Optical system and optical device

Abstract

[Problem] To provide an optical system further reduced in size compared to the conventional system. [Solution] This optical system comprises: an optical element provided with a diffraction surface MOE with controlled wavelength dispersion characteristics; and a lens LN. The Abbe number ν0 of the diffraction surface satisfies the condition of -0.2 < 1 / ν0 < 0.2. The diffraction surface has a rotationally asymmetric optical path difference function.

Description

Optical systems and optical devices

[0001] This disclosure relates to an optical system suitable for imaging and display, etc.

[0002] The optical system described above is required to be as compact as possible. Furthermore, Patent Document 1 discloses a diffraction surface capable of controlling wavelength dispersion characteristics.

[0003] U.S. Patent No. 10670782

[0004] There is a demand for optical systems that are even smaller than those currently in use.

[0005] An optical system, as one aspect of this disclosure, includes a diffracting surface (or metasurface) with controlled wavelength dispersion characteristics and a lens. The Abbe number of the diffracting surface is ν ０ -0.2 < 1 / ν ０ The condition < 0.2 is satisfied. Abbe number ν ０ This will be discussed later. The diffracted plane is characterized by having a rotationally asymmetric optical path difference function. An optical device having the above optical system also constitutes another aspect of this disclosure.

[0006] Cross-sectional view of the optical system of Example 1 at infinity focus Aberration diagram of the optical system of Example 1 at infinity focus Cross-sectional view of the optical system of Example 2 at infinity focus Aberration diagram of the optical system of Example 2 at infinity focus Cross-sectional view of the optical system of Example 3 at infinity focus Aberration diagram of the optical system of Example 3 at infinity focus Cross-sectional view of the optical system of Example 4 at infinity focus Aberration diagram of the optical system of Example 4 at infinity focus Cross-sectional view of the optical system of Example 5 at infinity focus Aberration diagram of the optical system of Example 5 at infinity focus Diagram showing the optical path of the optical system of Example 1 Diagram showing a smartphone and a head-mounted display having the optical systems of Examples 1 to 5

[0007] The embodiments of this disclosure will be described below with reference to the drawings.

[0008] Figures 1, 3, 5, 7, and 9 are cross-sectional views showing the configuration of the optical systems of Examples 1 to 5 in a state where they are in focus on an object at infinity (hereinafter referred to as the infinity focus state). In each figure, X, Y, and Z represent the X, Y, and Z axes of the XYZ absolute coordinate system, which is the coordinate axis of the entire optical system. The depth direction perpendicular to the plane of the paper is the Z-axis direction, and the two mutually orthogonal directions perpendicular to the Z-axis direction are the X-axis direction (thickness direction of the optical system) and the Y-axis direction (height direction of the optical system).

[0009] The optical systems of each embodiment are used in various optical devices, including imaging devices such as digital still / video cameras and cameras for broadcasting, surveillance, automotive, and smartphones, display devices such as head-mounted displays and VR goggles, and image projection devices such as projectors. Below, we will describe the case in which the optical system of each embodiment is used as the imaging optical system of an imaging device, that is, the case in which light incident from a subject, which is the object to be imaged, located on the object surface is imaged onto the image surface on which the imaging surface is located. The side with the object surface is also called the object side, and the side with the image surface is also called the image side.

[0010] In each cross-sectional view, IP represents the image plane, where the imaging surface of an image sensor such as a CCD sensor or CMOS sensor in an imaging device is located. In display devices and image projection devices, the display surface of a liquid crystal display element or organic EL display element is located on the object surface corresponding to the image plane IP of the imaging optical system, and light from the display surface is formed on the image plane (pupil plane or projection surface) corresponding to the object surface of the imaging optical system. FL represents an optical block corresponding to various optical filters or dustproof glass.

[0011] REF is a reflective surface and is provided on reflective elements such as mirrors and prisms. LN is a lens group. LA is the optical axis of the lens group LN (hereinafter referred to as the lens optical axis). A lens group is a collection of one or more lenses or optical elements. The lens group LN can use refractive lenses, diffracting lenses, metasurface lenses, etc. The lens optical axis LA is the central axis of the lens group LN positioned between the diffracting surface MOE and the reflective surface REF, and can also be described as the optical path of light rays passing through the center of the diffracting surface MOE and the center of the reflective surface REF (and further, the center of the image plane IP).

[0012] MOE is a diffractive surface with controlled wavelength dispersion characteristics and includes a metasurface. The metasurface is configured by calculating the phase delay amount of meta-atoms for each wavelength and arranging the meta-atoms to control the wavelength dispersion characteristics. The metasurface may be a so-called single-layer type metasurface consisting of one layer, or a so-called stacked type metasurface consisting of multiple layers.

