Folded optical lens assembly and optical system

Abstract

An optical system is disclosed. The optical system includes a display configured to form an image, a partial reflector, and a reflective polarizer defining an optical cavity therebetween. The optical system further includes a positive lens and a negative lens, at least one of which is disposed inside the optical cavity. The positive lens and the negative lens may both be disposed inside the optical cavity. The optical system may include a folded optical lens assembly including the partial reflector, the reflective polarizer, the positive lens, and the negative lens. The positive lens has an Abbe number having a magnitude Ap and a positive focal length Fp at a visible wavelength extending from about 420 nm to about 680 nm, the negative lens has an Abbe number having a magnitude An and a negative focal length having a magnitude Fn at the visible wavelength, Fn / Fp > Ap / An.

Description

[0001]FOLDED OPTICAL LENS ASSEMBLY AND OPTICAL SYSTEM Technical Field The present disclosure relates generally to a folded optical lens assembly and an optical system. Background Optical systems and folded optical lens assemblies may be used in head-mounted displays (HMDs) and / or near-eye-displays (NEDs) and may enhance performance of the HMDs and / or NEDs, for example, in Virtual reality (VR) and augmented reality (AR) applications. Summary In a first aspect, the present disclosure provides a folded optical lens assembly configured to display a virtual image of an image formed and emitted by a display to an eye of a viewer. The folded optical lens assembly includes a partial reflector and a reflective polarizer spaced apart from each other and defining an optical cavity therebetween, such that for a substantially normally incident light having at least a first visible wavelength in a visible wavelength range extending from about 420 nanometers (nm) to about 680 nm, the partial reflector, for each of mutually orthogonal first and second polarization states, reflects at least 25% of the incident light and transmits at least 25% of the incident light, and the reflective polarizer reflects at least about 60% of the incident light having the first polarization state and transmits at least about 60% of the incident light having the second polarization state. The folded optical lens assembly further includes a positive lens and a negative lens disposed inside the optical cavity. The positive lens has an Abbe number having a magnitude Ap and a positive focal length Fp at the first visible wavelength. The negative lens has an Abbe number having a magnitude An and a negative focal length having a magnitude Fn at the first visible wavelength. A ratio of Fn to Fp is greater than or equal to a ratio of Ap to An, i.e., Fn / Fp ≥ Ap / An. In a second aspect, the present disclosure provides an optical system. The optical system includes an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, and a positive lens and a negative lens at least one of which is disposed inside the optical cavity. The display is configured to form an image. The optical system is configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned proximate an eye- location on an eye-side of the optical system. When an imaging system centered on an imaging system axis is positioned proximate the eye-location so that the imaging system axis makes a first angle of less than about 5 degrees with the optical system axis, and the imaging system forms a captured image of the virtual image, then, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for each first field angle in a continuous first field angle range that is at least 5 degrees wide and is disposed at field angles greater than about 15 degrees, an average tangential modulation transfer function of the captured image averaged over a first wavelength range that is at least 30 nanometers (nm) wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.15. In a third aspect, the present disclosure provides an optical system. The optical system includes an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, and a positive lens and a negative lens at least one of which is disposed inside the optical cavity. The display is configured to form an image. The optical system is configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned proximate an eye- location on an eye-side of the optical system. The eye centered on an eye-axis includes a center of rotation of the eye. When an imaging system centered on an imaging system axis is positioned proximate the eye-location so that the imaging system axis passes through the center of rotation of the eye and makes a first angle of greater than about 10 degrees and less than about 30 degrees with the optical system axis, and the imaging system forms a captured image of the virtual image, then, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for each first field angle in a continuous first field angle range that is at least 5 degrees wide and is disposed between a field angle of about 5 degrees to a field angle of about 30 degrees, an average tangential modulation transfer function of the captured image averaged over a first wavelength range that is at least 30 nanometers (nm) wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.2. In a fourth aspect, the present disclosure provides an optical system. The optical system includes an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, and a positive lens and a negative lens at least one of which is disposed inside the optical cavity. The display is configured to form an image. The optical system is configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned proximate an eye- location on an eye-side of the optical system. The eye centered on an eye-axis includes a center of rotation of the eye. When an imaging system centered on an imaging system axis is positioned proximate the eye-location so that the imaging system axis passes through the center of rotation of the eye and in a first orientation, the imaging system axis makes a first angle of less than about 5 degrees with the optical system axis, in a second orientation, the imaging system axis makes a second angle of greater than about 10 degrees and less than about 30 degrees with the optical system axis, and the imaging system forms first and second captured images of the virtual image in the respective first and second orientations, then for each of the first and second orientations, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for at least one field angle greater than about 30 degrees, an average tangential modulation transfer function of the captured image averaged over a first wavelength range that is at least 30 nanometers (nm) wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.2. In a fifth aspect, the present disclosure provides an optical system. The optical system includes an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, a positive lens and a negative lens at least one of which is disposed inside the optical cavity, and a field stop substantially centered on the system axis and having a size of between about 1 millimeter (mm) and about 15 mm. The display is configured to form an image in a display image surface. The optical system is configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned at or proximate the field stop with a center of rotation of the eye disposed on the system axis. When the field stop is rotated about the center of rotation of the eye by a rotation angle of at least 15 degrees, and a substantially collimated light beam that propagates along a first direction and makes the rotation angle with the system axis and substantially fills the rotated field stop and focuses to a focal spot substantially at the display image surface after going through the optical cavity, and the positive and negative lenses, then for at least one spatial frequency of greater than about 15 cycles per millimeter, each of average tangential and average sagittal modulation transfer functions of the optical system averaged over a first wavelength range that is at least 30 nanometers (nm) wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.5. The details of one or more examples of the disclosure are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the disclosure will be apparent from the description and drawings, and from the claims. Brief Description of Drawings Exemplary embodiments disclosed herein are more completely understood in consideration of the following detailed description in connection with the following figures. The figures are not necessarily drawn to scale. Like numbers used in the figures refer to like components. However, it will be understood that the use of a number to refer to a component in a given figure is not intended to limit the component in another figure labelled with the same number. FIG. 1A is a schematic view of an optical system including a folded optical lens assembly, according to an embodiment of the present disclosure; FIG.1A is a schematic view of an eye of a viewer; FIG.2A is a schematic sectional view of a partial reflector of the optical system, according to an embodiment of the present disclosure; FIG.2B is a schematic sectional view of a reflective polarizer of the optical system, according to an embodiment of the present disclosure; FIG.3 is a schematic view of a folded optical lens assembly, according to another embodiment of the present disclosure; FIG.4 is a schematic view of the optical system with an imaging system in a first orientation, according to an embodiment of the present disclosure; FIG. 5 is a schematic view of the optical system with the imaging system in a second orientation, according to an embodiment of the present disclosure; FIGS. 6A-6E are schematic views of different examples of the folded optical lens assembly, according to an embodiment of the present disclosure; FIGS. 7 and 8 show a graph depicting variations of a tangential modulation transfer function and a sagittal modulation transfer function of the different examples of the folded optical lens assembly with respect to a field angle in the first orientation of the imaging system, according to an embodiment of the present disclosure; FIG. 9 shows a graph depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of the different examples of the folded optical lens assembly with respect to the field angle in the second orientation of the imaging system, according to an embodiment of the present disclosure; FIG.10 is a schematic view of the optical system with the imaging system and a substantially collimated light beam, according to an embodiment of the present disclosure; FIG.11A shows a graph depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of a comparative lens assembly with respect to a spatial frequency; and FIG. 11B illustrates a graph depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of the folded optical lens assembly with respect to the spatial frequency, according to an embodiment of the present disclosure. Detailed Description In the following description, reference is made to the accompanying figures that form a part thereof and in which various embodiments are shown by way of illustration. 