Liquid crystal for vision correction

Abstract

Aspects of the present disclosure provide an optical system, a head mounted display (HMD) system, and a method of tuning an optical system. The optical system may include one or more liquid crystal (LC) lenses as refractive optical elements. The one or more liquid crystal lenses may have a first chromatic aberration. The optical system may include a Pangulam-Bell (PB) phase lens as a diffractive optical element. The PB phase lens may have a second chromatic aberration complementary to the first chromatic aberration. A chromatic aberration of the optical system may be less than the first chromatic aberration. The HMD system may include a display device, an optical system, and a virtual reality (VR) viewing optical system.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. Patent Application No. 18 / 125,560, filed March 23, 2023, entitled "Liquid Crystal for Vision Correction," the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure includes embodiments related to display technologies, such as near-eye display technology. Background Technology

[0004] The background description provided herein is for the purpose of generally presenting the context of this disclosure. The work of the currently named inventor, within the scope described in this background section, and aspects of the description that may not conform to the prior art at the time of submission, are neither expressly nor implied to be acknowledged as prior art to this disclosure.

[0005] Near-eye display (NED) devices are being 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, smart glasses, and more. In one example, an HMD device consists of a relatively small display device and optics that can create virtual images within the field of view of one or both eyes. To the eye, the virtual image appears at a distance and appears much larger than the relatively small display device. Summary of the Invention

[0006] This disclosure provides an optical system. The optical system may include one or more liquid crystal (LC) lenses as refractive optical elements. The one or more liquid crystal lenses may have a first chromatic aberration. The optical system may include Pancharatnam-Berry (PB) phase lenses as diffractive optical elements. The PB phase lenses may have a second chromatic aberration complementary to the first chromatic aberration. The chromatic aberration of the optical system may be less than the first chromatic aberration.

[0007] In one embodiment, the first optical power of the one or more LC lenses is electrically tunable, the optical power of the optical system is based on at least a sum of the first optical power of the one or more LC lenses and the second optical power of the PB phase lens, and the first optical power, the second optical power, and the optical power of the optical system correspond to a focal length of the one or more LC lenses, a focal length of the PB phase lens, and a focal length of the optical system, respectively.

[0008] In one example, the one or more LC lenses include a plurality of LC lenses, each LC lens is electrically tunable, and the first optical power is a sum of respective optical powers of the plurality of LC lenses. In one example, the number of the plurality of LC lenses is 3.

[0009] In one embodiment, one of the one or more LC lenses includes a plurality of transparent ring electrodes disposed on a first substrate and a transparent electrode disposed on a second substrate. The first substrate and the second substrate can be parallel to a plane. A refractive index of this LC lens of the one or more LC lenses varies with a radial distance from a center of the plurality of transparent ring electrodes on the first substrate. The refractive index can be controlled by respective voltages of the plurality of transparent ring electrodes. The refractive index and the first optical power can be circularly symmetric in the plane.

[0010] In one embodiment, the PB phase lens includes a center grating and a plurality of annular gratings formed by a liquid crystal material on a substrate, each of the plurality of annular gratings surrounds the center grating, the PB phase lens is configured to generate an output beam from an input beam normally incident onto the substrate, a center diffracted portion of the output beam has a first diffraction angle θ1. The center diffracted portion corresponds to a center portion of the input beam incident onto the center grating. A plurality of peripheral diffracted portions of the output beam have a plurality of diffraction angles varying from the first diffraction angle θ1 to a second diffraction angle θ2, the second diffraction angle θ2 corresponds to an outermost annular grating of the plurality of annular gratings. The plurality of peripheral diffracted portions respectively correspond to a plurality of peripheral portions of the input beam incident onto the plurality of annular gratings. The second diffraction angle θ2 can be greater than the first diffraction angle θ1.

[0011] In one example, the PB phase lens functions as a converging lens based on a first polarization state of the input beam. In one example, the PB phase lens functions as a diverging lens based on a second polarization state of the input beam.

[0012] In one example, the input beam is left-handed circularly polarized, the output beam is right-handed circularly polarized, and the PB phase lens functions as a converging lens with a second optical power being positive.

[0013] In one example, the input beam is right-handed circularly polarized, the output beam is left-handed circularly polarized, and the PB phase lens functions as a diverging lens with a second optical power being negative.

[0014] In one example, the optical system includes one or more cylindrical LC lenses configured to correct astigmatism of a user’s eye using the optical system. For each of the one or more cylindrical LC lenses, the respective cylindrical LC lens includes a plurality of transparent electrodes disposed on a first substrate and a transparent electrode disposed on a second substrate. The first substrate and the second substrate can be parallel to an XZ plane that includes an X-axis and a Z-axis that are perpendicular to each other. The plurality of transparent electrodes can be parallel. The electrically tunable refractive index varies along a respective first dimension in the XZ plane.

[0015] In one example, the one or more cylindrical LC lenses include a first cylindrical LC lens, a second cylindrical LC lens, and a third cylindrical LC lens, the first dimension of the first, second, and third cylindrical LC lenses form 0, 45°, and 90° with the X-axis, respectively.

[0016] In one example, the optical system includes an LC spatial light modulator (SLM) configured to manipulate a polarization state of an input light beam to the LC SLM by changing a voltage input to the LC SLM. An output light beam of the LC SLM can be the input light beam to the PB phase lens. The LC SLM is electrically tunable.

[0017] In one example, the one or more LC lenses include a stack of electrically tunable LC lenses. The one or more cylindrical LC lenses include a stack of cylindrical LC lenses, the first dimension of the plurality of cylindrical LC lenses form different angles with the X-axis, respectively. The stack of cylindrical LC lenses can be electrically tunable. The electrically tunable lens system includes the stack of LC lenses and the stack of cylindrical LC lenses. The LC SLM is disposed between the electrically tunable lens system and the PB phase lens.

[0018] In one example, the input light beam incident on the electrically tunable lens system is linearly polarized, and the output light beam from the electrically tunable lens system incident on the LC SLM is linearly polarized. If the voltage of the LC SLM is a first voltage, the LC SLM is configured to convert the linearly polarized input light beam to the LC SLM to a left-handed circularly polarized output light beam from the LC SLM, and the PB phase lens is configured to convert the left-handed circularly polarized input light beam to the PB phase lens to a right-handed circularly polarized output light beam from the PB phase lens. If the voltage of the SLM is a second voltage, the LC SLM is configured to convert the linearly polarized input light beam to the LC SLM to a right-handed circularly polarized output light beam from the LC SLM, and the PB phase lens is configured to convert the right-handed circularly polarized input light beam to the PB phase lens to a left-handed circularly polarized output light beam from the PB phase lens.

[0019] Aspects of the disclosure provide a head-mounted display (HMD) system. The HMD system can include a display device and an optical system. An array of pixels in the display device can be configured to generate light beams. The optical system can include one or more liquid crystal (LC) lenses as refractive optical elements and a Pancharatnam-Berry (PB) phase lens as a diffractive optical element. The one or more LC lenses can have a first chromatic aberration. The PB phase lens can have a second chromatic aberration complementary to the first chromatic aberration. The chromatic aberration of the optical system is less than the first chromatic aberration.

[0020] In one embodiment, the HMD system includes a virtual reality (VR) viewing optical system disposed between the display device and the optical system.

[0021] In one embodiment, the HMD system includes an augmented reality (AR) viewing optical system disposed between the display device and the optical system. The AR viewing optical system can direct light beams from the display device and light beams from real objects to the optical system

[0022] Aspects of the disclosure provide a method of tuning an optical system. The method includes obtaining vision correction information for at least one of myopia or hyperopia. The method includes determining a respective optical power of each LC lens in a stack of LC lenses and an optical power of a Pancharatnam-Berry (PB) phase lens based on the vision correction information. The method includes determining respective voltages to be applied to the stack of LC lenses based on the respective optical powers of the LC lenses and a polarization state of light incident on the PB phase lens based on the optical power of the PB phase lens. The method includes applying the determined respective voltages to the stack of LC lenses and controlling the polarization state of light incident on the PB phase lens to correct for the at least one of myopia or hyperopia.

[0023] In one example, the method includes incrementally adjusting at least one of the respective voltages applied to the stack of LC lenses. BRIEF DESCRIPTION OF DRAWINGS

[0024] Other features, properties, and advantages of the disclosed subject matter will become apparent from the following detailed description, drawings, and claims, in which:

[0025] FIG. 1A A display system according to some embodiments of the disclosure is shown in side view.

[0026] FIG. 1B-1C A display system including a vision correction optical system according to some embodiments of the disclosure is shown in side view.

[0027] FIG. 1D-1E Examples of using a visual correction optical system in an augmented reality (AR) system are shown.

[0028] FIG. 2 Examples of a liquid crystal (LC) visual correction optical system according to embodiments of the present disclosure are shown.

[0029] FIG. 3 Examples of an electrically tunable LC lens according to embodiments of the present disclosure are shown.

[0030] FIG. 4 A relationship of refractive index of an LC lens to position of the LC lens on a first substrate according to embodiments of the present disclosure is shown.

[0031] FIG. 5A An example optical path difference (OPD) projection from three-dimension (3D) to XZ plane representing the correction phase delay from a corrected defocus LC lens according to embodiments of the present disclosure is shown.

[0032] FIG. 5B An example OPD projection from 3D to XZ plane representing the correction phase delay from a corrected defocus LC lens and a corrected astigmatism cylindrical LC lens according to embodiments of the present disclosure is shown.

[0033] FIG. 6A-6B A schematic diagram of the working principle of an LC spatial light modulator (SLM) according to embodiments of the present disclosure is shown.

[0034] FIG. 7A-7B A schematic diagram of a Pancharatnam-Berry (PB) phase lens according to embodiments of the present disclosure is shown.

[0035] FIG. 8A-8B A schematic diagram of the working principle of a PB phase lens according to embodiments of the present disclosure is shown.

[0036] FIG. 9 An example of the total optical power of one or more LC lenses and PB phase lenses according to embodiments of the present disclosure is shown.

[0037] FIG. 10A-10D Examples of chromatic aberration of a refractive optical element (ROE), a diffractive optical element (DOE), and chromatic correction and achromatization performance of a combined ROE and DOE lens are shown.

[0038] FIG. 11A flowchart showing an overview of a process according to some embodiments of the disclosure is shown.

[0039] FIG. 12 is a schematic illustration of a computer system according to embodiments. DETAILED DESCRIPTION

[0040] Eye characteristics, such as visual acuity (or visual sharpness), vary greatly for users of different display systems. When a display system (e.g., a head-mounted display (HMD) system) is used by various users or users with varying or different eye conditions (e.g., myopia, hyperopia, and / or astigmatism), certain users can not be able to clearly see images on the display without vision correction. In some cases, vision correction can be performed by the display system.

[0041] According to embodiments of the disclosure, a display system can include a liquid crystal (LC) optical system configured to adjust an optical power of the LC optical system and, thus, change a focal length of the LC optical system. The LC optical system can include one or more LC lenses. In some embodiments, the one or more LC lenses can be electrically tunable and / or polarization controlled. Using a variable optical power, the LC optical system can be configured as a diverging lens for correcting myopic eyes (i.e., nearsightedness) or as a converging lens for correcting hyperopic eyes (i.e., farsightedness). The LC optical system can include one or more cylindrical LC lenses that are electrically tunable to correct for astigmatism. In some embodiments, a refractive optical element (ROE) (e.g., one or more LC lenses) and a diffractive optical element (DOE) (e.g., a Pancharatnam-Berry (PB) phase lens) in the LC optical system can be electrically tunable and / or polarization controlled to correct for chromatic aberration. The LC optical system can be referred to as an LC vision correction optical system.

[0042] Optical power can indicate how much an optical system or optical component (e.g., a lens) converges or diverges light. In one example, the optical power of an optical component or system is equal to the inverse of the focal length of the optical component or system. A higher optical power indicates (i) a stronger focusing power for converging optical components / systems or (ii) a stronger diverging power for diverging optical components / systems.

[0043] In an example, to allow a user to enjoy augmented reality (AR), virtual reality (VR), mixed reality (MR), mixed reality, or some combination and / or derivative thereof without prescription eyewear, the LC optical system can adjust the optical power of the LC optical system (e.g., by adjusting the optical power of the respective LC lenses) to match different prescriptions to achieve focal adjustment or dynamic focusing.