[0013] The optical path difference function, focal length, and Abbe number of a diffractive surface with controlled wavelength dispersion characteristics (hereinafter referred to as dispersion-controlled) can be described as follows. Let the optical path difference function of the diffractive surface be ψ, the diffraction order be m, and the design wavelength of the diffractive surface be λ ０ the incident wavelength be λ, the optical path difference dispersion of the surface be P(λ), and the optical path difference function of the surface at the design wavelength be ψ ０ Then, it can be defined as follows.

[0014]

[0015]

[0016] Incidentally, the optical path difference function ψ ０ of the surface at the design wavelength λ ０ In the case of a rotationally asymmetric in-plane optical path difference representation, when y and z are the distances in the y-axis direction and the z-axis direction, which are two in-plane directions orthogonal to each other from the optical axis, respectively, it can be expressed by the following yz polynomial.

[0017]

[0018] The deflection angle α in the y-axis direction of the light ray by the dispersion-controlled diffractive surface can be described as follows using the first-order coefficient U １，０ of the y coordinate of the optical path difference function of the surface at the design wavelength expressed by the yz polynomial.

[0019]

[0020] On the other hand, the optical path difference function ψ ０ of the surface at the design wavelength is usually expressed by the following polynomial when it is a rotationally symmetric surface with a high usage frequency, with h being the distance from the optical axis.

[0021]

[0022] The focal length fmoe of a dispersion-controlled diffraction surface is the quadratic coefficient U of the optical path difference function of the surface at the design wavelength, expressed as a polynomial. ２ It can be written as follows using this method.

[0023]

[0024] The Abbe number ν when the reference wavelength of the dispersion-controlled diffraction plane is the d-line (wavelength 587.6 nm), and the main dispersions are the F-line (wavelength 486.1 nm) and the C-line (wavelength 656.3 nm). ０ This can be written as follows: ψ ｄ ψ Ｆ ψ Ｃ These are the optical path difference functions for the d-line, F-line, and C-line, respectively, and λ ｄ , λ Ｆ , λ Ｃ These represent the incident wavelengths of the d-line, F-line, and C-line, respectively.

[0025]

[0026] Furthermore, when the reference wavelength of the dispersion-controlled diffraction plane is the d-line, and the main dispersions are the g-line (wavelength 435.8 nm) and the F-line, the Abbe number ν in the short wavelength range below the F-line is... ０，ｇＦ This can be written as follows: ψ ｄ ψ ｇ ψ Ｆ These are the optical path difference functions for the d-line, g-line, and F-line, respectively, and λ ｄ , λ ｇ , λ Ｆ These represent the incident wavelengths of the d-line, g-line, and F-line, respectively.

[0027]

[0028] In each embodiment, the diffraction order m is treated as m=1 because the first diffracted light is used for the design. The design wavelength λ ０ The d-line is used as the incident wavelength when determining the focal length.

[0029] Next, the characteristic configuration of the optical system of each embodiment will be described. As mentioned above, the optical system of each embodiment has a dispersion-controlled rotationally asymmetric diffraction plane MOE, a lens group LN, and a reflecting surface REF. The diffraction plane MOE can control its wavelength dispersion characteristics. Therefore, it is possible to suppress the color shift that occurs at the diffraction plane MOE and to correct the magnification chromatic aberration of the entire optical system well. In addition, the diffraction plane MOE has an optical path difference function of a rotationally asymmetric surface and has the function of deflecting light incident on the optical system in a specific direction.

[0030] The reflective surface REF has the function of bending the optical path by reflecting light, thereby miniaturizing (especially thinning) the optical system. The lens LN is positioned between the diffracting surface MOE and the reflective surface REF.

[0031] Figure 11 shows the optical path of light incident on the optical system of Example 1 from the diffraction plane MOE and imaged at multiple image heights on the image plane IP. In the figure, X, Y, and Z represent the aforementioned XYZ absolute coordinate system (X axis, Y axis, Z axis), while x, y, and z represent the local coordinate system of the diffraction plane MOE (x axis, y axis, z axis). The y-axis and z-axis directions are the in-plane directions of the diffraction plane MOE, as described above, and the z-axis direction is perpendicular to the diffraction plane MOE.

[0032] The diffraction plane MOE deflects light incident from the object and transmitted through it in the Y-axis direction through diffraction. In this process, the diffraction plane MOE deflects all light rays of different heights from its center (the intersection with the lens optical axis LA) toward the same side (negative side) in the Y-axis direction. This increases the degree of freedom in the layout of the lens group LN, the reflective surface REF, and the image plane IP, allowing the size of the optical system in the X-direction (thickness direction) to be kept small. To achieve this deflection function, the optical path difference function ψ of the diffraction plane MOE is determined. ０ It has an asymmetric optical path difference shape centered on zero in the y-axis direction. In particular, to deflect light to the negative side in the y-axis direction, the coefficient U １，０ It is preferable that it has a negative value.

