Optical design method, optical element, and evaluation method thereof

Abstract

To provide an optical design method, an optical element, and an evaluation method suitable for chromatic aberration correction.SOLUTION: An optical design method has a chromatic aberration setting step of setting an optical system including a conventional lens, and a meta lens in which a fine pattern is formed, and the chromatic aberration setting step includes a comparison step of comparing a value based on first power of the conventional lens shown in the following expression (1) with a preset reference value: φc2=-V123*hma*φm2 / EV123...(1). In this case, characters in the expression (1) are as follows: φc2; the first power of the conventional lens, V123; Abbe number of the conventional lens, hma; the height of rays in the meta lens in tracking of paraxial rays relative to the height of parallel light allowed to enter the meta lens, φm2; second power of the metal lens, and EV123; the equivalent Abbe number of the metal lens (1, 2, 3 correspond to wavelengths λ1, λ2, λ3).SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to an optical design method, an optical element, and an optical element evaluation method. [Background technology]

[0002] Metalenses have attracted attention as thin and lightweight lenses, and research and development into them is progressing. The imaging performance of metalenses is based on diffraction, which differs from the refractive effect of conventional lenses. This results in the phenomenon of chromatic aberration occurring in the opposite direction in metalenses. By utilizing this phenomenon and combining a metalense with a conventional lens, it may be possible to achieve high-performance chromatic aberration correction in a thin and lightweight configuration. However, such a design method has not been proposed until now.

[0003] Therefore, the inventors proposed the "equivalent Abbe number" of a metalens, as described in Non-Patent Document 1. This "equivalent Abbe number" can be used as a criterion for quantitatively evaluating the chromatic aberration correction ability of a metalens. If this "equivalent Abbe number" is applied to the formula for chromatic aberration correction of a conventional lens, it may be possible to set the initial settings in a design method for an imaging system that combines a metalens and a conventional lens. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Hideki Ina et al., Equivalent Abbe Number of Metalens, Optics & Photonics Japan 2023 Sapporo Annual Academic Conference [Proceedings], Optical Society of Japan, p. 106, published November 20, 2023 (publication) Summary of the Invention [Problem to be solved by the invention]

[0005] The inventors proposed the above-mentioned "equivalent Abbe number" and considered applying it to the formula for correcting chromatic aberration, but encountered a problem in the process. Before explaining this problem, the formula for correcting chromatic aberration of conventional lenses will be explained.

[0006] 20 is a schematic diagram of an imaging system using two conventional lenses La and Lb in a conventional example. Here, when the lens thickness and spacing e' of each of the conventional lenses La and Lb are set to zero (0), the formula for correcting chromatic aberration is known as the following formula (501). fa / vb+fb / va=0 (501) Here, the letters in formula (501) are as follows: fa: focal length of conventional lens La fb: focal length of conventional lens Lb va: Abbe number of the glass material used in the conventional lens La vb: Abbe number of the glass material used in conventional lens Lb

[0007] The Abbe number mentioned above is known as the following formula (502). V = (N2 - 1) / (N1 - N3) (502) Here, the characters in equation (502) are as follows: V: Abbe number of the glass material N1: Refractive index of the glass material at any wavelength λ1 N2: Refractive index of the glass material at any wavelength λ2 longer than wavelength λ1 N3: Refractive index of the glass material at any wavelength λ3 longer than wavelength λ2

[0008] Below, we will explain the problems that arise when applying the formula for chromatic aberration correction to the "equivalent Abbe number." Figure 21 shows a schematic diagram of an imaging system using a conventional lens Lc in a conventional example and a metalens Lm on which a fine pattern is formed.

[0009] The following formula (503) represents an equation obtained by applying the equivalent Abbe number of the metalens Lm to formula (501), and the following formula (504) represents an equation obtained by modifying formula (503). fc / Ev+fm / vc=0 (503) -Ev / vc=fc / fm ···(504) Here, the characters in formulas (503) and (504) are as follows: fc: focal length of conventional lens Lc fm: focal length of metalens Lm vc: Abbe number of the glass material used in the conventional lens Lc Ev: equivalent Abbe number of metalens Lm

[0010] Here, the value of the equivalent Abbe number Ev has a smaller absolute value than the Abbe number vc of the glass material used in the conventional lens Lc. That is, according to equation (504), the focal length fc of the conventional lens Lc tends to be smaller than the focal length fm of the metalens Lm. Furthermore, the shorter the focal length fm of the metalens Lm, the easier it is to utilize the characteristics of the metalens Lm. For this reason, when pursuing the original role of the metalens Lm, it is important to make the focal length fm as small as possible. Furthermore, as the focal length fm of the metalens Lm is reduced, the focal length fc of the conventional lens Lc must also be reduced, and as a result, the radius of curvature of the conventional lens Lc must be reduced.

[0011] In this regard, Non-Patent Document 1 discloses a metalens with an equivalent Abbe number at the d-line of approximately -4, and a conventional lens made of a glass material with an Abbe number at the d-line of approximately 16 to 95 (approximately 4 to 24 times the absolute value of the equivalent Abbe number). Therefore, when formula (504) is satisfied for each lens disclosed in Non-Patent Document 1, the focal length of the conventional lens is approximately 1 / 4 to 1 / 24 times the focal length of the metalens. This indicates that the focal length of the conventional lens is short, and the associated radius of curvature of the lens is a small positive value, qualitatively increasing the amount of aberration. Furthermore, if the effective diameter is twice the radius of curvature and the diameter is at its maximum value, a small radius of curvature cannot meet the demand for a large effective diameter. Of course, formula (503) is used in the initial stage of optical design. Subsequent ray tracing is used to correct aberrations when adjusting the glass thickness and spacing of each lens from 0 to a finite value. However, if the optical system has poor initial aberrations, it may take a long time to converge and complete the design, and the design may become more difficult. Therefore, in an optical system including a metalens and a conventional lens, it is problematic to use the chromatic aberration correction formula (503) as it is, and a method suitable for correcting chromatic aberration is required.

[0012] The present invention has been devised in view of the above-mentioned problems, and an object of the present invention is to provide an optical design method, an optical element, and an evaluation method suitable for correcting chromatic aberration. [Means for solving the problem]

[0013] An optical design method according to a first aspect of the present invention includes a chromatic aberration setting step of setting an optical system including a conventional lens and a metalens on which a fine pattern is formed, and the chromatic aberration setting step includes a comparison step of comparing a value based on a first power of the conventional lens, as shown in the following formula (1), with a predetermined reference value: φc2=-V 123 ×hm a ×φm2 / EV 123 ···(1) φc2: the first power of the conventional lens V 123 : Abbe number of the conventional lens hm a : The height of the ray at the metalens in paraxial ray tracing relative to the height of the parallel light incident on the metalens φm2: second power of the metalens EV 123 : the equivalent Abbe number of the metalens (1, 2, 3 correspond to wavelengths λ1, λ2, λ3)

[0014] An optical design method according to a second aspect of the present invention is characterized in that, in the first aspect of the present invention, the reference value indicates 3.5, and the comparing step includes setting the shape of the conventional lens so as to satisfy the following formula (2) based on the first power: (Nc2-1) / φc2≧Th (2) Nc2: refractive index of the conventional lens at the second wavelength Th: the reference value (= 3.5)

[0015] An optical design method according to a third aspect of the present invention is characterized in that, in the second aspect of the present invention, when the wavelengths λ1, λ2, and λ3 are any of the d-line, C-line, and F-line, the equivalent Abbe number of the metalens at the d-line is not less than -10 and not more than -3.

[0016] An optical design method according to a fourth aspect of the present invention is any one of the first to third aspects of the present invention, further comprising, after the chromatic aberration setting step, a bonding step of bonding the conventional lens to a bonding surface of the metalens, wherein the bonding surface presents a main surface different from the micropattern and is formed in a planar shape.

[0017] An optical design method according to a fifth aspect of the present invention is the optical design method of the fourth aspect of the present invention, further comprising, before the cementing step, a first limiting condition step of specifying conditions for the diffractive optical element and the conventional lens that satisfy the following formula (3): B1∝λ0(N11-N12) / (R×(λ11-λ12)) ···(3) B1: Phase coefficient when modeling the diffractive optical element using the equivalent refractive index method using optical design software λ0: normalized wavelength of the diffractive optical element λ1: First wavelength to be corrected for axial chromatic aberration λ2: Second wavelength to be corrected for axial chromatic aberration N11: a first refractive index of the conventional lens for the first wavelength to be corrected N12: A second refractive index of the conventional lens for the second wavelength to be corrected R: Radius of curvature of the convex surface of the conventional lens

[0018] The optical design method of the sixth aspect of the present invention is characterized in that, in the fifth aspect of the present invention, it comprises a setting step of setting a first step pattern of the binary optics based on an optical design of a configuration including binary optics included in one of the diffractive optical elements that replaces the characteristics of the metalens; a first calculation step of calculating first phase data that indicates the relationship of phase with respect to the shape of the meta-atom based on a predetermined first wavelength; and a first identification step of calculating a first phase pattern from the first step pattern and identifying the fine pattern corresponding to the first phase pattern by referring to the first phase data.

[0019] An optical design method according to a seventh aspect of the present invention is characterized in that, in the sixth aspect of the present invention, the setting step sets the first step pattern based on an optical design that combines the binary optics with a conventional lens for initial setting.