[0044] FIG. 1A A display system (e.g., a near-eye display system) (100) is shown in side view, in accordance with some embodiments of the present disclosure. The display system (100) includes an optical system (110) and a controller (180). The controller (180) is coupled to the optical system (110) to control operation of the optical system (110). The optical system (110) can include a display device (120) and a viewing optical system (130) (e.g., a virtual reality (VR) viewing optical system). The display device (120) can include an array of pixels configured to emit light beams and display images. The viewing optical system (130) can direct the emitted light beams from the display device (120) to a region (151). In one example, the region (151) is in the XZ plane and is referred to as an exit pupil of the optical system (110). The XZ plane includes an X-axis and a Z-axis that is orthogonal to the X-axis. A light receiver or detector, such as a user’s eye, etc., can be located at the region (151). With reference to FIG. 1A , the optical system (110) can be configured to be positioned within a distance threshold (e.g., 35 mm) of a user’s eye (e.g., eye (60)), and the display system (100) can be referred to as a near-eye display (NED) system. For example, the display system (100) is a head-mounted display (HMD) system worn by a user.

[0045] In various examples, the display system (100) can be used by different users with different eye characteristics or conditions (e.g., different eye prescription (or vision correction) information). In one example, FIG. 1A , the lens in the first eye forms a sharp image on the retina of the first eye, so the first eye clearly sees the image displayed on the display device (120). In FIG. 1A , the lens (63) in the second eye (e.g., eye (60)) does not form an image on the retina (65) of the eye (60), and so the eye (60) does not clearly see the image displayed on the display device (120). For example, in FIG. 1A , when the eye (60) is myopic, the lens (63) in the eye (60) forms an image on a surface (66) in front of the retina (65) of the eye (60).

[0046] Various components in the eye, such as the cornea, the lens, etc., can manipulate light entering the eye to form an image. For brevity, the imaging function of the various components is represented by the lens of the eye (e.g., lens (63)).

[0047] In accordance with embodiments of the present disclosure, reference is made to FIG. 1BTo adapt the display system (100) to different eye characteristics or conditions and to form images on the retina of one or more eyes having different eye characteristics or conditions, the optical system (110) can include a vision correction optical system (140). In one embodiment, the vision correction optical system (140) is tunable (e.g., dynamically adjustable). Moreover, the vision correction optical system (140) can have a small thickness suitable for NED systems. With reference to FIG. 1B The vision correction optical system (140) can be based on LC materials, and thus can be referred to as an LC vision correction optical system (140).

[0048] In one embodiment, in FIG. 1A light rays (171) emitted from pixel A on the display device (120) become collimated (e.g., parallel to each other) after passing through the VR viewing optical system (130). If the eye (60) is myopic, the collimated light rays (171) can be focused onto a surface (66) in front of the retina (65), and thus the eye (60) cannot clearly see pixel A. Similarly, light rays (172) emitted from pixel B on the display device (120) become collimated after passing through the VR viewing optical system (130). The collimated light rays (172) can be focused onto a surface (66) in front of the retina (65), and thus the eye (60) cannot clearly see pixel B. Therefore, the eye (60) cannot clearly see the image on the display device (120).

[0049] In FIG. 1B embodiment, the collimated light rays (171) from the VR viewing optical system (130) are incident on the LC vision correction optical system (140). The LC vision correction optical system (140) can be electrically tuned to be a diverging lens. Therefore, the light rays (171) coming out of the LC vision correction optical system (140) diverge and can be focused onto the retina (65). Thus, the myopic eye (60) can clearly see pixel A. Similarly, the light rays (172) coming out of the LC vision correction optical system (140) diverge and can be focused onto the retina (65). Thus, the eye (60) can clearly see the image on the display device (120).

[0050] In an example, circularly polarized light incident on the VR viewing optical system (130) is converted to linearly polarized light by the VR viewing optical system (130). The linearly polarized light from the VR viewing optical system (130) can be incident on the LC vision correction optical system (140), which converts the linearly polarized light to circularly polarized light, which can be incident on the eye (60). In one example, the display device (120) is an organic light emitting diode (OLED)-based display device. The output light from the OLED-based display device is circularly polarized and can be incident on the VR viewing optical system (130).

[0051] The LC vision correction optical system (140) and the VR viewing optical system (130) can be arranged differently than shown in FIG. 1B In another example (not shown in FIG. 1B ), the LC vision correction optical system (140) is disposed between the display device (120) and the VR viewing optical system (130). In one example, the display device (120) (e.g., an LCD panel) generates linearly polarized light incident on the LC vision correction optical system (140). The LC vision correction optical system (140) can convert the linearly polarized light to circularly polarized light incident on the VR viewing optical system (130). The VR viewing optical system (130) can convert the circularly polarized light to linearly polarized light incident on the eye (60).

[0052] In one example, the positions of the LC vision correction optical system (140) and the VR viewing optical system (130) in the optical system (110) depend on the polarization state of the output light from the display device (120). If the output light from the display device (120) is linearly polarized, the LC vision correction optical system (140) is disposed between the display device (120) and the VR viewing optical system (130) FIG. 1B (not shown in FIG. 1B ), if the output light from the display device (120) is circularly polarized, the VR viewing optical system (130) is disposed between the display device (120) and the LC vision correction optical system (140) as shown in

[0053] In an example (not shown in FIG. 1A ), the eye is hyperopic, and the collimated light rays (171) from the VR viewing optical system (130) can be focused on a surface behind the retina of the eye, so the eye cannot clearly see the pixel A. Referring to FIG. 1B , the collimated light rays (171) from the VR viewing optical system (130) are incident on the LC vision correction optical system (140). InFIG. 1B In an example not shown, the LC vision correction optical system (140) can be electrically tuned to be a converging lens. Thus, the light rays (171) from the LC vision correction optical system (140) can converge and can be focused onto the retina. Thus, a hyperopic eye can clearly see the pixel A.

[0054] The LC vision correction optical system (140) can be configured to adjust the optical power of the LC vision correction optical system (140) and thus change the focal length of the LC vision correction optical system (140). Thus, the optical power and focal length of the optical system (110) can be adjusted. The LC vision correction optical system (140) or the optical system (110) can be referred to as a variable focus system. Using a variable optical power, the LC vision correction optical system (140) can be configured (e.g., electrically tuned and / or polarization controlled) to be a diverging lens for correcting myopia or a converging lens for correcting hyperopia. The LC vision correction optical system (140) can be configured (e.g., electrically tuned) to correct for astigmatism. In some embodiments, the LC vision correction optical system (140) can be configured to correct for chromatic aberration, for example, by electrically tuning and / or controlling the polarization of light.

[0055] FIG. 1C An example of a display system (100) corresponding to the display system (100) in FIG. 1B is shown. FIG. 1C The display system (100) in FIG. 1B may include the display device (120) and the LC vision correction optical system (140) described above with respect to the display system (100). The VR viewing optical system (130) can be configured to modify the light beams generated by the display device (120) and direct the modified light beams to the region (151). In some examples, the VR viewing optical system (130) can include diffractive elements (e.g., gratings and prisms), refractive elements (e.g., lenses), guiding elements (e.g., planar waveguides and / or optical fibers), and polarization elements (e.g., polarizers, half-wave plates, quarter-wave plates, polarization rotators, PB phase lenses, etc.). In the example shown, FIG. 1C The VR viewing optical system (130) includes ROEs such as a first lens (131) and a second lens (132). Each of the first lens (131) and the second lens (132) can have any suitable thickness and / or shape (e.g., spherical, aspherical, etc.).

[0056] In FIG. 1CIn the illustrated example, the 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)). The virtual image (199) appears at a distance DD2 from the region (151) (e.g., the eye (60)) and appears larger than the image on the display device (120). The distance DD2 is greater than the distance DD1 between the region (151) and the display device (120).

[0057] The display system (100) can be a component in a suitable artificial reality system. An artificial reality system can adjust reality in some way to create a simulated environment as an artificial reality, and then render the artificial reality to a user. Artificial reality can include, for example, a VR, an augmented reality (AR), a mixed reality (MR), a hybrid reality, or some combination and / or derivatives thereof. Artificial reality content can include completely generated content or generated content combined with captured (e.g., real-world) content. The artificial reality content can include video, audio, haptic feedback, or some combination thereof, any of which can be presented in a single channel or in multiple channels (such as stereo videos that produce a three- dimensional effect to the user). In some examples, the display system (100) can be applied to playback of real-time or pre-recorded video.

[0058] In embodiments, a “near-eye” display system can include an optical system (e.g., including one or more optical elements) configured to be placed within a distance threshold of a user’s eye when using the display system (100) (e.g., an HMD system or smart glasses). With reference to FIG. 1C The distance DD1 between the display device (120) and the region (151) (e.g., the eye (60)) can be less than or equal to the distance threshold.

[0059] The display system (100) can be an NED system implemented in various forms, such as an HMD system, smart glasses, a smartphone, etc. In some examples, an artificial reality system is implemented as a standalone NED system. In some examples, an artificial reality system is implemented as an NED system connected to a host computer system, such as a server device, a console device, etc.

[0060] The display device (120) can include an array of pixels. In some examples, the array of pixels includes a plurality of pixels arranged to form a two-dimensional surface. The two-dimensional surface of the display device (120) can be substantially flat or planar, can be curved, or can include a combination of flat and planar panels. The display device (120) can be a display panel. The display device (120) can include any suitable type of display panel, such as a liquid crystal display (LCD) panel, an organic light emitting diode (OLED) panel, and the like. The resolution of the display device (120) can be defined in terms of pixels in one or both of the two dimensions of the two-dimensional surface. Each pixel in the array of pixels can produce a light beam. Each light beam can 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 light ray (171), which is a subset of the bundle of light rays, can be directed to the region (151) by the VR viewing optical system (130) and the LC vision correction optical system (140).

[0061] The LC vision correction optical system (140) can be used in any suitable artificial reality system (e.g., a VR system, an AR system, an MR system, a mixed reality system) as shown in FIG. 1. FIG. 1B-1C FIG. 1D An example of using the LC vision correction optical system (140) in an AR system, such as a display system (100D), is shown in accordance with some embodiments of the present disclosure. The display system (100D) includes an optical system (110D) and a controller (180). The optical system (110D) can include an AR viewing optical system (e.g., including an AR waveguide) (130D) and the LC vision correction optical system (140). In one example, the optical system (110D) can include the VR viewing optical system (130).

[0062] Waveguides can be used in AR and / or MR devices. In NEDs, optical waveguides can bend and combine light to direct light into the eye and create virtual images that a user (e.g., a wearer) sees overlaid on the environment.

[0063] The AR viewing optical system (130D) can combine a light beam (176) (labeled with solid lines) from a real object (120D) (e.g., in the real world) and a light beam (175) (labeled with dashed lines) from the display device (120). Reference is made to FIG. 1. FIG. 1D ​, the light beam (176) is directed by the AR viewing optical system (130D) to the LC vision correction optical system (140). The light beam (175) from the VR viewing optical system (130) is directed (e.g., bent) by the AR viewing optical system (130D) to the LC vision correction optical system (140). The light beam (175) and the light beam (176) can pass through the LC vision correction optical system (140) and can be incident on the eye (such as the eye (60)) described in the FIG. 1A The optical system (110D) can be positioned within a distance threshold of the eye (e.g., the eye (60)), and the display system (100D) can be referred to as a NED system. For example, the display system (100D) is a HMD system worn by a user.

[0064] FIG. 1E A portion of the display system (100D) is shown in a side view according to some embodiments of the present disclosure. As described above, the LC vision correction optical system (140) in the AR system (100D) can be configured to adjust the optical power of the optical system (110D) and thus change the focal length of the optical system (110D) to correct for myopia or hyperopia of the eye (60). The LC vision correction optical system (140) can be electrically tuned to correct for astigmatism and / or chromatic aberration.

[0065] In an example, two points A’ and B’ from the real object (120D) emit light rays (191) and (192), respectively. The light ray (191) can become collimated after passing through the AR viewing optical system (130D). The collimated light ray (191) from the AR viewing optical system (130D) is incident on the LC vision correction optical system (140). The LC vision correction optical system (140) can be electrically tuned as a diverging lens. Thus, the light ray (191) out of the LC vision correction optical system (140) diverges and can be focused on the retina (65). Therefore, the myopic eye (60) can clearly see the point A’. Similarly, the light ray (192) out of the LC vision correction optical system (140) diverges and can be focused on the retina (65). Therefore, the eye (60) can clearly see the real object (120D).

[0066] When the two light beams (175)-(176) pass through the LC vision correction optical system (140), the myopia or hyperopia of the eye (60), the astigmatism of the eye (60), and / or the chromatic aberration can be corrected, and the eye (60) can clearly see the real object (120D) and the image displayed on the display device (120) at the same time.

[0067] Reference FIG. 1DIn one example, the AR viewing optical system (130D) and the VR viewing optical system (130) are combined into a viewing optical system. The display system (100D) can include the viewing optical system disposed between the display device (120) and the LC vision correction optical system (140). The viewing optical system can direct the light beams (175) from the display device (120) and the light beams (176) from the real object (120D) to the LC vision correction optical system (140).

