Foveated Optical Lens for Near-Eye Displays

Abstract

The optical system includes an optical system axis, a display, and at least one lens, and forms a virtual image of an image emitted by the display for viewing by the eye, the eye having an optical eye axis, and a first retinal image of the virtual image at a first virtual image location and an associated first viewing angle between about 5 degrees and about 30 degrees has a first image resolution when the eye axis is substantially aligned with the system axis, and has a second image resolution when the eye is rotated such that the eye axis is substantially aligned with a first viewing axis extending between the eye and the virtual image at the first viewing angle, the second image resolution being greater than the first image resolution.

Description

Summary of the Invention

[0001] In some aspects herein, an optical system is provided that includes an optical system axis, a display, and at least one lens. The optical system forms a virtual image of an image emitted by the display for viewing by the eye. The eye has an optical axis, and a first retinal image of the virtual image at a first virtual image location and an associated first viewing angle between about 5 degrees and about 30 degrees has a first image resolution when the optical axis is substantially aligned with the system axis, and has a second image resolution when the eye is rotated such that the optical axis is substantially aligned with a first viewing axis extending between the eye and the virtual image at the first viewing angle. The second image resolution is greater than the first image resolution.

[0002] Some aspects of the present disclosure provide an optical system including an optical system axis, a lens assembly having at least one lens, an eye side configured to be positioned proximate to an observer's eye, and a display side configured to be positioned proximate to a display. The optical system is configured to display a virtual image of an image emitted by the display to the observer's eye. When substantially collimated light propagating along a first direction that forms a first angle of about 5 degrees to about 30 degrees with respect to the system axis illuminates the optical system from the eye side of the optical system, passes through and substantially fills a field stop positioned proximate to the eye side of the optical system, enters the optical system, and focuses to a focal spot after passing through the lens assembly and exiting the optical system from the display side of the optical system, the focal spot has a first minimum size when the field stop is substantially centered on the system axis, and has a second minimum size when the field stop is rotated about a first center proximate to the center of the observer's eye such that the field stop is substantially perpendicular to the first direction, the second minimum size being smaller than the first minimum size.

[0003] In some aspects herein, an optical system is provided that includes an optical system axis, a display, and at least one lens. The optical system forms a virtual image of an image emitted by the display for viewing by the eye when the eye is positioned proximate an eye position on the eye side of the optical system. For each first virtual image position at a first viewing angle of about 5 degrees to about 30 degrees relative to the system axis, an imaging system (e.g., a camera having an objective lens) centered on the imaging system axis is positioned proximate the eye position and forms an image of the virtual image corresponding to the first virtual image position, and the resolution of the formed image increases at least as the imaging system is rotated such that the imaging system axis approaches the first viewing angle.

[0004] In some aspects herein, an optical system is provided that includes an optical system axis, a display, at least one lens, a partial reflector, and a reflective polarizer. The optical system forms a virtual image of an image emitted by the display for viewing by an eye. The eye has an optical axis extending from a center of the fovea of ​​the eye to a center of the pupil of the eye. A first retinal image of the virtual image at a first virtual image location and an associated first viewing angle between about 5 degrees and about 30 degrees has a first image resolution when the optical axis is substantially aligned with the system axis, and has a second image resolution when the eye is rotated such that the optical axis is substantially aligned with the first viewing axis. The first viewing axis extends between the eye and the virtual image at the first viewing angle. The second image resolution is greater than the first image resolution. [Brief description of the drawings]