[0033] Furthermore, in order to make the optical system thinner, it is preferable to arrange the diffraction plane MOE and the lens group LN adjacent to each other (in close proximity). Moreover, it is preferable that the lens in the lens group LN closest to the diffraction plane MOE has positive power, as this allows for a shorter telephoto ratio and thus a thinner design.

[0034] The optical system of each embodiment is an imaging optical system that images light incident from the object side onto the image plane IP or images light from the image plane IP on the object side, and has, in order from the object side to the image plane side, a diffraction plane MOE, a lens group LN, a reflective surface REF, and an optical block FL. The lens group may be arranged between the reflective surface REF and the optical block FL.

[0035] Furthermore, for ease of manufacturing, it is preferable that the diffraction plane MOE be formed on the plane of the optical substrate (i.e., the diffraction plane MOE has a planar shape). However, the diffraction plane MOE may also be formed in a curved shape. Similarly, the reflective surface REF may have a planar shape or a curved shape to have power.

[0036] Furthermore, it is preferable that the optical system of each embodiment satisfies at least one of the following conditions (1) to (5).

[0037] -0.2 < 1 / ν ０ <0.2 (1) -30°<α / 2-θdiff<30° (2) -30°<θrefl / 2-θdiff<30° (3) 0°<α<50° (4) 0°<θdiff<50° (5) -0.02<1 / ν ０，ｇＦ <0.02 (6) In the above formulas (1) to (6), ν ０ α is the Abbe number of a dispersion-controlled, rotationally asymmetric diffraction plane MOE, where the reference wavelength is the d-line and the main dispersions are the F-line and C-line. α is the deflection angle of the incident light deflected by the diffraction plane MOE, and is the deflection angle relative to the d-line when the reference wavelength (d-line) is incident perpendicularly to the center of the diffraction plane MOE. As mentioned above, the center of the diffraction plane MOE is the intersection of the diffraction plane MOE and the lens optical axis LA.

[0038] θdiff is the angle of inclination of the surface normal of the diffraction surface MOE with respect to the lens optical axis LA (the angle between the lens optical axis LA and the surface normal of the diffraction surface MOE), as shown in Figure 1. θrefl is the angle of inclination of the surface normal of the reflection surface REF with respect to the lens optical axis LA (the angle between the lens optical axis LA and the surface normal of the reflection surface REF). Note that when the diffraction surface MOE or the reflection surface REF has a curved shape, the surface normal referred to here is the surface normal at their center (the point of intersection with the lens optical axis LA).

[0039] ν ０，ｇＦ As mentioned above, this is the Abbe number in the short wavelength range below the F line of the dispersion-controlled diffraction plane MOE, when the reference wavelength is the d line and the main dispersions are the g line and the F line.

[0040] The condition in equation (1) is the Abbe number ν of the dispersed rotationally asymmetric diffraction plane MOE. ０ This represents the range of variance, which is the reciprocal of ν, and indicates an appropriate range for achieving good chromatic aberration control. 1 / ν ０ When the value falls below the lower limit of equation (1), the negative dispersion of the diffraction plane MOE increases, and the color shift of the light deflected by the diffraction plane MOE increases. As a result, the chromatic aberration of the entire display optical system increases, which is undesirable. 1 / ν ０ If the value exceeds the upper limit of equation (1), the positive dispersion of the diffraction plane MOE increases, and the color shift of the light deflected by the diffraction plane MOE increases. As a result, the chromatic aberration of the entire display optical system increases, which is undesirable.

[0041] Furthermore, it is more preferable to set the lower limit of formula (1) to -0.15, -0.10, -0.05, or -0.01. Also, it is more preferable to set the upper limit of formula (1) to 0.15, 0.10, 0.05, or 0.01.

[0042] The conditions in equation (2) show an appropriate relationship between the deflection angle α and the tilt θdiff of the diffraction plane MOE, and are conditions for obtaining good field curvature performance. If α / 2 - θdiff falls below the lower limit of equation (2), the meridional image plane deviates significantly from the sagittal image plane at the diffraction plane MOE, resulting in large astigmatism, which is undesirable. If α / 2 - θdiff exceeds the upper limit of equation (2), the meridional image plane deviates from the sagittal image plane towards the meridional side, resulting in large astigmatism, which is also undesirable.

