Foveal optical lenses 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 of this specification, 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 an eye. The eye has an optical axis of the eye, and a first retinal image of the virtual image at a first virtual image position and at a related first viewing angle between about 5 degrees and about 30 degrees has a first image resolution when the optical axis of the eye substantially coincides with the system axis, and has a second image resolution when the eye is rotated so that the optical axis of the eye substantially coincides 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] In some aspects of this specification, an optical system is provided that includes an optical system axis, a lens assembly having at least one lens, an eye side configured to be disposed proximate to an observer's eye, and a display side configured to be disposed 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. Substantially collimated light propagating along a first direction forming 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 a field stop disposed proximate to the eye side of the optical system, and substantially fills the field stop and enters the optical system. When the focused spot is focused after passing through the lens assembly and exiting the optical system from the display side of the optical system, the focused 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 rotates 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 is smaller than the first minimum size.

[0003] In some aspects of this specification, 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 the image emitted by the display for viewing by the eye when the eye is positioned close to the eye position on the eye side of the optical system. For each first virtual image position in a first field of view angle of about 5 to about 30 degrees with respect to the system axis, when an imaging system (e.g., a camera with an objective lens) centered on the imaging system axis is positioned close to the eye position and forms an image of the virtual image corresponding to the first virtual image position, the resolution of the formed image increases as the imaging system is rotated at least so that the imaging system axis approaches the first field of view angle.

[0004] In some aspects of this specification, an optical system is provided comprising 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 the image emitted by the display for viewing by the eye. The eye has an optical axial length extending from the center of the fovea to the center of the pupil. A first retinal image of the virtual image at a first virtual image position and a related first field of view angle, which is between about 5 degrees and about 30 degrees, has a first image resolution when the axial length is substantially coincided with the system axis, and a second image resolution when the eye is rotated so that the axial length is substantially coincided with the first field of view axis. The first field of view axis extends between the eye and the virtual image at the first field of view angle. The second image resolution is greater than the first image resolution. [Brief explanation of the drawing]

[0005] [Figure 1] This is a side view of an optical system including a foveal optical lens according to one embodiment of this specification. [Figure 2A] One embodiment of this specification provides a visual representation of the optical axis of an optical system. [Figure 2B] One embodiment of this specification provides a visual representation of the optical axis of an optical system. [Figure 3] A side view of a foveal optical lens according to one embodiment of this specification is provided. [Figure 4] An alternative diagram of the foveal optical lens shown in Figure 3, according to one embodiment of this specification, is provided. [Figure 5A] A side view of an optical system including an imaging system according to one embodiment of this specification is provided. [Figure 5B] A side view of an optical system including an imaging system according to one embodiment of this specification is provided. [Figure 6A] This specification provides details of an optical system including a lens with a defined surface curve, according to one embodiment of this specification. [Figure 6B] This specification provides details of an optical system including a lens with a defined surface curve, according to one embodiment of this specification. [Figure 7A] This specification provides a definition of the additional lens surface shown in Figures 6A and 6B according to one embodiment of this specification. [Figure 7B] This specification provides a definition of the additional lens surface shown in Figures 6A and 6B according to one embodiment of this specification. [Figure 8A] This specification provides a definition of the additional lens surface shown in Figures 6A and 6B according to one embodiment of this specification. [Figure 8B] This specification provides a definition of the additional lens surface shown in Figures 6A and 6B according to one embodiment of this specification. [Modes for carrying out the invention]

[0006] The following description refers to the accompanying drawings, which constitute part of this specification and illustrate various embodiments. The drawings are not necessarily to exact proportions. It should be understood that other embodiments can be conceived and implemented without departing from the scope or spirit of this disclosure. Therefore, the embodiments for carrying out the following inventions should not be construed as restrictive.

[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 so that the image appears at a certain distance (e.g., displayed in front of the user) and appears larger than the actual image produced by the corresponding small display that generates the virtual image. 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 surface). While lenses in eyeglasses can be designed to provide the best optical properties for a selected field of view and distance (e.g., focusing on a computer display at arm's length), the same method may not work similarly for head-mounted virtual reality (VR) headsets. This is because VR systems require a wide field of view (e.g., a field of view greater than 85 degrees), and eye rotation across that wide field of view can cause image problems. For example, as the pupil of the eye moves across a wider field of view, the image may lose sharpness or resolution when the line of sight deviates from the principal optical axis (e.g., when looking upwards and to the left).

