Achromatic lenses containing Fresnel optics for near-eye displays

Abstract

An embodiment of the present disclosure provides an achromatic lens. The achromatic lens may include a first lens and a second lens. The first lens has a negative focal length and includes a first optically transparent member having a first surface and a second surface. The second lens is attached to the first lens at the second surface. The second lens has a positive focal length and includes a second optically transparent member having a third surface and a fourth surface. The second chromatic aberration of the second lens is reduced by the first chromatic aberration of the first lens. The second surface of the first lens includes a first Fresnel structure.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of priority to U.S. Patent Application No. 18 / 143,484, filed May 4, 2023, entitled "ACCHROMATIC LENS INCLUDING FRESNEL OPTICAL ELEMENT FOR NEAR EYE DISPLAY," which is incorporated herein by reference in its entirety.

[0002] The present disclosure relates to near-eye display technology. [Background technology]

[0003] The discussion of the background art provided herein is intended to generally present the context for the present disclosure. The work of the presently named inventors is not expressly or implicitly admitted as prior art to the present disclosure, to the extent that that work is described in this background art section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing.

[0004] Near-eye display (NED) devices have been developed to provide improved user experiences in fields such as augmented reality (AR) and virtual reality (VR). NED devices can include various wearable devices such as head-mounted display (HMD) devices and smart glasses. In one example, an HMD device includes a relatively small display device and an optical system capable of creating a virtual image within the field of view of one or both eyes. To the eyes, the virtual image appears distant and much larger than the relatively small display device. Summary of the Invention [Means for solving the problem]

[0005] An embodiment of the present disclosure provides an achromatic lens. The achromatic lens may include a first lens and a second lens. The first lens, having a negative focal length, may include a first optically transparent member having a first surface and a second surface. The second lens may be attached to the first lens at the second surface. The second lens, having a positive focal length, may include a second optically transparent member having a third surface and a fourth surface. The second chromatic aberration of the second lens is reduced by the first chromatic aberration of the first lens, and the second surface of the first lens includes a first Fresnel structure.

[0006] In one embodiment, the second surface includes (i) a smooth central region and (ii) a first Fresnel structure surrounding the central region.

[0007] In one example, the second surface is aspheric.

[0008] In one example, a first ratio between the edge thickness of the first lens and the center thickness of the first lens is 1 to 1.2, and a second ratio between the edge thickness of the second lens and the center thickness of the second lens is 1 / 3 to 1.

[0009] In one example, the lens system includes an achromatic lens and a third lens. The third lens has a positive focal length and can include a third optically transparent member having a fifth surface and a sixth surface. The sixth surface can have a second Fresnel structure.

[0010] The second surface includes (i) a smooth central region and (ii) a first Fresnel structure surrounding the central region of the second surface. The fifth surface includes (i) a smooth central region and (ii) a second Fresnel structure surrounding the central region of the fifth surface. The central region of the second surface corresponds to the central region of the fifth surface.

[0011] In one example, a third ratio between the edge thickness of the third lens and the center thickness of the third lens is between 1 / 3 and 1.

[0012] In one embodiment, the optical system can include a lens system, a beam splitter configured to partially transmit and partially reflect a light beam from the display device, a reflective polarizer configured to pass light having a first linear polarization state and reflect light having a second linear polarization state orthogonal to the first linear polarization state, and a quarter-wave plate (QWP) positioned between the beam splitter and the reflective polarizer. The beam splitter is on a fourth surface of a third lens, and the reflective polarizer is on a first surface of the first lens. In one example, the QWP is on a surface of the first lens, the second lens, or the third lens.

[0013] In one example, the optical system includes a display device. A pixel array of the display device is configured to generate a light beam. The polarization state of the light beam can be a first circular polarization state. A third lens is positioned between the display device and the achromatic lens. A fifth surface of the third lens is configured to face the display device. A second lens is positioned between the first lens and the third lens. A third surface of the second lens is configured to face the third lens.

[0014] In one embodiment, the optical system can include a lens system, a beam splitter configured to partially transmit and partially reflect a light beam from the display device, a reflective polarizer configured to pass light having a first linear polarization state and reflect light having a second linear polarization state orthogonal to the first linear polarization state, and a quarter-wave plate (QWP) positioned between the beam splitter and the reflective polarizer. The reflective polarizer is on a fourth surface of a third lens, and the beam splitter is on a first surface of the first lens. In one example, the QWP is on a surface of the first lens, the second lens, or the third lens.

[0015] In one example, the optical system includes a display device. A pixel array of the display device is configured to generate a light beam. The polarization state of the light beam can be a first linear polarization state. A third lens is positioned between the display device and the achromatic lens. A fifth surface of the third lens is configured to face the display device. A second lens is positioned between the first lens and the third lens. A third surface of the second lens is configured to face the third lens.

[0016] An embodiment of the present disclosure provides an optical system. The optical system may include a lens system including an achromatic lens. The achromatic lens may include a first lens having a negative focal length, the first lens including a first optically transparent member having a first surface and a second surface, and a second lens attached to the first lens at the second surface. The second lens having a positive focal length may include a second optically transparent member having a third surface and a fourth surface. A second chromatic aberration of the second lens is reduced by the first chromatic aberration of the first lens, and the second surface of the first lens includes a first Fresnel structure. The lens system is configured to direct a light beam from a display device to a light receiver.

[0017] Further features, nature and various advantages of the disclosed subject matter will become more apparent from the following detailed description and accompanying drawings. [Brief explanation of the drawings]

[0018] [Figure 1] 1 illustrates a side view of a display system according to some embodiments of the present disclosure. [Figure 2] Examples of eye rotation and head rotation are shown. [Figure 3] This shows the relationship between visual acuity and eccentricity. [Figure 4] 1 illustrates the shape of a surface of a lens according to one embodiment of the present disclosure. [Figure 5]1 illustrates the relationship between surface deflection (in mm) and position along an axis perpendicular to the optical axis, according to one embodiment of the present disclosure. [Figure 6A] 1 illustrates a lens and a corresponding Fresnel lens according to one embodiment of the present disclosure. [Figure 6B] 1 illustrates a display system (eg, a near-eye display system) in a side view, according to some embodiments of the present disclosure. [Figure 6C] 1 illustrates a lens system according to one embodiment of the present disclosure. [Figure 7] 1 illustrates the relationship between surface deflection (in mm) and position along an axis perpendicular to the optical axis, according to one embodiment of the present disclosure. [Figure 8] 1 illustrates the relationship between surface deflection (in mm) and position along an axis perpendicular to the optical axis, according to one embodiment of the present disclosure. [Figure 9] FIG. 1 is a schematic diagram of a computer system according to one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0019] The display system may include a lens system that directs a light beam from a display device or a real object to a receiver. In one example, the lens system and the display device may be configured to be positioned within a distance threshold (e.g., 35 mm) of a user's eye, and the display system may be referred to as a near-eye display (NED) system. For example, the display system may be a head-mounted display (HMD) system worn by a user.

[0020] A lens system can include refractive optical element(s) (e.g., lenses) that refract light. For example, light is refracted at the surface(s) of the lens. In various embodiments, the refractive power or optical power of the lens (e.g., as indicated by the focal length) can be determined by the shape(s) (or surface curvature(s)) of each surface(s) of the lens. Lenses such as Fresnel lenses can be obtained by forming grooved (or uneven, segmented, or sectioned) surfaces that maintain the surface curvature of the continuous surfaces of the lens while using less optical material. Fresnel lenses can include at least one microstructure (also referred to as a Fresnel structure). In one embodiment, the Fresnel structure includes multiple grooves, such as concentric grooves or a set of concentric annular sections. In various examples, Fresnel lenses can be thinner or flatter than their corresponding lenses. The Fresnel lenses and their corresponding lenses can have the same or similar focal lengths.

[0021] The surfaces of the lenses of the lens system can have any suitable shape, such as planar shape(s) parallel to the XY plane, spherical shape(s) with any suitable radius of curvature (e.g., continuous (or grooved) spherical shape or discontinuous (or grooved) spherical shape with a Fresnel structure), aspherical shape(s) (e.g., smooth aspherical shape or grooved aspherical shape with a Fresnel structure), or other shape. As mentioned above, each shape can be smooth or grooved (e.g., a shape including a Fresnel structure).

[0022] In some embodiments, the lenses of the lens system are formed by injection molding and should meet certain requirements, such as low birefringence. To form lenses with low birefringence through injection molding, an appropriate mold flow is used. An appropriate mold flow can be achieved without annealing, for example, if the lens thickness ratio is within a range close to 1 / 1. The lens thickness ratio can be determined based on the minimum and maximum lens thicknesses. In one example, the thickness ratio is the ratio between the edge thickness of the lens and the center thickness of the lens. In some examples, such as FIG. 1, the thickness ratio of the lenses in the lens system can be substantially different from 1 / 1 (e.g., 5 / 3 for the concave lens (131(a)) and 1 / 6 or 1 / 12 for the convex lenses (131(b) or (132))), and manufacturing the lenses in the lens system shown in FIG. 1 can be difficult.

[0023] According to one embodiment of the present disclosure, the lenses in the lens system shown in Figure 1 can be modified to include Fresnel structure(s), and the modified lenses with Fresnel structure(s) in the modified lens system (as shown in Figure 6B) can have a more uniform thickness profile (e.g., along the Y axis), and thus the thickness ratio of the modified lenses with Fresnel structure(s) can be reduced (e.g., closer to 1) than the corresponding thickness ratio of the lenses in the lens system of Figure 1. Thus, the modified lens system with Fresnel structure(s) can have similar or identical parameters to those of the lens system and can have better mold flow in injection molding than the lens system of Figure 1.