[0068] LC materials and LC displays (LCDs) have been widely used, for example, in flat panel televisions, mobile phone screens, computer screens, etc. LC materials can include birefringent materials. LC materials can be electrically controlled by applying a voltage (e.g., a relatively low voltage, such as a few volts (V)) to manipulate the polarization or polarization state of light and to manipulate the wavefront of light to achieve different applications. In various embodiments, LC modulation schemes can include different types, including, for example, (i) intensity modulators, such as to modulate the intensity (or light intensity) of light for displaying information, (ii) polarization modulators, for manipulating and controlling the polarization of light, (iii) phase modulators, such as to manipulate the phase of light for wavefront control, interferometry, DOEs, etc. Various LC devices can include intensity modulators (e.g., LCD, Liquid crystal on silicon (LCoS)) for intensity modulation. Because the human eye is sensitive to changes in light intensity, and can be less sensitive to changes in light polarization and light phase, in one example, the human eye can not notice changes in light polarization and light phase.

[0069] FIG. 2 An example of an LC optical system (e.g., LC vision correction optical system) (240) is shown in accordance with embodiments of the present disclosure. In one example, the LC vision correction optical system (240) is used as the LC vision correction optical system (140) in the display system (100) or the display system (100D).

[0070] Before describing how the LC vision correction optical system (240) can correct (i) myopia or hyperopia, (ii) astigmatism, and / or (iii) chromatic aberration, examples of myopia, hyperopia, astigmatism, and chromatic aberration are described as follows.

[0071] In one embodiment, eye prescription information (or vision correction information) for an eye includes three parameters or three quantities of a lens or a stack of lenses: sphere (SPH), cylinder (CYL), and axis. The parameter “sphere (SPH)” can indicate the optical power of a lens or a stack of lenses used to correct for myopia (or nearsightedness) or hyperopia (farsightedness) of an eye (e.g., in diopters (D), such as -1 D or +2 D). The parameter “sphere (SPH)” can indicate the degree of myopia or hyperopia of an eye. A “plus” sign (+) in front of a number can indicate that the eye is farsighted, and the lens or stack of lenses can converge light. A “minus” sign (-) can indicate that the eye is nearsighted, and the lens or stack of lenses can diverge light. The further a number on an eye prescription is from zero, the worse the vision, and the more vision correction (e.g., a stronger prescription) is needed.

[0072] In one example, a converging lens used to correct for hyperopia is made of a transparent material (such as a glass or plastic material) and is thicker at the center than at the edges. In one example, a diverging lens used to correct for myopia is made of a transparent material (such as a glass or plastic material) and is thicker at the edges than at the center.

[0073] Astigmatism is a vision error that can occur, for example, when the cornea or lens of an eye is irregularly shaped. Astigmatism causes images to appear blurry or distorted because light rays are not properly focused on the retina of the eye. Astigmatism does not occur when the eye is uniformly rounded (e.g., has a spherical shape). Astigmatism can occur when the eye has an irregular shape (e.g., an oval shape). In one example, astigmatism is caused by a cornea and / or a lens in an eye having an irregular shape (e.g., an oval shape). For example, horizontal astigmatism can occur when the width of the eye is greater than the height of the eye, and vertical astigmatism can occur when the width of the eye is less than the height of the eye. Astigmatism can cause blurry vision.

[0074] Astigmatism of an eye can be indicated by the degree of astigmatism and the orientation of the astigmatism. The parameter cylinder (CYL) can indicate the degree of astigmatism of an eye and can be a negative or positive number. The parameter cylinder (CYL) can measure the degree of astigmatism of an eye in diopters. A larger cylinder (CYL) can indicate more astigmatism. The parameter axis can be a number between 0° and 180° that can indicate the orientation of the astigmatism.

[0075] To correct for astigmatism, a glasses prescription can specify the optical power of a cylindrical lens (e.g., using the parameter cylinder (CYL)) and an axis (e.g., using the parameter axis) on which the cylindrical lens is to be placed. The axis can be measured in degrees and can indicate the direction in which the cylindrical lens has the greatest optical power.

[0076] Chromatic aberration can indicate that a lens fails to focus light having multiple wavelengths of light to the same point or a predefined area. Chromatic aberration can include axial (longitudinal) aberration and transverse (lateral) aberration. Axial chromatic aberration can occur when different wavelengths of light are focused at different distances from the lens (e.g., a shift in focal point). Longitudinal chromatic aberration can occur at long focal lengths. Transverse chromatic aberration can occur when different wavelengths are focused at different locations in the focal plane, for example, when the magnification and / or distortion of the lens varies with wavelength. Transverse chromatic aberration can occur at short focal lengths.

[0077] Myopia, hyperopia, astigmatism, and / or chromatic aberration can be corrected by the LC vision correction optical system (240). Referring to FIG. 2 , the LC vision correction optical system (240) can include one or more LC lenses (e.g., a stack of LC lenses) (241), one or more cylindrical LC lenses (e.g., a stack of cylindrical LC lenses) (242), a spatial light modulator (SLM) (e.g., an LC SLM) (243), a PB phase lens (244), etc. In one embodiment, one or more components in the LC vision correction optical system (240) are electrically tunable (or electrically controlled), for example, by an electrically tunable controller (281). In one example, FIG. 1A-1D The controller (180) in the system (200) can include an electrically tunable controller (281). For example, one or more LC lenses (241), one or more cylindrical LC lenses (242), and an LC SLM (243) are electrically controlled by the electrically tunable controller (281). The PB phase lens (244) can be polarization controlled, for example, whether the PB phase lens (244) acts as a converging lens or a diverging lens is controlled by the polarization of light incident on the PB phase lens (244).

[0078] In one embodiment, each of the one or more LC lenses (241), the one or more cylindrical LC lenses (242), the LC SLM (243), and the PB phase lens (244) is flat and thin, and the LC vision correction optical system (240) is flat and thin. The LC vision correction optical system (240) can be an ultra-compact system for vision correction, including electrically tunable and / or polarization controlled LC devices (e.g., (241), (242), (243), and / or (244)).

[0079] In one example, the LC vision correction optical system (240) is referred to as a non-mechanical system because the LC vision correction optical system (240) is not mechanically tuned. For example, the LC vision correction optical system (240) uses a non-mechanical method, such as electrical tuning or by manipulating the polarization of light, to tune. In other embodiments, the LC vision correction optical system (240) can include a combination of electrical tuning elements and mechanical tuning elements. In other embodiments, the LC vision correction optical system (240) can include non-LC based optical elements, such as one or more lenses based on non-LCs.

[0080] The optical elements (e.g., (241), (242), (243), and / or (244)) perform different functions in the LC vision correction optical system (240) and are made from LC materials using corresponding manufacturing techniques. The combination of “flat” (e.g., thin) optical elements can enable the defocus function (or zoom function), astigmatism correction, chromatic aberration correction, etc. that can occur in virtual and / or augmented reality systems.

[0081] With reference to FIG. 2 , the electrically tunable LC lenses (e.g., (241) and (242)) as adaptive LC phase modulators, the polarization control PB phase lens (e.g., (244)) as a passive LC phase modulator, and the fast switchable SLM (e.g., (243)) as an LC polarization modulator can be combined in the LC vision correction optical system (240) for vision correction in, for example, VR and / or AR NED systems. Different functions including defocus (or zoom function), astigmatism correction, and / or chromatic aberration correction can be achieved by the LC vision correction optical system (240) using LC technology. In one example, each of the optical elements (e.g., (241)-(244)) employs LC technology. The LC vision correction optical system (240) with zoom function and wavefront dynamic adjustment can equivalently provide, for example, from -6D to +6D eyeglass prescriptions for different users by changing only the applied voltage, thereby reducing eye strain and fatigue due to long time use. The LC vision correction optical system (240) can compensate for chromatic aberration in a large portion of the spectrum of the LCD panel, for example, from 430 nanometers (nm) to 680 nm. In one example, the radius of each optical element in the LC vision correction optical system (240) is the same, such as from 15 mm to 30 mm. The LC vision correction optical system (240) can have a lighter weight due to having a thinner thickness and lower power consumption.

[0082] In mechanical zoom systems, (i) the lens distance can be manually adjusted or (ii) a voice coil actuator and flexure hinge array can be used. However, mechanical zoom systems can be bulky for VR headsets and can feel heavy on the user’s head over long periods of time. A combination of a PB phase lens and a switchable half wave plate (HWP) controlled only by polarization can be used to replace the mechanical adjustment in mechanical zoom systems. The combination of a PB phase lens and a switchable HWP can move the focal point between different depths to achieve smooth zooming. However, the astigmatism and chromatic aberration in the human eye can not be corrected by the zoom system. In embodiments of the LC vision correction optical system (240), the LC vision correction optical system (240) is controlled electrically and / or via polarization control, rather than mechanically. The electrical and / or polarization control can allow the LC vision correction optical system (240) to be lighter, thinner, and quickly switchable. Furthermore, the LC vision correction optical system (240) can be configured to change the focal length as well as correct astigmatism and / or chromatic aberration, and thus provide more comprehensive vision correction.

[0083] According to embodiments of the present disclosure, the LC vision correction optical system (240) can include one or more ROEs and one or more DOEs having complementary optical properties. The ROEs and DOEs are described in further detail below.

[0084] In one embodiment, a lens refracts light incident on the lens and causes the light to diverge or converge. The lens can be referred to as a ROE because the light is refracted by the lens. The focal length of the lens as a ROE can depend on the refractive index of the lens, and thus a change in the refractive index can affect the focusing.

[0085] Chromatic aberration can be caused by dispersion, in which the refractive index of the lens material varies with the wavelength of the light. For example, the refractive index corresponding to blue light is different from the refractive index corresponding to red light. In one example, the focal length of a lens (e.g., a ROE) increases with wavelength, and the chromatic aberration of the lens can be referred to as a first type of chromatic aberration.

[0086] When light is incident on a diffraction grating as a DOE at an angle θ i with respect to an axis normal to the surface of the diffraction grating, the light can be diffracted by the diffraction grating at a diffraction angle θ diff with respect to the axis. In one embodiment, the PB phase lens (244) includes a plurality of diffraction gratings having different periodicities. The focal length of the PB phase lens (244) can depend on the diffraction angle θ diff . In one embodiment, the focal length of the PB phase lens (244) decreases with the diffraction angle θ diff . In one embodiment, the focal length of the PB phase lens (244) decreases with the diffraction angle θ diffThe focal length of the PB phase lens (244) decreases with the wavelength. Thus, the chromatic aberration of the PB phase lens (244) can be referred to as a second type of chromatic aberration that can be opposite to the first type of chromatic aberration.

[0087] According to embodiments of the present disclosure, including a DOE (e.g., the PB phase lens (244)) having a chromatic aberration opposite to a chromatic aberration of an optical system (e.g., the LC vision correction optical system (240) or the optical system (110)) can correct (e.g., reduce or eliminate) the chromatic aberration of the optical system.

[0088] The one or more LC lenses (241) can have a first chromatic aberration. The PB phase lens (244) can have a second chromatic aberration that is complementary (e.g., opposite) to the first chromatic aberration. A chromatic aberration of the LC vision correction optical system (240) based at least on the first chromatic aberration and the second chromatic aberration is less than the first chromatic aberration.

[0089] In one embodiment, the one or more LC lenses (241) are ROEs, and the first chromatic aberration is a first type of chromatic aberration. The PB phase lens (244) is a DOE, and the second chromatic aberration is a second type of chromatic aberration. The first chromatic aberration is opposite to the second chromatic aberration, and the first chromatic aberration can be reduced by including the PB phase lens (244) in the LC vision correction optical system (240).

[0090] Reference is made to FIG. 2 In one embodiment, the one or more LC lenses (241) and the one or more cylindrical LC lenses (242) are ROEs. A third chromatic aberration of the one or more cylindrical LC lenses (242) is a first type of chromatic aberration. A chromatic aberration of the one or more LC lenses (241) and the one or more cylindrical LC lenses (242) can include the first chromatic aberration and the third chromatic aberration. The chromatic aberration (e.g., the first type of chromatic aberration) of the one or more LC lenses (241) and the one or more cylindrical LC lenses (242) is opposite to the second chromatic aberration, and can be reduced by including the PB phase lens (244) in the LC vision correction optical system (240).

[0091] Reference is made to FIG. 1C The VR viewing optical system (130) includes the lenses (131)-(132) as ROEs, and can have a fourth chromatic aberration that belongs to the first type of chromatic aberration. The chromatic aberration of the VR viewing optical system (130), the one or more LC lenses (241), and the one or more cylindrical LC lenses (242) is the first type of chromatic aberration, and can be reduced by the second chromatic aberration of the PB phase lens (244).