[0020] An optical design method according to an eighth aspect of the present invention is characterized in that, in the seventh aspect, it further comprises: a second calculation step of calculating second phase data different from the first phase data based on a second wavelength different from the preset first wavelength; a second identification step of referring to the second phase data and identifying a second phase pattern corresponding to the fine pattern; and a design step of designing the conventional lens based on the first phase pattern and the second phase pattern.

[0021] An optical element according to a ninth aspect of the present invention comprises a conventional lens and a metalens having a fine pattern formed thereon, wherein the conventional lens satisfies the following formula (1): φc2=-V 123 ×hm a ×φm2 / EV 123 ···(1) φc2: the first power of the conventional lens V 123 : Abbe number of the conventional lens hm a : The height of the ray at the metalens in paraxial ray tracing relative to the height of the parallel light incident on the metalens φm2: second power of the metalens EV 123 : the equivalent Abbe number of the metalens (1, 2, 3 correspond to wavelengths λ1, λ2, λ3)

[0022] The optical element according to the tenth aspect of the present invention is characterized in that, in the ninth aspect, when the wavelengths λ1, λ2, and λ3 are any of the d-line, C-line, and F-line, the reference value Th of the following formula (2) based on the first power is 3.5: (Nc2-1) / φc2≧Th (2) Nc2: refractive index of the conventional lens Th: the reference value (= 3.5)

[0023] An optical element evaluation method according to an eleventh aspect of the present invention is characterized by comprising a comparison step of comparing, for an optical system including a conventional lens and a metalens having a fine pattern formed thereon, a value based on a first power of the conventional lens, as shown in the following formula (1), with a predetermined reference value: φc2=-V 123 ×hm a ×φm2 / EV 123 ···(1) φc2: the first power of the conventional lens V 123: Abbe number of the conventional lens hm a : The height of the ray at the metalens in paraxial ray tracing relative to the height of the parallel light incident on the metalens φm2: second power of the metalens EV 123 : the equivalent Abbe number of the metalens (1, 2, 3 correspond to wavelengths λ1, λ2, λ3) [Effects of the Invention]

[0024] According to the first to eighth and eleventh inventions, the comparing step compares a value based on the first power of the conventional lens shown in formula (1) with a preset reference value. This makes it possible to set an optical system that satisfies the formula for chromatic aberration correction, taking into account the characteristics of the metalens as an equivalent Abbe number. This makes it possible to realize an optical design that is suitable for chromatic aberration correction.

[0025] In particular, according to the second aspect of the present invention, the comparison step sets the shape of the conventional lens so as to satisfy formula (2) based on the first power. Therefore, the shape of the conventional lens can be set by taking into consideration, as a reference value, a range in which manufacturing variations in the radius of curvature of the conventional lens can be suppressed. This makes it possible to realize an optical design that takes into consideration the manufacturing accuracy of the conventional lens.

[0026] In particular, according to the fourth aspect of the invention, the cementing step cements a conventional lens to a major surface of the metalens after the chromatic aberration setting step. This reduces the reflectance of the major surface of the metalens, and suppresses defects such as flare and ghosting caused by the major surface. This makes it possible to improve optical properties.

[0027] In particular, according to the fifth aspect of the present invention, the first limiting condition step specifies the conditions for the diffractive optical element and the conventional lens that satisfy formula (3) before the cementing step. This makes it possible to easily realize a design that takes into account the correction of axial chromatic aberration for two specific wavelengths. This makes it possible to easily realize the optical design of a configuration that includes a metalens.

[0028] In particular, according to the sixth aspect of the present invention, the setting step sets a first step pattern of the binary optics. Furthermore, the first specifying step calculates a first phase pattern from the first step pattern and specifies a fine pattern corresponding to the first phase pattern by referring to the first phase data. Therefore, the fine pattern required for designing a metalens can be specified using a first step pattern that can be set by a conventional method. This facilitates the optical design of a configuration that includes a metalens.

[0029] In particular, according to the seventh aspect of the present invention, the setting step sets the first step pattern based on the optical design of a configuration that combines binary optics with a conventional lens for initial setup. Therefore, the fine pattern required for designing the metalens can be specified using the first step pattern that takes into account its use in combination with the conventional lens. This makes it possible to facilitate the optical design of a configuration that combines a metalens with a conventional lens.

[0030] Furthermore, according to the ninth aspect of the present invention, the conventional lens satisfies formula (1). Therefore, it is possible to use an optical element that includes a conventional lens having a realistic radius of curvature and satisfies the formula for chromatic aberration correction. This makes it possible to realize an optical element that is suitable for chromatic aberration correction.

[0031] In particular, according to the tenth aspect of the present invention, the reference value is 3.5. Therefore, it is possible to use conventional lenses in which manufacturing variations in the radius of curvature of conventional lenses are suppressed. This makes it possible to realize optical elements that take into account the manufacturing accuracy of conventional lenses. [Brief explanation of the drawings]

[0032] [Figure 1] FIG. 1(a) is a schematic diagram showing an example of an optical element according to this embodiment, and FIG. 1(b) is a schematic diagram showing a modified example of the optical element. [Figure 2] FIG. 2 is a schematic diagram showing an example of the positional relationship between a metalens and a conventional lens. [Figure 3] 3(a) and 3(b) are schematic diagrams showing examples of configurations in which a metalens and a conventional lens are used together. [Figure 4] FIG. 4(a) is a flowchart showing an example of an optical design method according to this embodiment, and FIG. 4(b) is a flowchart showing an example of an optical design method including a bonding step. [Figure 5] 5(a) and 5(b) are schematic diagrams showing examples of configurations in which a diffractive optical element and a conventional lens are used in combination. [Figure 6] 6(a) and 6(b) are flowcharts showing a first modified example of the optical design method according to this embodiment. [Figure 7] FIG. 7(a) is a diagram for explaining the surface numbers when the optical system of FIG. 1(a) is taken as an example, and FIG. 7(b) is a diagram for explaining the surface numbers when the optical system of FIG. 5(a) is taken as an example. [Figure 8] FIG. 8 shows an example of inputting each plane number into "CODEV (registered trademark)" and the calculation results. [Figure 9] FIG. 9 is a flowchart showing a second modified example of the optical design method according to this embodiment. [Figure 10] FIG. 10 is a schematic diagram showing an example of a configuration when optical design is carried out using binary optics and a conventional lens in combination. [Figure 11] FIG. 11 is a graph showing an example of phase data. [Figure 12] FIG. 12 is a schematic diagram showing an example of a step in binary optics. [Figure 13] FIG. 13 is a schematic diagram showing an example of a process for identifying a fine pattern corresponding to a step pattern. [Figure 14]FIG. 14 is a schematic diagram showing an example of the difference between phase data of different wavelengths. [Figure 15] 15(a) to 15(c) are schematic diagrams showing an example of a configuration when optical design is performed using binary optics having different step patterns in combination with a conventional lens. [Figure 16] FIG. 16 is a flowchart showing a fourth modified example of the optical design method according to this embodiment. [Figure 17] FIG. 17 is a schematic diagram showing an example of an input state of the normalized wavelength and the phase coefficients of the polynomial of the phase distribution. [Figure 18] FIG. 18 is a graph showing the results of verifying the calculation results of the focal length. [Figure 19] FIG. 19 is a schematic diagram showing an example of the positional relationship between a diffractive optical element and a conventional lens. [Figure 20] FIG. 20 is a schematic diagram of a conventional imaging system using two conventional lenses. [Figure 21] FIG. 21 shows a schematic diagram of an imaging system using a conventional lens and a metalens in a conventional example. DETAILED DESCRIPTION OF THE INVENTION

[0033] Hereinafter, examples of an optical design method, an optical element, and an optical element evaluation method according to embodiments of the present invention will be described with reference to the drawings. Note that the configurations in each drawing are shown schematically for the purpose of explanation, and the shape, thickness, etc. of each configuration may differ from those shown in the drawings.

[0034] (Embodiment: Optical element 100) An example of the optical element 100 according to this embodiment will be described below. Fig. 1(a) is a schematic diagram showing an example of the optical element 100 according to this embodiment, and Fig. 1(b) is a schematic diagram showing a first modified example of the optical element 100 according to this embodiment.

[0035] As shown in FIG. 1( a), the optical element 100 of this embodiment includes a metalens 1 having a fine pattern formed thereon, and a conventional lens 2. The metalens 1 exhibits a light-collecting function (so-called lens function) that differs from that of conventional diffractive optical elements. The conventional lens 2 has characteristics different from those of the metalens 1 and is a typical lens such as a refractive lens, a diverging lens, or a reflective lens.

[0036] The optical element 100 has a configuration as shown in Fig. 2. The characters shown in Fig. 2 are as follows. fm2: focal length of metalens 1 fc2: Focal length of conventional lens 2 φm2: power of metalens 1 (= 1 / fm2) φc2: power of conventional lens 2 (= 1 / fc2) L: Incident light e´: The geometrical optical distance between metalens 1 and conventional lens 2 hm a : The height of the ray at metalens 1 in paraxial ray tracing relative to the height of the parallel light incident on metalens 1

[0037] Metalens 1 has a microstructured surface 11 and a main surface 12. Microstructured surface 11 is a surface on which a micropattern is formed. The micropattern is configured based on the shape of the meta-atoms, and the properties of metalens 1 change depending on the configuration of the micropattern. For example, multiple different micropatterns may be formed on microstructured surface 11. The characteristics and types of the micropatterns formed on microstructured surface 11 can be set as desired depending on the application.