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. The following detailed description, therefore, is not to be taken in a limiting sense. In the following disclosure, the following definitions are adopted. As used herein, “a,” “an,” “the,” “at least one,” and “one or more” are used interchangeably. As used herein as a modifier to a property or attribute, the term “generally,” unless otherwise specifically defined, means that the property or attribute would be readily recognizable by a person of ordinary skill but without requiring absolute precision or a perfect match (e.g., within + / - 20 % for quantifiable properties). The term “substantially,” unless otherwise specifically defined, means to a high degree of approximation (e.g., within + / - 10% for quantifiable properties) but again without requiring absolute precision or a perfect match. As used herein, all numbers should be considered modified by the term “about.” The term “about,” unless otherwise specifically defined, means to a high degree of approximation (e.g., within + / - 5% for quantifiable properties) but again without requiring absolute precision or a perfect match. As used herein, the terms “first” and “second” are used as identifiers. Therefore, such terms should not be construed as limiting of this disclosure. The terms “first” and “second” when used in conjunction with a feature or an element can be interchanged throughout the embodiments of this disclosure. As used herein, when a first material is termed as “similar” to a second material, at least 90 weight % of the first and second materials are identical and any variation between the first and second materials comprises less than about 10 weight % of each of the first and second materials. As used herein, “at least one of A and B” should be understood to mean “only A, only B, or both A and B.” As used herein, the term “layer” generally refers to a thickness of material within a film that has a relatively consistent chemical composition. Layers may be of any type of material including polymeric, cellulosic, metallic, or a blend thereof. A given polymeric layer may include a single polymer-type or a blend of polymers and may be accompanied by additives. A given layer may be combined or connected to other layers to form films. A layer may be either partially or fully continuous as compared to adjacent layers or the film. A given layer may be partially or fully coextensive with adjacent layers. A layer may contain sub-layers. As used herein, the term “between about,” unless otherwise specifically defined, generally refers to an inclusive or a closed range. For example, if a parameter X is between about A and B, then A ≤ X ≤ B. As used herein, the term “adhesive” generally refers to polymeric compositions useful to adhere together two adherends. Examples of adhesives may include curable adhesives, heat activated adhesives, pressure sensitive adhesives, or combinations thereof. As used herein, the term “modulation transfer function” or “MTF” refers to a measure of image quality characterizing the ability of an optical system to transfer contrast from an image to an eye location or a field stop. The MTF of an optical system can be expressed as a function of spatial frequency. Spatial frequency quantifies the level of detail present in an image at an eye location or a field stop and is often specified in units of line pairs per mm. High spatial frequency images have a larger amount of detail than images of lower spatial frequency. MTF can be determined for tangential and sagittal orientations at different wavelengths of light and at different angles of light with respect to an optical axis of the optical system. As used herein, the term “Abbe Number” refers to an approximate measure of a material’s dispersion, i.e., change of refractive index versus wavelength. The present disclosure relates to optical systems and folded optical lens assemblies used for virtual reality (VR) / augmented reality (AR) applications, such as entertainment, industrial applications, gaming, healthcare, etc. In some cases, the optical system may be used in a head-mounted display (HMD) and / or a near-eye-display (NED). In some embodiments, the optical system may be worn on a head of a viewer or may be included as a part of a headgear (e.g., helmet), that has a small display optic in front of an eye, such as in a monocular display device, or two eyes, such as in a binocular display device. The folded optical lens assembly may be used with a display device to provide a compact design, a high resolution, wide viewing angles, and low distortions in the optical systems. Typically, a display’s angular output profile centered on the normal to a display surface of the display device may result in high contrast at a center, but may result in lower light intensity and lower resolution due to vignetting at a far field. The present disclosure provides a folded optical lens assembly configured to display a virtual image of an image formed and emitted by a display to an eye of a viewer. The folded optical lens assembly includes a partial reflector and a reflective polarizer spaced apart from each other and defining an optical cavity therebetween, such that for a substantially normally incident light having at least a first visible wavelength in a visible wavelength range extending from about 420 nanometers (nm) to about 680 nm, the partial reflector, for each of mutually orthogonal first and second polarization states, reflects at least 25% of the incident light and transmits at least 25% of the incident light, and the reflective polarizer reflects at least about 60% of the incident light having the first polarization state and transmits at least about 60% of the incident light having the second polarization state. The folded optical lens assembly further includes a positive lens and a negative lens disposed inside the optical cavity. The positive lens has an Abbe number having a magnitude Ap and a positive focal length Fp at the first visible wavelength. The negative lens has an Abbe number having a magnitude An and a negative focal length having a magnitude Fn at the first visible wavelength. A ratio of Fn to Fp is greater than or equal to a ratio of Ap to An, i.e., Fn / Fp ≥ Ap / An. The present disclosure further provides an optical system including an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, and a positive lens and a negative lens at least one of which is disposed inside the optical cavity. The display is configured to form an image. The optical system is configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned proximate an eye-location on an eye- side of the optical system. The eye centered on an eye-axis includes a center of rotation of the eye. When an imaging system centered on an imaging system axis is positioned proximate the eye-location so that the imaging system axis passes through the center of rotation of the eye and in a first orientation, the imaging system axis makes a first angle of less than about 5 degrees with the optical system axis, in a second orientation, the imaging system axis makes a second angle of greater than about 10 degrees and less than about 30 degrees with the optical system axis, and the imaging system forms first and second captured images of the virtual image in the respective first and second orientations, then for each of the first and second orientations, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for at least one field angle greater than about 30 degrees, an average tangential modulation transfer function of the captured image averaged over a first wavelength range that is at least 30 nanometers (nm) wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.2. Since, for each of the first and second orientations, for the at least one spatial frequency and for the at least one field angle greater than about 30 degrees, the average tangential modulation transfer function of the captured image, averaged over the first wavelength range, is greater than about 0.2, the optical systems and the folded optical lens assemblies of the present disclosure may provide a higher contrast than conventional lens assemblies at higher field angles (i.e., greater than about 30 degrees). Further, the optical systems and the folded optical lens assemblies of the present disclosure may further provide a higher resolution, a lower chromatic aberration, a lower distortion, and / or a higher efficiency in a compact configuration that is useful in various applications, such as in the VR and AR applications compared to conventional optical lens assemblies, especially at the higher field angles. Referring now to the figures, FIG. 1A illustrates a schematic view of an optical system 400, according to an embodiment of the present disclosure. A coordinate system including mutually perpendicular x, y, and z-axes is also illustrated in FIG.1A. FIG.1B illustrates a schematic view of an eye 20 of a viewer. The x and y-axes are in-plane axes of optical system 400, while the z-axis is a transverse axis disposed along a thickness of the optical system 400. In other words, x and y-axes are along a plane of the optical system 400 defining a x-y plane, and the z-axis is perpendicular to the x-y plane of the optical system 400. Referring to FIGS. 1A and 1B, the optical system 400 includes an optical system axis 401 (interchangeably referred to as “the system axis 401”). The optical system axis 401 refers to an imaginary line defining a path along which light propagates through the optical system 400. In some embodiments, the optical system axis 401 is folded. In such embodiments, light may pass through, be reflected by, be refracted by, or otherwise affected by one or more optical components of the optical system 400, such that the path of the light is folded rather than strictly linear. The optical system axis 401 may be folded to reduce an overall footprint of the optical system 400. The optical system axis 401 extends substantially along the z-axis. The optical system 400 includes a display 10. The display 10 is configured to form an image 11. Specifically, the display 10 is configured to form the image 11 in a display image surface 12. The display 10 may be of any suitable type. In some embodiments, the display 10 includes an organic light emitting diode (OLED) display panel. In some other embodiments, the display 10 includes a liquid crystal display (LCD) panel. The optical system 400 further includes a partial reflector 30 and a reflective polarizer 40. The partial reflector 30 and the reflective polarizer 40 define an optical cavity 50 therebetween. The optical system 400 further includes a positive lens 70 and a negative lens 80 at least one of which is disposed inside the optical cavity 50. That is, at least one of the positive lens 70 and the negative lens 80 is disposed inside the optical cavity 50. In some