[0005] [Figure 1] FIG. 1 is a side view of an optical system including a foveated optical lens, according to an embodiment of the present disclosure. [Figure 2A] 1 provides a visual depiction of an optical axis of an optical system according to an embodiment of the present disclosure. [Figure 2B] 1 provides a visual depiction of an optical axis of an optical system according to an embodiment of the present disclosure. [Diagram 3] 1 provides a side view of a foveated optical lens according to one embodiment of the present disclosure. [Figure 4] 4 provides an alternative view of the foveal optical lens of FIG. 3 according to an embodiment herein. [Figure 5A] 1 provides a side view of an optical system including an imaging system according to an embodiment of the present disclosure. [Figure 5B] 1 provides a side view of an optical system including an imaging system according to an embodiment of the present disclosure. [Figure 6A] 1 provides details regarding an optical system including a lens with a defined surface curve, according to an embodiment of the present disclosure. [Figure 6B] 1 provides details regarding an optical system including a lens with a defined surface curve, according to an embodiment of the present disclosure. [Figure 7A] Additional definitions of the lens surfaces of Figures 6A and 6B are provided according to an embodiment of the present disclosure. [Figure 7B] Additional definitions of the lens surfaces of Figures 6A and 6B are provided according to an embodiment of the present disclosure. [Figure 8A] Additional definitions of the lens surfaces of Figures 6A and 6B are provided according to an embodiment of the present disclosure. [Figure 8B] Additional definitions of the lens surfaces of Figures 6A and 6B are provided according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0006] In the following description, reference is made to the accompanying drawings, which form a part hereof, and in which various embodiments are shown by way of illustration. The drawings are not necessarily to scale. It is to be understood that other embodiments are contemplated and may be made without departing from the scope or spirit of the present disclosure. Accordingly, the following detailed description is not to be taken in a limiting sense.

[0007] Near-eye displays (e.g., head-mounted displays, wearable displays, virtual reality headsets) are used to generate virtual images within the field of view of one or both eyes. Near-eye displays generate virtual images such that the images appear at a distance (e.g., displayed in front of the user) and appear larger than the actual images generated by a corresponding miniature display that generates the virtual images. Key performance metrics for optical lenses used in near-eye displays include visual resolution, pupil swim (image distortion as the eye moves around the lens), image contrast, and ghosting (undesirable images caused by reflections from the lens's surface). While lenses in glasses can be designed to provide the best optical properties for a selected viewing angle and distance (e.g., focusing on a computer display at arms length), the same method may not work as well for head-mounted virtual reality (VR) headsets. This is because VR systems require a wide field of view (e.g., greater than 85 degrees), and eye rotation across that wide field of view can cause image problems. For example, as the eye's pupil moves across a wider field of view, images may lose sharpness or resolution when the gaze moves away from the main optical axis (eg, gazing up and to the left).

[0008] According to some aspects of the present disclosure, the optical system is configured to provide optimal visual characteristics over a wide field of view. This may be done, for example, by designing lenses or lens assemblies within the optical system, where the lens components and surfaces are configured to provide equal or increased retinal image resolution when the user's eye is rotated at an angle with the optical system axis (e.g., at an upward angle of about 5 degrees to about 30 degrees with the optical system axis) compared to the retinal image resolution when the eye is substantially aligned with the optical system axis. In some embodiments, the optical system includes an optical system axis, a display, and at least one lens. In some embodiments, the optical system may form a virtual image of the image emitted by the display for viewing by the eye. In some embodiments, the eye may have an optical ocular axis, and a first retinal image of the virtual image at a first virtual image location and an associated first viewing angle between about 5 degrees and about 30 degrees may have a first image resolution when the ocular axis is substantially aligned with a system axis, and may have a second image resolution when the eye is rotated such that the ocular axis is substantially aligned with a first viewing axis extending between the eye and the virtual image at the first viewing angle. In some embodiments, the second image resolution is greater than the first image resolution. In some embodiments, the second image resolution may be greater than the first image resolution for all first viewing angles between about 5 degrees and about 30 degrees.

[0009] In some embodiments, the optical system may further include one or more of a partial reflector (e.g., a 50 / 50 beam splitter layer or coating), a reflective polarizer, and an optical retarder (e.g., a quarter wave plate). In some embodiments, the optical system axis may be a folded optical axis. In some embodiments, the optical system axis may be folded such that a first segment of the optical system axis substantially coincides with a different second segment of the optical system axis. For example, in some embodiments, the at least one lens may be a lens assembly with at least a first display side lens component and a second eye side lens component. The partial reflector may be disposed on a side of the display side lens component closest to the display. The optical retarder may be disposed between the display side lens component and the eye side lens component. The reflective polarizer may be disposed on a side of the eye side lens component closer to the viewer's eye. In such an embodiment, the optical axis may pass from the display through the partial reflector and the optical retarder, be reflected to the reflective polarizer, back through the optical retarder, then be reflected to the partial reflector, back through the optical retarder and the reflective polarizer (since the polarization state has now changed after three passes through the optical retarder), and finally leave the eye-side lens component through the reflective polarizer towards the observer's eye.