[0092] In one example, the LC SLM (243) does not introduce chromatic aberration, e.g., because the LC SLM (243) does not converge or diverge light.

[0093] The optical power of the LC vision correction optical system (240) can be electrically tunable, e.g., by an electrically tunable controller (281). One or more optical components in the LC vision correction optical system (240) can be tuned to adjust the optical power of the LC vision correction optical system (240). In one example, a first optical power of one or more LC lenses (241) is electrically tunable. The one or more LC lenses (241) are electrically tuned to adjust the first optical power. The optical power of the LC vision correction optical system (240) can be based on at least a sum of the first optical power of the one or more LC lenses (241) and a second optical power of the PB phase lens (244). In one example, the first optical power is +2D and the second optical power is -3D, and thus the optical power of the LC vision correction optical system (240) is -1D, which is a sum of +2D and -3D. The first optical power, the second optical power, and the optical power of the LC vision correction optical system (240) can correspond to a focal length of the one or more LC lenses (241), a focal length of the PB phase lens (244), and a focal length of the LC vision correction optical system (240), respectively.

[0094] In one example, the one or more LC lenses (241) include a plurality of LC lenses. Each LC lens can be electrically tunable, and the first optical power can be a sum of respective optical powers of the plurality of LC lenses. For example, the number of the plurality of LC lenses is 3.

[0095] In one embodiment, a light beam is randomly polarized if the light beam includes a series of rapidly varying different polarization states. A light beam can be polarized, such as linearly polarized (e.g., in a linear polarization state), circularly polarized (e.g., in a circular polarization state), elliptically polarized (e.g., in an elliptical polarization state), and the like. For linearly polarized light, the electric field vector of the light beam is along a particular line. For circularly polarized light, the electric field vector of the light beam rotates, e.g., the light propagates toward an observer, as seen by the observer, the light rotates clockwise or counterclockwise.

[0096] The degree of polarization (DOP) refers to an amount that indicates a portion of an electromagnetic wave (e.g., a light beam) that is polarized. A completely polarized wave can have a DOP of 100%, while an unpolarized wave can have a DOP of 0%. A partially polarized wave can be represented by a superposition of a polarized component and an unpolarized component, and thus can have a DOP between 0 and 100%. The DOP can be calculated as a fraction of total power carried by a polarized component of a wave (e.g., a light beam).

[0097] The light beam can have any suitable polarization state and / or DOP. In one example, the light beam is circularly polarized with 100% DOP, so the light beam is fully circularly polarized. In one example, the light beam is predominantly circularly polarized with a relatively large DOP above a threshold (e.g., 80% or above), such as a superposition of (i) a circularly polarized component and (ii) an unpolarized component and / or another polarized component. Hereinafter, a circularly polarized light with 100% DOP or a light beam predominantly circularly polarized with a relatively large DOP can be referred to as a circularly polarized light. In one example, the light beam is linearly polarized with 100% DOP, or is predominantly linearly polarized with a relatively large DOP above a threshold. Hereinafter, a linearly polarized light with 100% DOP or a light beam predominantly linearly polarized with a relatively large DOP can be referred to as a linearly polarized light.

[0098] In one embodiment, the PB phase lens (244) functions as a converging lens or a diverging lens based on the polarization state of the input light beam (e.g., (254) or (255)) to the PB phase lens (244). The second optical power of the PB phase lens (244) can be polarization controlled, for example, by controlling or manipulating the polarization state of the input light beam to the PB phase lens (244).

[0099] Referring to FIG. 2 When the input light beam (254) to the PB phase lens (244) is left circularly polarized (LCP), the output light beam (256) from the PB phase lens (244) is right circularly polarized (RCP), and the PB phase lens (244) can function as a converging lens with a second optical power (e.g., +3D) that is positive. When the input light beam (255) to the PB phase lens (244) is right circularly polarized, the output light beam (257) from the PB phase lens (244) is left circularly polarized, and the PB phase lens (244) can function as a diverging lens with a second optical power (e.g., -3D) that is negative. In one example, the magnitude of the second optical power (e.g., 3D) remains constant when the polarization state (e.g., LCP or RCP) of the input light beam to the PB phase lens (244) changes.

[0100] Referring to FIG. 2 The LC SLM (243) can be electrically tunable. The LC SLM (243) can be configured to manipulate the polarization state of the light beam (253) passing through the LC SLM (243) by changing the voltage to the LC SLM (243) via an electrically tunable controller (281).

[0101] In one example, when the voltage to the LC SLM (243) is a first voltage (e.g., 6V corresponding to an “on” state of the LC SLM (243)), the LC SLM (243) can convert the linearly polarized beam (253) to an LCP beam (254). Subsequently, the PB phase lens (244) can be configured to convert the LCP beam (254) incident on the PB phase lens (244) to an RCP beam (256) exiting the PB phase lens (244). In one example, when the voltage to the LC SLM (243) is a second voltage (e.g., 0V corresponding to an “off’ state of the LC SLM (243)), the LC SLM (243) can convert the linearly polarized beam (253) to an RCP beam (255). Subsequently, the PB phase lens (244) can be configured to convert the RCP beam (255) incident on the PB phase lens (244) to an LCP beam (257) exiting the PB phase lens (244). Thus, the polarization state of the beam entering the PB phase lens (244) (e.g., (254) or (255)) can be electrically controlled by controlling the LC SLM (243). Since the sign (e.g., “+” or “-”) of the second optical power is controlled by the polarization state of the beam entering the PB phase lens (244) (e.g., (254) or (255)), the sign (e.g., “+” or “-”) of the second optical power can be indirectly electrically controlled.

[0102] The one or more cylindrical LC lenses (242) can be configured to correct for astigmatism. The one or more cylindrical LC lenses (242) can include a stack of multiple cylindrical LC lenses with respective cylinder axes (e.g., in the XZ plane) forming different angles with an axis (e.g., the X-axis) in the XZ plane. The stack of multiple cylindrical LC lenses can be electrically tunable via the electrical tunable controller (281).

[0103] Reference is made to FIG. 2One or more LC lenses (241) may comprise a stack of electrically tunable LC lenses, and one or more cylindrical LC lenses (242) may comprise a stack of cylindrical LC lenses. An electrically tunable lens system (261) may comprise a stack of LC lenses (241) and a stack of cylindrical LC lenses (242). In one example, the stack of LC lenses (241) and the stack of cylindrical LC lenses (242) are separated by a gap (271). In another example, the stack of LC lenses (241) and the stack of cylindrical LC lenses (242) are stacked together with a gap (271) of zero. An LC SLM (243) may be disposed between the electrically tunable lens system (261) and the PB phase lens (244). In one example, the LC SLM (243) is separated from the electrically tunable lens system (261) and the PB phase lens (244) by gaps (272) and (273), respectively. In one example, an electrically tunable lens system (261), an LC SLM (243), and a PB phase lens (244) are stacked together with gaps (272) and (273) of 0.

[0104] In one embodiment, the light beam (e.g., the input beam) (251) incident on the electrically tunable lens system (261) is linearly polarized (LP). For example, the beam (251) is the output beam from the VR viewing optics system (130). The electrically tunable lens system (261) can convert the beam (251) into a beam (253), which is the output beam from the electrically tunable lens system (261) incident on the LC SLM (243). The beam (253) is linearly polarized. As described above, when the voltage of the LC SLM (243) is a first voltage (e.g., in an "on" state), the LC SLM (243) can convert the linearly polarized beam (253) into an LCP beam (254), and the PB phase lens (244) can convert the LCP beam (254) into an RCP beam (256). When the voltage of the LCSLM (243) is the second voltage (e.g., the "off" state), the LCSLM (243) can convert the linearly polarized beam (253) into an RCP beam (255), and the PB phase lens (244) can convert the RCP beam (255) into an LCP beam (257). In one example, either the RCP beam (256) or the LCP beam (257) is incident on the eye (60).

[0105] The positions of certain components in the LC vision correction optical system (240) can be interchanged. In one example, the stacking of multiple LC lenses (241) and the stacking of multiple cylindrical LC lenses (242) are interchangeable. FIG. 2In the illustrated example, the light beam (251) is incident on the stack of LC lenses (241), and the stack of LC lenses (241) converts the light beam (251) to a linearly polarized light beam (252). Subsequently, the light beam (252) is incident on the stack of cylindrical LC lenses (242), and the stack of cylindrical LC lenses (242) converts the light beam (252) to the light beam (253). In one example, the polarization state of each of the light beams (251)-(253) is the same, such as a linear polarization state along an axis in the XZ plane (e.g., the X axis) as illustrated in FIG. 2B. FIG. 2

[0106] In another example, the light beam (251) is incident on the stack of cylindrical LC lenses (242), and the stack of cylindrical LC lenses (242) converts the light beam (251) to another light beam. Subsequently, the other light beam is incident on the stack of LC lenses (241), and the stack of LC lenses (241) converts the other light beam to the light beam (253). In one example, the polarization state of the other light beam is the same as the polarization state of the light beams (251)-(253), such as a linear polarization state along the X axis.

[0107] In one example, a first HMD system includes a display device (e.g., the display device (120)), a VR viewing optical system (e.g., the VR viewing optical system (130)), and an LC vision correction optical system (240). A light beam from the display device can be guided to the eye through the VR viewing optical system and the LC vision correction optical system (240). The LC vision correction optical system (240) is configured to at least one of (i) correct astigmatism of the eye or (ii) change an optical power of the LC vision correction optical system (240). By changing the optical power of the LC vision correction optical system (240), the optical power of the first HMD system can be changed such that myopia or hypermetropia of the eye is corrected and a clear image can be formed on the retina of the eye based on an image on the display device. In one example, the VR viewing optical system is disposed between the display device and the LC vision correction optical system (240). In one example, the LC vision correction optical system (240) is disposed between the display device and the VR viewing optical system. In one example, the PB phase lens (244) corrects chromatic aberration of a lens that is an ROE in the first HMD.

[0108] ​In one example, the second HMD system includes an AR viewing optical system (e.g., an AR waveguide (130D)) and an LC vision correction optical system (240). Light beams from a real object can be guided to the eye by the AR viewing optical system and the LC vision correction optical system (240). The LC vision correction optical system (240) is configured to at least one of (i) correct astigmatism of the eye or (ii) change optical power of the LC vision correction optical system (240). By changing the optical power of the LC vision correction optical system (240), the optical power of the second HMD system can be changed so that myopia or hypermetropia of the eye is corrected and a clear image can be formed on the retina of the eye based on the real object. In one example, light beams from the AR viewing optical system are incident on the LC vision correction optical system (240). In one example, light beams from the LC vision correction optical system (240) are incident on the AR viewing optical system. In one example, the PB phase lens (244) corrects chromatic aberration as a lens of the ROE in the second HMD.

[0109] One or more LC lenses (241) and one or more cylindrical LC lenses (242) in the LC vision correction optical system (240) can be electrically tunable “flat” (thin) LC lenses. When the one or more LC lenses (241) and the one or more cylindrical LC lenses (242) are combined with the polarization control PB phase lens (244) and the fast-switchable TN LC SLM (243), multiple functions can be achieved, for example, a zoom function can be dynamically achieved, astigmatism can be dynamically corrected, and / or chromatic aberration can be simultaneously corrected. Users or wearers of myopia and hypermetropia no longer need prescription glasses to use the VR / AR display including the LC vision correction optical system (240).

[0110] In one example, including the LC vision correction optical system (240) in the NED can increase the resolution of the NED without affecting other parameters of the NED, such as the field of view (FOV).

[0111] FIG. 3 An example LC lens (301) that is electrically tunable is shown. In one example, each of the one or more LC lenses (241) is the same as or similar to the LC lens (301). The LC lens (301) can be a kind of ROE. The LC lens (301) can be referred to as a gradient refractive index (GRIN) lens because the LC lens (301) is based on gradual changes in refractive index without using curved surfaces. The LC lens (301) can correct myopia or hypermetropia, for example, as indicated by the parameter “spherical (SPH)” in a glasses prescription.

[0112] The LC lens (301) can include a plurality of electrodes. For example, the LC lens (301) can include an electrode (e.g., a circular center electrode) (313) and one or more ring electrodes (312)-(313) disposed on a first substrate (321) and an electrode (314) disposed on a second substrate (322). The first substrate (321) and the second substrate (322) can be parallel to each other, e.g., parallel to the XZ plane. The first substrate (321), the second substrate (322), and the electrodes (311)-(314) can be transparent. The first substrate (321) and the second substrate (322) can be flat, and thus the LC lens (301) can be flat. The thickness T1 of the LC lens (301) can be relatively small, e.g., less than or equal to 1 mm. The electrodes (311)-(314) can be controlled by a voltage controller, such as the electrically tunable controller (281).

