Optical system

Abstract

Provided is an optical system having good optical characteristics while satisfying requirements for size reduction and improvement of light amount efficiency.　This optical system comprises, in order from a pupil plane EP to a display surface IMG of an image display element: a first lens L1 having positive refractive power and having a biconvex shape in a paraxial direction; a half mirror HM; and a second lens L2 having positive refractive power and having a biconvex shape in the paraxial direction. The optical system has a first reflective polarizing plate 11 disposed between the pupil plane EP and the half mirror HM, a first quarter wavelength plate 21 disposed between the pupil plane EP and the half mirror HM, a second quarter wavelength plate 22 disposed between the half mirror HM and the display surface IMG, and a second reflective polarizing plate 12 disposed between the half mirror HM and the display surface IMG, and satisfies a predetermined conditional expression.

Description

optical system

[0001] The present invention relates to an optical system for magnifying an image (for example, an image displayed on an image display device).

[0002] 2. Description of the Related Art Known display devices using image display elements include electronic viewfinders, electronic binoculars, and head-mounted displays.

[0003] In such a display device, the distance between the image display element and the eye must be as short as possible, and the optical system for magnifying the image displayed on the image display element must be housed in a limited space. This often makes it difficult to eliminate various aberrations in the optical system, and the range of correction is also limited.

[0004] As is well known, visual acuity depends on the density of the cones in photoreceptor cells, and the eye has the characteristic of forming a clear image near the fovea of ​​the macula, i.e., the center of the pupil. Therefore, by utilizing this physiological optical characteristic of the eye to complement the aberration correction of the above-mentioned optical system, it is possible to obtain good optical performance. Specifically, narrowing the pupil increases the depth of focus and reduces the effects of spherical aberration and coma aberration, thereby reducing sensitivity to blur even if the aberration and refractive correction are excessive or insufficient. Furthermore, by utilizing the so-called Stiles-Crawford effect, a phenomenon in which the sensitivity of light rays incident from the periphery is lower than the sensitivity of light rays passing through the center of the pupil, the effects of spherical aberration, coma aberration, and chromatic aberration can be reduced. Furthermore, by maintaining this state, the eye gradually becomes accustomed to it, making it possible to reduce the effects of distortion aberrations and the like.

[0005] The optical systems installed in such display devices are required to be compact and have high light efficiency, where light efficiency refers to the ratio of the amount of light reaching the eye (pupil plane) when the amount of light on the display surface of the image display element is taken as 100%.

[0006] Known examples of conventional optical systems include the optical system described in Patent Document 1. Patent Document 1 discloses an optical system including a partial optical system having two semi-transmissive surfaces and a refractive optical element having power.

[0007] Patent No. 3441188

[0008] Even if one attempts to achieve miniaturization and improved light efficiency with the optical system described in Patent Document 1, the presence of two semi-transparent surfaces makes it difficult to improve light efficiency, and good optical performance cannot be obtained.

[0009] The present invention has been made in view of the above-mentioned problems, and aims to provide an optical system that has high resolving power with various aberrations well corrected, while satisfying the demands for compactness and improved light efficiency in a balanced manner.

[0010] The optical system according to the present invention has, in order from the pupil plane side to the display surface side, a first lens having a paraxial biconvex shape with positive refractive power, a half mirror, and a second lens having a paraxial biconvex shape with positive refractive power, wherein the optical system has a first reflective polarizer arranged between the pupil plane and the half mirror, a first quarter-wave plate arranged between the pupil plane and the half mirror, a second quarter-wave plate arranged between the half mirror and the display surface, and a second first reflective polarizer arranged between the half mirror and the display surface.In this specification, the terms convex, concave, and flat surfaces of the lens refer to the shape in the paraxial direction, and the refractive power refers to the refractive power in the paraxial direction unless otherwise specified.

[0011] A reflective polarizer reflects linearly polarized light having one polarization direction and transmits linearly polarized light having an orthogonal polarization direction.

[0012] A quarter-wave plate delays the phase of polarized light by 1 / 4λ, thereby converting linearly polarized light into circularly polarized light and circularly polarized light into linearly polarized light.

[0013] The first lens has positive refractive power and is biconvex in the paraxial direction, thereby suppressing spherical aberration, astigmatism, curvature of field, and distortion.

