Patent Application
20220107517
The present disclosure generally relates to optical devices and systems and, more specifically, to an off-axis focusing geometric phase lens and a system including the same.
In a conventional optical system, in order to correct off-axis aberration, conventional lenses may be tilted at relatively large angles. The tilting configuration of the conventional lenses may increase the size of the optical system. Diffractive off-axis focusing lenses can provide off-axis focusing without tilting, or with tilting at smaller angles as compared with the conventional lenses. Thus, diffractive off-axis focusing lenses may reduce a forma factor of the optical system. Moreover, diffractive off-axis focusing lenses may perform two or more functions simultaneously, such as deflection, focusing, spectral and polarization selection of light. Geometric phase (“GP”) lenses (also referred to as Pancharatnam-Berry phase (“PBP”) lenses) may be formed in an optically anisotropic material layer with an intrinsic or induced (e.g., photo-induced) optical anisotropy. The optically anisotropic material may be liquid crystals, liquid crystal polymers, or metasurfaces. In the optically anisotropic material, a desirable lens phase profile may be directly encoded into a local orientation of an optic axis of the optically anisotropic material layer. GP or PBP lenses modulate a circularly polarized light based on a lens phase profile provided through the geometric phase. PBP lenses may be flat or curved diffractive lenses sensitive to handedness of a circularly polarized incident light or an elliptically polarized incident light. PBP lenses may be switchable between a focusing state and a defocusing state by reversing the handedness of a circularly polarized incident light.
One aspect of the present disclosure provides a lens. The lens includes an optically anisotropic film. The optically anisotropic film has an optic axis configured with an in-plane rotation in at least two opposite in-plane directions from a lens pattern center to opposite lens peripheries. The optic axis rotates in a same rotation direction from the lens pattern center to the opposite lens peripheries. An azimuthal angle changing rate of the optic axis is configured to increase from the lens pattern center to the opposite lens peripheries in at least a portion of the lens including the lens pattern center. The lens pattern center is shifted from a geometry center of the lens by a predetermined distance in a predetermined direction.
Another aspect of the present disclosure provides a system. The system includes an optical combiner. The system also includes a display assembly. The display assembly includes a light source configured to emit a light. The lens includes an optically anisotropic film. The optically anisotropic film has an optic axis configured with an in-plane rotation in at least two opposite in-plane directions from a lens pattern center to opposite lens peripheries. The optic axis rotates in a same rotation direction from the lens pattern center to the opposite lens peripheries. An azimuthal angle changing rate of the optic axis is configured to increase from the lens pattern center to the opposite lens peripheries in at least a portion of the lens including the lens pattern center. The lens pattern center is shifted from a geometry center of the lens by a predetermined distance in a predetermined direction. The display assembly also includes a beam steering device configured to steer the light received from the lens toward the optical combiner. The optical combiner is configured to direct the light received from the beam steering device to an eye-box of the system.
Another aspect of the present disclosure provides a system. The system includes a light source configured to emit a light. The system also includes a lens configured to deflect the light to illuminate an object. The lens includes an optically anisotropic film. The optically anisotropic film has an optic axis configured with an in-plane rotation in at least two opposite in-plane directions from a lens pattern center to opposite lens peripheries. The optic axis rotates in a same rotation direction from the lens pattern center to the opposite lens peripheries. An azimuthal angle changing rate of the optic axis is configured to increase from the lens pattern center to the opposite lens peripheries in at least a portion of the lens including the lens pattern center. The lens pattern center is shifted from a geometry center of the lens by a predetermined distance in a predetermined direction. The system also includes a redirecting element configured to redirect the light reflected by the object. The system further includes an optical sensor configured to generate an image of the object based the redirected light received from the redirecting element.
Other aspects of the present disclosure can be understood by those skilled in the art in light of the description, the claims, and the drawings of the present disclosure.
The accompanying drawings are provided for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present disclosure. In the drawings:
Embodiments consistent with the present disclosure will be described with reference to the accompanying drawings, which are merely examples for illustrative purposes and are not intended to limit the scope of the present disclosure. Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or similar parts, and a detailed description thereof may be omitted.
Further, in the present disclosure, the disclosed embodiments and the features of the disclosed embodiments may be combined. The described embodiments are some but not all of the embodiments of the present disclosure. Based on the disclosed embodiments, persons of ordinary skill in the art may derive other embodiments consistent with the present disclosure. For example, modifications, adaptations, substitutions, additions, or other variations may be made based on the disclosed embodiments. Such variations of the disclosed embodiments are still within the scope of the present disclosure. Accordingly, the present disclosure is not limited to the disclosed embodiments. Instead, the scope of the present disclosure is defined by the appended claims.
As used herein, the terms “couple,” “coupled,” “coupling,” or the like may encompass an optical coupling, a mechanical coupling, an electrical coupling, an electromagnetic coupling, or a combination thereof. An “optical coupling” between two optical elements refers to a configuration in which the two optical elements are arranged in an optical series, and a light output from one optical element may be directly or indirectly received by the other optical element. An optical series refers to optical positioning of a plurality of optical elements in a light path, such that a light output from one optical element may be transmitted, reflected, diffracted, converted, modified, or otherwise processed or manipulated by one or more of other optical elements. In some embodiments, the sequence in which the plurality of optical elements are arranged may or may not affect an overall output of the plurality of optical elements. A coupling may be a direct coupling or an indirect coupling (e.g., coupling through an intermediate element).
The phrase “at least one of A or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “at least one of A, B, or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C. The phrase “A and/or B” may be interpreted in a manner similar to that of the phrase “at least one of A or B.” For example, the phrase “A and/or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “A, B, and/or C” has a meaning similar to that of the phrase “at least one of A, B, or C.” For example, the phrase “A, B, and/or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C.
When a first element is described as “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in a second element, the first element may be “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in the second element using any suitable mechanical or non-mechanical manner, such as depositing, coating, etching, bonding, gluing, screwing, press-fitting, snap-fitting, clamping, etc. In addition, the first element may be in direct contact with the second element, or there may be an intermediate element between the first element and the second element. The first element may be disposed at any suitable side of the second element, such as left, right, front, back, top, or bottom.
When the first element is shown or described as being disposed or arranged “on” the second element, term “on” is merely used to indicate an example relative orientation between the first element and the second element. The description may be based on a reference coordinate system shown in a figure, or may be based on a current view or example configuration shown in a figure. For example, when a view shown in a figure is described, the first element may be described as being disposed “on” the second element. It is understood that the term “on” may not necessarily imply that the first element is over the second element in the vertical, gravitational direction. For example, when the assembly of the first element and the second element is turned 180 degrees, the first element may be “under” the second element (or the second element may be “on” the first element). Thus, it is understood that when a figure shows that the first element is “on” the second element, the configuration is merely an illustrative example. The first element may be disposed or arranged at any suitable orientation relative to the second element (e.g., over or above the second element, below or under the second element, left to the second element, right to the second element, behind the second element, in front of the second element, etc.).
The term “communicatively coupled” or “communicatively connected” indicates that related items are coupled or connected through an electrical and/or electromagnetic coupling or connection, such as a wired or wireless communication connection, channel, or network.
The wavelength ranges, spectra, or bands mentioned in the present disclosure are for illustrative purposes. The disclosed optical device, system, element, assembly, and method may be applied to a visible wavelength range, as well as other wavelength ranges, such as an ultraviolet (“UV”) wavelength range, an infrared wavelength range, or a combination thereof.
The term “processor” used herein may encompass any suitable processor, such as a central processing unit (“CPU”), a graphics processing unit (“GPU”), an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or a combination thereof. Other processors not listed above may also be used. A processor may be implemented as software, hardware, firmware, or a combination thereof.
The term “controller” may encompass any suitable electrical circuit, software, or processor configured to generate a control signal for controlling a device, a circuit, an optical element, etc. A “controller” may be implemented as software, hardware, firmware, or a combination thereof. For example, a controller may include a processor, or may be included as a part of a processor.
The term “object-tracking system,” “object-tracking device,” “eye-tracking system,” or “eye-tracking device” may include suitable elements configured to obtain eye-tracking information, or to obtain sensor data for determining eye-tracking information. For example, the object-tracking (e.g., eye-tracking) system or device may include one or more suitable sensors (e.g., an optical sensor, such as a camera, motion sensors, etc.) to capture sensor data (e.g., images) of a tracked object (e.g., an eye of a user). In some embodiments, the object-tracking (e.g., eye-tracking) system or device may include a light source configured to emit a light to illuminate the tracked object (e.g., the eye of the user). The object-tracking (e.g., eye-tracking) system or device may also include a processor or controller configured to process the sensor data (e.g., the images) of the tracked object (e.g., the eye of the user) to obtain object-tracking information (e.g., eye-tracking information). The processor or controller may provide the object-tracking (e.g., eye-tracking) information to another device, or may process the object-tracking (e.g., eye-tracking) information to control another device, such as a grating, a lens, a waveplate, etc. The object-tracking (e.g., eye-tracking) system or device may also include a non-transitory computer-readable medium, such as a memory, configured to store computer-executable instructions, and sensor data or information, such as the captured image and/or the object-tracking (e.g., eye-tracking) information obtained from processing the captured image. In some embodiments, the object-tracking (e.g., eye-tracking) system or device may transmit the sensor data to another processor or controller (e.g., a processor of another device, such as a cloud-based device) for determining the object-tracking (e.g., eye-tracking) information.
The term “non-transitory computer-readable medium” may encompass any suitable medium for storing, transferring, communicating, broadcasting, or transmitting data, signal, or information. For example, the non-transitory computer-readable medium may include a memory, a hard disk, a magnetic disk, an optical disk, a tape, etc. The memory may include a read-only memory (“ROM”), a random-access memory (“RAM”), a flash memory, etc.