embodiments, the positive lens 70 and the negative lens 80 are both disposed inside the optical cavity 50. In some embodiments, the optical system 400 further includes a field stop 14 substantially centered on the system axis 401. The field stop 14 has a size P1 of between about 1 millimeter (mm) and about 15 mm. In some embodiments, the size P1 is between about 2 mm and about 12 mm, between about 2 mm and about 10 mm, between about 2 mm and about 8 mm, or between about 3 mm and about 7 mm. In some embodiments, the size P1 may be about 5 mm. In some embodiments, the optical system 400 is configured to display a virtual image 13 of the formed image 11 for viewing by the eye 20 when the eye 20 is positioned proximate an eye-location 21 on an eye-side 410 of the optical system 400. The field stop 14 may be positioned at or proximate the eye-location 21. In some embodiments, the optical system 400 is configured to display the virtual image 13 of the formed image 11 for viewing by the eye 20 when the eye 20 is positioned at or proximate the field stop 14 with a center of rotation 22 of the eye 20 disposed on the system axis 401. The eye 20 includes an eye-axis 23 (shown in FIG.1B). In the illustrated embodiment of FIG. 1A, the optical system 400 further includes a folded optical lens assembly 300. The folded optical lens assembly 300 is configured to display the virtual image 13 of the image 11 formed and emitted by the display 10 to the eye 20 of the viewer. The folded optical lens assembly 300 includes the partial reflector 30 and the reflective polarizer 40. The partial reflector 30 and the reflective polarizer 40 are spaced apart from each other and define the optical cavity 50 therebetween. FIG. 2A illustrates a schematic sectional view of the partial reflector 30, according to an embodiment of the present disclosure. FIG.2B illustrates a schematic sectional view of the reflective polarizer 40, according to an embodiment of the present disclosure. Referring to FIGS.2A and 2B, for a substantially normally incident light 60, 61 having at least a first visible wavelength in a visible wavelength range extending from about 420 nanometers (nm) to about 680 nm, the partial reflector 30, for each of mutually orthogonal first and second polarization states, reflects at least 25% of the incident light 60 and transmits at least 25% of the incident light 60, and the reflective polarizer 40 reflects at least about 60% of the incident light 61 having the first polarization state and transmits at least about 60% of the incident light 61 having the second polarization state. Specifically, for the substantially normally incident light 60 having at least the first visible wavelength, the partial reflector 30, for each of the mutually orthogonal first and second polarization states, reflects at least 25% of the incident light 60 and transmits at least 25% of the incident light 60. Further, for the substantially normally incident light 61 having at least the first visible wavelength, the reflective polarizer 40 reflects at least about 60% of the incident light 61 having the first polarization state and transmits at least about 60% of the incident light 61 having the second polarization state. In some embodiments, for the substantially normally incident light 60 having at least the first visible wavelength, the partial reflector 30, for each of the mutually orthogonal first and second polarization states, may reflect at least 30%, at least 35%, at least 40%, or at least 45% of the incident light 60 and transmit at least 30%, at least 35%, at least 40%, or at least 45% of the incident light 60. Further, in some embodiments, for the substantially normally incident light 61 having at least the first visible wavelength, the reflective polarizer 40 may reflect at least about 65%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, or at least about 95% of the incident light 61 having the first polarization state and transmit at least about 65%, at least about 70%, at least about 75%, at least about 80%, at least about 85%, at least about 90%, or at least about 95% of the incident light 61 having the second polarization state. In some embodiments, the incident light 60, 61 having the first polarization state may be polarized along the x-axis, and the incident light 60, 61 having the second polarization state may be polarized along the y-axis. In some other embodiments, the incident light 60, 61 having the first polarization state may be polarized along the y-axis, and the incident light 60, 61 having the second polarization state may be polarized along the x-axis. In some embodiments, the partial reflector 30 includes a metal. In some embodiments, the metal includes one or more of aluminum, titanium, copper, silver, and gold. In some embodiments, the reflective polarizer 40 includes a plurality of co-extruded and co- stretched polymeric layers 41, 42, 43. The plurality of co-extruded and co-stretched polymeric layers 41, 42, 43 includes a plurality of co-extruded and co-stretched polymeric microlayers 41, 42 (hereinafter referred to as “the polymeric microlayers 41, 42”) numbering at least 10 in total. In some embodiments, the polymeric microlayers 41, 42 may number at least 50, at least 100, at least 200, at least 300, at least 400, or at least 500 in total. In some embodiments, each of the polymeric microlayers 41, 42 has an average thickness t of less than about 500 nm. The term “average thickness t”, as used herein, refers to an average of thicknesses measured at multiple points across a plane (i.e., the x-y plane) of each of the polymeric microlayers 41, 42. In some embodiments, the average thickness t of each of the polymeric microlayers 41, 42 may be less than about 450 nm, less than about 400 nm, less than about 350 nm, less than about 300 nm, less than about 250 nm, or less than about 200 nm. In some embodiments, the plurality of co-extruded and co-stretched polymeric layers 41, 42, 43 further includes at least one macrolayer 43 having an average thickness ts of greater than about 500 nm. The term “average thickness ts”, as used herein, refers to an average of thicknesses measured at multiple points across a plane (i.e., the x-y plane) of the at least one macrolayer 43. In some embodiments, the average thickness ts of the at least one macrolayer 43 may be greater than about 750 nm, greater than about 1000 nm, greater than about 1500 nm, greater than about 2000 nm, greater than about 2500 nm, or greater than about 3000 nm. In the illustrated embodiment of FIG. 2B, the at least one macrolayer 43 includes a pair of macrolayers 43, and the polymeric microlayers 41, 42 are disposed between the pair of macrolayers 43. The at least one macrolayer 43 may protect polymeric microlayers 41, 42, and may also provide mechanical stability to the reflective polarizer 40. In some cases, the at least one macrolayer 43 may act as protective boundary layer (PBL). Referring again to FIG.1A, in the illustrated embodiment of FIG. 1A, the folded optical lens assembly 300 includes the positive lens 70 and the negative lens 80 disposed inside the optical cavity 50. That is, in the illustrated embodiment of FIG.1A, the positive lens 70 and the negative lens 80 are both disposed inside the optical cavity 50. In some embodiments, the positive lens 70 has an Abbe number having a magnitude Ap and a positive focal length Fp at the first visible wavelength. Similarly, the negative lens 80 has an Abbe number having a magnitude An and a negative focal length having a magnitude Fn at the first visible wavelength. In some embodiments, a ratio of Fn to Fp is greater than or equal to a ratio of Ap to An. That is, in some embodiments, Fn / Fp ≥ Ap / An. In some embodiments, Fn / Fp is greater than Ap / An by at least a factor of 1.5. In some embodiments, Fn / Fp may be greater than Ap / An by at least a factor of 2, at least a factor of 2.5, at least a factor of 3, at least a factor of 3.5, at least a factor of 4, at least a factor of 4.5, or at least a factor of 5. In some embodiments, Fn of the negative lens 80 is greater than about 20 millimeters (mm) and less than about 600 mm. Further, in some embodiments, Fp of the positive lens 70 is greater than about 20 mm and less than about 500 mm. In some embodiments, the Abbe number of the positive lens 70 is a positive number. That is, in some embodiments, Ap > 0. In some embodiments, Ap of the positive lens 70 is between about 20 and about 200. In some embodiments, the Abbe number of the negative lens 80 is a positive number. That is, in some embodiments, An > 0. In some embodiments, An of the negative lens 80 is between about 10 and about 300. In some embodiments, Ap / An is greater than or equal to 1. That is, in some embodiments, Ap / An ≥ 1. In some embodiments, Ap / An may be greater than or equal to 1.5, greater than or equal to 2, greater than or equal to 2.5, greater than or equal to 3, greater than or equal to 3.5, greater than or equal to 4, greater than or equal to 4.5, or greater than or equal to 5. The positive lens 70 includes opposing major first and second surfaces 71, 72. In other words, the positive lens 70 includes the major first surface 71 and the major second surface 72 that is opposite to the major first surface 71. In some embodiments, at least one of the major first and second surfaces 71, 72 has a radius of curvature less than about 300 mm. In some embodiments, the radius of curvature of the at least one of the major first and second surfaces 71, 72 may be less than about 275 mm, less than about 250 mm, less than about 225 mm, less than about 200 mm, less than about 175 mm, less than about 150 mm, less than about 125 mm, less than about 100 mm, less than about 75 mm, or less than about 50 mm. In some embodiments, the radius of curvature of the at least one of the major first and second surfaces 71, 72 may range from 39.29 mm to 150 mm. In the illustrated embodiment of FIG.1A, the major first surface 71 has a radius of curvature less than about 300 mm. Further, in some embodiments, one of the major first and second surfaces 71, 72 of the positive lens 70 is substantially planar. In the illustrated embodiment of FIG.1A, the major second surface 72 is substantially planar. The negative lens 80 includes opposing major first and second surfaces 81, 82. In other words, the negative lens 80 includes the major first surface 81 and the major second surface 82 that is opposite to the major first surface 81. In some embodiments, at least one of the major first and second surfaces 81, 82 has a radius of curvature having a magnitude of less than about 300 mm. In some embodiments, the magnitude of the radius of curvature of the at least one of the major first and second surfaces 81, 82 may be less than about 275 mm, less than about 250 mm, less than about 225 mm, less than about 200 mm, less than about 175 mm, less than about 150 mm, less than about 125 mm, less than about 100 mm, less than about 75 mm, or less than about 50 mm. In some embodiments, the magnitude of the radius of curvature of