[0008] According to some aspects of this specification, an 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, and 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 respect to the optical system axis (e.g., an upward angle of about 5 to about 30 degrees with respect to 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 with the eye. In some embodiments, the eye may have an optical axial length, and the first retinal image of the virtual image at a first virtual image position and a related first field of view angle between about 5 degrees and about 30 degrees may have a first image resolution when the axial length is substantially coincided with the system axis, and a second image resolution when the eye is rotated so that the axial length is substantially coincided with a first field of view axis extending between the eye and the virtual image at the first field of view 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 field of view angles between about 5 degrees and about 30 degrees.

[0009] In some embodiments, the optical system may further include one or more of the following: 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 bent optical axis. In some embodiments, the optical system axis may be bent 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, at least one lens may be a lens assembly comprising at least a first display-side lens component and a second eye-side lens component. The partial reflector may be located on the side of the display-side lens component closest to the display. The optical retarder may be located between the display-side lens component and the eye-side lens component. The reflective polarizer may be located on the side of the eye-side lens component closest to the observer's eye. In such embodiments, the optical axis may travel from the display, through a partial reflector and an optical retarder, be reflected by a reflective polarizer, return through the optical retarder, then be reflected by the partial reflector, return through the optical retarder and reflective polarizer (since the polarization state has changed here after passing through the optical retarder three times), and finally leave the eye-side lens component through the reflective polarizer towards the observer's eye.

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

[0011] In some embodiments, at least one lens may include a first optical lens with oppositely oriented first and second principal surfaces, and a second optical lens with oppositely oriented third and fourth principal surfaces. In some embodiments, the second and third principal surfaces may face each other. In some embodiments, the first to fourth principal surfaces may each have sags S1 to S4, each of which is defined by the following formula.

number

[0012] According to some aspects of this specification, an optical system may include an optical system axis, a lens assembly having at least one lens, an eye side configured to be positioned close to the observer's eye, and a display side configured to be positioned close 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 so that it can be viewed by an observer (e.g., the virtual image can be viewed when a user is wearing a VR headset). In some embodiments, substantially collimated light propagating along a first direction making a first angle of about 5 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 a field diaphragm positioned close to the eye side of the optical system, substantially fills the field diaphragm, passes through the lens assembly and exits the optical system from the display side of the optical system, and then converges to a focal spot, the focal spot may have a first minimum size when the field diaphragm is substantially centered on the system axis. The focal spot may have a second minimum size when the field diaphragm rotates about a first center close to the center of the observer's eye, such that the field diaphragm 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 diaphragm may have a size of about 1 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 this 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 which is a Fresnel lens having a structured principal 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 the image emitted by the display for viewing by the eye when the eye is positioned close to the eye position on the eye side of the optical system (e.g., near the near-eye display in a VR headset). In some embodiments, for each first virtual image position in a first field of view angle of about 5 to about 30 degrees with respect to the system axis, the resolution of the formed image may increase as the imaging system is rotated at least so that the imaging system axis approaches the first field of view angle, when an imaging system centered on the imaging system axis is positioned close to the eye position and forms an image of the virtual image corresponding to the first virtual image position.

[0014] According to some aspects of this specification, an 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 so that it can be viewed by an observer (for example, the virtual image is viewed when a user is wearing a virtual reality headset). In some embodiments, the eye may have an optical axial length extending from the center of the fovea to the center of the pupil. The fovea, or fovea centralis, is a small depression on 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 (for example, it is important for perceiving high visual detail). In some embodiments, the first retinal image of the virtual image at a first virtual image position and a related first field of view angle between about 5 and about 30 degrees may have a first image resolution when the eye axis substantially coincides with the system axis, and a second image resolution when the eye is rotated so that the eye axis substantially coincides with the first field of view axis. In some embodiments, the first field of view axis may extend between the eye and the virtual image at the first field of view 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 bent. For example, in some embodiments, the optical system axis may be bent 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 help to generate a bent optical system axis.

