Patent Publication Number: US-11651566-B2

Title: Systems and methods for mixed reality

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     The present application is a continuation of U.S. patent application Ser. No. 16/903,279, filed on Jun. 16, 2020, entitled “SYSTEMS AND METHODS FOR MIXED REALITY”, which claims priority to U.S. patent application Ser. No. 15/980,947, filed on May 16, 2018, entitled “SYSTEMS AND METHODS FOR MIXED REALITY”, and claims priority to U.S. Provisional Application Ser. No. 62/506,841, filed on May 16, 2017, entitled “SYSTEMS AND METHODS FOR MIXED REALITY” and U.S. Provisional Application Ser. No. 62/509,499, filed on May 22, 2017, titled “TECHNIQUE FOR MULTIPLYING BEAMS TO OBTAIN EFFECTIVELY WIDER BEAM IN VIRTUAL/AUGMENTED REALITY SYSTEM.” This application is related to U.S. Utility patent application Ser. No. 15/479,700, filed on Apr. 5, 2017 and entitled “SYSTEMS AND METHODS FOR AUGMENTED REALITY,” U.S. Utility patent application Ser. No. 14/331,218 filed on Jul. 14, 2014 and entitled “PLANAR WAVEGUIDE APPARATUS WITH DIFFRACTION ELEMENT(S) AND SYSTEM EMPLOYING SAME,” U.S. Utility patent application Ser. No. 14/555,585 filed on Nov. 27, 2014 and entitled “VIRTUAL AND AUGMENTED REALITY SYSTEMS AND METHODS,” U.S. Utility patent application Ser. No. 14/726,424 filed on May 29, 2015 and entitled “METHODS AND SYSTEMS FOR VIRTUAL AND AUGMENTED REALITY,” U.S. Utility patent application Ser. No. 14/726,429 filed on May 29, 2015 and entitled “METHODS AND SYSTEMS FOR CREATING FOCAL PLANES IN VIRTUAL AND AUGMENTED REALITY,” and U.S. Utility patent application Ser. No. 14/726,396 filed under on May 29, 2015 and entitled “METHODS AND SYSTEMS FOR DISPLAYING STEREOSCOPY WITH A FREEFORM OPTICAL SYSTEM WITH ADDRESSABLE FOCUS FOR VIRTUAL AND AUGMENTED REALITY.” The contents of the aforementioned patent applications are hereby expressly and fully incorporated by reference in their entirety, as though set forth in full. 
    
    
     FIELD OF THE INVENTION 
     The present disclosure relates to virtual reality, augmented reality, and mixed reality imaging and visualization systems. 
     BACKGROUND OF THE INVENTION 
     Modern computing and display technologies have facilitated the development of “mixed reality” (MR) systems for so called “virtual reality” (VR) or “augmented reality” (AR) experiences, wherein digitally reproduced images or portions thereof are presented to a user in a manner wherein they seem to be, or may be perceived as, real. A VR scenario typically involves presentation of digital or virtual image information without transparency to actual real-world visual input. An AR scenario typically involves presentation of digital or virtual image information as an augmentation to visualization of the real world around the user (i.e., transparency to real-world visual input). Accordingly, AR scenarios involve presentation of digital or virtual image information with transparency to the real-world visual input. 
     MR systems typically generate and display color data, which increases the realism of MR scenarios. Many of these MR systems display color data by sequentially projecting sub-images in different (e.g., primary) colors or “fields” (e.g., Red, Green, and Blue) corresponding to a color image in rapid succession. Projecting color sub-images at sufficiently high rates (e.g., 60 Hz, 120 Hz, etc.) may deliver a smooth color MR scenarios in a user&#39;s mind. 
     For example, referring to  FIG.  1   , an augmented reality scene  4  is depicted wherein a user of an AR/MR technology sees a real-world park-like setting  6  featuring people, trees, buildings in the background, and a concrete platform  8 . In addition to these items, the end user of the AR/MR technology also perceives that he “sees” a robot statue  10  standing upon the real-world platform  8 , and a cartoon-like avatar character  12  flying by which seems to be a personification of a bumble bee, even though these elements  10 ,  12  do not exist in the real world. As it turns out, the human visual perception system is very complex, and producing a VR, AR, and/or MR technology that facilitates a comfortable, natural-feeling, rich presentation of virtual image elements amongst other virtual or real-world imagery elements is challenging. 
     Some VR, AR, and/or MR systems employ head-worn displays (or helmet-mounted displays, or smart glasses) that are at least loosely coupled to a user&#39;s head, and thus move when the end user&#39;s head moves. If the end user&#39;s head motions are detected by the display subsystem, the data being displayed can be updated to take the change in head pose (i.e., the orientation and/or location of user&#39;s head) into account. Head-worn displays that enable AR/MR (i.e., the concurrent viewing of real and virtual objects) can have several different types of configurations. In one such configuration, often referred to as a “video see-through” display, a camera captures elements of a real scene, a computing system superimposes virtual elements onto the captured real scene, and a non-transparent display presents the composite image to the eyes. Another configuration is often referred to as an “optical see-through” display, in which the end user can see through transparent (or semi-transparent) elements in the display subsystem to view directly the light from real objects in the environment. The transparent element, often referred to as a “combiner,” superimposes light from the display over the end user&#39;s view of the real world. 
     Some head-worn VR/AR/MR systems employ a display screen in the field of view of the end user and an image projection assembly that projects images onto the display screen. As one example, the image projection assembly may take the form of an optical fiber scan-based image projection assembly, and the display screen may take the form of a optical waveguide-based display into which scanned and collimated light beams from the image projection assembly are injected via an in-coupling (IC) element, which the exit the surface of the optical waveguide-based display towards the user&#39;s eyes, thereby producing, e.g., images at single optical viewing distance closer than infinity (e.g., arm&#39;s length), images at multiple, discrete optical viewing distances or focal planes, and/or image layers stacked at multiple viewing distances or focal planes to represent volumetric 3D objects. 
     In a head-worn VR/AR/MR system, it is important that the entrance pupil of the user&#39;s eye (i.e., the image of the anatomical pupil as seen through the cornea) be aligned with and be of a similar size to the exit pupil of the display screen (i.e., the width of the cone of light that is available to the eye of the user) in order to properly couple the instrument to the eye (in the case of a monocular arrangement) or eyes (in the case of a binocular arrangement) of the user, given a fixed eye relief (i.e., the distance from the last surface of the display screen and the user&#39;s eye or eyes). An exit pupil of the display screen that is smaller than the entrance pupil of the user&#39; eye will often result in a vignette or clipped image, whereas an exit pupil of the display screen that is larger than the entrance pupil of the user&#39;s eye wastes some light, but allows for movement of the eye without vignetting or clipping of the image. 
     In order to increase the wearability and comfort of a head-worn VR/AR/MR system, it is desirable to miniaturize the image source, and in some cases, the image projection assembly, as much as possible. Such an image projection assembly will, without intervention, result in an exit pupil that is much smaller than the entrance pupil of some eyes, assuming a reasonable eye relief between the eye and the display screen. As such, optics are incorporated into the display subsystem to effectively expand the exit pupil of the display screen to match the entrance pupil of the user&#39;s eye. That is, the exit pupil of the display screen should create an “eye box” that is slightly larger (e.g., 10 mm) than the entrance pupil of the user&#39;s eye (e.g., 5-7 mm) to allow movement of the eye within that eye box to maintain a full view of the image presented by the display screen. 
     Besides matching the exit pupil of the display screen with the entrance pupil of the user&#39;s eye(s), it is desirable to maximize the angular resolution, minimize the depth of field, and maximize the density of the wavefront density of the display screen in a VR/AR/MR system. Maximizing the angular resolution results in a clearer and more vivid virtual image, maximizing the wavefront density alleviates image artifacts (such as the “screen door” effect (grid-like pattern and non-uniformity), and minimizing the depth of the field allows the user to more easily accommodate to virtual content on which the user is currently focused. That is, the smaller the depth of field, the easier it is for an eye to accommodate to the virtual content, providing for a more natural visual real-world experience, whereas the greater the depth of field, the more difficult it is for the eye to accommodate to the virtual content, resulting in a less natural, and perhaps a nauseating, visual experience. 
     There, thus, remains a need to provide a display screen of a VR/AR/MR system that is capable of producing a highly-saturated light beamlet array exit pupil that matches the entrance pupil of the user&#39;s eye(s), without diminishing the wearability of the VR/AR/MR system. 
     The visualization center of the brain gains valuable perception information from the motion of both eyes and components thereof relative to each other. Vergence movements (i.e., rolling movements of the pupils toward or away from each other to converge the lines of sight of the eyes to fixate upon an object) of the two eyes relative to each other are closely associated with focusing (or “accommodation”) of the lenses of the eyes. Under normal conditions, changing the focus of the lenses of the eyes, or accommodating the eyes, to focus upon an object at a different distance will automatically cause a matching change in vergence to the same distance, under a relationship known as the “accommodation-vergence reflex.” Likewise, a change in vergence will trigger a matching change in accommodation, under normal conditions. Working against this reflex, as do most conventional stereoscopic VR/AR/MR configurations, is known to produce eye fatigue, headaches, or other forms of discomfort in users. 
     Stereoscopic wearable glasses generally feature two displays for the left and right eyes that are configured to display images with slightly different element presentation such that a three-dimensional perspective is perceived by the human visual system. Such configurations have been found to be uncomfortable for many users due to a mismatch between vergence and accommodation (“vergence-accommodation conflict”) which must be overcome to perceive the images in three dimensions. Indeed, some VR/AR/MR users are not able to tolerate stereoscopic configurations. Accordingly, most conventional VR/AR/MR systems are not optimally suited for presenting a rich, binocular, three-dimensional experience/scenario in a manner that will be comfortable and maximally useful to the user, in part because prior systems fail to address some of the fundamental aspects of the human perception system, including the vergence-accommodation conflict. 