[0010] For purposes of this specification, the terms "optical system axis", "system axis", and "optical axis" are synonymous and shall be defined to mean an imaginary line that defines the path that light propagates through an optical system, the light path exhibiting some degree of rotational symmetry around it. In some embodiments, the optical system axis may be folded (i.e., light may pass through, be reflected by, refracted by, or otherwise affected by one or more optical components (e.g., lenses, optical films, optical retarders, etc.) such that the light path is not strictly linear but is folded). However, even in systems with folded optical axes, as used herein, these terms shall be defined to be an imaginary line along which rotational symmetry exists in the optical system.

[0011] In some embodiments, the at least one lens may include a first optical lens with oppositely facing first and second major surfaces and a second optical lens with oppositely facing third and fourth major surfaces. In some embodiments, the second and third major surfaces may face each other. In some embodiments, the first through fourth major surfaces may have sags S1 through S4, respectively, each defined by the following formula:

number

[0012] According to some aspects herein, an optical system may include an optical system axis, a lens assembly having at least one lens, an eye side configured to be positioned proximate to an eye of an observer, and a display side configured to be positioned proximate to a display (e.g., a light emitting diode display, a liquid crystal display, an organic LED display, etc.). In some embodiments, the optical system may be configured to form a virtual image of an image emitted by the display to be viewed by the observer (e.g., the virtual image is viewed when a user is wearing a VR headset). In some embodiments, when substantially collimated light propagating along a first direction that forms a first angle of about 5 degrees to about 30 degrees with respect to the system axis illuminates the optical system from the eye side of the optical system, enters the optical system through and substantially fills a field stop positioned proximate to the eye side of the optical system, and focuses to a focal spot after passing through the lens assembly and exiting the optical system from the display side of the optical system, the focal spot may have a first minimum size when the field stop is substantially centered on the system axis. The focal spot may have a second minimum size when the field stop is rotated about a first center proximate to the center of the observer's eye such that the field stop is substantially perpendicular to the first direction. In some embodiments, the second minimum size is smaller than the first minimum size. In some embodiments, the field stop may have a size of about 1 millimeter (mm) to about 10 mm, about 2 mm to about 9 mm, about 2 mm to about 8 mm, about 2 mm to about 7 mm, or about 3 mm to about 7 mm. In some embodiments, the optical system may further include one or more of a partial reflector, a reflective polarizer, and an optical retarder.

[0013] According to some aspects of the present specification, the optical system may include an optical system axis, a display, and at least one lens. In some embodiments, the at least one lens may include a first lens that is a Fresnel lens having a structured primary surface. In some embodiments, the optical system may further include a partial reflector, a reflective polarizer, and an optical retarder. In some embodiments, the optical system may form a virtual image of an image emitted by the display for viewing by the eye when the eye is placed proximate an eye position on the eye side of the optical system (e.g., placed proximate a near-eye display in a VR headset). In some embodiments, for each first virtual image position at a first viewing angle of about 5 degrees to about 30 degrees relative to the system axis, when an imaging system centered on the imaging system axis is placed proximate the eye position and forms an image of the virtual image corresponding to the first virtual image position, the resolution of the formed image may increase at least as the imaging system is rotated such that the imaging system axis approaches the first viewing angle.

[0014] According to some aspects herein, the optical system may include an optical system axis, a display, at least one lens, a partial reflector, and a reflective polarizer. In some embodiments, the optical system may be configured to form a virtual image of the image emitted by the display to be viewed by an observer (e.g., the virtual image is viewed when a user is wearing a virtual reality headset). In some embodiments, the eye may have an optical axis that extends from the center of the fovea of ​​the eye to the center of the pupil of the eye. The fovea or fovea centralis is a small depression at the posterior surface of the eye composed of closely packed cones and is responsible for sharp central vision (i.e., foveal vision). Foveal vision provides the highest resolution in the eye (e.g., important for perceiving high visual detail). In some embodiments, a first retinal image of the virtual image at a first virtual image location and an associated first viewing angle between about 5 degrees and about 30 degrees may have a first image resolution when the eye axis is substantially aligned with a system axis and a second image resolution when the eye is rotated such that the eye axis is substantially aligned with the first viewing axis. In some embodiments, the first viewing axis may extend between the eye and the virtual image at the first viewing angle. In some embodiments, the second image resolution may be greater than the first image resolution.