[0038] For example, as shown in Fig. 1(a), the first pattern P1, the second pattern P2, and the third pattern P3 are examples showing different types of fine patterns, and in the order of the first pattern P1, the second pattern P2, and the third pattern P3, they show a configuration where the area occupied by the element material such as glass is small (P1 < P2 < P3). In this case, the effective refractive index indicating the characteristics of the metalens 1 shows a tendency to be low in the order of the first pattern P1, the second pattern P2, and the third pattern P3 (P1 < P2 < P3). When referring to the cross-sectional view of the metalens 1, each pattern P1, P2, P3 is compared based on the area, but actually, it can be compared based on the volume (shape of meta-atoms) of each pattern P1, P2, P3.

[0039] As the material of the metalens 1, for example, known materials such as quartz (SiO2) and S-BSL7 are used. When selecting the material of the metalens 1, it is necessary to consider the trade-off between the required specifications of unwanted light and the required specifications of aberration.

[0040] The principal plane 12 is a plane that faces the fine-shaped surface 11 and is formed in a planar shape. No fine pattern is formed on the principal plane 12.

[0041] The conventional lens 2 has characteristics equivalent to those of an existing lens and is provided facing the principal plane 12. The conventional lens 2 has a first power φc2 that satisfies the following formula (1). φc2 = -V 123 ×hm a ×φm2 / EV 123 ···(1) Here, the characters in formula (1) are as follows. φc2: The first power of the conventional lens 2 V 123 : The Abbe number of the conventional lens 2 hm a : The height of the light ray in the metalens 1 in paraxial ray tracing with respect to the height of the parallel light incident on the metalens 1 φm2: The second power of the metalens 1 EV 123 : The equivalent Abbe number of the metalens 1

[0042] By having the conventional lens 2 satisfy the formula (1), it is possible to use an optical element 100 that includes the conventional lens 2 having a realistic radius of curvature and satisfies the formula for chromatic aberration correction. This makes it possible to realize an optical element 100 that is suitable for chromatic aberration correction.

[0043] The values ​​of each letter in formula (1) may be values ​​when three wavelengths λ1, λ2, and λ3 (λ1<λ2<λ3) are used, and the wavelengths corresponding to each letter are indicated with subscripts. For example, the first power φc2 indicates a value at an arbitrary wavelength λ2, and the Abbe number V 123 indicates the value at any three wavelengths λ1, λ2, and λ3, and the height ratio hm a indicates a value at an arbitrary wavelength λ2, and the second power φm2 indicates a value at an arbitrary wavelength λ2. Each of the wavelengths λ1, λ2, and λ3 can be set arbitrarily depending on the application.

[0044] For example, the equivalent Abbe number EV of Metalens 1 123 can be expressed as the following equation (11), for example. EV 123 =φm2 / (φm1-φm3) (11) Here, the letters in equation (11) are as follows: φm1: power of metalens 1 at any wavelength λ1 φm2: Power of metalens 1 at any wavelength λ2 longer than wavelength λ1 φm3: power of metalens 1 at any wavelength λ3 longer than wavelength λ2

[0045] For example, the following values ​​can be used as the wavelengths λ1, λ2, and λ3. λ1 = Fraunhofer F line (0.4861 μm) λ2 = Fraunhofer d line (0.58756 μm) λ3 = Fraunhofer C line (0.6563 μm) In this case, for example, the equivalent Abbe number EV of Metalens 1 123indicates a value between -10 and -3. This makes it easy to identify the characteristics of the conventional lens 2 that are suited to the characteristics of the metalens 1.

[0046] Furthermore, the conventional lens 2 may be bonded to the primary surface 12, as shown in FIG. 1(b), for example. The surface of the conventional lens 2 that is bonded to the primary surface 12 is formed, for example, into a flat surface. In this case, the reflectance of the primary surface 12 of the metalens 1 can be reduced, and defects such as flare and ghosting caused by the primary surface 12 can be suppressed. This makes it possible to improve the optical properties.

[0047] Furthermore, the conventional lens 2 may be disposed upstream of the metalens 1 in the optical path, as shown in FIG. 3(a), or may be disposed downstream of the metalens 1 in the optical path, as shown in FIG. 3(b), and can be arbitrarily set depending on the application.

[0048] The conventional lens 2 may include, for example, at least a first glass material and a second glass material. The first glass material is cemented to the principal surface 12. The second glass material is spaced from the principal surface 12 and cemented to the first glass material. Therefore, by changing the materials of the glass materials, the characteristics of the entire optical element 100 can be easily changed. This makes it possible to further expand the applications of the optical element 100. Note that the conventional lens 2 may include, for example, in addition to the first glass material and the second glass material, any glass material depending on the application.

[0049] The optical element 100 described above can realize an optical system suitable for correcting chromatic aberration, which makes it possible to expand the range of uses for the optical element 100.

[0050] (Embodiment: Optical design method) An example of an optical design method according to this embodiment will now be described: Fig. 4(a) is a flowchart showing an example of an optical design method according to this embodiment.

[0051] The optical design method of the present embodiment can be used to realize the optical design of an optical element 100 including a metalens 1 and a conventional lens 2, as shown in Figures 3(a) and 3(b), for example. The optical design method can obtain information about the concentration of light 5 when parallel light 4 is incident from an object at infinity, based on a configuration in which, for example, an aperture 3 and the optical element 100 are arranged in this order.

[0052] The optical design method includes a chromatic aberration setting step S10. The optical design method may include a bonding step S20, as shown in FIG.

[0053] <Chromatic aberration setting step S10> The chromatic aberration setting step S10 sets the characteristics of the optical system including the conventional lens 2 and the metalens 1. The chromatic aberration setting step S10 includes a comparison step.

[0054] The comparison step compares the power (first power φc2) of the conventional lens 2 shown in equation (1) with a preset reference value Th. The comparison step derives the characteristics of the conventional lens 2 that satisfy equation (1) based on, for example, the preset characteristics of the metalens 1, and compares the first power φc2 obtained from the derivation result with the reference value Th. For this purpose, the characteristics of the metalens 1 are compared with the equivalent Abbe number EV 123 Taking these factors into consideration, an optical system that satisfies the formula for chromatic aberration correction can be set.

[0055] In the chromatic aberration setting step S10, the optical design of the optical element 100 can be performed by any method using the comparison result in the comparison step.

[0056] For example, the comparison step includes setting the shape of the conventional lens 2 so as to satisfy the following formula (2) based on the first power φc2. (Nc2-1) / φc2≧Th (2) Here, the letters in equation (2) are as follows: Nc2: Refractive index of conventional lens 2 Th: Reference value

[0057] In equation (2), for example, values ​​at the Fraunhofer d-line are used as the refractive index Nc2 and first power φc2 of the conventional lens 2, and values ​​at an arbitrary wavelength λ2 may also be used.

[0058] The reference value Th is proportional to the radius of curvature of the conventional lens 2. For example, the reference value Th is 3.5. If the reference value Th is less than 3.5, the radius of curvature of the lens exceeds the limit of processing accuracy, which may reduce the processing accuracy of the lens and lead to a decrease in functionality. In response to this, the comparison step in this embodiment is performed using 3.5 as the reference value Th. Therefore, the shape of the conventional lens 2 can be set by taking into consideration the range of the reference value Th that can suppress manufacturing variations in the radius of curvature of the conventional lens 2.

[0059] <Joining step S20> For example, in the bonding step S20, after the chromatic aberration setting step S10, a conventional lens 2 is bonded to the main surface 12 (cemented surface) of the metalens 1. In the bonding step S20, the metalens 1 and the conventional lens 2 are bonded together using, for example, a known lens adhesive. This reduces the reflectance at the cemented surface of the metalens 1, and suppresses defects such as flare and ghosting that may result from the cemented surface. This makes it possible to improve the optical characteristics.

[0060] The optical design method of this embodiment is completed by performing each of the above-described steps. Note that the above-described comparison step can also be performed, for example, as a method for evaluating the optical element 100. The evaluation method for the optical element 100 can be used, for example, in an inspection process for manufacturing the optical element 100, or in an acceptance inspection of a product related to the optical element 100.

[0061] According to this embodiment, the comparison step compares a value based on the first power φc2 of the conventional lens 2 shown in equation (1) with a preset reference value Th. Therefore, the characteristics of the metalens 1 are expressed as the equivalent Abbe number EV 123Taking these factors into consideration, an optical system can be set that satisfies the formula for chromatic aberration correction. This makes it possible to realize an optical design that is suitable for chromatic aberration correction.

[0062] Furthermore, according to this embodiment, the comparing step sets the shape of the conventional lens 2 so as to satisfy equation (2) based on the first power φc2. Therefore, the shape of the conventional lens 2 can be set by taking into consideration, as the reference value Th, a range in which manufacturing variations in the radius of curvature of the conventional lens 2 can be suppressed. This makes it possible to realize an optical design that takes into consideration the formation accuracy of the conventional lens 2.

[0063] Furthermore, according to this embodiment, in the bonding step S20, which is performed after the chromatic aberration setting step S10, a conventional lens 2 is bonded to the primary surface 12 of the metalens 1. This reduces the reflectance at the primary surface 12 of the metalens 1, and can suppress defects such as flare and ghosting that may be caused by the primary surface 12. This makes it possible to improve the optical characteristics.

[0064] (First Modification: Optical Design Method) Next, a first modified example of the optical design method in this embodiment will be described. The difference between the above-described embodiment and the first modified example is that it includes a limiting condition step S30. Note that a description of the same content as in the above-described embodiment will be omitted.

