Optical system and display device

Abstract

Provided is an optical system comprising a first optical system and a second optical system. The first optical system includes: a first reflection surface for reflecting light emitted from a pupil side back to the pupil side; and a second reflection surface for reflecting the light reflected back to the pupil side to a display element side. The first reflection surface has a concave shape, and forms an intermediate image on the pupil side. The pupil side of the first reflection surface is filled with a material having a refractive index greater than 1. The second optical system is disposed closer to the display element side than an intermediate image-forming surface on which the intermediate image is formed, is configured such that the intermediate image-forming surface and the display element surface have a conjugate relationship, and includes at least three lenses. Two of the at least three lenses have different Abbe numbers. The entire second optical system has a positive power.

Description

Optical system and display device

[0001] The present disclosure relates to an optical system and a display device.

[0002] There is known a technique for displaying images rendered using AR (Augmented Reality) or VR (Virtual Reality) on, for example, a head-mounted display (HMD) or AR glasses (display device) worn by a user.

[0003] JP 2010-122573 A

[0004] The above-mentioned HMDs, AR glasses, and the like (display devices) are desired to be small because they are worn on the user's head. Furthermore, the optical systems of such HMDs and AR glasses are desired to have high optical performance and a wide viewing angle (wide angle of view) in order to provide the user with a realistic image. However, the conventional technologies proposed so far have had limitations in realizing an optical system that has high optical performance and a wide angle of view while enabling the miniaturization of HMDs and AR glasses.

[0005] Therefore, the present disclosure proposes an optical system that has high optical performance and a wide angle of view while enabling display devices such as HMDs and AR glasses to be miniaturized, and a display device including the optical system.

[0006] According to the present disclosure, there is provided an optical system comprising, in order from a user's pupil side to a display element side, a first optical system and a second optical system, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side toward the pupil side and a second reflecting surface that reflects the light reflected toward the pupil side toward the display element side, the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed and is configured so that the intermediate image plane and the display element surface have a conjugate relationship, the second optical system has at least three lenses, two lenses of the at least three lenses have different Abbe numbers, and the second optical system as a whole has positive power.

[0007] Furthermore, according to the present disclosure, there is provided a display device comprising, from a pupil side, a first optical system, a second optical system, and a display element, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side toward the pupil side and a second reflecting surface that reflects the light reflected toward the pupil side toward the display element side, the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed and is configured so that the intermediate image plane and the display element surface have a conjugate relationship, the second optical system has at least three lenses, two lenses of the at least three lenses have different Abbe numbers, and the second optical system as a whole has positive power.

[0008] FIG. 1 is an explanatory diagram (part 1) for describing an overview of an embodiment of the present disclosure. FIG. 2 is an explanatory diagram (part 3) for describing an overview of an embodiment of the present disclosure. FIG. 4 is an explanatory diagram (part 5) for describing an overview of an embodiment of the present disclosure. FIG. 6 is an explanatory diagram (part 7) for describing an overview of an embodiment of the present disclosure. FIG. 1 is an explanatory diagram (part 1) for describing an overview of an embodiment of the present disclosure. FIG. 2 is an explanatory diagram (part 2) for describing an overview of an embodiment of the present disclosure. FIG. 3 is an explanatory diagram (part 3) for describing an overview of an embodiment of the present disclosure. FIG. 4 is an explanatory diagram (part 4) for describing an overview of an embodiment of the present disclosure. FIG. 5 is an explanatory diagram (part 5) for describing an overview of an embodiment of the present disclosure. FIG. 6 is an explanatory diagram (part 6) for describing an overview of an embodiment of the present disclosure. FIG. 7 is an explanatory diagram (part 7) for describing an overview of an embodiment of the present disclosure. FIG. 1 is an aberration data diagram (part 1) for an optical system according to the first embodiment of the present disclosure. FIG. 2 is an aberration data diagram (part 2) for an optical system according to the first embodiment of the present disclosure. FIG. 3 is an explanatory diagram for describing an example of a schematic configuration of a modification of the first embodiment of the present disclosure. FIG. 4 is an explanatory diagram (part 4) for describing an example of a schematic configuration of an optical system according to a second embodiment of the present disclosure. FIG. 4 is an explanatory diagram (part 4) for describing an example of a lens data of an optical system according to a second embodiment of the present disclosure. FIG. 5 is an explanatory diagram (part 5) for describing an overview of an embodiment of the present disclosure. FIG. 1 is a diagram showing aberration data (part 1) of an optical system according to a second embodiment of the present disclosure. FIG. 2 is a diagram showing aberration data (part 2) of an optical system according to a second embodiment of the present disclosure. FIG. 3 is a diagram showing a schematic configuration example of an optical system according to a third embodiment of the present disclosure. FIG. 4 is a diagram showing example lens data of an optical system according to a third embodiment of the present disclosure. FIG. 5 is a diagram showing example aspherical coefficient data of an optical system according to a third embodiment of the present disclosure. FIG. 1 is a diagram showing aberration data (part 1) of an optical system according to a third embodiment of the present disclosure. FIG. 2 is a diagram showing aberration data (part 2) of an optical system according to a third embodiment of the present disclosure. FIG. 3 is a diagram showing a schematic configuration example of an optical system according to a fourth embodiment of the present disclosure. FIG. 4 is a diagram showing example lens data of an optical system according to a fourth embodiment of the present disclosure. FIG. 5 is a diagram showing example aspherical coefficient data of an optical system according to a fourth embodiment of the present disclosure. FIG. 6 is a diagram showing aberration data (part 1) of an optical system according to a fourth embodiment of the present disclosure. FIG. 6 is a diagram showing aberration data (part 2) of an optical system according to a fourth embodiment of the present disclosure.FIG. 10 is a diagram showing example lens data of an optical system according to a fifth embodiment of the present disclosure. FIG. 11 is a diagram showing example aspherical coefficient data of an optical system according to a fifth embodiment of the present disclosure. FIG. 12 is a diagram showing aberration data (part 1) of an optical system according to a fifth embodiment of the present disclosure. FIG. 13 is a diagram showing aberration data (part 2) of an optical system according to a fifth embodiment of the present disclosure. FIG. 14 is a diagram showing a schematic configuration example of an optical system according to a sixth embodiment of the present disclosure. FIG. 15 is a diagram showing example lens data of an optical system according to a sixth embodiment of the present disclosure. FIG. 16 is a diagram showing example aspherical coefficient data of an optical system according to a sixth embodiment of the present disclosure. FIG. 17 is a diagram showing aberration data (part 1) of an optical system according to a sixth embodiment of the present disclosure. FIG. 18 is a diagram showing aberration data (part 2) of an optical system according to a sixth embodiment of the present disclosure. FIG. 19 is a diagram showing a schematic configuration example of an optical system according to a modified example of the sixth embodiment of the present disclosure. FIG. 19 is an explanatory diagram for describing an overview of a seventh embodiment of the present disclosure. FIG. 19 is a diagram showing a schematic configuration example of an optical system according to a seventh embodiment of the present disclosure. FIG. 19 is a diagram showing example lens data of an optical system according to a seventh embodiment of the present disclosure. FIG. 19 is a diagram showing example aspherical coefficient data of an optical system according to a seventh embodiment of the present disclosure. FIG. 19 is a diagram showing aberration data of an optical system according to a seventh embodiment of the present disclosure. FIG. 12 is a diagram showing example lens data of an optical system according to an eighth embodiment of the present disclosure. FIG. 13 is a diagram showing example aspherical coefficient data of an optical system according to an eighth embodiment of the present disclosure. FIG. 14 is a diagram showing aberration data of an optical system according to an eighth embodiment of the present disclosure. FIG. 15 is a diagram showing a schematic configuration example of an optical system according to a ninth embodiment of the present disclosure. FIG. 16 is a diagram showing example lens data of an optical system according to a ninth embodiment of the present disclosure. FIG. 17 is a diagram showing example aspherical coefficient data of an optical system according to a ninth embodiment of the present disclosure. FIG. 18 is a diagram showing example lens data of an optical system according to a tenth embodiment of the present disclosure. FIG. 19 is a diagram showing example aspherical coefficient data of an optical system according to a tenth embodiment of the present disclosure. FIG. 19 is a diagram showing aberration data (part 1) of an optical system according to a tenth embodiment of the present disclosure. FIG. 19 is a diagram showing aberration data (part 2) of an optical system according to a tenth embodiment of the present disclosure. FIG. 11 is a diagram showing a schematic configuration example of an optical system according to an eleventh embodiment of the present disclosure. FIG. 12 is a diagram showing example lens data of an optical system according to an eleventh embodiment of the present disclosure.FIG. 12 is a diagram illustrating an example of aspherical coefficient data of an optical system according to an eleventh embodiment of the present disclosure. FIG. 13 is a diagram illustrating aberration data (part 1) of an optical system according to an eleventh embodiment of the present disclosure. FIG. 14 is a diagram illustrating aberration data (part 2) of an optical system according to an eleventh embodiment of the present disclosure. FIG. 15 is a diagram illustrating a first example of an arrangement of a light source and a camera according to an eleventh embodiment of the present disclosure. FIG. 16 is a diagram illustrating an example of an image captured by a camera according to an eleventh embodiment of the present disclosure. FIG. 17 is a diagram illustrating a second example of an arrangement of a light source and a camera according to an eleventh embodiment of the present disclosure. FIG. 18 is an explanatory diagram illustrating an overview of a twelfth embodiment of the present disclosure. FIG. 19 is a diagram illustrating an example of a schematic configuration of an optical system according to a twelfth embodiment of the present disclosure. FIG. 20 is a diagram illustrating example lens data of an optical system according to a twelfth embodiment of the present disclosure. FIG. 21 is a diagram illustrating example aspherical coefficient data of an optical system according to a twelfth embodiment of the present disclosure. FIG. 22 is a diagram illustrating aberration data (part 1) of an optical system according to a twelfth embodiment of the present disclosure. FIG. 12 is a diagram illustrating an example schematic configuration of an optical system according to a thirteenth embodiment of the present disclosure. FIG. 13 is a diagram illustrating example lens data of the optical system according to the thirteenth embodiment of the present disclosure. FIG. 14 is a diagram illustrating example lens data of the optical system according to the fourteenth embodiment of the present disclosure. FIG. 15 is a diagram illustrating example aspherical coefficient data of the optical system according to the fifteenth embodiment of the present disclosure. FIG. 16 is a diagram illustrating example aberration data of the optical system according to the fifteenth embodiment of the present disclosure. FIG. 17 is a diagram illustrating example data of the optical systems according to the thirteenth to fifteenth embodiments of the present disclosure. FIG. 18 is an external view of a head-mounted display.

[0009] Preferred embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. In this specification and the drawings, components having substantially the same functional configurations are designated by the same reference numerals, and redundant description will be omitted. Furthermore, in this specification and the drawings, multiple components having substantially the same or similar functional configurations may be distinguished by adding different letters after the same reference numeral. However, when there is no particular need to distinguish between multiple components having substantially the same or similar functional configurations, only the same reference numerals will be used.

[0010] The drawings referred to in the following description are for explaining and facilitating understanding of one embodiment of the present disclosure, and for the sake of clarity, the shapes, dimensions, ratios, etc. shown in the drawings may differ from the actual ones. Furthermore, the design of the devices shown in the drawings can be modified as appropriate, taking into consideration the following description and known technologies.

[0011] In the following description, the terms "positive power" and "negative power" used in relation to lenses refer to the strength with which a lens bends a light ray, and the power can be changed by adjusting the refractive index or curvature of the lens, for example. Furthermore, in the following description, the "positive power" of a lens refers to the strength with which light is bent in a converging direction (inside the lens), while the "negative power" refers to the strength with which light is bent in a diverging direction (outside the lens).

[0012] In the following description, the term "chief ray" refers to incident light passing through the center of the optical system. Furthermore, the term "upper ray" refers to incident light passing through an edge located above the central axis (optical axis) of the optical system to form an image, and the term "lower ray" refers to incident light passing through an edge located below the central axis of the optical system to form an image. Furthermore, the term "marginal ray" refers to light passing through the outer periphery of the pupil plane of the optical system. Furthermore, in the following description, the term "pupil plane" refers to the plane at which light entering the optical system intersects with the axis of the optical system.

[0013] The description will be given in the following order: 1. Background to the Creation of the Embodiments of the Present Disclosure 1.1 Background 1.2 Overview 1.2.1 Configuration 1 1.2.2 Configuration 2 1.2.3 Configuration 3 1.2.4 Configuration 4 1.2.5 Configuration 5 2. First Embodiment 2.1 Detailed Configuration 2.2 Modified Example 3. Second Embodiment 4. Third Embodiment 5. Fourth Embodiment 6. Fifth Embodiment 6.1 Configuration 6 6.2 Detailed Configuration 7. Sixth Embodiment 7.1 Detailed Configuration 7.2 Modified Example 8. Seventh Embodiment 8.1 Configuration 7 8.2 Detailed Configuration 9. Eighth Embodiment 10. Ninth Embodiment 11. Tenth Embodiment 12. Eleventh Embodiment 12.1 Detailed Configuration of Optical System 12.2 Eye Tracking Mechanism 13. Twelfth Embodiment 14. Thirteenth Embodiment 15. 14th embodiment 16. 15th embodiment 17. Summary 18. Application example 19. Supplementary information

[0014] <<1. Background to the Creation of the Embodiments of the Present Disclosure>> <1.1 Background> First, the background to the creation of the embodiments of the present disclosure by the inventors will be described.

[0015] As described above, there are known techniques for displaying images rendered using AR or VR on, for example, an HMD or AR glasses worn by a user. Such HMDs or AR glasses mainly include a display element that displays the image and an optical system that guides the display element to the user's eyes.

[0016] Such HMDs and AR glasses are desirably small because they are worn on the user's head. Furthermore, the optical systems of such HMDs and AR glasses are desirably high optical performance and a wide viewing angle (wide angle of view) to provide users with realistic images. Furthermore, in recent years, it has become desirable for such HMDs and AR glasses to be manufactured more inexpensively in order to further popularize them.

[0017] However, in the optical systems according to the conventional techniques proposed so far, it is difficult to avoid using a large display element when trying to achieve a wide angle of view. Furthermore, the conventional techniques have limitations in achieving a short focal length. In other words, the conventional techniques have limitations in realizing an optical system that has high optical performance, a wide angle of view, and yet allows for the miniaturization of HMDs and AR glasses.

[0018] In view of these circumstances, the present inventors have come up with an embodiment of the present disclosure that realizes an optical system that has high optical performance and a wide angle of view (e.g., FOV (Field Of View) = 80 to 120 degrees), while enabling the miniaturization of HMDs and AR glasses. In other words, according to the embodiment of the present disclosure, it is possible to provide an optical system that has high optical performance and a wide angle of view, while enabling the miniaturization of HMDs, AR glasses, and the like. Below, an outline of the embodiment of the present disclosure created by the present inventors will be sequentially described.

[0019] <1.2 Overview> Next, an overview of an embodiment of the present disclosure will be described with reference to FIGS. 1 to 7. FIG.

[0020] 1.2.1 Configuration 1 First, an overview of "Configuration 1" common to optical systems according to embodiments of the present disclosure will be described with reference to Fig. 1 to Fig. 3 and Fig. 8. Fig. 1 to Fig. 3 are explanatory diagrams for explaining the overview of embodiments of the present disclosure. Fig. 8 is a diagram showing a schematic configuration example of an optical system 1 according to a first embodiment, given as an example of an embodiment of the present disclosure.