[0015] In some embodiments, the optical system may further include one or more of a partial reflector, a reflective polarizer, and an optical retarder. In some embodiments, the optical system axis may be folded. For example, in some embodiments, the optical system axis may be folded such that a first segment of the system axis substantially coincides with a different second segment of the system axis. In some embodiments, the presence of one or more optical layers (e.g., a partial reflector, a reflective polarizer, an optical retarder, etc.) may assist in creating the folded optical system axis.

[0016] Referring to the drawings, FIG. 1 is a side view of an optical system including a foveated optical lens according to the present disclosure. In some embodiments, the optical system 300 includes a display 20, an optical system axis 10, and at least one lens (e.g., lens 30 / 40, etc.). In some embodiments, the lenses 30 and 40 may be separate lens components within a lens assembly. In some embodiments, the optical system may further include one or more of a partial reflector 50 (e.g., a 50 / 50 beam splitter coating or film), a reflective polarizer 60, and an optical retarder 90 (e.g., a quarter wave plate).

[0017] In some embodiments, the optical system 300 forms a virtual image 70 of the image 41 emitted by the display 20. The virtual image 70 is viewable by an observer's eye 80 as a first retinal image 82 on the retina of the eye 80. The eye 80 may have an optical axis 81. The eye 80 may be rotated such that the optical axis 81 of the eye 80 is substantially aligned with the optical system axis 10, or the eye 80 may be rotated such that the optical axis 81 is not aligned with the optical system axis 10 (e.g., the eye 80 may be rotated upward by an angle α1, as shown in FIG. 1, such that the observer sees a higher position on the virtual image 70).

[0018] The optical system 300 may have an eye side 301 that faces substantially toward the eye 80 and a display side 302 that faces away from the eye 80 and toward the display 20. The optical system 300 may be configured to optimally present the virtual image 70 to the eye 80 when the eye 80 is positioned proximate to the eye position 84. In some embodiments, the resolution of the retinal image 82 formed on the retina of the eye 80 when the optical axis 81 is rotated by an angle α1 may be greater than the resolution of the retinal image 82 when the optical axis 81 is substantially aligned with the optical system axis 10. In some embodiments, the angle α1 may be between about 5 degrees and about 30 degrees.

[0019] 2A and 2B provide a visual depiction of the optical axis of the optical system of FIG. 1 and provide further details. For simplicity, at least one lens and display shown in FIG. 1 are omitted in FIG. 2A and 2B, and thus the partial optical system shown is relabeled as 300a. The components shown in FIG. 2A and 2B have common functions and / or purposes with similarly numbered components in other figures herein, unless otherwise specified. FIG. 2A shows an observer's eye 80 located proximate to eye position 84 (i.e., a position where the optical system is configured to provide optical resolution for the entire field of view), with an optical axis 81 extending from the center of the fovea 87 of the eye 80 through the center 83 of the eye 80 to the pupil 88. In operation, a retinal image 82 of the virtual image 70 is formed on the retina 86. In FIG. 2A, the optical eye axis 81 is positioned to be substantially aligned with the optical system axis 10 (i.e., the eye 80 is rotated to look directly along or substantially parallel to the optical system axis 10).

[0020] 2B, eye 80 is rotated upward such that optical eye axis 81 is substantially aligned with first field of view axis 72 extending between eye 80 and first virtual image location 71. In some embodiments, first field of view axis 72 forms a first field of view angle α1 with optical system axis 10. In some embodiments, first field of view angle α1 may be between about 5 degrees and about 30 degrees.

[0021] In some embodiments, the first retinal image 82 has a first image resolution at the first virtual image location 71 when the optical eye axis 81 is substantially aligned with the optical system axis 10, and the first retinal image 82 has a second image resolution at the first virtual image location 71 when the optical eye axis is substantially aligned with the first field of view axis 72. In some embodiments, the second image resolution may be greater than the first image resolution. Stated differently, the first retinal image 82 may have a higher image resolution when the eye 80 is rotated to align with the first field of view axis 72 than when the eye 80 is aligned with the optical system axis 10.