[0014] A half mirror transmits 50% of the light and reflects the remaining 50%.

[0015] The second lens has positive refractive power and is biconvex in the paraxial direction, and therefore effectively corrects spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0016] In the optical system of the present invention, a pupil-side element group is composed of a first reflective polarizer, a first lens having positive refractive power, and a first quarter-wave plate, and a display-side element group is composed of a second quarter-wave plate, a second lens having positive refractive power, and a second reflective polarizer. The pupil-side element group and the display-side element group are arranged substantially symmetrically with respect to the semi-transmissive surface of the half mirror. Therefore, by ultimately superimposing two beams of light, one reflected by the half mirror and the other transmitted through it, it is possible to achieve an improvement in light efficiency while miniaturizing the optical system.

[0017] It is desirable that the optical system having the above configuration satisfy the following condition (1): (1) 2.75<(D2 / f2)×100<5.95 where D2 is the thickness of the second lens on the optical axis, and f2 is the focal length of the second lens.

[0018] By satisfying the range of conditional expression (1), it becomes possible to achieve a low profile and to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0019] It is desirable that the optical system having the above configuration satisfy the following conditional expression (2): (2) −1.00<r1 / r2<−0.13 where r1 is the paraxial radius of curvature of the surface of the first lens on the pupil plane side, and r2 is the paraxial radius of curvature of the surface of the first lens on the display plane side.

[0020] By satisfying the range of conditional expression (2), it becomes possible to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0021] It is desirable that the optical system having the above configuration satisfy the following conditional expression (3): (3) −1.50<r2 / r3<−0.50, where r2 is the paraxial radius of curvature of the surface of the first lens on the display surface side, and r3 is the paraxial radius of curvature of the surface of the second lens on the pupil plane side.

[0022] By satisfying the range of conditional expression (3), it becomes possible to make good corrections for coma, astigmatism, curvature of field, and distortion.

[0023] It is desirable that the optical system having the above configuration satisfy the following conditional expression (4): (4) −4.00<r2 / f1<−0.75 where r2 is the paraxial radius of curvature of the surface of the first lens facing the display screen, and f1 is the focal length of the first lens.

[0024] By satisfying the range of conditional expression (4), it becomes possible to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0025] It is desirable that the optical system having the above configuration satisfy the following conditional expression (5): (5) −5.50<r3 / r4<−0.80, where r3 is the paraxial radius of curvature of the surface of the second lens on the pupil plane side, and r4 is the paraxial radius of curvature of the surface of the second lens on the display plane side.

[0026] By satisfying the range of conditional expression (5), it becomes possible to make good corrections for coma, astigmatism, curvature of field, and distortion.

[0027] It is desirable that the optical system having the above configuration satisfy the following conditional expression (6): (6) -6.50<r4 / f2×D2<-2.70, where r4 is the paraxial radius of curvature of the surface of the second lens facing the display screen, f2 is the focal length of the second lens, and D2 is the thickness of the second lens on the optical axis.

[0028] By satisfying the range of conditional expression (6), it becomes possible to achieve a low profile and to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0029] It is desirable that the optical system having the above configuration satisfy the following conditional expression (7): (7) -26<r4 / D2<-8 where r4 is the paraxial radius of curvature of the surface of the second lens facing the display surface, and D2 is the thickness of the second lens on the optical axis.

[0030] By satisfying the range of conditional expression (7), it becomes possible to achieve a low profile and to make good corrections for coma, astigmatism, curvature of field, and distortion.

[0031] It is desirable that the optical system having the above configuration satisfy the following conditional expression (8): (8) 2.75<(D1 / f1)×100<5.95 where D1 is the thickness of the first lens on the optical axis, and f1 is the focal length of the first lens.

[0032] By satisfying the range of conditional expression (8), it becomes possible to achieve a low profile and to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0033] It is desirable that the optical system having the above configuration satisfy the following conditional expression (9): (9) 0.6<(T1 / f1)×100<5.5, where T1 is the distance on the optical axis from the surface of the first lens on the display surface side to the surface of the second lens on the pupil plane side, and f1 is the focal length of the first lens.

[0034] By satisfying the range of conditional expression (9), it becomes possible to achieve a low profile and to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0035] It is desirable that the optical system having the above configuration satisfy the following conditional expression (10): (10) 9.5<r1 / T1<100.0, where r1 is the paraxial radius of curvature of the pupil plane side surface of the first lens, and T1 is the distance on the optical axis from the display plane side surface of the first lens to the pupil plane side surface of the second lens.