     One possible approach to address these problems (including the vergence-accommodation conflict) is to project images at multiple depth planes. To implement this type of system, one approach is to use a plurality of light guiding optical elements to direct light at the eyes of a user such that the light appears to originate from multiple depth planes. The light guiding optical elements are designed to in-couple virtual light corresponding to digital or virtual objects and propagate it by total internal reflection (“TIR”), then to out-couple the virtual light to display the digital or virtual objects to the user&#39;s eyes. In AR/MR systems, the light guiding optical elements are also designed to be transparent to light from (e.g., reflecting off of) actual real-world objects. Therefore, portions of the light guiding optical elements are designed to reflect virtual light for propagation via TIR while being transparent to real-world light from real-world objects. 
     Various optical systems generate images at various depths for displaying VR/AR/MR scenarios. Some such optical systems are described in U.S. Utility patent application Ser. No. 14/555,585, the contents of which have been previously incorporated by reference. Some VR/AR/MR systems employ wearable display devices (e.g., head-worn displays, helmet-mounted displays, or smart glasses) that are at least loosely coupled to a user&#39;s head, and thus move when the user&#39;s head moves. 
     Some three-dimensional (“3-D”) optical systems, such as those in VR/AR/MR systems, optically render virtual objects. Objects are “virtual” in that they are not real physical objects located in respective positions in 3-D space. Instead, virtual objects only exist in the brains (e.g., the optical centers) of viewers and/or listeners when stimulated by light beams directed to the eyes of audience members. 
     VR/AR/MR systems must also be capable of displaying virtual digital content at various perceived positions and distances relative to the user. The design of VR/AR/MR systems presents numerous other challenges, including the speed of the system in delivering virtual digital content, quality of virtual digital content, eye relief of the user (addressing the vergence-accommodation conflict), size and portability of the system, and other system and optical challenges. 
     Further, VR/AR/MR systems must be capable of displaying virtual digital content in sharp focus to generate photo-realistic imagery required for a believable, immersive, enjoyable VR/AR/MR experience/scenario. The lens of an eye must change shape (i.e., accommodate) to bring images or portions thereof into better focus. 
     Size restrictions of head-worn displays also result in image resolution limitations. Head-worn VR/AR/MR display systems, such as those described in U.S. Utility patent application Ser. No. 14/555,585, the contents of which have been previously incorporated by reference, display images to users with light beams transmitted by TIR through light guiding optical elements which conserve light beam angles. Light beam diameters remain essentially the same through light guiding optical elements. Size limitations of head-worn displays limited the size of various optical components (e.g., light sources, light guiding optical elements, lenses, etc.), which limits the diameters of light beams generated by the head-worn displays. These light beam diameter limitations result in resolution and FOV limitations described above. 
     The systems and methods described herein are configured to address these challenges. 
     SUMMARY OF THE INVENTION 
     In accordance with a first aspect of the present disclosure, a virtual image generation system comprises a planar optical waveguide (which may be a single unitary substrate) having opposing first and second faces, and an in-coupling (IC) element configured for optically coupling a collimated light beam from an image projection assembly into the planar optical waveguide as an in-coupled light beam. The image projection assembly may comprise a scanning device configured for scanning the collimated light beam. 
     The virtual image generation system further comprises a first orthogonal pupil expansion (OPE) element associated with the first face of the planar optical waveguide for splitting the in-coupled light beam into a first set of orthogonal light beamlets, and a second orthogonal pupil expansion (OPE) element associated with the second face of the planar optical waveguide for splitting the in-coupled light beam into a second set of orthogonal light beamlets. In some embodiments, the first OPE element is disposed on the first face of the planar optical waveguide, and the second OPE element is disposed on the second face of the planar optical waveguide. The IC element may be configured for optically coupling the collimated light beam from the image projection assembly as the in-coupled light beam for propagation within the planar optical waveguide via total internal reflection (TIR) along a first optical path that alternately intersects the first OPE element and the second OPE element, such that portions of the in-coupled light beam are deflected as the respective first set of orthogonal light beamlets and the second set of orthogonal light beamlets that propagate within the planar optical waveguide via TIR along second parallel optical paths. In this case, the second parallel optical paths may be orthogonal to the first optical path. 
     The virtual image generation system further comprises an exit pupil expansion (EPE) element associated with the planar optical waveguide for splitting the first and second sets of orthogonal light beamlets into an array of out-coupled light beamlets (e.g., a two-dimensional out-coupled light beamlet array) that exit the planar optical waveguide. The collimated light beam may define an entrance pupil, and the out-coupled light beamlet array may define an exit pupil larger than the entrance pupil, e.g., at least ten times larger than the entrance pupil, or even at least one hundred times larger than the entrance pupil. 
     In some embodiments, the EPE element is disposed on one of the first and second surfaces of the planar optical waveguide. The first set of orthogonal light beamlets and the second set of orthogonal light beamlets may intersect the EPE element, such that portions of the first set of orthogonal light beamlets and the second set of orthogonal light beamlets are deflected as the out-coupled light beamlet array out of the planar optical waveguide. In some embodiments, the EPE element is configured for imparting a convex wavefront profile on the out-coupled light beamlet array exiting the planar optical waveguide. In this case, the convex wavefront profile may have a center of radius at a focal point to produce an image at a given focal plane. In another embodiment, each of the IC element, OPE element, and EPE element is diffractive. 
     In accordance with a second aspect of the present disclosure, a virtual image generation system comprises a planar optical waveguide comprising a plurality of substrates including a primary substrate having a first thickness, at least two secondary substrates having second thicknesses, and at least two semi-reflective interfaces respectively disposed between the substrates. 
     In some embodiments, each of the second thicknesses is less than the first thickness. For example, the first thickness may be at least twice each of the second thicknesses. In another embodiment, the second thicknesses are substantially equal to each other. In an alternative embodiment, two or more of the secondary substrate(s) have second thicknesses that are not equal to each other. In this case, at least two of the unequal second thicknesses may be non-multiples of each other. In still another embodiment, the first thickness is a non-multiple of at least one of the second thicknesses, and may be a non-multiple of each of the second thicknesses. In yet another embodiment, at least two of the plurality of secondary substrates have second thicknesses that are not substantially equal to each other. 
     In yet another embodiment, each of the semi-reflective interfaces comprises a semi-reflective coating, which may be, e.g., respectively disposed between the substrates via one of physical vapor deposition (PVD), ion-assisted deposition (IAD), and ion beam sputtering (IBS). Each of the coatings may, e.g., be composed of one or more of a metal (Au, Al, Ag, Ni—Cr, Cr and so on), dielectric (Oxides, Fluorides and Sulfides), and semiconductors (Si, Ge). In yet another embodiment, adjacent ones of the substrates are composed of materials having different indices of refraction. 
     The virtual image generation system further comprises an in-coupling (IC) element configured for optically coupling a collimated light beam from an image projection assembly for propagation as an in-coupled light beam within the planar optical waveguide. The image projection assembly may comprise a scanning device configured for scanning the collimated light beam. The semi-reflective interfaces are configured for splitting the in-coupled light beam into a plurality of primary light beamlets that propagate within the primary substrate. 
     The virtual image generation system further comprises one or more diffractive optical elements (DOEs) associated with the planar optical waveguide for further splitting the plurality of primary light beamlets into an array of out-coupled light beamlets (e.g., a two-dimensional out-coupled beamlet array) that exit a face of the planar optical waveguide. The collimated light beam may define an entrance pupil, and the out-coupled light beamlet array may define an exit pupil larger than the entrance pupil, e.g., at least ten times larger than the entrance pupil, or even at least one hundred times larger than the entrance pupil. In some embodiments, the first thickness of the primary substrate and the second thicknesses of the secondary substrates are selected, such that spacings between centers of at least two adjacent ones of the out-coupled light beamlets are equal to or less than a width of the collimated light beam. In another embodiment, the first thickness and the second thicknesses are selected, such that no gap resides between edges of greater than half of adjacent ones of the out-coupled light beamlets. 
     In some embodiments, the semi-reflective interfaces are configured for splitting the in-coupled light beam into at least two in-coupled light beamlets. In this case, the DOE(s) comprises an orthogonal pupil expansion (OPE) element configured for respectively splitting the at least two in-coupled light beamlets into at least two sets of orthogonal light beamlets, the semi-reflective interfaces are further configured for splitting the at least two sets of orthogonal light beamlets into at least four sets of orthogonal light beamlets, and the DOE(s) comprises an exit pupil expansion (EPE) element configured for splitting the at least four sets of orthogonal light beamlets into the set of out-coupled light beamlets. The OPE element and EPE element may be disposed on a face of the optical planar waveguide. 
     The at least two in-coupled light beamlets may propagate within the planar optical waveguide via total internal reflection (TIR) along a first optical path that intersects the OPE element, such that portions of the at least two in-coupled light beamlets are diffracted as the at least two sets of orthogonal light beamlets that propagate within the planar optical waveguide via TIR along second parallel optical paths. The second parallel optical paths may be orthogonal to the first optical path. The at least two sets of orthogonal light beamlets may intersect the EPE element, such that portions of the at least two sets of orthogonal light beamlets are diffracted as the out-coupled set of light beamlets out of the face of the planar optical waveguide. In some embodiments, the EPE element may be configured for imparting a convex wavefront profile on the out-coupled light beamlet array exiting the planar optical waveguide. In this case, the convex wavefront profile may have a center of radius at a focal point to produce an image at a given focal plane. 
     In accordance with a third aspect of the present disclosure, a virtual image generation system comprises a planar optical waveguide comprising a plurality of substrates including a primary substrate having a first thickness, at least one secondary substrate respectively having at least one second thicknesses, and at least one semi-reflective interface respectively disposed between the substrates. 