[0022] Figures 3 and 4 provide side views of a foveal optical lens as part of an optical system according to the present specification. Figures 3 and 4 show essentially the same optical system, but with the eye 80 at two different rotation angles. Figures 3 and 4 should be referred to together for the following discussion. Similar numbered components common to both Figures 3 and 4 shall have the same function and description unless otherwise specified herein.

[0023] The optical system 300 includes an optical system axis 10, a lens assembly 130, and a display 20. In some embodiments, the lens assembly 130 has an eye side 301 configured to be positioned proximate an observer's eye 80 and a display side 302 configured to be positioned proximate the display 20. In some embodiments, the lens assembly 130 includes a first lens component 30 positioned closer to the display 20 and a second lens component 40 positioned proximate the first lens component 30 on the opposite side (i.e., the side facing away from the display 20). In some embodiments, the lens assembly 130 may further include a partial reflector 50 positioned on a side of the first lens component 30 closest to the display 20 (e.g., the display side 302), an optical retarder positioned between the first lens component 30 and the second lens component 40, and a reflective polarizer 60 positioned on a side of the second lens component 40 closest to the eye 80 (e.g., the eye side 301). In some embodiments, the optical system 300 is configured to display a virtual image 70 of the image 41 emitted by the display 20 to an eye 80 of an observer.

[0024] In some embodiments, the substantially collimated light 110 propagates along a first direction 111. The first direction 111 forms a first angle θ1 with the optical system axis 10. In some embodiments, the first angle θ1 may be between about 5 degrees and about 30 degrees. When the substantially collimated light 110 illuminates the optical system 300 from the eye side 301, enters the optical system 300, and substantially fills a field stop 120 / 121 located proximate to the eye side 301, the light 110 passes through the lens assembly 130 and is focused to a focal spot 112 after exiting the optical system 300 from the display side 302.

[0025] In some embodiments, when the eye 80 is positioned proximate the eye position 84, the focal spot 112 may have a first minimum size when the field stop 120 / 121 is substantially centered on the optical system axis 10 (at position 120, the eye 80 is rotated as shown in FIG. 3), and the focal spot 112 may have a second minimum size when the field stop 120 / 121 is rotated about a first center 83 proximate the center of the observer's eye 80 such that the field stop 120 / 121 is substantially perpendicular to the first direction 111 (at position 121, the eye 80 is rotated as shown in FIG. 4). In some embodiments, the second minimum size may be smaller than the first minimum size. In some embodiments, the maximum dimension of the field stop 120 / 121 may be based on the nominal size of an adult human pupil. In some embodiments, the maximum dimension of the field stop 120 / 121 may be between about 2 millimeters (mm) and about 8 mm.

[0026] 5A and 5B provide a visual depiction of the optical axis of an optical system such as optical system 300 of FIG. 1, where the observer's eye 80 has been replaced with an imaging system 40 (e.g., a camera having an objective lens capable of focusing on a virtual image) centered on imaging system axis 141. For simplicity, as described elsewhere herein and as done in FIGS. 2A and 2B, the lens (at least one lens) and display shown in FIG. 1 have been omitted, and the partial optical system shown has thus been relabeled 300b. Components shown in FIGS. 5A and 5B have common function and / or purpose with similarly numbered components in other figures herein, unless otherwise specified.

[0027] Optical system 300b includes an optical system axis 10, a display (such as display 20 as shown in FIG. 1), and at least one lens (such as lens components 30 and 40 as shown in FIG. 1). In some embodiments, optical system 300b may form a virtual image 70 for viewing by an eye (such as eye 80 shown in FIG. 1) when the eye is positioned proximate eye position 84. In some embodiments, for each first virtual image position 71 at the first field of view angle α1, when the imaging system 140 is positioned close to the eye position 84 centered on the imaging system axis 141 and forms an image of the virtual image 70 corresponding to the first virtual image position 71, the resolution of the formed virtual image 70 may increase as the imaging system 140 is rotated so that the imaging system axis 141 moves away from being aligned with the optical system axis 10 and approaches the first field of view angle α1 (i.e., as it rotates upwardly to substantially coincide with the first field of view axis 72 extending between the imaging system 140 and the first virtual image position 71 at the first field of view axis α1).