the at least one of the major first and second surfaces 81, 82 may range from 49.8 mm to 200 mm. In the illustrated embodiment of FIG.1A, the major second surface 82 has the radius of curvature less having the magnitude of than about 300 mm. Further, in some embodiments, one of the major first and second surfaces 81, 82 of the negative lens 80 is substantially planar. In the illustrated embodiment of FIG.1A, the major first surface 81 is substantially planar. In some embodiments, the positive and negative lenses 70, 80 are bonded to each other. In the illustrated embodiment of FIG.1A, the major second surface 72 of the positive lens 70 and the major first surface 81 of the negative lens 80 face, and are bonded to, each other. The positive and negative lenses 70, 80 may be bonded to each other by any suitable technique, such as by use of an optically clear adhesive (OCA). In some embodiments, the optical system 400 further includes a third lens 100 disposed outside, and on a reflective polarizer side 51 of, the optical cavity 50. Specifically, in some embodiments, the folded optical lens assembly 300 further includes the third lens 100 disposed outside, and on the reflective polarizer side 51 of, the optical cavity 50. In some embodiments, the third lens 100 is a positive lens having a positive focal length F at the first visible wavelength. That is, in some embodiments, the third lens 100 has the positive focal length F at the wavelength range extending from about 420 nm to about 680 nm. In some embodiments, the positive focal length F is greater than about 20 mm and less than about 500 mm. In some embodiments, the positive focal length F is greater than about 30 mm, greater than about 40 mm, greater than about 50 mm, greater than about 60 mm, greater than about 70 mm, greater than about 80 mm, greater than about 90 mm, or greater than about 100 mm, and less than about 450 mm, less than about 400 mm, less than about 350 mm, less than about 300 mm, less than about 250 mm, less than about 200 mm, or less than about 150 mm. In some embodiments, the positive focal length F may be about 303.6 mm, about 142.8 mm, about 134.9 mm, or about 79.5 mm. The third lens 100 includes opposing major first and second surfaces 101, 102. In other words, the third lens 100 includes the major first surface 101 and the major second surface 102 that is opposite to the major first surface 101. In some embodiments, at least one of the major first and second surfaces 101, 102 may have a radius of curvature less than about 300 mm. In some embodiments, the radius of curvature of the at least one of the major first and second surfaces 101, 102 may be less than about 250 mm, less than about 200 mm, less than about 150 mm, less than about 100 mm, or less than about 50 mm. The major first surface 101 may have the radius of curvature less than about 300 mm. Further, in some embodiments, one of the major first and second surfaces 101, 102 of the third lens 100 may be substantially planar. As shown in FIG.1A, the major second surface 102 of the third lens 100 may be substantially planar. In some embodiments, the partial reflector 30 is disposed on, and substantially conforms to, the major first surface 71 of the positive lens 70. Further, in some embodiments, the reflective polarizer 40 is disposed on, and substantially conforms to, the major first surface 101 of the third lens 100. In some embodiments, the folded optical lens assembly 300 further includes a retarder layer 90 disposed in the optical cavity 50. The retarder layer 90 is configured to change a phase of a normally incident light having the at least the first visible wavelength by at least 40 degrees. In some embodiments, the retarder layer 90 may be configured to change the phase of the normally incident light having the at least the first visible wavelength by at least 50 degrees, at least 60 degrees, at least 70 degrees, at least 80 degrees, or at least 90 degrees. In the illustrated embodiment of FIG. 1A, the retarder layer 90 is disposed between the reflective polarizer 40 and the negative lens 80. In some other embodiments, the retarder layer 90 may be disposed between the positive lens 70 and the negative lens 80, as will be described with reference to FIG.3. The positive lens 70, the negative lens 80, and the third lens 100 may be made from any suitable material as per desired application attributes. In some embodiments, the positive lens 70 may include a polymethyl methacrylate (PMMA). In some embodiments, the negative lens 80 includes a polycarbonate (PC). In some embodiments, the negative lens 80 includes a PMMA or a crown glass. In some embodiments, the positive and negative lenses 70, 80 have substantially a same composition. For example, each of the positive and negative lenses 70, 80 may include a PMMA. In some embodiments, the positive and negative lenses 70, 80 have two different compositions. For example, the positive lens 70 may include a PMMA and the negative lens 80 may include a PC. In some embodiments, the third lens 100 includes a PMMA. FIG.3 illustrates a schematic view of a folded optical lens assembly 310, according to another embodiment of the present disclosure. The folded optical lens assembly 310 is substantially similar to the folded optical lens assembly 300 of FIG. 1A, with like elements designated by like reference characters. Some elements of the optical system 400 shown in FIG.1A are also shown in FIG.3. The folded optical lens assembly 310 has a different configuration of the retarder layer 90 than that of the folded optical lens assembly 300. Specifically, in the illustrated embodiment of FIG.3, the retarder layer 90 is disposed between the positive lens 70 and the negative lens 80. In some embodiments, the retarder layer 90 is bonded to both the positive lens 70 and the negative lens 80. In some embodiments, the optical system 400 includes the folded optical lens assembly 310. FIGS.4 and 5 illustrate schematic views of the optical system 400 with an imaging system 110 positioned proximate the eye-location 21 and the field stop 14 on the eye-side 410 of the optical system 400 in first and second orientations 118, 119, respectively, according to an embodiment of the present disclosure. Specifically, FIG. 4 illustrates the optical system 400 with the imaging system 110 in the first orientation 118 and FIG. 5 illustrates the optical system 400 with the imaging system 110 in the second orientation 119. Referring to FIGS. 4 and 5, in some embodiments, the imaging system 110 includes one or more of a complementary metal oxide semiconductor (CMOS) camera and a charge-coupled device (CCD) camera. In some embodiments, the imaging system 110 includes a pixelated image sensor comprising a two-dimensional array of photosensing pixels. In some embodiments, the imaging system 110 has a higher resolution than the display 10. FIGS. 6A-6E illustrate schematic views of different examples of the folded optical lens assembly 300 with some components not shown for illustrative purposes, according to an embodiment of the present disclosure. Specifically, the partial reflector 30 and the reflective polarizer 40 are not shown in FIGS.6A-6E. In particular, FIG.6A illustrates a folded optical lens assembly 610, FIG.6B illustrates a folded optical lens assembly 620, FIG.6C illustrates a folded optical lens assembly 630, FIG.6D illustrates a folded optical lens assembly 640, FIG. 6E illustrates a folded optical lens assembly 650. FIG. 6F illustrates a schematic view of a comparative lens assembly 660. The comparative lens assembly 660 includes a positive lens 70’ and a lens 100’. The comparative lens assembly 660 does not include any negative lens. Table 1 provided below includes various parameters of the positive lens 70 for the different examples of the folded optical lens assembly 300 illustrated in FIGS.6A-6E. Table 1 further includes various parameters of the positive lens 70’ of the comparative lens assembly 660 illustrated in FIGS. 6F. Table 1 R1a Example R1b (mm) n1 (540 nm) Fp (mm) Ap Material (mm) Folded Optical Lens 51.9 NA 1.49 105 107.1 PMMA Assembly 610 Folded Optical Lens 56.3 NA 1.49 114.0 107.1 PMMA Assembly 620 Folded Optical Lens 47.4 NA 1.49 96 107.1 PMMA Assembly 630 Folded Optical Lens 34.7 NA 1.49 70.3 107.1 PMMA Assembly 640 Folded Optical Lens 78.2 NA 1.49 158.4 107.1 PMMA Assembly 650 Comparative Lens 74.3 infinity 1.52 143.2 120.9 BK7 Assembly 660 Where, for the folded optical lens assemblies 610, 620, 630, 640, 650, R1a is the radius of curvature of one of the major surfaces (e.g., the major first surface 71) of the positive lens 70, R1b is the radius of curvature of the other of the major surfaces (e.g., the major second surface 72) of the positive lens 70, and n1 is a refractive index of the positive lens 70 at 540 nm. Further, for the comparative lens assembly 660, R1a is the radius of curvature of one of the major surfaces of the positive lens 70’, R1b is the radius of curvature of the other of the major surfaces of the positive lens 70’, and n3 is a refractive index of the positive lens 70’ at 540 nm. Table 2 below includes various parameters of the negative lens 80 for the different examples of the folded optical lens assembly 300 illustrated in FIGS.6A-6E. Table 2 R2a Example R2b (mm) n2 (540 nm) Fn (mm) An Material (mm) Folded Optical Lens NA -81.8 1.59 -138.4 55.3 PC Assembly 610 Folded Optical Lens NA -89.7 1.59 -151.9 55.3 PC Assembly 620 Folded Optical Lens NA -73.8 1.59 -125.0 55.3 PC Assembly 630 Folded Optical Lens NA -49.8 1.59 -84.3 55.3 PC Assembly 640 Folded Optical Lens NA -89.1 1.59 -145.8 55.3 PC Assembly 650 Comparative Lens NA Assembly 660 Where, R2a is the radius of curvature of the major first surface 81 of the negative lens 80, R2b is the radius of curvature of the major second surface 82 of the negative lens 80, and n2 is a refractive index of the negative lens 80 at 540 nm. Table 3 below includes various parameters of the third lens 100 for the different examples of the folded optical lens assembly 300 illustrated in FIGS. 6A-6E. Table 3 further includes various parameters of the lens 100’ of the comparative lens assembly 660 illustrated in FIGS.6F. Table 3 R3a Example R3b (mm) n3 (540 nm) F (mm) Abbe No. Material (mm) Folded Optical Lens 70.5 NA 1.49 142.8 107.1 PMMA Assembly 610 Folded Optical Lens 77.9 infinity 1.49 157.7 107.1 PMMA Assembly 620 Folded Optical Lens 63.8 infinity 1.49 129.1 107.1 PMMA Assembly 630 Folded Optical Lens 39.3 NA 1.49 79.5 107.1 PMMA Assembly 640 Folded Optical Lens 200 infinity 1.49 404.7 107.1 PMMA Assembly 650 Comparative Lens 200 400 1.49 269.8 107.1 PMMA Assembly 660 Where, for the folded optical lens assemblies 610, 620, 630, 640, 650, R3a is the radius of curvature of one of the major surfaces (e.g., the major first surface 101) of the third lens 100, R3b is the radius of curvature of the other of the major surfaces (e.g., the major second surface 102) of the third lens 100, and n3 is a refractive index of the third lens 100 at 540 nm. Further, for the comparative