[0024] FIG. 1 shows a side view of a display system (e.g., a near-eye display system) (100) according to some embodiments of the present disclosure. The display system (100) includes an optical system (110). Optionally, in one example, the display system includes a shift block (170) and a controller (180). The optical system (110) may include a display device (120), a lens system (130), a beam splitter (BS) (141), a reflective polarizer (139), and a quarter-wave plate (QWP) (142). The display device (120) may include a pixel array configured to emit a light beam to display an image. The lens system (130), the beam splitter (141), the reflective polarizer (139), and the QWP (142) may direct the emitted light beam from the display device (120) to an area (151). In one example, the area (151) is located in the XY plane. In one example, the region (151) is referred to as the exit pupil of the optical system (110). The XY plane includes an X axis and a Y axis orthogonal to the X axis. A light receiver or detector, such as a user's eye (60), can be located in the region (151). In one example, a lens (63) in the eye (60) forms an image on the retina (65) of the eye (60), and thus the eye (60) perceives the image on the display device (120) as a virtual image, such as the virtual image (199) in FIG. 1. The virtual image (199) is displayed at a distance D2 from the region (151) and is larger than the image on the display device (120). The distance D2 is greater, and in some cases much greater, than the distance D1 between the region (151) and the display device (120).

[0025] Referring to FIG. 1 , an optical cavity may be formed between the beam splitter (141) and the reflective polarizer (139). The optical cavity may include one or more lenses in the lens system (130) and the QWP (142). As described below, the optical paths of the light rays in the light beam are folded within the optical cavity between the beam splitter (141) and the reflective polarizer (139). Therefore, the optical system (110) may be positioned within a distance threshold (e.g., 35 mm) of a user's eye (e.g., eye (60)), and the display system (100) may be referred to as an NED system. For example, the display system (100) may be a HMD system worn by a user.

[0026] The lens system (130) may include a lens such as an achromatic lens (131). The achromatic lens (131) may include a first lens (131(a)) and a second lens (131(b)). The first chromatic aberration of the first lens (131(a)) may be complementary (e.g., opposite) to the second chromatic aberration of the second lens (131(b)). The second chromatic aberration may be reduced by the first chromatic aberration. The chromatic aberration of the achromatic lens (131) may be smaller than the first chromatic aberration and the second chromatic aberration. The first lens (131(a)) may include an optically transparent member (145) having two opposing surfaces (135) and (136). The second lens (131(b)) may include an optically transparent member (147) having two opposing surfaces (171) and (172). In one example, the first lens (131(a)) is a diverging lens with a negative focal length, the second lens (131(b)) is a converging lens with a positive focal length, and the achromatic lens (131) is a converging lens with a positive focal length. The second lens (131(b)) can be attached to the first lens (131(a)) at the interface between surfaces (135) and (172). The optical axis (160) of the lens system (130) can be parallel to the Z axis, which is perpendicular to the XY plane. The achromatic lens (131) can have circular symmetry around the optical axis (160).

[0027] In one example, the lens system (130) may include one or more additional lenses. For example, the lens system (130) may include a third lens (132). The third lens (132) may include an optically transparent member (146) having two opposing surfaces (137) and (138). The achromatic lens (131) and the third lens (132) may be separated by a gap (133). In one example, the gap (133) is greater than zero. In another example, a portion of the achromatic lens (131) may be in contact with a portion of the third lens (132), e.g., the minimum distance between the achromatic lens (131) and the third lens (132) is zero. The third lens (132) may have circular symmetry around the optical axis (160).

[0028] Surfaces (135)-(138) and (171)-(172) can have any suitable shape or surface curvature, such as planar shape(s) parallel to the XY plane, spherical shape(s) with any suitable radius of curvature, aspherical shape(s), or other shape(s). The shapes of surfaces (135)-(138) and (171)-(172) can be determined based on design parameters such as focal length, aberration requirements, and lens thickness. The first lens (131(a)) can be a plano-aspherical negative lens, e.g., surface (136) is planar and surface (135) is aspherical, as shown in Figures 1 and 4. In the example shown in Figure 1, a reflective polarizer (139) is disposed on surface (136).

[0029] The surface (172) of the second lens (131(b)) can be aspherical. The shape of the surface (172) of the second lens (131(b)) can match the shape of the surface (135) of the first lens (131(a)). The surface (171) of the second lens (131(b)) can be spherical or aspherical. In one example, the second lens (131(b)) is an aspherical-aspherical positive lens in which the surfaces (171) to (172) are aspherical.

[0030] The third lens (132) may be a spherical-spherical lens, a plano-spherical lens, an aspheric-spherical lens, an aspheric-aspheric lens, etc. The third lens (132) may be referred to as a BS lens, for example, if the BS (141) is disposed on one of the surfaces (137) to (138). In the example shown in FIG. 1, the BS (141) is disposed on the surface (138).

[0031] The optically transparent members (145)-(147) can comprise any suitable material(s), including, but not limited to, glass (e.g., borosilicate glass, heavy flint glass), polymer, plastic material(s) such as poly(methyl methacrylate) (PMMA), polyimide, acrylic, styrene, cyclic olefin polymer, cyclic olefin copolymer, polycarbonate, etc. Glass lenses can be made by grinding and polishing, glass molding, etc. Polymer or plastic lenses can be processed by diamond turning, polishing, injection molding, casting, etc.

[0032] In one example, the material(s) or composition of the material(s) of the optically transparent member (145) is different from the material(s) or composition of the material(s) of the optically transparent member (147) such that a first chromatic aberration of the first lens (131(a)) is complementary to a second chromatic aberration of the second lens (131(b)).

[0033] In some embodiments, a lens with low birefringence (e.g., the first lens (131(a)), the second lens (131(b)), or the third lens (132)) is made by injection molding. To form a lens with low birefringence, an appropriate or good mold flow (e.g., a relatively smooth mold flow) is used. An appropriate mold flow can be achieved without annealing, for example, when the lens thickness ratio is within a range, such as close to 1 / 1. In one example, the lens thickness ratio is defined as (i) the ratio of the minimum lens thickness to the maximum lens thickness, or (ii) the ratio of the maximum lens thickness to the minimum lens thickness. In one example, the lens thickness ratio is defined as the ratio of the lens edge thickness to the lens center thickness, where the maximum lens thickness and the lens minimum thickness include the lens edge thickness and the lens center thickness.

[0034] The first lens (131(a)) can be formed by injection molding using a material(s) such as polycarbonate. The first lens (131(a)) should have low birefringence. Good mold flow (e.g., relatively smooth mold flow) can be achieved without annealing, for example, if the first thickness ratio (e.g., the ratio of the edge thickness of the first lens (131(a)) to the center thickness of the first lens (131(a))) of the first lens (131(a)) is within a first range R1. In one example, the first lens (131(a)) is a concave lens. For a concave lens, R1 may be greater than 1, such as 1 to 1.2. In one example, good mold flow can be achieved without annealing if the first thickness ratio is 1 / 1 or approximately 1 / 1. Referring to FIG. 1, the first thickness ratio of the first lens (131(a)) is relatively large (e.g., 5 / 3) and is outside the first range R1; for example, a first thickness ratio of 5 / 3 may be too large for the injection-molded lens to have low birefringence.

[0035] The second lens (131(b)) can be formed by injection molding. The second lens (131(b)) should have low birefringence. Appropriate mold flow (e.g., a relatively smooth mold flow) can be achieved, for example, when the second thickness ratio (e.g., the ratio of the edge thickness of the second lens (131(b)) to the center thickness of the second lens (131(b))) of the second lens (131(b)) is within a second range R2. In one example, the second lens (131(b)) is a convex lens. For a convex lens, R2 can be less than 1, such as between 1 / 3 and 1 / 1. The second range R2 (e.g., between 1 / 3 and 1 / 1) associated with a convex lens can be greater than the first range R1 (e.g., between 1 and 1.2) associated with a concave lens. Referring to FIG. 1, the second thickness ratio of the second lens (131(b)) is relatively small (e.g., 1 / 12) and is outside the second range R2; for example, a second thickness ratio of 1 / 12 may be too small for the injection-molded lens to have low birefringence.

[0036] The explanation for the second lens (131(b)) can also be applied to the third lens (132), which is a convex lens shown in FIG. 1 . For example, when the third thickness ratio of the third lens (132) (e.g., the ratio of the edge thickness of the third lens (132) to the center thickness of the third lens (132)) is within a third range R3, a suitable mold flow (e.g., a relatively smooth mold flow) can be achieved. In one example, R3 is equal to R2. Referring to FIG. 1 , the third thickness ratio is relatively small (e.g., 1 / 12 to 1 / 6) and falls outside the third range R3. For example, the third thickness ratio may be too small for the injection-molded lens to have low birefringence.

[0037] The display system (100) can be a component within a virtual reality system. The virtual reality system can adjust reality in some way to artificial reality and then present the artificial reality to a user. The virtual reality can include, for example, virtual reality (VR), augmented reality (AR), mixed reality (MR), hybrid reality, or some combination and / or derivative thereof. The virtual reality content can include fully generated content or generated content combined with captured (e.g., real-world) content. The virtual reality content can include video, audio, haptic feedback, or some combination thereof, any of which can be presented in a single channel or multiple channels (such as stereo video to create a three-dimensional effect for the user). In some examples, the display system (100) can be applied to playback of live or pre-recorded video.

[0038] In one embodiment, the "near-eye" display system may include an optical system (e.g., including one or more optical elements) positioned within a distance threshold of a user's eye when the NED system (100) (e.g., HMD, or smart glasses) is utilized. Referring to FIG. 1, the distance D1 between the display device (120) and the region (151) may be less than or equal to the distance threshold. In one example, the distance D1 is between the display device (120) and the eye (60).

[0039] The display system (100) may be an NED system implemented in various forms, such as an HMD system, smart glasses, a smartphone, etc. In some examples, the artificial reality system is implemented as a standalone NED system. In some examples, the artificial reality system is implemented as an NED system connected to a host computer system, such as a server device, a console device, etc.