As used herein, the term “liquid crystal compound” or “mesogenic compound” may refer to a compound including one or more calamitic (rod- or board/lath-shaped) or discotic (disk-shaped) mesogenic groups. The term “mesogenic group” may refer to a group with the ability to induce liquid crystalline phase (or mesophase) behavior. In some embodiments, the compounds including mesogenic groups may not exhibit a liquid crystal (“LC”) phase themselves. Instead, the compounds may exhibit the LC phase when mixed with other compounds. In some embodiments, the compounds may exhibit the LC phase when the compounds, or the mixture containing the compounds, are polymerized. For simplicity of discussion, the term “liquid crystal” is used hereinafter for both mesogenic and LC materials. In some embodiments, a calamitic mesogenic group may include a mesogenic core including one or more aromatic or non-aromatic cyclic groups connected to each other directly or via linkage groups. In some embodiments, a calamitic mesogenic group may include terminal groups attached to the ends of the mesogenic core. In some embodiments, a calamitic mesogenic group may include one or more lateral groups attached to a long side of the mesogenic core. These terminal and lateral groups may be selected from, e.g., carbyl or hydrocarbyl groups, polar groups such as halogen, nitro, hydroxy, etc., or polymerizable groups.
As used herein, the term “reactive mesogen” (“RM”) may refer to a polymerizable mesogenic or a liquid crystal compound. A polymerizable compound with one polymerizable group may be also referred to as a “mono-reactive” compound. A compound with two polymerizable groups may be referred to as a “di-reactive” compound, and a compound with more than two polymerizable groups may be referred to as a “multi-reactive” compound. Compounds without a polymerizable group may be also referred to as “non-reactive” compounds.
As used herein, the term “director” may refer to a preferred orientation direction of long molecular axes (e.g., in case of calamitic compounds) or short molecular axes (e.g., in case of discotic compounds) of the LC or RM molecules. In a film including a uniaxially positive birefringent LC or RM material, the optic axis may be provided by the director.
The term “optic axis” may refer to a direction in a crystal. A light propagating in the optic axis direction may not experience birefringence (or double refraction). An optic axis may be a direction rather than a single line: lights that are parallel to that direction may experience no birefringence. The term “lens plane” or “lens layer” of a lens refers to a film plane or a film layer of an optically anisotropic film included in the lens.
As used herein, the term “film” and “layer” may include rigid or flexible, self-supporting or free-standing film, coating, or layer, which may be disposed on a supporting substrate or between substrates. The term “in-plane” in phrases “in-plane direction,” “in-plane orientation,” “in-plane alignment pattern,” “in-plane rotation pattern,” and “in-plane pitch” means within a plane of a film or a layer (e.g., a surface plane of the film or layer, or a plane parallel to the surface plane of the film or layer).
As used herein, the phrase “aperture of a lens” refers to an effective light receiving area of the lens. A “geometry center” of a lens refers to a center of a shape of the effective light receiving area (e.g., aperture) of the lens. The geometry center may be a point of intersection of (i.e., a crossing point between) a first symmetric axis and a second symmetric axis of the shape of the aperture. When the entire shape of the lens constitutes the effective light receiving area of the lens, the geometry center of the lens is the center of the shape of the lens. For example, when the aperture has a circular shape, the geometry center is a point of intersection of a first diameter (also a first symmetric axis) and a second diameter (also a second symmetric axis) of the aperture of the lens. When the aperture has a rectangular shape, the geometry center is a point of intersection of a longitudinal symmetric axis (also a first symmetric axis) and a lateral symmetric axis (also a second symmetric axis) of the aperture of the lens.
Pancharatnam-Berry phase (“PBP”) is a geometric phase (“GP”) related to changes in the polarization state experienced by a light while the light propagates in an optically anisotropic material. Such a geometric phase may be proportional to a solid angle defined by the polarization state along the light propagation path on the Poincarè sphere. In an optically anisotropic material, a transverse gradient of PBP may be induced by local rotations of the optic axis. When the thickness of an optically anisotropic plate corresponds to a half-wave plate phase difference between the ordinary and the extraordinary lights, the PBP between two points across a light beam profile may be equal to twice the relative rotation of the optic axis at the two points. Thus, the wavefront of the light may be polarization-dependent and may be configured by a spatial rotation of the optic axis in the in-plane.
PBP lenses may be formed by a thin layer of one or more birefringent materials with intrinsic or induced (e.g., photo-induced) optical anisotropy (referred to as an optically anisotropic film), such as liquid crystals, liquid crystal polymers, amorphous polymers, or metasurfaces. The birefringent materials may include optically anisotropic molecules. A desirable lens phase profile may be directly encoded into local orientations of the optic axis of the optically anisotropic film. PBP lenses have features such as flatness, compactness, high efficiency, high aperture ratio, absence of on-axis aberrations, possibility of switching, flexible design, simple fabrication, and low cost, etc. Thus, the GP lenses or PBP lenses can be implemented in various applications such as portable or wearable optical devices or systems.
The in-plane orientation of the optic axis of the optically anisotropic film may be determined by orientations (e.g., alignment directions) of the elongated molecules or molecular units (e.g., small molecules or fragments of polymeric molecules) in the film. For discussion purposes, elongated optically anisotropic molecules are used as examples for describing the alignment pattern in the PBP lens. The alignment of the elongated optically anisotropic molecules may also be referred to as the orientation of the directors of the elongated optically anisotropic molecules. In some embodiments, the alignment pattern may include an in-plane orientation pattern, i.e., the orientation pattern in a plane, such as a surface plane of the film or a plane parallel with the surface of the film. The in-plane orientation pattern of the optically anisotropic molecules may result in an in-plane orientation pattern of the optic axis of the optically anisotropic film. In some embodiments, the molecules may have a continuous in-plane rotation in at least two opposite directions along a film plane (e.g., a surface plane) of the optically anisotropic film. The at least two opposite in-plane directions may be opposite directions from a lens pattern center to opposite lens peripheries of the PBP lens. The least two opposite directions along the surface plane of the optically anisotropic film may be referred to as at least two opposite in-plane directions. Correspondingly, the optic axis of the optically anisotropic film may have a continuous in-plane rotation in the at least two opposite in-plane directions of the optically anisotropic film.
An in-plane orientation of the optic axis of the optically anisotropic film may correspond to an in-plane projection of the optic axis, e.g., a projection of the optic axis on a film plane. An angle formed by the projection with a predetermined reference direction in the film plane (e.g., +x-axis direction) may be defined as an azimuthal angle of the optic axis at a local point, which may be the same as the azimuthal angle of a corresponding molecule. The azimuthal angle of the optic axis (or the azimuthal angles of the molecules) may change from one local point to another local point, resulting in changes in the in-plane projection of the optic axis.
A lens pattern (or an optic axis pattern) of the PBP lens refers to the orientation pattern of the optic axis of the optically anisotropic film, or the orientation pattern of the elongated molecules or elongated molecular units, the pattern of change of the azimuthal angles of the optic axis of the optically anisotropic film, or the pattern of change of the azimuthal angles of the optically anisotropic molecules in the optically anisotropic film. The azimuthal angles of the optic axis of the optically anisotropic film may change in at least two opposite in-plane directions of the optically anisotropic film. The at least two opposite in-plane directions may be opposite directions from a lens pattern center to opposite lens peripheries of the PBP lens. At the same distance from the lens pattern center in the at least two opposite in-plane directions, the optic axis of the optically anisotropic film of the PBP lens may rotate in the same rotation direction (e.g., clockwise or counter-clockwise) respectively. The lens pattern (or the optic axis pattern) of the PBP lens may correspond to an alignment pattern of the elongated molecules or molecular units (e.g., small molecules or fragments of polymeric molecules) in the optically anisotropic film. A fringe of the PBP lens refers to a set of local points at which the azimuthal angles of the optic axis (or the rotation angles of the optic axis starting from the lens pattern center to the local points in the radial direction) are the same. The PBP lens may have a plurality of fringes. For a PBP lens functioning as a spherical lens or an aspherical lens, the fringes may be concentric rings. For a PBP lens functioning as a cylindrical lens, the fringes may be parallel lines.
A center of the lens pattern of an on-axis focusing PBP lens is referred to as a lens pattern center, which may be a symmetry center of the lens pattern. The lens pattern center of the on-axis focusing PBP lens may coincide with a geometry center of the on-axis focusing PBP lens. An off-axis focusing PBP lens may be considered as a lens obtained by shifting the lens pattern center of a corresponding on-axis focusing PBP lens with respect to the geometry center of the on-axis focusing PBP lens. The lens pattern center of the corresponding on-axis focusing PBP lens may also be a lens pattern center of the off-axis focusing PBP lens. That is, the off-axis focusing PBP lens may have an on-axis focusing counterpart with the same lens pattern center.
A geometry center of a PBP lens may be defined as a center of a shape of the effective light receiving area (i.e., an aperture) of the PBP lens. When the entire area of the PBP lens constitutes the effective light receiving area, the geometry center of the PBP lens may correspond to the center of the shape of the PBP lens. An out-of-plane geometry center axis (also referred to as a lens axis) refers to an axis passing through the geometry center that is perpendicular to the surface plane of the optically anisotropic film of the PBP lens. An in-plane geometry center axis refers to an axis passing through the geometry center that is within the surface plane of the optically anisotropic film of the PBP lens. The out-of-plane geometry center axis may be parallel with the out-of-plane lens pattern center axis.