[0043] Furthermore, it is more preferable to set the lower limit of equation (2) to -25°, -20°, or -16°. Also, it is more preferable to set the upper limit of equation (2) to 25°, 20°, 15°, or 10°.

[0044] The conditions in equation (3) represent an appropriate relationship between the inclination θdiff of the diffraction plane MOE and the inclination of the reflection plane REF, and are conditions for thinning the optical system and obtaining good field curvature performance. If θrefl / 2-θdiff falls below the lower limit of equation (3), the reflection plane REF and the diffraction plane MOE are tilted too much, increasing the thickness of the optical system, which is undesirable for thinning the optical system. If θrefl / 2-θdiff exceeds the upper limit of equation (3), the angle of the light rays emitting from the diffraction plane MOE becomes too large compared to the angle of the light rays incident on the diffraction plane MOE, resulting in an imbalance between the two angles and causing astigmatism, which is undesirable.

[0045] Furthermore, it is more preferable to set the lower limit of equation (3) to -25°, -20°, or -16°. Also, it is more preferable to set the upper limit of equation (3) to 25° or 20°.

[0046] The conditions in equation (4) indicate an appropriate range for the deflection angle α of the diffractive surface MOE, and are conditions for obtaining good image performance while making the optical system thinner. If α falls below the lower limit of equation (4), the deflection angle becomes too small, which is undesirable because it reduces the effect of thinning the optical system. If α exceeds the upper limit of equation (4), the deflection power at the diffractive surface MOE becomes too large, which is undesirable because it increases the deterioration of aberration performance due to positional displacement of the diffractive surface MOE caused by assembly errors in the optical system, etc.

[0047] Furthermore, it is more preferable to set the upper limit of equation (4) to 48°, 45°, or 40°.

[0048] The conditions in equation (5) indicate an appropriate range for the tilt angle θdiff of the diffraction plane MOE, and are conditions for obtaining good image performance while making the optical system thinner. If θdiff falls below the lower limit of equation (5), the diffraction plane MOE tilts too much in the direction that increases the thickness of the optical system, which is undesirable for thinning the optical system. If θdiff exceeds the upper limit of equation (5), the angle of the light rays emitting from the diffraction plane MOE becomes too large compared to the angle of the light rays incident on the diffraction plane MOE, resulting in an imbalance between the two angles and causing astigmatism, which is undesirable.

[0049] Furthermore, it is more preferable to set the upper limit of equation (5) to 45°, 40°, or 35°.

[0050] The condition in equation (6) is the Abbe number ν in the short wavelength range of the dispersion-controlled diffraction plane MOE. ０，ｇＦ This represents the range of variance, which is the reciprocal of ν, and indicates an appropriate range for achieving good chromatic aberration correction. 1 / ν ０，ｇＦ If the value falls below the lower limit of equation (6), the negative dispersion of the diffraction plane MOE in the short-wavelength region becomes too large, resulting in a large chromatic shift in the short-wavelength region of the diffraction plane MOE. This is undesirable because it increases the magnification chromatic aberration of the entire display optical system in the short-wavelength region. 1 / ν ０，ｇＦ If the value exceeds the upper limit of equation (6), the positive dispersion of the diffraction plane MOE in the short wavelength range becomes too large, which is undesirable because it increases the magnification chromatic aberration of the entire display optical system.

[0051] Furthermore, it is more preferable to set the lower limit of formula (6) to -0.015, -0.010, or -0.005. Also, it is more preferable to set the upper limit of formula (6) to 0.02, 0.01, 0.005, or 0.001.

[0052] The optical systems of Examples 1 to 5 will be described in detail below. Numerical examples 1 to 5 corresponding to each of Examples 1 to 5 are shown after Example 5.

[0053] The optical system of Embodiment 1 (Numerical Example 1) shown in Figure 1 comprises optical elements such as lenses with dispersed, rotationally asymmetric diffraction planes MOE arranged sequentially from the object side (object plane side) to the image side (image plane side), a lens group LN, a reflective surface REF, and an image plane side lens group (unsigned). The surface normals of the diffraction plane MOE and the reflective surface REF are each inclined with respect to the lens optical axis LA.

[0054] Figure 2 shows the longitudinal aberrations (spherical aberration, astigmatism, and chromatic aberration) of the optical system in numerical example 1 at infinity focus. In the spherical aberration diagram, Fno is the F number, the solid line shows the spherical aberration with respect to the d line (wavelength 587.6 nm), and the dashed line shows the spherical aberration with respect to the g line (wavelength 435.8 nm). The horizontal axis shows the amount of defocus in the range of -0.003 to +0.003 [mm]. In the astigmatism diagram, the solid line S shows the astigmatism of the sagittal image plane, and the dashed line M shows the astigmatism of the meridional image plane. The horizontal axis is the same as for spherical aberration. The chromatic aberration diagram shows the chromatic aberration at the g line. The horizontal axis shows the range of -0.003 to +0.003 [mm]. ω is the half-angle of view [°]. The explanation of these longitudinal aberration diagrams is the same for the other numerical examples.