[0040] The display device (120) may include a pixel array. In some examples, the pixel array includes a plurality of pixels arranged to form a two-dimensional surface. The two-dimensional surface of the display device (120) may be substantially flat or planar, curved, or may include a combination of flat and planar panels. The display device (120) may be a display panel. The display device (120) may include any suitable type(s) of display panel(s), such as liquid crystal display (LCD) panel(s), organic light-emitting diode (OLED) panel(s), etc. The resolution of the display device (120) may be defined according to the pixels in two dimensions or one of the two dimensions of the two-dimensional surface. Each pixel in the pixel array may generate a light beam. Each light beam may include a bundle of light rays in any suitable direction. For example, pixel A on the display device (120) emits a light beam including a bundle of light rays in a suitable direction. A subset of rays (124) within the light beam can be directed toward the region (151) by the lens system (130). The angular span of the subset of light beams (124) can be determined based on the acceptance angle ω of the lens system (130). Three rays (121)-(123) of the subset of light beams (124) are shown in Figure 1. The three rays (121)-(123) can include two boundary rays (121) and (123) and a central ray (122).

[0041] Generally, a light beam is randomly polarized if it contains a rapidly changing series of different polarization states. A light beam can be linearly polarized (e.g., linear polarization states), circularly polarized (e.g., circular polarization states), elliptically polarized (e.g., elliptically polarized states), etc. For linearly polarized light, the electric field vector of the light beam lies along a particular line. For circularly polarized light, the electric field vector of the light beam rotates, for example, clockwise or counterclockwise, as seen by an observer through which the light beam propagates.

[0042] The degree of polarization (DOP) is a quantity that indicates the portion of an electromagnetic wave (e.g., a light beam) that is polarized. A fully polarized wave can have a DOP of 100%, and an unpolarized wave can have a DOP of 0%. A partially polarized wave can be represented by the superposition of polarized and unpolarized wave components and therefore can have a DOP between 0 and 100%. DOP can be calculated as the percentage of the total power carried by the polarized components of a wave (e.g., a light beam).

[0043] The light beam (e.g., the light beam generated from each pixel) can have any suitable polarization state(s) or DOP. In one example, the light beam is circularly polarized with 100% DOP. In one example, the light beam is primarily circularly polarized and has a relatively large DOP above a threshold (e.g., 80% or greater), such as a superposition of (i) a circularly polarized component and (ii) an unpolarized component and / or another polarization component. A circularly polarized beam with 100% DOP or a primarily circularly polarized light beam with a relatively large DOP may be referred to hereinafter as a circularly polarized beam. In one example, the light beam is linearly polarized with 100% DOP or primarily linearly polarized with a relatively large DOP above a threshold. A linearly polarized beam with 100% DOP or a primarily linearly polarized beam with a relatively large DOP may be referred to hereinafter as a linearly polarized beam.

[0044] According to one embodiment of the present disclosure, the light beam generated by the display device (120) can be circularly polarized or linearly polarized.

[0045] The lens system (130) can be configured to modify the light beam generated by the display device (120) and direct the modified light beam toward the region (151). In some embodiments, the lens system (130) can include diffractive elements (gratings and prisms), refractive elements (lenses), guiding elements (e.g., planar waveguides and / or fibers), and polarizing elements (e.g., polarizers, half-wave plates, quarter-wave plates, polarization rotators, Pancharatnam-Berry (PB) phase lenses, etc.). In the example shown in FIG. 1, the lens system (130) includes an achromatic lens (131) and a third lens (132).

[0046] The achromatic lens (131) can be disposed between the display device (120) and the region (151). The third lens (132) can be disposed between the achromatic lens (131) and the display device (120). In one example, the achromatic lens (131) can be referred to as an eye lens depending on its proximity to the region (151) (e.g., the eye (60)), and the third lens (132) can be referred to as a display lens depending on its proximity to the display device (120).

[0047] The beam splitter (141) and the reflective polarizer (139) can be disposed between the region (151) and the display device (120). The quarter-wave plate (142) can be disposed between the beam splitter (141) and the reflective polarizer (139), such as on surface (136), surface (135), surface (171), surface (138), or surface (137). Anti-reflection (AR) coating(s) can be applied to any appropriate surface(s) of the lens system (130) to reduce unwanted reflections of the light beam.

[0048] The beam splitter (141) can be configured to partially transmit and partially reflect the light beam incident on the beam splitter (141). The beam splitter (141) can have an average light transmittance T and an average light reflectance R. In one example, the sum of T and R is 1 (i.e., 100%) over a certain wavelength range (e.g., 380 to 780 nanometers (nm)). The average light transmittance T and average light reflectance R of the beam splitter (141) can be referred to as T / R. T or R can be within a certain range (e.g., 40% to 60%). In one example, the beam splitter (141) has a T / R of 40 / 60, 50 / 50, or 60 / 40. For example, if T and R are 50%, the beam splitter (141) transmits 50% and reflects 50% of the light beam incident on the beam splitter (141). Generally, the beam splitter may include one or more thin films coated or deposited on the surfaces of the lenses in the lens system 130. The beam splitter 141 may include, for example, one or more thin films coated or deposited on the surface 138 of the third lens 132. The beam splitter 141 partially transmits and partially reflects the light beam from the display device 120.

[0049] The polarization state of a light beam can be changed as the light beam passes through certain optical elements. In one embodiment, the polarization state of a light beam can be changed by a wave plate or a retarder as the light beam passes through the wave plate. The quarter-wave plate (142) can change the polarization state of a light beam passing through the quarter-wave plate (142) by 90° or π / 2. In one example, the quarter-wave plate (142) converts linearly polarized light to circularly polarized light or circularly polarized light to linearly polarized light. The quarter-wave plate (142) can be formed on a surface within the lens system (130).

[0050] The reflective polarizer (139) can be configured to pass a light beam having a first linear polarization state and reflect a light beam having a second linear polarization state. The second linear polarization state is orthogonal to the first linear polarization state. The reflective polarizer (139) can include one or more layers of optical film. In one example, the reflective polarizer (139) is formed on a surface within the lens system (130).

[0051] 1, the beam splitter (141), the quarter-wave plate (142), and the reflective polarizer (139) can conform to the shape of their respective surfaces. For example, the beam splitter (141) and the quarter-wave plate (142) are curved to conform to the shape of the surfaces (138) and (171), respectively. The reflective polarizer (139) is planar to conform to the shape of the surface (136). In another example, the quarter-wave plate (142) is formed on the surface (136).

[0052] Referring to Figure 1, the beam splitter (141) is disposed on the surface (138) of the third lens (132), and the reflective polarizer (139) is disposed on the surface (136) of the first lens (131(a)). The quarter-wave plate (142) is formed on the surface (171) of the second lens (131(b)). An optical cavity can be formed between the beam splitter (141) and the reflective polarizer (139). The optical cavity can include the achromatic lens (131), the gap (133), and the QWP (142).

[0053] The light beam emitted from the display device (120) can pass through a third lens (132) and partially transmit through a beam splitter (141). The light beam then passes through the optical cavity multiple times. In one example, the light beam passes through the optical cavity a first time and is reflected by the reflective polarizer (139). The light beam then passes through the optical cavity a second time and is partially reflected by the beam splitter (141). After passing through the optical cavity a third time, the light beam passes through the reflective polarizer (139) and reaches the region (151).

[0054] The optical system (110) includes a catadioptric system, for example, a catadioptric system (110) that includes (i) a refractive optical component (e.g., a lens system (130)) and (ii) a reflective optical component (e.g., a beam splitter (141) when acting as a reflector that reflects light, and a reflective polarizer (139) when acting as a reflector that reflects light).

[0055] The catadioptric system (110) may include a polarized catadioptric system. For example, each time a light beam passes through the QWP (142), the polarization state of the light beam is manipulated by the QWP (142). Thus, the light beam is in one polarization state and is reflected by the reflective polarizer (139) after the first pass, and the light beam is in another polarization state and is transmitted by the reflective polarizer (139) after the third pass through the optical cavity.

[0056] The optical system (110) is sometimes referred to as a folded optical system. Because the light beam is reflected between the beam splitter (141) and the reflective polarizer (139) and travels through the optical cavity multiple times (e.g., three times), the optical path between the display device (120) and the region (151) includes a folded path (125) between the beam splitter (141) and the reflective polarizer (139). The folded optical path allows the distance D1 to be reduced, allowing the display system (100) including the optical system (110) to be used as an NED system. In one example, the lens system (130) is designed to have a relatively small thickness D5, which may be referred to as a pancake lens system.

[0057] 1, a light ray (122) emitted from pixel A of a display device (120) passes through a third lens (132) and is partially transmitted by a beam splitter (141). The light ray (122) then makes a first pass through the optical cavity, where the light ray (122) passes sequentially through a gap (133), a QWP (142), an optically transparent member (147), and an optically transparent member (145).

[0058] After the light beam (122) passes through the optical cavity for the first time, it is reflected back into the optical cavity by the reflective polarizer (139). The light beam (122) then passes through the optical cavity a second time, where it passes sequentially through the optically transparent member (145), the optically transparent member (147), the QWP (142), and the gap (133).

[0059] After the light ray (122) passes through the optical cavity a second time, the light ray (122) is partially reflected back into the optical cavity by the beam splitter (141). Subsequently, the light ray (122) passes through the optical cavity a third time, where the light ray (122) passes sequentially through the gap (133), the QWP (142), the optically transparent member (147), and the optically transparent member (145). The light ray (122) is then transmitted by the reflective polarizer (139) and proceeds to the region (151). In one embodiment, the light ray (122) is focused onto the retina (65) by the lens (63) of the eye (60), and the eye (60) perceives the light ray (122) as if it were from a virtual point A″ on the virtual image (199).

[0060] A light beam emitted from a pixel (e.g., including pixel A) in the display device (120) may be circularly polarized to a first circular polarization state. The beam splitter (141) partially transmits the light beam (122) with the first circular polarization state. The light beam (122) then passes through the optical cavity as described above. During the first pass, the first circular polarization state of the light beam (122) is converted to a second linear polarization state by the QWP (142). The second linear polarization state is aligned with the block direction of the reflective polarizer (139). The block direction of the reflective polarizer (139) refers to the direction in which the light beam is blocked by the reflective polarizer (139) and is not transmitted through the reflective polarizer (139) if the electric field vector of the light beam is aligned with the block direction. The reflective polarizer (139) reflects the light beam (122) having the second linear polarization state with a relatively high average reflectance, for example, greater than or equal to 90%, over a wavelength range (e.g., 380-780 nm). The light beam (122) then passes through the optical cavity a second time, as described above, where the light beam (122) is partially reflected by the beam splitter (141). The light beam (122) then passes through the optical cavity a third time, as described above. On both the second and third passes, the QWP (142) changes the polarization state of the light beam (122). Thus, the second linear polarization state of the light beam (122) is converted to a first linear polarization state parallel to the transmission direction of the reflective polarizer (139). Thus, the reflective polarizer (139) transmits light rays (122) having a first linear polarization state such that the light rays (122) are directed into a region (151) of relatively high transmittance, e.g., 90% or greater, across a wavelength range (e.g., 380-780 nm).