[0036] By satisfying the range of conditional expression (10), it becomes possible to achieve a low profile and to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0037] It is desirable that the optical system having the above configuration satisfy the following conditional expression (11): (11) 4.5<r1 / (D1+T1)<28.0, where r1 is the paraxial radius of curvature of the pupil-plane side surface of the first lens, D1 is the optical axial thickness of the first lens, and T1 is the optical axial distance from the display-plane side surface of the first lens to the pupil-plane side surface of the second lens.

[0038] By satisfying the range of conditional expression (11), it becomes possible to achieve a low profile and to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0039] It is desirable that the optical system having the above configuration satisfy the following conditional expression (12): (12) 0.3<r1 / f1<1.3 where r1 is the paraxial radius of curvature of the pupil plane side surface of the first lens, and f1 is the focal length of the first lens.

[0040] By satisfying the range of conditional expression (12), it becomes possible to make good corrections for spherical aberration, astigmatism, curvature of field, and distortion.

[0041] It is desirable that the optical system having the above configuration satisfy the following conditional expression (13): (13) 0.15<r1 / (f1+f2)<0.65, where r1 is the paraxial radius of curvature of the pupil plane side surface of the first lens, f1 is the focal length of the first lens, and f2 is the focal length of the second lens.

[0042] By satisfying the range of conditional expression (13), it becomes possible to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0043] It is desirable that the optical system having the above configuration satisfy the following conditional expression (14): (14) -1.5<(r1 / r4) / (f1 / f2)<-0.5, where r1 is the paraxial radius of curvature of the surface of the first lens on the pupil plane side, r4 is the paraxial radius of curvature of the surface of the second lens on the display plane side, f1 is the focal length of the first lens, and f2 is the focal length of the second lens.

[0044] By satisfying the range of conditional expression (14), it becomes possible to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0045] It is desirable that the optical system having the above configuration satisfy the following conditional expression (15): (15) -15.2<r2 / f<-4.0 where r2 is the paraxial radius of curvature of the surface of the first lens on the display surface side, and f is the focal length of the entire optical system.

[0046] By satisfying the range of conditional expression (15), it becomes possible to make good corrections for astigmatism, curvature of field, and distortion.

[0047] It is desirable that the optical system having the above configuration satisfy the following conditional expression (16): (16) -165<r2 / T1<-30, where r2 is the paraxial radius of curvature of the display surface side of the first lens, and T1 is the distance on the optical axis from the display surface side of the first lens to the pupil plane side of the second lens.

[0048] By satisfying the range of conditional expression (16), it becomes possible to achieve a low profile and to make good corrections for astigmatism, curvature of field, and distortion.

[0049] It is desirable that the optical system having the above configuration satisfy the following conditional expression (17): (17) -330<r2 / hm1<-65, where r2 is the paraxial radius of curvature of the display surface side of the first lens, and hm1 is the distance on the optical axis from the display surface side of the first lens to the pupil plane side of the half mirror.

[0050] By satisfying the range of conditional expression (17), it becomes possible to achieve a low profile and to make good corrections for astigmatism, curvature of field, and distortion.

[0051] It is desirable that the optical system having the above configuration satisfy the following conditional expression (18): (18) 4.0<r3 / f<15.2 where r3 is the paraxial radius of curvature of the surface of the second lens on the pupil plane side, and f is the focal length of the entire optical system.

[0052] By satisfying the range of conditional expression (18), it becomes possible to make good corrections for coma, astigmatism, curvature of field, and distortion.

[0053] It is desirable that the optical system having the above configuration satisfy the following conditional expression (19): (19) 0.75<r3 / f2<4.00 where r3 is the paraxial radius of curvature of the pupil plane side surface of the second lens, and f2 is the focal length of the second lens.

[0054] By satisfying the range of conditional expression (19), it becomes possible to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0055] It is desirable that the optical system having the above configuration satisfy the following conditional expression (20): (20) −7.5<r4 / f<−2.0 where r4 is the paraxial radius of curvature of the surface of the second lens on the display surface side, and f is the focal length of the entire optical system.