[0065] <Restriction Condition Step S30> In the limiting condition step S30, as shown in FIGS. 5(a) and 5(b), known optical design software is used to specify the conditions for a configuration that combines a diffractive optical element 101 that substitutes for the characteristics of metalens 1 with a conventional lens 2. For example, in the limiting condition step S30, by considering the use of a plano-convex lens as the conventional lens 2, it is possible to achieve a more accurate design than when other lenses are considered. In this case, the limiting condition step S30 is performed on the premise that the flat surface of the conventional lens 2 will be cemented to the flat surface of the diffractive optical element 101 that substitutes for the main surface 12. For example, after the limiting condition step S30, the chromatic aberration setting step S10 and the cementing step S20 are performed.

[0066] The optical design method can perform the optical design of the optical element 100 by any method using the conditions specified in the limiting condition step S30, for example.

[0067] The limiting condition step S30 may include, for example, a first limiting condition step S31 shown in FIG. 6(a) and, for example, a second limiting condition step S32 shown in FIG. 6(b). For example, if the limiting condition step S30 includes the first limiting condition step S31 and the second limiting condition step S32, it is expected that the optimization of the conditions can be accelerated. The first limiting condition step S31 and the second limiting condition step S32 can be performed using known optical design software such as "CODEV (registered trademark)." Note that, for example, the optical design method may include a preparation step S0 of determining the specifications to be designed.

[0068] <First Restriction Condition Step S31> The first limiting condition step S31 specifies the condition of the diffractive optical element 101 and the conventional lens 2 that satisfies the following formula (3). B1∝λ0(N11-N12) / (R×(λ1-λ2)) ···(3) Here, the letters in equation (3) are as follows: B1: Phase coefficient when modeling the diffractive optical element 101 using the equivalent refractive index method using optical design software λ0: normalized wavelength of the diffractive optical element 101 λ1: First wavelength to be corrected for axial chromatic aberration λ2: Second wavelength to be corrected for axial chromatic aberration N11: First refractive index of conventional lens 2 for the first correction target wavelength N12: the second refractive index of the conventional lens 2 for the second correction target wavelength R: Radius of curvature of the convex surface of conventional lens 2

[0069] The present inventors have found that, for example, in "CODEV (registered trademark)", it can be expressed by the equal sign shown in the following equation (3A) instead of the proportionality shown in equation (3). C1=-λ0(N11-N12) / (2R×(λ1-λ2)) ···(3A) Here, the letters in formula (3A) are as follows: C1: Phase coefficient when modeling the diffractive optical element 101 using the equivalent refractive index method with "CODEV (registered trademark)"

[0070] By satisfying formula (3), it is possible to easily realize a design that takes into account the correction of axial chromatic aberration for two specific wavelengths. This ultimately makes it possible to easily realize an optical design that includes metalens 1. The derivation of formula (3) will be described later.

[0071] For example, the phase coefficient C1 shown in equation (3A) indicates a coefficient multiplied by the square of the radius when the amount of deformation of the phase of the optical wavefront when passing through only the diffractive optical element 101 is expressed as a polynomial when the diffractive optical element 101 is modeled by the equivalent refractive index method in "CODEV (registered trademark)."

[0072] The first wavelength λ1 to be corrected and the second wavelength λ2 to be corrected can be set arbitrarily depending on the application, and for example, the wavelengths λ1, λ2, and λ3 described above may be used.

[0073] Below, an example of calculating the phase coefficient C1 when modeling the diffractive optical element 101 by the equivalent refractive index method using "CODEV (registered trademark)" will be described.

[0074] Taking the optical system of FIG. 1(a) described above as an example, the surface numbers are shown as in FIG. 7(a). Taking the optical system of FIG. 5(a) described above as an example, the surface numbers are shown as in FIG. 7(b). The surface numbers are assigned sequentially from the upstream side to the downstream side of the optical path. Below, the surface numbers will be explained, starting from the upstream side of the optical path. Surface number "object" refers to the surface of an object located at a position away from the aperture 3, and surface number "aperture surface" refers to the surface of the aperture 3. Surface number "2" refers to the object-side surface of the conventional lens 2, in other words, the upstream side of the optical path, and surface number "3" refers to the metalens 1 side of the conventional lens 2, in other words, the downstream side of the optical path. Surface number "4" refers to the major surface 12 of the metalens 1, and surface number "5" refers to the boundary surface between the major surface 12 of the metalens 1 and the micropattern formed on the microstructure surface 11. Surface number "6" refers to the microstructure surface 11 of the metalens 1. The surface number "image" is the image point.

[0075] Examples 1 to 3 in Figure 8 show examples of input to "CODEV (registered trademark)" and calculation results. The surface spacing in Figure 8 indicates the distance between surfaces near the center of the optical axis. The distance between surfaces near the center of the optical axis indicated by each surface number indicates the distance from the surface with the adjacent surface number more upstream on the optical path. For example, the surface spacing indicated by surface number "4" indicates the distance from the surface with surface number "3" more upstream on the optical path. Incidentally, the surface spacing for surface number "object," which is located at the most upstream side of the optical path, is indicated as "infinite" because there is no surface located more upstream on the optical path.

[0076] The surface type is a microscopic representation of the shape of the surface of each surface number, and displays the lens classification (spherical lens, aspherical lens, etc.). The radius of curvature indicates the radius of curvature of the surface of each surface number. The material indicates the material of the surface of each surface number; for example, "SUP" written on surface number "3" indicates quartz. The refraction mode indicates whether or not the light is refracted.

[0077] By inputting these parameters into "CODEV (registered trademark)" for each surface number, the phase coefficient C1 can be determined.

[0078] 8, examples 1 to 3 show examples in which the second wavelength λ1 has a second order phase coefficient C12, the second wavelength λ2 has a second order phase coefficient C22, and the third wavelength λ3 has a second order phase coefficient C32, which are obtained by actually inputting each parameter into "CODEV (registered trademark)" for each surface number. In all of examples 1 to 3, the second wavelength λ2 has a wavelength of 589 nm, the first wavelength λ1 has a wavelength of 546 nm, and the third wavelength λ3 has a wavelength of 633 nm (λ1<λ2<λ3), resulting in an achromatic optical system in which chromatic aberrations of the first wavelength λ1 and the third wavelength λ3 are corrected.

[0079] In all of Examples 1 to 3, the quadratic phase coefficients C12 to C32 are the same at the wavelengths λ1 to λ3, but the lens material, radius of curvature, and surface spacing are changed. In this way, even if the lens material, radius of curvature, and surface spacing are different, optical design can be performed to achieve the same quadratic phase coefficients C12 to C32. Therefore, the convenience of optical design can be improved by obtaining in advance a table of design examples of lens material, radius of curvature, and surface spacing for each quadratic phase coefficient C12 to C32. Note that the above-described optical system embodiments have been described using examples in which axial chromatic aberration is corrected. However, imaging optical systems can also be designed for other aberrations based on the above-described embodiments and known techniques. Furthermore, in the above-described embodiments, design examples of a single optical element 100 composed of a metalens 1 and a conventional lens 2 have been described. However, optical systems including two or more optical elements 100 can also be designed based on the above-described embodiments and known techniques.

[0080] <Second Restriction Condition Step S32> The second limiting condition step S32 specifies the condition of the diffractive optical element 101 and the conventional lens 2 that satisfies the following formula (4). B1∝λ0(φpc2-φpc1) / (-λ1(1-e´φpc1)+λ2(1-e´φpc2)) ···(4) Here, the letters in equation (4) are as follows: B1: Phase coefficient when modeling the diffractive optical element 101 using the equivalent refractive index method using optical design software λ0: normalized wavelength of the diffractive optical element 101 λ1: First wavelength to be corrected for axial chromatic aberration λ2: Second wavelength to be corrected for axial chromatic aberration φpc1: the reciprocal of the focal length of conventional lens 2 (power) φpc2: the reciprocal of the focal length (power) of the diffractive optical element 101 e': geometrical optical distance between the diffractive optical element 101 and the conventional lens 2

[0081] The present inventors have found that, for example, in "CODEV (registered trademark)", it can be expressed by the equal sign shown in the following equation (4A) instead of the proportionality shown in equation (4). C1=λ0(φpc2-φpc1) / (-2λ1(1-e´φpc1)+2λ2(1-e´φpc2)) ···(4A)

[0082] By satisfying formula (4), it is possible to easily realize a design that takes into account the thicknesses of the diffractive optical element 101 and the conventional lens 2, which will ultimately result in the metalens 1. This makes it possible to improve the accuracy of the optical design of a configuration that includes the diffractive optical element 101.

[0083] By carrying out at least one of the first limiting condition step S31 and the second limiting condition step S32 described above, the optical design method in this embodiment is completed, and the above-mentioned optical element 100 can be manufactured by carrying out a known manufacturing method, for example, based on the conditions specified in each of steps S31 and S32.

[0084] According to this modification, the first limiting condition step S31 specifies the conditions for the diffractive optical element 101 and the conventional lens 2 that satisfy formula (3). This makes it possible to easily realize a design that takes into account the correction of axial chromatic aberration for two specific wavelengths. This makes it possible to easily realize the optical design of a configuration that includes the metalens 1.

[0085] Furthermore, according to this embodiment, the second limiting condition step S32 specifies the conditions for the diffractive optical element 101 and the conventional lens 2 that satisfy formula (4). This makes it possible to easily achieve a design that takes the lens thickness into consideration. This makes it possible to improve the accuracy of the optical design of a configuration that includes the metalens 1.