[0028] Figures 6A and 6B provide details of one embodiment of an optical system including a lens with a specifically defined surface curve. Optical system 400 may be any of the optical systems discussed herein, including optical system 300 of Figures 1 and 4, optical system 300a of Figures 2A and 2B, and optical system 300b of Figures 5A and 5B.

[0029] In some embodiments, the optical system 400 may include a first optical lens 40 and a second optical lens 30. In some embodiments, the first optical lens 40 includes a first major surface 41 and an oppositely facing second major surface 42. In some embodiments, the second optical lens 30 includes a third major surface 31 and an oppositely facing fourth major surface 32. In some embodiments, the second major surface 42 and the third major surface 31 of the first optical lens 40 face each other. In some embodiments, the first major surface 41 may have a convex central portion 43 surrounded by an annular concave outer portion 44. FIG. 6B provides a front view of the first major surface 41 identifying the convex central portion 43 and the annular concave outer portion 44 for one embodiment. In some embodiments, the second major surface 42 may be convex, the third major surface may be substantially flat, and the fourth major surface may be convex.

[0030] In some embodiments, the optical system 400 may further include one or more of a partial reflector 50 (e.g., a 50 / 50 beam splitter coating or film), a reflective polarizer 60, and an optical retarder 90 (e.g., a quarter wave plate). In such embodiments, the partial reflector 50 may be disposed on the fourth major surface 32 of the second optical lens 30, the reflective polarizer may be disposed on the second major surface 42 of the first optical lens 40, and the optical retarder 90 may be disposed between the second major surface 42 of the first optical lens 40 and the third major surface 31 of the second optical lens 30. In such embodiments in which one or more of the partial reflector 50, the reflective polarizer 60, and the optical retarder 90 are present, the optical system axis 10 may be folded (e.g., reflected one or more times from one or more surfaces of the lens and the reflective film), as shown by the optical path 85 in FIG. 6A. That is, light 85 emitted by image 41 on display 20 may be redirected multiple times through optical system 400 before reaching optical sensing system 145 (e.g., an imaging system such as 140 in FIG. 5, or the eye of observer 80 as shown in FIG. 1).

[0031] In some embodiments, the first major surface (41), the second major surface (42), the third major surface (31), and the fourth major surface (32) may each have a sag S1-S4, each of which is defined by:

number

[0032] Figure 7B provides a definition of sag, s, used in Figure 7A. As used herein, sag, s, applies to either convex or concave curvature of a lens and represents the physical distance, r, along a curve between the vertex (the highest or lowest point of the curve) and the center point of a line 99 drawn perpendicular to the curve. Sag, s, is sometimes referred to as the sagittal depth for a given point on the curve.

[0033] Finally, Figures 8A and 8B define the relationship between some of the major curve sag values ​​of the first optical lens 40 and the second optical lens 30 of Figure 6A. Figure 8A shows a plot of S1 / S2 (i.e., S1 sag of the first major surface 41 divided by S2 sag of the second major surface 42) for one embodiment of the optical system. Figure 8B shows a plot of S1 / S4 (i.e., S1 sag of the first major surface 41 divided by S4 sag of the fourth major surface 32). In some embodiments, for values ​​of r ranging from about 1 mm to at least about 25 mm, -0.7≦S1 / S2≦1 and -0.2≦S1 / S4≦0.4.

[0034] In some embodiments, the best fourth order polynomial fits for each of S1 / S2 and S1 / S4 have an r-squared value greater than about 0.95 (see, for example, the plot of the best fourth order polynomial fits shown in FIG. 8B (substantially identical to the plot for S1 / S4).

[0035] Terms such as "about" will be understood by those of skill in the art in the context in which they are used and described herein. Unless otherwise clear to those of skill in the art in the context in which they are used and described herein, the use of "about" as applied to quantities describing feature sizes, quantities, and physical properties will be understood to mean within 10 percent of a particular value. A quantity given as about, approximately a particular value may be exactly that particular value. For example, unless otherwise clear to those of skill in the art in the context in which they are used and described herein, an amount having a value of about 1 means that the amount has a value between 0.9 and 1.1, and may even be 1.