     The first thickness is at least twice each of the at least one second thickness. In some embodiments, the first thickness is a non-multiple of each of the second thickness(es). In another embodiment, the secondary substrate(s) comprises a plurality of secondary substrates. In this case, the second thicknesses may be equal to each other or two or more of the secondary substrate(s) may have second thicknesses that are not equal to each other. The first thickness may be a non-multiple of at least one of the second thicknesses. At least two of the unequal second thicknesses may be non-multiples of each other. 
     In some embodiments, each of the semi-reflective interface(s) comprises a semi-reflective coating, which may be, e.g., respectively disposed between the substrates via one of physical vapor deposition (PVD), ion-assisted deposition (IAD), and ion beam sputtering (IBS). Each of the coatings may, e.g., be composed of one or more of a metal (Au, Al, Ag, Ni—Cr, Cr and so on), dielectric (Oxides, Fluorides and Sulfides), and semiconductors (Si, Ge). In yet another embodiment, adjacent ones of the substrates are composed of materials having different indices of refraction. 
     The virtual image generation system further comprises an in-coupling (IC) element configured for optically coupling a collimated light beam from an image projection assembly for propagation as an in-coupled light beam within the planar optical waveguide. The image projection assembly may comprise a scanning device configured for scanning the collimated light beam. The semi-reflective interface(s) are configured for splitting the in-coupled light beam into a plurality of primary light beamlets that propagate within the primary substrate. 
     The virtual image generation system further comprises one or more diffractive optical elements (DOEs) associated with the planar optical waveguide for further splitting the plurality of primary light beamlets into an array of out-coupled light beamlets (e.g., a two-dimensional out-coupled beamlet array) that exit a face of the planar optical waveguide. The collimated light beam may define an entrance pupil, and the out-coupled light beamlet array may define an exit pupil larger than the entrance pupil, e.g., at least ten times larger than the entrance pupil, or even at least one hundred times larger than the entrance pupil. In some embodiments, the first thickness of the primary substrate and the second thickness(es) of the secondary substrate(s) are selected, such that spacings between centers of at least two adjacent ones of the out-coupled light beamlets are equal to or less than a width of the collimated light beam. In another embodiment, the first thickness and the second thickness(es) are selected, such that no gap resides between edges of greater than half of adjacent ones of the out-coupled light beamlets. 
     In some embodiments, the semi-reflective interface(s) are configured for splitting the in-coupled light beam into at least two in-coupled light beamlets. In this case, the DOE(s) comprises an orthogonal pupil expansion (OPE) element configured for respectively splitting the at least two in-coupled light beamlets into at least two sets of orthogonal light beamlets, the semi-reflective interface(s) are further configured for splitting the at least two sets of orthogonal light beamlets into at least four sets of orthogonal light beamlets, and the DOE(s) comprises an exit pupil expansion (EPE) element configured for splitting the at least four sets of orthogonal light beamlets into the set of out-coupled light beamlets. The OPE element and EPE element may be disposed on a face of the optical planar waveguide. 
     The at least two in-coupled light beamlets may propagate within the planar optical waveguide via total internal reflection (TIR) along a first optical path that intersects the OPE element, such that portions of the at least two in-coupled light beamlets are diffracted as the at least two sets of orthogonal light beamlets that propagate within the planar optical waveguide via TIR along second parallel optical paths. The second parallel optical paths may be orthogonal to the first optical path. The at least two sets of orthogonal light beamlets may intersect the EPE element, such that portions of the at least two sets of orthogonal light beamlets are diffracted as the out-coupled set of light beamlets out of the face of the planar optical waveguide. In some embodiments, the EPE element may be configured for imparting a convex wavefront profile on the out-coupled light beamlet array exiting the planar optical waveguide. In this case, the convex wavefront profile may have a center of radius at a focal point to produce an image at a given focal plane. 
     In accordance with a fourth aspect of the present disclosure, a virtual image generation system comprises a pre-pupil expansion (PPE) element configured for receiving a collimated light beam from an imaging element and splitting the collimated light beam into a set of initial out-coupled light beamlets. The virtual image generations system further comprises a planar optical waveguide, an in-coupling (IC) element configured for optically coupling the set of initial out-coupled light beamlets into the planar optical waveguide as a set of in-coupled light beamlets, and one or more diffractive elements associated with the planar optical waveguide for splitting the set of in-coupled light beamlets into a set of final out-coupled light beamlets that exit a face of the planar optical waveguide. The diffractive element(s) may comprises an orthogonal pupil expansion (OPE) element associated with the planar optical waveguide for further splitting the set of in-coupled light beamlets into a set of orthogonal light beamlets, and an exit pupil expansion (EPE) element associated with the planar optical waveguide for splitting the set of orthogonal light beamlets into the set of final out-coupled light beamlets. 
     In some embodiments, the collimated light beam defines an entrance pupil, the set of initial out-coupled light beamlets define a pre-expanded pupil larger than the entrance pupil, and the set of final out-coupled light beamlets define an exit pupil larger than the pre-expanded pupil. In one example, the pre-expanded pupil is at least ten times larger than the entrance pupil, and the exit pupil is at least ten times larger than the pre-expanded pupil. In some embodiments, the set of initial out-coupled light beamlets is optically coupled into the planar optical waveguide as a two-dimensional light beamlet array, and the set of final out-coupled light beamlets exits the face of the planar optical waveguide as a two-dimensional light beamlet array. In another embodiment, the set of initial out-coupled light beamlets is optically coupled into the planar optical waveguide as a one-dimensional light beamlet array, and the set of final out-coupled set of light beamlets exits the face of the planar optical waveguide as a two-dimensional light beamlet array. 
     In some embodiments, the PPE element comprises a mini-planar optical waveguide, a mini-OPE element associated with the mini-planar optical waveguide for splitting the collimated light beam into a set of initial orthogonal light beamlets, and a mini-EPE element associated with the mini-planar optical waveguide for splitting the set of initial orthogonal light beamlets into the set of initial out-coupled light beamlets that exit a face of the mini-planar optical waveguide. The PPE may further comprise a mini-IC element configured for optically coupling the collimated light beam into the planar optical waveguide. 
     In another embodiment, the PPE element comprises a diffractive beam splitter (e.g., a 1×N beam splitter or a M×N beam splitter) configured for splitting the collimated light beam into an initial set of diverging light beamlets, and a lens (e.g., a diffractive lens) configured for re-collimating the initial set of diverging light beamlets into the set of initial out-coupled light beamlets. 
     In still another embodiment, the PPE element comprises a prism (e.g., a solid prism or a cavity prism) configured for splitting the collimated light beam into the set of in-coupled light beamlets. The prism may comprise a semi-reflective prism plane configured for splitting the collimated light beam into the set of in-coupled light beamlets. The prism may comprise a plurality of parallel prism planes configured for splitting the collimated light beam into the set of in-coupled light beamlets. In this case, the parallel prism planes may comprise the semi-reflective prism plane. The plurality of parallel prism planes may comprise a completely reflective prism plane, in which case, a portion of the collimated light beam may be reflected by the at least one semi-reflective prism in a first direction, and a portion of the collimated light beam may be transmitted to the completely reflective prism plane for reflection in the first direction. The prism may comprise a first set of parallel prism planes configured for splitting the collimated light beam into a set of initial orthogonal light beamlets that are reflected in a first direction, and a second set of parallel prism planes configured for splitting the initial orthogonal light beamlets into the set of in-coupled light beamlets that are reflected in a second direction different from the first direction. The first and second directional may be orthogonal to each other. 
     In yet another embodiment, the PPE element comprises a first planar optical waveguide assembly configured for splitting the collimated light beam into a two-dimensional array of out-coupled light beamlets (e.g., an N×N light beamlet array) that exits a face of the first planar optical waveguide assembly, and a second planar optical waveguide assembly configured for splitting the two-dimensional out-coupled light beamlet array into multiple two-dimensional arrays of out-out-coupled light beamlets that exit a face of the second planar optical waveguide assembly as the set of in-coupled light beamlets. The first and second planar optical waveguide assemblies may respectively have unequal thicknesses. 
     The two-dimensional out-coupled light beamlet array has an inter-beamlet spacing, and the multiple two-dimensional out-coupled light beamlet arrays are spatially offset from each other by an inter-array spacing different from the inter-beamlet spacing of the two-dimensional out-coupled light beamlet array. In some embodiments, the inter-array spacing of the multiple two-dimensional out-coupled light beamlet arrays and the inter-beamlet spacing of the two-dimensional out-coupled light beamlet array are non-multiples of each other. The inter-array spacing of the multiple two-dimensional out-coupled light beamlet arrays may be greater than the inter-beamlet spacing of the two-dimensional out-coupled light beamlet array. 
     In some embodiments, the first planar optical waveguide assembly comprises a first planar optical waveguide having opposing first and second faces, a first in-coupling (IC) element configured for optically coupling the collimated light beam for propagation within the first planar optical waveguide via total internal reflection (TIR) along a first optical path, a first exit pupil expander (EPE) element associated with the first planar optical waveguide for splitting the collimated light beam into a one-dimensional light beamlet array that exit the second face of the first planar optical waveguide, a second planar optical waveguide having opposing first and second faces, a second IC element configured for optically coupling the one-dimensional light beamlet array for propagation within the second planar optical waveguide via TIR along respective second optical paths that are perpendicular to the first optical path, and a second exit pupil expander (EPE) element associated with the second planar optical waveguide for splitting the one-dimensional light beamlet array into the two-dimensional light beamlet array that exit the second face of the second planar optical waveguide. In this case, the first face of the second planar optical waveguide may be affixed to the second face of the first planar optical waveguide. The first and second planar optical waveguides may respectively have substantially equal thicknesses. 