[0086] (Second Modification: Optical Design Method) Next, a second modified example of the optical design method in this embodiment will be described. The difference between the above-described embodiment and the second modified example is that the setting step S110 etc. is performed. Note that a description of the same content as the above-described embodiment will be omitted.

[0087] 9, the optical design method further includes a setting step S110, a first calculation step S120, a first identification step S130, a second calculation step S140, a second identification step S150, and a design step S160. When this modification is implemented, for example, the "diffractive optical element 101" in the above-described limiting condition step S30 may be read as "binary optics 21" included in the diffractive optical element 101.

[0088] <Setting step S110> In the setting step S110, as shown in FIG. 10, for example, the optical characteristics are determined based on an optical design of a configuration that combines binary optics 21 (hereinafter also referred to as BO (Binary Optics) as necessary) that substitutes for the characteristics of metalens 1 with a conventional lens 22 for initial setup. The optical characteristics include, for example, the step pattern (e.g., first step pattern) of the binary optics 21, and can be calculated using known optical design software for ray tracing. The optical characteristics may include parameters such as wavelength, focal length, F-number, and various allowable aberration amounts, and may also include, for example, the characteristics of the transmitted wavefront or reflected wavefront.

[0089] <First calculation step S120> The first calculation step S120 calculates first phase data that indicates the relationship between the phase and the shape of the meta-atom based on a preset first wavelength λ1 (e.g., a first wavelength to be corrected). The first phase data indicates the relationship, for example, taking into account the influence of nonlinear components. The first calculation step S120 can calculate phase data such as the first phase data, for example, using optical simulations of a known vector model. Note that the phase data is calculated using parameters such as the material and refractive index of the metalens 1 to be designed, the shape of the meta-atom (e.g., cylindrical), the height of the meta-atom, and the corresponding wavelength.

[0090] <First Identification Step S130> In the first identification step S130, a first phase pattern is calculated from the first step pattern, and a fine pattern indicating the shape of the meta-atom corresponding to the first phase pattern is identified by referring to the first phase data. An example of a method for identifying the fine pattern will be described later.

[0091] <Second calculation step S140> In the second calculation step S140, second phase data different from the first phase data is calculated based on a second wavelength λ2 (e.g., a second wavelength to be corrected) different from the preset first wavelength λ1. The second phase data can be calculated using, for example, known optical software with a vector model, similar to the first phase data described above.

[0092] In addition, the second calculation step S140 may calculate a plurality of phase data in addition to the second phase data, for example. In this case, the second calculation step S140 calculates a plurality of phase data based on different wavelengths.

[0093] <Second Identification Step S150> In the second specifying step S150, the second phase data is referenced to specify a second phase pattern corresponding to the fine pattern specified in the first specifying step S130. An example of a method for specifying the second phase pattern will be described later.

[0094] In the second specifying step S150, a plurality of phase patterns may be specified by referring to the plurality of phase data calculated in the second calculating step S140, in addition to the second phase pattern. The number of phase patterns to be specified is arbitrary.

[0095] <Design Step S160> In the design step S160, the conventional lens 2 is designed based on, for example, the first phase pattern and the two-phase pattern. In the design step S160, optical design for the conventional lens 2 can be performed using, for example, known optical design software for ray tracing. Note that the designed conventional lens 2 may be the same as, for example, the conventional lens 22 used for initial setting in the setting step S110, or may have different characteristics. Note that whether or not to perform the design step S160 is optional.

[0096] In the design step S160, the conventional lens 2 may be designed based on, for example, the phase data (e.g., the second phase data) calculated in the second calculation step S140. Also, in the design step S160, the conventional lens 2 may be designed based on, for example, the first phase pattern or the first step pattern in addition to the second phase pattern. Even in these cases, in the design step S160, optical design for the conventional lens 2 can be performed using, for example, known optical design software for ray tracing.

[0097] Here, the first phase pattern and the second phase pattern are each associated with the same fine pattern of the metalens 1. For this reason, by using the first phase pattern and the second phase pattern, the characteristics of the metalens 1 can be easily represented, and the conventional lens 2 to be used in combination with the metalens 1 can be easily designed.

[0098] In the design step S160, the conventional lens 2 may be designed based on the second phase pattern as well as the multiple phase patterns identified in the second identification step S150.

[0099] The second modified example of the optical design method will be described in detail below. Here, correction for two or more wavelengths is considered. In the following, among the binary optics 21, the binary optics 21 having the first phase pattern in the setting step S110 will be referred to as BO-A, the binary optics 21 having the second phase pattern in the second specifying step S150 will be referred to as BO-B, and n binary optics 21 having any one of the multiple phase patterns in the second specifying step S150 will be referred to as BO-n (n is an integer equal to or greater than 1). In addition, BO-n may have the same characteristics as BO-A or BO-B.

[0100] In the setting step S110, optical characteristics are determined based on the optical design of a configuration that combines the BO-A and the conventional lens 22 for initial setup. The optical characteristics include, for example, the first step pattern of the BO-A. In the setting step S110, the conditions for the configuration are set based on, for example, the specifications determined in the preparation step S0.

[0101] In the setting step S110, optical characteristics are determined using the equivalent refractive index method based on an optical design of a configuration that combines, for example, a BO-A and a conventional lens 22. In the setting step S110, the optical design is performed to achieve optical characteristics that satisfy required specifications for, for example, on-axis and off-axis angles of view and multiple wavelengths. Note that the type and number of conventional lenses 22 for initial setup are arbitrary.

[0102] In the first calculation step S120, first phase data is calculated based on a preset first wavelength λ1. In the first calculation step S120, the phase data is calculated using known vector model optical software. Therefore, the calculated phase data takes into account the nonlinear effects of the "light trapping" described above. This makes it possible to design the fine pattern of metalens 1 for the first step pattern of BO-A.

[0103] As shown in FIG. 11, the first phase data indicates the shape of the meta-atom (e.g., cylindrical diameters P1, P2, P3, etc.) on the horizontal axis and the phase (e.g., p1, p2, p3, etc.) on the vertical axis. The first phase data exhibits a characteristic in which the phase changes nonlinearly with changes in the shape of the meta-atom. This makes it possible to design a fine pattern of metalens 1 with complex characteristics with high precision. Note that the relationship between the phase and the shape of the meta-atom differs for each wavelength in the phase pattern. Therefore, when phase data is calculated based on a wavelength other than the first wavelength λ1, phase data different from the first phase data is obtained.

[0104] In the first specifying step S130, a first phase pattern is calculated from the first step pattern of BO-A, and a fine pattern corresponding to the first phase pattern is specified by referring to the first phase data.

[0105] Here, the relationship between the step d included in the step pattern of the binary optics 21 (here, BO-A) and the phase will be described. For example, as shown in Fig. 12, if the step d of the binary optics 21 is set to satisfy the relationship of the following formula (5), when plane wave light that is perpendicularly incident on the binary optics 21 passes through it, a phase difference of αλ occurs due to the influence of the step d. Nd-d = αλ (5) Here, the letters in equation (5) are as follows: λ: wavelength of light N: Refractive index of the material of the binary optics 21 (e.g., relative refractive index to air) α: Arbitrary coefficient (varies depending on specifications)

[0106] According to formula (5), the height of each step in the binary optics 21 can obtain a phase difference suited to the specifications by setting the coefficient α to a different value. For example, when α is set to 1, a step d that satisfies a phase difference of 2π can be derived. In the first specifying step S130, the first phase pattern can be calculated from the first step pattern by using formula (5), for example.

[0107] In the first identification step S130, as shown in FIG. 13, for example, a phase pattern (p1, p2, and p3 in FIG. 13) is calculated from the step pattern (d1, d2, and d3 in FIG. 13) using equation (5). Then, in the first identification step S130, the first phase data is referenced to identify a fine pattern (P1, P2, and P3 in FIG. 13) that corresponds to the calculated phase pattern (p1, p2, and p3). In this way, in the first identification step S130, the fine pattern is identified by reference to the first phase data, which makes it possible to easily design a metalens 1 that takes into account the influence of nonlinearity due to "light trapping."

[0108] In the second calculation step S140, one or more pieces of phase data (e.g., second phase data and third phase data) corresponding to each wavelength are calculated based on one or more preset wavelengths (e.g., second wavelength λ2 and third wavelength λ3). Note that, like the first phase data described above, the phase data can be calculated using optical simulation of a known vector model.

[0109] In the second specifying step S150, one or more phase patterns that differ for each of the phase data are specified with reference to the one or more phase data calculated in the second calculating step S140.

[0110] In the second identification step S150, a phase pattern is identified using the characteristics of the phase data. For example, as shown in Fig. 14, when the second wavelength λ2 is longer than the first wavelength λ1, the second phase data exhibits a characteristic of being generally shifted to the right compared to the first phase data. Also, when the third wavelength λ3 is shorter than the first wavelength λ1, the third phase data exhibits a characteristic of being generally shifted to the left compared to the first phase data.

[0111] Based on the above-described characteristics, a phase pattern is identified for each piece of phase data corresponding to the fine patterns (P1 and P3 in FIG. 14) calculated in the first identification step S130. That is, when the second phase data is referenced, a phase pattern (second phase pattern) including a phase p1L corresponding to the diameter P1 and a phase p3L corresponding to the diameter P3 is identified. Furthermore, when the third phase data is referenced, a phase pattern (third phase pattern) including a phase p1S corresponding to the diameter P1 and a phase p3S corresponding to the diameter P3 is identified.