[0056] By satisfying the range of conditional expression (20), it becomes possible to make good corrections for coma, astigmatism, curvature of field, and distortion.

[0057] It is desirable that the optical system having the above configuration satisfy the following conditional expression (21): (21) −1.3<r4 / f2<−0.3 where r4 is the paraxial radius of curvature of the surface of the second lens on the display surface side, and f2 is the focal length of the second lens.

[0058] By satisfying the range of conditional expression (21), it becomes possible to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0059] It is desirable that the optical system having the above configuration satisfy the following conditional expression (22): (22) −0.65<r4 / (f1+f2)<−0.15, where r4 is the paraxial radius of curvature of the surface of the second lens facing the display screen, f1 is the focal length of the first lens, and f2 is the focal length of the second lens.

[0060] By satisfying the range of conditional expression (22), it becomes possible to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0061] It is desirable that the optical system having the above configuration satisfy the following conditional expression (23): (23) -13<r4 / (D1+D2)<-4, where r4 is the paraxial radius of curvature of the surface of the second lens facing the display surface, D1 is the thickness of the first lens on the optical axis, and D2 is the thickness of the second lens on the optical axis.

[0062] By satisfying the range of conditional expression (23), it becomes possible to achieve a low height and to make good corrections for coma, astigmatism, curvature of field, and distortion.

[0063] It is desirable that the optical system having the above configuration satisfy the following conditional expression (24): (24) 5<(f1+f2) / f<20, where f1 is the focal length of the first lens, f2 is the focal length of the second lens, and f is the focal length of the entire optical system.

[0064] By satisfying the range of conditional expression (24), it becomes possible to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0065] It is desirable that the optical system having the above configuration satisfy the following conditional expression (25): (25) 30<f2 / hm2<845 where f2 is the focal length of the second lens, and hm2 is the distance on the optical axis from the surface of the half mirror on the display surface side to the surface of the second lens on the pupil plane side.

[0066] By satisfying the range of conditional expression (25), it becomes possible to achieve a low height and to make good corrections for spherical aberration, coma, astigmatism, curvature of field, and distortion.

[0067] The present invention makes it possible to obtain an optical system with high resolution and excellent correction of aberrations while satisfying the requirements for miniaturization and improved light efficiency in a well-balanced manner. Furthermore, the optical system according to the present invention improves light efficiency, thereby reducing power consumption in the image display element and providing an environmentally friendly optical system.

[0068] FIG. 10A is a cross-sectional view showing a schematic configuration of an optical system according to Example 1 of the present invention. FIG. 10B is a partially enlarged view of the optical system shown in FIG. 1. FIG. 10C is an aberration diagram showing spherical aberration, astigmatism, and distortion of the optical system shown in FIG. 1. FIG. 10D is a cross-sectional view showing a schematic configuration of an optical system according to Example 2 of the present invention. FIG. 10E is a partially enlarged view of the optical system shown in FIG. 4. FIG. 10F is an aberration diagram showing spherical aberration, astigmatism, and distortion of the optical system shown in FIG. 4. FIG. 10G is a cross-sectional view showing a schematic configuration of an optical system according to Example 3 of the present invention. FIG. 10H is a partially enlarged view of the optical system shown in FIG. 7. FIG. 10H is an aberration diagram showing spherical aberration, astigmatism, and distortion of the optical system shown in FIG. 7.

[0069] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will now be described in detail with reference to the accompanying drawings.

[0070] 1, 4, and 7 are cross-sectional views showing the schematic configurations of the optical systems of Examples 1 to 3 according to this embodiment, respectively. Also, Fig. 2, 5, and 8 show enlarged partial views of the optical systems of Examples 1 to 3, respectively. The optical system according to this embodiment will be described in detail below with reference to the optical system of Example 1.

[0071] As shown in Figure 1, the optical system of this embodiment is an optical system that has, in order from a pupil plane EP to a display surface IMG of an image display element, a first lens L1 that has a paraxially biconvex shape with positive refractive power, a half mirror HM, and a second lens L2 that has a paraxially biconvex shape with positive refractive power, and the optical system has a first reflective polarizer 11 arranged between the pupil plane EP and the half mirror HM, a first quarter-wave plate 21 arranged between the pupil plane EP and the half mirror HM, a second quarter-wave plate 22 arranged between the half mirror HM and the display surface IMG, and a second reflective polarizer 12 arranged between the half mirror HM and the display surface IMG.