     The second planar optical waveguide assembly may comprise a third planar optical waveguide having opposing first and second faces, a third IC element configured for optically coupling the first two-dimensional light beamlet array for propagation within the third planar optical waveguide via TIR along respective third optical paths, a third EPE element associated with the third planar optical waveguide for splitting the two-dimensional light beamlet array into a plurality of two-dimensional light beamlet arrays that exit the second face of the third planar optical waveguide, a fourth planar optical waveguide having opposing first and second faces, a fourth IC element configured for optically coupling the plurality of two-dimensional light beamlet arrays for propagation within the fourth planar optical waveguide via TIR along respective fourth optical paths that are perpendicular to the third optical paths, and a fourth EPE element associated with the fourth planar optical waveguide for splitting the plurality of two-dimensional light beamlet arrays into the multiple two-dimensional light beamlet arrays that exit the second face of the fourth planar optical waveguide as the input set of light beamlets. In this case, the first face of the fourth planar optical waveguide may be affixed to the second face of the third planar optical waveguide, and first face of the third planar optical waveguide may be affixed to the second face of the second planar optical waveguide. The first and second planar optical waveguides may respectively have substantially equal thicknesses, and the third and fourth planar optical waveguides may respectively have substantially equal thicknesses. In this case, the substantially equal thicknesses of the first and second planar optical waveguides may be different from the substantially equal thicknesses of the third and fourth planar optical waveguides. The equal thicknesses of the third and fourth planar optical waveguides may be greater than the equal thicknesses of the first and second planar optical waveguides. 
     In some embodiments, a mixed reality system includes a light source configured to generate a virtual light beam. The system also includes a light guiding optical element having an entry portion, an exit portion, a first light guiding optical sub-element, and a second light guiding optical sub-element. The first light guiding optical sub-element has a first thickness, and the second light guiding optical sub-element has a second thickness different from the first thickness. 
     In one or more embodiments, the light source and the light guiding optical element are configured such that the virtual light beam enters the light guiding optical element through the entry portion, propagates through the light guiding optical element by substantially total internal reflection, and divides into a plurality of virtual light beamlets. At least some of the plurality of virtual light beamlets may exit the light guiding optical element through the exit portion. The light guiding optical element may be transparent to a real-world light beam. 
     In one or more embodiments, neither a first quotient of the first and second thicknesses nor a second quotient of the second and first thicknesses are integers. The entry portion may include an in-coupling grating on the first light guiding optical sub-element. The exit portion may include an exit pupil expander on the first light guiding optical sub-element. The second light guiding optical sub-element may not overlay the exit pupil expander on the first light guiding optical sub-element. 
     In one or more embodiments, the second thickness of the second light guiding optical sub-element facilitates substantially total internal reflection of light having a predetermined wavelength. The predetermined wavelength may be from 515 nm to 540 nm. The predetermined wavelength may be 520 nm or 532 nm. The predetermined wavelength may be 475 nm or 650 nm. The second thickness of the second light guiding optical sub-element may facilitate substantially total internal reflection of light beams substantially parallel to an optical axis of the system to a greater degree than light beams oblique to the optical axis. 
     In one or more embodiments, the second light guiding optical sub-element overlays substantially all of the first light guiding optical sub-element. The second thickness may be substantially equal to a whole number multiple of a wavelength of the virtual light beam. The second thickness may be a whole number multiple of 475 nm, 520 nm, or 650 nm. 
     In one or more embodiments, each of the first and second light guiding optical sub-elements includes respective substantially flat sheets, such that the light guiding optical element includes a stack of substantially flat sheets. The light guiding optical element may also have a refractive index gap between the first and second light guiding optical sub-elements. The refractive index gap may be an air layer. 
     In one or more embodiments, the second light guiding optical sub-element includes two reflective surfaces that reflect light in substantially the same direction. The second light guiding optical sub-element may include two reflective surfaces that reflect light in substantially opposite directions. The system may also include a third light guiding optical sub-element. 
     In another embodiment, a mixed reality system includes a light source configured to generate a virtual light beam. The system also includes a light guiding optical element having an entry portion, an exit portion, a first light guiding optical sub-element, and a second light guiding optical sub-element. The first light guiding optical sub-element has a first diffractive index. The second light guiding optical sub-element has a second diffractive index different from the first diffractive index. 
     In one or more embodiments, the light source and the light guiding optical element are configured such that the virtual light beam enters the light guiding optical element through the entry portion, propagates through the light guiding optical element by substantially total internal reflection, and divides into a plurality of virtual light beamlets. At least some of the plurality of virtual light beamlets exit the light guiding optical element through the exit portion. The light guiding optical element may be transparent to a real-world light beam. 
     In one or more embodiments, neither a first quotient of the first and second diffractive indices nor a second quotient of the second and first diffractive indices are integers. The entry portion may include an in-coupling grating on the first light guiding optical sub-element. The exit portion may include an exit pupil expander on the first light guiding optical sub-element. The second light guiding optical sub-element may not overlay the exit pupil expander on the first light guiding optical sub-element. 
     In one or more embodiments, the second diffractive index of the second light guiding optical sub-element facilitates substantially total internal reflection of light have a predetermined wavelength. The predetermined wavelength may be from 515 nm to 540 nm. The predetermined wavelength may be 520 nm or 532 nm. The predetermined wavelength may be 475 nm or 650 nm. 
     In one or more embodiments, the second diffractive index of the second light guiding optical sub-element facilitates substantially total internal reflection of light beams substantially parallel to an optical axis of the system to a greater degree than light beams oblique to the optical axis. The second light guiding optical sub-element may overlay substantially all of the first light guiding optical sub-element. 
     In one or more embodiments, each of the first and second light guiding optical sub-elements includes respective substantially flat sheets, such that the light guiding optical element includes a stack of substantially flat sheets. The light guiding optical element may also have a refractive index gap between the first and second light guiding optical sub-elements. The refractive index gap may be an air layer. 
     In one or more embodiments, the second light guiding optical sub-element includes two reflective surfaces that reflect light in substantially the same direction. The second light guiding optical sub-element may include two reflective surfaces that reflect light in substantially opposite directions. The system may also include a third light guiding optical sub-element. 
     In still another embodiment, a mixed reality system includes a light source configured to generate a virtual light beam. The system also includes a light guiding optical element having an entry portion, an orthogonal pupil expander and a plurality of exit pupil expanders. The light source and the light guiding optical element are configured such that the virtual light beam enters the light guiding optical element through the entry portion, propagates through the light guiding optical element by substantially total internal reflection, divides into a plurality of first virtual light beamlets by interacting with the orthogonal pupil expander, the plurality of first virtual light beamlets entering respective ones of the plurality of exit pupil expanders, and divides into a plurality of second virtual light beamlets by interacting with the plurality of exit pupil expanders. At least some of the plurality of second virtual light beamlets exit the light guiding optical element through the exit pupil expander. 
     In one or more embodiments, the light guiding optical element is transparent to a real-world light beam. Each of the plurality of exit pupil expanders may include a substantially flat sheet, such that the plurality of exit pupil expanders includes a stack of substantially flat sheets. 
     In one or more embodiments, the orthogonal pupil expander facilitates substantially total internal reflection of light have a predetermined wavelength. The predetermined wavelength may be from 515 nm to 540 nm. The predetermined wavelength may be 520 nm or 532 nm. The predetermined wavelength may be 475 nm or 650 nm. 
     In one or more embodiments, the system also includes a plurality of light blockers to selectively block light to the plurality of exit pupil expanders. The plurality of light blockers may include LC shutters or PDLC out-coupling gratings. At least one of the plurality of light blockers may be disposed adjacent an edge of the orthogonal pupil expander. At least one of the plurality of light blockers may be disposed adjacent a central portion of the orthogonal pupil expander. 
     In yet another embodiment, a mixed reality system includes a light source configured to generate a virtual light beam. The system also includes a light guiding optical element having an entry portion, an orthogonal pupil expander and an exit portion. The light source and the light guiding optical element are configured such that the virtual light beam enters the light guiding optical element through the entry portion, propagates through the light guiding optical element by substantially total internal reflection, and divides into a plurality of virtual light beamlets by interacting with the orthogonal pupil expander. At least some of the plurality of virtual light beamlets exit the light guiding optical element through the exit portion. 
     In one or more embodiments, the orthogonal pupil expander includes a first orthogonal pupil sub-expander and a second orthogonal pupil sub-expander. Each of the first and second orthogonal pupil sub-expanders divides light beams entering the respective first and second orthogonal pupil sub-expanders. Each of the first and second orthogonal pupil sub-expanders may be a respective flat sheet. The first and second orthogonal pupil sub-expanders may be stacked on top of each other. 
     In one or more embodiments, the first orthogonal pupil sub-expander includes a first exit edge to direct beamlets into the second orthogonal pupil sub-expander. The first exit edge may include a mirror. The first orthogonal pupil sub-expander may include a second exit edge to direct beamlets into the second orthogonal pupil sub-expander. The first and second exit edges may each include a respective mirror. 
     In one or more embodiments, the orthogonal pupil expander includes first and second reflective edges. The first and second reflective edges may be orthogonal to each other. The orthogonal pupil expander may also include a third reflective edge. 
     In one or more embodiments, the orthogonal pupil expander includes an in-coupling grating and a region of high diffraction disposed opposite of the in-coupling grating. The orthogonal pupil expander may include a first light modifier configured to absorb light in a first wavelength range. The orthogonal pupil expander may also include a second light modifier configured to absorb light in a second wavelength range. The first and second light modifiers may be orthogonal to each other. 
     In one or more embodiments, the orthogonal pupil expander also includes a third light modifier configured to absorb light in a third wavelength range. The orthogonal pupil expander may include diffractive optical elements forming a “V” shape. The orthogonal pupil expander may include a plurality of PDLC swatches. 
     In still another embodiment, a mixed reality system includes a light source configured to generate a virtual light beam. The system also includes a light guiding optical element having an entry portion, an exit portion, a first light guiding optical sub-element, and a second light guiding optical sub-element. The first light guiding optical sub-element has a first light modifying characteristic. The second light guiding optical sub-element has a second light modifying characteristic different from the first light modifying characteristic. 