[0016] Referring to the drawings, FIG. 1 is a side view of an optical system including a foveal optical lens according to this specification. 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, 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 can be viewed by the 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 can be rotated so that the optical axis 81 of the eye 80 substantially coincides with the optical system axis 10, and the eye 80 can be rotated so that the optical axis 81 is misaligned with the optical system axis 10 (e.g., the eye 80 can be rotated upward by an angle α1 as shown in FIG. 1, and as a result, the observer is looking at a higher position on the virtual image 70).

[0018] The optical system 300 may have an eye side 301 that faces substantially the eye 80 and a display side 302 that faces away from the eye 80 and faces the display 20. The optical system 300 may be configured to optimally provide the virtual image 70 to the eye 80 when the eye 80 is disposed 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 the 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] Figures 2A and 2B provide a visual depiction of the optical axis of the optical system of FIG. 1 and provide further details. For the sake of simplicity, at least one lens and the display shown in FIG. 1 are omitted in FIGS. 2A and 2B, and thus the partial optical system shown is relabeled as 300a. The components shown in FIGS. 2A and 2B have common functions and / or purposes with components having similar numbers in other figures of this specification unless otherwise specified. FIG. 2A shows an observer's eye 80 positioned close to the eye position 84 (i.e., the position where the optical system is configured to provide optical resolution over the entire field of view), and the optical eye axis 81 extends from the center of the fovea 87 of the eye 80 through the center 83 of the eye 80 to the pupil 88. During 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 arranged to be substantially aligned with the optical system axis 10 (i.e., the eye 80 is rotated so as to look directly or substantially parallel along the optical system axis 10).

[0020] In FIG. 2B, the eye 80 is rotated upward so that the optical eye axis 81 is substantially aligned with a first field axis 72 extending between the eye 80 and the first virtual image position 71. In some embodiments, the first field axis 72 forms a first field angle α1 with the optical system axis 10. In some embodiments, the first field 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 position 71 when the optical eye axis 81 substantially coincides with the optical system axis 10, and the first retinal image 82 has a second image resolution at the first virtual image position 71 when the optical eye axis substantially coincides with the first field axis 72. In some embodiments, the second image resolution may be greater than the first image resolution. Stated another way, the first retinal image 82 may have a higher image resolution when the eye 80 is rotated so as to be aligned with the first field 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, as provided herein. Figures 3 and 4 show essentially the same optical system, but the eye 80 is at two different rotation angles. Figures 3 and 4 should be referred to together in the following discussion. Components with similar numbering 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 close to the observer's eye 80 and a display-side 302 configured to be positioned close to 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 close to 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 the 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 the 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 the observer's eye 80.

[0024] In some embodiments, substantially collimated light 110 propagates along a first direction 111, which makes 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 substantially collimated light 110 illuminates the optical system 300 from the eye side 301 and enters the optical system 300, substantially filling the field aperture 120 / 121 positioned close to the eye side 301, the light 110 passes through the lens assembly 130, exits the optical system 300 from the display side 302, and then focuses to the focal spot 112.

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

[0026] Figures 5A and 5B provide a visual representation of the optical axis of an optical system, such as the optical system 300 in Figure 1, where the observer's eye 80 is replaced by an imaging system 40 (e.g., a camera with an objective lens capable of focusing on a virtual image) centered on the imaging system axis 141. For simplification, the lenses (at least one) and display shown in Figure 1 are omitted, as described elsewhere in this specification and as done in Figures 2A and 2B, and the partial optical system shown is therefore relabeled as 300b. The components shown in Figures 5A and 5B have common functions and / or purposes with similarly numbered components in other figures in this specification, unless otherwise specified.

[0027] The optical system 300b includes an optical system axis 10, a display (such as a display 20 as shown in Figure 1), and at least one lens (such as lens components 30 and 40 as shown in Figure 1). In some embodiments, the optical system 300b may form a virtual image 70 for viewing by the eye (such as eye 80 as shown in Figure 1) when the eye is positioned close to the eye position 84. In some embodiments, for each first virtual image position 71 in a first field of view α1, the imaging system 140 is positioned close to the eye position 84 with respect to the imaging system axis 141, and when forming an image of a 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 a state in which it coincides with the optical system axis 10 and approaches the first field of view α1 (i.e., as it rotates upward and approaches so as to substantially coincide with the first field of view axis 72 extending between the imaging system 140 and the first virtual image position 71 in the first field of view axis α1).