[0061] Referring to FIG. 1, the optical path includes a folded path (125) between the reflective polarizer (139) and the beam splitter (141) due to the polarization change.

[0062] In one embodiment, the positions of the beam splitter (141) and the reflective polarizer (139) are interchangeable, for example, the reflective polarizer (139) is disposed on the surface (138) of the third lens (132) and the beam splitter (141) is disposed on the surface (136) of the first lens (131(a)).

[0063] To achieve high-quality imaging, the reflective polarizer (139) should have high quality, such as high reflectivity (e.g., high average reflectivity) in the block direction, high transmittance (e.g., high average transmittance) in the pass direction, relatively low surface roughness, etc. Additionally, AR coatings can be applied to any appropriate surface(s) within the optical system (110) to reduce or eliminate ghosting due to multiple reflections at various interfaces.

[0064] Polarized catadioptric systems are an emerging solution for virtual reality HMDs. Good VR optics can accommodate multiple interpupillary distances and include a large pupil volume (also referred to as the eyebox) to allow for eye rotation as the user scans across the FOV. In one example, the eyebox refers to the volume within which the eye receives an acceptable view of the image. The size and location of the eyebox can be related to several constraints, such as FOV and image quality. In one example, the eyebox refers to the range of eye positions at the eye relief distance within which the image generated by the optical system (110) is visible. The eyebox can accommodate eye movements, such as eye rotation and / or lateral movement.

[0065] Refractive power can indicate the degree to which an optical system or optical component (e.g., a lens or curved mirror) converges or diverges light. In one example, the refractive power of an optical component or system is equal to the reciprocal of the focal length f of the optical component or system. A higher refractive power indicates (i) a stronger optical power of a converging optical component / system, or (ii) a stronger diverging power of a diverging optical component / system.

[0066] Polarized catadioptric systems, such as optical system (110), can achieve relatively high optical power in a compact form factor by using a folded optical path (e.g., folded path (125)). In the example shown in FIG. 1, the beam splitter (141) is a curved mirror that partially reflects and partially transmits light, and the reflective polarizer (139) can either reflect as a flat mirror or transmit light depending on the polarization state of the light. The design freedom available in folded optical systems (e.g., optical system (110)) can provide benefits to HMD systems. Advantages may include high resolution achieved with reflective imaging, a wide FOV (e.g., by using low-aberration lenses), compact size, reduced weight, the ability to adjust focus, and the creation of a larger eyebox. The FOV can refer to the extent of the observable world seen or detected by a light receiver (also referred to as a light sensor). In one example, the FOV is indicated by the solid angle over which the light detector can detect or receive light. The optical system (110) shown in Figure 1 can be fabricated by controlling the curvature and surface finish of the achromatic lens (131). Pancake optical systems (e.g., optical system (110)) can provide a comfortable and immersive user experience.

[0067] The optical system (110) can have a large pupil volume to accommodate multiple interpupillary distances and allow for eye rotation as the user scans across the FOV. The interpupillary distance (IPD) is the distance between the centers of the pupils of a user's eyes. The IPD can vary with age, gender, etc. The optical system (110) can be designed by taking into account the variance in IPD so that the optical system (110) can accommodate a variety of users with different IPDs. In one example, the IPD varies from approximately 50 mm to 80 mm.

[0068] In one example, to allow a user to enjoy VR without prescription glasses or with dynamic focus, the optical system (110) can adjust the diopter of the lenses in the lens system (130) to match the prescription. In one example, the diopter indicates the virtual object distance. Increasing the diopter can make objects appear closer. Focus adjustment can be achieved by changing the optical power of the optical system. The optical power of the folding mirror cavity (e.g., the optical cavity between the beam splitter (141) and the reflective polarizer (139)) can be changed by changing the cavity length (or gap) relative to a reference cavity length corresponding to a reference refractive power.

[0069] The controller (180) is coupled to the optical system (110) and the shift block (170) and controls the operation of the optical system (110) and the shift block (170).

[0070] The shift block (170) can include a mechanical shifter. In some examples, the mechanical shifter can shift the position of the display device (120). In some examples, the mechanical shifter can shift the position(s) of at least one optical element (e.g., the achromatic lens (131) or the third lens (132) in the lens system (130)). Relatively small adjustments to the gap (133) can be amplified, for example, by a factor of three, by the folded path (125) in the optical cavity.

[0071] The display system (100) may include other suitable mechanical, electrical, and optical components. For example, the display system (100) may include a frame (101) that may protect other components of the display system (100). In another example, the display system (100) may include a strap (not shown) for attaching the display system (100) to a user's head. In another example, the display system (100) may include communication components (not shown, e.g., communication software and hardware) for wirelessly communicating with a network, a host device, and / or other devices. In some examples, the display system (100) may include an optical combiner that may combine virtual content with a see-through real-world environment.

[0072] Considering human factors such as human vision (e.g., FOV of the human eye, eye rotation), head rotation, etc., can be helpful in designing the optical parameters of the optical system 110. An optical design with high resolution across the range of eye rotation can make the user's viewing experience more natural.

[0073] Unconstrained or involuntary eye rotation may be less than 20°. FIG. 2 shows examples of eye rotation and head rotation. Horizontal involuntary eye rotation may be less than a value (e.g., 20°) to the left or right of center, such as 15°±2°. Horizontal conscious eye rotation may be greater than horizontal involuntary eye rotation. In one example, horizontal conscious eye rotation is up to a value such as 30°±2°. In another example, the eyes may rotate approximately 28°±8° up and 47°±8° down. FIG. 2 also shows examples of natural head movement. In one example, the natural head movement is 45°±2° horizontally.

[0074] In one example, a human has a forward-facing horizontal arc of vision without eye movement of slightly more than 210°. The horizontal FOV of both human eyes may be 210°. The vertical extent of a human's field of vision (or vertical FOV) is approximately 150°.

[0075] The human eye is not a perfect lens across a wide FOV. Visual acuity can refer to the clarity or sharpness of vision. Eccentricity can refer to the angular distance from the center of the visual field or the retinal fovea. Figure 3 illustrates the relationship between visual acuity (including peripheral vision) and eccentricity. Visual acuity can decrease with eccentricity. Therefore, the resolution of an optical system in the peripheral field can be lower than the resolution of the optical system in the central field because the eye lacks visual acuity in the peripheral field without rotation to directly gaze at the peripheral field. Considering visual acuity can help avoid over-designing an optical system.

[0076] In some examples, the parameters of the display system (100) include the field of view (FOV), eye relief, lens track length, display size, size of the region (151), etc. The eye relief (e.g., distance D3) can refer to the distance between the optical receiver (e.g., region (151)) and the lens system (130). In one example, the distance D3 between the region (151) and the last optical component (e.g., the achromatic lens (131)) in the optical system (110) before the region (151) is 14 mm. The lens track length (e.g., distance D4) can refer to the distance between the display device (120) and the lens system (130). The distance D4 between the display device (120) and the achromatic lens (131) is 19.5 mm. In the example shown in FIG. 1, the distance D4 is measured from the display device (120) to the surface (136). In one example, D1 is equal to the sum of D3 and D4. In another example, distance D4 is measured from the display device (120) to the surface (137). The display size is indicated by a display image circle imaged by the optical system (110) onto the area (151), and the radius of the display image circle is 18.9 mm. The size of the area (151) (e.g., pupil size) is 5 mm. The FOV of the optical system (110) is 110°. The optical system (110) can form a virtual image (199) from the image on the display device (120) for a suitable range of polychromatic wavelengths, such as visible wavelengths (e.g., 380-780 nm in a 400 nm bandwidth) and polychromatic wavelengths near green (e.g., 500-540 nm in a 40 nm bandwidth). The parameter values ​​provided herein are merely exemplary and are not intended to limit the scope of the present disclosure.

[0077] FIG. 4 illustrates the shape of the surface (135) according to one embodiment of the present disclosure. The shape of the surface (135) can be represented by sagitta. The sagitta or deflection can indicate the material removed to create the optical surface (or optical curve). FIG. 4 illustrates the relationship between the deflection (in mm) of the surface (135) and the position along an axis perpendicular to the optical axis (160) (e.g., the Y-axis). In one example, the deflection indicates the distance along the optical axis (160) between a line (173) and a respective point on the curve (135) formed by the intersection of the surface (135) of the first lens (131(a)) with the YZ plane. The line (173) passes through a vertex V2 of the surface (135) and is tangent to the surface (135). The position of V2 is the center (e.g., 0 mm) of the first lens (131(a)), and the deflection at V2 is 0 mm. (i) Minimum sagitta S of the surface (135) min (e.g., 10 mm or −10 mm), and (ii) the maximum sagitta S of the surface (135). max The sagitta difference (e.g., maximum sagitta difference) between the sagitta values ​​(e.g., 30 mm or -30 mm) is about 3 mm. The shape of surface (172) can match the shape of surface (135). In one example, the shape of surface (172) is dictated by the shape of surface (135).

[0078] Figure 5 shows an example relationship between the deflection (in mm) of surface (137) and the position along an axis perpendicular to the optical axis (160) (e.g., the Y-axis). The deflection can be the distance along the optical axis (160) between line (174) and a respective point on the curve (137) formed by the intersection of surface (137) with the YZ plane. Line (174) passes through vertex V1 of surface (137) and is tangent to surface (137). In Figure 5, (i) the minimum sagitta S of surface (137) is shown. min (e.g., about 30 mm or -30 mm) and (ii) the maximum sagitta S of the surface (137). max The sagitta difference (e.g., maximum sagitta difference) between the first lens (131(b)) and the second lens (131(c)) (e.g., 0 mm) is about 8.5 mm. In one example, the shape of the surface (171) of the second lens (131(b)) is the same as or similar to the shape of the surface (137), as can be seen in FIG.