lens assembly 660, R3a is the radius of curvature of one of the major surfaces of the lens 100’, R3b is the radius of curvature of the other of the major surfaces of the lens 100’, and n3 is a refractive index of the lens 100’ at 540 nm. Table 4 below includes the ratio of Ap / An and the ratio of Fn / Fp for the different examples of the folded optical lens assembly 300 illustrated in FIGS.6A-6E. Table 4 Example Ap / An Fn / Fp Folded Optical Lens Assembly 610 1.9 1.3 Folded Optical Lens Assembly 620 1.9 1.3 Folded Optical Lens Assembly 630 1.9 1.3 Folded Optical Lens Assembly 640 1.9 1.2 Folded Optical Lens Assembly 650 1.9 0.9 Comparative Lens Assembly 660 NA FIGS. 7, 8, and 9 illustrate graphs 700, 900 depicting variations of a tangential modulation transfer function and a sagittal modulation transfer function of the different examples (i.e., the folded optical lens assemblies 610, 620, 630, 640, 650) of the folded optical lens assembly 300 with respect to a field angle, according to an embodiment of the present disclosure. The field angle is expressed in degrees (Deg) in the abscissa. A modulation transfer function (MTF) is expressed in the ordinate. Specifically, FIGS. 7 and 8 illustrate the graph 700 depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of the different examples of the folded optical lens assembly 300 with respect to the field angle in the first orientation 118 of the imaging system 110 shown in FIG. 4. FIG.9 illustrates the graph 900 depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of the different examples of the folded optical lens assembly 300 with respect to the field angle in the second orientation 119 of the imaging system 110 shown in FIG.5. The graph 700 includes a curve 702 depicting the tangential modulation transfer function of the folded optical lens assembly 610 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 704 depicting the tangential modulation transfer function of the folded optical lens assembly 620 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 706 depicting the tangential modulation transfer function of the folded optical lens assembly 630 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 708 depicting the tangential modulation transfer function of the folded optical lens assembly 640 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 710 depicting the tangential modulation transfer function of the folded optical lens assembly 650 with respect to the field angle in the first orientation 118 of the imaging system 110, and a curve 712 depicting the tangential modulation transfer function of the comparative lens assembly 660 with respect to the field angle in the first orientation 118 of the imaging system 110. The graph 700 further includes a curve 752 depicting the sagittal modulation transfer function of the folded optical lens assembly 610 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 754 depicting the sagittal modulation transfer function of the folded optical lens assembly 620 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 756 depicting the sagittal modulation transfer function of the folded optical lens assembly 630 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 758 depicting the sagittal modulation transfer function of the folded optical lens assembly 640 with respect to the field angle in the first orientation 118 of the imaging system 110, a curve 760 depicting the sagittal modulation transfer function of the folded optical lens assembly 650 with respect to the field angle in the first orientation 118 of the imaging system 110, and a curve 762 depicting the sagittal modulation transfer function of the comparative lens assembly 660 with respect to the field angle in the first orientation 118 of the imaging system 110. Referring now to FIGS. 1A, 4, and 7, in some embodiments, the optical system 400 is configured to display the virtual image 13 of the formed image 11 for viewing by the eye 20 when the eye 20 is positioned proximate the eye-location 21 on the eye-side 410 of the optical system 400. In the first orientation 118, the imaging system axis 111 makes a first angle of less than about 5 degrees with the optical system axis 401. Specifically, the imaging system 110 is centered on the imaging system axis 111 (shown in FIG.5) positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle of less than about 5 degrees with the optical system axis 401. Further, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle with the optical system axis 401, and the imaging system 110 forms a captured image 112 (interchangeably referred to as “the first captured image 112”) of the virtual image 13, then, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for each first field angle F1 in a continuous first field angle range 120 that is at least 5 degrees wide and is disposed at field angles greater than about 15 degrees, an average tangential modulation transfer function Tavg of the captured image 112 averaged over a first wavelength range that is at least 30 nm wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.15. For example, as is apparent from the curves 702, 704, 706, 708, 710, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle with the optical system axis 401, and the imaging system 110 forms the captured image 112 of the virtual image 13, then for the at least one spatial frequency and for each first field angle F1 in the continuous first field angle range 120, the average tangential modulation transfer function Tavg of the captured image 112 averaged over the first wavelength range ranges from M1a to M1b, and is greater than about 0.15 for each of the folded optical lens assemblies 610, 620, 630, 640, 650. In some embodiments, the first angle may be less than about 4 degrees, less than about 3 degrees, less than about 2 degrees, less than about 1 degree, or less than about 0.5 degrees. In the illustrated embodiment of FIG.4, the first angle is 0 degrees. In some embodiments, the at least one spatial frequency may be greater than 25 line pairs per millimeter or greater than 30 line pairs per millimeter. In some embodiments, the at least one spatial frequency may be 30 line pairs per millimeter. In some embodiments, the continuous first field angle range 120 may be at least 6 degrees, at least 7 degrees, at least 8 degrees, at least 9 degrees, or at least 10 degrees wide. In some embodiments, the continuous first field angle range 120 may be about 6 degrees wide and range from about 16 degrees to about 22 degrees. In some embodiments, the first wavelength range may be at least 40 nm, at least 50 nm, at least 60 nm, at or least 70 nm wide. In some embodiments, the first wavelength range may be 70 nm wide. In some embodiments, the first wavelength range may extend from about 500 nm to about 570 nm. In some embodiments, for the at least one spatial frequency and for each first field angle F1 in the continuous first field angle range 120, the Tavg of the captured image 112 averaged over the first wavelength range may be greater than about 0.2, greater than about 0.25, greater than about 0.3, greater than about 0.35, greater than about 0.4, greater than about 0.45, greater than about 0.5, greater than about 0.55, greater than about 0.6, greater than about 0.65, greater than about 0.7, greater than about 0.75, or greater than about 0.8. On the other hand, as is apparent from the curve 712, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle with the optical system axis 401, and the imaging system 110 forms the captured image 112 of the virtual image 13, then for the at least one spatial frequency and for each first field angle F1 in the continuous first field angle range 120, the average tangential modulation transfer function Tavg of the captured image 112 averaged over the first wavelength range is less than about 0.15 for the comparative lens assembly 660. In some embodiments, for the at least one spatial frequency and for at least one second field angle F2 (interchangeably referred to as “the field angle F2”) greater than about 30 degrees, the Tavg of the captured image 112 averaged over the first wavelength range is greater than about 0.15. For example, as is apparent from the curves 702, 704, 706, 708, for the at least one spatial frequency and for at least one second field angle F2 greater than about 30 degrees, the Tavg of the captured image 112 averaged over the first wavelength range ranges from M1 to M2 and is greater than about 0.15 for each of the folded optical lens assemblies 610, 620, 630, 640. In some embodiments, the at least one second field angle F2 may be greater than about 35 degrees, greater than about 40 degrees, or greater than about 45 degrees. In some embodiments, the at least one second field angle F2 may be about 37 degrees. In some embodiments, for the at least one spatial frequency and for the at least one second field angle F2, the Tavg of the captured image 112 averaged over the first wavelength range may be greater than about 0.2, greater than about 0.25, greater than about 0.3, greater than about 0.35, greater than about 0.4, greater than about 0.45, greater than about 0.5, greater than about 0.55, greater than about 0.6, greater than about 0.65, greater than about 0.7, greater than about 0.75, or greater than about 0.8. On the other hand, as is apparent from the curve 712, for the at least one spatial frequency and for the at least one second field angle F2 greater than about 30 degrees, the Tavg of the captured image 112 averaged over the first wavelength range is about 0.5 for the comparative lens assembly 660. Referring to FIGS. 4 and 8, in some embodiments, for the at least one spatial frequency of greater than about 20 line pairs per millimeter and for each third field angle F3 in a continuous third field angle range 122 that is at least 5 degrees wide and is disposed at field angles greater than about 15 degrees, each of the Tavg and an average sagittal modulation transfer function Savg of the captured image 112 averaged over the first wavelength range is greater than about 0.7. For example, as is apparent from the curves 706, 756, for the at least one spatial frequency and for each third field angle F3 in the continuous third field angle range 122, each of the Tavg (i.e., a Tavg M3a) and the Savg (i.e., a Savg M3b) of the captured image 112 averaged over the first wavelength range is greater than about 0.7 for the folded optical lens assembly 630. In some embodiments, the continuous third field angle range 122 may be at least 10 degrees wide or at least 15 degrees wide. In some embodiments, the continuous third field angle range 122 may be about 15 degrees wide and between 20 degrees and 35 degrees. In some embodiments, for the at least one spatial frequency and for each third field angle F3 in the continuous third field angle range 122, each of the Tavg and the Savg of the captured image 112 averaged over the first wavelength range may be greater than about 0.75. For example, as is apparent from the curves 702, 752, for the at least one spatial frequency