In some embodiments, when the PBP lens is an on-axis focusing PBP lens, the lens pattern center may correspond to the geometry center of the PBP lens (i.e., the center of the shape of the effective light receiving area of the lens). In some embodiments, when the PBP lens is an off-axis focusing PBP lens, the lens pattern center of the PBP lens may not correspond to a geometry center of the PBP lens. Instead, the lens pattern center of the PBP lens may be shifted from the geometry center of the PBP lens. An “out-of-plane lens pattern center axis” refers to an axis passing through the lens pattern center that is perpendicular to the surface plane of the optically anisotropic film of the PBP lens. An in-plane lens pattern center axis refers to an axis passing through the lens pattern center that is within the surface plane of the optically anisotropic film of the PBP lens. Thus, the in-plane lens pattern center axis is perpendicular to the out-of-plane lens pattern center axis.
For a PBP lens functioning as a spherical lens or an aspherical lens (referred to as a PBP spherical lens or aspherical lens), the at least two opposite in-plane directions may include a plurality of opposite radial directions. A PBP spherical/aspherical lens may focus a light into a point (e.g., a focal point or focus). A PBP spherical/aspherical lens may have a geometry center that is a point of intersection of a first in-plane symmetric axis (e.g., a first diameter) and a second in-plane symmetric axis (e.g., a second diameter) of the shape of the aperture. In some embodiments, the lens pattern center and the geometry center of the PBP spherical/aspherical lens may be located on a same in-plane symmetric axis of the aperture of the PBP spherical/aspherical lens.
For a PBP lens functioning as an on-axis focusing PBP spherical lens or aspherical lens, the alignment pattern and the fringes of the PBP lens may be centrosymmetric with respect to the lens pattern center of the PBP lens. In addition, the fringes of the PBP lens may be symmetric with respect to an axis passing through the lens pattern center of the PBP lens. The alignment pattern of the PBP lens may be asymmetric with respect to the axis passing through the lens pattern center of the PBP lens.
For a PBP lens functioning as an off-axis focusing PBP spherical lens or aspherical lens, the alignment pattern and the fringes of the PBP lens over the entire PBP lens may not be centrosymmetric with respect to the lens pattern center of the PBP lens. Instead, the alignment pattern and the fringes of an off-axis focusing PBP lens in a predetermined region of the entire PBP lens including the lens pattern center may be centrosymmetric with respect to the lens pattern center of the PBP lens. In addition, the fringes of an off-axis focusing PBP lens in a predetermined region of the entire PBP lens including the lens pattern center may be symmetric with respect to an axis passing through the lens pattern center of the PBP lens. The alignment pattern of the PBP lens in a predetermined region of the entire off-axis focusing PBP lens including the lens pattern center may be asymmetric with respect to the axis passing through the lens pattern center of the PBP lens.
A PBP spherical lens (e.g., an on-axis or off-axis focusing PBP spherical lens) may have a point at which an azimuthal angle changing rate of the optic axis (or an azimuthal angle changing rate of the optically anisotropic molecules) of the optically anisotropic film in the opposite radial directions is the smallest, as compared to the remaining points of the PBP spherical lens. That is, in the PBP spherical lens, the azimuthal angle changing rate of the optic axis of the optically anisotropic film may be configured to increase in substantially the entire PBP lens in opposite radial directions from the lens pattern center to the opposite lens peripheries. In the PBP spherical lens, the lens pattern center may also be defined as the point at which an azimuthal angle changing rate of the optic axis (or an azimuthal angle changing rate of the optically anisotropic molecules) of the optically anisotropic film in the at least two opposite in-plane directions is the smallest. As a comparison, in a PBP aspherical lens (e.g., an on-axis or off-axis focusing PBP aspherical lens), the azimuthal angle changing rate of the optic axis of the optically anisotropic film may be configured to increase in at least a portion of the PBP lens including a lens pattern center (less than the entire PBP lens) from the lens pattern center to the opposite lens peripheries in opposite radial directions.
For a PBP lens functioning as a cylindrical lens (referred to as a PBP cylindrical lens), which may be considered as a 1D case of a PBP lens functioning as a spherical lens, the at least two opposite in-plane directions may include two opposite lateral directions. A PBP cylindrical lens may focus a light into a line (e.g., a line of focal points or line focus). A PBP cylindrical lens may have two symmetric axes of the shape of the aperture, e.g., a lateral symmetric axis in a lateral direction (or width direction) of the PBP cylindrical lens and a longitudinal symmetric axis in a longitudinal direction (or length direction) of the PBP cylindrical lens. The geometry center of the PBP cylindrical lens may be a point of intersection of the two symmetric axes. When the cylindrical lens has a rectangular shape, the geometry center may also be a point of intersection of two diagonals. A PBP cylindrical lens may have a plurality of points, at each of which an azimuthal angle changing rate of the optic axis (or an azimuthal angle changing rate of the optically anisotropic molecules) of the optically anisotropic film in the at least two opposite in-plane directions may be the smallest. The plurality of points, at each of which an azimuthal angle changing rate is the smallest may be arranged in a line. The line may be referred to as an “in-plane lens pattern center axis” of the PBP cylindrical lens. The in-plane lens pattern center axis may be in the longitudinal direction. A lens pattern center of the PBP cylindrical lens may also be considered as one of the plurality of points, which is located on a same symmetric axis (e.g., the lateral symmetric axis) with the geometry center of the PBP cylindrical lens. In other words, the lens pattern center is also a point of intersection of the in-plane lens pattern center axis and the lateral symmetric axis.
A PBP cylindrical lens may have a central symmetry of fringes and alignment pattern with respect to the lens pattern center in the two opposite lateral directions (and in some embodiments, only in the two opposite lateral directions). For a PBP lens functioning as an on-axis focusing PBP cylindrical lens, the alignment pattern and the fringes of the PBP lens over the entire PBP lens may be centrosymmetric with respect to the lens pattern center in the two opposite lateral directions (and in some embodiments, only in the two opposite lateral directions). In addition, the fringes of the PBP lens may be symmetric with respect to the in-plane lens pattern center axis of the PBP lens. The alignment pattern of the PBP lens may be asymmetric with respect to the in-plane lens pattern center axis of the PBP lens.
For a PBP lens functioning as an off-axis focusing PBP cylindrical lens, the alignment pattern and the fringes of the PBP lens over the entire PBP lens may not be centrosymmetric with respect to the lens pattern center in the two opposite lateral directions. Instead, the alignment pattern and the fringes of the PBP lens in a predetermined region of the entire PBP lens including the lens pattern center may be centrosymmetric with respect to the lens pattern center of the PBP lens in the two opposite lateral directions. In addition, the fringes of the PBP lens in the predetermined region of the entire PBP lens including the lens pattern center may be symmetric with respect to the in-plane lens pattern center axis of the PBP lens. The alignment pattern of the PBP lens in the predetermined region of the entire PBP lens including the lens pattern center may be asymmetric with respect to the in-plane lens pattern center axis of the PBP lens.
The present discourse provides an off-axis focusing GP lens or PBP lens configured to provide an off-axis focusing capability to an incoming light without tilting the off-axis focusing PBP lens. The off-axis focusing PBP lens may include an optically anisotropic film. An optic axis of the optically anisotropic film (or the off-axis focusing PBP lens) may be configured with a continuous in-plane rotation in at least two opposite in-plane directions of the optically anisotropic film from a lens pattern center, thereby creating a geometric phase profile for the off-axis focusing PBP lens. The at least two opposite in-plane directions may be opposite directions from a lens pattern center to opposite lens peripheries of the off-axis focusing PBP lens. The optic axis of the optically anisotropic film may rotate in a same rotation direction (e.g., a clockwise direction or a counter-clockwise direction) along the at least two opposite in-plane directions from the lens pattern center. The rotation of the optic axis of the optically anisotropic film in a predetermined rotation direction (e.g., a clockwise direction or a counter-clockwise direction) may exhibit a handedness, e.g., right handedness or left handedness. An azimuthal angle changing rate of the optic axis of the optically anisotropic film may be configured to increase from the lens pattern center in the at least two opposite in-plane directions in at least a predetermined portion of the off-axis focusing PBP lens including the lens pattern center. The lens pattern center may be shifted from a geometry center of the off-axis focusing PBP lens by a predetermined distance in a predetermined direction. In some embodiments, the lens pattern center of the off-axis focusing PBP lens may be a point at which the azimuthal angle changing rate of the optic axis of the optically anisotropic film is the smallest in at least the portion of the lens including the lens pattern center. In some embodiments, the lens pattern center of the off-axis focusing PBP lens may be a symmetric center of a lens pattern of a corresponding on-axis focusing PBP lens.
The lens pattern of the off-axis focusing PBP lens may have a period P that is defined as a distance over which the azimuthal angle θ of the optic axis of the optically anisotropic film changes by π in the at least two opposite in-plane directions. The period P of the lens pattern may vary in the at least two opposite in-plane directions. The period P of the lens pattern may monotonically decrease from the lens pattern center in the at least two opposite in-plane directions in at least the predetermined portion of the off-axis focusing PBP lens including the lens pattern center. In some embodiments, the predetermined portion of the off-axis focusing PBP lens including the lens pattern center may be substantially the entire off-axis focusing PBP lens. In some embodiments, the predetermined portion of the off-axis focusing PBP lens including the lens pattern center may be less than the entire off-axis focusing PBP lens. For example, the period P of the lens pattern may monotonically decrease from the lens pattern center in the at least two opposite in-plane directions in a first predetermined portion of the off-axis focusing PBP lens including the lens pattern center, and increase from the lens pattern center in the at least two opposite in-plane directions from the lens pattern center to the periphery in a second predetermined portion of the off-axis focusing PBP lens. The first predetermined portion may be different from the second predetermined portion. In some embodiments, the first predetermined portion may be adjacent to the second predetermined portion.