     A virtual image generation system comprises a planar optical waveguide comprising a plurality of substrates including a primary substrate having a first thickness and at least two secondary substrates having second thicknesses, and at least two semi-reflective interfaces respectively disposed between the substrates. The first thickness may be at least twice each of the second thicknesses. The system further comprises an in-coupling (IC) element configured for optically coupling a collimated light beam for propagation as an in-coupled light beam within the planar optical waveguide. The semi-reflective interfaces are configured for splitting the in-coupled light beam into a plurality of primary light beamlets that propagate within the primary substrate. The system further comprises one or more diffractive optical elements (DOEs) associated with the planar optical waveguide for further splitting the plurality of primary light beamlets into an array of out-coupled light beamlets that exit a face of the planar optical waveguide. 
     A virtual image generation system comprises a pre-pupil expansion (PPE) element configured for receiving a collimated light beam from an imaging element and splitting the collimated light beam into a set of initial out-coupled light beamlets, a planar optical waveguide, an in-coupling (IC) element configured for optically coupling the set of initial out-coupled light beamlets into the planar optical waveguide as a set of in-coupled light beamlets, and one or more diffractive elements associated with the planar optical waveguide for splitting the set of in-coupled light beamlets into a set of final out-coupled light beamlets that exit a face of the planar optical waveguide. 
     A mixed reality system includes a light source configured to generate a virtual light beam. The system also includes a light guiding optical element having an entry portion, an exit portion, a first light guiding optical sub-element, and a second light guiding optical sub-element. The first light guiding optical sub-element has a first thickness, and the second light guiding optical sub-element has a second thickness different from the first thickness. 
     Additional and other objects, features, and advantages of the disclosure are described in the detail description, figures and claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The drawings illustrate the design and utility of preferred embodiments of the present disclosure, in which similar elements are referred to by common reference numerals. In order to better appreciate how the above-recited and other advantages and objects of the present disclosure are obtained, a more particular description of the present disclosure briefly described above will be rendered by reference to specific embodiments thereof, which are illustrated in the accompanying drawings. Understanding that these drawings depict only typical embodiments of the disclosure and are not therefore to be considered limiting of its scope, the disclosure will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG.  1    is a picture of a three-dimensional augmented reality scene that can be displayed to an end user by a prior art augmented reality generation device; 
         FIG.  2    is a block diagram of a virtual image generation system constructed in accordance with some embodiments of the present disclosure; 
         FIG.  3 A  is a plan view of one technique that can be used to wear the virtual image generation system of  FIG.  2   ; 
         FIG.  3 B  is a plan view of another technique that can be used to wear the virtual image generation system of  FIG.  2   ; 
         FIG.  3 C  is a plan view of still another one technique that can be used to wear the virtual image generation system of  FIG.  2   ; 
         FIG.  3 D  is a plan view of yet another one technique that can be used to wear the virtual image generation system of  FIG.  2   ; 
         FIGS.  4 ,  7 , and  8    are detailed schematic views of various mixed reality systems; 
         FIG.  5    is a plan view of some embodiments of a display subsystem used in the virtual image generation system of  FIG.  2   ; 
         FIG.  6    is a conceptual view of some embodiments of a primary waveguide apparatus used in the display subsystem of  FIG.  5   ; 
         FIG.  9    is a diagram depicting the focal planes of an mixed reality system; 
         FIG.  10    is a detailed schematic view of a light-guiding optical element of an mixed reality system; 
         FIGS.  11 A,  12 A,  13 A,  14 A, and  15 A  are schematic views of light beams entering an eye according to various embodiments; 
         FIGS.  11 B,  12 B,  13 B,  14 B, and  15 B  are energy distribution patterns of the light beams in corresponding  FIGS.  11 A,  12 A,  13 A,  14 A, and  15 A  as focused by a lens onto a retina according to various embodiments; 
         FIG.  16 A  is a schematic view of light beamlets entering an eye according to some embodiments; 
         FIG.  16 B  is an energy distribution pattern of the light beamlets in  FIG.  16 A  as focused by a lens onto a retina according to some embodiments; 
         FIG.  17 A  is a schematic view of a light guiding optical element generating an array of beamlets according to some embodiments; 
         FIG.  17 B  is a schematic view of light beamlets in relationship to a pupil formed by an iris according to some embodiments; 
         FIGS.  18 A- 18 C  are schematic views showing light beamlets on retinas according to various embodiments; 
         FIG.  19    is a schematic view of light beams and beamlets propagating through a beam multiplier according to some embodiments; 
         FIG.  20    is a schematic view of light beams and beamlets propagating through a beam multiplier and into an eye according to some embodiments; 
         FIG.  21    is a schematic view of light beams and beamlets propagating through two beam multipliers and into an eye according to some embodiments; 
         FIGS.  22 A- 33 I  are schematic views of light beams and beamlets propagating through beam multipliers according to various embodiments; 
         FIG.  34    is a plan view of some embodiments of the primary waveguide apparatus of  FIG.  6   ; 
         FIG.  35    is a cross-sectional view of the primary waveguide apparatus of  FIG.  34   , taken along the line  35 - 35 ; 
         FIG.  36    is a cross-sectional view of the primary waveguide apparatus of  FIG.  34   , taken along the line  36 - 36 ; 
         FIG.  37    is a plan view of another embodiment of the primary waveguide apparatus of  FIG.  6   ; 
         FIG.  38    is a plan view of still another embodiment of the primary waveguide apparatus of  FIG.  6   ; 
         FIGS.  39 A- 39 C  are perspective views of the primary waveguide apparatus of  FIG.  34   , particularly showing the emission of out-coupled light beamlets at different focal planes; 
         FIG.  40 A  is a conceptual view of a relatively sparse exit pupil of a waveguide apparatus of a display screen; 
         FIG.  40 B  is a conceptual view of a relatively dense exit pupil of a modified embodiment of the primary waveguide apparatus of  FIG.  34   ; 
         FIG.  41    is a plan view of some embodiments of the modified primary waveguide apparatus of  FIG.  40 B ; 
         FIG.  42    is a cross-sectional view of the primary waveguide apparatus of  FIG.  41   , taken along the line  42 - 42 ; 
         FIG.  43    is a cross-sectional view of the primary waveguide apparatus of  FIG.  41   , taken along the line  43 - 43 ; 
         FIG.  44    is a plan view of another embodiment of the modified primary waveguide apparatus of  FIG.  40 B ; 
         FIG.  45    is a cross-sectional view of a first variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  45 - 45 ; 
         FIG.  46    is a cross-sectional view of the first variation primary waveguide apparatus of  FIG.  44   , taken along the line  46 - 46 ; 
         FIGS.  47 A- 47 D  are profile views illustrating the beam splitting technique employed in the modified primary waveguide apparatus of  FIG.  45   ; 
         FIG.  48    is a cross-sectional view of the first variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  48 - 48 , particularly showing the overlap of light beamlets; 
         FIG.  49    is a cross-sectional view of the first variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  49 - 49 , particularly showing the overlap of light beamlets; 
         FIG.  50    is a cross-sectional view of a second variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  50 - 50 ; 
         FIG.  51    is a cross-sectional view of the second variation primary waveguide apparatus of  FIG.  44   , taken along the line  51 - 51 ; 
         FIG.  52    is a cross-sectional view of the second variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  52 - 52 , particularly showing the overlap of light beamlets; 
         FIG.  53    is a cross-sectional view of the second variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  53 - 53 , particularly showing the overlap of light beamlets; 
         FIG.  54    is a cross-sectional view of a third variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  54 - 54 ; 
         FIG.  55    is a cross-sectional view of the third variation primary waveguide apparatus of  FIG.  44   , taken along the line  55 - 55 ; 
         FIG.  56    is a cross-sectional view of a fourth variation of the primary waveguide apparatus of  FIG.  44   , taken along the line  56 - 56 ; 
         FIG.  57    is a cross-sectional view of the fourth variation primary waveguide apparatus of  FIG.  44   , taken along the line  57 - 57 ; 
         FIG.  58    is a plan view of another embodiment of a display subsystem used in the virtual image generation system of  FIG.  2   ; 
         FIGS.  59 A and  59 B  are conceptual views of a relatively dense exit pupil of a primary waveguide apparatus of a display screen that has been pre-expanded with a pre-pupil expander (PPE); 
         FIG.  60    is a plan view of some embodiments of the PPE of  FIGS.  59 A and  59 B  used with the primary waveguide apparatus of  FIG.  6   ; 
         FIG.  61    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  60   , taken along the line  61 - 61 ; 
         FIG.  62    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  60   , taken along the line  62 - 62 ; 
         FIG.  63    is a conceptual view of the pre-expansion and conventional expansion of the entrance pupil of the collimated light beam to an exit pupil using the PPE of  FIG.  60   ; 
         FIG.  64    is a plan view of another embodiment of the PPE of  FIGS.  59 A and  59 B  used with the primary waveguide apparatus of  FIG.  34   ; 
         FIG.  65    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  64   , taken along the line  65 - 65 ; 
         FIG.  66    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  64   , taken along the line  66 - 66 ; 
         FIGS.  67 A and  67 B  are profile views of different variations of the PPE of  FIG.  64   ; 
         FIG.  68    is a plan view of still another embodiment of the PPE of  59 A and  59 B used with the primary waveguide apparatus of  FIG.  34   ; 
         FIG.  69    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  68   , taken along the line  69 - 69 ; 
         FIG.  70    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  68   , taken along the line  70 - 70 ; 
         FIG.  71    is a perspective view of the PPE of  FIG.  68   ; 
         FIG.  72    is a cross-sectional view of a first variation of the PPE of  FIG.  71   , taken along the line  72 - 72 ; 
         FIG.  73    is a cross-sectional view of the first variation of the PPE of  FIG.  71   , taken along the line  73 - 73 ; 
         FIG.  74    is a cross-sectional view of a second variation of the PPE of  FIG.  71   , taken along the line  74 - 74 ; 
         FIG.  75    is a cross-sectional view of the second variation of the PPE of  FIG.  71   , taken along the line  75 - 75 ; 
         FIG.  76    is a plan view of still another embodiment of the PPE of  FIGS.  31 A and  31 B  used with the primary waveguide apparatus of  FIG.  34   ; 
         FIG.  77    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  76   , taken along the line  77 - 77 ; 
         FIG.  78    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  76   , taken along the line  78 - 78 ; 
         FIG.  79    is a perspective view of the PPE of  FIG.  76   ; 
         FIG.  80    is a plan view of yet another embodiment of the PPE of  FIGS.  59 A and  59 A  used with the primary waveguide apparatus of  FIG.  34   ; 
         FIG.  81    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  80   , taken along the line  81 - 81 ; 
         FIG.  82    is a cross-sectional view of the primary waveguide apparatus and PPE of  FIG.  80   , taken along the line  82 - 82 ; 
         FIG.  83    is a perspective exploded view of the PPE of  FIG.  80   ; 
         FIG.  84    is a perspective view of some embodiments of a planar waveguide assembly used in the PPE of  FIG.  83   ; 
         FIGS.  85 A and  85 B  are perspective views of top and bottom planar orthogonal waveguide units used in the planar waveguide assembly of  FIG.  84   ; 
         FIG.  86 A  and  FIG.  86 B  are cross-sectional views of the PPE of  FIG.  80   ; 
         FIGS.  87 A- 87 C  are plan views of transfer functions of the top and bottom planar orthogonal wave guide units of  FIGS.  85 A and  85 B ; 
         FIG.  88    is one diagram illustrating various generations of beam splitting performed by a top planar waveguide assembly used in the PPE of  FIG.  80    to split a two-dimensional array of beamlets into multiple two-dimensional arrays of beamlets that accumulated to define a highly-saturated exit pupil; 
         FIGS.  89 A- 89 H  are plan views illustrating the generation of the multiple two-dimensional arrays of light beamlets from a single two-dimensional array of light beamlets using the PPE of  FIG.  80   ; and 
         FIGS.  90 A- 90 D  are plan views illustrating the correspondence of four different families of beamlets in the beam pattern of  FIGS.  89 A and  89 A  to four different initial beamlets in the single two-dimensional array of light beamlets of  FIG.  89 A . 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     The description that follows relates to display subsystems and methods to be used in an augmented reality system. However, it is to be understood that while the disclosure lends itself well to applications in augmented reality systems, the disclosure, in its broadest aspects, may not be so limited, and may be applied to any waveguide-based imaging system. For example, the disclosure can be applied to virtual reality systems. Thus, while often described herein in terms of an augmented reality system, the teachings should not be limited to such systems of such uses. 