[0021] As shown in FIG. 8 , the optical system 1 according to the embodiment of the present disclosure includes a first optical system 10 and a second optical system 20, arranged in this order from the user's pupil 500 side (pupil plane 500a side) to the display element 502 side (display element surface 502a side). Note that FIG. 8 also illustrates a display element 502 that constitutes a display device in combination with the optical system 1. The first optical system 10 includes a first reflecting surface (semi-transmissive reflecting surface) 102 that reflects light emitted from the pupil 500 side toward the pupil 500 side, and a second reflecting surface 112 that reflects light reflected toward the pupil 500 side toward the display element 502 side. Hereinafter, this configuration of the first optical system 10 will be referred to as "element 1." Furthermore, the first reflecting surface 102 has a concave shape with a concave surface facing the pupil 500 side, and can form an intermediate image 510 on the pupil 500 side. Hereinafter, this configuration of the first reflecting surface 102 will be referred to as "element 2." Furthermore, the pupil 500 side of the first reflecting surface 102 is filled with a material having a refractive index greater than 1. Hereinafter, this configuration of the first reflecting surface 102 will be referred to as "element 3." Furthermore, the second optical system 20 is disposed closer to the display element 502 than the intermediate image plane 510a where the intermediate image 510 is formed, and is configured so that the intermediate image plane and the display element surface have a conjugate relationship. Furthermore, the second optical system 20 has at least three lenses, at least two of which have different Abbe numbers, and the second optical system 20 as a whole has positive power. Hereinafter, this configuration of the second optical system will be referred to as "element 4." Furthermore, the entire configuration including the above-described elements 1 to 4 will be referred to as "configuration 1." The Abbe number is a quantity related to the dispersion of light in transparent materials such as optical glass, and is the reciprocal of the dispersive power. The larger the Abbe number, the smaller the change in refractive index with wavelength.

[0022] (Element 1) First, element 1 will be described with reference to Fig. 1. In detail, the upper part of Fig. 1 shows a first optical system 10 having one reflecting surface 102, and the lower part of Fig. 1 shows a first optical system 10 having two reflecting surfaces 102 and 112. As is clear from Fig. 1, by providing the first optical system 10 with two reflecting surfaces 102 and 112, the optical path can be folded, and therefore the length of the optical system 1 in the optical axis direction can be shortened.

[0023] (Element 2) Next, element 2 will be described with reference to Fig. 2. Fig. 2 shows a typical eyepiece optical system that does not have an intermediate image plane. The size d of the panel (display element) ＬＣＯＳ While maintaining the angle of view θ ＦＯＶ If we try to increase the focal length f, as can be seen from the equation in Figure 2, we will have to reduce the focal length f. For example, if the panel size d ＬＣＯＳ has been reduced in size from 1.3 inches to 0.7 inches, and the angle of view θ ＦＯＶ Increasing the focal length f from 70 degrees to 120 degrees would require reducing the focal length f to approximately 1 / 5. However, in a typical eyepiece optical system configuration such as that shown in Figure 2, this is difficult to achieve, given that optical performance such as correction of field curvature and lateral chromatic aberration must also be ensured.

[0024] Therefore, in the embodiment of the present disclosure, by providing the optical system 1 with an intermediate image plane 510a, it is possible to separate the optical system into two optical systems with the intermediate image plane 510a in between, that is, the functions and roles of the first optical system 10 for increasing the angle of view and the second optical system 20 for reducing the size of the panel (display element 502) can be separated. Then, in the embodiment of the present disclosure, by using the two optical systems 10 and 20 with different roles in this way, it is possible to achieve both an increase in the angle of view and a reduction in the size of the panel (display element 502).

[0025] (Element 3) Next, element 3 will be described with reference to FIG. 3 . There are two advantages to filling the pupil 500 side of the first reflecting surface 102 with a material having a refractive index greater than 1. The first advantage is that, as shown on the left side of FIG. 3 , by further imparting semi-transmissive reflecting properties to the first reflecting surface 102, the height direction of the first optical system 10 can be shortened. The second advantage is that, as shown on the right side of FIG. 3 , the first optical system 10 can increase the optical path length to (n−1)L by the refractive index n, which is longer than the air length L. Therefore, the curvature can be reduced while keeping the size of the first optical system 10 the same, thereby suppressing the occurrence of aberrations and improving optical performance.

[0026] (Element 4) Next, element 4 will be described. The second optical system 20 is conjugate between the intermediate image plane and the display element surface, and therefore the second optical system 20 itself must compensate for each aberration. Therefore, in an embodiment of the present disclosure, a technique called anastigmatism is used, which eliminates spherical aberration, coma, field curvature, and astigmatism. In an embodiment of the present disclosure, for example, a configuration of three lenses or three lens groups is used to correct all spherical aberration, coma, field curvature, and astigmatism. However, when correcting chromatic aberration using refractive lenses, it is not possible to achieve this with three lenses having the same Abbe number. Therefore, in an embodiment of the present disclosure, two of the multiple lenses have different Abbe numbers.

[0027] In each embodiment of the present disclosure, since the configuration 1 includes elements 1 to 4 described above, it is possible to provide an optical system 1 that has high optical performance, a wide angle of view, and yet enables miniaturization of HMDs, AR glasses, and the like.

[0028] 4 and 8, an overview of the optical system according to an embodiment of the present disclosure, specifically, "Configuration 2" common to the first to sixth, tenth, and eleventh embodiments of the present disclosure, will be described. Fig. 4 is an explanatory diagram for explaining the overview of the embodiment of the present disclosure.

[0029] 8 , the first optical system 10 according to the embodiment of the present disclosure includes a first optical element 100 and a second optical element 110, arranged in this order from the pupil 500 side to the display element 502 side. The first optical element 100 has a function of reflecting a portion of light as a second reflecting surface 112. The second optical element 110 has a transmitting surface 104 and a semi-transmitting reflective surface 102 having a concave shape, which serves as the first reflecting surface and is disposed on the display element 502 side of the transmitting surface 104. Furthermore, the space between the transmitting surface 104 and the semi-transmitting reflective surface 102 is filled with a material having a refractive index greater than 1.4 and less than 2.2. In detail, the first optical system 10 is configured so that light emitted from the pupil 500 side passes through the first optical element 100, passes through the transmissive surface 104, is reflected by the semi-transmissive reflective surface 102, passes through the transmissive surface 104, is reflected by the first optical element 100, passes through the transmissive surface 104, and passes through the semi-transmissive reflective surface 102. The second optical system 20 is configured to have a positive power overall with respect to light from the first optical system 10. In detail, all surfaces of the second optical system 20 have a common axis of rotational symmetry. In the embodiment of the present disclosure, the intermediate image 510 is formed between the semi-transmissive reflective surface 102 of the second optical element 110 and the first optical element 100. Furthermore, when the focal length of the semi-transmissive reflective surface 102 is fR and the physical length between the vertices of the surface of the first optical element 100 facing the display element 502 to the semi-transmissive reflective surface 102 is LR, it is preferable that the following mathematical expression (1) is satisfied: Hereinafter, this optical system configuration will be referred to as "Configuration 2."

[0030] Next, configuration 2 will be described with reference to FIG. 4 . Generally, in order to reduce the overall size of an optical system, it is necessary to increase the power of each surface included in the optical system. Therefore, in the embodiment of the present disclosure, by increasing the power of the semi-transmissive reflective surface 102, the focal point is formed closer to the first optical element 100 side than in the comparative example, as shown in FIG. 4 . As a result, the distance between the first optical element 100 and the display element 502 can be shortened, which enables the optical system 1 to be reduced in size.

[0031] Furthermore, if LR / fR exceeds the upper limit (1.2), the power of the semi-transmissive reflective surface 102 increases, which contributes to the miniaturization of the optical system 1, but causes aberrations and degrades the optical performance. On the other hand, if LR / fR falls below the lower limit (0.5), the power of the semi-transmissive reflective surface 102 decreases, which causes the intermediate image plane 510a to move toward the display element 502, resulting in an increase in the size of the optical system 1. Therefore, in an embodiment of the present disclosure, it is preferable to set LR / fR as shown in the above-mentioned formula (1) in order to miniaturize the optical system 1 while avoiding degradation of optical performance.

[0032] As described above, it is preferable to have configuration 2 in an embodiment of the present disclosure, and by doing so, it is possible to provide an optical system 1 that has high optical performance, a wide angle of view, and yet enables miniaturization of HMDs, AR glasses, and the like.

[0033] 5 and 8, an overview of the optical system according to an embodiment of the present disclosure, specifically, "Configuration 3" common to the first to fourth embodiments of the present disclosure, will be described. Fig. 5 is an explanatory diagram for explaining the overview of the embodiment of the present disclosure.

[0034] 8, the second optical system 20 according to the embodiment of the present disclosure has, in order from the pupil 500 side to the display element 502 side, a first lens group 210 having negative power and a second lens group 220 having positive power. Furthermore, when the power of the first lens group 210 is Φ1 and the overall power of the second optical system 20 is Φ, it is preferable that the following mathematical formula (2) be satisfied. Hereinafter, the configuration of such an optical system will be referred to as "Configuration 3."

[0035] Next, configuration 3 will be described with reference to FIG. 5 . In detail, the upper part of FIG. 5 shows a second optical system 20 configured with lenses having positive power, and the lower part of FIG. 5 shows a second optical system 20 configured with lenses having positive power and lenses having negative power. In the first optical system 10, the power of the semi-transmissive reflective surface 102 is increased to achieve a wider angle and a smaller size. As a result, the curvature of the semi-transmissive reflective surface 102 increases, and light reflected by the semi-transmissive reflective surface 102 enters the second optical system 20 while maintaining a large angle. In such a case, as shown in the upper part of FIG. 5 , in the second optical system 20 configured only with lenses having positive power, if the length in the optical axis direction of the optical system 1 is to be shortened, it becomes difficult to guide a group of light rays having a large angle incident on the outermost periphery of the entrance surface of the second optical system 20 toward the display element 502. 5, in the second optical system 20 including a lens having positive power and a lens having negative power, even if the length in the optical axis direction of the optical system 1 is shortened, a group of light rays having a large angle that are incident on the outermost periphery of the entrance surface of the second optical system 20 can be deflected and guided toward the display element 502. Therefore, configuration 3 makes it possible to reduce the size of the display element 502 while shortening the length in the optical axis direction of the optical system 1. For example, in this embodiment, it is possible to achieve a size (diagonal length) of the display element 502 of 1 inch or less.

[0036] Furthermore, if Φ1 / Φ exceeds the upper limit (−0.2), the power Φ1 of the first lens group 210 having negative power becomes too large, resulting in increased aberrations and thus degradation of optical performance. On the other hand, if Φ1 / Φ falls below the lower limit (−0.5), the power Φ1 of the first lens group 210 having negative power becomes small, resulting in an increase in the size of the optical system 1. Therefore, in the embodiments of the present disclosure, it is preferable to set Φ1 / Φ as in the above-mentioned formula (2) in order to achieve a reduction in the size of the optical system 1 while avoiding degradation of optical performance.

[0037] As described above, it is preferable to have configuration 3 in an embodiment of the present disclosure, and by doing so, it is possible to provide an optical system 1 that has high optical performance, a wide angle of view, and yet enables miniaturization of HMDs, AR glasses, and the like.

[0038] 5, 6, and 8, an overview of the optical system according to an embodiment of the present disclosure, specifically, "Configuration 4" common to the first to fourth embodiments of the present disclosure, will be described. Fig. 6 is an explanatory diagram for explaining the overview of the embodiment of the present disclosure.

[0039] The first lens group 210 according to the embodiment of the present disclosure is adjacent to the second optical element 110 on the display element 502 side, for example, as shown in Fig. 8 , and has the function of reducing the light ray angle at the peripheral edge. Furthermore, as shown in Fig. 6 , when the chief ray angle at the outermost periphery from the second optical element 110 to the display element 502 side is Ang1, and the chief ray angle at the outermost periphery from the first lens group 210 to the second lens group 220 is Ang2, it is preferable that the following mathematical formula (3) be satisfied. Hereinafter, such an optical system configuration will be referred to as "Configuration 4."

[0040] If Ang1 / Ang2 exceeds the upper limit (3.5), the amount of light that is reflected by the first lens group 210 becomes too large, making it difficult to guide the light toward the display element 502. On the other hand, if Ang1 / Ang2 falls below the lower limit (1.7), the amount of light that is reflected by the first lens group 210 becomes too small, resulting in an increase in the size of the optical system 1. Therefore, in an embodiment of the present disclosure, in order to reduce the size of the optical system 1, it is preferable to set Ang1 / Ang2 as shown in the above-mentioned formula (3).

[0041] As described above, it is preferable to have configuration 4 in an embodiment of the present disclosure, and by doing so, it is possible to provide an optical system 1 that has high optical performance, a wide angle of view, and yet allows for the miniaturization of HMDs, AR glasses, and the like.

[0042] 6, 7, and 8, an overview of the optical system according to an embodiment of the present disclosure, specifically, "Configuration 5" common to the first, second, and tenth embodiments of the present disclosure, will be described. Fig. 7 is an explanatory diagram for explaining the overview of an embodiment of the present disclosure.

[0043] In an embodiment of the present disclosure, for example, as shown in Fig. 6 , the ray angle at which a lower ray of marginal rays among light rays incident from the pupil plane 500a at a field of view of 60 degrees is incident on the second lens group 220 is defined as Ang3, and the ray angle at which the lower ray is incident from the second lens group 220 on the display element 502 is defined as Ang4. Furthermore, as shown in Fig. 7 , the distance on the optical axis 520 from the pupil plane 500a to the surface of the first optical element 100 located closest to the pupil plane 500a is defined as A. Furthermore, when the pupil 500 is moved away from the first optical element 100 in the direction of the optical axis 520, the field of view is set to 60 degrees, and there is no ray vignetting in the second optical system 20, the distance on the optical axis 520 from the pupil plane 500a to the surface of the first optical element 100 located closest to the pupil plane 500a is defined as A'. Furthermore, the exit pupil position of the first optical system 10 when the distance is A is defined as P, and the exit pupil position of the first optical system 10 when the distance is A' is defined as P'. In such a case, in an embodiment of the present disclosure, it is preferable to satisfy the following mathematical expression (4). Hereinafter, such an optical system configuration will be referred to as "Configuration 5."

[0044] As shown in Fig. 7 , when a user changes from a central gaze state (top left of Fig. 7 ) to a state in which the eyeball is rotated to view the periphery (bottom right of Fig. 7 ), the user's pupil shifts from the optical axis 520 to a direction substantially perpendicular to the optical axis 520 while being tilted. Therefore, in an embodiment of the present disclosure, in such a case, a design is performed assuming that the distance A changes to a distance A', thereby dealing with the change in the optical path between the pupil 500 and the display element 502. Because of this change in optical path, the light rays from the first optical system 10 pass below the optical axis 520. Therefore, if the distance A' is made longer than the distance A, the light rays will deviate from the second optical system 20, i.e., there is an increased possibility of vignetting of the light rays.

[0045] Therefore, in order to avoid such vignetting of the light beams, it is necessary to move the light beams incident on the second lens group 220 closer to the optical axis 520. Therefore, in order to return the angle of the light beams incident on the second lens group 220 to the optical axis 520, it is preferable to satisfy the above-mentioned mathematical formula (4). Note that when Ang4 / Ang3 falls below the lower limit (-7), Ang3 becomes large, causing vignetting. On the other hand, when Ang4 / Ang3 exceeds the upper limit (1.5), the positive power of the second lens group 220 becomes too large, degrading the optical performance of the optical system 1. Therefore, in the embodiments of the present disclosure, it is preferable to satisfy the above-mentioned mathematical formula (4).

[0046] As described above, it is preferable to have configuration 5 in an embodiment of the present disclosure, and by doing so, it is possible to provide an optical system 1 that has high optical performance and a wide angle of view, even when taking into account the rotation of the pupil 500, and that enables the miniaturization of HMDs, AR glasses, and the like.

[0047] That is, as described above, in this embodiment, the optical system 1, 1a having at least one of the above-described configurations 1 to 5 has high optical performance and a wide angle of view, while enabling miniaturization of HMDs, AR glasses, etc. Details of each embodiment of the present disclosure will be described below.

[0048] <<2. First Embodiment>> <2.1 Detailed Configuration> First, an optical system 1 according to a first embodiment of the present disclosure will be described with reference to FIGS. 8 to 10 . FIG. 8 is a diagram illustrating a schematic configuration example of the optical system 1 according to this embodiment. FIG. 9 is a diagram illustrating example lens data for the optical system 1 according to this embodiment. In detail, surface numbers are assigned in the order of surfaces reached by light from the pupil 500 side, and the shape type (symbols are assigned in the case of aspherical surfaces), radius of curvature, thickness (mm), refractive index (nd), Abbe number (vd), and annotations of each surface are shown in that order. In detail, for example, in the lens data, the surface indicated by surface number s1 indicates the pupil surface 500a (pupil 500). Note that in this lens data, the first optical element 100 is referred to as "optical element 1," the second optical element 110 as "optical element 2," the first lens group 210 as "lens group 1," and the second lens group 220 as "lens group 2." FIG. 10 is a diagram showing an example of aspherical coefficient data for the optical system 1 according to this embodiment, in which the numbers "SXX" assigned to each surface correspond to the surface numbers in FIG. 8, and K and Am (m=3, 4, 5, 6, 7, 8, 9, 10) in FIG. 10 are the values ​​of the coefficients K and Am in the aspherical formula given by the following mathematical formula (5):

[0049] In the formula (5), Zd is the depth of the aspherical surface, Y is the height, and C is the curvature.