[0028] Figures 6A and 6B provide details of one embodiment of an optical system including a lens having a specifically defined surface curve. The optical system 400 may be any of the optical systems discussed herein, including the optical system 300 in Figures 1 and 4, the optical system 300a in Figures 2A and 2B, and the optical system 300b in 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 principal surface 41 and a second principal surface 42 facing the opposite direction. In some embodiments, the second optical lens 30 includes a third principal surface 31 and a fourth principal surface 32 facing the opposite direction. In some embodiments, the second principal surface 42 and the third principal surface 31 of the first optical lens 40 face each other. In some embodiments, the first principal surface 41 may have a convex central portion 43 surrounded by an annular concave outer portion 44. Figure 6B provides a front view of the first principal surface 41 identifying the convex central portion 43 and the annular concave outer portion 44 in one embodiment. In some embodiments, the second principal surface 42 may be convex, the third principal surface may be substantially flat, and the fourth principal surface may be convex.

[0030] In some embodiments, the optical system 400 may further include one or more of the following: 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 located on the fourth principal surface 32 of the second optical lens 30, the reflective polarizer may be located on the second principal surface 42 of the first optical lens 40, and the optical retarder 90 may be located between the second principal surface 42 of the first optical lens 40 and the third principal surface 31 of the second optical lens 30. In such embodiments where 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 bent (e.g., reflected once or more from one or more surfaces of the lens and reflective film) as shown by the optical path 85 in Figure 6A. In other words, the light 85 emitted by the image 41 of the display 20 may pass through the optical system 400 and be redirected multiple times before reaching the optical sensing system 145 (for example, an imaging system such as 140 in Figure 5, or the eye of an observer 80 as shown in Figure 1).

[0031] In some embodiments, the first main surface (41), the second main surface (42), the third main surface (31), and the fourth main surface (32) may each have sags S1 to S4, each of which is defined as follows:

number

[0032] Figure 7B provides the definition of sag s used in Figure 7A. As used herein, sag s applies to either the convex or concave curvature of a lens and represents the physical distance r between a vertex along the curve (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 also called sagittal depth for a given point on the curve.

[0033] Finally, Figures 8A and 8B define the relationships between some of the sag values ​​of the principal curves of the first optical lens 40 and the second optical lens 30 in Figure 6A. Figure 8A shows a plot of S1 / S2 (i.e., the S1 sag of the first principal surface 41 divided by the S2 sag of the second principal surface 42) for one embodiment of the optical system. Figure 8A also shows a plot of S1 / S4 (i.e., the S1 sag of the first principal surface 41 divided by the S4 sag of the fourth principal surface 32). In some embodiments, for r values ​​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 quartic polynomial fittings for S1 / S2 and S1 / S4, respectively, have an r-squared value greater than approximately 0.95. See, for example, the plot of the best quartic polynomial fitting shown in Figure 8B (substantially identical to the plot for S1 / S4).

[0035] Terms such as “about” will be understood by those skilled in the art in the context in which they are used and described herein. Where the use of “about” in relation to the size, quantity, and physical properties of a feature is not otherwise obvious to those skilled in the art in the context in which it is used and described herein, “about” will be understood to mean within 10 percent of a particular value. A quantity given as about or approximately of a particular value may be exactly that particular value. For example, where it is not otherwise obvious to those skilled in the art in the context in which it is used and described herein, a quantity having a value of about 1 means that the quantity has a value between 0.9 and 1.1, and that the value may also be 1.

[0036] Terms such as “substantially” will be understood by those skilled in the art in the context in which they are used and described herein. If the use of “substantially equal” is not obvious to those skilled in the art in the context in which they are used and described herein, “substantially equal” means approximately equal, with “about” as described above. If the use of “substantially parallel” is not obvious to those skilled in the art in the context in which they are used and described herein, “substantially parallel” means within 30 degrees of parallelism. Directions or surfaces described as substantially parallel to each other may, in some embodiments, be within 20 degrees or 10 degrees of parallelism, or be parallel or nominally parallel. If the use of “substantially aligned” is not obvious to those skilled in the art in the context in which they are used and described herein, “substantially aligned” means aligned within 20 percent of the width of the aligned objects. Objects described as substantially aligned may, in some embodiments, be aligned within 10 percent or 5 percent of the width of the aligned objects.