[0055] The optical system of Embodiment 2 (Numerical Example 2) shown in Figure 3 comprises optical elements arranged sequentially from the object side to the image side, each having a dispersed, rotationally asymmetric diffraction plane MOE; a lens group LN; a reflective surface REF formed on one surface of an optical prism; an image-side lens group (unsigned); and an image-side reflective surface (unsigned). The surface normals of the diffraction plane MOE and the reflective surface REF are each inclined with respect to the lens optical axis LA.

[0056] Figure 4 shows the longitudinal aberration of the optical system in numerical example 2 when it is focused at infinity.

[0057] The optical system of Embodiment 3 (Numerical Example 3) shown in Figure 5 comprises optical elements with dispersed, rotationally asymmetric diffraction planes MOE arranged sequentially from the object side to the image side, a lens group LN, and a reflective surface REF. The surface normals of the diffraction plane MOE and the reflective surface REF are each inclined with respect to the lens optical axis LA.

[0058] Figure 6 shows the longitudinal aberration of the optical system in numerical example 3 when it is focused at infinity.

[0059] The optical system of Embodiment 4 (Numerical Example 4) shown in Figure 7 comprises optical elements having dispersed, rotationally asymmetric diffraction planes MOE arranged sequentially from the object side to the image side, a lens group LN including a diffraction plane with a light-gathering effect, and a reflective surface REF. The surface normals of the diffraction plane MOE and the reflective surface REF are each inclined with respect to the lens optical axis LA.

[0060] Figure 8 shows the longitudinal aberration of the optical system in numerical example 4 when it is focused at infinity.

[0061] The optical system of Embodiment 5 (Numerical Example 5) shown in Figure 9 comprises optical elements having dispersed, rotationally asymmetric diffraction planes MOE arranged sequentially from the object side to the image side, a lens group LN including a diffraction plane with a light-gathering effect, a half mirror (unsigned: transmission), a reflective surface REF, a half mirror (unsigned: reflection), a first image-side reflective surface (unsigned), a second image-side reflective surface (unsigned), and a lens (unsigned). The surface normals of the diffraction plane MOE and the reflective surface REF are each inclined with respect to the lens optical axis LA.

[0062] Figure 10 shows the longitudinal aberration of the optical system of numerical example 5 when it is focused at infinity.

[0063] Numerical examples 1 to 5 are shown below. In each numerical example, the maximum image height is half the diagonal length of the imaging plane (or display plane) on the image plane. In the surface data, r represents the paraaxial radius of curvature of the i-th plane (i = 0, 1, 2, 3, ...) counted from the object plane. Nd represents the refractive index of the optical material at the d line between the i-th plane and the (i+1)th plane. νd represents the Abbe number of the optical material at the d line between the i-th plane and the (i+1)th plane. The Abbe number νd at the d line is expressed as νd = (Nd - 1) / (NF - NC), where the refractive indices at the d-line, F-line, and C-line are Nd, NF, and NC, respectively. X and Y represent the X and Y coordinate values ​​in the XYZ absolute coordinate system of the vertices of each plane. Angle represents the angle that the plane normal of each plane makes with the X axis. The unit of length in each numerical example is [mm]. However, since optical systems can achieve equivalent optical performance even when proportionally enlarged or reduced, the unit is not limited to [mm] and other units can be used. Also, the unit of angle is [°].

[0064] The asterisk (*) next to the surface number indicates that the surface has an aspherical shape. The aspherical shape is expressed by the following formula, where x is the displacement from the surface vertex in the direction of the optical axis, h is the height from the optical axis in the direction perpendicular to the optical axis, the direction of light propagation is positive, R is the radius of paraxial curvature at the surface vertex, k is the cone constant, and A2, A4, A6, A8, and A10 are aspherical coefficients. The cone constant and aspherical coefficients "e±x" are multiplied by 10⁻¹⁰ ±x It means...

[0065]

[0066] Furthermore, the optical path difference function of a rotationally asymmetric surface at the design wavelength is given by ψ0 = U1,0 × y, where U1,0, U0,1, U2,0, U1,1, U0,2,... are the coefficients of the optical path difference function of the surface, and the in-plane coordinates are y and z. １ z ０ +U0, 1×y ０ z １ +U2,0×y ２ z ０ +U1, 1×y １ z １ +U0, 2×y ０ z ２ It is represented as follows.