[0072] In this optical system, the first reflective polarizer 11, the first lens L1, and the first quarter-wave plate 21 constitute an element group on the pupil EP side, and the second quarter-wave plate 22, the second lens L2, and the second reflective polarizer 12 constitute an element group on the display surface IMG side. The element group on the pupil side and the element group on the display surface IMG side are arranged approximately symmetrically with respect to the semi-transmissive surface of the half mirror HM.

[0073] The optical system according to this embodiment may be mounted on any object, but may be mounted on a head-mounted display, for example, as an optical system for enlarging an image displayed on a display surface IMG. In this case, the pupil plane EP is where the observer's pupil is located. An aperture stop may be disposed on the pupil plane EP.

[0074] In the optical system according to the present embodiment, anti-reflection films may be attached to both sides of the half mirror HM. Since anti-reflection films have the function of preventing light reflection, this configuration can prevent a decrease in image contrast due to reflection of external light.

[0075] As shown in Figure 2, the surface of the first reflective polarizer 11 facing the display surface IMG and the surface of the first lens L1 facing the pupil plane have the same shape, and they are attached with an adhesive or the like. The first lens L1 has a convex surface on the pupil plane side paraxially. The first lens L1 of this embodiment has a biconvex shape paraxially. This shape of the first lens L1 allows the distance from the first reflective polarizer 11 to the half mirror HM to be reduced, thereby reducing the effective diameter of the lens and thereby miniaturizing the optical system, while suppressing spherical aberration, astigmatism, field curvature, and distortion.

[0076] In the optical system according to this embodiment, the first quarter-wave plate 21 is attached to the surface of the half mirror HM on the pupil plane EP side, and the second quarter-wave plate 22 is attached to the surface of the half mirror HM on the display surface IMG side. This reduces the size of the optical system while improving ease of assembly. However, the positions of the first quarter-wave plate 21 and the second quarter-wave plate 22 are not limited to this. The first quarter-wave plate 21 may be located between the pupil plane EP and the half mirror HM, and the second quarter-wave plate 22 may be located between the half mirror HM and the display surface IMG.

[0077] As shown in Fig. 1, the second lens L2 has a convex surface on the display surface side in the paraxial direction. The second lens L2 in this embodiment has a biconvex shape in the paraxial direction. This shape of the second lens L2 allows for excellent correction of spherical aberration, coma, astigmatism, field curvature, and distortion.

[0078] The surface of the second lens L2 on the display surface IMG side and the surface of the second reflective polarizer 12 on the pupil plane EP side have the same shape, and the two are attached together with an adhesive or the like.

[0079] As described above, in the optical system according to this embodiment, the first lens L1 and the second lens L2 are arranged in such a manner that they sandwich the half mirror HM from both sides. In addition to this basic configuration, the first reflective polarizer 11, the first quarter-wave plate 21, the second quarter-wave plate 22, and the second reflective polarizer 12 are each arranged in an appropriate position, thereby improving the light efficiency of the optical system. This point will be described in detail below.

[0080] As a device having a display surface IMG, for example, a liquid crystal display or a micro OLED (Organic Light Emitting Diode) display can be adopted.

[0081] As shown in Fig. 10A of Fig. 10, light emitted from the display surface IMG is converted into linearly polarized light by the second reflective polarizer 12, then converted into circularly polarized light by the second quarter-wave plate 22, and then enters the half mirror HM. A portion of the light that enters the half mirror HM passes through it and is converted by the first quarter-wave plate 21 into linearly polarized light with the same polarization direction as when it passed through the second reflective polarizer 12, and then enters the first reflective polarizer 11. This linearly polarized light is reflected by the polarization selectivity of the first reflective polarizer 11. The light reflected by the first reflective polarizer 11 is converted into circularly polarized light by the first quarter-wave plate 21, and then enters the half mirror HM, where it is reflected. The light reflected by the half mirror HM becomes circularly polarized in the opposite direction to the light before reflection. Hereinafter, for convenience, light traveling along this path will be referred to as "light on path 1." In the cross-sectional views of the optical system according to this embodiment shown in FIGS. 1, 4 and 7, only the light of path 1 is shown in order to clarify the general configuration of the optical system.