[0113] The LC lens (301) can include a plurality of LC cells. Each LC cell can include a stack of (i) a transparent substrate (e.g., a glass substrate), such as the second substrate (322), (ii) a transparent electrode (e.g., ITO, such as (314)), (iii) an alignment material (e.g., polyimide) for aligning the LC material, (iv) an LC material (e.g., a nematic LC material), (v) a transparent electrode (e.g., ITO, such as (313)), and (vi) a transparent substrate (e.g., (321)). In one example, the nematic LC material does not twist along the optical path.

[0114] In one embodiment, a plurality of voltages are applied to the respective electrodes (311)-(313) with reference to the voltage of the reference electrode (314) (e.g., 0 V or another suitable voltage). A first voltage is applied to the electrode (311), a second voltage is applied to the electrode (312), and a third voltage is applied to the electrode (313). In one example, the electrode (311) is at the edge of the LC lens (301), and the first voltage is the maximum voltage of the plurality of voltages, such as 6 V. The electrode (313) is at the center of the LC lens (301), and the third voltage is the minimum voltage of the plurality of voltages, e.g., 0 V. In one example (not shown), no electrode is formed at the center of the LC lens (301), and thus the third voltage can be 0 V.

[0115] The LC material (in the LC lens (301)) between the respective electrodes (311)-(313) and the electrode (314) can be manipulated differently when the plurality of voltages are applied to the electrodes (311)-(313), respectively. FIG. 3The orientations of the respective directors of the LC material vary in different apertures (e.g., corresponding to electrodes (311)-(313)) of the LC lens (301), and thus the refractive indices (such as a first refractive index n1, a second refractive index n2, and a third refractive index n3) corresponding to the respective electrodes (311)-(313) can be different. In one example, the LC material is birefringent, and has two refractive indices n e and n o The first refractive index n1 at the edge (e.g., corresponding to (311)) of the LC lens (301) can be the smallest (e.g., n o ), and the third refractive index n3 at the center (e.g., corresponding to (313)) of the LC lens (301) can be the largest (e.g., n e ).

[0116] FIG. 3 An example with two ring-shaped electrodes (312)-(313) is shown. However, the number of the one or more ring-shaped electrodes can be any positive integer, such as 1, 2, or greater than 2.

[0117] FIG. 4 A relationship of the refractive indices of the LC lens (301) with the position on the first substrate (321) is shown. The position of 0 mm is at the center of the first substrate (321). When the number of the one or more ring-shaped electrodes is relatively large, the distribution (401) of the refractive indices of the LC lens (301) with respect to the position can be relatively smooth. Referring to FIG. 3-4 , the refractive indices of the LC lens (301) can vary with a radial distance r (e.g., an absolute value of the position) from the center of the first substrate (321). The refractive indices can be controlled by the respective voltages of the electrodes (311)-(313). The refractive indices can be circularly symmetric in the XZ plane.

[0118] Referring back to FIG. 3 , a light beam (e.g., linearly polarized) can be incident on the LC lens (301) along the directions indicated by arrows (331)-(333). The light beam can include a central portion (e.g., associated with arrow (333)) passing through the center of the electrode (313) and a peripheral portion (e.g., associated with arrows (331)-(332)) passing through the electrodes (311)-(312), respectively. The dashed lines associated with arrows (331)-(333) can represent wavefronts of the central portion and the peripheral portion of the light beam, respectively. Due to the refractive indices varying with the radial distance r (e.g., the absolute value of the position), the wavefronts of the central portion and the peripheral portion of the light beam can be different. FIG. 4As shown in the positional changes, the wavefronts of the beam inside and outside the LC lens (301) can be tilted, as indicated by the dashed lines inside and outside the LC lens (301), respectively. Therefore, the central and peripheral portions of the output beam can be focused at the same focal point P with a focal length f, for example, measured as the distance between focal point P and the first substrate (321). In one example, the directions of the central and peripheral portions of the output beam are indicated by arrows (343) and (341) to (342), respectively. The LC lens (301) can be equivalent to a lens made of glass (e.g., a convex lens).

[0119] When FIG. 3 When multiple voltages are applied, the distribution (401) of the refractive index of the LC lens (301) can be aspherical, such as parabolic, in a cross-section (e.g., the XY plane) passing through the principal axis (e.g., the Y-axis). The phase and optical path length (OPL) (or optical path (OP)) of the beam in the material can be proportional to the refractive index and the distance traveled in the material. The first phase and first OP of the beam in the LC lens (301) can be proportional to the refractive index and the distance d, and therefore the first phase distribution or the first OPL distribution can have the same shape as the distribution (401), for example, when... FIG. 3 The cross-section (e.g., XY plane) through the principal axis (e.g., Y-axis) when multiple voltages are applied is aspherical (e.g., parabolic). d1 can be the distance between electrodes (311)-(313) and electrode (314). d1 can be the thickness of the LC lens (301) excluding the first substrate (321) and the second substrate (322). The parabolic phase distribution can perform better than the spherical distribution when a beam emitted from a point source is collimated by the LC lens (301) or when a collimated beam is focused by the LC lens (301). For example, the first optical path difference (OPD) between a first OP associated with a position on the first substrate (321) and a first reference OP associated with a reference position (e.g., at an edge on the first substrate (321)) can have a similar shape to the first reference OP. FIG. 4 The distribution (401) has the same shape, wherein the first OP and the first reference OP are in the LC lens (301). In one example, the first OPD between the first OP at the center position (e.g., 0 mm) and the first OP at the edge position is (n e -n o )×d is proportional.

[0120] The second OPD between a second OP associated with a location on the first substrate (321) and a second reference OP associated with a reference location on the first substrate (321) has a parabolic shape, where the second OP and the second reference OP are between the LC lens (301) and the focal point P. In one example, the second OPD is estimated using Equation 1, where r indicates a radial distance.

[0121]

[0122] In one example, a total OP that is a sum of a first OP in the LC lens (301) and a second OP from the LC lens (301) to the focal point P is the same or similar for each location on the first substrate (321), and thus different portions of the light beam can be focused onto the same focal point P.

[0123] In one example, a theoretical limit of optical power of the LC lens (301) (e.g., a GRIN lens) can be derived based on Equation 2.

[0124] Optical power = 2 x An x d / R 2 (Equation 2) where R is a radius of the LC lens (301) for converging or diverging light, the optical power (e.g., in diopters, i.e., m -1 ) can be an inverse of the focal length f, An is equal to (n e - n o ), indicating birefringence of the LC material. The radial distance r in Equation 1 can be from 0 to R. In one example, the refractive index of the LC lens (301) at the edge (e.g., r = R) is n e , and the refractive index of the LC lens (301) at the center (e.g., r = 0) is n o . In one example, if the diameter of the LC lens (301) (e.g., a diameter of a portion of the LC lens (301) for converging or diverging light) is 30 mm, An is 0.3, and dl is 375 micrometers, then the optical power is estimated to be 2 x 0.3 x 375 x 10 -6 / (15 x 10 -3 ) 2 = 1 D according to Equation 2. By reversing the voltage, the LC lens (301) can become a diverging lens with the same diopter size (e.g., -1 D). By adjusting the plurality of voltages, a continuous zoom manipulation between the strongest positive optical power (e.g., +1 D) and the strongest negative optical power (e.g., -1 D) can be achieved.

[0125] In one example, the LC material in the LC lens (301) includes rod-like molecules exhibiting positive birefringence, n e is 1.56 to 1.89, and n oT1 is 0.5 mm to 0.8 mm, An is 0.05 to 0.45, d1 is 5 to 400 microns, R is 1 mm to 25 mm, and the voltage is 0 V to 6 V. The electrodes (311)-(314) can be made of indium tin oxide (ITO). The first and second substrates can be made of glass, plastic, and / or any suitable material. In one example, the first and second substrates are glass substrates with a total thickness of 0.5 mm, and thus T1 can be 0.5 mm to 0.8 mm. Additional materials (e.g., alignment layers) can be used in the LC lens (301).

[0126] The width of each electrode (e.g., 311, 312, or 313) can be determined by a phase step within the respective electrode. In one example, for f of 400 mm and a design wavelength l of 543.5 nm, the phase step is 1 / 10 l. In one example, the center electrode disk (e.g., 313) has a radius of about 200 pm, and the width of the outermost electrode (e.g., 311) is about 15 pm. In one example, the gap between two adjacent electrodes (e.g., 312 and 311) is 3 pm, and the LC cell has a thickness d1 of 10 pm.

[0127] The one or more cylindrical LC lenses (242) can be configured to correct astigmatism. The cylindrical LC lens can include a plurality of transparent electrodes disposed on a first substrate and a transparent electrode disposed on a second substrate. The first and second substrates can be parallel to the XZ plane. In one example, the cylindrical LC lens has a structure and materials similar or identical to the LC lens (301) shown in FIG. 3A, and a refractive index or OP distribution similar to the distribution (401) shown in FIG. 4A. FIG. 3 FIG. 4 The one or more cylindrical LC lenses (242) can be configured to correct astigmatism. The cylindrical LC lens can include a plurality of transparent electrodes disposed on a first substrate and a transparent electrode disposed on a second substrate. The first and second substrates can be parallel to the XZ plane. In one example, the cylindrical LC lens has a structure and materials similar or identical to the LC lens (301) shown in FIG. 3A, and a refractive index or OP distribution similar to the distribution (401) shown in FIG. 4A.

[0128] For each of the one or more cylindrical LC lenses (242), in one example, the LC material in the cylindrical LC lens is similar or identical to the LC material in the LC lens (301), and has a similar or identical refractive index. For example, the LC material in the cylindrical LC lens includes rod-like molecules exhibiting positive birefringence, n e is 1.56 to 1.89, n o ​T1 can be less than or equal to 1 mm, such as 0.5 mm to 0.8 mm. The electrodes (311)-(314) can be made of indium tin oxide (ITO). The first and second substrates can be made of glass and / or any suitable material. In one example, the first and second substrates are glass substrates with a total thickness of 0.5 mm, and thus T1 can be 0.5 mm to 0.8 mm. Additional materials (e.g., alignment layers) can be used in the LC lens (301).

[0129] A difference between the LC lens (301) and a cylindrical LC lens is that the plurality of transparent electrodes of the cylindrical LC lens can be parallel, and the refractive index of the electrically tunable cylindrical LC lens can vary only along a dimension in the XZ plane (e.g., the X-axis). The plurality of transparent electrodes of the cylindrical LC lens can include rectangular electrodes that are parallel to each other. In one example, the plurality of transparent electrodes of the cylindrical LC lens are parallel to the Z-axis within the XZ plane, and the refractive index of the cylindrical LC lens varies only along the X-axis and not the Z-axis. On the other hand, the refractive index of the LC lens (301) varies, for example, radially along the X-axis and the Z-axis.

[0130] A cylindrical LC lens can converge or diverge light only in a first dimension (e.g., the X-axis) and not affect light in a second dimension (e.g., the Z-axis) that is perpendicular to the first dimension. In one example, the first and second dimensions are perpendicular to an axis along which light propagates (e.g., the Y-axis). A cylindrical LC lens can have optical power only in the first dimension. There are two types of cylindrical lenses, such as converging (or positive) cylindrical lenses and diverging (or negative) cylindrical lenses.

[0131] Advantages of the electrically tunable cylindrical LC lens can include achieving various prescriptions (e.g., indicated by a parameter cylinder (CYL) and a parameter axis) by programming and dynamically adjusting the voltages applied to each cylindrical LC lens (e.g., including the voltages of the plurality of transparent electrodes). For example, three cylindrical LC lenses (e.g., a first cylindrical LC lens, a second cylindrical LC lens, and a third cylindrical LC lens) are stacked at 0°, 45°, and 90° with respect to the X-axis (e.g., in the XZ plane) and are electrically tunable. The first cylindrical LC lens can have a positive cylindrical power along the X-axis and a zero cylindrical power along the Z-axis. The second cylindrical LC lens can have a positive cylindrical power along the X-axis and a positive cylindrical power along the Z-axis. The third cylindrical LC lens can have a positive cylindrical power along the X-axis and a negative cylindrical power along the Z-axis. FIG. 3The three cylindrical LC lenses can be individually tuned by controlling the electrically tunable controller (281). As a wavefront corrector, one or more cylindrical LC lenses (242) can be attached to one or more LC lenses (241) to obtain a customized phase distribution, and thus obtain astigmatism-free corrected vision for different users.