[0050] 11 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically longitudinal aberration, astigmatism, and distortion, and FIG. 12 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically lateral aberration.

[0051] As shown in FIG. 8 , the optical system 1 according to this embodiment includes a first optical system 10 and a second optical system 20, arranged in that order from the user's pupil 500 side to the display element 502 side. The first optical system 10 includes a first reflecting surface (semi-transmissive reflecting surface) 102 that reflects light emitted from the pupil 500 side toward the pupil 500 side, and a second reflecting surface 112 that reflects the light reflected toward the pupil 500 side toward the display element 502 side. The first reflecting surface 102 has a concave shape and can form an intermediate image 510 on the pupil 500 side. The pupil 500 side of the first reflecting surface 102 is filled with a material whose refractive index is greater than 1. The second optical system 20 is disposed closer to the display element 502 than an intermediate image plane on which the intermediate image 510 is formed, and is configured so that the intermediate image plane and the display element plane have a conjugate relationship. The second optical system 20 has at least three lenses, two of which have different Abbe numbers, and the second optical system 20 as a whole has positive power.

[0052] Furthermore, the first optical system 10 according to this embodiment includes a first optical element 100 and a second optical element 110, arranged in this order from the pupil 500 side to the display element 502 side. The first optical element 100 has a second reflecting surface 112 that functions to reflect a portion of light. The second optical element 110 has a transmitting surface 104 and a semi-transmitting reflecting surface 102 that has a concave shape and is disposed on the display element 502 side with respect to the transmitting surface 104 as the first reflecting surface. Furthermore, the space between the transmitting surface 104 and the semi-transmitting reflecting surface 102 is filled with a material having a refractive index greater than 1.4 and less than 2.2. In detail, the first optical system 10 is configured such that light emitted from the pupil 500 side passes through the first optical element 100, passes through the transmitting surface 104, is reflected by the semi-transmitting reflecting surface 102, passes through the transmitting surface 104, is reflected by the first optical element 100, passes through the transmitting surface 104, and passes through the semi-transmitting reflecting surface 102. Furthermore, the second optical system 20 is configured to have a positive power overall with respect to light from the first optical system 10. More specifically, all surfaces of the second optical system 20 have a common axis of rotational symmetry. Furthermore, the intermediate image 510 is formed between the semi-transmissive reflective surface 102 of the second optical element 110 and the first optical element 100. Furthermore, in this embodiment, when the focal length of the semi-transmissive reflective surface 102 is defined as fR and the physical length between the vertices of the surface of the first optical element 100 on the display element 502 side and the semi-transmissive reflective surface 102 is defined as LR, LR / fR is 1.01, which satisfies the above formula (1).

[0053] Furthermore, the second optical system 20 according to this embodiment has, in order from the pupil 500 side to the display element 502 side, a first lens group 210 having negative power and a second lens group 220 having positive power. Furthermore, when the power of the first lens group 210 is Φ1 and the overall power of the second optical system 20 is Φ, Φ1 / Φ is "-0.15", which satisfies the above formula (2).

[0054] Furthermore, the first lens group 210 according to this embodiment is adjacent to the second optical element 110 on the display element 502 side, and has the function of reducing the light ray angle at the periphery. Furthermore, if the chief ray angle at the outermost periphery from the second optical element 110 to the display element 502 side is Ang1, and the chief ray angle at the outermost periphery from the first lens group 210 to the second lens group 220 is Ang2, Ang1 / Ang2 is 1.74, which satisfies the following mathematical expression (3).

[0055] Furthermore, in this embodiment, the ray angle at which a lower ray of the marginal rays among the rays incident from the pupil plane 500a at a field of view of 60 degrees is incident on the second lens group 220 is defined as Ang3, and the ray angle at which the lower ray is incident from the second lens group 220 on the display element 502 is defined as Ang4. Furthermore, the distance on the optical axis 520 from the pupil plane 500a to the surface of the first optical element 100 located closest to the pupil plane 500a is defined as A. Furthermore, when the pupil 500 is moved away from the first optical element 100 in the direction of the optical axis 520, the field of view is set to 60 degrees, and there is no ray vignetting in the second optical system 20, the distance on the optical axis 520 from the pupil plane 500a to the surface of the first optical element 100 located closest to the pupil plane 500a is defined as A'. Furthermore, the exit pupil position of the first optical system 10 when the distance is A is denoted by P, and the exit pupil position of the first optical system 10 when the distance is A' is denoted by P'. In this case, in this embodiment, Ang4 / Ang3 is "-0.17" and (A'-A) / (P'-P) is "-0.59", which satisfies the above formula (4).

[0056] Furthermore, the optical system 1 according to this embodiment may have a third optical element 300 arranged on the display element 502 side with respect to the second optical element 110. In this embodiment, the first optical element 100 and the third optical element 300 may be parallel flat plates. Details (modifications) of the first optical element 100 and the third optical element 300 will be described later.

[0057] In addition, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Figures 11 and 12 were obtained. As shown in Figures 11 and 12, in this embodiment, it was found that focus variation (aberration) was suppressed over a wide wavelength range, and aberration was improved. In other words, as can be seen from the aberrations shown in Figures 11 and 12 obtained by optical simulation, the optical system 1 according to this embodiment has high optical characteristics.

[0058] That is, this embodiment includes the above-described configurations 1, 2, 3, 4, and 5. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while enabling miniaturization of HMDs, AR glasses, and the like.

[0059] <2.2 Modification> Next, a modification of this embodiment will be described with reference to Fig. 13. Fig. 13 is an explanatory diagram for explaining a schematic configuration example of a modification of this embodiment, showing the main parts of this modification.

[0060] In this modification, the first optical element 100 of the first optical system 10 may include a first wave plate 402 that shifts the phase of the vertically polarized component of light by 90 degrees. Furthermore, in this modification, the second optical system 20 may include second wave plates 404a and 404b that shift the phase of the vertically polarized component of light by 90 degrees. The slow axes of the first wave plate 402 and the second wave plates 404a and 404b are orthogonal or parallel to each other. Furthermore, in this modification, the first wave plate 402 may further include a first polarizing plate 412 that transmits only linearly polarized light and reflects other polarized light, located closer to the pupil 500 than the first wave plate 402. The first polarizing plate 412 can limit the polarized light that enters the first wave plate 402. Furthermore, the second optical system 20 may further include a second polarizing plate 414 that transmits only linearly polarized light and reflects other polarized light, located closer to the display element 502 than the second wave plates 404a and 404b. The second polarizing plate 414 can limit the polarized light that enters the second wave plate 404b.

[0061] 13 shows an example of the arrangement of the first wave plate 402, the second wave plates 404a and 404b, the first polarizing plate 412, and the second polarizing plate 414. For example, the optical system 1 may have the first polarizing plate 412 and the first wave plate 402 as the first optical element 100 of the first optical system 10. Furthermore, the optical system 1 may have the second wave plates 404a and 404b as the third optical element 300 arranged on the display element 502 side of the second optical element 110, as shown in FIG.

[0062] In this modification, by combining the optical system 1 with the configuration shown in FIG. 13, it is possible to achieve higher optical performance.

[0063] <<3. Second Embodiment>> Next, an optical system 1 according to a second embodiment of the present disclosure will be described with reference to FIGS. 14 to 18 . FIG. 14 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. FIG. 15 is a diagram showing example lens data of the optical system 1 according to this embodiment, and the contents are the same as those in FIG. 9 . FIG. 16 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, and the contents are the same as those in FIG. 10 . FIG. 17 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 18 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0064] Although detailed description will be omitted, the optical system 1 according to this embodiment also includes the above-described configurations 1, 2, 3, 4, and 5, similarly to the first embodiment. More specifically, in this embodiment, LR / fR is "1.01", satisfying the above mathematical formula (1). In this embodiment, Φ1 / Φ is "-0.21", satisfying the above mathematical formula (2). In this embodiment, Ang1 / Ang2 is "2.01", satisfying the following mathematical formula (3). In this embodiment, Ang4 / Ang3 is "-0.60", and (A'-A) / (P'-P) is "-0.61", satisfying the above mathematical formula (4).

[0065] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 17 and Fig. 18 were obtained. As can be seen from the aberrations shown in Fig. 17 and Fig. 18 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while enabling the miniaturization of HMDs, AR glasses, and the like.

[0066] <<4. Third Embodiment>> Next, an optical system 1 according to a third embodiment of the present disclosure will be described with reference to FIGS. 19 to 23 . FIG. 19 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. FIG. 20 is a diagram showing example lens data of the optical system 1 according to this embodiment, the contents of which are the same as those of FIG. 9 . FIG. 21 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, the contents of which are the same as those of FIG. 10 . FIG. 22 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 23 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0067] Although detailed description will be omitted, the optical system 1 according to this embodiment also includes the above-described configurations 1, 2, 3, 4, and 5, similarly to the first embodiment. More specifically, in this embodiment, LR / fR is "0.96", satisfying the above-described formula (1). In this embodiment, Φ1 / Φ is "-0.38", satisfying the above-described formula (2). In this embodiment, Ang1 / Ang2 is "3.24", satisfying the following formula (3). In this embodiment, Ang4 / Ang3 is "-1.48", and (A'-A) / (P'-P) is "-0.51", satisfying the above-described formula (4). Ang1 and Ang2 in this embodiment are shown in FIG. 19 .

[0068] 22 and 23 obtained by optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while enabling miniaturization of HMDs, AR glasses, and the like.

[0069] 5. Fourth Embodiment Next, an optical system 1 according to a fourth embodiment of the present disclosure will be described with reference to FIGS. 24 to 28 . FIG. 24 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. FIG. 25 is a diagram showing example lens data of the optical system 1 according to this embodiment, the contents of which are the same as those of FIG. 9 . FIG. 26 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, the contents of which are the same as those of FIG. 10 . FIG. 27 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 28 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0070] Although detailed description will be omitted, the optical system 1 according to this embodiment also includes the above-described configurations 1, 2, 3, 4, and 5, similarly to the first embodiment. More specifically, in this embodiment, LR / fR is "0.98", which satisfies the above formula (1). In this embodiment, Φ1 / Φ is "-0.29", which satisfies the above formula (2). In this embodiment, Ang1 / Ang2 is "1.86", which satisfies the following formula (3). In this embodiment, Ang4 / Ang3 is "-1.44", and (A'-A) / (P'-P) is "-0.15", which satisfies the above formula (4).

[0071] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 27 and Fig. 28 were obtained. As can be seen from the aberrations shown in Fig. 27 and Fig. 28 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while enabling the miniaturization of HMDs, AR glasses, and the like.

[0072] <<6. Fifth Embodiment>> <6.1 Configuration 6> Next, "Configuration 6" included in the fifth and sixth embodiments will be described with reference to Fig. 29 and Fig. 30. Fig. 29 is an explanatory diagram for explaining an overview of this embodiment, and Fig. 30 is a diagram showing a schematic configuration example of an optical system 1 according to a fifth embodiment of the present disclosure.

[0073] 30 , for example, the second optical system 20 has a first lens group 210 with positive power on the pupil 500 side, and a second lens group 220 with positive power on the display element 502 side, the chief ray of the second optical system 20 intersecting with an optical axis 520. When the power of the first lens group 210 is Φ1 and the overall power of the second optical system 20 is Φ, it is preferable that the following mathematical expression (6) is satisfied. Hereinafter, this optical system configuration will be referred to as "Configuration 6."

[0074] As shown in Figure 29, in order to converge a light beam that diverges with a large numerical aperture (NA) from an intermediate image 510 (intermediate image plane 510a) on the optical axis 520 while maintaining its size and with good aberration, it is preferable to make the power Φ1 of the first lens group 210 equal to or greater than the overall power Φ of the second optical system 20.

[0075] However, if Φ1 / Φ falls below the lower limit (0.8), the power Φ1 of the first lens group 210 becomes small, resulting in a large optical system 1. On the other hand, if Φ1 / Φ exceeds the upper limit (2.0), the amount of spherical aberration in the first lens group 210 becomes large, resulting in a deterioration in the imaging performance of the optical system 1. Therefore, in the fifth and sixth embodiments, it is preferable to set Φ1 / Φ as in the above-mentioned formula (6).

[0076] As described above, in the fifth and sixth embodiments of the present disclosure, it is preferable to have configuration 6, and by doing so, it is possible to provide an optical system 1 that has high optical performance, a wide angle of view, and yet enables miniaturization of HMDs, AR glasses, and the like.

[0077] 6.2 Detailed Configuration Next, an optical system 1 according to a fifth embodiment of the present disclosure will be described with reference to FIGS. 30 to 34. FIG. 31 is a diagram showing example lens data for the optical system 1 according to this embodiment, and the contents are the same as those in FIG. 9. FIG. 32 is a diagram showing example aspherical coefficient data for the optical system 1 according to this embodiment, and the contents are the same as those in FIG. 10. FIG. 33 is a diagram showing aberration data for the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 34 is a diagram showing aberration data for the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0078] As shown in FIG. 30 , the optical system 1 according to this embodiment includes a first optical system 10 and a second optical system 20, arranged in that order from the user's pupil 500 side to the display element 502 side. The first optical system 10 includes a first reflecting surface (semi-transmissive reflecting surface) 102 that reflects light emitted from the pupil 500 side toward the pupil 500 side, and a second reflecting surface 112 that reflects the light reflected toward the pupil 500 side toward the display element 502 side. The first reflecting surface 102 has a concave shape and can form an intermediate image 510 on the pupil 500 side. The pupil 500 side of the first reflecting surface 102 is filled with a material whose refractive index is greater than 1. The second optical system 20 is disposed closer to the display element 502 than an intermediate image plane on which the intermediate image 510 is formed, and is configured so that the intermediate image plane and the display element plane have a conjugate relationship. The second optical system 20 has at least three lenses, two of which have different Abbe numbers, and the second optical system 20 as a whole has positive power.

[0079] Furthermore, the first optical system 10 according to this embodiment includes a first optical element 100 and a second optical element 110, arranged in this order from the pupil 500 side to the display element 502 side. The first optical element 100 has a second reflecting surface 112 that functions to reflect a portion of light. The second optical element 110 has a transmitting surface 104 and a semi-transmitting reflecting surface 102 that has a concave shape and is disposed on the display element 502 side with respect to the transmitting surface 104 as the first reflecting surface. Furthermore, the space between the transmitting surface 104 and the semi-transmitting reflecting surface 102 is filled with a material having a refractive index greater than 1.4 and less than 2.2. In detail, the first optical system 10 is configured such that light emitted from the pupil 500 side passes through the first optical element 100, passes through the transmitting surface 104, is reflected by the semi-transmitting reflecting surface 102, passes through the transmitting surface 104, is reflected by the first optical element 100, passes through the transmitting surface 104, and passes through the semi-transmitting reflecting surface 102. Furthermore, the second optical system 20 is configured to have a positive power overall with respect to light from the first optical system 10. More specifically, all surfaces of the second optical system 20 have a common axis of rotational symmetry. Furthermore, the intermediate image 510 is formed between the semi-transmissive reflective surface 102 of the second optical element 110 and the first optical element 100. Furthermore, in this embodiment, when the focal length of the semi-transmissive reflective surface 102 is defined as fR and the physical length between the vertices of the surface of the first optical element 100 on the display element 502 side and the semi-transmissive reflective surface 102 is defined as LR, LR / fR is "0.80", which satisfies the above formula (1).

[0080] 30 , the second optical system 20 has a first lens group 210 with positive power on the pupil 500 side, and a second lens group 220 with positive power on the display element 502 side, the chief ray of the second optical system 20 intersecting the optical axis 520. When the power of the first lens group 210 is Φ1 and the overall power of the second optical system 20 is Φ, Φ1 / Φ is 0.96, which satisfies the above formula (6).

[0081] Furthermore, the optical system 1 according to this embodiment may have a third optical element 300 arranged on the display element 502 side relative to the second optical element 110, as shown in FIG. 30, similar to the first embodiment.