[0082] On the other hand, as shown in Fig. 10B of Fig. 10, a portion of the light converted to circularly polarized light by the second quarter-wave plate 22 and incident on the half mirror HM is reflected and becomes reverse-circularly polarized light, returning to the second quarter-wave plate 22. The circularly polarized light returning to the second quarter-wave plate 22 is converted by the second quarter-wave plate 22 into linearly polarized light having a polarization direction perpendicular to the polarization direction when it first passed through the second reflective polarizer 12, and then incident on the second reflective polarizer 12. This linearly polarized light is reflected by the polarization selectivity of the second reflective polarizer 12. The light reflected by the second reflective polarizer 12 is converted to circularly polarized light by the second quarter-wave plate 22, and then incident on the half mirror HM and transmitted therethrough. Hereinafter, for convenience, the light traveling along this path will be referred to as "path 2 light."

[0083] The light of path 1 and the light of path 2 converge at the half mirror HM. The circularly polarized light converged at the half mirror HM is converted by the first quarter-wave plate 21 into linearly polarized light having a polarization direction perpendicular to the polarization direction when the light first passed through the second reflective polarizer 12, and then enters the first reflective polarizer 11. This linearly polarized light passes through the first reflective polarizer 11 due to its polarization selectivity and is guided to the pupil plane EP. Therefore, the optical system according to this embodiment improves the light efficiency of the optical system, and can increase the light efficiency by up to 50%. Additionally, power consumption in the image display element can be reduced.

[0084] On the other hand, this type of conventional optical system has a low light efficiency of 25% or less, and in order to obtain a bright image at the pupil plane, it is necessary to increase the brightness of the display surface. Here, a brief description of this conventional optical system will be given. Conventional optical systems are generally configured, in order from the pupil plane side to the display surface side, with a reflective polarizer, a first quarter-wave plate, a lens with refractive power, a half mirror, and a second quarter-wave plate. In this optical system, light emitted from the display surface passes through the second quarter-wave plate, the half mirror, the lens, and the first quarter-wave plate, is reflected by the reflective polarizer, and then re-enters the half mirror. The light incident on the half mirror is reflected by the half mirror, passes through the first quarter-wave plate and the reflective polarizer, and reaches the pupil plane. In this light path, light enters the half mirror twice, so the amount of light that ultimately reaches the pupil plane from the display surface is 25% or less. This means that in the conventional optical system, in order to obtain the same level of brightness at the pupil plane as the optical system of this embodiment, it is necessary to increase the brightness of the display surface, which means that the power consumption of the image display element will increase.

[0085] In this regard, the optical system according to this embodiment actively utilizes the light emitted from the display surface IMG and reflected by the half mirror HM as light for path 2, thereby achieving a higher light efficiency than ever before.

[0086] The optical system of this embodiment achieves desirable effects by satisfying the following conditional expressions (1) to (25). (1) 2.75<(D2 / f2)×100<5.95 (2) -1.00<r1 / r2<-0.13 (3) -1.50<r2 / r3<-0.50 (4) -4.00<r2 / f1<-0.75 (5) -5.50<r3 / r4<-0.80 (6) -6.50<r4 / f2×D2<-2.70 (7)-26<r4 / D2<-8 (8)2.75<(D1 / f1)×100<5.95 (9)0.6<(T1 / f1)×100<5.5 (10)9.5<r1 / T1<100.0 (11) 4.5<r1 / (D1+T1)<28.0 (12) 0.3<r1 / f1<1.3 (13)0.15<r1 / (f1+f2)<0.65 (14)-1.5<(r1 / r4) / (f1 / f2)<-0.5 (15)-15.2<r2 / f<-4.0 (16)-165<r2 / T1<-30 (17) -330<r2 / hm1<-65 (18)4.0<r3 / f<15.2 (19)0.75<r3 / f2<4.00 (20)-7.5<r4 / f<-2.0 (21)-1.3<r4 / f2<-0.3 (22)-0.65<r4 / (f1+f2)<-0.15 (23) -13 < r4 / (D1 + D2) < -4 (24) 5 < (f1 + f2) / f < 20 (25) 30 < f2 / hm2 < 845 where, D1: thickness on the optical axis X of the first lens L1 D2: thickness on the optical axis X of the second lens L2 T1: distance on the optical axis X from the surface of the first lens L1 on the display surface side to the surface of the second lens L2 on the pupil surface side hm1: distance on the optical axis X from the surface of the first lens L1 on the display surface side to the surface of the half mirror HM on the pupil surface side hm2: distance on the optical axis X from the surface of the half mirror HM on the display surface side to the surface of the second lens L2 on the pupil surface side f: focal length of the entire optical system f1: focal length of the first lens L1 f2: focal length of the second lens L2 r1: paraxial radius of curvature of the surface of the first lens L1 on the pupil surface side r2: paraxial radius of curvature of the surface of the first lens L1 on the display surface side; r3: paraxial radius of curvature of the surface of the second lens L2 on the pupil surface side; r4: paraxial radius of curvature of the surface of the second lens L2 on the display surface side.