[0079] In some examples, one of the first thickness ratio of the first lens (131(a)), the second thickness ratio of the second lens (131(b)), and the third thickness ratio of the third lens (132) is outside its respective range, and therefore, it may be difficult to manufacture the lens system (130). Referring to FIG. 1, the first thickness ratio of the first lens (131(a)) (e.g., 5 / 3) is outside the first range R1, the second thickness ratio of the second lens (131(b)) (e.g., 1 / 12) is outside the second range R2, and the third thickness ratio of the third lens (132) (e.g., 1 / 12 to 1 / 6) is outside the third range R3. Therefore, it may be difficult to form the first lens (131(a)), the second lens (131(b)), and the third lens (132) with low birefringence using, for example, injection molding. According to one embodiment of the present disclosure, the lens system (130) can be modified by including one or more microstructures, such as, for example, Fresnel structures, to allow for a compact lens shape that is more compatible with certain manufacturing methods (e.g., injection molding) while maintaining optical power. In one embodiment, the achromatic lens (131) can be modified to include a Fresnel optical element or Fresnel lens.

[0080] 6A shows a lens (190) and a corresponding Fresnel lens (191) according to one embodiment of the present disclosure. The lens (190) includes an optically transparent member between surfaces (193) and (194). The lens (190) has a maximum thickness T1, for example, at the center of the lens (190). The Fresnel lens (191) may include an optically transparent member between surfaces (195) and (196). The surface curvature of surface (193) of the lens (190) can be maintained by the grooved surface (195) of the Fresnel lens (191), and therefore, the Fresnel lens (191) can have the same or substantially the same focal length as the lens (190). For example, the smooth surface 193 of the lens 190 is divided into smaller concentric portions 181-185, and the portions 181-185 are shifted along the optical axis of the lens 190 (e.g., parallel to the Z axis in FIG. 6A ) to form the Fresnel lens 191. In one example, the shapes of the portions 181-185 of the lens 190 are identical or substantially identical to the shapes of the portions 181-185 of the Fresnel lens 191, respectively.

[0081] Portions 181-185 of Fresnel lens 191 correspond to portions 181-185 of lens 190; for example, portions 181-185 of Fresnel lens 191 have the same shape and material as portions 181-185 of lens 190. To explain the relationship between lens 190 and Fresnel lens 191, portions 161-164 of lens 190 can be considered to have been removed, and the remaining portions 181-185 of lens 190 can be considered to have been realigned (e.g., parallel to the XY plane) with respect to surface 196. Lens 190 can be considered to be folded back into Fresnel lens 191 while maintaining the surface curvature of surface 193 and, therefore, the refractive power of lens 190. The continuous surface 193 can be a grooved surface 195 having discontinuities between adjacent portions 181-185. For example, the Fresnel lens 191 has a maximum thickness T2 at its center that is less than the thickness T1 at the center of the lens 190. Various methods can be used to manufacture the Fresnel lens 191.

[0082] In some embodiments, the surface of a portion (e.g., central portion) 181 of the Fresnel lens 191 is continuous (or smooth) and does not include a Fresnel structure. The surface of a peripheral portion (e.g., including portions 182-185) of the Fresnel lens 191 surrounding the central portion 181 may be discontinuous or grooved and may include a Fresnel structure. The size of the central portion 181 that does not include a Fresnel structure and the size of the peripheral portion that includes a Fresnel structure can be selected based on, for example, design requirements.

[0083] Referring to FIG. 6A, the Fresnel structure can include multiple grooves (e.g., prisms), such as portions 182-185. In one example, portions 182-185 are concentric grooves. A pitch (e.g., prism pitch) P can represent the spacing between adjacent grooves (e.g., prisms). The pitch P can be non-uniform (as shown in FIG. 6A) or uniform. A tilt angle θ can represent the angle between surface 196 and each portion (e.g., 195(1)) of surface 195. Parameters of the Fresnel lens 191, including, but not limited to, the size of the pitch P, the distribution of the pitch P across the Fresnel structure, and the tilt angle θ, can be determined based on, for example, design requirements.

[0084] In some examples, the size(s) of each central portion(s) of the Fresnel lens, such as the size of central portion (181), is less than a threshold value, for example, the size of central portion (181) is comparable to or the same as the pitch of another groove (e.g., (182)), and multiple grooves can include central portion(s) (e.g., (181)), and the Fresnel structure can include the entire Fresnel lens.

[0085] Achromatic lenses can reduce chromatic aberrations in optical lens systems. Head-mounted and / or near-eye display optical systems can use compact optical lens modules to provide devices with compact forms, such as pancake optics. Fresnel structures can be used to reduce lens thickness or lens size, for example, by flattening the lens in a relatively uniform manner. The inclusion of Fresnel-like structures can facilitate the manufacture of compact achromatic lenses.

[0086] FIG. 6B shows a side view of a display system (e.g., a near-eye display system) (600) according to some embodiments of the present disclosure. The display system (600) includes an optical system (610), a shift block (670), and a controller (680). The optical system (610) may include a display device (620), a lens system (630), a BS (641), a reflective polarizer (639), and a QWP (642). The lens system (630) may include an achromatic lens (631). The achromatic lens (631) may include a first lens (631(a)) and a second lens (631(b)). The first lens (631(a)) may include an optically transparent member (645) having two opposing surfaces (635)-(636). The second lens (631(b)) may include an optically transparent member (647) having two opposing surfaces (671)-(672). The second lens (631(b)) may be attached to the first lens (631(a)) at the interface between the surfaces (635) and (672). In one example, the second lens (631(b)) is directly attached to the first lens (631(a)). In another example, the second lens (631(b)) is attached to the first lens (631(a)) via a transparent layer. The thickness of the layer is much smaller (e.g., 1 / 10) than the thicknesses of the first lens (631(a)) and the second lens (631(b)). The optical axis (660) of the lens system (630) may be parallel to a Z-axis perpendicular to the XY plane. In one example, the lens system 630 includes a third lens 632. The third lens 632 can include an optically transparent member 646 having two opposing surfaces 637-638. The achromatic lens 631 and the third lens 632 can be separated by a gap 633.

[0087] The lens system (630), optical system (610), and display system (600) of FIG. 6B may be related to the lens system (130), optical system (110), and display system (100), respectively, of FIG. 1. According to one embodiment of the present disclosure, the lens system (630) may be a variation of the lens system (130). Thus, the optical system (110) and the display system (100) may be modified as the optical system (610) and the display system (600), respectively. At least one of the surfaces (135)-(138) and (171)-(172) may be modified such that at least one of the surfaces (635)-(638) and (671)-(672) includes a Fresnel structure, such as a plurality of grooves. Thus, the lens system (630) includes at least one Fresnel lens.

[0088] FIG. 6C illustrates a lens system (630) according to one embodiment of the present disclosure. Referring to FIGS. 6B-6C, the interface between surfaces (635) and (672) can have a surface profile based on a Fresnel structure (681). Surface (635) can include the Fresnel structure (681). Surface (672) can include a Fresnel structure having the same profile as Fresnel structure (681). Surface (637) can include the Fresnel structure (682). Thus, the first lens (631(a)), the second lens (631(b)), and the third lens (632) are Fresnel lenses. The surface curvature of the surface (135) of the first lens (131(a)) in FIG. 1 can be maintained by the grooved surface (635) of the first lens (631(a)), and the first lens (631(a)) can have the same or similar focal length as the first lens (131(a)). Referring to FIG. 6C, the central portion (or central region) (683) of the first lens (631(a)) can be smooth and free of Fresnel structures, and the Fresnel structures (681) can surround the central region (683).

[0089] The lens may include a central region and a peripheral region surrounding the central region. The central region of the lens may be used for high-resolution and low-ghost viewing / imaging, while viewing / imaging through the peripheral region of the lens may have low resolution. Fresnel structures (also referred to as Fresnel lens structures or Fresnel features) may cause diffraction artifacts, and therefore viewing and / or imaging through a region including a Fresnel structure may reduce resolution. In some examples, incorporating Fresnel features in a lens region used for a high-resolution and low-ghost optical (viewing / imaging) path (e.g., the central region of the lens) may be less desirable. In various embodiments, a good optical viewing area may be within an FOV threshold, such as a 70° on-axis field of view. Thus, the Fresnel structure or Fresnel feature may be included outside the FOV threshold (e.g., a 70° FOV), ensuring that the Fresnel structure only affects low-resolution far-field peripheral vision, for example, while improving lens manufacturability, as described above.

[0090] Referring to FIG. 6C , a central portion (or central region) (683) of the first lens (631(a)) within an FOV threshold (e.g., an FOV of 70°) does not include a Fresnel structure. The Fresnel structure (681) surrounding the central region (683) may be disposed outside the FOV threshold. The size (e.g., diameter) of the central region (683) may depend on the FOV threshold (e.g., 70°). In one example, the size of the central region (683) depends on the FOV threshold (e.g., 70°) and the distance D3 (or eye relief). The size of the central region (683) may increase with the FOV threshold (e.g., 70°) and the distance D3 (or eye relief).

[0091] FIG. 7 illustrates the relationship between the deflection (in mm) of the surface (635) and the position along an axis (e.g., the Y-axis) perpendicular to the optical axis (660). In one example, the deflection represents the distance along the optical axis (660) between a line (673) and a respective point on the curve (635) formed by the intersection of the surface (635) of the first lens (631(a)) with the YZ plane. The line (673) passes through the vertex V2 of the surface (635) and is tangent to the surface (635). Referring to FIG. 7, the position of V2 is at the center (e.g., 0 mm) of the first lens (631(a)), and the deflection at V2 is 0 mm. (i) The minimum sagitta S of the surface (635) min( (e.g., about 10 mm or -10 mm), and (ii) the maximum sagitta S of the surface (635). max The sagittability difference (e.g., maximum sagittability difference) between the Fresnel structure (681) and the Fresnel structure (631(a)) is approximately 0.5 mm. The Fresnel structure (681) in FIG. 6B corresponds to region (711) in FIG. 7. The central region (683) without the Fresnel structure corresponds to region (712) in FIG. 7. As can be seen from FIGS. 6B, 6C, and 7, by incorporating the Fresnel structure (681) into the first lens (631(a)), the first lens (631(a)) can be flattened, resulting in a more uniform thickness profile, and the first thickness ratio of the first lens (631(a)) is closer to 1 / 1 than the first thickness ratio of the first lens (131(a)).