[0082] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Figures 32 and 33 were obtained. As shown in Figures 32 and 33, in this embodiment, it was found that focus variation (aberration) was suppressed over a wide wavelength range, and aberration was improved. In other words, as can be seen from the aberrations shown in Figures 32 and 33 obtained by optical simulation, the optical system 1 according to this embodiment has high optical characteristics.

[0083] That is, this embodiment includes the above-described configurations 1, 2, and 6. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while enabling miniaturization of HMDs, AR glasses, and the like.

[0084] <<7. Sixth Embodiment>> <7.1 Detailed Configuration> Next, an optical system 1 according to a sixth embodiment of the present disclosure will be described with reference to FIGS. 35 to 39 . FIG. 35 is a diagram showing an example of a schematic configuration of the optical system 1 according to this embodiment. FIG. 36 is a diagram showing example lens data for the optical system 1 according to this embodiment, the contents of which are the same as those in FIG. 9 . FIG. 37 is a diagram showing example aspherical coefficient data for the optical system 1 according to this embodiment, the contents of which are the same as those in FIG. 10 . FIG. 38 is a diagram showing aberration data for the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 39 is a diagram showing aberration data for the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0085] Although detailed description will be omitted, the optical system 1 according to this embodiment also includes the above-described configurations 1, 2, and 6, similarly to the fifth embodiment. More specifically, in this embodiment, LR / fR is "0.85", which satisfies the above-described formula (1). In this embodiment, Φ1 / Φ is "1.84", which satisfies the above-described formula (6). In this embodiment, as shown in FIG. 35 , a fourth optical element 302 may be disposed in the second lens group 220 of the second optical system 20. Details of the fourth optical element 302 will be described later.

[0086] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 38 and Fig. 39 were obtained. As can be seen from the aberrations shown in Fig. 38 and Fig. 39 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while allowing for the miniaturization of HMDs, AR glasses, and the like.

[0087] <7.2 Modification> Next, a modification of this embodiment will be described with reference to Fig. 40. Fig. 40 is an explanatory diagram for describing a schematic configuration example of an optical system 1 according to a modification of this embodiment, and shows the main parts of this modification.

[0088] In this modification, as shown in Fig. 40, a polarizing element that separates polarized light and has a surface inclined at 45 degrees with respect to the optical axis may be provided as the fourth optical element 302 shown in Fig. 35. In this modification, by using such a configuration, a light source 550 can be provided on the back side of the fourth optical element 302. The light source 550 can irradiate light via the field lens 304. Details of the light source 550 will be described in the eleventh embodiment of the present disclosure.

[0089] <<8. Seventh Embodiment>> <8.1 Configuration 7> Next, a description will be given of "Configuration 7" included in the seventh to ninth embodiments with reference to Fig. 41 and Fig. 42. Fig. 41 is an explanatory diagram for explaining an overview of this embodiment, and Fig. 42 is a diagram showing a schematic configuration example of an optical system 1a according to a seventh embodiment of the present disclosure.

[0090] 42 , for example, the first optical system 10 has a first refractive surface 182 and a second refractive surface 184 in this order from the pupil 500 side to the display element 502 side. Furthermore, the first optical system 10 has, as the first reflecting surface, a first concave reflecting surface 172 that reflects light from the first refractive surface 182 toward the pupil 500 side, and a second concave reflecting surface 174 that reflects light from the first concave reflecting surface 172 toward the display element 502 side. Furthermore, the second refractive surface 184 has a function of refracting light from the second concave reflecting surface 174. Furthermore, in these embodiments, the space between the first refractive surface 182 and the second refractive surface 184 is filled with a material having a refractive index greater than 1.4 and less than 2.2. Furthermore, in these embodiments, the intermediate image 510 is formed between the first concave reflecting surface 172 and the second concave reflecting surface 174. The second optical system 20 also forms the intermediate image on the display element 502, and the light ray from the center of the display element 502 becomes a light ray that is perpendicular to the pupil plane 500a. Hereinafter, this optical system configuration will be referred to as "element 1 of configuration 7."

[0091] (Element 2) Furthermore, in the seventh and ninth embodiments of the present disclosure, for example, as shown in FIG. 42 , the second optical system 20 is configured to be rotationally symmetric, and the pupil plane 500a and the display element surface 502a are arranged parallel to each other. Furthermore, let L1 be the distance from the pupil plane 500a to the first concave reflecting surface 172, in the direction perpendicular to the pupil plane 500a, of the light ray with the longest optical path among the optical paths from the pupil plane 500a to the first concave reflecting surface 172. Furthermore, when let L2 be the distance from the pupil plane 500a to the center of the surface of the second optical system 20 on the pupil 500 side, in the direction perpendicular to the pupil plane 500a, it is preferable that the following mathematical expression (7) be satisfied. Hereinafter, such an optical system configuration will be referred to as "element 2 of configuration 7."

[0092] Furthermore, the optical systems 1 according to the first to sixth embodiments and the optical systems 1a according to the seventh to ninth embodiments of the present disclosure described above can be used in combination with a light guide 350, as shown on the right side of Fig. 41 . In particular, as shown on the right side of Fig. 41 , the light guide 350 is attached to the user's head by being instructed by a frame 352 so as to be positioned in front of the user's pupil 500, and can guide an image projected by a display element 502 to the pupil 500. For example, as shown in the upper right part of Fig. 41 , the optical systems 1 according to the first to sixth embodiments are disposed between the display element 502 and the light guide 350 along the frame 352. Furthermore, as shown in the lower right part of Fig. 41 , the optical systems 1a according to the seventh to ninth embodiments are disposed between the display element 502 and the light guide 350 along the frame 352. The light guide 350 can form an image of light from the first optical system 10 and the second optical system 20 of the optical systems 1 and 1a on the pupil 500.

[0093] Incidentally, light traveling inside the light guide 350 is guided to the pupil 500 while repeatedly reflecting inside (on the inner wall of) the light guide 350, and the more times the light is reflected, the more the brightness of the light deteriorates. Therefore, in order to avoid deterioration in brightness, it is preferable to shorten the length of the light guide 350.

[0094] For example, as shown in the upper right part of FIG. 41 , if the optical system 1 according to the first to sixth embodiments is arranged along the frame 352, the length of the light guide 350 increases and the design freedom of the frame 352 decreases. Therefore, for example, as shown in the lower right part of FIG. 41 , if the optical system 1a according to the seventh to ninth embodiments is arranged along the frame 352, the length of the light guide 350 decreases and the design freedom of the frame 352 increases. Furthermore, the light guide 350 and the frame 352 are generally arranged so as to intersect perpendicularly. Therefore, it is preferable that the pupil plane 500a of the optical system 1a that guides light to the light guide 350 and the display element surface 502a are arranged parallel to each other. Therefore, in order to reduce the length of the light guide 350 and the size of the optical system 1a while keeping these arrangement constraints in mind, it is more preferable to make L1 / L2 satisfy the above formula (7), as shown in the left part of FIG. 41 .

[0095] If the second optical system 20 is moved to the right in the left diagram of Fig. 41 so that L1 / L2 falls below the lower limit (0.8), the optical system 1 becomes larger. On the other hand, if the second optical system 20 is moved to the left in the left diagram of Fig. 41 so that L1 / L2 exceeds the upper limit (1.25), the second optical system 20 interferes with the first optical system 10. Therefore, in the seventh and ninth embodiments, it is preferable to set L1 / L2 as in the above-mentioned formula (7).

[0096] As described above, in the seventh to ninth embodiments of the present disclosure, it is preferable to have element 1 of configuration 7, and it is further preferable to have element 2 of configuration 7. In this way, according to these embodiments, it is possible to provide an optical system 1a that has high optical performance and a wide angle of view, while enabling the miniaturization of HMDs, AR glasses, and the like.

[0097] 8.2 Detailed Configuration Next, an optical system 1a according to a seventh embodiment of the present disclosure will be described with reference to FIGS. 42 to 45 . FIG. 43 is a diagram showing example lens data for the optical system 1a according to this embodiment. In detail, surface numbers are assigned in the order of the surfaces reached by light from the pupil 500 side, and the shape type (symbols are assigned in the cases of aspherical surfaces, free-form surfaces, etc.), radius of curvature, thickness (mm), refractive index (nd), Abbe number (vd), and annotations for each surface are shown in that order. In detail, for example, in the lens data, the surface indicated by surface number s1 indicates the pupil surface 500a (pupil 500). Furthermore, FIG. 44 is a diagram showing example aspherical coefficient data and example free-form surface data for the optical system 1 according to this embodiment. The numbers "SXX" assigned to each surface correspond to the surface numbers in FIG. 43 . In Fig. 44, K, Am, and ARm (m = 3, 4, 5, 6, 7, 8, 9, 10) are the values ​​of the coefficients K and Am (ARm) in the aspherical surface formula shown in the above formula (5). In Fig. 44, XnYm is the coefficient indicated by Cj (coefficient of the xy polynomial) in the free-form surface formula shown in the following formula (8). Furthermore, XDE, YDE, and ZDE are decentering data and indicate the shift amounts in the X, Y, and Z directions, respectively.

[0098] In equation (8), Z is the amount of sag parallel to the central axis, c is the curvature at the vertex of the surface, k is the conic constant, and h is the distance from the origin on the central axis in a plane that intersects with the origin perpendicularly.

[0099] FIG. 45 is a diagram showing aberration data of the optical system 1a according to this embodiment, specifically showing lateral aberration.

[0100] As shown in FIG. 42 , the optical system 1a according to this embodiment includes a first optical system 10 and a second optical system 20, arranged in that order from the user's pupil 500 side to the display element 502 side. The first optical system 10 includes a first reflecting surface that reflects light emitted from the pupil 500 side toward the pupil 500 side, and a second reflecting surface that reflects the light reflected toward the pupil 500 side toward the display element 502 side. The first reflecting surface has a concave shape and can form an intermediate image 510 on the pupil 500 side. The pupil 500 side of the first reflecting surface is filled with a material whose refractive index is greater than 1. The second optical system 20 is arranged closer to the display element 502 than an intermediate image plane on which the intermediate image 510 is formed, and is configured so that the intermediate image plane and the display element plane have a conjugate relationship. The second optical system 20 has at least three lenses, two of which have different Abbe numbers, and the second optical system 20 as a whole has positive power.

[0101] 42 , the first optical system 10 has, in order from the pupil 500 side to the display element 502 side, a first refractive surface 182 and a second refractive surface 184. Furthermore, the first optical system 10 has, as the first reflecting surface, a first concave reflecting surface 172 that reflects light from the first refractive surface 182 toward the pupil 500 side, and, as the second reflecting surface, a second concave reflecting surface 174 that reflects light from the first concave reflecting surface 172 toward the display element 502 side. Furthermore, the second refractive surface 184 has a function of refracting light from the second concave reflecting surface 174. Furthermore, in this embodiment, the space between the first refractive surface 182 and the second refractive surface 184 is filled with a material whose refractive index is greater than 1.4 and less than 2.2. Furthermore, in these embodiments, intermediate image 510 is formed between first concave reflecting surface 172 and second concave reflecting surface 174. Second optical system 20 also forms the intermediate image on display element 502, and the light ray at the center of display element 502 becomes a light ray that is perpendicularly incident on pupil plane 500a.

[0102] 42 , the second optical system 20 is rotationally symmetric, and the pupil plane 500a and the display element surface 502a are arranged parallel to each other. Furthermore, let L1 be the distance from the pupil plane 500a to the first concave reflecting surface 172, in the direction perpendicular to the pupil plane 500a, of the light ray with the longest optical path among the optical paths from the pupil plane 500a to the first concave reflecting surface 172. Furthermore, if L2 be the distance from the pupil plane 500a to the center of the surface of the second optical system 20 on the pupil 500 side, in the direction perpendicular to the pupil plane 500a, then L1 / L2 is 0.90, which satisfies the above formula (7).

[0103] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 45 were obtained. As shown in Fig. 45, in this embodiment, it was found that the variation in focus (aberration) was suppressed over a wide wavelength range, and the aberration was improved. In other words, as can be seen from the aberrations shown in Fig. 45 obtained by optical simulation, the optical system 1a according to this embodiment has high optical characteristics.

[0104] That is, this embodiment includes the elements 1 and 2 of the above-described configurations 1 and 7. Therefore, the optical system 1a according to this embodiment has high optical performance and a wide angle of view, while enabling miniaturization of HMDs, AR glasses, and the like.

[0105] <<9. Eighth Embodiment>> Next, an optical system 1a according to an eighth embodiment of the present disclosure will be described with reference to FIGS. 46 to 49 . FIG. 46 is a diagram showing a schematic configuration example of the optical system 1a according to this embodiment. FIG. 47 is a diagram showing example lens data of the optical system 1a according to this embodiment, the contents of which are similar to those of FIG. 43 . FIG. 48 is a diagram showing example aspherical coefficient data and example free-form surface data of the optical system 1 according to this embodiment, the contents of which are similar to those of FIG. 44 . Furthermore, FIG. 49 is a diagram showing aberration data of the optical system 1a according to this embodiment, specifically showing lateral aberration.

[0106] Although detailed description will be omitted, in the optical system 1a according to this embodiment, the first optical system 10 has, in order from the pupil 500 side to the display element 502 side, a first refractive surface 182 and a second refractive surface 184. Furthermore, the first optical system 10 has, as the first reflecting surface, a first concave reflecting surface 172 that reflects light from the first refractive surface 182 toward the pupil 500 side, and, as the second reflecting surface, a second concave reflecting surface 174 that reflects light from the first concave reflecting surface 172 toward the display element 502 side. Furthermore, the second refractive surface 184 has a function of refracting light from the second concave reflecting surface 174. Furthermore, in this embodiment, the space between the first refractive surface 182 and the second refractive surface 184 is filled with a material whose refractive index is greater than 1.4 and less than 2.2. Furthermore, in this embodiment, the intermediate image 510 is formed between the first concave reflecting surface 172 and the second concave reflecting surface 174. The second optical system 20 also forms the intermediate image on the display element 502, and the light ray from the center of the display element 502 becomes a light ray that is perpendicularly incident on the pupil plane 500a. Therefore, the optical system 1a according to this embodiment includes elements 1 of the above-described configurations 1 and 7.

[0107] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 49 were obtained. As can be seen from the aberrations shown in Fig. 49 obtained by the optical simulation, the optical system 1a according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while allowing for the miniaturization of HMDs, AR glasses, and the like.

[0108] <<10. Ninth Embodiment>> Next, an optical system 1a according to a ninth embodiment of the present disclosure will be described with reference to Figs. 50 to 53 . Fig. 50 is a diagram showing a schematic configuration example of the optical system 1a according to this embodiment. Fig. 51 is a diagram showing example lens data of the optical system 1a according to this embodiment, the contents of which are similar to those of Fig. 43 . Fig. 52 is a diagram showing example aspherical coefficient data and example free-form surface data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 44 . Furthermore, Fig. 53 is a diagram showing aberration data of the optical system 1a according to this embodiment, specifically showing lateral aberration.

[0109] Although detailed description will be omitted, the optical system 1a according to this embodiment includes the elements 1 and 2 of the above-described configuration 1 and configuration 7. In particular, in this embodiment, L1 / L2 is "0.80", which satisfies the above formula (7), and therefore includes configuration 7.

[0110] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 53 were obtained. As can be seen from the aberrations shown in Fig. 53 obtained by the optical simulation, the optical system 1a according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while allowing for the miniaturization of HMDs, AR glasses, and the like.

[0111] <<11. Tenth Embodiment>> Next, an optical system 1 according to a tenth embodiment of the present disclosure will be described with reference to FIGS. 54 to 58 . FIG. 54 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. FIG. 55 is a diagram showing example lens data of the optical system 1 according to this embodiment, the contents of which are the same as those in FIG. 9 . FIG. 56 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, the contents of which are the same as those in FIG. 10 . FIG. 57 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 58 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0112] Although detailed description will be omitted, the optical system 1 according to this embodiment includes the above-described configurations 1, 2, and 5. More specifically, in this embodiment, LR / fR is 0.86, which satisfies the above formula (1). In this embodiment, Ang4 / Ang3 is 1.00, and (A'-A) / (P'-P) is -0.78, which satisfies the above formula (4).