In some embodiments, the off-axis focusing PBP lens may be obtained by cropping or cutting an on-axis PBP lens asymmetrically. In some embodiments, the off-axis focusing PBP lens may be fabricated by one or more of holographic recording, direct writing, exposure through a master mask, or a photocopying, etc. In some embodiments, the orientation pattern of the optic axis of the optically anisotropic film may be holographically recorded in a layer of a recording medium by two coherent polarized lights. In some embodiments, the two polarized lights may be two circularly polarized lights with opposite handednesses irradiated onto the same surface of the recording medium. The fabricated off-axis focusing PBP lens may be a transmissive type optical element. In some embodiments, one of the two circularly polarized lights may be a collimated light and the other may be a converging or diverging light.
In some embodiments, the two circularly polarized lights may be two circularly polarized lights with a same handedness irradiated onto different surfaces (e.g., two opposite surfaces) of the recording medium. The fabricated off-axis focusing PBP lens may be a reflective type optical element. In some embodiments, one of the two circularly polarized lights may be a collimated light and the other may be a converging or diverging light.
The recording medium may include one or more optically recordable and polarization sensitive materials configured to generate a photo-induced anisotropy when subjected to a polarized light irradiation. The molecules (fragments) and/or the photo-products of the recording medium may be configured to generate orientational ordering under a light irradiation. The interference of the two circularly polarized lights may result in patterns of light polarization (or polarization interference patterns), without resulting in intensity modulation. In some embodiments, the molecules of the optically recordable and polarization sensitive materials may include elongated anisotropic photo-sensitive units (e.g., small molecules or fragments of polymeric molecules). The patterns of light polarization may induce a local alignment direction of the anisotropic photo-sensitive units in the layer of recording medium, resulting in a modulation of an optic axis due to a photo-alignment of the anisotropic photo-sensitive units. The optic axis orientation inscribed in the recording medium may be further enhanced by disposing a layer of birefringent materials having an intrinsic birefringence, such as liquid crystals (“LCs”) or reactive mesogens (“RMs”), on the recording medium. LCs or RMs may be aligned along the local alignment direction of the anisotropic photo-sensitive units in the layer of the recording medium. Thus, the orientational pattern of the optic axis in the recording medium may be transferred to the LCs or RMs. That is, the irradiated layer of the recording medium may function as an photo-alignment (“PAM”) layer for the LCs or RMs. Such an alignment procedure may be referred to as a surface-mediated photo-alignment.
In some embodiments, the photo-alignment of photo-sensitive units may occur in a volume of one or more optically recordable and polarization sensitive materials. When irradiation is provided with holographically created patterns of light polarization, the alignment patterns of photo-sensitive units may occur in the layer of the recording medium. Such an alignment procedure may be referred to as a bulk-mediated photo-alignment. In some embodiments, the optically recordable and polarization sensitive materials for bulk-mediated photo-alignment may include photo-sensitive polymers, such as amorphous polymers, liquid crystal (“LC”) polymers, etc. In some embodiments, the amorphous polymers may be initially optically isotropic prior to undergoing the recording process, and may exhibit an induced (e.g., photo-induced) optical anisotropy during the recording process. In some embodiments, the birefringence and orientational patterns may be recorded in the LC polymers due to an effect of photo-induced optical anisotropy. The photo-induced optical anisotropy in the LC polymers may be considerably enhanced by a subsequent heat treatment (e.g., annealing) in a temperature range corresponding to liquid crystalline state of the LC polymers due to intrinsic self-organization of mesogenic fragments of the LC polymers.
The molecules of photo-sensitive polymers may include polarization sensitive photo-reactive groups embedded in a main or a side polymer chain. In some embodiments, the polarization sensitive groups may include an azobenzene group, a cinnamate group, or a coumarin group, etc. In some embodiments, the photo-sensitive polymer may include an LC polymer with a polarization sensitive cinnamate group incorporated in a side polymer chain. An example of the LC polymer with a polarization sensitive cinnamate group incorporated in a side polymer chain is a polymer M1. The polymer M1 has a nematic mesophase in a temperature range of about 115° C. to about 300° C. An optical anisotropy may be induced by irradiating the M1 film with a polarized UV light (e.g., a laser light with a wavelength of 325 nm or 355 nm) and subsequently enhanced by more than an order of magnitude by annealing at a temperature range of about 115° C. to about 300° C. It is to be noted that the material M1 is for illustrative purposes, and is not intended to limit the scope of the present disclosure. The dependence of the photo-induced birefringence on exposure energy is qualitatively similar for other materials from liquid crystalline polymers of M series. Liquid crystalline polymers of M series are discussed in U.S. patent application Ser. No. 16/443,506, filed on Jun. 17, 2019, titled “Photosensitive Polymers for Volume Holography,” which is incorporated by reference for all purposes. In some embodiments, with suitable photo-sensitizers, a visible light (e.g., a violet light) may also be used to induce anisotropy in this material.
In some embodiments, the PAM layer 110 may be used to fabricate, store, or transport the off-axis focusing PBP lens 100. In some embodiments, the PAM layer 110 may be detachable or removable from other portions of the off-axis focusing PBP lens 100 after the other portions of the off-axis focusing PBP lens 100 are fabricated or transported to another place or device. That is, the PAM layer 110 may be used in fabrication, transportation, and/or storage to support the optically anisotropic film 105 provided at a surface of the PAM layer 110, and may be separated or removed from the optically anisotropic film 105 of the off-axis focusing PBP lens 100 when the fabrication of the off-axis focusing PBP lens 100 is completed, or when the off-axis focusing PBP lens 100 is to be implemented in an optical device.
In some embodiments, the off-axis focusing PBP lens 100 may include one or more substrates 115 for support and protection purposes. The optically anisotropic film 105 may be disposed at (e.g., formed at, attached to, deposited at, bonded to, etc.) a surface of the substrate 115. For discussion purposes,
In some embodiments, the substrate 115 may be used to fabricate, store, or transport the off-axis focusing PBP lens 100. In some embodiments, the substrate 115 may be detachable or removable from other portions of the off-axis focusing PBP lens 100 after the other portions of the off-axis focusing PBP lens 100 are fabricated or transported to another place or device. That is, the substrate 115 may be used in fabrication, transportation, and/or storage to support the PAM layer 110 and the optically anisotropic film 105 provided on the substrate 115, and may be separated or removed from the PAM layer 110 and the optically anisotropic film 105 when the fabrication of the off-axis focusing PBP lens 100 is completed, or when the off-axis focusing PBP lens 100 is to be implemented in an optical device.
In the following, orientation of the anisotropic molecules in an off-axis focusing PBP lens will be described in detail. For discussion purposes, calamitic (rod-like) LC molecules will be used as examples of the anisotropic molecules.
For a recorded PBP lens including an optically anisotropic film,
As shown in
In some embodiments, the azimuthal angle of the optic axis of the optically anisotropic film 201 may change in proportional to the distance from the lens pattern center to a local point on the optic axis. For example, the azimuthal angle of the optic axis of the optically anisotropic film 201 may change according to an equation of
where θ is the azimuthal angle of the optic axis at a local point of the optically anisotropic film 201, r is a distance from the lens pattern center (OL) 210 of the optic lens (also the origin O of the x-y plane) to the local point in the lens plane, L is a distance between a lens plane and a focal plane of the PBP lens 200 (i.e., the focal distance in case of an on-axis focusing PBP lens), and λ is a wavelength of a light incident onto the on-axis focusing PBP lens 200. The azimuthal angle changing rate (that is a changing rate of θ or a rotational velocity of θ) is a derivative
which is zero when r=0. Thus, the point at which r=0 may be a point with the smallest rotation rate of θ or the smallest azimuthal angle changing rate.
In some embodiments, the optically anisotropic film 201 may include calamitic (rod-like) LC molecules 205. The LC molecules 205 may be aligned with directors of the LC molecules 205 (or LC directors) arranged in a continuous in-plane rotation pattern. As a result, the optic axis of the optically anisotropic film 201 may be configured in a continuous in-plane rotation pattern. As shown in
As shown in
In the x-y plane, the LC director of the LC molecules 205 may continuously rotate in a rotation pattern having a varying pitch (Λ0, Λ1, . . . , Λr) along the opposite radial axes or directions, and an LC director field may have a rotational symmetry about the lens pattern center (OL) 210. In the on-axis focusing PBP lens 200 shown in
The on-axis focusing PBP lens 200 may be a PBP grating with a varying periodicity in the opposite radial directions, from the lens pattern center (OL) 210 to the opposite lens peripheries 215. A period P of the lens pattern of the on-axis focusing PBP lens 200 may be defined as a distance over which the azimuthal angle θ of the optic axis of the optically anisotropic film 201 changes by π in the radial directions. Fringes of the PBP grating (i.e., the on-axis focusing PBP lens 200) may have a central symmetry about the lens pattern center (OL) 210. A fringe of the PBP grating refers to a set of local points at which the azimuthal angle of the optic axis (or the rotation angle of the optic axis starting from the lens pattern center (OL) 210 to the local point in the radial direction) is the same. For example, when the rotation angle of the optic axis starting from the lens pattern center (OL) 210 to the local point in the radial direction is expressed as θ=θ1+nπ (0<θ1<π), both θ1 and n may be the same for the local points on the same fringe. A difference in the rotation angle θ of the neighboring fringes is π, i.e., the distance between the neighboring fringes is a period P. The set of local points corresponding to the same θ may be on the same circle for an on-axis focusing PBP lens functioning as a spherical lens or an aspherical lens.
