 to #11 are shaped like a ring (a concentric shape forming a part of an arc), and Var1 and Var2 indicate the radii of the concentric circles, and Var3 and Var4 indicate the central angles that define a part of the arc. The shape of the lens segments is not limited to a rectangle, hexagon, or ring, but may be, for example, a triangle, a pentagon, a polygon having heptagons or more, a circle, a semicircle, an ellipse, or the like.

[0045] Generally, the free curved surface shape of a lens generates spherical aberration in which parallel light incident thereon focuses at different positions on the optical axis depending on the incident position of the lens. Hereinafter, a method for specifying a free curved surface shape for specifying an initial free curved surface shape for reducing spherical aberration will be described. The free curved surface shape specifying method can be performed by executing a computer program 62 shown in FIG. 5. In this case, data input to the input unit 52 includes data such as the distance (first distance) S0 from the center of the lens to the target object, the distance (second distance) S1 from the center of the lens to the imaging plane (focal plane), and the refractive index n of the lens.

[0046] 9 is a diagram showing an example of a processing procedure of the free curved surface shape specifying method. For convenience, the following description will be given with the control unit 51 acting as the main processor of the processing. The control unit 51 calculates a focal length based on a distance (first distance) from the center of the lens to the object and a distance (second distance) from the center of the lens to the imaging plane (focal plane) (S11).

[0047]

number

[0048] The focal length f can be calculated using formula (1), where S0 is the distance from the center of the lens to the object (first distance), and S1 is the distance from the center of the lens to the imaging plane (focal plane) (second distance).

[0049] The control unit 51 calculates the optimal radius of curvature of the lens based on a first conditional equation that specifies a combination of radii of curvature of the lens having the calculated focal length, and a second conditional equation that makes the Condington shape factor calculated based on the radii of curvature equal to the shape factor that minimizes spherical aberration, calculated based on the first distance and the second distance (S12).

[0050] The first conditional expression can be expressed by the following expression (2). In the expression (2), n represents the refractive index of the lens, and R1 and R2 represent the radii of curvature of both surfaces of the lens. As shown in the expression (2), there are an infinite number of combinations of the radii of curvature of both surfaces of a lens having a specific focal length.

[0051] The second conditional expression can be expressed by expression (3). The left side of expression (3) represents the Condington shape factor C. In other words, the Condington shape factor C = (R1 + R2) / (R1 - R2). The right side of expression (3) represents the shape factor at which spherical aberration is minimized. Since there are two conditional expressions (2) and (3) for the two variables R1 and R2, the variables R1 and R2 can be calculated.

[0052] The control unit 51 uses the calculated optimum radius of curvature to specify the initial free curved surface shapes of both surfaces (front and rear surfaces) of the lens (S13).

[0053] The control unit 51 identifies an intersection between the free-form surface shape of the lens and the incident light ray (or the outgoing light ray), calculates a normal vector at the identified intersection, and identifies a new free-form surface shape based on a surface perpendicular to the calculated normal vector (S14). The number of incident light rays may be set to one or more incident light rays for each lens segment of the entrance surface of the lens. The number of outgoing light rays may be set to one or more incident light rays for each lens segment of the exit surface of the lens. A specific method of step S14 may be, for example, a method described in a paper such as "Automated design of freeform imaging system", Tong Yang, Guo-Fan Jin and Jun Zhu, Light: Science & Applications (2017).

[0054] The control unit 51 determines whether the number of times of processing to identify the free curved surface shape has reached a predetermined number (S15), and if the predetermined number has not been reached (NO in S15), the control unit 51 continues the processing of step S14. The predetermined number of times can be, for example, about 5 times, but is not limited to this. If the predetermined number of times has been reached (YES in S15), the control unit 51 sets the identified free curved surface shape as the shape of the lens segment (S16) and ends the processing.

[0055] The free-form surface shape specifying method of the present embodiment can optimize only the front surface (e.g., the light entrance surface) or the front and back surfaces (e.g., the light exit surface) of the lens segment. That is, the free-form surface shape specifying method of the present embodiment can make the back surface of the lens segment have a free-form surface shape.

[0056] As described above, in the method for specifying the free-form surface shape of the present embodiment, the control unit 51 calculates the focal length based on the first distance from the center of the lens to the object and the second distance from the center of the lens to the focal plane, calculates the optimum radius of curvature of the lens based on the first conditional expression specifying the combination of the radii of curvature of the lens having the calculated focal length, and the second conditional expression in which the Condington shape factor calculated based on the radii of curvature of the lens is equal to the shape factor with the smallest spherical aberration calculated based on the first and second distances, and can specify the initial free-form surface shapes of the multiple lens segments using the calculated optimum radius of curvature. Then, based on the specified initial free-form surface shape, a known method can be applied to find the shape of each lens segment of the lens. This allows the lens 10 with the smallest spherical aberration to be realized.

[0057] The lens of this embodiment may have lens segments formed on both sides, or only one side.