[0113] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 57 and Fig. 58 were obtained. As can be seen from the aberrations shown in Fig. 57 and Fig. 58 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while allowing for the miniaturization of HMDs, AR glasses, and the like.

[0114] <<12. Eleventh Embodiment>> <12.1 Detailed Configuration of the Optical System> The eleventh embodiment of the present disclosure has a function of tracking the movement of the user's pupil and adjusting the optical system 1 according to the position of the pupil so that the image from the display element 502 is suitably formed on the pupil (eye tracking).

[0115] First, an optical system 1 according to an eleventh embodiment of the present disclosure will be described with reference to FIGS. 59 to 65 . FIG. 59 is a diagram illustrating a schematic configuration example of the optical system 1 according to this embodiment. In detail, the upper row illustrates a state (Wide) in which the user directs their gaze in the optical axis direction, and the lower row illustrates a state (Tele) in which the user directs their gaze diagonally upward. FIG. 60 is a diagram illustrating example lens data for the optical system 1 according to this embodiment, the contents of which are the same as those in FIG. 9 . FIG. 61 is a diagram illustrating example aspherical coefficient data for the optical system 1 according to this embodiment, the contents of which are the same as those in FIG. 10 . FIG. 62 is a diagram illustrating aberration data for the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion in Wide mode. FIG. 63 is a diagram illustrating aberration data for the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion in Tele mode. Also, Figure 64 is a diagram of aberration data for the optical system 1 according to this embodiment, specifically showing the lateral aberration in Wide, and Figure 65 is a diagram of aberration data for the optical system 1 according to this embodiment, specifically showing the lateral aberration in Tele.

[0116] Although detailed description will be omitted, the optical system 1 according to this embodiment includes the above-described configurations 1, 2, 4, and 5. More specifically, in this embodiment, LR / fR is "0.77", which satisfies the above mathematical formula (1). In this embodiment, Φ1 / Φ is "-0.15", which satisfies the above mathematical formula (2). In this embodiment, Ang1 / Ang2 is "1.74", which satisfies the following mathematical formula (3). In this embodiment, Ang4 / Ang3 is "0.01", and (A'-A) / (P'-P) is "-0.41", which satisfies the above mathematical formula (4).

[0117] Furthermore, optical simulations were performed using light having wavelengths of 460.0000 nm, 550.0000 nm, and 620.0000 nm, and the aberration results shown in Fig. 62 to Fig. 65 were obtained. As can be seen from the aberrations shown in Fig. 62 to Fig. 65 obtained by the optical simulations, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while allowing for the miniaturization of HMDs, AR glasses, and the like.

[0118] <12.2 Eye Tracking Mechanism> Next, a configuration example of the eye tracking mechanism according to this embodiment will be described with reference to Fig. 59 and Fig. 66 to Fig. 68. Fig. 66 and Fig. 68 are diagrams showing an example of the arrangement of a light source and a camera according to this embodiment, and Fig. 67 is a diagram showing an example of image capture by a camera according to this embodiment.

[0119] As shown in FIG. 66 , the optical system 1, 1a according to this embodiment includes a camera (image capturing optical system) 560, which serves as a detector for capturing the movement of the user's pupil, and is located on the display element 502 side of the first reflecting surface 102 and at a position that does not overlap with the second optical system 20, and is capable of detecting infrared light having a wavelength of, for example, 400 nm to 700 nm. Furthermore, the optical system 1, 1a according to this embodiment also includes a light source 550, which is located on the display element 502 side of the first reflecting surface 102 and at a position that does not overlap with the second optical system 20 and the camera 560, and which irradiates the user's pupil with infrared light having a wavelength of, for example, 400 nm to 700 nm. For example, the light source 550 can be configured with an LED (light-emitting diode). To achieve this configuration, in the optical system 1, it is preferable that the semi-transmissive reflective surface 102 of the second optical element 110 function as a transmissive surface for infrared light having a wavelength of 400 nm to 700 nm. Alternatively, in the optical system 1a, it is preferable that the first concave reflecting surface 172 functions as a transmissive surface for infrared light having a wavelength of 400 nm to 700 nm.

[0120] As shown in FIG. 67 , in this embodiment, the detection unit detects the movement of the user's pupil as a radial movement amount relative to the center of the eyeball. Specifically, the upper part of FIG. 67 shows a state in which the pupil faces forward and the center of the pupil overlaps the center of the eyeball. Furthermore, the lower part of FIG. 67 shows a state in which the pupil has moved, in which the detection unit detects the radial movement amount of the pupil relative to the center of the eyeball. Furthermore, in this embodiment, a control unit (not shown) is provided that changes the overall power of the second optical system 20 based on the detected movement amount. In this way, in this embodiment, the optical system 1 can be adjusted (eye tracking) according to the position of the pupil so that the image from the display element 502 is optimally focused on the pupil.

[0121] 59 , the control unit can change the overall power of the second optical system 20 by moving at least two lens groups 210, 220 included in the second optical system 20 along the optical axis 520. At this time, in this embodiment, the distance between the first optical element 100 and the display element 502 is not changed, and therefore the size of the entire optical system 1 (the length in the direction of the optical axis 520) does not change.

[0122] In this embodiment, the control unit is not limited to changing the overall power of the second optical system 20 by moving at least two lens groups 210, 220 included in the second optical system 20 along the optical axis 520. In this embodiment, for example, at least two liquid lenses may be provided in the second optical system 20, and the control unit may change the overall power of the second optical system 20 by applying voltages to the liquid lenses to change the curvatures of the liquid lenses.

[0123] Furthermore, in this embodiment, a plurality of cameras 560 and a plurality of light sources 550 may be provided. In this case, as shown in Fig. 68 , the plurality of cameras 560 are preferably arranged symmetrically with respect to the central axis of the first reflecting surface 102. Furthermore, the plurality of light sources 550 are preferably arranged symmetrically with respect to the central axis of the first reflecting surface 102. By arranging the cameras 560 and the light sources 550 in this manner, blind spots are eliminated, and therefore the movement of the user's pupils can be tracked with high accuracy.

[0124] As described above, in this embodiment, high optical performance can be achieved and a wide angle of view can be maintained even when taking into consideration the rotation of the pupil 500. Furthermore, since the optical system 1 itself can be made compact, display devices such as HMDs and AR glasses can also be made compact.

[0125] <<13. Twelfth Embodiment>> In many of the embodiments of the present disclosure described so far, the pupil plane 500 a and the display element surface 502 a face each other, and the optical system 1 according to an embodiment of the present disclosure guides light to travel along a predetermined optical path between the pupil plane 500 a and the display element surface 502 a.

[0126] However, since HMDs and AR glasses are worn on the user's head, they are strongly desired to be small. Therefore, the inventors came up with the idea of ​​further miniaturizing HMDs and AR glasses by reviewing the positional relationship between the pupil plane 500a and the display element surface 502a. Specifically, in this embodiment, the display element 502 is provided above the user's pupil 500 by an optical system 1 that utilizes a total internal reflection surface. This allows the optical system 1 to be miniaturized, and ultimately the HMD, AR glasses, and the like to be miniaturized. Based on this idea, the inventors have created an optical system 1 according to a twelfth embodiment of the present disclosure that utilizes a total internal reflection surface.

[0127] An optical system 1 according to a twelfth embodiment of the present disclosure will be described below with reference to Fig. 69. Fig. 69 is an explanatory diagram for explaining an overview of this embodiment.

[0128] As shown in FIG. 69 , in this embodiment, a display element 502 is provided above a user's pupil 500. Furthermore, the optical system 1 according to this embodiment includes a first optical system 10 and a second optical system 20, arranged in this order from the pupil plane 500a side to the display element 502 side. The first optical system 10 includes a second optical element 110 and a first optical element 100. The second optical element 110 includes a first reflecting surface (semi-transmissive reflecting surface) 102 that reflects light emitted from the pupil 500 side toward the pupil 500 side, and a transmitting surface (first transmitting surface) 104. Furthermore, the first optical element 100 includes a second reflecting surface that reflects light reflected toward the pupil 500 side toward the opposite side of the pupil 500 (the display element 502 side). Furthermore, as in the embodiments of the present disclosure described above, in this embodiment as well, the second reflecting surface has the function of reflecting a portion of light. Furthermore, in this embodiment, the first reflecting surface (semi-transmissive reflecting surface) 102 is disposed on the opposite side of the pupil 500 (the display element 502 side) with respect to the transmitting surface (first transmitting surface) 104, has a concave shape, and is capable of forming an intermediate image on the pupil 500 side. Also in this embodiment, the pupil 500 side of the first reflecting surface (semi-transmissive reflecting surface) 102 is filled with a material whose refractive index is greater than 1. In detail, also in this embodiment, it is preferable that the space between the transmitting surface (first transmitting surface) 104 and the first reflecting surface (semi-transmissive reflecting surface) 102 be filled with a material whose refractive index is greater than 1.4 and less than 2.2.

[0129] Furthermore, in this embodiment, when the focal length of the first reflecting surface (semi-transmissive reflecting surface) 102 is defined as fR and the physical length between the surface vertices from the surface on the opposite side of the pupil 500 of the first optical element 100 (the surface on the display element 502 side) to the first reflecting surface (semi-transmissive reflecting surface) 102 is defined as LR, it is preferable that the following mathematical formula (1a) be satisfied.

[0130] In this embodiment, the first optical system 10 is configured so that light emitted from the pupil 500 side passes through the first optical element 100, passes through the transmitting surface (first transmitting surface) 104 of the second optical element 110, is reflected by the first reflecting surface (semi-transmitting reflecting surface) 102 of the second optical element 110, passes through the transmitting surface (first transmitting surface) 104 of the second optical element 110, is reflected by the pupil 500 side or the display element 502 side of the first optical element 100, passes through the transmitting surface (first transmitting surface) 104 of the second optical element 110, and passes through the first reflecting surface (semi-transmitting reflecting surface) 102 of the second optical element 20.

[0131] Furthermore, similar to the embodiments described so far, the second optical system 20 is arranged closer to the display element 502 (on the optical path) than the intermediate image plane where the intermediate image is formed, and is configured so that the intermediate image plane and the display element plane 502 a have a conjugate relationship. Also, in this embodiment, the second optical system 20 includes at least two surfaces with positive power and one surface with negative power, and the second optical system 20 as a whole has positive power.

[0132] 69, the second optical system 20 is an optical system having positive power overall for the light beam from the first optical system 10, and includes a fifth optical element 450 filled with a material having a refractive index greater than 1.4 and less than 2.2. Also, in this embodiment, the second optical system 20 further includes a third lens group 460 having at least three lenses.

[0133] In this embodiment, the fifth optical element 450 has, in order from the pupil plane 500a side to the display element 502 side, a transmitting surface (second transmitting surface) 702, a third reflecting surface 711, and a fourth reflecting surface 712. Furthermore, in this embodiment, the fifth optical element 450 is configured so that light emitted from the first optical system 10 side passes through the transmitting surface (second transmitting surface) 702, is reflected by the third reflecting surface 711, is totally reflected by the same surface (total reflection surface 700) as the transmitting surface (second transmitting surface) 702, is reflected by the fourth reflecting surface 712, and passes through the same surface (transmitting surface 703) as the transmitting surface (second transmitting surface) 702. In this embodiment, the light that has passed through the transmitting surface 703 is condensed by the third lens group 460 to form an image.

[0134] In this embodiment, the third reflecting surface 711 can be, for example, a diffractive element surface.

[0135] In this embodiment, by utilizing the total reflection surface 700 of the fifth optical element 450, it is possible to further reduce the size of the optical system 1. More specifically, in order to reduce the size of the optical system 1, it is necessary to reduce the depth D and width W of the optical system as shown in Fig. 69 . Therefore, in this embodiment, when the angle of the third reflection surface 711 of the fifth optical element 450 with respect to the pupil plane 500a is Ang5, and when the pupil plane 500a is 0°, a clockwise angle is a negative angle and a semi-counterclockwise angle is a positive angle, it is preferable to configure the third reflection surface 711 so as to satisfy the following mathematical formula (9):

[0136] If the angle Ang5 of the third reflecting surface 711 of the fifth optical element 450 with respect to the pupil plane 500a exceeds the upper limit of formula (9), total reflection will not be possible at the total reflecting surface 700. Furthermore, if the angle Ang5 is below the lower limit of formula (9), the depth D of the optical system 1 will increase, which may result in an increase in the size of the optical system 1. Therefore, in this embodiment, it is preferable to satisfy formula (9).

[0137] Furthermore, in this embodiment, when the angle of the fourth reflecting surface 712 of the fifth optical element 450 with respect to the pupil plane 500a is Ang6, and the pupil plane 500a is 0°, clockwise is a negative angle and semi-counterclockwise is a positive angle, it is preferable to configure the fourth reflecting surface 712 so as to satisfy the following mathematical formula (10):

[0138] 69 , the transmitting surface (second transmitting surface) 702, the total reflecting surface 700, and the transmitting surface 703 of the fifth optical element 450 are configured as a single surface. Furthermore, in this embodiment, when the angle of the total reflecting surface 700, which is the same surface as the totally reflecting transmitting surface (second transmitting surface) 702 of the fifth optical element 450, with respect to the direction A of light traveling perpendicularly from the pupil plane 500 a is Ang7, it is preferable that the transmitting surface (second transmitting surface) 702, the total reflecting surface 700, and the transmitting surface 703 are configured as a single surface so as to satisfy the following mathematical expression (11):

[0139] By doing so, in this embodiment, the depth D and width W of the optical system 1 can be made smaller.

[0140] Furthermore, in this embodiment, when the angle of a light ray B, which is incident on the transmitting surface (second transmitting surface) 702 (shown by the dashed line in FIG. 69 ), reflected by the third reflecting surface 711, and totally reflected by the total reflecting surface 700, when the light ray B enters the transmitting surface (second transmitting surface) 702 is taken as Ang9, relative to the direction A of light traveling perpendicularly from the pupil plane 500 a, it is preferable to configure the fifth optical element 450 so as to satisfy the following mathematical formula (12):

[0141] In this embodiment, the smaller the angle Ang9, the smaller the angles Ang5 and Ang6, and therefore the smaller the depth D of the optical system 1. Specifically, if the angle Ang9 of the light ray B relative to the direction A of the light traveling perpendicularly from the pupil plane 500a when the light ray B is incident on the transmitting surface (second transmitting surface) 702 exceeds the upper limit of formula (12), the angle Ang5 becomes large, and the depth D of the optical system 1 becomes large. Furthermore, if the angle Ang9 falls below the lower limit of formula (12), the light incident on the transmitting surface (second transmitting surface) 702 will travel to the fourth reflecting surface 712. This makes it necessary to extend the fifth optical element 450 in the vertical direction in the figure, and as a result, the width D of the optical system 1 will become large. Therefore, in this embodiment, it is preferable to satisfy formula (12).

[0142] Next, FIGS. 70 to 74 show specific examples of the optical system 1 according to this embodiment. FIG. 70 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. FIG. 71 is a diagram showing example lens data for the optical system 1 according to this embodiment, the contents of which are the same as those of FIG. 9 , except that in this lens data, the fifth optical element 450 is referred to as the "optical element 3" and the third lens group 460 is referred to as the "lens group 1." FIG. 72 is a diagram showing example aspherical coefficient data for the optical system 1 according to this embodiment, the contents of which are the same as those of FIG. 10 . FIG. 73 is a diagram showing aberration data for the optical system 1 according to this embodiment, specifically showing longitudinal aberration, astigmatism, and distortion. FIG. 74 is a diagram showing aberration data for the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0143] Furthermore, optical simulations were performed using light having wavelengths of 450.0000 nm, 522.0000 nm, and 630.0000 nm, and the aberration results shown in Fig. 73 and Fig. 74 were obtained. As can be seen from the aberrations shown in Fig. 73 and Fig. 74 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance and a wide angle of view, while allowing for the miniaturization of HMDs, AR glasses, and the like.

[0144] <<14. Thirteenth Embodiment>> The thirteenth to fifteenth embodiments described below, like the twelfth embodiment described above, are embodiments that enable the HMD and AR glasses to be further miniaturized by revising the positional relationship between the pupil plane 500a and the display element surface 502a. In detail, in these embodiments, the display element 502 is provided above the user's pupil 500 by an optical system 1 that utilizes a total internal reflection surface. According to these embodiments, this allows the optical system 1 to be miniaturized, and ultimately the HMD, AR glasses, and the like to be miniaturized. Therefore, the configurations of these embodiments will be described below after sequentially presenting specific examples of the thirteenth to fifteenth embodiments.