In some embodiments, the azimuthal angle (or rotation angle) θ may monotonically change approximately according to the equation
providing a quadratic phase shift
for a PBP spherical lens, where r is a distance from the lens pattern center (OL) 210 to a local point on the lens, and L is a distance between a lens plane and a focal plane. At a local point at which the distance r is much longer than the period P of the lens pattern (r>>P), the period P may change according to an equation
That is, the period P of the lens pattern may be roughly inversely proportional to the distance r from the lens pattern center (OL) 210 to the local point on the optic axis. In some embodiments, the period P of the lens pattern of an on-axis focusing PBP lens may not monotonically change (e.g., may not monotonically decrease) in the opposite radial directions from a lens pattern center (OL) to opposite lens peripheries in the entire lens. Instead, the period P of the lens pattern of the on-axis focusing PBP lens may monotonically change (e.g., monotonically decrease) only in a portion of the lens including the lens pattern center (OL) (less than the entire lens), in the opposite radial directions from a lens pattern center (OL) to opposite lens peripheries. Accordingly, the on-axis focusing PBP lens may functions as an aspherical PBP lens (referred to as an on-axis focusing PBP aspherical lens). For example, the period P of the lens pattern of the on-axis focusing PBP aspherical lens may first decrease then increase in the radial directions from the lens pattern center (OL) to the lens periphery. The lens pattern center (OL) may correspond to a geometry center in the on-axis focusing PBP aspherical lens.
For the on-axis focusing PBP lens 250 having a rectangular shape (or a rectangular lens aperture), a width direction of the on-axis focusing PBP lens 250 may be referred to as a lateral direction (e.g., an x-axis direction in
An optic axis of the optically anisotropic film 251 may be configured with a continuous in-plane rotation pattern from the lens pattern center (OL) 260 to a lens periphery 265 of the on-axis focusing PBP lens 250 in the lateral direction (e.g., the x-axis direction). An azimuthal angle changing rate of the optic axis of the optically anisotropic film 251 may increase from the lens pattern center (OL) 260 to the lens periphery 265 in the lateral direction. That is, the continuous in-plane rotation of the optic axis of the optically anisotropic film of the on-axis focusing PBP lens 250 may accelerate from the lens pattern center (OL) 260 to the lens periphery 265 in the lateral direction. The azimuthal angles of the optic axis at locations on the same side of the in-plane lens pattern center axis 263 and having a same distance from the in-plane lens pattern center axis 263 in the lateral direction, may be substantially the same.
The on-axis focusing PBP lens 250 may be a PBP grating with a varying periodicity in the opposite lateral directions from the in-plane lens pattern center axis 263 to the opposite lens periphery 265 (e.g., to the left side lens periphery and to the right side lens periphery). A period P of the lens pattern of the on-axis focusing PBP lens 250 may be defined as a distance over which the azimuthal angle θ of the optic axis of the optically anisotropic film 251 changes by π in the radial directions. Fringes of the PBP grating may have an axial symmetry about the in-plane lens pattern center axis 263. The alignment pattern of the PBP grating may be asymmetric about the in-plane lens pattern center axis 263. A fringe of the PBP grating (i.e., the on-axis focusing PBP lens 250) refers to a set of local points at which the azimuthal angle of the optic axis (or the rotation angle of the optic axis starting from the in-plane lens pattern center axis 263 to the local point in the lateral direction) is the same. For example, when the rotation angle of the optic axis from the in-plane lens pattern center axis 263 to the local point in the lateral direction is expressed as θ=θ1+nπ (0<θ1<π), both θ1 and n may be the same for the local points on the same fringe. A difference in the rotation angles of the neighboring fringes is π, i.e., the distance between the neighboring fringes is the period P. The set of local points may be on the same line parallel to the longitudinal direction for the on-axis focusing PBP lens 250 functioning as cylindrical lens.
In some embodiments, the on-axis focusing PBP lens 250 functioning as a cylindrical lens may be considered to have a central symmetry of fringes and alignment pattern with respect to the lens pattern center in the two opposite lateral directions (and in some embodiments, only in the two opposite lateral directions). The equation
and corresponding phase shift equation
for a PBP spherical lens may also be applied to the on-axis focusing PBP lens 250 functioning as a cylindrical lens, but only in the two opposite lateral directions. That is, r is a distance from the lens pattern center (OL) 260 to a local point of the on-axis focusing PBP lens 250 in the two opposite lateral directions. In this sense, cylindric lens can be considered as a 1d case of spherical lens.
In some embodiments, the optically anisotropic film 251 may include calamitic (rod-like) LC molecules 255. The directors of the LC molecules 255 (LC directors) may continuously rotate within the surface plane, resulting in a continuous in-plane rotation of the optic axis. As shown in
The optically anisotropic film 301 may include one or more birefringent materials including LC molecules 305. An optic axis of the optically anisotropic film 301 may be configured with a continuous in-plane rotation (or rotation pattern) from the lens pattern center (OL) 310 to a lens periphery 315 of the off-axis focusing PBP lens 300 in a plurality of radial directions. That is, the directors of the optically anisotropic molecules included in the optically anisotropic film 301 may continuously rotate along a plurality of radial directions. In other words, the azimuthal angles of the optically anisotropic molecules of the optically anisotropic film 301 may continuously change in a plurality of radial directions. An azimuthal angle changing rate of the optic axis of the optically anisotropic film 301 may increase from the lens pattern center (OL) 310 to the lens periphery 315 of the off-axis focusing PBP lens 300 in the radial directions. The lens pattern center (OL) 310 of the off-axis focusing PBP lens 300 may be a point at which the azimuthal angle changing rate is the smallest. That is, the in-plane rotation of the optic axis of the optically anisotropic film 301 may accelerate from the lens pattern center (OL) 310 to the lens periphery 315 in the radial directions. In some embodiments, the azimuthal angle of the optic axis of the optically anisotropic film 301 may be proportional to the distance from the lens pattern center (OL) 310 (also the origin O of the x-y plane) to the local point in the lens plane.
For example, the azimuthal angle θ of the optic axis of the optically anisotropic film 301 in the off-axis focusing PBP lens 300 functioning as a spherical lens may change approximately according to an equation of
where θ is the azimuthal angle of the optic axis at a local point of the optically anisotropic film 301, r is a distance from the lens pattern center (OL) 310 (also the origin θ of the x-y plane) to the local point on the optic axis, L is a distance between a lens plane and a focal plane of the off-axis focusing PBP lens 300, and λ is a wavelength of a light incident onto the off-axis focusing PBP lens 300, is a phase shift experienced by a light incident onto the lens with a wavelength λ. The azimuthal angle changing rate (that is a changing rate of θ or a rotational velocity of θ) is a derivative
which is zero when r=0. Thus, the point at which r=0 may be a point with the smallest rotation rate of θ or the smallest azimuthal angle changing rate.
In some embodiments, the optically anisotropic film 301 may include calamitic (rod-like) LC molecules 305. The directors of the LC molecules 305 (LC directors) may continuously rotate in a surface plane (e.g., the x-y plane) in a continuous in-plane rotation pattern. As a result, the optic axis of the optically anisotropic film 301 may have a continuous in-plane rotation (or rotation pattern). As shown in
In some embodiments, the origin (point “O” in
where K is a non-zero coefficient, r is a distance from the lens pattern center (OL) 310 of the off-axis focusing PBP lens 300 to a local point of the off-axis focusing PBP lens 300, L is a distance between a lens plane and a focal plane of the of the off-axis focusing PBP lens 300, and x is a coordinate in the predetermined direction of the predetermined shift of the lens pattern center (OL) 310 with respect to the geometry center (OG). The corresponding equation for the azimuthal angle θ is
The first term
corresponds to an optical power of the off-axis focusing PBP lens 300, and the second term corresponds to a shift of the lens pattern center (OL) 310 with respect to the geometry center (OG). The azimuthal angle changing rate in a shifting direction (e.g., an x-axis direction, r=x) may be calculated according to
The azimuthal angle changing rate may be the smallest at a point xc=D=KL when
A phase shift experienced by the light with the wavelength λ incident onto an on-axis focusing PBP lens corresponding to the off-axis focusing PBP lens 300 may be expressed as
The off-axis focusing PBP lens 300 may be a PBP grating with a varying periodicity in the opposite radial directions, from the lens pattern center (OL) 310 to the opposite lens peripheries 315. A period P of the lens pattern of the off-axis focusing PBP lens 300 may be defined as a distance over which the azimuthal angle θ of the optic axis of the optically anisotropic film 301 changes by π in the radial directions. Fringes of the PBP grating over the entire PBP grating may not have a central symmetry about the lens pattern center (OL) 310. Fringes of the PBP grating in a predetermined region of the entire PBP grating including the lens pattern center (OL) 310 may have a central symmetry with respect to the lens pattern center center (OL) 310. A fringe of the PBP grating (i.e., the off-axis focusing PBP lens 300) refers to a set of local points at which the azimuthal angle of the optic axis (or the rotation angle of the optic axis starting from the lens pattern center (OL) 310 to the local point in the radial direction) is the same. For example, when the rotation angle of the optic axis starting from the lens pattern center (OL) 310 to the local point in the radial direction is expressed as θ=θ1+nπ (0<θ1<π), both θ1 and n may be the same for the local points on the same fringe. A difference in the rotation angles of the neighboring fringes is π, i.e., the distance between the neighboring fringes is a period P. The set of local points may be on the same circle for an off-axis focusing PBP lens functioning as a spherical lens or an aspherical lens.
In some embodiments, when the azimuthal angle θ of the optic axis changes approximately according to the equation
the period P of the lens pattern may change approximately according to an equation
The period P may be roughly inversely proportional to the distance r from the lens pattern center (OL) 310 to the local point on the optic axis, when the distance r from the lens pattern center (OL) 310 is much larger than the period P of the lens pattern (r>>P). In some embodiments, the period P of the lens pattern of the off-axis focusing PBP lens 300 may monotonically change (e.g., monotonically decrease) in the entire off-axis focusing PBP lens from the lens pattern center (OL) 310 in the opposite radial directions, i.e., from the lens pattern center (OL) 310 to the opposite lens peripheries 315. Accordingly, the off-axis focusing PBP lens 300 may function as a spherical PBP lens.