and for each third field angle F3 in the continuous third field angle range 122, each of the Tavg and the Savg of the captured image 112 averaged over the first wavelength range may be greater than about 0.75 for the folded optical lens assembly 610. On the other hand, as is apparent from the curves 712, 762, for the at least one spatial frequency and for each third field angle F3 in the continuous third field angle range 122, each of the Tavg and the Savg of the captured image 112 averaged over the first wavelength range is less than or equal to about 0.7 for the comparative lens assembly 660. Specifically, for the at least one spatial frequency and for each third field angle F3 in the continuous third field angle range 122, the Tavg of the captured image 112 averaged over the first wavelength range is less than or equal to about 0.1 for the comparative lens assembly 660 and for the at least one spatial frequency and for each third field angle F3 in the continuous third field angle range 122, the Savg of the captured image 112 averaged over the first wavelength range is less than or equal to about 0.7 for the comparative lens assembly 660. Since, for the at least one spatial frequency and for greater field angles (i.e., greater than about 15 degrees), the Tavg of the captured image 112 averaged over the first wavelength range of the folded optical lens assembly 300 is greater than that of the comparative lens assembly 660, the folded optical lens assembly 300 may provide a higher contrast of the captured image 112 for field angles greater than about 15 degrees than the comparative lens assembly 660. The graph 900 includes a curve 902 depicting the tangential modulation transfer function of the folded optical lens assembly 610 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 904 depicting the tangential modulation transfer function of the folded optical lens assembly 620 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 906 depicting the tangential modulation transfer function of the folded optical lens assembly 630 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 908 depicting the tangential modulation transfer function of the folded optical lens assembly 640 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 910 depicting the tangential modulation transfer function of the folded optical lens assembly 650 with respect to the field angle in the second orientation 119 of the imaging system 110, and a curve 912 depicting the tangential modulation transfer function of the comparative lens assembly 660 with respect to the field angle in the second orientation 119 of the imaging system 110. The graph 900 further includes a curve 952 depicting the sagittal modulation transfer function of the folded optical lens assembly 610 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 954 depicting the sagittal modulation transfer function of the folded optical lens assembly 620 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 956 depicting the sagittal modulation transfer function of the folded optical lens assembly 630 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 958 depicting the sagittal modulation transfer function of the folded optical lens assembly 640 with respect to the field angle in the second orientation 119 of the imaging system 110, a curve 960 depicting the sagittal modulation transfer function of the folded optical lens assembly 650 with respect to the field angle in the second orientation 119 of the imaging system 110, and a curve 962 depicting the sagittal modulation transfer function of the comparative lens assembly 660 with respect to the field angle in the second orientation 119 of the imaging system 110. Now referring to FIGS. 1A, 5, and 9, in the second orientation 119, the imaging system axis 111 makes a first angle θ1 (interchangeably referred to as “the second angle θ1”) of greater than about 10 degrees and less than about 30 degrees with the optical system axis 401. Specifically, the eye 20 is centered on the eye-axis 23 including the center of rotation 22 of the eye 20, such that when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 passes through the center of rotation 22 of the eye 20 and makes the first angle θ1 with the optical system axis 401, and the imaging system 110 forms a captured image 113 (interchangeably referred to as “the second captured image 113”) of the virtual image 13, then, for the at least one spatial frequency and for each first field angle T1 in a continuous first field angle range 121 that is at least 5 degrees wide and is disposed between a field angle of about 5 degrees to a field angle of about 30 degrees, an Tavg of the captured image 113 averaged over the first wavelength range that is at least 30 nm and is disposed in the wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.2. For example, as is apparent from the curves 902, 904, 906, 908, 910, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle θ1 with the optical system axis 401, and the imaging system 110 forms the captured image 113 of the virtual image 13, then for the at least one spatial frequency and for each first field angle T1 in the continuous first field angle range 121, the Tavg of the captured image 113 averaged over the first wavelength range ranges from N1a to N1b, and is greater than about 0.2 for each of the folded optical lens assemblies 610, 620, 630, 640, 650. In some embodiments, the first angle θ1 may be greater than about 11 degrees, greater than about 12 degrees, greater than about 13 degrees, greater than about 14 degrees, or greater than about 15 degrees and less than about 25, less than about 20 degrees, or less than about 15 degrees. In some embodiments, the first angle θ1 may be 15 degrees. In some embodiments, the continuous first field angle range 121 may be at least 7 degrees, at least 9 degrees, at least 11 degrees, or at least 13 degrees wide. In some embodiments, the continuous first field angle range 121 may be about 13 degrees wide and range from 9 degrees to 22 degrees. In some embodiments, for the at least one spatial frequency and for each first field angle T1 in the continuous first field angle range 121, the Tavg of the captured image 113 averaged over the first wavelength range may be greater than about 0.25, greater than about 0.3, greater than about 0.35, greater than about 0.4, greater than about 0.45, greater than about 0.5, greater than about 0.55, greater than about 0.6, greater than about 0.65, greater than about 0.7, or greater than about 0.75. On the other hand, as is apparent from the curve 912, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle θ1 with the optical system axis 401, and the imaging system 110 forms the captured image 113 of the virtual image 13, then for the at least one spatial frequency and for each first field angle T1 in the continuous first field angle range 121, the Tavg of the captured image 113 averaged over the first wavelength range is less than about 0.2 for the comparative lens assembly 660. In some embodiments, for the at least one spatial frequency and for each second field angle in a continuous second field angle range 123 that extends from about 5 degrees to at least about 25 degrees, the Tavg of the captured image 113 averaged over the first wavelength range is greater than about 0.6. For example, as is apparent from the curve 902, for the at least one spatial frequency and for each second field angle in the continuous second field angle range 123, the Tavg of the captured image 113 averaged over the first wavelength range is greater than about 0.6 for the folded optical lens assembly 610. In some embodiments, the continuous second field angle range 123 may extend from about 5 degrees to at least about 30 degrees, or from about 5 degrees to at least about 35 degrees. Further, for the at least one spatial frequency and for each second field angle in the continuous second field angle range 123, the Tavg of the captured image 113 averaged over the first wavelength range may be greater than about 0.65, greater than about 0.7, greater than about 0.75, greater than about 0.8, or greater than about 0.85. On the other hand, as is apparent from the curve 912, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle θ1 with the optical system axis 401, and the imaging system 110 forms the captured image 113 of the virtual image 13, then for the at least one spatial frequency and for each second field angle in the continuous second field angle range 123, the Tavg of the captured image 113 averaged over the first wavelength range is less than about 0.6 (i.e., less than about 0.2) for the comparative lens assembly 660. In some embodiments, for the at least one spatial frequency and for each third field angle in a continuous third field angle range 124 that extends from about 10 degrees to at least about 25 degrees, the Tavg of the captured image 113 averaged over the first wavelength range is greater than about 0.2. For example, as is apparent from the curves 902, 904, 906, 908, for the at least one spatial frequency and for each third field angle in the continuous third field angle range 124, the Tavg of the captured image 113 averaged over the first wavelength range is greater than about 0.2 for each of the folded optical lens assemblies 610, 620, 630, 640. In some embodiments, the continuous third field angle range 124 may extend from about 10 degrees to at least about 30 degrees or from about 10 degrees to at least about 35 degrees. Further, in some embodiments, for the at least one spatial frequency and for each third field angle in the continuous third field angle range 124, the Tavg of the captured image 113 averaged over the first wavelength range may be greater than about 0.25, greater than about 0.3, greater than about 0.35, greater than about 0.4, greater than about 0.45, greater than about 0.5, greater than about 0.55, or greater than about 0.6. On the other hand, as is apparent from the curve 912, when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 makes the first angle θ1 with the optical system axis 401, and the imaging system 110 forms the captured image 113 of the virtual image 13, then for the at least one spatial frequency and for each third field angle in the continuous third field angle range 124, the Tavg of the captured image 113 averaged over the first wavelength range is less than about 0.2 (i.e., about 0.1) for the comparative lens assembly 660. Referring to FIGS.1A, 4, 5, 6A-6F, and 7-9, in some embodiments, the optical system 400 is configured to display the virtual image of the formed image 11 for viewing by the eye 20 when the eye 20 is positioned proximate the eye-location 21 on the eye-side 410 of the optical system 400, the eye 20 centered on the eye-axis 23 including the center of rotation 22 of the eye 20, such that when the imaging system 110 centered on the imaging system axis 111 is positioned proximate the eye-location 21 so that the imaging system axis 111 passes through the center of rotation 22 of the eye 20 and in the first orientation 