[0067] On the other hand, the optical path difference function of a rotationally symmetric surface at the design wavelength is given by ψ0 = U2 × h, where U2, U4, U6, U8, and U10 are coefficients of the optical path difference function of the surface. ２ +U4×h ４ +U6×h ６ +U8×h ８ +U10×h １０ It is represented as follows.

[0068] The (diffraction) of the second surface indicates a surface whose optical design has been carried out using the surface's optical path difference function. The optical path difference dispersion P(λ) of the surface is expressed by an equation in which the incident wavelength λ is a variable. The incident wavelength λ used when calculating the optical path difference dispersion of the surface is in units of [μm]. The (reflection) appended to the surface number indicates a reflective surface, which is a reflective surface due to total internal reflection at the glass-air interface or mirror reflection by a metal film.

[0069] Table 1 summarizes the values ​​of equations (1) to (6) described above for numerical examples 1 to 5. Each numerical example satisfies all the conditions of equations (1) to (6). [Numerical Example 1] Unit: mm Object distance: -1e30 Focal length: f=1.00 Maximum image height: 0.1709 Surface data

[0070] The second surface of the aspherical data (asymmetric refracted surface) has a design wavelength of 0.58756 μm. U1,0 = -2.079117e-01 U0,2 = 9.83896e-05 The optical path difference dispersion λ unit [μm] is: P(λ) = 527.57657λ10 - 3174.19670λ9 + 8657.87534λ8 - 14126.68701λ7 + 15317.54115λ6 - 11587.24417λ5 + 6239.36490λ4 - 2391.27108λ3 + 639.21962λ2 - 113.49263λ + 12.05454 P(λd) = 1.0000e+00 P(λC) = 8.9933e-01 P(λF) = 1.2032e+00 3rd face k = 0.00000e+00 A4 = 1.20586e+00 A6 = 8.98576e+00 A8 = -1.82227e+02 4th face k = 0.00000e+00 A4 = 4.47986e+00 A6 = -5.12325e+01 A8 = 3.01105e+02 5th face k = 0.00000e+00 A4 = -1.04478e+01 A6 = 1.35878e+02 A8 = -3.16868e+02 6th face k = 0.00000e+00 A 4 = -1.29157e+01 A 6 = 2.21840e+02 A 8 = -1.13266e+03 Page 8 k = 2.63122e+00 A 4 = 4.79468e+00 A 6 = -1.72269e+02 A 8 = 1.33012e+04 A10 = -2.11595e+05 Page 9 k = -1.03415e+01 A 4 = -3.58510e+00 A 6 = -2.94229e+02 A 8 = 3.77558e+04 A10 = -9.98007e+05 Page 10 k = 2.61649e+00 A 4 = -2.59002e+01 A 6 = 1.62112e+03 A 8 = -2.77462e+04 A10 = -9.69094e+05 Page 11 k = 3.93507e+00 A 4 = 6.53905e+00 A 6 = 2.15643e+03 A 8 = -7.25790e+04 A10 = 1.00999e+06 [Numerical Example 2] Unit: mm Object Distance: -1e30 Focal Length: f=1.00 Maximum Image Height: 0.1636 Surface Data: .

[0071] Aspheric data 2nd surface (rotation asymmetric diffraction surface) Design wavelength 0.58756 [μm] U1,0=-6.840978e-01 Surface optical path difference dispersion λ unit [μm] P(λ)=0.58756 / λ P(λd) = 1.0000e+00 P(λC) = 8.9530e-01 P(λF) = 1.2086e+00 3rd side k = 0.00000e+00 A 4= 6.58447e-01 A 6= 9.48907e+00 A 8=-3.30503e+02 4th side k = 0.00000e+00 A 4= 8.90350e+00 A 6=-1.17770e+02 A 8= 7.99854e+02 Fifth face k = 0.00000e+00 A 4 = 3.54355e+00 A 6 = 3.95168e+01 A 8 = -5.66294e+01 Sixth face k = 0.00000e+00 A 4 = -5.52202e+00 A 6 = 2.90222e+02 A 8 = -1.31225e+03 Tenth face k = -8.95602e-04 A 4 = 1.02326e+01 A 6 = 4.36553e+01 A 8 = 1.68329e+03 A10 = 2.38035e+02 [Numerical example 3] Unit: mm Object distance: -1e30 Focal length f=1.00 Maximum image height 0.1687 Surface data