[0132] FIG. 5A An exemplary OPD projection from three-dimensional (3D) to XZ plane is shown, which represents the corrected phase retardation from a corrected defocus (power compensation of changing focal length) LC lens (e.g., one or more LC lenses (241)). FIG. 5B An exemplary OPD projection from 3D to XZ plane is shown, which represents the corrected phase retardation from a corrected defocus LC lens (e.g., one or more LC lenses (241)) and a cylindrical LC lens (e.g., one or more cylindrical LC lenses (242)) of corrected astigmatism (cylindrical power compensation with a desired axis). In one example, FIG. 5A-5B An interference pattern is shown, in which the phase difference between two adjacent lines (e.g., FIG. 5A a circle in FIG. 5B an ellipse in

[0133] When a light beam passes through certain optical elements, the polarization state of the light beam can be changed. In one embodiment, the polarization state of a light beam can be changed by a waveplate or a retarder when the light beam travels through the waveplate. A quarter-waveplate (QWP) can change the polarization state of a light beam passing through the QWP by 90° or π / 2. In one example, a QWP converts linearly polarized light to circularly polarized light or converts circularly polarized light to linearly polarized light. The phase distribution (or phase retardation) introduced by a waveplate can be given by Γ = OPD x 2π / λ. When Γ = π / 2, the retarder (or waveplate) is a QWP, and when Γ = π, the retarder (or waveplate) is a HWP.

[0134] FIG. 6A-6BA schematic diagram showing the working principle of the LC SLM (243) is shown. In one example, the LC SLM (243) is made of a twisted nematic (TN) LC material (604) that has been arranged in a 90° twisted configuration, and is referred to as a TN SLM. The TN LC material can be disposed between two electrodes (e.g., ITO) (601) and (602). Each electrode can be disposed on a respective transparent substrate (e.g., a glass substrate). In one example, an alignment material (e.g., polyimide) is disposed between the TN LC material (604) and the electrode (e.g., (601)) to align the TN LC material (604).

[0135] The LC SLM (243) can be a TN LC polarization modulator, as the LC SLM (243) can modulate the polarization state of light. Similar to a HWP, the TN LC SLM (243) can be used to rotate the polarization plane of light. Advantages of using the LC SLM (243) include that the LC SLM (243) can be easily controlled and turned on and off using an electric field. As a result, the polarization plane can be quickly changed or switched, for example, in a display or an optical switch. The LC SLM (243) can be a fast-switchable TN SLM.

[0136] FIG. 6A A schematic diagram showing a 90° TN SLM with a voltage of “off” (e.g., 0 V) is shown. FIG. 6B A schematic diagram showing a 90° TN SLM with a voltage of “on” (e.g., 6 V) is shown. A linearly polarized light beam (603), for example, polarized along the X-axis, is incident on the LC SLM (243). Referring to FIG. 6A When the voltage is “off”, the TN LC material can rotate 90° along the optical path (e.g., along the Y-axis) when no voltage is applied. The LC SLM (243) rotates the polarization of the light beam (603) by 90° (e.g., from the X-axis to the Z-axis), and thus the output light beam (613) is linearly polarized along the Z-axis. Referring to FIG. 6B When the voltage is “on”, the TN LC material is oriented by the electric field, for example, along the Y-axis, and the LC SLM (243) does not change the polarization of the light beam (603). Thus, the output light beam (623) is linearly polarized along the X-axis.

[0137] The output light beam (613) or (623) can subsequently pass through a QWP (e.g., a broadband QWP suitable for covering different wavelengths of a large wavelength range) to become circularly polarized light, such as an RCP light beam (614) or an LCP light beam (615), respectively, before entering the PB phase lens (244).

[0138] In one example, the LC material (604) in the LC SLM (243) comprises rod-like molecules exhibiting positive birefringence, n e is 1.56 to 1.89, n o is 1.47 to 1.55, An is 0.05 to 0.45, and the voltage is 0 to 6V. In one example, the thickness of the QWP (660) is 0.05mm, the total thickness of the substrate is 0.5mm, the thickness d3 of the TN LC layer can be 5 to 15 microns, and thus the total thickness of the LC SLM (243) can be estimated to be less than 1mm (e.g., 0.555mm to 0.57mm).

[0139] FIG. 7A-7B A schematic diagram of a PB phase device (such as a PB phase lens (244)) is shown in accordance with an embodiment of the disclosure. In FIG. 7A-7B A local region (e.g., a peripheral region) (700) of the PB phase lens (244) is shown in (e.g., near the edge of the PB phase lens (244)).

[0140] The PB lens can also be referred to as a geometric phase lens or a volume holographic lens. In one example, the PB phase lens (244) is a passive LC lens, e.g., not electrically tunable. The PB phase lens (244) can be polarization controlled as described above.

[0141] The PB phase lens (244) can be formed by spin-coating a multi-layer LC material (e.g., LC monomer RM257 mixture, then UV exposure) onto a photo-alignment layer (702) (e.g., a photo-alignment material, such as bright yellow dye), which can have the function of a Fresnel-type lens pattern exposed by using two circularly polarized interference beams and achieving imaging. For example, after UV exposure, the LC material (e.g., LC monomer) can become an LC polymer (703). The radius of the PB phase lens (244) can be 2mm to 30mm, e.g., 2.5mm to 25mm. The PB phase lens (244) can be designed as a few microns of a DOE with a uniform thickness d2 on a substrate (e.g., made of glass, plastic material, and / or other materials) (701), and can act as a HWP for a specific wavelength (e.g., such as a wavelength in a wavelength range from 430nm to 680nm).

[0142] The input circularly polarized light (711) and the output circularly polarized light (712) can be represented using the following Jones matrix.

[0143]

[0144] Reference is made to FIG. 7A , may represent the fast-axis orientation angle of the local LC director (e.g., the local average orientation of the liquid crystal molecules). A phase change of may occur when the handedness (e.g., LCP or RCP) of the circular polarization is reversed, such as (i) from LCP to RCP or (ii) from RCP to LCP. Thus, as FIG. 7A-7B indicated, a PB phase lens (244) can be fabricated by patterning the LC molecule orientation. In one example, is a linear function of x, such as may be referred to as the half-pitch. In one example, the LC orientation does not change along the Y-axis.

[0145] The half-pitch A can be defined as the distance over which the LC molecules rotate by p radians around the Y-axis. In one embodiment, the half-pitch A is relatively large (e.g., between 100 to 300 microns) at the center of the PB phase lens (244) and decreases towards the edges of the PB phase lens (244). For example, the half-pitch A is less than 5 microns (e.g., 2 pm) at the edges. Thus, a local region of the PB phase lens (244) with a particular half-pitch A can act as a diffraction grating that can periodically modulate the incident light. As mentioned above, the PB phase lens (244) can include multiple diffraction gratings with different periodicities (such as different half-pitches A).

[0146] Referring to FIG. 7B , a local region (700) with a half-pitch A can deflect an incident light wave (711) to a diffraction angle q diff where l represents the wavelength of the light.

[0147] sin(q diff ) = l / A (Equation 4)

[0148] When the half-pitch A decreases with the radial distance from the center of the PB phase lens (244), the diffraction angle q diff may increase with the radial distance. In one example, the half-pitch A varies continuously, thus the phase distribution can vary continuously with the radial distance. Due to the continuous phase distribution and flat geometry, the PB phase lens (244) can provide higher optical quality and less stray light compared to other types of lenses, such as Fresnel-type lenses.

[0149] In one example, the thickness of the substrate (e.g., glass substrate) (701) is 0.25 mm, and the thickness d2 is about 2 microns, thus the total thickness of the PB phase lens (244) can be about 0.25 mm. In one example, the thickness of the photo-alignment layer (702) is less than 100 nm (e.g., 20 nm).

[0150] Referring back to FIG. 2When the components in the LC vision correction optical system (240) are stacked together, the total thickness of the LC vision correction optical system (240) can be about 0.8 + (N1 + N2) x 0.8 (mm), where d1 is 0.3 mm, and N1 and N2 are the number of LC lenses in the stack of LC lenses (241) and the number of cylindrical LC lenses in the stack of cylindrical LC lenses (242), respectively. If N1 = N2 = 3, the total thickness of the LC vision correction optical system (240) is about 5.6 mm, and thus the LC vision correction optical system (240) can be considered thin.

[0151] If d1 is 8 micrometers, the total thickness of the LC vision correction optical system (240) is about 0.8 + (N1 + N2) x 0.5 (mm). If N1 = N2 = 3, the total thickness of the LC vision correction optical system 240 is about 3.8 mm.

[0152] FIG. 8A-8B A schematic diagram showing the working principle of the PB phase lens (244) is shown. Referring to FIG. 8A , the input beam on the PB phase lens (244) is LCP. The input beam can include portions (801)-(802) that are incident on a peripheral region and a central region of the PB phase lens (244), respectively. The output beam diffracted by the PB phase lens (244) can include portions (811)-(812) that correspond to the portions (801)-(802), respectively. In the central region, the half pitch Λ is large, and the portion (802) is diffracted at a diffraction angle θ diff without bending.

[0153] In the peripheral region, the half pitch Λ is small, and the portion (801) is diffracted at a diffraction angle θ diff1 without bending.

[0154] For brevity, FIG. 8A-8B Two regions (e.g., two diffraction gratings with two different half pitches) such as the peripheral region and the central region of the PB phase lens (244) are shown in

[0155] Referring to FIG. 8A, is a converging lens or a diverging lens can depend on the polarization state of the input beam. In one example, when the input beam is LCP, the output beam is RCP. Further, the portion (811) can be curved towards the axis, and the PB phase lens (244) is a converging lens with a second optical power that is positive.

[0156] Referring to FIG. 8B , the input beam on the PB phase lens (244) is RCP. The input beam can include portions (821)-(822) that are incident on a peripheral region and a central region of the PB phase lens (244), respectively. The output beam diffracted by the PB phase lens (244) can include portions (831)-(832) that correspond to the portions (821)-(822), respectively. In the central region, the portion (822) is diffracted at a diffraction angle of 0° (or approximately 0°) with respect to an axis (e.g., the Y-axis) that is normal to the PB phase lens (244). Thus, the portion (832) can propagate along (or substantially along) the axis (e.g., the Y-axis) without being curved.

[0157] In the peripheral region, the portion (821) is diffracted at a diffraction angle of diff2 Thus, the portion (831) is curved away from the axis (e.g., the Y-axis).

[0158] Referring to FIG. 8B , the output beam is LCP when the input beam is RCP. Further, the portion (831) can be curved away from the axis, and the PB phase lens (244) is a diverging lens with a second optical power that is negative.

[0159] As described above, FIG. 8A-8B exemplary optical paths of the PB phase lens (244) that have converging FIG. 8A ) and diverging FIG. 8B ) characteristics by changing only the handedness of the circular polarization of the input beam. The PB phase lens (244) can be polarization controlled. In one example, the PB phase lens (244) has only two fixed optical powers on the positive or negative side by switching the handedness of the input beam.

[0160] Adding the PB phase lens (244) to the LC vision correction optical system (240) can serve multiple purposes. The combination of the one or more LC lenses (241) and the PB phase lens (244) can achieve, for example, FIG. 9The illustrated zoom function has a greater range of optical power. In one example, the optical power of the PB phase lens (244) is +3D or -3D depending on the polarization state of the incident light onto the PB phase lens (244). For example, by stacking three LC lenses, one or more LC lenses (241) can have a tunable focal point or tunable optical power from +3D to -3D. Each of the three LC lenses can have a tunable optical power from +1D to -1D. FIG. 9 An example of the total optical power of one or more LC lenses (241) and the PB phase lens (244) is shown. In one example, the total optical power of one or more LC lenses (241) and the PB phase lens (244) is the sum of the first optical power of one or more LC lenses (241) and the optical power of the PB phase lens (244). The total optical power of one or more LC lenses (241) and the PB phase lens (244) can be -6D to +6D.

[0161] In some embodiments, in addition to correcting for astigmatism indicated by the cylindrical (CYL) and axis parameters, one or more cylindrical LC lenses (242) can have a power that can correct for the parameter “sphere” (SPH) (e.g., radially, e.g., along the X and Z axes). For example, the optical power of the LC vision correction optical system (240) can be the sum of the first optical power of one or more LC lenses (241), the optical power of one or more cylindrical LC lenses (242), and the optical power of the PB phase lens (244).

[0162] In addition to achieving integer total optical powers, such as +6D, +5D, etc. More fine-tuned total optical powers can be achieved by tuning the multiple voltages applied to one or more LC lenses (241). In one example, the first optical power is +1.5, so the total optical power can be +4.5 or -1.5. In one embodiment, fractional steps smaller than 1D (e.g., 0.5D steps) can be used to tune the first optical power of one or more LC lenses (241), and thus the total optical power with fractional steps.

[0163] Because the PB phase lens (244) is a DOE, the PB phase lens (244) can compensate for chromatic aberration of one or more LC lenses (241) (e.g., ROEs) and / or other ROEs in the optical system (110) or (110D). As described above and as shown in FIG. 6, the ROEs and the PB phase lens (244) (DOE) can exhibit opposite chromatic aberration. FIG. 10A-10C As shown, the ROEs and the PB phase lens (244) (DOE) can exhibit opposite chromatic aberration.