[0087] It is not necessary to satisfy all of the above conditional expressions, and by satisfying each conditional expression individually, it is possible to obtain the effects corresponding to each conditional expression.

[0088] Furthermore, the optical system of this embodiment will exhibit more preferable effects if it satisfies the following conditional expressions (1a) to (25a). (1a) 3.00<(D2 / f2)×100<4.95 (2a)-0.8<r1 / r2<-0.2 (3a)-1.25<r2 / r3<-0.75 (4a)-3.15<r2 / f1<-1.00 (5a)-4.50<r3 / r4<-1.25 (6a) -5.25<r4 / f2×D2<-2.90 (7a)-25.8<r4 / D2<-13 (8a)3.00<(D1 / f1)×100<4.95 (9a)1.0<(T1 / f1)×100<4.5 (10a)14.5<r1 / T1<82.0 (11a) 7<r1 / (D1+T1)<23 (12a)0.5<r1 / f1<1.1 (13a)0.25<r1 / (f1+f2)<0.55 (14a)-1.25<(r1 / r4) / (f1 / f2)<-0.75 (15a)-15.2<r2 / f<-6.0 (16a) -135<r2 / T1<-50 (17a) -270<r2 / hm1<-100 (18a) 6.0<r3 / f<15.2 (19a) 1.05<r3 / f2<3.30 (20a) -6.2<r4 / f<-3.0 (21a) -1.1<r4 / f2<-0.5 (22a) -0.55<r4 / (f1+f2)<-0.25 (23a) -12.9<r4 / (D1+D2)<-6.5 (24a) 8.5<(f1+f2) / f<16.0 (25a) 50<f2 / hm2<700 However, the symbols in each conditional expression are the same as those explained in the previous paragraph. Note that for conditional expressions (1a) to (25a), the lower limit or upper limit may be the lower limit or upper limit of the corresponding conditional expressions (1) to (25).

[0089] In this embodiment, the aspherical shape adopted for the aspherical surface of the lens surface is expressed by Equation 1, where Z is the axis in the optical axis direction, H is the height in the direction perpendicular to the optical axis, R is the paraxial radius of curvature, k is the conic coefficient, and An is the n-th order aspherical coefficient.

[0090]

[0091] Next, examples of the optical system according to the present embodiment will be shown. In each example, f represents the focal length of the entire optical system, Fno represents the F-number, ω represents the half angle of view, ih represents the maximum image height, and TTL represents the total optical length. Here, the total optical length is the distance on the optical axis from the pupil plane to the display surface.

[0092] In addition, i denotes the surface number counted from the pupil surface side, r denotes the paraxial radius of curvature, d denotes the distance between lens surfaces on the optical axis (surface spacing), Nd denotes the refractive index of the d-line (reference wavelength), and νd denotes the Abbe number for the d-line. Aspherical surfaces are indicated by adding an asterisk (*) after the surface number i.

[0093] In the optical systems of each embodiment, the distance between the pupil plane EP, which is the eyepoint on the optical axis, and the lens surface closest to the pupil plane is called the pupil distance. In evaluating aberrations, there is a one-to-one correspondence between the aberration of a light ray that reaches the pupil plane EP when a light emitting point is provided on the display surface side and the aberration of a light ray that reaches the display surface IMG when a light emitting point is provided on the pupil plane EP side. For this reason, in each embodiment, the aberration of the light ray that reaches the display surface IMG is evaluated.

[0094] Example 1

[0095] The basic lens data is shown in Table 1 below.

[0096]

[0097] The optical system of Example 1 satisfies conditional expressions (1) to (25) as shown in Table 4.