[0036] Terms such as "substantially" will be understood by those of skill in the art in the context in which they are used and described herein. In the context in which the use of "substantially equal" is not clear to those of skill in the art in the context in which they are used and described herein, "substantially equal" means approximately equal, with about as above. In the context in which the use of "substantially parallel" is not clear to those of skill in the art in the context in which they are used and described herein, "substantially parallel" means within 30 degrees of parallel. Directions or surfaces described as substantially parallel to one another may, in some embodiments, be within 20 degrees of parallel, or within 10 degrees, or may be parallel or nominally parallel. In the context in which the use of "substantially aligned" is not clear to those of skill in the art in the context in which they are used and described herein, "substantially aligned" means aligned within 20% of the width of the objects being aligned. Objects described as substantially aligned may, in some embodiments, be aligned within 10% or within 5% of the width of the objects being aligned.

[0037] All references, patents, or patent applications referenced above are hereby incorporated by reference in their entirety. In the event of any inconsistency or contradiction between any of the incorporated references and this application, the information in the foregoing description shall prevail.

[0038] Descriptions of elements in the drawings should be understood to apply equally to corresponding elements in other drawings unless otherwise indicated. Although specific embodiments have been illustrated and described herein, those skilled in the art will appreciate that the specific embodiments illustrated and described may be replaced by various alternative and / or equivalent embodiments without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific embodiments discussed herein. Accordingly, it is intended that the present disclosure be limited only by the claims and the equivalents thereof.

Claims

1. 1. An optical system comprising an optical system axis, a display, and at least one lens, forming a virtual image of an image emitted by the display for viewing by an eye, the eye having an optical axis, a first retinal image of the virtual image at a first virtual image position and an associated first viewing angle between about 5 degrees and about 30 degrees having a first image resolution when the ocular axis is substantially aligned with the system axis, and a second image resolution when the eye is rotated such that the ocular axis is substantially aligned with a first viewing axis extending between the eye and the virtual image at the first viewing angle, the second image resolution being greater than the first image resolution.

2. The at least one lens comprises a first optical lens including oppositely facing first and second major surfaces facing a second optical lens including oppositely facing third and fourth major surfaces, the second and third major surfaces facing each other, the first to fourth major surfaces having sags S1 to S4 respectively, each of the sags being defined by: [0010] where c is 1 / the radius of curvature of the principal surface, k is the conic constant of the surface, r is the distance from the optical system axis, and α is an aspheric deformation constant; the first major surface includes a convex central portion surrounded by an annular concave outer portion, the second major surface is convex, the third major surface is substantially flat, and the fourth major surface is convex; For r ranging from about 1 mm to at least about 25 mm, −0.7≦S1 / S2≦1, -0.2≦S1 / S4≦0.4, a best fourth order polynomial fit for each of S1 / S2 and S1 / S4 has an r-squared value greater than about 0.95; 10. The optical system of claim 1 .

3. The optical system of claim 1 , wherein the second image resolution is greater than the first image resolution for all first viewing angles between about 5 degrees and about 30 degrees.

4. The optical system of claim 1 further comprising one or more of a partial reflector, a reflective polarizer, and an optical retarder.

5. The optical system of claim 1 , wherein the optical system axis is folded.

6. an optical system including an optical system axis, a lens assembly including at least one lens, an eye side configured to be placed proximate to an eye of an observer, and a display side configured to be placed proximate to a display, configured to display a virtual image of an image emitted by the display to the eye of the observer; when substantially collimated light propagating along a first direction that forms a first angle of about 5 degrees to about 30 degrees with respect to the optical system axis illuminates the optical system from the eye side of the optical system, enters the optical system through and substantially fills a field stop positioned proximate the eye side of the optical system, and focuses to a focal spot after passing through the lens assembly and exiting the optical system from the display side of the optical system, the focal spot has a first minimum size when the field stop is substantially centered on the optical system axis and has a second minimum size when the field stop is rotated about a first center proximate a center of the eye of the observer such that the field stop is substantially perpendicular to the first direction, the second minimum size being smaller than the first minimum size. Optical system.

7. The optical system of claim 6 further comprising one or more of a partial reflector, a reflective polarizer, and an optical retarder.

8. The optical system of claim 6 , wherein the optical system axis is folded.

9. The optical system of claim 6 , wherein the optical system axis is folded such that a first segment of the optical system axis substantially coincides with a different second segment of the optical system axis.

10. The optical system of claim 6 , wherein the field stop has a size of about 2 mm to about 8 mm.

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