[0092] The above description of surface (635) and first lens (631(a)) can be applied to surface (672) and second lens (631(b)). The surface curvature of surface (172) of second lens (131(b)) shown in FIG. 1 can be maintained by grooved surface (672) of second lens (631(b)), and second lens (631(b)) can have the same or similar focal length as second lens (131(b)). In the example of FIGS. 6B-6C, the central portion (or central region) of second lens (631(b)) coincident with central portion (683) can be smooth and free of Fresnel structures, and a Fresnel structure consistent with Fresnel structure (681) can surround central region (683). In one embodiment, a central portion (or central region) of the smooth second lens (631(b)) is within an FOV threshold (e.g., a 70° FOV), and a Fresnel structure matching the Fresnel structure (681) surrounding the central region may be outside the FOV threshold. As can be seen from FIGS. 6C and 7 , incorporating a Fresnel structure matching the Fresnel structure (681) into the second lens (631(b)) can flatten the second lens (631(b)), resulting in a more uniform thickness profile, with the second thickness ratio of the second lens (631(b)) being closer to 1 / 1 than the second thickness ratio of the second lens (131(b)) in FIG. 1 .

[0093] The above description of surface (635) and first lens (631(a)) can be applied to surface (637) and third lens (632). The surface curvature of surface (137) of third lens (132) shown in FIG. 1 can be maintained by the discontinuous surface (637) of third lens (632), and third lens (632) can have the same or similar focal length as third lens (132).

[0094] FIG. 8 illustrates the relationship between the deflection (in mm) of the surface (637) and the position along an axis perpendicular to the optical axis (660) (e.g., the Y-axis). In one example, the deflection represents the distance along the optical axis (660) between a line (674) and a respective point on the curve (637) formed by the intersection of the surface (637) of the third lens (632) with the YZ plane. The line (674) passes through the vertex V1 of the surface (637) and is tangent to the surface (637). In FIG. 8, the position of V1 is 0 mm, and the amount of deflection at V1 is 0 mm. In FIG. 8, (i) the minimum sagitta S of the surface (637) is shown. min (e.g., about 30 mm or -30 mm) and (ii) the maximum sagitta S of the surface (637). max The sagitta difference (or maximum sagitta difference) between the Fresnel structure (682) and the third lens (632) (e.g., 0 mm) is approximately 6 mm. The Fresnel structure (682) in FIGS. 6B-6C corresponds to region (811) in FIG. 8. The smooth central region (684) without the Fresnel structure corresponds to region (812) in FIG. 8. As can be seen from FIGS. 6C and 8, by incorporating the Fresnel structure (682) into the third lens (632), the third lens (632) can be flattened, resulting in a more uniform thickness profile, and the third thickness ratio of the third lens (632) is closer to 1 / 1 than the third thickness ratio of the third lens (132).

[0095] Referring to FIG. 6C , the central portion (or central region) (684) of the third lens (632) may be smooth and free of Fresnel structures, with the Fresnel structures (682) surrounding the central region (684). The central portion (or central region) (684) of the third lens (632) within an FOV threshold (e.g., an FOV of 70°) may be free of Fresnel structures. The Fresnel structures (682) surrounding the central region (684) may be disposed outside the FOV threshold. The size (e.g., diameter) of the central region (684) may depend on the FOV threshold (e.g., 70°). In one example, the size of the central region (684) depends on the FOV threshold (e.g., 70°) and the distance D3 (or eye relief). The size of the central region (684) may increase with the FOV threshold (e.g., 70°) and the distance D3 (or eye relief).

[0096] Referring back to FIG. 6B, the first chromatic aberration of the first lens (631(a)) can be complementary (e.g., opposite) to the second chromatic aberration of the second lens (631(b)). The second chromatic aberration can be reduced by the first chromatic aberration. The chromatic aberration of the achromatic lens (631) can be smaller than the first chromatic aberration or the second chromatic aberration.

[0097] The surfaces (635)-(638) and (671)-(672) can have any suitable shape, such as planar shape(s) parallel to the XY plane, spherical shape(s) with any suitable radius of curvature, aspherical shape(s), or other shape(s). The shapes of the surfaces (635)-(638) and (671)-(672) can be determined based on design parameters such as the thickness ratio, focal length, aberration requirements, and lens thickness of the first lens (631(a)), second lens (631(b)), and third lens (632). The first lens (631(a)) can be, for example, a plano-aspherical negative lens in which the surface (636) is planar and the surface (635) is aspherical, as shown in Figures 6C and 7. In the example shown in Figure 6B, a reflective polarizer (639) is disposed on the surface (636).

[0098] The surface (672) of the second lens (631(b)) can be aspheric. The shape of the surface (672) of the second lens (631(b)) can match the shape of the surface (635) of the first lens (631(a)). The surface (671) of the second lens (631(b)) can be spherical or aspheric. In one example, the second lens (631(b)) is an aspheric-aspheric positive lens.

[0099] The third lens 632 may be a spherical-spherical lens, a plano-spherical lens, an aspheric-spherical lens, an aspheric-aspheric lens, etc. The third lens 632 may be referred to as a BS lens, for example, if the BS 641 is disposed on one of the surfaces 637-638. In the example shown in FIG. 6B, the BS 641 is disposed on the surface 638.

[0100] The descriptions of the optically transparent members (145)-(147), surface (136), surface (171), surface (138), beam splitter (141), reflective polarizer (139), QWP (142), display device (120), region (151), controller (180), and shift block (170) in Figure 1 are applicable to the optically transparent members (645)-(647), surface (636), surface (671), surface (638), beam splitter (641), reflective polarizer (639), QWP (642), display device (620), region (651), controller (680), and shift block (670) in Figure 6B, respectively. In another example, the quarter-wave plate (642) is formed on surface (636). Rays 121-123 and a subset of rays 124 in Figure 6B are described in Figure 1. The folded path 625 in Figure 6B can be between the BS 141 and the reflective polarizer 639, and the description of folded path 125 can be appropriately adapted to folded path 625. Distances D3-D5 in Figure 6B are described in Figure 1.

[0101] The positions of the beam splitter (641) and the reflective polarizer (639) may be interchangeable, and the above description of the optical path may be adapted appropriately. For example, the reflective polarizer (639) is disposed between the display device (620) and the beam splitter (641). In one example, the reflective polarizer (639) is disposed on the surface (638) of the third lens (632), and the beam splitter (641) is disposed on the surface (636) of the first lens (631(a)). A QWP (642) may be disposed on the surface (636). An optical cavity is formed between the reflective polarizer (639) disposed on the surface (638) and the beam splitter (641) disposed on the surface (636). The light beam emitted from a pixel (including, for example, pixel A) in the display device (120) may be linearly polarized, for example, in a first linear polarization state. The light beam then passes through the second lens (632) and enters the reflective polarizer (639). The reflective polarizer (639) can transmit the light beam having a first linear polarization state with a relatively high transmittance (e.g., 90% or more) across a certain wavelength range (e.g., 380-780 nm). The light beam then passes through the optical cavity for the first time and enters the beam splitter (141), which partially transmits the light beam and partially reflects it back into the optical cavity. The light beam reflected by the beam splitter (641) then passes through the optical cavity a second time. During both the first and second passes, the QWP (642) changes the polarization state of the light beam. Thus, the first linear polarization state of the light beam is converted by the QWP (642) to a second linear polarization state. The second linear polarization state is along the block direction of the reflective polarizer (639). After the second pass, the light beam enters the reflective polarizer (639). The light beam is blocked by the reflective polarizer (639) and does not transmit through it. The reflective polarizer (639) can reflect the light beam having the second linear polarization state with a relatively high average reflectance, for example, greater than or equal to 90%, over a wavelength range (e.g., 380-780 nm). The light beam then passes through the optical cavity a third time and enters the beam splitter (641).The light beam can be partially transmitted by the beam splitter (641) and directed to the area (651).

[0102] The material(s) of the optically transparent member (645) can be different from the material(s) of the optically transparent member (647) such that a first chromatic aberration of the first lens (631(a)) is complementary to a second chromatic aberration of the second lens (631(b)).

[0103] The Abbe number of a material can indicate the dispersion or chromatic dispersion of the material (e.g., the change in refractive index with wavelength). In one embodiment, a larger value of the Abbe number indicates lower dispersion. The achromatic lens (631) can be formed from two different materials with different Abbe numbers (indicating two different dispersions). In one embodiment, the first lens (631(a)) is a negative lens, the optically transparent member (645) has a first Abbe number, and the second lens (631(b)) is a positive lens, and the optically transparent member (647) has a second Abbe number. The second Abbe number can be greater than the first Abbe number. The chromatic dispersion of the optically transparent member (647) (or the second lens (631(b))) can be less than the chromatic dispersion of the optically transparent member (645) (or the first lens (631(a))).

[0104] In some embodiments, a lens with low birefringence (e.g., the first lens (631(a)), the second lens (631(a)), or the third lens (632)) is made by injection molding. To form a lens with low birefringence, a suitable or good mold flow (e.g., a relatively smooth mold flow) is used. As described above, if the thickness ratio of the lens, e.g., the ratio of the edge thickness of the lens to the center thickness of the lens, is within a certain range, such as close to 1 / 1, a suitable mold flow can be achieved without annealing.