[0164] FIG. 10A-10D Examples of chromatic aberration of ROEs, DOEs, and chromatic correction and achromatization performance of combined ROE and DOE lenses are shown. FIG. 10AA first type of chromatic aberration is shown, in which the focal length of one or more LC lenses (241) as a DOE can increase with wavelength. An optical axis (1010) of the one or more LC lenses (241) can be perpendicular to the one or more lenses (241) and pass through the center of the one or more LC lenses (241). When a light ray (1001) that is normally incident on the one or more LC lenses (241) includes polychromatic wavelengths such as in the visible wavelengths (e.g., 380 to 780 nm), the output light rays corresponding to the polychromatic wavelengths can intersect the optical axis (1010) at different points. The output light rays include light rays (1021)-(1023) corresponding to three different wavelengths λ B , λ G , and λ R , respectively, where the light rays (1021)-(1023) intersect the optical axis (1010) at three different points P B , P G , and P R , respectively. For brevity, FIG. 10A only the light rays (1021)-(1023) are shown. The three different points P B , P G , and P R may correspond to three different focal lengths f B , f G , and f R , respectively. In one example, the light ray (1001) is white, and the three different wavelengths λ B , λ G , and λ R correspond to blue, green, and red.

[0165] FIG. 10B A second type of chromatic aberration is shown, in which the focal length of a PB phase lens (244) as a DOE can decrease with wavelength. An optical axis of the PB phase lens (244) can be perpendicular to the PB phase lens (244) and pass through the center of the PB phase lens (244). In one example, the optical axis of the PB phase lens (244) is the optical axis (1010). When a light ray (1002) that is normally incident on the PB phase lens (244) includes polychromatic wavelengths such as in the visible wavelengths (e.g., 380 to 780 nm), the output light rays corresponding to the polychromatic wavelengths can intersect the optical axis (1010) at different points. The output light rays include light rays (1031)-(1033) corresponding to three different wavelengths λ FIG. 10A described in λ B , λ G , and λ R , respectively, where the light rays (1031)-(1033) intersect the optical axis (1010) at three different points PB, P G , and P RIt intersects the optical axis (1010) at this point. For the sake of simplicity, FIG. 10B Only light rays (1031)-(1033) are shown. Three distinct points PB, P... G and P R These can correspond to three different focal lengths f. B f G and f R .

[0166] FIG. 10C Exemplary color difference compensation according to embodiments of this disclosure is illustrated. For example... FIG. 2 As shown, the PB phase lens (244) can be used in conjunction with one or more LC lenses (241). The optical system (1040) may include one or more LC lenses (241) and the PB phase lens (244). When the light rays (1003) incident on the optical system (1040) include polychromatic wavelengths such as visible wavelengths (e.g., 380 to 780 nm), the output light rays corresponding to the polychromatic wavelengths may intersect the optical axis (1010) at different points. The output light rays include those corresponding to... FIG. 10A The three different wavelengths λ described in B , λ G , and λ R The light rays (1041)-(1043) intersect the optical axis (1010) at three different points P1, P2 and P3. For simplicity, FIG. 10C Only light rays (1041)-(1043) are shown. The three distinct points P1, P2, and P3 can each correspond to three different focal lengths f. B f G and f R .Will FIG. 10C and FIG. 10A-10B Comparison, FIG. 10C The chromatic aberration compensation (or correction) of the PB phase lens (244) in the image can reduce the diffusion of points P1, P2, and P3 along the optical axis (1010), thereby reducing (f B -f R The absolute difference of the chromatic aberration of the PB phase lens (244) is less than that of the chromatic aberration of the optical system (1040) when the chromatic aberration of the PB phase lens (244) does not cancel out the chromatic aberration of one or more LC lenses (241).

[0167] FIG. 10D An exemplary elimination of chromatic aberration according to an embodiment of the present disclosure is shown. In addition to the chromatic aberration of one or more LC lenses (241) being canceled (e.g., fully compensated) by the chromatic aberration of the PB phase lens (244), FIG. 10C-10Dis similar. For example, achromatic performance can occur when one or more LC lenses (241) and PB phase lenses (244) have comparable power in a vision correction system. Output light rays (including (1041)-(1043)) can become a single light ray, such as light ray (1041). Light ray (1041) can intersect optical axis (1010) at a single point P B , corresponding to three different wavelengths λ G , λ R , and λ RGB . Point P RGB may correspond to a single focal length f RGB .

[0168] Chromatic aberration can depend on the focal length of a lens (e.g., the absolute value of the focal length). In one example, as the absolute value of the focal length decreases, the lens is more divergent or more convergent, and the chromatic aberration increases. In one example, the absolute value of the focal length of a PB phase lens (244) is fixed in the case where the optical power of the PB phase lens (244) is +3D or -3D, so the chromatic aberration of the PB phase lens (244) can be fixed. The focal length of one or more LC lenses (241) can vary, e.g., have a first optical power of 0, + / - 1D, + / - 2D, or + / - 3D, and the chromatic aberration of the one or more LC lenses (241) can vary with the first optical power. Referring to FIG. 10D , when the first optical power of the one or more LC lenses (241) is at a first value (e.g., 3D), the chromatic aberration of the one or more LC lenses (241) is canceled out (e.g., completely compensated for) by the PB phase lens (244). Thus, referring to FIG. 10C , when the first optical power of the one or more LC lenses (241) is at a value different from the first value (e.g., 3D), the chromatic aberration of the one or more LC lenses (241) is not canceled out (e.g., not completely compensated for) by the PB phase lens (244), but is reduced.

[0169] As described above, one or more cylindrical LC lenses (242) can have a third chromatic aberration. FIG. 10A-10D The third chromatic aberration of the one or more cylindrical LC lenses (242) can be appropriately adapted to.

[0170] FIG. 11 A flowchart showing an overview of a process (e.g., a vision correction process) (1100) in accordance with some embodiments of the present disclosure is shown. In one example, a display system, such as display system (100) or (100D), includes a vision correction optical system, such as an LC vision correction optical system (240), and a viewing optical system, such as viewing optical system (130) or (130D), such as described above. For example, FIG. 1A-1DAs described in the background, the viewing optical system can be configured to direct a light beam from a display device or a real object to an eye of a user of the display system.

[0171] In various examples, multiple users can use the display system. In one example, a user with changing eye prescription information can use the display system. Accordingly, the display system will adapt to different eye conditions corresponding to different eye prescription information. In one embodiment, prior to a user using the display system, a vision correction procedure (1100) can be implemented to tune (e.g., electronically and optionally via control of polarization) a vision correction optical system based at least on an eye condition of the user. The vision correction procedure (1100) can correct myopia / hyperopia, astigmatism, chromatic aberration, additional aberration, etc. The vision correction optical system can be configured to correct myopia or hyperopia, astigmatism, chromatic aberration, etc. The vision correction optical system can include a stack of LC lenses (e.g., (241)) and a PB phase lens (e.g., (244)). In one example, the vision correction procedure is performed by processing circuitry, such as processing circuitry in a controller (180). The procedure (1100) starts from step (SI lOl), proceeds to step (SI l lO).

[0172] In step (SI l lO), vision correction information (or eye prescription information) to be used by the vision correction optical system can be obtained. As described above, the vision correction information can include information indicated by one or more of a parameter sphere (SPH), a parameter cylinder (CYL), and a parameter axis. The parameter sphere (SPH) can indicate myopia or hyperopia. The parameter cylinder (CYL) and the parameter axis can indicate astigmatism. The vision correction information can be eye prescription information of a user.

[0173] In step (SI 120), a respective optical power of each LC lens in the stack of LC lenses and an optical power of the PB phase lens can be determined, e.g., based on a lookup table such as shown in FIG. 9 For example, if the parameter sphere (SPH) indicates -2D of myopia. The stack of LC lenses has an optical power of +1D, and the PB phase lens has an optical power of -3D. If the stack of LC lenses includes 3 LC lenses, then any suitable optical power can be assigned to the 3 LC lenses if the sum of the optical powers of the 3 LC lenses is +1D. In one example, each LC lens has an optical power of +1 / 3D.

[0174] In step (SI 130), the respective voltages of the stack of LC lenses and the polarization state of light incident on the PB phase lens can be determined. Such as described in FIG. 8B As described in the background, the polarization state of light incident on the PB phase lens can be determined based on the optical power of the PB phase lens. Referring to FIG. 3-4Since the optical power of the PB phase lens is negative, the polarization state of the light incident on the PB phase lens is determined to be RCP. As described in FIG. 2 The respective voltages for the stack of LC lenses can be determined based on the respective optical powers of the plurality of LC lenses.

[0175] At step (S1140), the determined respective voltages can be applied to the stack of LC lenses, and the polarization state of the light incident on the PB phase lens can be manipulated, e.g., to correct myopia or hyperopia. In one example, the polarization state of the light incident on the PB phase lens can be manipulated by electrically controlling an SLM, such as an LC SLM (243) as described in FIG. 1C

[0176] Then, the process (1100) proceeds to step (S1199) and ends.

[0177] The process (1100) can be adapted to various scenarios, and the steps in the process (1100) can be adjusted accordingly. One or more steps in the process (1100) can be adjusted, omitted, repeated, and / or combined. The process (1100) can be implemented using any suitable order. Additional steps can be added.

[0178] In one embodiment, the above-described vision correction process can be performed iteratively. For example, after performing step (S1140), if the user cannot clearly see the real object or the content displayed by the display device, the process (1100) can return to step (S1110), and the vision correction information can be adjusted to obtain updated vision correction information. Steps (S1120), (S1130), and (S1140) can be implemented. Thus, the process (1100) can be implemented iteratively, e.g., until certain criteria are met. The certain criteria can include (i) the user can clearly see the real object or the content displayed by the display device, (ii) the number of iterations reaches a threshold, etc. In one example, at least one of the respective voltages applied to the stack of LC lenses can be adjusted incrementally.

[0179] At step (S1110), the vision correction information can include default values (or initialization values) of the parameters, e.g., if no specific vision correction information is available for the user.

[0180] In one example, astigmatism is corrected by determining a respective optical power (e.g., along a single dimension associated with a respective cylindrical lens) and a respective axis of each cylindrical LC lens in a stack of cylindrical LC lenses. Respective voltages for the stack of cylindrical LC lenses are determined based on the optical power and the axis of the respective cylindrical LC lenses. The determined respective voltages are applied to the stack of the plurality of cylindrical LC lenses to correct the astigmatism. ​

[0181] In one example, when the stack of cylindrical LC lenses is used in a vision correction optical system, steps (S1120), (S1130), and (S1140) can be modified because the stack of cylindrical LC lenses can affect the optical power (radially along multiple dimensions) of the vision correction optical system. For example, if the parameter sphere (SPH) indicates -2D of myopia, the optical power of the PB phase lens is -3D, and the stack of cylindrical LC lenses that corrects astigmatism has an optical power (radially along multiple dimensions) of +0.5D. The optical power of the stack of LC lenses can be determined to be +0.5D.

[0182] The display system (100) can include other suitable mechanical, electrical, and optical components. For example, referring to FIG. 12 The display system (100) includes a frame (101) or housing that can protect other components of the display system (100). In another example, the display system (100) can include a strap (not shown) to fit the display system (100) on a user’s head. In another example, the display system (100) can include a communication component (not shown, e.g., communication software and hardware) to wirelessly communicate with a network, a host device, and / or other devices. In some examples, the display system (100) can include a light combiner that can combine virtual content and see-through real environment.

[0183] Embodiments in the present disclosure can be used individually or in any order in combination.

[0184] A computer or computer-readable medium can control various aspects of an HMD system of the display system (100) including the optical system (110). Various aspects of the display system (100), including implementing a vision correction process and / or controlling vision correction via the electrically tunable controller (281), can be implemented as computer software and physically stored in one or more computer-readable media using computer-readable instructions. For example, FIG. 12 A computer system (1200) suitable for implementing certain embodiments of the disclosed subject matter is shown.

[0185] Computer software can be coded using any suitable machine code or computer language that can be subject to assembly, compilation, linking, or similar

[0186] Instructions can 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.

[0187] ​ The components shown for the computer system 1200 are exemplary and are not intended to suggest any limitation as to the scope of use or functionality of the computer software implementing embodiments of the present application. Neither should the configuration of components be interpreted as having any dependency or requirement relating to any one or combination of components illustrated in the exemplary embodiment of a computer system 1200.