[0112] In design step S160, the conventional lens 2 is designed based on a plurality of phase patterns including, for example, the second phase pattern. When using known optical design software in design step S160, the conventional lens 2 can be designed using parameters such as, for example, the number of lenses different from that of the conventional lens 22 for initial setting, and material properties such as different glass materials.

[0113] For example, when three wavelengths (first wavelength λ1, second wavelength λ2, and third wavelength λ3) are targeted as the multiple wavelengths, a conventional lens 2 that is common to each of the three wavelengths can be designed based on binary optics 21 (BO-A, BO-B, and BO-1 in Figures 15(a) to 15(c)) that correspond to each of the three wavelengths, thereby realizing the design of a conventional lens 2 that corresponds to the three wavelengths.

[0114] For example, a case will be described in which "CODEV (registered trademark)" is used as known optical design software in the design step S160.

[0115] First, as a premise, when "CODEV (registered trademark)" is used, it can be expressed by a continuous phase distribution on the optical surface to which the diffractive optical element 101 is applied, regardless of the manufacturing method. In the case of rotational symmetry, the phase distribution is expressed by Φ = f(r), and is converted to a fringe distribution by dividing by a reference wavelength λ0 called the normalized wavelength HWL.

[0116] The normalized wavelength HWL specifies the wavelength at which optimal efficiency can be obtained, and in the case of binary optics 21, it is used to calculate the depth of the steps. Regarding the phase distribution Φ, in the case of binary optics 21, it is not expressed in a stepped form like the shape of binary optics 21, but is expressed as an analog continuous quantity using phase coefficients HCO(Cj). For example, 10 phase coefficients HCO(Cj) (Cj: C1 to C10) can be input, and the phase shape can be expressed.

[0117] For example, in the setting step S110, the phase of the analog quantity can be calculated using "CODEV (registered trademark)," and the first step pattern can be determined from the calculation result. To fabricate an eight-step shape, known as a three-step, first step pattern, three lithographic exposures and etchings are performed. The ideal relative ratio of these etching amounts is 1:2:4, and the amount of each step can be constant. Note that calculations using "CODEV (registered trademark)" are possible by setting the "Type (DIF)" to "Step," and the shape of the first step pattern is determined from the normalized wavelength HWL and phase coefficient HCO(Cj) described above. The amount of the step can be constant, as in the case of manufacturing. The above-mentioned "Type (DIF)" can be, for example, a "linear diffraction grating," a "phase polynomial (kinoform / binary)," or a "holographic optical element."

[0118] Based on the above, in design step S160, the normalized wavelength HWL can be calculated using equation (5). In this case, by setting α to 1 and associating the largest phase of the second phase pattern with Nd and the smallest phase with d, the wavelength λ obtained on the right side of equation (5) can be used as the normalized wavelength HWL.

[0119] Furthermore, the phase coefficient HCO(Cj) can be set based on the values ​​of each phase included in the fine pattern identified in the first identification step S130, for example. In "CODEV (registered trademark)," the set value is calculated as a continuous phase. In contrast, each phase value included in the fine pattern represents a discrete value. Therefore, for example, by unwrapping the discrete values ​​of each phase with respect to the normalized wavelength HWL, a continuous (analog) value can be obtained. By fitting this process for each phase coefficient HCO(Cj), the set value of the phase coefficient HCO(Cj) can be optimized. Note that using the phase coefficient HCO(Cj) set in the setting step S110 as the initial value for fitting the phase coefficient HCO(Cj) enables early convergence of the optimization.

[0120] For example, by using the method described above, it is possible to design a conventional lens 2 by using the normalized wavelength HWL and phase coefficient HCO(Cj) of the binary optics 21 corresponding to the second wavelength, together with those for the first wavelength. The reason why the normalized wavelength HWL does not necessarily correspond to the second wavelength, etc., is that this reduces the diffraction efficiency of the metalens 1 having a fine pattern for the second wavelength, etc. Therefore, if the normalized wavelength HWL is set as the second wavelength, etc., it may cause unwanted light, flare, and ghosting, resulting in reduced optical performance. Therefore, it is preferable to set the normalized wavelength HWL to a value close to the second wavelength, etc., which can be achieved by specifying a fine pattern of meta-atoms corresponding to the first wavelength.

[0121] For example, the evaluation step may be performed after the design step S160. The evaluation step determines whether the designed configuration satisfies the specifications determined in the preparation step S0 or the like, and ends if it does, and performs the first restriction condition step S31 again if it does not. Note that the evaluation step may perform any of the second restriction condition step S32 to the design step S160 again if the specifications are not satisfied, for example. Furthermore, the joining step S20 may be performed after the design step S160.

[0122] According to the optical design method of this modified example, the setting step S110 sets a first step pattern of the binary optics 21. Furthermore, the first identification step S130 calculates a first phase pattern from the first step pattern, and identifies a fine pattern indicating the shape of the meta-atom corresponding to the first phase pattern by referring to the first phase data. Therefore, the fine pattern required for designing the metalens 1 can be identified using the first step pattern that can be set by conventional methods. This makes it possible to easily realize optical design of a configuration that includes the metalens 1.

[0123] Furthermore, according to the optical design method of this modified example, the setting step S110 sets a first step pattern based on the optical design of a configuration that uses both binary optics 21 and a conventional lens 22 for initial setup. Furthermore, the first identification step S130 calculates a first phase pattern from the first step pattern, and identifies a fine pattern that indicates the shape of meta-atoms that corresponds to the first phase pattern by referring to the first phase data. Therefore, the fine pattern required for designing metalens 1 can be identified by using the first step pattern that takes into account the use in combination with the conventional lens 22. This makes it possible to facilitate the optical design of a configuration that uses both metalens 1 and a conventional lens 2.

[0124] According to this modification, for example, the following becomes possible. First, the design time for metalens 1 alone can be shortened. If only metalens 1 were used in an imaging system, optimization would be required to bring the optical performance of metalens 1 alone within specifications, which would require multiple calculations using vector model optical simulations, which would take several hours per condition. In contrast, according to this modification, the optical performance of metalens 1, together with that of conventional lens 2, only needs to be brought within specifications, eliminating the need for multiple calculations using vector model optical simulations for optimization to converge the optical performance of metalens 1. Therefore, it is possible to achieve the objective by optimizing only conventional lens 2.

[0125] (Third Modification: Optical Design Method) Next, a third modified example of the optical design method in this embodiment will be described. The difference between the above-described embodiment and the third modified example is that a second step pattern is specified in design step S160. Note that a description of the same content as in the above-described embodiment will be omitted.

[0126] In the design step S160, a step pattern corresponding to the identified phase pattern can be identified, for example, using equation (5) described in the first identification step S130. For example, in the design step S160, the step d derived for each phase included in the second phase pattern can be identified as the second step pattern of B-O-B, and the step d derived for each phase included in the third phase pattern can be identified as the third step pattern of B-O-1. That is, in the design step S160, a step pattern of the binary optics 21 that differs for each specific wavelength can also be identified.

[0127] In the design step S160, the conventional lens 2 is designed based on the one or more identified step patterns (for example, the second step pattern). At this time, known optical design software such as the above-mentioned "CODEV (registered trademark)" can be used. This makes it possible to design the conventional lens 2 that can accommodate multiple wavelengths.

[0128] In this modified example, as in the above-described embodiment, the setting step S110 sets a first step pattern of the binary optics 21. Furthermore, the first identification step S130 calculates a first phase pattern from the first step pattern, and identifies a fine pattern indicating the shape of the meta-atoms corresponding to the first phase pattern by referring to the first phase data. Therefore, the fine pattern required for designing the metalens 1 can be identified using the first step pattern that can be set by conventional methods. This makes it possible to easily realize the optical design of a configuration that includes the metalens 1.

[0129] Conventional binary optics creates a pattern with a staircase shape of 2 to the Nth power by performing exposure and etching a natural number N times. If N=2, 4, or 6, the resulting pattern is a staircase shape of 4, 8, or 16.

[0130] The binary optics 21 considered for the proposed metalens 1 does not need to have the conventional 2N step shape, but can have 7 or 10 steps. The reason for this is that if metalens 1 is considered to be in the category of metasurface, it is sufficient to have a meta-atom shape that results in an effective refractive index that generates the same amount of phase as the phase that forms the step shape with a single exposure and etching.

[0131] (Fourth Modification: Optical Design Method) Next, a fourth modified example of the optical design method according to this embodiment will be described with reference to Fig. 16, which is a flowchart of the fourth modified example of the optical design method.

[0132] The difference between the above-described embodiment and the fourth modified example is that the second calculation step S140 and the second specification step S150 are not performed. Note that a description of the same content as in the above-described embodiment will be omitted.

[0133] The optical design method in this modified example includes, for example, a first limiting condition step S31, a second limiting condition step S32, a chromatic aberration setting step S10, a setting step S110, a first calculation step S120, and a first identification step S130, and may also include, for example, a design step S160.

[0134] In the setting step S110, the first step pattern may be set based on an optical design using both the binary optics 21 and the conventional lens 22, or, for example, an optical design using only the binary optics 21. That is, in the setting step S110 in this modified example, it is optional whether or not to use the conventional lens 22.

[0135] In this modified example, as in the above-described embodiment, the setting step S110 sets a first step pattern of the binary optics 21. Furthermore, the first identification step S130 calculates a first phase pattern from the first step pattern, and identifies a fine pattern indicating the shape of the meta-atoms corresponding to the first phase pattern by referring to the first phase data. Therefore, the fine pattern required for designing the metalens 1 can be identified using the first step pattern that can be set by conventional methods. This makes it possible to easily realize the optical design of a configuration that includes the metalens 1.