[0105] Referring to FIG. 6C, the first lens (631(a)) can be formed by injection molding using a material(s) such as polycarbonate. The first lens (631(a)) should have low birefringence. In one example, the first lens (631(a)) is a concave lens. Good mold flow (e.g., relatively smooth mold flow) can be achieved without annealing, for example, when the first thickness ratio (e.g., the ratio of the edge thickness of the first lens (631(a)) to the center thickness of the first lens (631(a))) of the first lens (631(a)) is within a first range R1, such as 1 to 1.2. In the example shown in FIG. 6C, the first thickness ratio is 1 / 1 or approximately 1 / 1, and good mold flow can be achieved without annealing.

[0106] The second lens (631(b)) can be formed by injection molding. The second lens (631(b)) should have low birefringence. In one example, the second lens (631(b)) is a convex lens. A suitable mold flow (e.g., a relatively smooth mold flow) can be achieved, for example, when the second thickness ratio (e.g., the ratio of the edge thickness of the second lens (631(b)) to the center thickness of the second lens (631(b))) of the second lens (631(b)) is within a second range R2, such as 1 / 3 to 1 / 1. Referring to FIG. 6C, the second thickness ratio of the second lens (631(b)) is 1 / 3 or approximately 1 / 3, and a good mold flow can be achieved without annealing.

[0107] The above description regarding the second lens (631(b)) may be applicable to the third lens (632), which is a convex lens in the example shown in FIG. 6C. For example, when the third thickness ratio of the third lens (632) (e.g., the ratio of the edge thickness of the third lens (632) to the center thickness of the third lens (632)) is within a third range R3, such as 1 / 3 to 1 / 1, a suitable mold flow (e.g., a relatively smooth mold flow) can be achieved. Referring to FIG. 6C, the third thickness ratio of the third lens (632) is 1 / 1 or approximately 1 / 1, and a good mold flow can be achieved without annealing. The edge thicknesses of the second lens (631(b)) and the third lens (632) are thick enough to enable a good mold flow.

[0108] The achromatic lens (e.g., 131 or 631) can include a negative lens (e.g., 131(a) or 631(a)) and a positive lens (e.g., 131(b) or 631(b)). Various methods can be used to manufacture the achromatic lens. In one example, the negative lens is cemented with the positive lens using a liquid optically clear adhesive. In another example, a first lens of the negative and positive lenses can be a molded lens, and a second lens of the negative and positive lenses can be molded onto the first lens to create a single hybrid achromatic lens. In one example, the first lens is a negative lens and the second lens is a positive lens.

[0109] In one example, the system parameters of the display system 600 are the same as or similar to those of the display system 100. The distance D3 (or eye relief) between the region 651 and the last optical component (e.g., the achromatic lens 631) before the region 651 in the optical system 610 is 14 mm. The distance D4 (i.e., the lens track length) between the display device 620 and the achromatic lens 631 is 19.5 mm. The display size is indicated by the display image circle imaged onto the region 651 by the optical system 610, and the radius of the display image circle is 18.9 mm. The size of the region 651 (e.g., pupil size) is 5 mm. The FOV of the optical system 610 is 110°. The optical system (610) can form a virtual image (699) from the image on the display device (620) for a suitable range of polychromatic wavelengths, such as visible wavelengths (e.g., 380-780 nm at 400 nm), polychromatic wavelengths near green (e.g., 500-540 nm at a 40 nm bandwidth), etc.

[0110] Embodiments of the present disclosure describe an achromatic lens (631) that includes a first lens (631(a)) and a second lens (631(b)) attached to one another. The description may be applied appropriately to a lens combination of (i) a first lens identical or similar to the first lens (631(a)) and (ii) a second lens identical or similar to the second lens (631(b)), where the first lens and the second lens are separated by a gap. The lens combination may have an achromatic aberration that is less than the achromatic aberration of the first lens and the achromatic aberration of the second lens.

[0111] The embodiments in this disclosure may be used separately or combined in any order.

[0112] In one embodiment, a polarized catadioptric VR optical system, such as the display system 600, can utilize achromatic lenses, including Fresnel optics. The use of achromatic lenses, including negative Fresnel lenses, allows for compact lens shapes that are more amenable to certain manufacturing methods (e.g., injection molding).

[0113] The display system (600) can include one or more Fresnel lenses having Fresnel structures. Compared to lenses with the same or similar optical power, the thickness variation of a Fresnel lens can be more uniform than the thickness variation of a lens without a Fresnel structure, and the Fresnel lens can be flatter than a lens without a Fresnel structure. Thus, in various embodiments, the Fresnel lenses can be easily manufactured and / or manufactured with low birefringence. The display system (600) including one or more Fresnel lenses can have the same or similar parameters (e.g., FOV, eye relief, lens track length, display size, etc.) as the display system (100) without a Fresnel lens. The lens system (630) of the display system (600) can be manufactured more easily, with better quality, and / or in a more compact package than the lens system (130) of the display system (100).

[0114] A computer or computer-readable medium can control various aspects of an HMD system incorporating a display system (e.g., (100) or (600)) including an optical system (e.g., (110) or (610)). Various aspects of the display system, including controlling the movement and positioning of optical components (e.g., achromatic lens (131) or (631), third lens (132) or (632), display device (120) or (620)), can be implemented as computer software using computer-readable instructions and physically stored in one or more computer-readable media. For example, FIG. 9 illustrates a computer system (900) suitable for implementing certain embodiments of the disclosed subject matter.

[0115] Computer software may be coded using any suitable machine code or computer language that may be subject to assembly, compilation, linking, or similar mechanisms to create code containing instructions that may be executed by one or more computer central processing units (CPUs), graphics processing units (GPUs), etc., either directly or via interpretation, microcode execution, etc.

[0116] The instructions may be executed on various types of computers or components thereof, including, for example, personal computers, tablet computers, servers, smartphones, gaming devices, Internet of Things devices, and the like.

[0117] 9 for computer system (900) are exemplary in nature and are not intended to suggest any limitation on the scope of use or functionality of the computer software implementing embodiments of the present disclosure. The arrangement of components should not be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the exemplary embodiment of computer system (900).

[0118] The computer system (900) may include certain human interface input devices that can respond to input by one or more human users, for example, via tactile input (e.g., keystrokes, swipes, data glove movements), audio input (e.g., voice, clapping), visual input (e.g., gestures), and olfactory input (not shown). The human interface devices may also be used to capture certain media that are not necessarily directly associated with conscious human input, such as audio (e.g., voice, music, ambient sounds), images (e.g., scanned images, photographic images obtained from a still image camera), and video (e.g., two-dimensional video, three-dimensional video, including stereoscopic video).

[0119] The input human interface devices may include one or more (only one of each shown) of a keyboard (901), a mouse (902), a trackpad (903), a touchscreen (910), a data glove (not shown), a joystick (905), a microphone (906), a scanner (907), and a camera (908).

[0120] The computer system (900) may also include certain human interface output devices. Such human interface output devices may stimulate one or more of the human user's senses, for example, through tactile output, sound, light, and smell / taste. Such human interface output devices may include haptic output devices (e.g., haptic feedback via a touchscreen (910), data gloves (not shown), or joystick (905), although some haptic feedback devices may not function as input devices), audio output devices (such as speakers (909), headphones (not shown)), visual output devices (such as touchscreens (910), including CRT screens, LCD screens, plasma screens, and OLED screens, each with or without touchscreen input capabilities and each with or without haptic feedback, some of which may output two-dimensional visual output or three-dimensional or higher-dimensional output via means such as stereographic output), virtual reality glasses (not shown), holographic displays and smoke tanks (not shown), and printers (not shown).

[0121] The computer system (900) may also include human-accessible storage devices and their associated media, such as optical media including CD / DVD ROM / RW (920) with media (921) such as CD / DVD, thumb drives (922), removable hard drives or solid state drives (923), legacy magnetic media (not shown) such as tape and floppy disks, and dedicated ROM / ASIC / PLD-based devices (not shown) such as security dongles.

[0122] Those skilled in the art should also understand that the term "computer-readable medium" as used in connection with the subject matter of this disclosure does not encompass transmission media, carrier waves, or other transitory signals.

[0123] The computer system (900) also includes an interface (954) to one or more communication networks (955). The networks may be, for example, wireless, wired, or optical. The networks may further be local, wide-area, metropolitan, vehicular, industrial, real-time, delay-tolerant, or the like. Examples of networks include local area networks such as Ethernet; wireless LANs; cellular networks including GSM, 3G, 4G, 5G, LTE, and the like; TV wired or wireless wide-area digital networks including cable TV, satellite TV, and terrestrial broadcast TV; vehicular and industrial networks including CANbus; and the like. Certain networks generally require an external network interface adapter attached to a particular general-purpose data port or peripheral bus (949) (e.g., a USB port on the computer system (900)); while other networks are generally integrated into the core of the computer system (900) by attaching to a system bus, as described below (e.g., an Ethernet interface to a PC computer system or a cellular network interface to a smartphone computer system). Using any of these networks, the computer system (900) can communicate with other entities. Such communication may be unidirectional, receive only (e.g., broadcast TV), unidirectional transmit only (e.g., CANbus to a particular CANbus device), or bidirectional, e.g., communication to other computer systems using local or wide area digital networks. Specific protocols and protocol stacks may be used with each of these networks and network interfaces, as described above.

[0124] The above-mentioned human interface devices, human-accessible storage devices, and network interfaces may be attached to the core (940) of the computer system (900).

[0125] The core (940) may include one or more central processing units (CPUs) (941), graphics processing units (GPUs) (942), dedicated programmable processing units in the form of field programmable gate arrays (FPGAs) (943), hardware accelerators for specific tasks (944), graphics adapters (950), etc. These devices, along with read-only memory (ROM) (945), random access memory (946), and internal mass storage (947), such as an internal non-user-accessible hard drive or SSD, may be connected via a system bus (948). In some computer systems, the system bus (948) may be accessible in the form of one or more physical plugs to allow expansion with additional CPUs, GPUs, etc. Peripheral devices may be attached directly to the core's system bus (948) or via a peripheral bus (949). In one example, a touchscreen (910) may be connected to the graphics adapter (950). Peripheral bus architectures include PCI, USB, etc.