[0145] First, with reference to Figs. 75 to 78, a specific example of an optical system 1 according to a thirteenth embodiment of the present disclosure will be shown. Fig. 75 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. Fig. 76 is a diagram showing example lens data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 9. Fig. 77 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 10. Fig. 78 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0146] As shown in FIG. 75 , in this embodiment, a display element 502 (display element surface 502a) is provided above a user's pupil 500 (pupil plane 500a). In this embodiment, the optical system 1 includes a first optical system 10 and a second optical system 20, arranged in this order from the user's pupil 500 side to the display element 502 side. The first optical system 10 includes a first reflecting surface 142 that reflects light emitted from the pupil 500 side toward the pupil plane 500a side, and a second reflecting surface 143 that reflects the light reflected toward the pupil 500 side toward the opposite side from the pupil plane 500a (the display element surface 502a side). The first reflecting surface 142 has a concave shape and can form an intermediate image 510 on the pupil plane 500a side. The pupil 500 side of the first reflecting surface 142 is filled with a material having a refractive index greater than 1.

[0147] Furthermore, in this embodiment, the second optical system 20 is arranged closer to the display element surface 502a than the intermediate image plane on which the intermediate image 510 is formed, and is configured so that the intermediate image plane and the display element surface 502a have a conjugate relationship. Also, in this embodiment, the second optical system 20 includes at least two surfaces having positive power and one surface having negative power, and the second optical system 20 as a whole has positive power.

[0148] 75 , the first optical system 10 has, in order from the pupil plane 500a side to the display element surface 502a side, a third refractive surface 131 and a fourth refractive surface 133. The first optical system 10 also has, as a first reflecting surface, a third concave reflecting surface 142 that reflects light from the third refractive surface 131 toward the pupil plane 500a side, and a fourth concave reflecting surface 143 that reflects light from the third concave reflecting surface 142 toward the display element surface 502a side. In this embodiment, the fourth refractive surface 133 can refract light from the fourth concave reflecting surface 143. Furthermore, in this embodiment, the space between the third refractive surface 131 and the fourth refractive surface 133 is preferably filled with a material having a refractive index greater than 1.4 and less than 2.2. In this embodiment, the intermediate image 510 is formed between the third concave reflecting surface 142 and the fourth concave reflecting surface 143 .

[0149] Furthermore, in this embodiment, the second optical system 20 forms an intermediate image 510 on the display element surface 502a, and the light ray from the center of the display element 502 becomes a light ray that is perpendicularly incident on the pupil surface 500a.

[0150] 75 , the first optical system 10 has, from the pupil plane 500a side, a concave third refracting surface 131 and a first reflecting surface 142 which is a concave reflecting surface. Furthermore, the first optical system 10 has a second reflecting surface 143 which is the same surface as the third refracting surface 131 and which has a convex shape with respect to the light rays reflected by the first reflecting surface 142, and a fourth refracting surface 133 on which the light rays reflected by the second reflecting surface 143 are incident. Furthermore, in this embodiment, of the group of light rays incident on the second reflecting surface 143, the light beam incident on the third refracting surface 131 satisfies the total reflection condition with respect to the third refracting surface 131, which is expressed by the following mathematical expression (13). Furthermore, in this embodiment, among the group of light rays incident on the second reflecting surface 143, the light beam that is incident on a region other than the third refracting surface 131 does not satisfy the total reflection condition expressed by the following mathematical expression (13) with respect to the region other than the third refracting surface 131. Furthermore, in this embodiment, the intermediate image position of the reference light ray 522 is inside the first optical system 10.

[0151] In the above formula (13), θ is the angle of incidence and n is the refractive index.

[0152] Furthermore, in this embodiment, the second optical system 20 has four refractive surfaces 231, 233, 234, and 236, a fifth reflecting surface 242, and a reflecting surface 245. Furthermore, in this embodiment, the light reflected by the fifth reflecting surface 242 of the second optical system 20 forms an image on the display element surface 502a.

[0153] In this embodiment, an optical simulation was performed using light having wavelengths of 450.0000 nm, 525.0000 nm, and 630.0000 nm, and the aberration results shown in Fig. 78 were obtained. As can be seen from the aberrations shown in Fig. 78 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance.

[0154] <<15. Fourteenth Embodiment>> Next, with reference to Figs. 79 to 82 , a specific example of an optical system 1 according to a fourteenth embodiment of the present disclosure will be shown. Fig. 79 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. Fig. 80 is a diagram showing example lens data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 9 . Fig. 81 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 10 . Fig. 82 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0155] In this embodiment, as shown in Fig. 79, the optical system 1 has the same configuration as the above-mentioned thirteenth embodiment. Furthermore, in this embodiment, the optical system 1 has a lens 230 between the fourth refractive surface 133 of the first optical system 10 and the refractive surface 231 of the second optical system 20. In addition, in this embodiment, the optical system 1 has a lens 240 between the refractive surfaces 233 and 234 of the second optical system 20.

[0156] In this embodiment, an optical simulation was performed using light having wavelengths of 450.0000 nm, 525.0000 nm, and 630.0000 nm, and the aberration results shown in Fig. 82 were obtained. As can be seen from the aberrations shown in Fig. 82 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance.

[0157] <<16. Fifteenth Embodiment>> Next, with reference to Figs. 83 to 86 , a specific example of an optical system 1 according to a fifteenth embodiment of the present disclosure will be shown. Fig. 83 is a diagram showing a schematic configuration example of the optical system 1 according to this embodiment. Fig. 84 is a diagram showing example lens data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 9 . Fig. 85 is a diagram showing example aspherical coefficient data of the optical system 1 according to this embodiment, the contents of which are similar to those of Fig. 10 . Fig. 86 is a diagram showing aberration data of the optical system 1 according to this embodiment, specifically showing lateral aberration.

[0158] In this embodiment, as shown in Fig. 83, the optical system 1 has a first optical system 10 having a configuration similar to that of the above-mentioned thirteenth embodiment. Furthermore, in this embodiment, the optical system 1 has a second optical system 20 having a configuration different from that of the above-mentioned thirteenth embodiment.

[0159] In this embodiment, the second optical system 20 has two refractive surfaces 231 and 233 and a fifth reflecting surface 242. In this embodiment, light reflected by the fifth reflecting surface 242 of the second optical system 20 passes through the refractive surface 233 and is imaged by the fourth lens group 470 on the display element surface 502a.

[0160] In this embodiment, an optical simulation was performed using light having wavelengths of 450.0000 nm, 525.0000 nm, and 630.0000 nm, and the aberration results shown in Fig. 86 were obtained. As can be seen from the aberrations shown in Fig. 86 obtained by the optical simulation, the optical system 1 according to this embodiment has high optical characteristics. Therefore, the optical system 1 according to this embodiment has high optical performance.

[0161] As described above, in the thirteenth to fifteenth embodiments of the present disclosure, the display element 502 (display element surface 502a) is provided above the user's pupil 500 (pupil plane 500a). In these embodiments, the optical system 1 includes a first optical system 10 and a second optical system 20, arranged in order from the user's pupil 500 side to the display element 502 side. The first optical system 10 includes a first reflecting surface 142 that reflects light emitted from the pupil 500 side toward the pupil plane 500a side, and a second reflecting surface 143 that reflects the light reflected toward the pupil 500 side toward the opposite side from the pupil plane 500a (the display element surface 502a side). The first reflecting surface 142 has a concave shape and can form an intermediate image 510 on the pupil plane 500a side. The pupil 500 side of the first reflecting surface 142 is filled with a material having a refractive index greater than 1.

[0162] Furthermore, in these embodiments, the second optical system 20 is disposed closer to the display element surface 502a than the intermediate image plane where the intermediate image 510 is formed, and is configured so that the intermediate image plane and the display element surface 502a have a conjugate relationship. The second optical system 20 also includes at least two surfaces with positive power and one surface with negative power, and the second optical system 20 as a whole has positive power.

[0163] 75, 79, and 83, the first optical system 10 has, in order from the pupil plane 500a side to the display element surface 502a side, a third refractive surface 131 and a fourth refractive surface 133. The first optical system 10 also has, as a first reflecting surface, a third concave reflecting surface 142 that reflects light from the third refractive surface 131 toward the pupil plane 500a side, and a fourth concave reflecting surface 143 that reflects light from the third concave reflecting surface 142 toward the display element surface 502a side. In these embodiments, the fourth refractive surface 133 can refract light from the fourth concave reflecting surface 143. In these embodiments, the space between the third refractive surface 131 and the fourth refractive surface 133 is preferably filled with a material having a refractive index greater than 1.4 and less than 2.2. Also, in these embodiments, intermediate image 510 is formed between third concave reflecting surface 142 and fourth concave reflecting surface 143 .

[0164] Furthermore, in these embodiments, the second optical system 20 forms an intermediate image 510 on the display element surface 502a, and the light ray at the center of the display element 502 is a light ray that is perpendicular to the pupil surface 500a.

[0165] 75, 79, and 83, the first optical system 10 has, from the pupil plane 500a side, a concave third refractive surface 131 and a first reflecting surface 142 which is a concave reflecting surface. Furthermore, the first optical system 10 has a second reflecting surface 143 which is the same surface as the third refractive surface 131 and which has a convex shape with respect to the light rays reflected by the first reflecting surface 142, and a fourth refractive surface 133 on which the light rays reflected by the second reflecting surface 143 are incident. Furthermore, in these embodiments, of the group of light rays incident on the second reflecting surface 143, the light beam incident on the third refractive surface 131 satisfies the total reflection condition expressed by the above mathematical expression (13) with respect to the third refractive surface 131. Furthermore, in these embodiments, among the group of light rays incident on the second reflecting surface 143, the light beam that is incident on a region other than the third refracting surface 131 does not satisfy the condition for total reflection expressed by the above mathematical formula (13) with respect to the region other than the third refracting surface 131. Furthermore, in these embodiments, the intermediate image position of the reference light ray 522 is inside the first optical system 10.

[0166] Furthermore, in these embodiments, the second optical system 20 has at least two refractive surfaces 231, 233, 234, and 236, and at least one reflective surface including the fifth reflective surface 242. Also, in these embodiments, the light reflected by the fifth reflective surface 242 of the second optical system 20 forms an image on the display element surface 502a.

[0167] Furthermore, in these embodiments, when the direction of the light rays emitted from the pupil plane 500a is the Z direction and the Y direction is the direction perpendicular to the Z direction, when the focal length of the first optical system 10 in the Y cross section is fy1 and the optical path length from the third refractive surface 131 to the fourth refractive surface 133 is OP1, it is preferable to configure the system so as to satisfy the following mathematical formula (14):

[0168] If fy1 / OP1 is below the lower limit of the above formula (14), the optical path length through the first optical system 10 becomes longer, resulting in an increase in the size of the first optical system 10. Also, if fy1 / OP1 exceeds the upper limit of the above formula (14), the focal plane is located in the second optical system 20, so that the entire optical system 1 is focused, resulting in an increase in the size of the entire optical system 1. Therefore, in these embodiments, it is preferable to satisfy formula (14).

[0169] Furthermore, in these embodiments, when the focal length of the Y cross section of the first reflecting surface 142 that reflects the reference ray is fr1y and the focal length of the entire optical system 1 in the Y cross section is fy, it is preferable to satisfy the following equation (15):

[0170] If fy / fr1y is below the lower limit of the above formula (15), the power of the first reflecting surface 142 becomes large, resulting in the generation of aberrations. On the other hand, if fy / fr1y exceeds the upper limit of the above formula (15), the power of the first reflecting surface 142 becomes small, making it impossible to create an intermediate image plane within the first optical system 10, resulting in an increase in the size of the first optical system 10. Therefore, in these embodiments, it is preferable to satisfy formula (15).

[0171] Furthermore, in these embodiments, it is preferable to satisfy the following formula (16):

[0172] If fy1 / fr1y is below the lower limit of the above formula (16), the power of the first reflecting surface 142 becomes large, resulting in the occurrence of aberrations. On the other hand, if fy1 / fr1y exceeds the upper limit of the above formula (16), the power of the first reflecting surface 142 becomes small, making it impossible to form an intermediate image plane within the first optical system 10, resulting in an increase in the size of the first optical system 10. Therefore, in these embodiments, it is preferable to satisfy formula (16).

[0173] Furthermore, in these embodiments, for a given ray 522a that has the largest angle of incidence on the third refracting surface 131 and passes through a region of the first optical system 10 where the third refracting surface 131 and the first reflective surface 142 are physically close to each other, it is preferable that the following mathematical formula (17) be satisfied, where fray is the focal length of the Y cross section of the first reflective surface 142 and fay is the composite focal length of the Y cross section when the given ray 522a passes through the third refracting surface 131 and the first reflective surface 142.

[0174] When fay / fray is below the lower limit of the above formula (17), the power of the first reflecting surface 142 that reflects the predetermined light ray 522a is small. Therefore, the angle of the light ray incident on the pupil plane 500a of the predetermined light ray 522a becomes large, and the second reflecting surface 143, which is on the same plane as the third refractive surface 131, no longer satisfies the total reflection condition. Furthermore, when fay / fray exceeds the upper limit of the above formula (17), the power of the first reflecting surface 142 that reflects the predetermined light ray 522a becomes large, resulting in aberrations. In addition, physical interference occurs between the third refractive surface 131 and the first reflecting surface 142, preventing the predetermined light ray 522a from being incident on the second reflecting surface 143. Therefore, in these embodiments, it is preferable to satisfy formula (17).

[0175] Furthermore, in these embodiments, it is preferable to satisfy the following formula (18):

[0176] When fra1y / fr1y is below the lower limit of the above formula (18), the power of the first reflecting surface 142 that reflects the predetermined light ray 522a becomes large, resulting in aberrations. In addition, physical interference occurs between the third refracting surface 131 and the first refracting surface 142, preventing the predetermined light ray 522a from entering the second refracting surface 143. Furthermore, when fra1y / fr1y exceeds the upper limit of the above formula (18), the power of the first refracting surface 142 that reflects the predetermined light ray 522a becomes small. Therefore, the angle of the light ray incident on the pupil plane 500a of the predetermined light ray 522a becomes large, and the second refracting surface 143, which is on the same plane as the third refracting surface 131, no longer satisfies the total reflection condition. Therefore, in these embodiments, it is preferable to satisfy formula (18).

[0177] Furthermore, in these embodiments, when the focal length of the fifth reflecting surface 242 in the Y cross section is fr3y and the focal length of the entire optical system 1 in the Y cross section is fy, it is preferable to satisfy the following equation (19):

[0178] If fy / fr3y is below the lower limit of the above formula (19), the divergence of the light beam from the fifth reflecting surface 242 increases, resulting in an increase in the overall size of the optical system 1. If fy / fr3y exceeds the upper limit of the above formula (19), the converging power increases, resulting in the occurrence of aberrations. Therefore, in these embodiments, it is preferable to satisfy formula (19).

[0179] In addition, the values ​​of fy1 / OP1, fy / fr1y, fy1 / fr1y, fay / fra1y, fray / fr1y / fr1y, and fy / fr3y in the thirteenth to fifteenth embodiments are shown in Figure 87, which is a diagram illustrating example data for the optical system 1 according to the thirteenth to fifteenth embodiments of the present disclosure.

[0180] As described above, the optical systems 1 according to the thirteenth to fifteenth embodiments of the present disclosure have high optical performance and a wide angle of view, while allowing for miniaturization of HMDs, AR glasses, and the like.

[0181] <<17. Summary>> As described above, in each embodiment of the present disclosure, it is possible to provide optical systems 1 and 1a that have high optical performance and a wide angle of view (for example, FOV (Field Of View) = 80 to 120 degrees), while also being capable of being miniaturized into HMDs, AR glasses, and the like.

[0182] In the embodiments of the present disclosure, the optical systems 1 and 1a are not limited to the forms shown in the drawings, but can be modified into various forms.

[0183] The optical systems 1 and 1a according to the above-described embodiments of the present disclosure are not limited to applications in projection-type HMDs and AR glasses, but can also be applied to light-emitting devices such as small projectors, imaging devices such as wide-angle stereo 3D cameras, and the like.