[0136] In the above-described embodiment, three different wavelengths have been used as shown in FIG. 14, for example, but the first wavelength does not necessarily have to be shorter than the second wavelength and longer than the third wavelength (i.e., the central wavelength among the three wavelengths). For example, the following case can be considered. When the lengths of the three wavelengths λ21, λ22, and λ23 are λ21>λ22>λ23 and there is a function to switch and use the illumination wavelength, the illumination wavelength condition is 1 Wavelength λ21+λ22+λ23 (broad) 2. Only wavelength λ23 (e.g., using a laser) When setting specifications to optimize the imaging performance and diffraction efficiency for wavelength λ23 alone, it is obvious that the object of the present invention can be achieved by designing wavelength λ23 as the first wavelength and applying this proposal to wavelengths λ21 and λ22.

[0137] (Fifth Modification: Optical Design Method) Next, a fifth modified example of the optical design method in this embodiment will be described. In the fifth modified example, it becomes possible to deal with problems that occur during "standard alignment."

[0138] First, when manufacturing the above-mentioned conventional lens 2, a gauge called a "Newton prototype" is used to determine the accuracy of the lens's radius of curvature. The radius of curvature of the polishing plate used to polish the lens and the Newton prototype used for inspection are made up of discrete values. For this reason, the final stage of design involves a design process called "prototype alignment."

[0139] In fact, when the conventional lens 2 includes a plurality of glass materials (lenses), each lens surface can be set as a variable for "matching to a master", allowing for flexibility in design; however, when the conventional lens 2 is made of only one glass material, there is no flexibility in design, which may cause problems depending on the application of the optical element 100.

[0140] For example, if the radius of curvature of the design value before "standard alignment" is an intermediate value between the two standards, then either standard's radius of curvature will be outside the specifications, which will cause problems in terms of the focal length of the paraxial amount, axial chromatic aberration, and other image formation performance.

[0141] In the above case, for example, the variable used during redesign in design step S160 in FIG. 9 was the conventional lens 22. However, this alone may not be enough to resolve the aforementioned problem of "prototype alignment." While this can be addressed by creating a new "prototype," this may result in additional manufacturing steps and increased overall costs. Therefore, as a solution, for example, after design step S160, return to setting step S110, intentionally shift the problematic optical performance out of specification, and then perform the first calculation step S120 (e.g., the flow in FIG. 9 ). In this case, not only the conventional lens 22 but also the diffractive optical element 101 are used as variables. The amount of shift cannot be uniquely determined because it depends on the configuration and other factors of the "prototype." Therefore, a solution can be achieved by shifting the lens by a certain amount, and if the problem persists, further shifting the lens can be performed using a so-called "trial and error" approach. Therefore, as described above, by configuring the diffractive optical element 101 and the conventional lens 22 in the order of "conventional lens 22 followed by diffractive optical element 101," design freedom is increased, which may resolve problems that occur during "prototype alignment." Of course, since the sensitivity of various optical performances to the spacing between the diffractive optical element 101 and the conventional lens 22 increases, it may become necessary to set high precision for parts and assembly.

[0142] (Derivation of Equation (3)) An example of the derivation of formula (3) will be described below. In the example of the optical design method for the "optical element 100 including metalens 1 and conventional lens 2" described above, the first limiting condition step S31 uses formula (3), which indicates the relationship of "thin + lens spacing 'zero'". Formula (3) is a new proposal by the present inventor, and use of formula (3) makes it possible to efficiently design optical element 100, for example.

[0143] Therefore, before explaining the introduction of equation (3), the related technology will be explained below for better understanding.

[0144] First, we will explain the phase distribution for ray tracing modeled using the equivalent refractive index method for the diffractive optical element 101 when using "CODEV (registered trademark)." Regardless of how it is manufactured, the diffractive optical element 101 expressed using "CODEV (registered trademark)" expresses a continuous phase distribution on its surface for each (lens) surface.

[0145] In "CODEV (registered trademark)", in the case of a diffractive optical element 101 having a rotationally symmetric shape with respect to an optical axis called HCT R, the phase distribution Φ is expressed by the following equation (6).

[0146]

number

[0147] Furthermore, in "CODEV (registered trademark)", a variable called "normalized wavelength" is set and used for the diffractive optical element 101, separate from the definition of the wavelength for which the optical system is designed, and the diffractive optical element 101 can be treated at this wavelength (assuming the physical optical path length for the wavelength is 2π).

[0148] For example, Fig. 17 is a schematic diagram showing an example of input state of the normalized wavelength and the phase coefficient Cn of the polynomial of the phase distribution as parameters used in "CODEV (registered trademark)." In the setting shown in Fig. 17, the diffracted light is tracked as first order, the normalized wavelength is set to 500 nm, the value of the phase coefficient C1 is set to -0.005, and the values ​​of the other phase coefficients C2 to C10 are set to 0.

[0149] Furthermore, in "CODEV (registered trademark)", the relationship between the focal length EFL and the phase coefficient C1 of the single surface on which the diffractive optical element 101 is set is given by the following formula (7). C1=-0.5 / EFL (7)

[0150] Furthermore, the relationship between the focal length EFLi and the phase coefficient C1 for a specific wavelength λi on a single surface of the diffractive optical element 101 is not published as "CODEV (registered trademark)." Therefore, the inventors have estimated that the above relationship is as shown in the following formula (8). C1=-0.5×λ0(EFLi×λi) ···(8) Here, the letters in equation (8) are as follows: λ0: Normalized wavelength

[0151] Equation (8) conforms to the following equation (9) which indicates the focal length of a hologram lens in, for example, "T. Stones and N. George: 'Hybrid diffractive-refractive lenses and achromats,' Appl. Opt., 27 (1998) 2960-2971."

[0152]

number

[0153] Furthermore, the inventors actually defined the diffractive optical element 101 under multiple conditions in "CODEV (registered trademark)" and calculated its focal length EFL, thereby confirming the validity of equation (8) (see FIG. 18).

[0154] Here, a method for expressing an optical system using thin lenses will be described. This method can be based on the content described in "Introduction to Lens Design (Kyoritsu Shuppan) by Yoshiya Matsui" (particularly page 28), for example.

[0155] For example, by expressing a conventional single lens (radius of curvature r1, r2, glass thickness D, refractive index N) as a "thin lens" using paraxial optics theory, the power φ of the single lens and the reciprocal of the focal length EFL can be expressed by the following equation (10). φ=φ1+φ2-e´φ1φ2 ···(10)

[0156] By using equation (10), a system of multiple lenses can be expressed as a single thin lens with a thickness of "zero".

[0157] The derivation of equation (3) in the first limiting condition step S31 will be described below.

[0158] First, the embodiments relate to metalens 1, and unlike diffractive optical elements that have generally been referred to up to now, metalens 1 must be handled with consideration given to nonlinearity. However, since consideration is given here within the scope of paraxial optical theory, only linearity is considered, and this also applies to diffractive optical element 101, so the derivation of formula (3) will be explained by expressing metalens 1 as diffractive optical element 101. Furthermore, in the following explanation, conventional lens 2 will be expressed as a conventional lens.

[0159] In this embodiment, it is considered that the optical system has optical characteristics in which the focal plane is well aligned for at least two wavelengths (for example, a first wavelength to be corrected and a second wavelength to be corrected), so equation (3) is applied to the two wavelengths λ1 and λ2, and FIG. 19 shows a configuration in which the diffractive optical element 101 (DOE in FIG. 19) and the conventional lens are replaced with thin lenses. Furthermore, the distance e' between the two thin lenses is set to "zero." Note that if the distance e' is strictly set to "zero," it becomes difficult to see the positional relationship between the lenses on the drawing, so in FIG. 19, the distance e'=0 is set, and the positions of the lenses are shifted.

[0160] By substituting the power φd of the diffractive optical element 101 and the power φc of the conventional lens into equation (10), the following equation (11) is obtained, which shows the power φ of the entire system (however, the distance e' is set to "zero"). φ=φd+φc (11)

[0161] Furthermore, if the power φ of the entire system for the two wavelengths λ1 and λ2 is φ1 and φ2, respectively, the absence of axial chromatic aberration at the two wavelengths λ1 and λ2 is indicated by the following formula (12) (i.e., the powers φ1 and φ2 of the entire system are equal). φ1=φ2 (12)

[0162] Furthermore, when wavelength information is added to equation (11) in equation (12), the following equation (13) is obtained. φd1+φc1=φd2+φc2 (13)

[0163] Moreover, rearranging equation (13) yields the following equation (14): The left side of equation (14) indicates the power related to the diffractive optical element 101, and the right side indicates the power related to the conventional lens. φd1-φd2=-φc1+φc2 (14)

[0164] Furthermore, taking into consideration that the powers φd1 and φd2 on the left side of equation (14) are the reciprocals of the focal length EFL, the following equations (15) and (16) can be obtained using equation (8). φd1=1 / EFL1=-2×λ1 / (C1×λ0) ···(15) φd2=1 / EFL2=-2×λ2 / (C1×λ0) ···(16)

[0165] Further, based on the following formulas (17) to (19) described on page 19 of "Introduction to Lens Design (Kyoritsu Shuppan), by Matsui Yoshiya," the right-hand side of formula (14) can be expressed as formula (20). φ1=(N-1) / r1 (17) φ2=(1-N) / r2 (18) e´=d / N (19) -φc1+φc2=-(1-N1) / rc+(1-N2) / rc=(N1-N2) / rc (20) Here, the characters in the formulas (17) to (20) are as follows: N: Refractive index of the glass material N1: Refractive index of the glass material corresponding to wavelength λ1 (for example, the first refractive index) N2: Refractive index of the glass material corresponding to wavelength λ2 (e.g., second refractive index) r1, r2: Radius of curvature of glass material rc: Radius of curvature of conventional lens

[0166] Based on the above, equation (3A) is obtained by substituting equations (15), (16), and (20) into equation (14) and rearranging. Here, equation (3A), which shows a proportional relationship, can be derived from equation (3A), which shows an equal relationship, taking into account units and coefficients that differ for each software. This derives equation (3) in the first limiting condition step S31.