     Various embodiments of the disclosure are directed to systems, methods, and articles of manufacture for implementing optical systems in a single embodiment or in multiple embodiments. Other objects, features, and advantages of the disclosure are described in the detailed description, figures, and claims. 
     Various embodiments will now be described in detail with reference to the drawings, which are provided as illustrative examples of the disclosure so as to enable those skilled in the art to practice the disclosure. Notably, the figures and the examples below are not meant to limit the scope of the present disclosure. Where certain elements of the present disclosure may be partially or fully implemented using known components (or methods or processes), only those portions of such known components (or methods or processes) that are necessary for an understanding of the present disclosure will be described, and the detailed descriptions of other portions of such known components (or methods or processes) will be omitted so as not to obscure the disclosure. Further, various embodiments encompass present and future known equivalents to the components referred to herein by way of illustration. 
     The optical systems may be implemented independently of AR/MR systems, but many embodiments below are described in relation to AR/MR systems for illustrative purposes only. 
     Referring to  FIG.  2   , some embodiments of a virtual image generation system  100  constructed in accordance with present disclosure will now be described. The virtual image generation system  100  may be operated as an augmented reality subsystem, providing images of virtual objects intermixed with physical objects in a field of view of an end user  50 . There are two fundamental approaches when operating the virtual image generation system  100 . A first approach employs one or more imagers (e.g., cameras) to capture images of the ambient environment. The virtual image generation system  100  inter-mixes the virtual images into the data representing the images of the ambient environment. A second approach employs one or more at least partially transparent surfaces through which the ambient environment can be seen and onto which the virtual image generation system  100  produces images of virtual objects. 
     The virtual image generation system  100 , and the various techniques taught herein, may be employed in applications other than augmented reality and virtual reality subsystems. For example, various techniques may be applied to any projection or display subsystem, or may be applied to pico projectors where movement may be made by an end user&#39;s hand rather than the head. Thus, while often described herein in terms of an augmented reality subsystem or virtual reality subsystem, the teachings should not be limited to such subsystems of such uses. 
     At least for augmented reality applications, it may be desirable to spatially position various virtual objects relative to respective physical objects in a field of view of the end user  50 . Virtual objects, also referred to herein as virtual tags or tag or call outs, may take any of a large variety of forms, basically any variety of data, information, concept, or logical construct capable of being represented as an image. Non-limiting examples of virtual objects may include: a virtual text object, a virtual numeric object, a virtual alphanumeric object, a virtual tag object, a virtual field object, a virtual chart object, a virtual map object, a virtual instrumentation object, or a virtual visual representation of a physical object. 
     The virtual image generation system  100  comprises a frame structure  102  worn by an end user  50 , a display subsystem  104  carried by the frame structure  102 , such that the display subsystem  104  is positioned in front of the eyes  52  of the end user  50 , and a speaker  106  carried by the frame structure  102 , such that the speaker  106  is positioned adjacent the ear canal of the end user  50  (optionally, another speaker (not shown) is positioned adjacent the other ear canal of the end user  50  to provide for stereo/shapeable sound control). The display subsystem  104  is designed to present the eyes  52  of the end user  50  with photo-based radiation patterns that can be comfortably perceived as augmentations to physical reality, with high-levels of image quality and three-dimensional perception, as well as being capable of presenting two-dimensional content. The display subsystem  104  presents a sequence of frames at high frequency that provides the perception of a single coherent scene. 
     In the illustrated embodiment, the display subsystem  104  employs “optical see-through” display through which the user can directly view light from real objects via transparent (or semi-transparent) elements. The transparent element, often referred to as a “combiner,” superimposes light from the display over the user&#39;s view of the real world. To this end, the display subsystem  104  comprises a projection subsystem  108  and a partially transparent display screen  110  on which the projection subsystem  108  projects images. The display screen  110  is positioned in the end user&#39;s  50  field of view between the eyes  52  of the end user  50  and an ambient environment, such that direct light from the ambient environment is transmitted through the display screen  110  to the eyes  52  of the end user  50 . 
     In the illustrated embodiment, the image projection assembly  108  provides a scanned light to the partially transparent display screen  110 , thereby combining with the direct light from the ambient environment, and being transmitted from the display screen  110  to the eyes  52  of the user  50 . In the illustrated embodiment, the projection subsystem  108  takes the form of an optical fiber scan-based projection device, and the display screen  110  takes the form of a waveguide-based display into which the scanned light from the projection subsystem  108  is injected to produce, e.g., images at a single optical viewing distance closer than infinity (e.g., arm&#39;s length), images at multiple, discrete optical viewing distances or focal planes, and/or image layers stacked at multiple viewing distances or focal planes to represent volumetric 3D objects. These layers in the light field may be stacked closely enough together to appear continuous to the human visual subsystem (i.e., one layer is within the cone of confusion of an adjacent layer). Additionally or alternatively, picture elements may be blended across two or more layers to increase perceived continuity of transition between layers in the light field, even if those layers are more sparsely stacked (i.e., one layer is outside the cone of confusion of an adjacent layer). The display subsystem  104  may be monocular or binocular. 
     The virtual image generation system  100  further comprises one or more sensors (not shown) mounted to the frame structure  102  for detecting the position and movement of the head  54  of the end user  50  and/or the eye position and inter-ocular distance of the end user  50 . Such sensor(s) may include image capture devices (such as cameras), microphones, inertial measurement units, accelerometers, compasses, GPS units, radio devices, and/or gyros). 
     The virtual image generation system  100  further comprises a user orientation detection module  112 . The user orientation module  112  detects the instantaneous position of the head  54  of the end user  50  and may predict the position of the head  54  of the end user  50  based on position data received from the sensor(s). Detecting the instantaneous position of the head  54  of the end user  50  facilitates determination of the specific actual object that the end user  50  is looking at, thereby providing an indication of the specific textual message to be generated for that actual object and further providing an indication of the textual region in which the textual message is to be streamed. The user orientation module  112  also tracks the eyes  52  of the end user  50  based on the tracking data received from the sensor(s). 
     The virtual image generation system  100  further comprises a control subsystem that may take any of a large variety of forms. The control subsystem includes a number of controllers, for instance one or more microcontrollers, microprocessors or central processing units (CPUs), digital signal processors, graphics processing units (GPUs), other integrated circuit controllers, such as application specific integrated circuits (ASICs), programmable gate arrays (PGAs), for instance field PGAs (FPGAs), and/or programmable logic controllers (PLUs). 
     The control subsystem of virtual image generation system  100  comprises a central processing unit (CPU)  114 , a graphics processing unit (GPU)  116 , one or more frame buffers  118 , and three-dimensional data base  120  for storing three-dimensional scene data. The CPU  114  controls overall operation, while the GPU  116  renders frames (i.e., translating a three-dimensional scene into a two-dimensional image) from the three-dimensional data stored in the three-dimensional data base  120  and stores these frames in the frame buffer(s)  116 . While not illustrated, one or more additional integrated circuits may control the reading into and/or reading out of frames from the frame buffer(s)  116  and operation of the image projection assembly  108  of the display subsystem  104 . 