[0184] <<18. Application Examples>> For example, the technology according to the present disclosure may be applied to the display units of various electronic devices, etc. Therefore, examples of electronic devices to which the technology can be applied will be described below.

[0185] 88 is an external view of a head-mounted display 600. The head-mounted display 600 has, for example, ear hooks 612 for wearing on the user's head on both sides of a glasses-shaped display unit 611. In this head-mounted display 600, the optical system 1 according to the embodiment of the present disclosure can be used as the optical system of the display unit 611.

[0186] <<19. Supplementary Information>> Although preferred embodiments of the present disclosure have been described above in detail with reference to the accompanying drawings, the technical scope of the present disclosure is not limited to such examples. It is clear that a person skilled in the art of the present disclosure can conceive of various modified or altered examples within the scope of the technical idea described in the claims, and it is understood that these also naturally fall within the technical scope of the present disclosure.

[0187] Furthermore, the effects described herein are merely descriptive or exemplary and are not limiting. In other words, the technology according to the present disclosure may achieve other effects that will be apparent to those skilled in the art from the description of this specification, in addition to or in place of the above-described effects.

[0188] Note that the present technology can also have the following configuration: (1) An optical system including a first optical system and a second optical system, in that order from a user's pupil side to a display element side, wherein the first optical system has: a first reflecting surface that reflects light emitted from the pupil side toward the pupil side; and a second reflecting surface that reflects the light reflected toward the pupil side toward the display element side, wherein the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, and the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, and the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed, and is configured so that the intermediate image plane and the display element surface have a conjugate relationship, and includes at least three lenses, two lenses of the at least three lenses have different Abbe numbers, and the second optical system as a whole has positive power. (2) The optical system according to (1) above, wherein the first optical system has, in order from the pupil side to the display element side, a first optical element and a second optical element, the first optical element having a function of reflecting a part of the light as the second reflecting surface, the second optical element having a transmitting surface and a semi-transmitting reflective surface as the first reflecting surface, the semi-transmitting reflective surface being arranged on the display element side of the transmitting surface and having a concave shape, the space between the transmitting surface and the semi-transmitting reflective surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, all surfaces of the second optical system have a common axis of rotational symmetry, the intermediate image is formed between the semi-transmitting reflective surface of the second optical element and the first optical element, and the optical system satisfies the following mathematical formula (1), where fR is a focal length by the semi-transmitting reflective surface and LR is a physical length between vertices of the surface of the first optical element on the display element side and the semi-transmitting reflective surface. (3) The optical system according to (2) above, wherein the second optical system has, in order from the pupil side to the display element side, a first lens group having negative power and a second lens group having positive power, and satisfies the following formula (2) when the power of the first lens group is Φ1 and the overall power of the second optical system is Φ. (4) The optical system according to (3) above, wherein the first lens group is adjacent to the second optical element on the display element side and has a function of reducing a light ray angle at a periphery, and satisfies the following mathematical expression (3) when a chief ray angle at the outermost periphery from the second optical element to the display element side is Ang1 and a chief ray angle at the outermost periphery from the first lens group to the second lens group is Ang2. (5) The optical system according to (4) above, wherein, at a field of view of 60 degrees, a ray angle at which a lower ray of marginal rays among light rays incident from a pupil plane enters the second lens group is Ang3, and a ray angle at which the lower ray enters the display element from the second lens group is Ang4, a distance on the optical axis from the pupil plane to the surface of the first optical element located closest to the pupil plane is A, and a distance on the optical axis from the pupil plane to the surface of the first optical element located closest to the pupil plane is A' when the pupil is separated from the first optical element in the optical axis direction, the field of view is 60 degrees, and there is no ray vignetting in the second optical system, an exit pupil position of the first optical system at the distance A is P, and an exit pupil position of the first optical system at the distance A' is P', the following mathematical expression (4) is satisfied. (6) The optical system according to (2) above, wherein the second optical system has a first lens group having a positive power on the pupil side, and a second lens group having a positive power on the display element side, the second lens group having a chief ray of the second optical system intersecting an optical axis, and satisfies the following formula (6) when the power of the first lens group is Φ1 and the overall power of the second optical system is Φ. (7) The optical system according to (1), wherein the first optical system has, in order from the pupil side to the display element side, a first refractive surface and a second refractive surface, and further has, as the first reflecting surface, a first concave reflecting surface that reflects the light from the first refractive surface toward the pupil side, and as the second reflecting surface, a second concave reflecting surface that reflects the light from the first concave reflecting surface toward the display element side, the second refractive surface refracts the light from the second concave reflecting surface, the space between the first refractive surface and the second refractive surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, the intermediate image is formed between the first concave reflecting surface and the second concave reflecting surface, and the second optical system forms the intermediate image on the display element, and a ray from the center of the display element becomes a ray that is perpendicularly incident on a pupil plane. (8) The optical system described in (7) above, wherein the second optical system is rotationally symmetric, the pupil plane and the display element surface are arranged parallel to each other, and the optical path from the pupil plane to the first concave reflecting surface of a light ray having the longest optical path among the optical paths from the pupil plane to the first concave reflecting surface is defined as L1, and the distance from the pupil plane to the center of the pupil-side surface of the second optical system in the direction perpendicular to the pupil plane is defined as L2, satisfies the following mathematical expression (7). (9) The optical system according to any one of (2) to (6), wherein the first optical element has a first wave plate that shifts the phase of the vertically polarized component of light by 90 degrees, and the second optical system has a third optical element made of a second wave plate that shifts the phase of the vertically polarized component of light by 90 degrees, and the slow axes of the first wave plate and the second wave plate are orthogonal or parallel to each other. (10) The optical system according to (9), further comprising a first polarizing plate that transmits linearly polarized light on the pupil side of the first wave plate. (11) The optical system according to (9), further comprising a second polarizing plate that transmits linearly polarized light on the display element side of the second wave plate. (12) The optical system according to (9), wherein the first optical element and the third optical element are parallel flat plates. (13) The optical system according to (9), wherein the third optical element is arranged on the display element side of the second optical element. (14) The optical system according to (9) above, wherein the second optical system further includes a fourth optical element that separates polarized light and has a surface inclined at 45 degrees with respect to the optical axis. (15) The optical system according to any one of (1) to (14) above, further including a light guide that is worn by the user so as to be positioned in front of the pupil and that guides an image projected by the display element to the pupil, wherein the first optical system and the second optical system are disposed between the display element and the light guide, and the light guide forms an image of light from the first optical system and the second optical system on the pupil. (16) The optical system according to any one of (2) to (6) above, wherein the semi-transmissive reflective surface functions as a transmissive surface for light with a wavelength of 400 nm to 700 nm. (17) The optical system according to (7) or (8) above, wherein the first concave reflective surface functions as a transmissive surface for light with a wavelength of 400 nm to 700 nm. (18) The optical system according to (16), further comprising an imaging optical system capable of detecting infrared light, which is provided on the display element side of the first reflecting surface and at a position not overlapping with the second optical system, as a detection unit for capturing movement of the user's pupil. (19) The optical system according to (18), further comprising a plurality of the imaging optical systems including a first imaging optical system and a second imaging optical system, which are arranged symmetrically with respect to a central axis of the first reflecting surface.(20) The optical system according to (18) above, further comprising a light source that is provided on the display element side of the first reflecting surface and at a position that does not overlap with the second optical system and the imaging optical system, and that irradiates the infrared light. (21) The optical system according to (20) above, comprising a plurality of light sources including a first light source and a second light source, and the first light source and the second light source are arranged in a symmetrical relationship with respect to the central axis of the first reflecting surface. (22) The optical system according to (20) or (21) above, wherein the light source is an LED. (23) The optical system according to any one of (18) to (22) above, further comprising a control unit that changes the overall power of the second optical system, wherein the detection unit detects movement of the user's pupil as an amount of radial movement based on the center of the eyeball, and the control unit changes the overall power of the second optical system based on the detected amount of movement. (24) The optical system according to (23) above, wherein the control unit changes the overall power of the second optical system by moving at least two lens groups included in the second optical system along an optical axis. (25) The optical system according to (23) above, wherein the second optical system includes at least two liquid lenses, and the control unit changes the overall power of the second optical system by applying voltages to the liquid lenses. (26) The optical system according to (24) or (25) above, wherein the distance between the first optical element and the display element does not change when the control unit changes the overall power of the second optical system. (27) The optical system according to any one of (18) to (26) above, wherein the detection unit detects light of a wavelength of 400 nm to 700 nm that has passed through the first optical system.(28) A display device comprising, from a pupil side, a first optical system, a second optical system, and a display element, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side toward the pupil side, and a second reflecting surface that reflects the light reflected toward the pupil side toward the display element side, the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed, and is configured so that the intermediate image plane and the display element surface have a conjugate relationship, and has at least three lenses, two lenses of the at least three lenses have different Abbe numbers, and the second optical system as a whole has positive power. (29) An optical system comprising a first optical system and a second optical system in the order from a user's pupil side to a display element side, wherein the first optical system has: a first reflecting surface that reflects light emitted from the pupil side toward the pupil side; and a second reflecting surface that reflects the light reflected toward the pupil side toward the display element side, wherein the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, and the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, and the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed, and is configured so that the intermediate image plane and the display element plane have a conjugate relationship, and includes at least two surfaces having positive power and one surface having negative power, and wherein the second optical system as a whole has positive power.(30) The optical system according to (29) above, wherein the first optical system has, in order from the pupil side to the display element side, a first optical element and a second optical element, the first optical element having a function of reflecting a part of the light as the second reflecting surface, the second optical element having a first transmitting surface and a semi-transmitting reflective surface as the first reflecting surface, the semi-transmitting reflective surface being arranged on the display element side of the first transmitting surface and having a concave shape, the space between the first transmitting surface and the semi-transmitting reflective surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, the intermediate image is formed between the semi-transmitting reflective surface of the second optical element and the first optical element, and the optical system satisfies the following mathematical formula (1a), where fR is a focal length by the semi-transmitting reflective surface and LR is a physical length between vertices of a surface of the first optical element on the display element side and the semi-transmitting reflective surface. (31) The optical system according to (29) above, wherein the first optical system has, in order from the pupil side to the display element side, a third refractive surface and a fourth refractive surface, and further has, as the first reflecting surface, a third concave reflecting surface that reflects the light from the third refractive surface toward the pupil side, and as the second reflecting surface, a fourth concave reflecting surface that reflects the light from the third concave reflecting surface toward the display element side, the fourth refractive surface refracts the light from the fourth concave reflecting surface, a space between the third refractive surface and the fourth refractive surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, the intermediate image is formed between the third concave reflecting surface and the fourth concave reflecting surface, the second optical system forms the intermediate image on the display element, and a ray from the center of the display element becomes a ray that is incident perpendicularly on a pupil plane. (32) The first optical system has, in order from the pupil side to the display element side, a first optical element and a second optical element, the first optical element having a function of reflecting a part of the light as the second reflecting surface, the second optical element has: a first transmitting surface; and a semi-transmitting reflecting surface as the first reflecting surface, the semi-transmitting reflecting surface being arranged on the display element side with respect to the first transmitting surface and having a concave shape, the space between the first transmitting surface and the semi-transmitting reflecting surface being filled with a material having a refractive index greater than 1.4 and less than 2.2, the second optical system has a fifth optical element which is an optical system having positive power as a whole for the light flux from the first optical system and is filled with a material having a refractive index greater than 1.4 and less than 2.2, the fifth optical element having, in order from the pupil side to the display element side, a second transmitting surface and a third reflecting surface, The optical system described in (29) above, wherein the first optical system is configured such that light emitted from the pupil side passes through the first optical element, passes through the first transmitting surface of the second optical element, is reflected by the semi-transmitting reflective surface of the second optical element, passes through the first transmitting surface of the second optical element, is reflected by the pupil side or the display element side of the first optical element, passes through the first transmitting surface of the second optical element, and passes through the semi-transmitting reflective surface of the second optical element; and the fifth optical element is configured such that light emitted from the first optical system side passes through the second transmitting surface, is reflected by the third reflective surface, and is totally reflected by the same surface as the second transmitting surface.(33) The optical system according to (32), wherein the following formula (9) is satisfied when the angle of the third reflecting surface of the fifth optical element with respect to a pupil plane is Ang5, the pupil plane is 0°, and a clockwise direction is negative. (34) The optical system according to (32), wherein the third reflecting surface is a diffractive element surface. (35) The second optical system further includes a third lens group having at least three lenses, and the fifth optical element further includes a fourth reflecting surface, and the fifth optical element is configured such that light emitted from the first optical system side passes through the second transmitting surface, is reflected by the third reflecting surface, is totally reflected by the same surface as the second transmitting surface, is reflected by the fourth reflecting surface, and passes through the same surface as the second transmitting surface, and the light that has passed through the same surface as the second transmitting surface is condensed by the third lens group and forms an image. (36) The optical system according to (35), wherein the angle of the fourth reflecting surface of the fifth optical element with respect to the pupil plane is Ang6, and when the pupil plane is 0°, a clockwise direction is a negative angle, the following mathematical formula (10) is satisfied. (37) The optical system according to (35), wherein, when an angle of the same surface as the second transmitting surface that totally reflects the fifth optical element with respect to the direction of light that travels perpendicularly from the pupil plane is Ang7, the following mathematical expression (11) is satisfied: (38) The first optical system has, from the pupil side, a concave third refractive surface, the first reflecting surface which is a concave reflecting surface, the second reflecting surface which is the same surface as the third refractive surface and has a convex shape with respect to the light ray reflected by the first reflecting surface, and a fourth refractive surface onto which the light ray reflected by the second reflecting surface is incident, wherein among a group of light rays incident on the second reflecting surface, a light beam incident on the third refractive surface satisfies the total reflection condition shown in the following mathematical formula (13) with respect to the third refractive surface, and among a group of light rays incident on the second reflecting surface, a light beam incident on a region other than the third refractive surface does not satisfy the total reflection condition shown in the following mathematical formula (13) with respect to the region other than the third refractive surface, an intermediate imaging position of a reference ray is inside the first optical system, and the second optical system has at least two refractive surfaces and at least one reflecting surface including a fifth reflecting surface, The optical system according to (29) above, wherein the light reflected by the fifth reflecting surface of the second optical system forms an image on the display element surface. (39) The optical system according to (38), wherein the optical system satisfies the following formula (14): where the direction of a ray of light emerging from a pupil plane is a Z direction and the direction perpendicular to the Z direction is a Y direction, the focal length of the first optical system in a Y cross section is fy1, and the optical path length from the third refracting surface to the fourth refracting surface is OP1. (40) The optical system according to (38) above, wherein the following formula (15) is satisfied, where fr1y is a focal length of the Y cross section of the first reflecting surface that reflects the reference ray, and fy is a focal length of the entire optical system in the Y cross section. (41) The optical system according to (40) above, wherein when the focal length of the first optical system in the Y cross section is fy1, the following formula (16) is satisfied. (42) The optical system according to (38) above, wherein, for a given ray of light having a maximum angle of incidence on the third refracting surface and passing through a region of the first optical system where the third refracting surface and the first reflective surface are physically close to each other, the optical system satisfies the following formula (17), where fray is the focal length of the Y cross section of the first reflective surface and fay is the composite focal length of the Y cross section when the given ray passes through the third refracting surface and the first reflective surface. (43) The optical system according to (42) above, wherein the following formula (18) is satisfied when the focal length of the Y cross section of the first reflecting surface that reflects the reference ray is fr1y. (44) The optical system according to (38) above, wherein the following formula (19) is satisfied, where fr3y is a focal length of the fifth reflecting surface in the Y cross section, and fy is a focal length of the entire optical system in the Y cross section. (45) A display device comprising, from a pupil side, a first optical system, a second optical system, and a display element, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side toward the pupil side, and a second reflecting surface that reflects the light reflected toward the pupil side toward the display element side, the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, the second optical system is arranged on the display element side of an intermediate image forming surface on which the intermediate image is formed, and is configured so that the intermediate image forming surface and the display element surface have a conjugate relationship, and includes at least two surfaces having positive power and one surface having negative power, and the second optical system as a whole has positive power.