[0167] Note that the configuration in FIG. 19 is a configuration in which, from the left, the diffractive optical element 101 is followed by a conventional lens; however, the application of formula (3) is not limited to this, and for example, the configuration may be reversed, with a conventional lens followed by the diffractive optical element 101 from the left.

[0168] For example, it is considered unrealistic to set the distance e' to "zero," but one of the advantages of applying metalenses to ToF, etc., as shown in the previous example, is that it is possible to achieve a thin optical system. For this reason, it is preferable to configure the distance e' to be as small as possible, so we believe that setting the distance e' to "zero" will not result in a large error.

[0169] Of course, in reality, the distance e' will never be "zero," and the lens will not be thin; therefore, it must be "thickened." This process corresponds to step S32 of the second constraint shown in Figure 6(b) and other figures. In this case, the configuration of a conventional lens and a diffractive optical element 101 (from left) offers greater design freedom than the reverse configuration of a diffractive optical element 101 and a conventional lens. This is because, when the object is at infinity, incident light enters parallel, and in the configuration of the diffractive optical element 101 and a conventional lens, the light enters the first surface in paraxial tracking, i.e., the surface of the diffractive optical element 101, with a height h of 1. The equivalent Abbe number of the diffractive optical element 101 for the d-line, C-line, and F-line is -3.452, which is a small negative absolute value (=large dispersion). Therefore, the chromatic aberration generated will be larger than that of a conventional lens. Therefore, correcting chromatic aberration throughout the entire system imposes a greater correction burden on the conventional lens.

[0170] On the other hand, in the configuration of the conventional lens and diffractive optical element 101 with the opposite configuration, the height h at the surface of the diffractive optical element 101 varies from a value of 1 depending on the distance, and actually the glass material thickness and refractive index. In other words, the degree of freedom in design is increased.

[0171] However, this high degree of freedom in design also means that it is sensitive to errors, and if the glass thickness and refractive index deviate from the designed values, the optical performance will deteriorate. As such, there are advantages and disadvantages, so it is necessary to take them into consideration when selecting the configuration.

[0172] Up to this point, we have described the use of commercially available optical design software called "CODEV (registered trademark)," but the application of the present invention is not limited to "CODEV (registered trademark)" and can be applied to any optical design software that models the diffractive optical element 101 using the equivalent refractive index method. Of course, the variables set by the user are defined differently in each optical design software, so they will not have the same values.

[0173] When considering another optical design software, Ansys ZEMAX OPTICSTUDIO (registered trademark), if the variable of the polynomial coefficient expressing the phase distribution corresponding to C1 in equation (3) etc. is defined as A1, the inventors have found through their investigations that the relationship between C1 and A1 is expressed by the following equations (21) and (22) (when a variable called the normalized radius in Ansys ZEMAX OPTICSTUDIO (registered trademark) is set to 1): C1=A1×(λ / 2π) / 1000 (21) λ0=λ1 (22)

[0174] Note that the units of input variables and the like differ depending on the optical design software; for example, the unit of wavelength may be nm or μm, but the above relationship between A1 and C1 is the relationship when the input values ​​are used as is.

[0175] In this way, it is obvious that the present invention can be applied by determining the relationship between the variables defined and used in other optical design software and the variables in "CODEV (registered trademark)" and using this to transform the relational equation proposed in the present invention. Note that equations (3) and (4) can be used when using either "CODEV (registered trademark)" or Ansys ZEMAX OPTICSTUDIO (registered trademark).

[0176] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0177] 1: Metalens 2: Conventional lens 2a: 1st glass material 2b: Second glass material 3: Aperture 4: Parallel light 5: Light collection 11: Fine shape surface 12: Main surface 21: Binary Optics 22: Conventional lens 100: Optical elements 101: Diffractive optical element S0: Preparation step S10: Chromatic Aberration Setting Step S20: Joining step S30: Restriction condition step S31: First restriction step S32: Second restriction condition step S110: Setting step S120: First calculation step S130: First identification step S140: Second calculation step S150: Second identification step S160: Design Step d: Step e´ :distance h: height

Claims

1. a chromatic aberration setting step of setting an optical system including a conventional lens and a metalens on which a fine pattern is formed, The chromatic aberration setting step includes a comparison step of comparing a value based on a first power of the conventional lens shown in the following formula (1) with a preset reference value: An optical design method comprising: φc 2 =-V 123 ×hm a ×φm 2 / EV 123 ・・・(1) φc 2 : the first power of the conventional lens V 123 : Abbe number of the conventional lens hm a : The height of a ray at the metalens in paraxial ray tracing relative to the height of parallel light incident on the metalens φm 2 : the second power of the metalens EV 123 : equivalent Abbe number of the metalens (1, 2, 3 are wavelengths λ 1 , λ 2 , λ 3 (corresponding to

2. The reference value indicates 3.5, the comparing step includes setting the shape of the conventional lens so as to satisfy the following formula (2) based on the first power:

2. The optical design method according to claim 1, wherein: (Nc 2 -1) / φc 2 ≧Th ・・・(2) Nc 2 : refractive index of the conventional lens at the second wavelength Th: the reference value (= 3.5)

3. wavelength λ 1 , λ 2 , λ 3 is any one of the d-line, C-line, and F-line, the equivalent Abbe number of the metalens for the d-line is -10 or more and -3 or less.

3. The optical design method according to claim 2, wherein:

4. further comprising, after the chromatic aberration setting step, a bonding step of bonding the conventional lens to a bonding surface of the metalens, The bonding surface is a main surface different from the fine pattern and is formed in a flat shape.

4. The optical design method according to claim 1, wherein:

5. The method further includes, before the cementing step, a first limiting condition step of specifying a condition for the diffractive optical element and the conventional lens that satisfies the following formula (3):

5. The optical design method according to claim 4, wherein: B1∝λ0(N11-N12) / (R×(λ11-λ12))...(3) B1: Phase coefficient when modeling the diffractive optical element using optical design software using the equivalent refractive index method λ0: normalized wavelength of the diffractive optical element λ1: First wavelength to be corrected for axial chromatic aberration λ2: Second wavelength to be corrected for axial chromatic aberration N11: a first refractive index of the conventional lens for the first wavelength to be corrected N12: a second refractive index of the conventional lens for the second wavelength to be corrected R: radius of curvature of the convex surface of the conventional lens

6. a setting step of setting a first step pattern of the binary optics included in one of the diffractive optical elements based on an optical design of a configuration including the binary optics that replaces the characteristics of the metalens; a first calculation step of calculating first phase data indicating a phase relationship with respect to the shape of the meta-atom based on a preset first wavelength; a first specifying step of calculating a first phase pattern from the first step pattern and specifying the fine pattern corresponding to the first phase pattern by referring to the first phase data; To be prepared 6. The optical design method according to claim 5,

7. The setting step sets the first step pattern based on an optical design using the binary optics and a conventional lens for initial setting.

7. The optical design method according to claim 6, wherein:

8. a second calculation step of calculating second phase data different from the first phase data based on a second wavelength that is set in advance and different from the first wavelength; a second identification step of referring to the second phase data and identifying a second phase pattern corresponding to the fine pattern; a design step of designing the conventional lens based on the first phase pattern and the second phase pattern; Further provide 8. The optical design method according to claim 7, wherein:

9. A conventional lens and a metalens on which a micropattern is formed, The conventional lens satisfies the following formula (1): An optical element characterized by: φc 2 =-V 123 ×hm a ×φm 2 / EV 123 ・・・(1) φc 2 : the first power of the conventional lens V 123 : Abbe number of the conventional lens hm a : The height of a ray at the metalens in paraxial ray tracing relative to the height of parallel light incident on the metalens φm 2 : the second power of the metalens EV 123 : equivalent Abbe number of the metalens (1, 2, 3 are wavelengths λ 1 , λ 2 , λ 3 (corresponding to

10. wavelength λ 1 , λ 2 , λ 3 is any one of the d-line, C-line, and F-line, the reference value Th of the following formula (2) based on the first power indicates 3.

5.

10. The optical element according to claim 9, (Nc 2 -1) / φc 2 ≧Th ・・・(2) Nc 2 : Refractive index of the conventional lens Th: the reference value (= 3.5)

11. a comparison step of comparing a value based on the first power of the conventional lens shown in the following formula (1) with a predetermined reference value for an optical system including a conventional lens and a metalens on which a fine pattern is formed: A method for evaluating an optical element, comprising: φc 2 =-V 123 ×hm a ×φm 2 / EV 123 ・・・(1) φc 2 : the first power of the conventional lens V 123 : Abbe number of the conventional lens hm a : The height of a ray at the metalens in paraxial ray tracing relative to the height of parallel light incident on the metalens φm 2 : the second power of the metalens EV 123 : equivalent Abbe number of the metalens (1, 2, 3 are wavelengths λ 1 , λ 2 , λ 3 (corresponding to

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