[0072] Aspheric data 2nd surface (rotation asymmetric diffraction surface) Design wavelength 0.58756 [μm] U1,0=-5.000000e-01 Surface optical path difference dispersion λ unit [μm] P(λ)=0.58756 / λ P(λd) = 1.0000e+00 P(λC) = 8.9530e-01 P(λF) = 1.2086e+00 3rd side k = 0.00000e+00 A 4= 9.05073e-01 A 6= 6.19227e+01 A 8=-6.60058e+02 4th side k = 0.00000e+00 A 4= 2.72106e+01 A 6=-2.82674e+02 A 8= 2.70664e+02 Fifth face k = 0.00000e+00 A 4 = 1.22278e+01 A 6 = -7.26521e+01 Sixth face k = -9.96929e-02 A 4 = -3.73118e+01 A 6 = 4.93371e+01 Seventh face k = 1.95291e-04 A 4 = 7.47533e+00 A 6 = -7.30413e+02 Eighth face k = 0.00000e+00 A 4 = 1.06083e+01 A 6 = -4.42946e+02 A 8 = -3.55538e+03 [Numerical example 4] Unit: mm Object distance: -1e30 Focal length f=1.00, maximum image height 0.1648, surface data

[0073] Aspherical Data 2nd Surface (Reflex Asymmetric Reflection Surface) Design Wavelength 0.58756 [μm] U1,0=-3.459701e-01 Surface Optical Path Difference Dispersion λ Unit [μm] P(λ)= 514.85586λ10-3120.72379λ9+8564.02289λ8-14045.78557λ7+15297.54185λ6-11617.00000λ5+6276.73734λ4-2412.89836λ3+646.74064λ2-115.11227λ+12.24250 P(λd) = 1.0000e+00 P(λC) = 8.9429e-01 P(λF) = 1.2100e+00 3rd plane (retrograde symmetric fold plane) Design wavelength 0.58756 [μm] U2=-4.47549e-01 U4= 3.31953e-01 U6=-1.08658e+01 Surface optical path difference dispersion λ unit [μm] P(λ)=0.58756 / λ P(λd) = 1.0000e+00 P(λC) = 8.9530e-01 P(λF) = 1.2086e+00 5th plane k = 0.00000e+00 A4=-8.28235e+00 A6=-7.24949e+01 6th plane k =-2.93125e-05 A 4=-1.68056e+01 A 6= 2.70867e+01 7th face k =-3.32584e-05 A 4= 2.47878e+01 A 6= 8.89100e+01 8th face k = 0.00000e+00 A 4= 3.25749e+01 A 6= 1.38217e+02 A 8= 5.50824e+03 [Value Example 5] Unit mm Object distance -1e30 Focal distance f=1.00 Maximum image height 0.1709 Face data

[0074] Aspheric data 2nd surface (rotation asymmetric diffraction surface) Design wavelength 0.58756 [μm] U1,0=-6.008954e-01 Surface optical path difference dispersion λ unit [μm] P(λ)=0.58756 / λ P(λd) = 1.0000e+00 P(λC) = 8.9530e-01 P(λF) = 1.2086e+00 Third surface (rotationally symmetrical diffraction surface) Design wavelength 0.58756 [μm] U 2=-3.56954e-01 U 4=-3.03515e-02 U 6= 5.01286e-01 Optical path difference dispersion of surface λ unit [μm] P(λ)=0.58756 / λ P(λd) = 1.0000e+00 P(λC) = 8.9530e-01 P(λF) = 1.2086e+00 5th side k = 9.14991e-01 A 4=-1.63991e+00 A 6=-8.34075e+00 6th side k = 2.25391e+00 A 4=-1.39947e+00 A 6= 5.51291e+00 13th side k = 5.96308e+00 A 4=-1.96327e+01 A 6= 1.68880e+02 A 8=-8.46664e-02 14th side k =-3.88389e+00 A 4=-1.80744e+01 A 6= 2.58679e+02 A 8 = -2.24108e+03

[0075]

[0076] [Imaging Device] Figure 12(a) shows a smartphone 10 as an imaging device including the optical system OS of Examples 1 to 5. A display 11, a microphone 12, and a speaker 13 are arranged on the front of the smartphone 10. The optical system OS takes in light from an object from the back of the smartphone 10, bends the optical path to form an image on an image sensor (imaging surface) not shown. This makes it possible to image an object. By using the optical system OS of Examples 1 to 5, it is possible to provide a smartphone that is thin and can produce high-quality images.

[0077] [Display Device] Figure 12(b) shows a head-mounted display 20 as a display device including the optical system OS of Examples 1 to 5. The optical system OS guides light from an unshown display element (display surface) to the observer's eye E by bending the optical path. This allows the observer to view the image. By using the optical system OS of Examples 1 to 5, a head-mounted display that is thin and can observe high-resolution display images can be provided.

[0078] The embodiments described above are merely representative examples, and various modifications and changes can be made to each embodiment when implementing this disclosure.