[0188] The computer system 1200 can include certain human interface input devices. Such a human interface input device can be responsive to user input data being in the form of physical motion, physical interaction with software, audio signals, and / or haptic signals through, for example, tactile, audio, and / or olfactory feedback. User input data can be captured and interpreted by the computer system 1200 through, for example, a keyboard 1201, a mouse 1202, a touchpad 1203, a

[0189] Input human interface devices can include one or more of: a keyboard 1201, a mouse 1202, a

[0190] The computer system 1200 can also, or instead, include certain human interface output devices. Such human interface output devices can be stimulating one or more of the human senses to convey information to one or more people. Examples of such human interface output devices can include tactile output devices (for example, tactile feedback by the touch screen 1210, or data glove, or tactile feedback by the joystick 1205, but there can also be tactile feedback devices that are not input devices), audio output devices (for example, speakers 1209, headphones (not depicted)), visual output devices (for example, the touch screen 1210 including a visual display, one or more projection devices (not depicted), one or more light-emitting panels, one or more retinal display devices, one or more virtual retinal display devices, one or more holographic displays, and one or more printers (not depicted) to convey information to one or more people), and one or more olfactory output devices (not depicted).

[0191] The computer system 1200 can also include human accessible storage such as optical, electrical or magnetic storage (e.g. a flash drive, CD-ROM, etc. 1220) and their associated media interfaces (e.g. CD-ROM drive 1221). It is considered a braod aspect of the disclosure that computer- readable storage medium 1220, or any components thereof, can include a computer- readable storage medium. As indicated previously, these human accessible storage and media interfaces 1220, 1221 can provide storage or playback of information such as computer- readable and computer-executable instructions, data, and / or data structures used or produced by computer system 1200.

[0192] Those skilled in the art will further appreciate that the term "computer-readable medium" is used herein in a broad sense, encompassing both computer storage media and communication media.

[0193] The computer system 1200 can also include an interface 1254 to one or more communication networks 1255. The network(s) can be wireless, wireline, optical, etc. The network(s) can further be a local, wide-area, metropolitan, vehicular and industrial, real-time, delay-tolerant, etc. network. Examples of networks include local area networks such as Ethernet, wireless LANs, cellular networks to include GSM, 3G, 4G, 5G, LTE, etc., TV wireline or wireless wide area digital networks to include cable TV, satellite TV, and terrestrial broadcast TV, vehicular and industrial to include CANBus, etc. Certain networks commonly require external network interface adapters that attached to certain general purpose data ports or peripheral buses (1249) (e.g. universal serial bus (USB) ports of the computer system 1200); others are commonly integrated into computer systems by connection to system bus (e.g. Ethernet interface into a PC computer system or cellular network interface into a smartphone computer system). The computer system 1200 can be communicatively coupled to other

[0194] The above human interface devices, human-accessible storage devices, and network interfaces can be attached to the computer system 1200 via the peripheral bus 1249, a universal serial bus (USB) port, a wireless data port, etc.

[0195] The core 1240 can include one or more Central Processing Units (CPU) 1241, Graphics Processing Units (GPU) 1242, specialized programmable processing units in the form of Field Programmable Gate Areas (FPGA) 1243, hardware accelerators 1244 for certain tasks, graphics adapters 1250, and so forth. These devices, along with Read-only memory (ROM) 1245, Random-access memory (RAM) 1246, internal mass storage such as internal non-user accessible hard drives, SSDs, and the like, can be connected through a system bus 1248. In some computer systems, the system bus 1248 can appear as a physical plugin connector, allowing for additional CPUs, graphics adapters, and the like to be

[0196] The CPUs 1241, GPUs 1242, FPGAs 1243, and accelerators 1244 can execute certain instructions that can be combined to form the computer code described above. That computer code can be stored in ROM 1245 or RAM 1246. Transitional data can be also stored in RAM 1246, whereas permanent data can be stored for example, in the internal mass storage 1247. Fast storage and retrieval speeds of any stored data can be enabled through the use of cache memory, which can be closely associated with one or more CPU 1241, GPU 1242, mass storage 1247, ROM 1245, RAM 1246, and the like.

[0197] The computer software can be implemented as computer code that comprises one or more instructions that are stored in a computer readable medium at least partially during execution. The computer software can be implemented as one or more separate programs or components or, alternatively, the computer software can be implemented as aggregates of several programs or components.

[0198] As non-limiting examples, the computer system 1200, with architecture, specifically the core 1240, can provide functionality as a result of processor(s) (including CPUs, GPUs, FPGA, accelerators, and the like) executing software embodied in one or more tangible, computer-readable media. Such computer-readable media can be media associated with user-accessible mass storage as introduced above, as well as certain high-speed caches (e.g., that are typically internal to the core 1240 and / or accessible only on a high-speed bus) storing software. Software can include code running on the core 1240 (e.g., neural network code), as well as data on which the code runs. Additionally or alternatively, the computer system 1200 can provide functionality as a result of logic hardwired into the core 1240 or accelerated by the core 1240, as opposed to being implemented in software. As noted above, this implementation is not intended to limit the scope of the present disclosure, but is merely one exemplary implementation. Thus, the systems and methods described herein include software, firmware, hardware, or any suitable combination thereof.

[0199] While several exemplary embodiments have been described and illustrated, it is recognized that modifications, substitutions, and various other equivalents and alternatives exist that fall within the scope of this disclosure. Accordingly, it is to be understood that the systems and methods described herein can be designed to perform a variety of alternative and equivalent functions to those described herein, and that the claims are not limited to the embodiments set forth herein.

Claims

1. An optical system comprising: one or more liquid crystal (LC) lenses as refractive optical elements, the one or more LC lenses having a first chromatic aberration, and a Pancharatnam-Berry (PB) phase lens as a diffractive optical element, the PB phase lens having a second chromatic aberration complementary to the first chromatic aberration, wherein a chromatic aberration of the optical system is less than the first chromatic aberration.

2. The optical system of claim 1, wherein: a first optical power of the one or more LC lenses is electrically tunable, an optical power of the optical system is based at least on a sum of the first optical power of the one or more LC lenses and a second optical power of the PB phase lens, and the first optical power, the second optical power, and the optical power of the optical system correspond to respective focal lengths of the one or more LC lenses, the PB phase lens, and the optical system.

3. The optical system of claim 2, wherein: the one or more LC lenses comprise a plurality of LC lenses, each LC lens is electrically tunable, and the first optical power is a sum of respective optical powers of the plurality of LC lenses.

4. The optical system of claim 3, wherein, a number of the plurality of LC lenses is three.

5. The optical system of claim 2, wherein: one of the one or more LC lenses comprises a plurality of transparent ring electrodes disposed on a first substrate and a transparent electrode disposed on a second substrate, the first substrate and the second substrate being parallel to a plane, and a refractive index of the one of the one or more LC lenses varies with a radial distance from a center of the plurality of transparent ring electrodes on the first substrate, the refractive index being controlled by respective voltages of the plurality of transparent ring electrodes, the refractive index and the first optical power being circularly symmetric in the plane.

6. The optical system of claim 2, wherein: the PB phase lens comprises a central grating and a plurality of annular gratings formed by a liquid crystal material on a substrate, each annular grating of the plurality of annular gratings surrounds the central grating, the PB phase lens is configured to generate an output beam from an input beam normally incident onto the substrate, a central diffracted portion of the output beam has a first diffraction angle θ1, the central diffracted portion corresponding to a central portion of the input beam incident onto the central grating, and a plurality of peripheral diffracted portions of the output beam have a plurality of diffraction angles varying from the first diffraction angle θ1 to a second diffraction angle θ2, the second diffraction angle θ2 corresponding to an outermost annular grating of the plurality of annular gratings, the plurality of peripheral diffracted portions respectively corresponding to a plurality of peripheral portions of the input beam incident onto the plurality of annular gratings, the second diffraction angle θ2 being greater than the first diffraction angle θ1.

7. The optical system of claim 6, wherein: the PB phase lens acts as a converging lens based on a first polarization state of the input beam; and the PB phase lens acts as a diverging lens based on a second polarization state of the input beam.

8. The optical system of claim 7, wherein: the input beam is left-handed circularly polarized, the output beam is right-handed circularly polarized, and the PB phase lens functions as the converging lens with the second optical power being positive.

9. The optical system of claim 7, wherein: the input beam is right-handed circularly polarized, the output beam is left-handed circularly polarized, and the PB phase lens functions as the diverging lens with the second optical power being negative.

10. The optical system of claim 7, wherein: the optical system comprises one or more cylindrical LC lenses configured to correct astigmatism of a user’s eye using the optical system, for each of the one or more cylindrical LC lenses, the respective cylindrical LC lens comprises a plurality of transparent electrodes disposed on a first substrate and a transparent electrode disposed on a second substrate, the first and second substrates being parallel to an XZ plane comprising mutually perpendicular X and Z axes, the plurality of transparent electrodes being parallel, and an electrically tunable refractive index varies along a respective first dimension in the XZ plane.

11. The optical system of claim 10, wherein: the one or more cylindrical LC lenses comprise a first, a second, and a third cylindrical LC lens, the first, second, and third cylindrical LC lenses having their first dimensions forming 0, 45°, and 90°, respectively, with the X axis.

12. The optical system of claim 10, further comprising: an LC spatial light modulator (SLM) configured to manipulate a polarization state of an input beam to the LC SLM by changing a voltage input to the LC SLM, the LC SLM’s output beam being the input beam to the PB phase lens, the LC SLM being electrically tunable.

13. The optical system of claim 12, wherein: the one or more LC lenses comprise a stack of electrically tunable LC lenses, the one or more cylindrical LC lenses comprise a stack of cylindrical LC lenses having their first dimensions forming different angles with the X axis, respectively, the stack of cylindrical LC lenses being electrically tunable, the electrically tunable lens system comprises the stack of LC lenses and the stack of cylindrical LC lenses, and the LC SLM is disposed between the electrically tunable lens system and the PB phase lens.

14. The optical system of claim 13, wherein: an input beam incident on the electrically tunable lens system is linearly polarized, an output beam from the electrically tunable lens system incident on the LC SLM is linearly polarized, in response to the LC SLM’s voltage being a first voltage, the LC SLM is configured to convert the linearly polarized input beam to the LC SLM into a left-handed circularly polarized output beam emitted by the LC SLM, and in response to the LC SLM’s voltage being a second voltage different from the first voltage, the LC SLM is configured to convert the linearly polarized input beam to the LC SLM into a right-handed circularly polarized output beam emitted by the LC SLM. the PB phase lens is configured to convert a left-handed circularly polarized input beam to the PB phase lens into a right-handed circularly polarized output beam emitted by the PB phase lens, in response to the voltage of the LC SLM being a second voltage, the LC SLM is configured to convert the linearly polarized input beam to the LC SLM into a right-handed circularly polarized output beam emitted by the LC SLM, and the PB phase lens is configured to convert a right-handed circularly polarized input beam to the PB phase lens into a left-handed circularly polarized output beam emitted by the PB phase lens.

15. A head-mounted display (HMD) system comprising: a display device, an array of pixels in the display device configured to generate beams of light; and an optical system comprising: one or more liquid crystal (LC) lenses as refractive optical elements, the one or more LC lenses having a first chromatic aberration, and a Pancharatnam-Berry (PB) phase lens as a diffractive optical element, the PB phase lens having a second chromatic aberration complementary to the first chromatic aberration, wherein a chromatic aberration of the optical system is less than the first chromatic aberration.

16. The HMD system of claim 15, further comprising: a virtual reality (VR) viewing optical system disposed between the display device and the optical system.

17. The HMD system of claim 16, wherein, the one or more LC lenses comprise a stack of electrically tunable LC lenses, and the optical system comprises: a stack of cylindrical LC lenses having first dimensions at different angles to an X-axis, respectively, the stack of cylindrical LC lenses being electrically tunable, an electrically tunable lens system comprising the stack of LC lenses and the stack of cylindrical LC lenses, and an LC spatial light modulator (SLM) disposed between the electrically tunable lens system and the PB phase lens.

18. The HMD system of claim 15, further comprising: an augmented reality (AR) viewing optical system disposed between the display device and the optical system, the AR viewing optical system directing beams of light from the display device and beams of light from real objects to the optical system.

19. A method of tuning an optical system comprising: obtaining vision correction information for at least one of myopia or hyperopia; determining respective optical powers of each liquid crystal (LC) lens in a stack of LC lenses and an optical power of a Pancharatnam-Berry (PB) phase lens based on the vision correction information; determining respective voltages to be applied to the stack of LC lenses based on the respective optical powers of the LC lenses; determining a polarization state of light incident on the PB phase lens based on the optical power of the PB phase lens; and applying the determined respective voltages to the stack of LC lenses and controlling the polarization state of light incident on the PB phase lens to correct for the at least one of myopia or hyperopia.

20. The method of tuning an optical system of claim 19, further comprising: ​ incrementally adjusting at least one of the individual voltages applied to the stack of the LC lens.

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