In some embodiments, the period P of the lens pattern of an off-axis focusing PBP lens may not monotonically change (e.g., may not monotonically decrease) in the opposite radial directions from a lens pattern center (OL) to opposite lens peripheries. Instead, the period P of the lens pattern of the off-axis focusing PBP lens may monotonically change (e.g., monotonically decrease) only in a portion of the lens including the lens pattern center (OL) (less than the entire lens), in the opposite radial directions from a lens pattern center (OL) to opposite lens peripheries. Accordingly, the off-axis focusing PBP lens may function as an aspherical PBP lens (referred to as an off-axis focusing PBP aspherical lens). For example, the period P of the lens pattern of the off-axis focusing PBP aspherical lens may first decrease then increase in the radial directions from the lens pattern center (OL) to the lens periphery. The lens pattern center (OL) of the off-axis focusing PBP aspherical lens may not correspond to a geometry center of the off-axis focusing PBP aspherical lens.
For the off-axis focusing PBP lens 350 having a rectangular shape (or a rectangular lens aperture), a width direction of the off-axis focusing PBP lens 350 may be referred to as a lateral direction (e.g., an x-axis direction in
An optic axis of the optically anisotropic film 351 may be configured with a continuous in-plane rotation from the lens pattern center (OL) 360 to a lens periphery 365 of the off-axis focusing PBP lens 350 in the lateral direction. An azimuthal angle changing rate of the optic axis of the optically anisotropic film 351 may increase from the lens pattern center (OL) 360 to the lens periphery 365 of the off-axis focusing PBP lens 350 in the lateral direction. That is, the continuous in-plane rotation of the optic axis of the optically anisotropic film 351 of the off-axis focusing PBP lens 350 may accelerate from the lens pattern center (OL) 360 to the lens periphery 365 in the lateral direction. The azimuthal angles of the optic axis at locations on the same side of the in-plane lens pattern center axis 363 and having a same distance from the in-plane lens pattern center axis 363 in the lateral direction may be substantially the same.
In some embodiments, the optically anisotropic film 351 may include calamitic (rod-like) LC molecules 355. The directors of the molecules 355 (or LC directors) may continuously rotate in a predetermined in-plane direction in the surface plane of the optically anisotropic film 351. The in-plane continuous rotation of the directors of the molecules 355 may result in a continuous in-plane rotation (or rotation pattern) of the optic axis of the optically anisotropic film 351. As shown in
In the optically anisotropic film 351 shown in
The off-axis focusing PBP lens 350 may be a PBP grating with a varying periodicity in the opposite lateral directions from the in-plane lens pattern center axis 363 to the opposite lens periphery 365. A period P of the lens pattern of the off-axis focusing PBP lens 350 may be defined as a distance over which the azimuthal angle θ of the optic axis of the optically anisotropic film 351 changes by π in the lateral directions. Fringes of the PBP grating over the entire PBP grating may not have an axial symmetry about the in-plane lens pattern center axis 363. Fringes of the PBP grating in a predetermined region of the entire PBP grating may have a central symmetry about the lens pattern center (OL) 360. A fringe of the PBP grating refers to a set of local points at which the azimuthal angle of the optic axis (or the rotation angle of the optic axis starting from the in-plane lens pattern center axis 363 to the local point in the lateral direction) is the same. For example, when the rotation angle of the optic axis from the in-plane lens pattern center axis 363 to the local point in the lateral direction is expressed θ=θ1+nπ (0<θ1<π), both θ1 and n may be the same for the local points on the same fringe. A difference in the rotation angles of the neighboring fringes is it, i.e., the distance between the neighboring fringes is the period P. The set of local points may be on the same line parallel to the longitudinal direction for an off-axis focusing PBP lens functioning as cylindrical lens.
The off-axis focusing PBP lens 400 may be configured to operate in a focusing state for a circularly polarized light having a predetermined handedness (e.g., left handedness or right handedness). For example, as shown in
As shown in
As shown in
In addition to focusing or defocusing an on-axis collimated light, the off-axis focusing PBP lens 400 may also have other features.
The off-axis focusing PBP lens in accordance with an embodiment of the present disclosure may be indirectly switchable between a focusing state and a defocusing state via changing a handedness of an incident light of the off-axis focusing PBP lens through an external polarization switch.
In some embodiments, the off-axis focusing PBP lens 500 may operate in a focusing state for an RHCP incident light, and may operate in a defocusing state for an LHCP incident light. Thus, the SHWP 515 may be configured to control an optical state (focusing or defocusing state) of the off-axis focusing PBP lens 500 by controlling the handedness of the circularly polarized light incident onto the off-axis focusing PBP lens 500. In some embodiments, the SHWP 515 may include an LC layer. The operating state (switching or non-switching state) of the SHWP 515 may be controllable by controlling an external electric field applied to LC layer.
As shown in
As described above, an off-axis focusing PBP lens may operate in a focusing or a defocusing state depending on the handedness of the circularly polarized light incident onto the off-axis focusing PBP lens and the handedness of the rotation of the LC directors in the off-axis focusing PBP lens. In some embodiments, an active off-axis focusing PBP lens may be switched between a focusing state (or a defocusing state), in which a positive (or a negative) optical power is provided to the incident light, and a neutral state, in which substantially zero optical power is provided to the incident light. For discussion purposes,
As shown in
At a voltage-off state, as shown in
At a voltage-on state, as shown in
In some embodiments, an active off-axis focusing PBP lens operating at a neutral state with a substantially zero optical power may also affect the handedness of the transmitted light.
As shown in
At a voltage-off state, as shown in
At a voltage-on state, as shown in
For discussion purposes,
The present disclosure further provides a lens stack including a plurality of lenses. The plurality of lenses may include one or more disclosed off-axis focusing PBP lenses. In some embodiments, all of the lenses included in the lens stack may be off-axis focusing PBP lenses. In some embodiments, the lens stack may include a combination of at least one on-axis focusing PBP lens and at least one off-axis focusing PBP lens.
The plurality of lenses 805 may provide a plurality of optical states. The plurality of optical states may provide a range of adjustments of optical powers and a range of adjustments of beam deviations for the lens stack 800. An optical power P of the lens stack 800 may be calculated by P=1/f (unit: diopter), where f is the focal length of the lens stack 800. The optical power P of the lens stack 800 may be a sum of the optical powers of the respective lenses 805 included in the lens stack 800. The optical powers of the respective lenses 805 may be positive, negative, or zero. The resultant beam deviations may depend on the shift of the structural center (or structural center shift) in the respective lenses 805 and the relative orientations between the lenses 805. For example, when the structural center is shifted in the x-axis by the lenses 805, the resultant structural center shift may be in the x-axis. The structural center shift of the lens stack 800 may be a sum of the structural center shifts of the lenses 805 included in the lens stack 800. The structural center shift of each of the lenses 805 may be positive, negative, or zero. For example, a structural center shift in the +x-axis with respective to the lens aperture center may be defined as a positive structural center shift, and a structural center shift in the −x-axis with respective to the lens aperture center may be defined as a negative lens aperture center shift.
In some embodiments, the lens stack 800 may be switchable between a focusing state (or a defocusing state) and a neutral state. In some embodiments, a focal distance and a deflection angle of a focused beam (or beam deviation of a focused beam) may be adjustable. Accordingly, a 2D and 3D beam steering with focusing may be realized. A 3D positioning of focal point may be, for example, useful for direct 3D optical recording in photo-sensitive materials. The switchable lens stack 800 may include one or more active PBP lenses, which may be directly switchable between the focusing state (or the defocusing state) and the neutral state by an electric field, as described in
In some embodiments, the lens stack 800 may include at least one SHWP arranged adjacent to a PBP lens. For illustrative purposes,
In some embodiments, the lens stack 800 may include one or more passive off-axis focusing PBP lenses, which may provide an optical power (zero or non-zero optical power) depending on the handedness of a circularly polarized light incident on the PBP lens 805 and the handedness of LC director rotation in the PBP lens 805. Thus, through controlling the operating state (switching or non-switching state) of the at least one SHWP 810 coupled with a corresponding off-axis focusing PBP lens 805, the lens stack 800 may provide a plurality of optical states. The plurality of optical states may provide a range of adjustments of optical powers and a range of adjustments of beam deviations for an incident light.
In some embodiments, the lens stack 800 may include both passive off-axis focusing PBP lenses and active off-axis focusing PBP lenses. Through controlling the operating state (switching or non-switching state) of the at least one SHWP 810 coupled with a corresponding passive off-axis focusing PBP lens, and controlling the operating state (switching or non-switching state) of the at least one SHWP 810 coupled with a corresponding active off-axis focusing PBP lens and an applied voltage of the active off-axis focusing PBP lens, the lens stack 800 may provide a plurality of optical states. The plurality of optical states may provide a range of adjustments of optical powers and a range of adjustments of beam deviations for the incident light.
The disclosed off-axis focusing PBP lens and the lens stack including one or more off-axis focusing PBP lenses may include features such as flatness, compactness, small weight, thin thickness, high efficiency, high aperture ratio, flexible design, simply fabrication, and low cost, etc. Thus, the disclosed off-axis focusing PBP lens and the lens stack may be implemented in various applications such as portable or wearable optical devices and systems. The disclosed off-axis focusing PBP lens and the lens stack including one or more off-axis focusing PBP lenses may provide complex optical functions while maintaining a small form factor, compactness and light weight. For example, the disclosed off-axis focusing PBP lenses and/or the lens stack including one or more off-axis focusing PBP lenses may be implemented in a near-eye display (“NED”). In some embodiments, the disclosed off-axis focusing PBP lenses and/or the lens stack including one or more off-axis focusing PBP lenses may be implemented in object-tracking (e.g., eye-tracking) components, display components, adaptive optical components for human eye vergence-accommodation, etc.