118, the imaging system axis 111 makes the first angle with the optical system axis 401, and in the second orientation 119, the imaging system axis 111 makes the second angle θ1 with the optical system axis 401, and the imaging system 110 forms the first and second captured images 112, 113 of the virtual image 13 in the respective first and second orientations 118, 119, then for each of the first and second orientations 118, 119, for the at least one spatial frequency and for at least one field angle F2, T2 greater than about 30 degrees, the Tavg of the captured image 112, 113 averaged over the first wavelength range, is greater than about 0.2. In other words, in some embodiments, for the at least one spatial frequency and for the at least one field angle F2, the Tavg of the captured image 112 averaged over the first wavelength range is greater than about 0.2. As is apparent from the curves 702, 704, 706, for the at least one spatial frequency and for at least one field angle F2, the Tavg of the captured image 112 averaged over the first wavelength range is greater than about 0.2 for each of the folded optical lens assemblies 610, 620, 630. For example, as is apparent from the curve 704 for the folded optical lens assembly 620, for the at least one spatial frequency and for at least one field angle F2, the Tavg (i.e., a Tavg M3) of the captured image 112 averaged over the first wavelength range is greater than about 0.2. In some embodiments, for the at least one spatial frequency and for the at least one field angle F2, the Tavg M3 of the captured image 112 averaged over the first wavelength range may be about 0.63. Further, in some embodiments, for the at least one spatial frequency and for the at least one field angle T2, the Tavg of the captured image 113 averaged over the first wavelength range is greater than about 0.2. As is apparent from the curves 902, 904, 906, 908, for the at least one spatial frequency and for the at least one field angle T2, the Tavg of the captured image 113 averaged over the first wavelength range is greater than about 0.2 for each of the folded optical lens assemblies 610, 620, 630, 640. For example, as is apparent from the curve 904 for the folded optical lens assembly 620, for the at least one spatial frequency and for at least one field angle T2, the Tavg (i.e., the Tavg N2) of the captured image 113 averaged over the first wavelength range is greater than about 0.2. In some embodiments, for the at least one spatial frequency and for the at least one field angle T2, the Tavg N2 of the captured image 113 averaged over the first wavelength range may be about 0.42. In some embodiments, the at least one field angle F2, T2 may be greater than about 31, greater than about 32, greater than about 33, greater than about 34, greater than about 35, greater than about 36, or greater than about 37 degrees. In some embodiments, the at least one field angle F2 may be 37 degrees and the at least one angle T2 may be about 35 degrees. In some embodiments, for the at least one spatial frequency and for the at least one field angle F2, the Tavg of the captured image 112 averaged over the first wavelength range may be greater than about 0.25, greater than about 0.3, greater than about 0.35, greater than about 0.4, greater than about 0.45, greater than about 0.5, greater than about 0.55, greater than about 0.6, greater than about 0.65, greater than about 0.7, greater than about 0.75, or greater than about 0.8. In some embodiments, for the at least one spatial frequency and for the at least one field angle T2, the Tavg of the captured image 113 averaged over the first wavelength range may be greater than about 0.25, greater than about 0.3, greater than about 0.35, greater than about 0.4, greater than about 0.45, greater than about 0.5, greater than about 0.55, greater than about 0.6, greater than about 0.65, greater than about 0.7, greater than about 0.75, or greater than about 0.8. FIG.10 illustrates a schematic view of the optical system 400 with the imaging system 110 and a substantially collimated light beam 130, according to an embodiment of the present disclosure. The collimated light beam 130 may be generated using a suitable optical device, such as a collimator (not shown). FIGS. 11A and 11B illustrate graphs 1100, 1150 depicting variations of the tangential modulation transfer function and the sagittal modulation transfer function of the comparative lens assembly 660 and the folded optical lens assembly 300, respectively, with respect to a spatial frequency. The spatial frequency is expressed in cycles per millimeter in the abscissa. The MTF is expressed in the ordinate. Specifically, FIG. 11A illustrates the graph 1100 depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of the comparative lens assembly 660 with respect to the spatial frequency. FIG.11B illustrates the graph 1150 depicting the variations of the tangential modulation transfer function and the sagittal modulation transfer function of the folded optical lens assembly 300 with respect to the spatial frequency. The graph 1100 includes a curve 1102 depicting the sagittal modulation transfer function of the comparative lens assembly 660 with respect to the spatial frequency. The graph 1100 further includes a curve 1104 depicting the tangential modulation transfer function of the comparative lens assembly 660 with respect to the spatial frequency. The graph 1150 includes a curve 1152 depicting the sagittal modulation transfer function of the folded optical lens assembly 300 with respect to the spatial frequency. The graph 1150 further includes a curve 1154 depicting the tangential modulation transfer function of the folded optical lens assembly 300 with respect to the spatial frequency. Referring to FIGS.10 and 11A-11B, in some embodiments, when the eye 20 (shown in FIGS. 1A and 1B) is positioned at or proximate the field stop 14 with the center of rotation 22 of the eye 20 disposed on the system axis 401, such that when the field stop 14 is rotated about the center of rotation 22 of the eye 20 by a rotation angle α1 of at least 15 degrees, and the substantially collimated light beam 130 that propagates along a first direction 131 and makes the rotation angle α1 with the system axis 401 and substantially fills the rotated field stop 14’ and focuses to a focal spot 132 substantially at the display image surface 12 after going through the optical cavity 50, and the positive and negative lenses 70, 80, then for at least one spatial frequency Q1 (shown in FIG. 11B) of greater than about 15 cycles per millimeter, each of average tangential and average sagittal modulation transfer functions T1avg, S1avg of the optical system 400 averaged over the first wavelength range that is at least 30 nm wide and is disposed in the wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.5. In some embodiments, the rotation angle α1 may be at least 20 degrees. In some embodiments, the rotation angle α1 may be about 20 degrees. In some embodiments, the at least one spatial frequency Q1 may be greater than about 20, greater than about 25, greater than about 30, or greater than about 35 cycles per millimeter. In some embodiments, the at least one spatial frequency Q1 may be about 22 cycles per millimeter. In some embodiments, for the rotated field stop 14’, the substantially collimated light beam 130, the focal spot 132, and for the at least one spatial frequency Q1, each of the average tangential and average sagittal modulation transfer functions T1avg, S1avg of the optical system 400 averaged over the first wavelength range may be greater than about 0.55, greater than about 0.6, greater than about 0.7, or greater than about 0.75. In some embodiments, for the rotated field stop 14’, the substantially collimated light beam 130, the focal spot 132, and for the at least one spatial frequency Q1, the T1avg averaged over the first wavelength range may be about 0.85 and the S1avg averaged over the first wavelength range may be about 0.75. In some embodiments, for the rotated field stop 14’, the substantially collimated light beam1 30, the focal spot 132, and for each spatial frequency between about 20 cycles per millimeter and at least about 40 cycles per millimeter, the T1avg averaged over the first wavelength range is greater than about 0.3. In some embodiments, for the rotated field stop 14’, the substantially collimated light beam 130, the focal spot 132, and for each spatial frequency between about 20 cycles per millimeter and at least about 45, at least about 50, or at least about 55 cycles per millimeter, the T1avg averaged over the first wavelength range may be greater than about 0.35, greater than about 0.40, greater than about 0.45, greater than about 0.50, greater than about 0.55, greater than about 0.60, or greater than about 0.65. On the other hand, as is apparent from the curve 1104, for the rotated field stop 14’, the substantially collimated light beam 130, the focal spot 132, and for each spatial frequency between about 20 cycles per millimeter and at least about 40 cycles per millimeter, the average tangential modulation transfer function T1avg the comparative lens assembly 660 averaged over the first wavelength range is less than about 0.3. Since the optical system 400 and the folded optical lens assemblies 300, 310 may provide, for each of the first and second orientations 118, 119, for the at least one spatial frequency and for the at least one field angle greater than about 30 degrees, an improved average tangential modulation transfer function Tavg of the captured image 112, 113 averaged over the first wavelength range than conventional optical lens assemblies (e.g., the comparative lens assembly 660), the optical system 400 and the folded optical lens assemblies 300, 310 may provide a higher contrast than conventional lens assemblies at higher field angles (i.e., greater than about 30 degrees). Further, the optical system 400 and the folded optical lens assemblies 300, 310 may provide a higher resolution, a lower chromatic aberration, a lower distortion, and / or a higher efficiency in a compact configuration that is useful in various applications, such as in the VR and AR applications compared to the conventional optical lens assemblies, especially at the higher field angles. Unless otherwise indicated, all numbers expressing feature sizes, amounts, and physical properties used in the specification and claims are to be understood as being modified by the term “about”. Accordingly, unless indicated to the contrary, the numerical parameters set forth in the foregoing specification and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by those skilled in the art utilizing the teachings disclosed herein. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and / or equivalent implementations can be substituted for the specific embodiments shown and described 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. Therefore, it is intended that this disclosure be limited only by the claims and the equivalents thereof.