[0126] The CPU (941), GPU (942), FPGA (943), and accelerator (944) can execute specific instructions that, in combination, can constitute the aforementioned computer code. The computer code can be stored in ROM (945) or RAM (946). Temporary data can also be stored in RAM (946), while persistent data can be stored, for example, in internal mass storage (947). Cache memory, which can be closely associated with one or more of the CPU (941), GPU (942), mass storage (947), ROM (945), RAM (946), etc., can be used to enable fast storage and retrieval in any of the memory devices.

[0127] The computer-readable medium may bear computer code for performing various computer-implemented operations. The medium and computer code may be those specially designed and constructed for the purposes of the present disclosure, or they may be of the kind well known and available to those skilled in the computer software arts.

[0128] By way of example and not limitation, a computer system (900) having an architecture, specifically a core (940), can provide functionality as a result of processor(s) (including CPUs, GPUs, FPGAs, accelerators, etc.) executing software embodied in one or more tangible computer-readable media. Such computer-readable media can be user-accessible mass storage, as introduced above, as well as media associated with the core's (940) specific storage of a non-transitory nature, such as the core's internal mass storage (947) or ROM (945). Software implementing various embodiments of the present disclosure can be stored on such devices and executed by the core (940). The computer-readable media can include one or more memory devices or chips, depending on particular needs. The software can cause the core (940), specifically the processor (including CPU, GPU, FPGA, etc.) therein, to perform particular processes or particular portions of particular processes described herein, including defining data structures stored in RAM (946) and modifying such data structures according to the software-defined processes. Additionally or alternatively, a computer system may provide functionality as a result of logic hardwired or otherwise embodied in circuitry (e.g., accelerator (944)), which may operate in place of or in conjunction with software to perform particular processes or portions of particular processes described herein. References to software may encompass logic, where appropriate, and vice versa. References to computer-readable media may encompass circuitry (such as an integrated circuit (IC)) that stores software for execution, circuitry that embodies logic for execution, or both, where appropriate. The present disclosure encompasses any suitable combination of hardware and software.

[0129] While this disclosure has described several exemplary embodiments, there are alterations, permutations, and various substitute equivalents that fall within the scope of this disclosure. It should therefore be understood that those skilled in the art will be able to devise numerous systems and methods that, although not explicitly shown or described herein, embody the principles of the present disclosure and are therefore within its spirit and scope. [Explanation of symbols]

[0130] 60 eye, 63 lens, 65 retina, 100 display system, 110 optical system, 120 display device, 121 boundary ray, 122 central ray, 123 boundary ray, 124 subset, 125 folded path, 130 lens system, 131 achromatic lens, 131(a) first lens, 131(b) second lens, 133 gap, 135-138 surface, 139 reflective polarizer, 141 beam splitter, 142 quarter-wave plate, 145-147 optically transparent member, 151 region, 160 optical axis, 161-164 portion, 170 shift block, 171-172 surface, 180 controller, 181-185 portion, 190 lens, 191 Fresnel lens, 193 Surface, 195-196 Surface, 199 Virtual image, 600 Display system, 610 Optical system, 620 Display device, 630 Lens system, 631 Achromatic lens, 631(a) First lens, 631(b) Second lens, 632 Third lens, 635 Surface, 637-638 Surface, 639 Reflective polarizer, 641 Beam splitter, 642 QWP, 645 Optically transparent member, 647 Optically transparent member, 651 Area, 660 Optical axis, 670 Shift block, 671-672 Surface, 673 Line, 680 Controller, 681 Fresnel structure, 683 Central area, 811 Area, 812 Area, 900 Computer system, 901 Keyboard, 902 Mouse, 903 Trackpad, 905 joystick, 906 microphone, 907 scanner, 908 camera, 909 speaker, 910 touch screen, 920 CD / DVD ROM / RW, 921 media, 922 thumb drive, 940 core, 941 central processing unit, 942 graphics processing unit, 943 field programmable gate area, 944 hardware accelerator, 945 ROM, 946 random access memory, 947 internal mass storage, 948 system bus, 949 peripheral bus, 950 graphics adapter, 954 interface, 955 communication network

Claims

1. a first lens having a negative focal length including a first optically transparent member having a first surface and a second surface; a second lens attached to the first lens at the second surface, the second lens having a positive focal length including a second optically transparent member having a third surface and a fourth surface; Equipped with a second chromatic aberration of the second lens is reduced by a first chromatic aberration of the first lens; the second surface of the first lens includes a first Fresnel structure; Achromatic lens.

2. the second surface includes (i) a smooth central region and (ii) the first Fresnel structure surrounding the central region; 2. The achromatic lens according to claim 1.

3. the second surface is aspherical; 3. The achromatic lens according to claim 2.

4. a first ratio of an edge thickness of the first lens to a center thickness of the first lens is between 1 and 1.2; a second ratio of the edge thickness of the second lens to the center thickness of the second lens is between 1 / 3 and 1; 3. The achromatic lens according to claim 2.

5. a first lens having a negative focal length including a first optically transparent member having a first surface and a second surface; a second lens attached to the first lens at the second surface, the second lens having a positive focal length including a second optically transparent member having a third surface and a fourth surface; an achromatic lens including a third lens having a positive focal length including a third optically transparent member having a fifth surface and a sixth surface, the sixth surface having a second Fresnel structure; Equipped with a second chromatic aberration of the second lens is reduced by a first chromatic aberration of the first lens; the second surface of the first lens includes a first Fresnel structure; Lens system.

6. the second surface includes (i) a smooth central region and (ii) the first Fresnel structure surrounding the central region; the sixth surface includes (i) a smooth central region; and (ii) the second Fresnel structure surrounding the central region of the sixth surface.

6. The lens system of claim 5.

7. a first ratio of an edge thickness of the first lens to a center thickness of the first lens is between 1 and 1.2; a second ratio of the edge thickness of the second lens to the center thickness of the second lens is between 1 / 3 and 1; a third ratio of the edge thickness of the third lens to the center thickness of the third lens is between 1 / 3 and 1; 6. The lens system of claim 5.

8. A lens system according to claim 5; a beam splitter configured to partially transmit and partially reflect a light beam from the display device; a reflective polarizer configured to pass light having a first linear polarization state and reflect light having a second linear polarization state that is orthogonal to the first linear polarization state; a quarter wave plate (QWP) positioned between the beam splitter and the reflective polarizer; Equipped with the QWP is on a surface of the first lens, the second lens, or the third lens; the beam splitter is on the fourth surface of the third lens; the reflective polarizer is on the first surface of the first lens. optical system.

9. the optical system includes the display device, a pixel array of the display device configured to generate a light beam, the polarization state of the light beam being a first circular polarization state; the third lens is positioned between the display device and the achromatic lens, the fifth surface of the third lens being configured to face the display device; the second lens is positioned between the first lens and the third lens, and the third surface of the second lens is configured to face the third lens. The optical system according to claim 8 .

10. A lens system according to claim 5; a beam splitter configured to partially transmit and partially reflect a light beam from the display device; a reflective polarizer configured to pass light having a first linear polarization state and reflect light having a second linear polarization state that is orthogonal to the first linear polarization state; a quarter wave plate (QWP) positioned between the beam splitter and the reflective polarizer; Equipped with the QWP is on a surface of the first lens, the second lens, or the third lens; the reflective polarizer is on the fourth surface of the third lens; the beam splitter is on the first surface of the first lens; optical system.

11. the optical system includes the display device, a pixel array of the display device configured to generate a light beam, the polarization state of the light beam being a first linear polarization state; the third lens is positioned between the display device and the achromatic lens, the fifth surface of the third lens being configured to face the display device; the second lens is positioned between the first lens and the third lens, and the third surface of the second lens is configured to face the third lens. The optical system of claim 10.

12. Lens system including achromatic lenses Equipped with The achromatic lens is a first lens having a negative focal length including a first optically transparent member having a first surface and a second surface; a second lens attached to the first lens at the second surface, the second lens having a positive focal length including a second optically transparent member having a third surface and a fourth surface; Including, a second chromatic aberration of the second lens is reduced by a first chromatic aberration of the first lens; the second surface of the first lens includes a first Fresnel structure; the lens system is configured to direct a light beam from a display device to a light receiver; optical system.

13. the second surface includes (i) a smooth central region and (ii) the first Fresnel structure surrounding the central region; The optical system of claim 12.

14. the second surface is aspherical; The optical system of claim 13.

15. a first ratio of an edge thickness of the first lens to a center thickness of the first lens is between 1 and 1.2; a second ratio of the edge thickness of the second lens to the center thickness of the second lens is between 1 / 3 and 1; The optical system of claim 13.

16. the lens system includes a third lens having a positive focal length; the third lens includes a third optically transparent member having a fifth surface and a sixth surface, the sixth surface having a second Fresnel structure; The optical system of claim 12.

17. the second surface includes (i) a smooth central region and (ii) the first Fresnel structure surrounding the central region; the sixth surface includes (i) a smooth central region; and (ii) the second Fresnel structure surrounding the central region of the sixth surface.

17. The optical system of claim 16.

18. a first ratio of an edge thickness of the first lens to a center thickness of the first lens is between 1 and 1.2; a second ratio of the edge thickness of the second lens to the center thickness of the second lens is between 1 / 3 and 1; a third ratio of the edge thickness of the third lens to the center thickness of the third lens is between 1 / 3 and 1; 17. The optical system of claim 16.

19. a beam splitter configured to partially transmit and partially reflect a light beam from the display device; a reflective polarizer configured to pass light having a first linear polarization state and reflect light having a second linear polarization state that is orthogonal to the first linear polarization state; a quarter wave plate (QWP) positioned between the beam splitter and the reflective polarizer; Furthermore, the QWP is on a surface of the first lens, the second lens, or the third lens; the beam splitter is on the fourth surface of the third lens; the reflective polarizer is on the first surface of the first lens.

17. The optical system of claim 16.

20. the optical system includes the display device, a pixel array of the display device configured to generate a light beam, the polarization state of the light beam being a first circular polarization state; the third lens is positioned between the display device and the achromatic lens, the fifth surface of the third lens being configured to face the display device; the second lens is positioned between the first lens and the third lens, and the third surface of the second lens is configured to face the third lens.

20. The optical system of claim 19.

Images