The NED 900 may function as a virtual reality (“VR”) device, an augmented reality (“AR”) device, a mixed reality (“MR”) device, or a combination thereof. In some embodiments, when the NED 900 functions as an AR and/or an MR device, the right and left display windows may be at least partially transparent to a light from a real-world environment to provide the user a view of the surrounding real-world environment. In some embodiments, when the NED 900 functions as a VR device, the right and left display windows may be opaque, such that the user may be immersed in the VR imagery provided via the NED 900. In some embodiments, the NED 900 may further include a dimming element, which may dynamically adjust the transmittance of real-world lights transmitted through the dimming element, thereby switching the NED 900 between functioning as a VR device and an AR device or between functioning as a VR device and an MR device. In some embodiments, along with switching between functioning as an AR or MR device and the VR device, the dimming element may be implemented in the AR device to mitigate differences in brightness of real and virtual image lights.
In some embodiments, the NED 900 may include one or more optical elements between the right and left display systems 910R and 910L and the eye 920. The optical elements may be configured to correct aberrations in an image light emitted from the right and left display systems 910R and 910L, magnify an image light emitted from the right and left display system 910R and 910L, or perform other optical adjustments of an image light emitted from the right and left display system 910R and 910L. Examples of the optical elements may include an aperture, a Fresnel lens, a convex lens, a concave lens, a filter, a polarizer, or any other suitable optical element that affects the image light. Exemplary right and left display systems 910R and 910L including one or more of the disclosed off-axis focusing PBP lenses or lens stacks will be described in detail with reference to
The display assembly 930 shown in
The NED 900 may include a controller 990. The controller 990 may include a processor 991, a memory 991, and an input/output device (e.g., a communication device) 993. The processor 991 may be any suitable processor configured with a computing capability, such as a central processing unit (“CPU”), a graphics processing unit (“GPU”), etc. The memory 991 may be any suitable memory, such as a read-only memory (“ROM”), a random-access memory (“RAM”), a flash memory, etc. The input/output device 993 may include any suitable input/output interface or port configured to output or receive data to or from an external device. In some embodiments, the input/output device 993 may be a communication device configured for wired and/or wireless communications, such as a WiFi module, a Bluetooth module, etc. In some embodiments, the controller 990 may not be included in the NED 900. Instead, the controller 990 may be a remote controller communicatively coupled with the NED 900. For discussion purposes, the controller 990 is presumed to be included in the NED 900. The controller 990 may be communicatively coupled with various devices included in the NED 900, and may be configured to control the operations of the devices or receive information from the devices. For example, the controller 990 may be configured to control the light source 1020 and the off-axis focusing PBP lens 1045, and/or the MEMS 1050.
In some embodiments, the display assembly 930 may be a laser beam scanning projector. The light source 1020 may be configured to emit an image light 1022 with a narrow emission spectrum, e.g., a light beam 1022. For example, the light source 1020 may include at least one of a laser diode or a vertical cavity surface emitting laser (“VCSEL”) configured to emit a laser beam. The light beam 1022 may be a diverging on-axis laser beam with the divergence degree depending on the light source 1020. The light source 1020 may be disposed at an off-axis location with respect to the optical combiner 1010. The display assembly 930 may include one or more optical elements (including the off-axis focusing PBP lens 1045) configured to condition the light beam 1022 received from the light source 1020. Conditioning the light beam 1022 may include, e.g., transmitting, attenuating, expanding, collimating, polarizing, and/or adjusting orientation of the light beam 1022. The off-axis focusing PBP lens 1045 may be disposed at an off-axis location with respect to the optical combiner 1010. The light source 1020 may be disposed at an intersection of an out-of-plane geometry center axis and a focal plane of the off-axis focusing PBP lens 1045 configured for a wavelength of interest or a wavelength range of interest. In the embodiment shown in
In some embodiments, the light beam 1022 may be a circularly polarized light beam with a predetermined handedness. In some embodiments, the light beam 1022 may be a linearly polarized light beam. The display assembly 930 may include a quarter-wave plate (not shown in
The MEMS 1050 may be disposed between the off-axis focusing PBP lens 1045 and the optical combiner 1010. The MEMS 1050 may include electrically rotatable mirrors that are rotatable to steer the light beam 1026, thereby scanning the light beam 1026 across the optical combiner 1010. In some embodiments, each scanned angle of the light beam 1026 may correspond to a point (pixel) of the image. In some embodiments, the light source 1020 may include a single illuminator, e.g., a single laser diode or a single VCSEL. The off-axis focusing PBP lens 1045 may function as a spherical lens that converts the on-axis diverging light beam 1022 into the off-axis collimated light beam 1024. The MEMS 1050 may be a two-dimensional (“2D”) scanning MEMS configured to steer the light beam 1026 across the optical combiner 1010 in two dimensions. Thus, the light beam 1026 may be scanned in two dimensions by the MEMS 1050 across the optical combiner 1010 to provide a 2D image. In some embodiments, the light source 1020 may include a one-dimensional (“1D”) array of illuminators, e.g., a 1D array of micro-lasers or micro-LEDs. The off-axis focusing PBP lens 1045 may function as a cylindrical off-axis focusing PBP lens or a 1D off-axis focusing PBP lens array. The MEMS 1050 may be a one-dimensional (“1D”) scanning MEMS configured to steer the light beam 1026 across the optical combiner 1010 in one dimension. Thus, the light beam 1026 may be scanned by the MEMS 1050 across the optical combiner 1010 in one dimension to provide a 2D image.
In some embodiments, the optical combiner 1010 may be disposed at a substrate 1015 facing the eye 1040 of a user. The substrate 1015 may be transparent in at least a portion of the visible band (e.g., about 380 nm to about 700 nm). In some embodiments, the optical combiner 1010 and the substrate 1015 may be integrated as an eyepiece in a monocular or binocular NED. In some embodiments, the optical combiner 1010 may be configured to direct the light beam 1026 received from the MEMS 1050 to the eye-box of the NED 900, such that the eye 1040 of the user may observe a virtual image. When configured for AR applications, the optical combiner 1010 may combine the light beam 1026 forming a virtual image and a light from a real-world environment, and direct the combined lights toward the eye-box of the NED 900. Accordingly, the user may observe the virtual image optically combined with a view of real-world objects (e.g., with the virtual image superimposed on the user's view of real-world scene).
In some embodiments, the optical combiner 1010 may be configured to direct the light beam 1026 that is scanned across the optical combiner 1010 to an eye-box of the NED 900, such that the eye 1040 of the user may observe a virtual image. The optical combiner 1010 may be any suitable optical combiner. In some embodiments, the optical combiner 1010 may include a holographic optical element (“HOE”). In some embodiments, the HOE may include one or more multiplexed reflective Bragg gratings configured to redirect the light beam 1026 that is scanned across the optical combiner 1010 to the eye 1040. In some embodiments, the reflective Bragg gratings may be strongly wavelength selective, and the light source 1020 may be configured to emit an image light with a narrow emission spectrum, e.g., a laser beam. In the disclosed embodiments, the off-axis focusing PBP lens 1045 may allow for a more compact design of the NED 900. The more compact design may be desirable when the NED 900 is worn as an eyewear to the user's head. The off-axis design provides an optical path that more closely conforms to the shape of the head and the shape of a conventional eyewear. Thus, the off-axis design enables the NED 900 to have a smaller form factor than a conventional on-axis design.
The use of a disclosed off-axis focusing PBP lens in the laser beam scanning projector shown in
In some embodiments, the disclosed off-axis focusing PBP lens or lens stack may be used in other types of projection display systems to improve the form factor, such as a liquid-crystal-on-silicon (“LCoS”) projector system, a digital light processing (“DLP”) projector system, or a liquid crystal display (“LCD”) projector system, etc. In some embodiments, the light source 1020 may include a display panel, such as a liquid crystal display (“LCD”) panel, a liquid-crystal-on-silicon (“LCoS”) display panel, a light-emitting diode (“LED”) display panel, an organic light-emitting diode (“OLED”) display panel, a micro light-emitting diode (“micro-LED”) display panel, a digital light processing (“DLP”) display panel, or a combination thereof. In some embodiments, the light source 1020 may include a self-emissive panel, such as an OLED display panel or a micro-LED display panel. In some embodiments, the light source 1020 may include a display panel that is illuminated by an external source, such as an LCD panel, an LCoS display panel, or a DLP display panel. Examples of an external sources may include a micro-LED, an LED, an OLED, or a combination thereof.
The optical combiner 1010 that includes an HOE shown in
As shown in
In some embodiments, the light source 1115 may emit a light having a relatively narrow spectrum or a relatively broad spectrum. One or more wavelengths of the light may be in the infrared (“IR”) spectrum, i.e., the spectrum of the light source 1115 may be within, overlap, or encompass the IR spectrum. In some embodiments, the light source 1115 may emit lights in the near infrared (“NIR”) band (centered at about 750 nm to 1250 nm), or some other portion of the electromagnetic spectrum. NIR spectrum lights may be desirable in eye-tracking applications because the NIR spectrum lights are not visible to the human eye and thus, do not distract the user of the NED 900 during operation. The lights at the IR spectrum or the NIR spectrum are collectively referred to as infrared lights. The infrared lights may be reflected by at least a pupil area of the eye 1110 (including an eye pupil and skins surrounding the eye pupil). The light source 1115 may have a small size to reduce or suppress disturbance of an image light that is emitted from a light source and directed to the eye 1110. The light source 1115 may include, e.g., a laser diode, a fiber laser, a vertical-cavity surface-emitting laser (“VCSEL”), and/or an LED. In some embodiments, the light source 1110 may include a micro-LED.