     The various processing components of the virtual image generation system  100  may be physically contained in a distributed subsystem. For example, as illustrated in  FIGS.  3 A- 3 D , the virtual image generation system  100  comprises a local processing and data module  130  operatively coupled, such as by a wired lead or wireless connectivity  136 , to the display subsystem  104  and sensors. The local processing and data module  130  may be mounted in a variety of configurations, such as fixedly attached to the frame structure  102  ( FIG.  3 A ), fixedly attached to a helmet or hat  56  ( FIG.  3 B ), embedded in headphones, removably attached to the torso  58  of the end user  50  ( FIG.  3 C ), or removably attached to the hip  60  of the end user  50  in a belt-coupling style configuration ( FIG.  3 D ). The virtual image generation system  100  further comprises a remote processing module  132  and remote data repository  134  operatively coupled, such as by a wired lead or wireless connectivity  138 ,  140 , to the local processing and data module  130 , such that these remote modules  132 ,  134  are operatively coupled to each other and available as resources to the local processing and data module  130 . 
     The local processing and data module  130  may comprise a power-efficient processor or controller, as well as digital memory, such as flash memory, both of which may be utilized to assist in the processing, caching, and storage of data captured from the sensors and/or acquired and/or processed using the remote processing module  132  and/or remote data repository  134 , possibly for passage to the display subsystem  104  after such processing or retrieval. The remote processing module  132  may comprise one or more relatively powerful processors or controllers configured to analyze and process data and/or image information. The remote data repository  134  may comprise a relatively large-scale digital data storage facility, which may be available through the internet or other networking configuration in a “cloud” resource configuration. In some embodiments, all data is stored and all computation is performed in the local processing and data module  130 , allowing fully autonomous use from any remote modules. 
     The couplings  136 ,  138 ,  140  between the various components described above may include one or more wired interfaces or ports for providing wires or optical communications, or one or more wireless interfaces or ports, such as via RF, microwave, and IR for providing wireless communications. In some implementations, all communications may be wired, while in other implementations all communications may be wireless. In still further implementations, the choice of wired and wireless communications may be different from that illustrated in  FIGS.  3 A- 3 D . Thus, the particular choice of wired or wireless communications should not be considered limiting. 
     In the illustrated embodiment, the user orientation module  112  is contained in the local processing and data module  130 , while CPU  114  and GPU  116  are contained in the remote processing module  132 , although in alternative embodiments, the CPU  114 , GPU  124 , or portions thereof may be contained in the local processing and data module  130 . The 3D database  120  can be associated with the remote data repository  134 . 
     Before describing the details of embodiments of the light guiding optical elements, this disclosure will now provide a brief description of illustrative MR systems. 
     One possible approach to implementing an MR system uses a plurality of volume phase holograms, surface-relief holograms, or light guiding optical elements that are embedded with depth plane information to generate images that appear to originate from respective depth planes. In other words, a diffraction pattern, or diffractive optical element (“DOE”) may be embedded within or imprinted/embossed upon a light guiding optical element (“LOE”; e.g., a planar waveguide) such that as collimated light (light beams with substantially planar wavefronts) is substantially totally internally reflected along the LOE, it intersects the diffraction pattern at multiple locations and exits toward the user&#39;s eye. The DOEs are configured so that light exiting therethrough from an LOE are verged so that they appear to originate from a particular depth plane. The collimated light may be generated using an optical condensing lens (a “condenser”). 
     For example, a first LOE may be configured to deliver collimated light to the eye that appears to originate from the optical infinity depth plane (0 diopters). Another LOE may be configured to deliver collimated light that appears to originate from a distance of 2 meters (½ diopter). Yet another LOE may be configured to deliver collimated light that appears to originate from a distance of 1 meter (1 diopter). By using a stacked LOE assembly, it can be appreciated that multiple depth planes may be created, with each LOE configured to display images that appear to originate from a particular depth plane. It should be appreciated that the stack may include any number of LOEs. However, at least N stacked LOEs are required to generate N depth planes. Further, N,  2 N or  3 N stacked LOEs may be used to generate RGB colored images at N depth planes. 
     In order to present 3-D virtual content to the user, the mixed reality (MR) system projects images of the virtual content into the user&#39;s eye so that they appear to originate from various depth planes in the Z direction (i.e., orthogonally away from the user&#39;s eye). In other words, the virtual content may not only change in the X and Y directions (i.e., in a 2D plane orthogonal to a central visual axis of the user&#39;s eye), but it may also appear to change in the Z direction such that the user may perceive an object to be very close or at an infinite distance or any distance in between. In other embodiments, the user may perceive multiple objects simultaneously at different depth planes. For example, the user may see a virtual dragon appear from infinity and run towards the user. Alternatively, the user may simultaneously see a virtual bird at a distance of 3 meters away from the user and a virtual coffee cup at arm&#39;s length (about 1 meter) from the user. 
     Multiple-plane focus systems create a perception of variable depth by projecting images on some or all of a plurality of depth planes located at respective fixed distances in the Z direction from the user&#39;s eye. Referring now to  FIG.  9   , it should be appreciated that multiple-plane focus systems may display frames at fixed depth planes  502  (e.g., the six depth planes  502  shown in  FIG.  9   ). Although MR systems can include any number of depth planes  502 , one exemplary multiple-plane focus system has six fixed depth planes  502  in the Z direction. In generating virtual content one or more of the six depth planes  502 , 3-D perception is created such that the user perceives one or more virtual objects at varying distances from the user&#39;s eye. Given that the human eye is more sensitive to objects that are closer in distance than objects that appear to be far away, more depth planes  502  are generated closer to the eye, as shown in  FIG.  9   . In other embodiments, the depth planes  502  may be placed at equal distances away from each other. 
     Depth plane positions  502  may be measured in diopters, which is a unit of optical power equal to the inverse of the focal length measured in meters. For example, in some embodiments, depth plane  1  may be ⅓ diopters away, depth plane  2  may be 0.3 diopters away, depth plane  3  may be 0.2 diopters away, depth plane  4  may be 0.15 diopters away, depth plane  5  may be 0.1 diopters away, and depth plane  6  may represent infinity (i.e., 0 diopters away). It should be appreciated that other embodiments may generate depth planes  502  at other distances/diopters. Thus, in generating virtual content at strategically placed depth planes  502 , the user is able to perceive virtual objects in three dimensions. For example, the user may perceive a first virtual object as being close to him when displayed in depth plane  1 , while another virtual object appears at infinity at depth plane  6 . Alternatively, the virtual object may first be displayed at depth plane  6 , then depth plane  5 , and so on until the virtual object appears very close to the user. It should be appreciated that the above examples are significantly simplified for illustrative purposes. In another embodiment, all six depth planes may be concentrated on a particular focal distance away from the user. For example, if the virtual content to be displayed is a coffee cup half a meter away from the user, all six depth planes could be generated at various cross-sections of the coffee cup, giving the user a highly granulated 3-D view of the coffee cup. 
     In some embodiments, the AR system may work as a multiple-plane focus system. In other words, all six LOEs may be illuminated simultaneously, such that images appearing to originate from six fixed depth planes are generated in rapid succession with the light sources rapidly conveying image information to LOE  1 , then LOE  2 , then LOE  3  and so on. For example, a portion of the desired image, comprising an image of the sky at optical infinity may be injected at time  1  and the LOE  1090  retaining collimation of light (e.g., depth plane  6  from  FIG.  9   ) may be utilized. Then an image of a closer tree branch may be injected at time  2  and an LOE  1090  configured to create an image appearing to originate from a depth plane 10 meters away (e.g., depth plane  5  from  FIG.  9   ) may be utilized; then an image of a pen may be injected at time  3  and an LOE  1090  configured to create an image appearing to originate from a depth plane 1 meter away may be utilized. This type of paradigm can be repeated in rapid time sequential (e.g., at 360 Hz) fashion such that the user&#39;s eye and brain (e.g., visual cortex) perceives the input to be all part of the same image. 
     AR systems are required to project images (i.e., by diverging or converging light beams) that appear to originate from various locations along the Z axis (i.e., depth planes) to generate images for a 3-D experience/scenario. As used in this application, light beams include, but are not limited to, directional projections of light energy (including visible and invisible light energy) radiating from a light source. Generating images that appear to originate from various depth planes conforms the vergence and accommodation of the user&#39;s eye for that image, and minimizes or eliminates vergence-accommodation conflict. 
       FIG.  4    depicts a basic optical system  400  for projecting images at a single depth plane. The system  400  includes a light source  420  and an LOE  490  having a diffractive optical element (not shown) and an in-coupling grating  492  (ICG) associated therewith. The diffractive optical elements may be of any type, including volumetric or surface relief. In some embodiments, the ICG  492  is a reflection-mode aluminized portion of the LOE  490 . In another embodiment, the ICG  492  is a transmissive diffractive portion of the LOE  490 . When the system  400  is in use, the light beam from the light source  420  enters the LOE  490  via the ICG  492  and propagates along the LOE  490  by substantially total internal reflection (“TIR”) for display to an eye of a user. It is understood that although only one beam is illustrated in  FIG.  4   , a multitude of beams may enter LOE  490  from a wide range of angles through the same ICG  492 . A light beam “entering” or being “admitted” into an LOE includes, but is not limited to, the light beam interacting with the LOE so as to propagate along the LOE by substantially TIR. The system  400  depicted in  FIG.  4    can include various light sources  420  (e.g., LEDs, OLEDs, lasers, and masked broad-area/broad-band emitters). In other embodiments, light from the light source  420  may be delivered to the LOE  490  via fiber optic cables (not shown). 
     Referring now to  FIG.  5   , the image projection assembly  108  includes one or more light sources  150  that produces the light (e.g., emits light of different colors in defined patterns). The light source(s)  150  may take any of a large variety of forms, for instance, a set of RGB lasers (e.g., laser diodes capable of outputting red, green, and blue light) operable to respectively produce red, green, and blue coherent collimated light according to defined pixel patterns specified in respective frames of pixel information or data. Laser light provides high color saturation and is highly energy efficient. 