Claims

1. An optical element comprising a diffracting surface with controlled wavelength dispersion characteristics and a lens, wherein the Abbe number of the diffracting surface is ν ０ Let the reference wavelength of the diffraction plane be the d-line, and the principal dispersions be the F-line and C-line, and the optical path difference function at each wavelength be ψ ｄ ψ Ｆ ψ Ｃ P(λ) is the optical path difference dispersion of the surface at each wavelength. ｄ ), P(λ Ｆ ), P(λ Ｃ ) as, When this is the case, -0.2 < 1 / ν ０ An optical system that satisfies the condition < 0.2, and the diffracted surface has a rotationally asymmetric optical path difference function.

2. The optical system according to claim 1, wherein the diffraction plane deflects incident light, and when α is the deflection angle by the diffraction plane with respect to a d-line incident perpendicularly at the intersection of the diffraction plane with the optical axis of the lens, and θdiff is the angle between the optical axis of the lens and the surface normal of the diffraction plane, the condition -30° < α / 2 - θdiff < 30° is satisfied.

3. The optical system according to claim 1 or 2, characterized in that the optical system includes a reflective element having a reflective surface.

4. The optical system according to any one of claims 1 to 3, characterized in that, when θrefl is the angle between the optical axis of the lens and the surface normal of the reflective surface, and θdiff is the angle between the optical axis and the surface normal of the diffracting surface, the condition -30° < θrefl / 2 - θdiff < 30° is satisfied.

5. The optical system according to any one of claims 1 to 4, characterized in that when the deflection angle of the light rays due to the diffraction plane is α, the condition 0° < α < 60° is satisfied.

6. The optical system according to any one of claims 1 to 5, characterized in that when the angle between the optical axis of the lens and the surface normal of the diffraction plane is θdiff, the condition 0° < θdiff < 30° is satisfied.

7. The optical system according to any one of claims 1 to 6, characterized in that the diffraction plane deflects all light rays of different heights from the intersection point with the optical axis of the lens toward the same side.

8. The optical system according to any one of claims 1 to 7, characterized in that the lens is a refractive lens, a diffracting lens, or a metasurface lens.

9. The optical system according to any one of claims 1 to 8, characterized in that the diffraction plane and the lens are arranged adjacent to each other.

10. The optical system according to any one of claims 1 to 9, characterized in that the optical system forms an image of light incident from the surface of an object onto the image plane.

11. The optical system according to claim 10, characterized in that it is an imaging optical system characterized in that it guides light from a subject located on the object surface to an imaging surface arranged on the image surface.

12. The optical system according to claim 11, characterized in that the diffraction plane is arranged between the object plane and the lens.

13. The optical system according to claim 12, characterized in that it has the diffraction surface, the lens, and the reflection surface in order from the object surface side to the image surface side.

14. The optical system according to claim 10, characterized in that it is a display optical system that guides light from a display surface located on the object surface to the eye of an observer positioned on the image surface.

15. The optical system according to claim 14, characterized in that the diffraction plane is arranged between the lens and the image plane.

16. The optical system according to claim 15, characterized in that it has the reflective surface, the lens, and the diffracting surface in order from the side of the object surface to the side of the image surface.

17. The optical system according to any one of claims 1 to 16, characterized in that the diffraction surface has a planar shape.

18. The optical system according to any one of claims 1 to 17, characterized in that the lens closest to the diffraction plane is a positive lens.

19. The Abbe number in the wavelength range below the F line when the main dispersion of the diffractive surface is the g line and the F line is ν ０，ｇＦ , and the optical path difference functions of the d line, the g line, and the F line are ψ ｄ , ψ ｇ , ψ Ｆ , and the incident wavelengths of the d line, the g line, and the F line are λ ｄ , λ ｇ , λ Ｆ respectively. When is satisfied, the optical system according to any one of claims 1 to 18, characterized in that the condition -0.02 < 1 / ν ０，ｇＦ < 0.02 is satisfied.

20. An optical element comprising a metasurface with controlled wavelength dispersion characteristics and a lens, wherein the Abbe number of the metasurface is ν ０ Let the reference wavelength of the metasurface be the d-line and the principal dispersions be the F-line and C-line, and the optical path difference function at each wavelength be ψ ｄ ψ Ｆ ψ Ｃ P(λ) is the optical path difference dispersion of the surface at each wavelength. ｄ ), P(λ Ｆ ), P(λ Ｃ ) as, When this is the case, -0.2 < 1 / ν ０ An optical system that satisfies the condition < 0.2, and the metasurface has a rotationally asymmetric optical path difference function.

21. An optical device characterized by having an optical system according to any one of claims 1 to 20 and an image sensor or display element.

Images