In some embodiments, the eye-tracking system 1100 may further include a redirecting element 1145 configured to direct a light reflected by the eye 1110 toward an optical sensor 1150 (or imaging device 1150). In some embodiments, when the NED 900 is used for AR applications, the redirecting element 1145 may also function as an eye-tracking combiner. The eye-tracking combiner may be configured to redirect the light reflected by the eye 1110 toward the optical sensor 1150. The eye-tracking combiner may also be configured to superimpose computer-generated virtual images onto a direct view of the real world. The redirecting element 1145 (e.g., eye tracking combiner) may be substantially transparent for real-world lights and may not cause distortion in a visible light. In the embodiment shown in
The optical sensor 1150 may be arranged relative to the redirecting element 1145, to receive the light from the redirecting element 1145 and generate an image of the eye 1110 (or a portion of the eye 1110 including an eye pupil) based on the received light for eye-tracking purposes. The optical sensor 1150 may be configured to form images based on lights having a wavelength within a spectrum that includes the IR spectrum. In some embodiments, the optical sensor 1150 may be configured to form images based on IR lights but not visible lights. In some embodiments, the optical sensor 1150 may include a suitable type of camera, for example, a silicon-based charge-coupled device (“CCD”) array camera, a complementary metal-oxide-semiconductor (“CMOS”) sensor array camera, a camera having an infrared sensitive (e.g. near-infrared, short-infrared, mid-wave infrared, long-wave infrared sensitive) focal plane array (e.g., a mercury cadmium telluride array, an indium antimonide array, an indium gallium arsenide array, a vanadium oxide array, etc). In some embodiments, the optical sensor 1150 may include a position sensitive detector (“PSD”). The optical sensor 1150 may be mounted at any suitable part of the eye-tracking system 1100 to face the redirecting element 1145 to receive the lights reflected from the eye 1110.
In some embodiments, the optical sensor 1150 may be mounted on a frame 1101 of the NED 900. In some embodiments, the optical sensor 1150 may include a processor configured to process the received IR lights to generate one or more images of the eye 1110, and/or to analyze the images of the eye 1110 to obtain the eye-tracking information. The eye-tracking information may be transmitted to the controller 990 for determining controls of other optical devices or systems, for determining information to be presented to the user, and/or for determining the layout of the presentation of the information, etc. In some embodiments, the optical sensor 1150 may also include a non-transitory computer-readable storage medium (e.g., a computer-readable memory) configured to store data, such as the generated images. In some embodiments, the non-transitory computer-readable storage medium may store codes or instructions that may be executable by the processor to perform various steps of any method disclosed herein. In some embodiments, the processor and the non-transitory computer-readable medium may be provided separately from the optical sensor 1150. For example, the processor may be communicatively coupled with the optical sensor 1150 and configured to receive data (e.g., image data) from the optical sensor 1150. The processor may be configured to analyze the data (e.g., image data of the eye 1110) received from the optical sensor 1150 to obtain the eye-tracking information.
In one embodiment, as shown in
In some embodiments, the light emitted from the light source 1115 may be a linearly polarized light. A quarter-wave plate may be disposed between the light source 1115 and the off-axis focusing PBP lens 1120 to convert the linearly polarized light into a circularly polarized light with a desirable handedness. In some embodiments, the light emitted from the light source 1115 may be an unpolarized light. A suitable optical element (e.g., a circular polarizer) or a suitable combination of optical elements (e.g., a combination of a linear polarizer and a quarter-wave plate) that converts an unpolarized light to a circularly polarized light may be disposed between the light source 1115 and the off-axis focusing PBP lens 1120.
Through configuring the parameters of the off-axis focusing PBP lens 1120 and the polarization of the light 1125 incident onto the off-axis focusing PBP lens 1120, the off-axis diverging RHCP light 1130 output from the off-axis focusing PBP lens 1120 may provide a substantially uniform illumination of at least a corneal area of the eye 1110). For example, the off-axis focusing PBP lens 1120 may provide a uniform illumination of the entire eye 1110 of the user, of an area adjacent the eye 1110, such as above, below, left to, or right to the eye 1110 of the user, or of an area including the eye 1110 and an area surrounding the eye 1110, within a limited distance between the eye 1110 and the light source 1115. With the uniform illumination of the eye 1110, better images of the eye 1110 can be captured by the optical sensor 1150. Accordingly, the accuracy of the eye-tracking may be enhanced. In addition, the eye-tracking system 1100 may have attractive features, such as a small form factor, compactness, and light weight.
In the disclosed embodiments, as shown in
The optical combiner 1315 may have a first surface facing the eye 1310 and an opposing second surface facing the real world. In some embodiments, the eye-tracking system 1300 may further include a circular polarizer 1325 disposed at the second surface of the optical combiner 1315. The circular polarizer 1325 may be configured to substantially transmit the light output from the optical combiner 1315 toward the optical sensor 1320. When the NED 900 is implemented in AR applications, an unpolarized light from the real-world may be converted into a circularly polarized light after passing through the circular polarizer 1325. The optical combiner 1315 may be configured to redirect (and converge when the optical combiner 1315 includes a disclosed off-axis focusing transmissive PBP lens) the received circularly polarized light toward the eye 1310.
In some embodiments, the light 1330 emitted from the light source 1305 may be a linearly polarized light, and a quarter-wave plate may be coupled to the light source 1305 to convert the linearly polarized light into a circularly polarized light with a desirable handedness. In some embodiments, the light 1330 emitted from the light source 1305 may be an unpolarized light. A suitable optical element (e.g., a circular polarizer) or a suitable combination of optical elements (e.g., a combination of a linear polarizer and a quarter-wave plate) may be coupled to the light source 1305 to convert the unpolarized light into a circularly polarized light with a desirable handedness.
In some embodiments, the eye-tracking system 1300 may also include an off-axis focusing PBP lens 1317 disposed between the light source 1035 and the eye 1310. The off-axis focusing PBP lens 1317 may be an embodiment of the off-axis focusing PBP lens 1120 shown in
Some portions of this description may describe the embodiments of the disclosure in terms of algorithms and symbolic representations of operations on information. These operations, while described functionally, computationally, or logically, may be implemented by computer programs or equivalent electrical circuits, microcode, or the like. Furthermore, it has also proven convenient at times, to refer to these arrangements of operations as modules, without loss of generality. The described operations and their associated modules may be embodied in software, firmware, hardware, or any combinations thereof.
Any of the steps, operations, or processes described herein may be performed or implemented with one or more hardware and/or software modules, alone or in combination with other devices. In one embodiment, a software module is implemented with a computer program product including a computer-readable medium containing computer program code, which can be executed by a computer processor for performing any or all of the steps, operations, or processes described. In some embodiments, a hardware module may include hardware components such as a device, a system, an optical element, a controller, an electrical circuit, a logic gate, etc.
Embodiments of the disclosure may also relate to an apparatus for performing the operations herein. This apparatus may be specially constructed for the specific purposes, and/or it may include a general-purpose computing device selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a non-transitory, tangible computer readable storage medium, or any type of media suitable for storing electronic instructions, which may be coupled to a computer system bus. The non-transitory computer-readable storage medium can be any medium that can store program codes, for example, a magnetic disk, an optical disk, a read-only memory (“ROM”), or a random access memory (“RAM”), an Electrically Programmable read only memory (“EPROM”), an Electrically Erasable Programmable read only memory (“EEPROM”), a register, a hard disk, a solid-state disk drive, a smart media card (“SMC”), a secure digital card (“SD”), a flash card, etc. Furthermore, any computing systems described in the specification may include a single processor or may be architectures employing multiple processors for increased computing capability. The processor may be a central processing unit (“CPU”), a graphics processing unit (“GPU”), or any processing device configured to process data and/or performing computation based on data. The processor may include both software and hardware components. For example, the processor may include a hardware component, such as an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or a combination thereof. The PLD may be a complex programmable logic device (“CPLD”), a field-programmable gate array (“FPGA”), etc.
Further, when an embodiment illustrated in a drawing shows a single element, it is understood that the embodiment or another embodiment not shown in the figures but within the scope of the present disclosure may include a plurality of such elements. Likewise, when an embodiment illustrated in a drawing shows a plurality of such elements, it is understood that the embodiment or another embodiment not shown in the figures but within the scope of the present disclosure may include only one such element. The number of elements illustrated in the drawing is for illustration purposes only, and should not be construed as limiting the scope of the embodiment. Moreover, unless otherwise noted, the embodiments shown in the drawings are not mutually exclusive. The disclosed embodiments described in the specification and/or shown in the drawings be combined in any suitable manner. For example, elements shown in one embodiment (e.g., in one figure) but not another embodiment (e.g., in another figure) may nevertheless be included in the other embodiment. Elements shown in one embodiment (e.g., in one figure) may be repeated to form a stacked configuration. Elements shown in different embodiments (e.g., in different figures) may be combined to form a variation of the disclosed embodiments. Elements shown in different embodiments may be repeated and combined to form variations of the disclosed embodiments. Elements mentioned in the descriptions but not shown in the figures may still be included in a disclosed embodiment or a variation of the disclosed embodiment. For example, in an optical device or system disclosed herein including one or more optical layers, films, plates, or elements, the numbers of the layers, films, plates, or elements shown in the figures are for illustrative purposes only. In other embodiments not shown in the figures, which are still within the scope of the present disclosure, the same or different layers, films, plates, or elements shown in the same or different figures/embodiments may be combined and/or repeated in various manners to form variations of the disclosed embodiments. These variations of the disclosed embodiments are also within the scope of the present disclosure.
Various embodiments have been described to illustrate the exemplary implementations. Based on the disclosed embodiments, a person having ordinary skills in the art may make various other changes, modifications, rearrangements, and substitutions without departing from the scope of the present disclosure. Thus, while the present disclosure has been described in detail with reference to the above embodiments, the present disclosure is not limited to the above described embodiments. The present disclosure may be embodied in other equivalent forms without departing from the scope of the present disclosure. The scope of the present disclosure is defined in the appended claims.