[0058] (Additional Note 1) The lens is a lens having a plurality of lens segments, each of which focuses light from the lens at a different focal position onto a focal plane that is an appropriate distance away from the lens, and each of which has a different numerical aperture so that the amount of light focused by each of the plurality of lens segments is equal.

[0059] (Supplementary Note 2) In the lens according to Supplementary Note 1, the numerical aperture is different by differentiating the areas of the light incident surfaces of the plurality of lens segments.

[0060] (Additional Note 3) In the lens of Additional Note 1 or Additional Note 2, the shapes of the lens segments are defined by two line segments in a radial direction from the center of the lens, and the numerical apertures of the lens segments differ because the central angles enclosed by the two line segments of each of the lens segments are different.

[0061] (Additional Note 4) In the lens of any one of Additional Notes 1 to 3, the shapes of the plurality of lens segments are defined by two concentric circles that share a center of the lens, and the numerical apertures differ by varying the radial dimension between the two concentric circles of each of the plurality of lens segments.

[0062] (Additional Note 5) In the lens according to Additional Note 1, the lens segments are rectangular in shape, and the numerical apertures are different for each of the lens segments by differing at least one of the vertical and horizontal dimensions of the rectangular shape.

[0063] (Appendix 6) A simulation method for determining a lens segment layout of a lens having a plurality of lens segments, comprising the steps of: setting an initial pattern having a plurality of regions within a boundary of the lens; assigning a required thermal expansion coefficient to each of the plurality of regions; changing a temperature within the boundary of the lens to thermally expand the plurality of regions within the boundary; and determining the lens segment layout based on the thermally expanded plurality of regions.

[0064] (Additional Note 7) A free-form surface shape specifying method is a method for specifying a free-form surface shape of a lens segment of a lens having a plurality of lens segments, the method comprising: calculating a focal length based on a first distance from the center of the lens to an object and a second distance from the center of the lens to a focal plane; calculating an optimal radius of curvature of the lens based on a first conditional equation that specifies a combination of radii of curvature of the lens having the calculated focal length and a second conditional equation such that a Condington shape factor calculated based on the radii of curvature is equal to a shape factor that minimizes spherical aberration, the shape factor being calculated based on the first distance and the second distance; and specifying an initial free-form surface shape of the plurality of lens segments using the calculated optimal radius of curvature.

[0065] The matters described in each embodiment can be combined with each other. In addition, the independent claims and dependent claims described in the claims can be combined with each other in any and all combinations regardless of the citation format. Furthermore, the claims use a format in which a claim cites two or more other claims (multiple claim format), but this is not limited to this. A multiple claim (multi-multi claim) that cites at least one multiple claim may also be used. [Explanation of symbols]

[0066] 10 Lenses 50 Simulator 51 Control section 52 Input section 53 Memory 54 Operation section 55 Display section 56 Memory section 61, 62 Computer Programs

Claims

1. A lens comprising a plurality of lens segments, Each of the plurality of lens segments focuses light having different focal positions from the lens onto a focal surface that is an appropriate distance away from the lens; The numerical apertures of the plurality of lens segments are different so that the amount of light collected by each of the plurality of lens segments is equal. lens.

2. The numerical aperture is different by differentiating the areas of the light incident surfaces of the plurality of lens segments. The lens of claim 1 .

3. the shapes of the lens segments are defined by two line segments in a radial direction from a center of the lens; The central angle between the two line segments of each of the plurality of lens segments is different, so that the numerical aperture is different. The lens of claim 2.

4. the shape of the lens segments is defined by two concentric circles that share a common center of the lens; The numerical aperture is varied by varying the radial dimension between the two concentric circles of each of the plurality of lens segments. The lens of claim 2.

5. The lens segments are rectangular in shape, The numerical aperture is different by varying at least one of the vertical dimension and the horizontal dimension of the rectangular shape of each of the plurality of lens segments. The lens of claim 1 .

6. 1. A simulation method for determining a lens segment layout for a lens comprising a plurality of lens segments, comprising the steps of: defining an initial pattern having a plurality of regions within a boundary of the lens; assigning a desired coefficient of thermal expansion to each of the plurality of regions; Varying a temperature within the confines of the lens to cause thermal expansion of the regions within the confines; determining the plurality of lens segment layouts based on the plurality of thermally expanded regions; Simulation method.

7. A method for specifying a free curved surface shape of a plurality of lens segments of a lens comprising the plurality of lens segments, comprising the steps of: calculating a focal length based on a first distance from the center of the lens to an object and a second distance from the center of the lens to a focal plane; calculating an optimal radius of curvature of the lens based on a first conditional expression specifying a combination of radii of curvature of the lens having the calculated focal length, and a second conditional expression specifying that a Condington shape factor calculated based on the radii of curvature is equal to a shape factor that minimizes spherical aberration, the shape factor being calculated based on the first distance and the second distance; identifying an initial freeform surface shape of the plurality of lens segments using the calculated optimal radii of curvature; Free-form surface shape identification method.

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