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

[0038] Unless otherwise indicated, the descriptions of elements in the drawings should be understood to apply equally to the corresponding elements in other drawings. While specific embodiments are illustrated and described herein, it will be understood by those skilled in the art that these specific embodiments may be replaced by various alternative and / or equivalent embodiments without departing from the scope of this disclosure. This application is intended to encompass any adaptation or modification of any specific embodiment discussed herein. Therefore, this disclosure is intended to be limited only by the claims and their equivalents. The following are exemplary embodiments. [Claim 1] An optical system comprising an optical system axis, a display, and at least one lens, which forms a virtual image of an image emitted by the display for viewing by the eye, wherein the eye has an optical eye axis, and the first retinal image of the virtual image at a first virtual image position and a related first field of view angle between about 5 degrees and about 30 degrees has a first image resolution when the eye axis substantially coincides with the system axis, and has a second image resolution when the eye is rotated so that the eye axis substantially coincides with a first field of view axis extending between the eye and the virtual image at the first field of view angle, wherein the second image resolution is greater than the first image resolution. [Claim 2] The at least one lens comprises a first optical lens having opposite first and second principal surfaces, and facing a second optical lens having opposite third and fourth principal surfaces, wherein the second and third principal surfaces face each other, and the first to fourth principal surfaces each have sags S1 to S4, each of which is defined as follows:

number

Claims

1. An optical system comprising an optical system axis, a display, and at least one lens, which forms a virtual image of an image emitted by the display for viewing by the eye, wherein the eye has an optical eye axis, and the first retinal image of the virtual image at a first virtual image position and a related first field of view angle between about 5 degrees and about 30 degrees has a first image resolution when the optical eye axis substantially coincides with the optical system axis, based on the imaging characteristics of the optical system in accordance with the line of sight direction of the eye, and has a second image resolution when the eye is rotated so that the optical eye axis substantially coincides with a first field of view axis extending between the eye and the virtual image at the first field of view angle, wherein the second image resolution is greater than the first image resolution.

2. The at least one lens is a first optical lens having opposite first and second principal surfaces, and the first optical lens facing the second optical lens having opposite third and fourth principal surfaces, the second and third principal surfaces facing each other, and the first to fourth principal surfaces each having sags S1 to S4, each of which is defined as follows: 【Number 1】 In the formula, c is 1 / radius of curvature of the principal surface, k is the cone constant of the surface, r is the distance from the optical system axis, and α is the aspherical deformation constant. The first main surface includes a convex central portion surrounded by an annular concave outer portion, the second main surface is convex, the third main surface is substantially flat, and the fourth main surface is convex. For r ranging from approximately 1 mm to at least approximately 25 mm, -0.7 ≤ S1 / S2 ≤ 1, -0.2 ≤ S1 / S4 ≤ 0.4, The best quartic polynomial fitting for each of S1 / S2 and S1 / S4 has an r-squared value greater than approximately 0.

95. The optical system according to claim 1.

3. The optical system according to claim 1, wherein the second image resolution is greater than the first image resolution for all first field of view angles between approximately 5 degrees and approximately 30 degrees.

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

5. The optical system according to claim 1, wherein the optical system axis is bent.

6. An optical system comprising an optical system axis, a lens assembly including at least one lens, an eye side configured to be positioned close to the observer's eye, and a display side configured to be positioned close to a display, wherein the 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 forming a first angle of about 5 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 a field diaphragm positioned close to the eye side of the optical system and substantially fills the field diaphragm, passes through the lens assembly and exits the optical system from the display side of the optical system, and then focuses to a focal spot, the focal spot has a first minimum size when the field diaphragm is substantially at the center of the optical system axis without changing the aperture size of the field diaphragm, and a second minimum size when the field diaphragm is rotated about a first center close to the center of the observer's eye such that the field diaphragm is substantially perpendicular to the first direction, the second minimum size being smaller than the first minimum size. Optical system.

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

8. The optical system according to claim 6, wherein the optical system axis is bent.

9. The optical system according to claim 6, wherein the optical system axis is bent 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 according to claim 6, wherein the field diaphragm has a size of approximately 2 mm to approximately 8 mm.

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