Claims

CLAIMS What is claimed is:

1. A folded optical lens assembly configured to display a virtual image of an image formed and emitted by a display to an eye of a viewer and comprising: a partial reflector and a reflective polarizer spaced apart from each other and defining an optical cavity therebetween, such that for a substantially normally incident light having at least a first visible wavelength in a visible wavelength range extending from about 420 nm to about 680 nm, the partial reflector, for each of mutually orthogonal first and second polarization states, reflects at least 25% of the incident light and transmits at least 25% of the incident light, and the reflective polarizer reflects at least about 60% of the incident light having the first polarization state and transmits at least about 60% of the incident light having the second polarization state; and a positive lens and a negative lens disposed inside the optical cavity, the positive lens having an Abbe number having a magnitude Ap and a positive focal length Fp at the first visible wavelength, the negative lens having an Abbe number having a magnitude An and a negative focal length having a magnitude Fn at the first visible wavelength, wherein Fn / Fp ≥ Ap / An.

2. The folded optical lens assembly of claim 1, wherein Ap / An ≥ 1.

3. An optical system comprising an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, and a positive lens and a negative lens at least one of which is disposed inside the optical cavity, the display configured to form an image, the optical system configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned proximate an eye-location on an eye-side of the optical system, such that when an imaging system centered on an imaging system axis is positioned proximate the eye-location so that the imaging system axis makes a first angle of less than about 5 degrees with the optical system axis, and the imaging system forms a captured image of the virtual image, then, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for each first field angle in a continuous first field angle range that is at least 5 degrees wide and is disposed at field angles greater than about 15 degrees, an average tangential modulation transfer function Tavg of the captured image averaged over a first wavelength range that is at least 30 nm wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.

15.

4. The optical system of claim 3, wherein for the at least one spatial frequency of greater than about 20 line pairs per millimeter and for each third field angle in a continuous third field angle rangethat is at least 5 degrees wide and is disposed at field angles greater than about 15 degrees, each of the Tavg and an average sagittal modulation transfer function Savg of the captured image averaged over the first wavelength range is greater than about 0.

7.

5. An optical system comprising an optical system axis, a display, a partial reflector and a reflective polarizer defining an optical cavity therebetween, and a positive lens and a negative lens at least one of which is disposed inside the optical cavity, the display configured to form an image, the optical system configured to display a virtual image of the formed image for viewing by an eye when the eye is positioned proximate an eye-location on an eye-side of the optical system, the eye centered on an eye-axis comprising a center of rotation of the eye, such that when an imaging system centered on an imaging system axis is positioned proximate the eye-location so that the imaging system axis passes through the center of rotation of the eye and makes a first angle of greater than about 10 degrees and less than about 30 degrees with the optical system axis, and the imaging system forms a captured image of the virtual image, then, for at least one spatial frequency of greater than about 20 line pairs per millimeter and for each first field angle in a continuous first field angle range that is at least 5 degrees wide and is disposed between a field angle of about 5 degrees to a field angle of about 30 degrees, an average tangential modulation transfer function Tavg of the captured image averaged over a first wavelength range that is at least 30 nm wide and is disposed in a wavelength range extending from about 420 nm to about 680 nm, is greater than about 0.

2.

6. The optical system of claim 5, wherein the positive lens and the negative lens are both disposed inside the optical cavity.

7. The optical system of claim 5 further comprising a third lens disposed outside, and on a reflective polarizer side of, the optical cavity.

8. The optical system of claim 5, wherein the imaging system has a higher resolution than the display.

9. The optical system of claim 5, wherein for the at least one spatial frequency of greater than about 20 line pairs per millimeter and for each second field angle in a continuous second field angle range that extends from about 5 degrees to at least about 25 degrees, the Tavg of the captured image averaged over the first wavelength range is greater than about 0.

6.

10. The optical system of claim 5, wherein for the at least one spatial frequency of greater than about 20 line pairs per millimeter and for each third field angle in a continuous third field angle range that extends from about 10 degrees to at least about 25 degrees, the Tavg of the captured image averaged over the first wavelength range is greater than about 0.2.

Images