[0189] 1, 1a Optical system 10 First optical system 20 Second optical system 100 First optical element 102 First reflecting surface 104, 702, 703 Transmitting surface 110 Second optical element 112 Second reflecting surface 131 Third refractive surface 133 Fourth refractive surface 142 Third concave reflecting surface 143 Fourth concave reflecting surface 172 First concave reflecting surface 174 Second concave reflecting surface 182 First refractive surface 184 Second refractive surface 210 First lens group 220 Second lens group 230, 240 Lens 231, 233, 234, 236 Refractive surface 242 Fifth reflecting surface 245 Reflecting surface 300 Third optical element 302 Fourth optical element 304 Field lens 350 Light guide 352 Frame 402 First wave plate 404a, 404b Second wave plate 412 First polarizer 414 Second polarizer 450 Fifth optical element 460 Third lens group 470 Fourth lens group 500 Pupil 500a Pupil plane 502 Display element 502a Display element plane 510 Intermediate image 510a Intermediate image plane 520 Optical axis 522 Reference light ray 522a Light ray 550 Light source 560 Camera 600 Head-mounted display 611 Display unit 612 Ear hook unit 700 Total reflection surface 711 Third reflection surface 712 Fourth reflection surface

Claims

1. An optical system comprising, in the order from a user's pupil side to a display element side, a first optical system and a second optical system, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side towards the pupil side, and a second reflecting surface that reflects the light reflected towards the pupil side towards the display element side, wherein the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, and the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, and the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed, and is configured so that the intermediate image plane and the display element surface have a conjugate relationship, and has at least three lenses, two of the at least three lenses have different Abbe numbers, and the second optical system as a whole has positive power.

2. The optical system according to claim 1, wherein the first optical system has, in that order from the pupil side to the display element side, a first optical element and a second optical element, the first optical element having a function of reflecting a portion of the light as the second reflective surface, the second optical element has a transmitting surface and a semi-transmissive reflective surface having a concave shape and arranged on the display element side of the transmitting surface as the first reflective surface, the space between the transmitting surface and the semi-transmissive reflective surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, all surfaces of the second optical system have a common axis of rotational symmetry, the intermediate image is formed between the semi-transmissive reflective surface of the second optical element and the first optical element, and the following mathematical formula (1) is satisfied, where fR is a focal length by the semi-transmissive reflective surface and LR is a physical length between the vertices of the surface of the first optical element on the display element side and the semi-transmissive reflective surface.

3. The optical system according to claim 2, wherein the second optical system has, in order from the pupil side to the display element side, a first lens group having negative power and a second lens group having positive power, and when the power of the first lens group is Φ1 and the overall power of the second optical system is Φ, the following formula (2) is satisfied.

4. The optical system described in claim 3, wherein the first lens group is adjacent to the display element side of the second optical element and has a function of reducing peripheral light ray angles, and when a chief ray angle at the outermost periphery from the second optical element to the display element side is Ang1 and a chief ray angle at the outermost periphery from the first lens group to the second lens group is Ang2, the optical system satisfies the following formula (3).

5. The optical system according to claim 4, wherein the following mathematical formula (4) is satisfied when, at a viewing angle of 60 degrees, a ray angle at which a lower ray of marginal rays among light rays incident from a pupil plane enters the second lens group is Ang3 and a ray angle at which the lower ray enters the display element from the second lens group is Ang4; the distance on the optical axis between the pupil plane and the surface of the first optical element located closest to the pupil plane is A; when the pupil is separated from the first optical element in the optical axis direction, the viewing angle is 60 degrees, and there is no light vignetting in the second optical system, A' is the distance on the optical axis between the pupil plane and the surface of the first optical element located closest to the pupil plane; when the pupil is separated from the first optical element in the optical axis direction, the viewing angle is 60 degrees, and there is no light vignetting in the second optical system, P is the exit pupil position of the first optical system at the distance A; and P' is the exit pupil position of the first optical system at the distance A', the following mathematical formula (4) is satisfied.

6. The optical system according to claim 2, wherein the second optical system has a first lens group having positive power on the pupil side, and a second lens group having positive power on the display element side, the chief ray of the second optical system intersecting the optical axis, and satisfies the following formula (6) when the power of the first lens group is Φ1 and the overall power of the second optical system is Φ.

7. The optical system according to claim 1, wherein the first optical system has, in the order from the pupil side to the display element side, a first refractive surface and a second refractive surface, and further has, as the first reflecting surface, a first concave reflecting surface that reflects the light from the first refractive surface to the pupil side, and as the second reflecting surface, a second concave reflecting surface that reflects the light from the first concave reflecting surface to the display element side, the second refractive surface refracts the light from the second concave reflecting surface, the space between the first refractive surface and the second refractive surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, the intermediate image is formed between the first concave reflecting surface and the second concave reflecting surface, the second optical system forms the intermediate image on the display element, and a light ray at the center of the display element becomes a light ray that is incident perpendicularly on the pupil plane.

8. The optical system described in claim 7, wherein the second optical system is rotationally symmetric, the pupil surface and the display element surface are arranged in parallel, and the following mathematical formula (7) is satisfied when L1 is the distance perpendicular to the pupil surface from the pupil surface to the first concave reflecting surface of a light ray having the longest optical path among the optical paths from the pupil surface to the first concave reflecting surface, and L2 is the distance perpendicular to the pupil surface from the pupil surface to the center of the pupil-side surface of the second optical system.

9. The optical system described in claim 2, wherein the first optical element has a first wave plate that shifts the phase of the vertically polarized component of the light by 90 degrees, the second optical system has a third optical element consisting of a second wave plate that shifts the phase of the vertically polarized component of the light by 90 degrees, and the slow axes of the first wave plate and the second wave plate are orthogonal or parallel to each other.

10. The optical system according to claim 9, further comprising a first polarizing plate, which transmits linearly polarized light, on the pupil side of said first wave plate.

11. The optical system according to claim 9, further comprising a second polarizing plate, which transmits linearly polarized light, on the display element side of the second wave plate.

12. The optical system according to claim 9, wherein the first optical element and the third optical element are parallel flat plates.

13. The optical system according to claim 9, wherein the third optical element is disposed on the display element side relative to the second optical element.

14. The optical system according to claim 9, wherein the second optical system further comprises a fourth optical element that separates polarized light and has a surface inclined at 45 degrees with respect to the optical axis.

15. The optical system described in claim 1, further comprising a light guide that is worn by the user so as to be positioned in front of the pupil and that guides an image projected by the display element to the pupil, the first optical system and the second optical system being disposed between the display element and the light guide, and the light guide forming an image of light from the first optical system and the second optical system on the pupil.

16. The optical system according to claim 2, wherein the semi-transmissive reflective surface functions as a transmissive surface for light having a wavelength of 400 nm to 700 nm.

17. The optical system according to claim 7, wherein the first concave reflecting surface functions as a transmissive surface for light having a wavelength of 400 nm to 700 nm.

18. The optical system according to claim 16, further comprising an imaging optical system capable of detecting infrared light, the imaging optical system being provided on the display element side of the first reflecting surface and at a position not overlapping with the second optical system as a detection unit for capturing the movement of the user's pupil.

19. The optical system according to claim 18, comprising a plurality of imaging optical systems including a first imaging optical system and a second imaging optical system, the first imaging optical system and the second imaging optical system being arranged in a symmetrical relationship with respect to the central axis of the first reflecting surface.

20. The optical system according to claim 18, further comprising a light source that irradiates the infrared light, the light source being provided on the display element side of the first reflecting surface and at a position not overlapping with the second optical system and the imaging optical system.

21. The optical system according to claim 20, comprising a plurality of the light sources including a first light source and a second light source, the first light source and the second light source being arranged in a symmetrical relationship with respect to a central axis of the first reflecting surface.

22. The optical system of claim 20, wherein the light source comprises an LED.

23. The optical system described in claim 18, further comprising a control unit that changes the overall power of the second optical system, wherein the detection unit detects movement of the user's pupil as a radial movement amount based on the center of the eyeball, and the control unit changes the overall power of the second optical system based on the detected movement amount.

24. The optical system according to claim 23, wherein the control unit changes the overall power of the second optical system by moving at least two lens groups included in the second optical system along an optical axis.

25. The optical system of claim 23, wherein the second optical system includes at least two liquid lenses, and the control unit changes the overall power of the second optical system by applying a voltage to the liquid lenses.

26. The optical system according to claim 24, wherein when the control unit changes the overall power of the second optical system, the distance between the first optical element and the display element does not change.

27. The optical system according to claim 18, wherein the detection section detects light having a wavelength of 400 nm to 700 nm that has passed through the first optical system.

28. A display device comprising, from a pupil side, a first optical system, a second optical system, and a display element, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side towards the pupil side, and a second reflecting surface that reflects the light reflected towards the pupil side towards the display element side, the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, the second optical system is arranged on the display element side of an intermediate image plane on which the intermediate image is formed, and is configured so that the intermediate image plane and the display element surface have a conjugate relationship, and has at least three lenses, two of the at least three lenses have different Abbe numbers, and the second optical system as a whole has positive power.

29. An optical system comprising a first optical system and a second optical system in the order from the user's pupil side to the display element side, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side to the pupil side, and a second reflecting surface that reflects the light reflected to the pupil side to the display element side, wherein the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, and the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, and the second optical system is arranged on the display element side of an intermediate image surface on which the intermediate image is formed, and is configured so that the intermediate image surface and the display element surface have a conjugate relationship, and includes at least two surfaces having positive power and one surface having negative power, and wherein the second optical system as a whole has positive power.

30. The optical system according to claim 29, wherein the first optical system has, in that order from the pupil side to the display element side, a first optical element and a second optical element, the first optical element having a function of reflecting a portion of the light as the second reflective surface, the second optical element has: a first transmitting surface; and, as the first reflective surface, a semi-transmissive reflective surface arranged on the display element side of the first transmitting surface and having a concave shape, the space between the first transmitting surface and the semi-transmissive reflective surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, the intermediate image is formed between the semi-transmissive reflective surface of the second optical element and the first optical element, and the following mathematical formula (1a) is satisfied, where fR is a focal length by the semi-transmissive reflective surface and LR is a physical length between the vertices of the surface of the first optical element on the display element side and the semi-transmissive reflective surface.

31. The optical system according to claim 29, wherein the first optical system has, in the order from the pupil side to the display element side, a third refractive surface and a fourth refractive surface, and further has, as the first reflecting surface, a third concave reflecting surface that reflects the light from the third refractive surface to the pupil side, and as the second reflecting surface, a fourth concave reflecting surface that reflects the light from the third concave reflecting surface to the display element side, the fourth refractive surface refracts the light from the fourth concave reflecting surface, the space between the third and fourth refractive surfaces is filled with a material having a refractive index greater than 1.4 and less than 2.2, the intermediate image is formed between the third and fourth concave reflecting surfaces, the second optical system forms the intermediate image on the display element, and a light ray at the center of the display element becomes a light ray that is incident perpendicularly on a pupil plane.

32. The first optical system has, in order from the pupil side to the display element side, a first optical element and a second optical element, the first optical element having a function of reflecting a part of the light as the second reflecting surface, the second optical element has: a first transmitting surface; and, as the first reflecting surface, a semi-transmitting reflective surface having a concave shape and arranged on the display element side with respect to the first transmitting surface, the space between the first transmitting surface and the semi-transmitting reflective surface is filled with a material having a refractive index greater than 1.4 and less than 2.2, the second optical system is an optical system having positive power overall for the light flux from the first optical system, and has a fifth optical element filled with a material having a refractive index greater than 1.4 and less than 2.2, the fifth optical element has, in order from the pupil side to the display element side, a second transmitting surface and a third reflective surface, 30. The optical system of claim 29, wherein the first optical system is configured such that light emitted from the pupil side passes through the first optical element, passes through the first transmitting surface of the second optical element, is reflected by the semi-transmissive reflective surface of the second optical element, passes through the first transmitting surface of the second optical element, is reflected at the pupil side or the display element side of the first optical element, passes through the first transmitting surface of the second optical element, and passes through the semi-transmissive reflective surface of the second optical element; and the fifth optical element is configured such that light emitted from the first optical system side passes through the second transmitting surface, is reflected at the third reflective surface, and is totally reflected at the same surface as the second transmitting surface.

33. The optical system according to claim 32, wherein the angle of the third reflecting surface of the fifth optical element with respect to a pupil plane is Ang5, the pupil plane is 0°, and a clockwise direction is negative, satisfying the following formula (9).

34. The optical system of claim 32, wherein the third reflecting surface is a diffractive element surface.

35. The optical system described in claim 33, wherein the second optical system further has a third lens group having at least three lenses, the fifth optical element further has a fourth reflecting surface, and the fifth optical element is configured so that light emitted from the first optical system side passes through the second transmitting surface, is reflected by the third reflecting surface, is totally reflected by the same surface as the second transmitting surface, is reflected by the fourth reflecting surface, and passes through the same surface as the second transmitting surface, and the light that has passed through the same surface as the second transmitting surface is focused by the third lens group and forms an image.

36. The optical system according to claim 35, wherein the angle of the fourth reflecting surface of the fifth optical element with respect to the pupil plane is Ang6, the pupil plane is 0°, and a clockwise direction is negative, thereby satisfying the following formula (10).

37. The optical system according to claim 35, wherein, when the angle of the same surface of the fifth optical element as the second transmitting surface which undergoes total reflection with respect to the direction of light traveling perpendicularly from the pupil plane is Ang7, the following mathematical formula (11) is satisfied.

38. The first optical system has, from the pupil side, a third refractive surface having a concave shape, the first reflecting surface which is a concave reflecting surface, the second reflecting surface which is the same surface as the third refractive surface and has a convex shape with respect to the light reflected by the first reflecting surface, and a fourth refractive surface on which the light reflected by the second reflecting surface is incident, wherein, among a group of light rays incident on the second reflecting surface, a light beam incident on the third refractive surface satisfies the total reflection condition shown in the following formula (13) with respect to the third refractive surface, and, among a group of light rays incident on the second reflecting surface, a light beam incident on a region other than the third refractive surface does not satisfy the total reflection condition shown in the following formula (13) with respect to the region other than the third refractive surface, an intermediate imaging position of a reference light ray is inside the first optical system, and the second optical system has at least two refractive surfaces and at least one reflecting surface including a fifth reflecting surface, The optical system according to claim 29 , wherein the light reflected by the fifth reflecting surface of the second optical system forms an image on the display element surface. In the above formula (13), θ is the angle of incidence and n is the refractive index.

39. The optical system described in claim 38, which satisfies the following formula (14), when the direction of light rays emitted from the pupil plane is the Z direction and the Y direction is a direction perpendicular to the Z direction, the focal length of the first optical system in the Y cross section is fy1, and the optical path length from the third refractive surface to the fourth refractive surface is OP1.

40. The optical system according to claim 38, wherein the following formula (15) is satisfied, where fr1y is a focal length in a Y cross section of the first reflecting surface that reflects the reference ray, and fy is a focal length of the entire optical system in the Y cross section.

41. The optical system according to claim 40, wherein the following formula (16) is satisfied, where fy1 is the focal length of the first optical system in the Y cross section.

42. The optical system according to claim 38, wherein, for a given ray having a maximum angle of incidence on the third refracting surface and passing through a region of the first optical system where the third refracting surface and the first reflective surface are physically close to each other, the focal length of the Y cross section of the first reflective surface is fray, and the composite focal length of the Y cross section of the given ray passing through the third refracting surface and the first reflective surface is fay, the optical system satisfies the following formula (17).

43. The optical system according to claim 42, wherein the following formula (18) is satisfied, where fr1y is the focal length of the Y cross section of the first reflecting surface that reflects the reference ray.

44. The optical system according to claim 38, wherein the following formula (19) is satisfied, where fr3y is a focal length in the Y cross section of the fifth reflecting surface, and fy is a focal length of the entire optical system in the Y cross section.

45. A display device comprising, from a pupil side, a first optical system, a second optical system, and a display element, wherein the first optical system has a first reflecting surface that reflects light emitted from the pupil side towards the pupil side, and a second reflecting surface that reflects the light reflected towards the pupil side towards the display element side, wherein the first reflecting surface has a concave shape and forms an intermediate image on the pupil side, and the pupil side of the first reflecting surface is filled with a material having a refractive index greater than 1, and the second optical system is arranged on the display element side of an intermediate image surface on which the intermediate image is formed, and is configured so that the intermediate image surface and the display element surface have a conjugate relationship, and includes at least two surfaces having positive power and one surface having negative power, and the second optical system as a whole has positive power.

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