[0098] FIG. 3 shows the spherical aberration (mm), astigmatism (mm), and distortion (%) for the optical system of Example 1. The spherical aberration diagram shows the amount of aberration for each wavelength of the F-line (486 nm), d-line (588 nm), and C-line (656 nm). The astigmatism diagram also shows the amount of aberration for the d-line at the sagittal image plane S (solid line) and the amount of aberration for the d-line at the tangential image plane T (dashed line) (the same applies to FIGS. 6 and 9). As shown in FIG. 3, each aberration is well corrected.

[0099] Example 2

[0100] The basic lens data is shown in Table 2 below.

[0101]

[0102] The optical system of Example 2 satisfies conditional expressions (1) to (25) as shown in Table 4.

[0103] 6 shows the spherical aberration (mm), astigmatism (mm), and distortion (%) for the optical system of Example 2. As shown in FIG. 6, each aberration is well corrected.

[0104] Example 3

[0105] The basic lens data is shown in Table 3 below.

[0106]

[0107] The optical system of Example 3 satisfies conditional expressions (1) to (25) as shown in Table 4.

[0108] 9 shows the spherical aberration (mm), astigmatism (mm), and distortion (%) for the optical system of Example 3. As shown in FIG. 9, each aberration is well corrected.

[0109] Table 4 shows the values ​​of the conditional expressions (1) to (25) in the optical systems of Examples 1 to 3.

[0110]

[0111] When the optical system according to the present invention is applied to an image display device, it is possible to contribute to the miniaturization of the image display device and the improvement of the light quantity efficiency, and also to achieve high performance.

[0112] EP pupil surface 11 first reflective polarizer L1 first lens 21 first quarter-wave plate HM half mirror 22 second quarter-wave plate L2 second lens 12 second reflective polarizer IMG display surface

Claims

1. An optical system having, in order from the pupil surface side to the display surface side, a first lens having a paraxial biconvex shape with positive refractive power, a half mirror, and a second lens having a paraxial biconvex shape with positive refractive power, the optical system has a first reflective polarizing plate arranged between the pupil surface and the half mirror, a first ¼ wave plate arranged between the pupil surface and the half mirror, a second ¼ wave plate arranged between the half mirror and the display surface, and a second reflective polarizing plate arranged between the half mirror and the display surface, characterized in that the optical system satisfies the following conditional formula (1): (1) 2.75<(D2 / f2)×100<5.95, where D2 is the thickness of the second lens on the optical axis, and f2 is the focal length of the second lens.

2. The optical system according to claim 1, characterized in that the following conditional expression (2) is satisfied: (2) -1.00<r1 / r2<-0.13, where r1 is the paraxial radius of curvature of the surface of the first lens on the pupil plane side, and r2 is the paraxial radius of curvature of the surface of the first lens on the display surface side.

3. The optical system according to claim 1, characterized in that the following conditional expression (3) is satisfied: (3) -1.50<r2 / r3<-0.50, where r2 is the paraxial radius of curvature of the surface of the first lens on the display surface side, and r3 is the paraxial radius of curvature of the surface of the second lens on the pupil surface side.

4. The optical system according to claim 1, characterized in that the following conditional expression (4) is satisfied: (4) -4.00<r2 / f1<-0.75, where r2 is the paraxial radius of curvature of the surface of the first lens facing the display screen, and f1 is the focal length of the first lens.

5. The optical system according to claim 1, characterized in that the following conditional expression (5) is satisfied: (5) -5.50<r3 / r4<-0.80, where r3 is the paraxial radius of curvature of the surface of the second lens on the pupil plane side, and r4 is the paraxial radius of curvature of the surface of the second lens on the display plane side.

6. The optical system according to claim 1, characterized in that the following conditional expression (6) is satisfied: (6) -6.50<r4 / f2×D2<-2.70, where r4 is the paraxial radius of curvature of the surface of the second lens facing the display screen, f2 is the focal length of the second lens, and D2 is the thickness of the second lens on the optical axis.

7. The optical system according to claim 1, characterized in that the following conditional expression (7) is satisfied: (7) -26<r4 / D2<-8, where r4 is the paraxial radius of curvature of the surface of the second lens on the display surface side, and D2 is the thickness on the optical axis of the second lens.

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