     The image projection assembly  108  further comprises a scanning device  152  that scans the light in a predetermined scan pattern in response to control signals. The scanning device  152  comprises one or more optical fibers  154  (e.g., single mode optical fiber), each of which has a proximal end  154   a  into which light is received from the light source(s)  150  and a distal end  154   b  from which light is provided to the display screen  110 . The scanning device  152  further comprises a mechanical drive assembly  156  to which the optical fiber(s)  154  is mounted. The drive assembly  156  is configured for displacing the distal end  154   b  of each optical fiber  154  about a fulcrum  158  in accordance with a scan pattern. 
     To this end, the drive assembly  156  comprises a piezoelectric element  160  to which the optical fiber(s)  154  is mounted, and drive electronics  162  configured for conveying electrical signals to the piezoelectric element  160 , thereby causing the distal end  154   b  of the optical fiber  154  to vibrate in accordance with the scan pattern. Thus, operation of the light source(s)  150  and drive electronics  162  are coordinated in a manner that generates image data that is encoded in the form of light that is spatially and/or temporally varying. Descriptions of optical fiber scanning techniques are provided in U.S. Patent No. 2015/0309264, which is expressly incorporated herein by reference. 
     The image projection assembly  108  further comprises an optical coupling assembly  164  that couples the light from the scanning device  152  into the display screen  110 . The optical coupling assembly  164  comprises a collimation element  166  that collimates the light emitted by the scanning device  152  into a collimated light beam  250 . Although the collimation element  166  is illustrated in  FIG.  5    as being physically separated from the optical fiber(s)  154 , a collimation element may be physically mounted to the distal end  154   b  of each optical fiber  154  in a “micro-lens” arrangement, as described in U.S. patent application Ser. No. 15/286,215, entitled “Microlens Collimator for Scanning Optical Fiber in Virtual/Augmented Reality System,” which is expressly incorporated herein by reference. The optical coupling subsystem  164  further comprises an in-coupling (IC) element  168 , for instance, one or more reflective surfaces, diffraction gratings, mirrors, dichroic mirrors, or prisms to optically couple light into the end of the display screen  110  at an angle that ensures that the light propagates within the display screen  110  in a desired direction, as will be described in further detail below. 
     As will be described in further detail below, the optical coupling subsystem  164  optically couples the collimated light beam  250  into the display screen  110 , which will expand the pupil size of the collimated light beam  250  to be commensurate with the entrance pupil size of the end user  50 . In the embodiments described below, the display screen  110  employs a technique known as “beam multiplication,” which refers to methods of exit pupil expansion that are specifically designed to expand a small diameter entrance pupil of each collimated light beam  250  from the image projection assembly  108  (e.g., on the order of 50 microns to 1 mm) by multiplying the respective light beam  250  into multiple light beamlets, resulting in a light beamlet array exit pupil that effectively matches the entrance pupil of the user&#39;s eye or eyes (e.g., on the order of 5 mm-7 mm) for a fixed eye relief. Notably, although the “beam multiplication” techniques are described herein as being performed in the display screen  110 , it should be appreciated that such “beam multiplication” techniques can be applied anywhere in the image generation system  100 , including any similar substrate system/subsystem upstream from the display screen  110 . 
     The extent to which the beam of collimated light  250  needs to be multiplied to achieve a given fill factor will depend upon the original pupil size of the collimated light beam  250 . For example, if the original pupil size of the collimated light beam output by the image projection assembly  108  is 500 microns, such pupil size may need to be multiplied ten times to achieve desired fill factor, whereas if the original pupil size of the collimated light beam  250  output by the image projection assembly  108  is 50 microns, such pupil may need to be multiplied one hundred times to achieve a desired fill factor. 
     Preferably, the light beamlet array exit pupil of the display screen is completely in-filled or saturated with light beamlets to maximize the wavefront density and minimize the depth of field. If the in-fill of the light beamlets in the exit pupil is too sparse, the wavefront density and depth of field of the display screen will be compromised, and if the diameter of the light beamlets is too small, the angular resolution of the display screen will be compromised. 
     Theoretically, the thickness of display screen  110  can be reduced to increase the number of light beamlets created from a single collimated light beam  250  input into the display screen  110 , thereby increasing the in-fill of the exit pupil with the light beamlets. However, due to durability and manufacturing limitations, a display screen  110  can only be made so thin, thereby limiting the in-fill of the exit pupil. Also, although the entrance pupil of the collimated light beam  250  transmitted from the image projection assembly  108  into the display screen  110  can theoretically be increased in order to increase the in-fill of the exit pupil with the light beamlets, this would require a commensurate increase in the size of the image projection assembly  108 , thereby affecting the wearability of the VR/AR system in a negative manner. Significantly, the embodiments described below increase the in-fill of the exit pupil without requiring an increase in the size of the image projection assembly  108 . 
     To this end, the display screen  110  serves as a pupil expander (PE) that expands the effective entrance pupil of the collimated light beam  250  (carrying the image information) for display to the eye  52  (monocular) or eyes  52  (binocular) of the end user  50 . The display screen  110  takes the form of a waveguide apparatus  170  that includes a planar optical waveguide  172  and one or more diffractive optical elements (DOEs)  174  associated with the planar optical waveguide  172  for two-dimensionally expanding the effective entrance pupil of the collimated light beam  250  optically coupled into the planar optical waveguide  172 . In alternative embodiments, the waveguide apparatus  170  may comprise multiple planar optical waveguides  172  and DOEs  174  respectively associated with the planar optical waveguides  172 . 
     As best illustrated in  FIG.  6   , the planar optical waveguide  172  has a first end  176   a  and a second end  176   b , the second end  176   b  opposed to the first end  176   a  along a length  178  of the planar optical waveguide  172 . The planar optical waveguide  172  has a first face  180   a  and a second face  180   b , at least the first and the second faces  180   a ,  180   b  (collectively  180 ) forming at least one partially internally reflective optical path (illustrated by solid line arrow  182   a  and broken line arrow  182   b , collectively  182 ) along at least a portion of the length  178  of the planar optical waveguide  172 . The planar optical waveguide  172  may take a variety of forms that provide for substantially total internal reflection (TIR) for light striking the faces  180  at less than a defined critical angle. 
     The DOE(s)  174  (illustrated in  FIGS.  5  and  6    by dash-dot double lines) may take a large variety of forms which interrupt the TIR optical path  182 , providing a plurality of optical paths (illustrated by solid line arrows  184   a  and broken line arrows  184   b , collectively  184 ) between an interior  185   a  and an exterior  185   b  of the planar optical waveguide  172  extending along at least a portion of the length  178  of the planar optical waveguide  172 . As will be described in further detail below, the light propagates within the planar optical waveguide  172  along an internally reflective optical path and intersects with the DOE(s)  174  at various positions to split the light into light beamlets that are either diffracted along a different internally reflective optical path or diffracted out of the face  180   b  of the planar optical waveguide  172 . 
     In the illustrated embodiment, the DOE(s)  174  comprise one or more diffraction gratings, each of which can be characterized as an optical component with a periodic structure on the order of the light wavelength that splits and diffracts light into several beams travelling in different directions. The diffraction gratings can be composed of, e.g., surface nano-ridges, nano-patterns, slits, etc. that may be photolithographically printed on a substrate. The DOE(s)  174  may allow positioning of apparent objects and focus plane for apparent objects. Such may be achieved on a frame-by-frame, subframe-by-subframe, or even pixel-by-pixel basis. 
     As illustrated in  FIG.  6   , the light propagates along the planar optical waveguide  172  with at least some reflections or “bounces” resulting from the TIR propagation. It is noted that some implementations may employ one or more reflectors in the internal optical path, for instance thin-films, dielectric coatings, metalized coatings, etc., which may facilitate reflection. Light propagates along the length  178  of the planar optical waveguide  172 , and intersects with the DOE(s)  174  at various positions along the length  178 . The DOE(s)  174  may be incorporated within the planar optical waveguide  172  or abutting or adjacent one or more of the faces  180  of the planar optical waveguide  172 . The DOE(s)  174  accomplishes at least two functions. The DOE(s)  174  shifts an angle of the light, causing a portion of the light to escape TIR, and emerge from the interior  185   a  to the exterior  185   b  via a face  180  of the planar optical waveguide  172 . The DOE(s)  174  focuses the out-coupled light at a viewing distance. Thus, someone looking through the face  180  of the planar optical waveguides  172  can see digital imagery at one or more viewing distances. 
     A collimated light beam  250  entering the waveguide  172  at one of two different angles will follow one of the two TIR optical paths  182   a ,  182   b , resulting in light beamlets  256  exiting the planar optical waveguide  172  along one of the two sets of external optical paths  185   a ,  185   b . That is, a collimated light beam  250   a  that enters the waveguide  172  at an angle represented by the TIR optical path  182   a  will result in the light beamlets  256   a  exiting the planar optical waveguide  172  along the set of external optical paths  185   a , and a collimated light beam  250   b  that enters the waveguide  172  at an angle represented by the TIR optical path  182   b  will result in the light beamlets  256   b  exiting the planar optical waveguide  172  along the set of external optical paths  185   b.    
     In can be appreciated from the foregoing, the display subsystem  104  generates a series of synthetic image frames of pixel information that present an image of one or more virtual objects to the user. Further details describing display subsystems are provided in U.S. patent application Ser. No. 14/212,961, entitled “Display Subsystem and Method,” and U.S. patent application Ser. No. 14/696,347, entitled “Planar optical waveguide Apparatus With Diffraction Element(s) and Subsystem Employing Same,” which are expressly incorporated herein by reference. 
     As described above,  FIG.  4    depicts a basic optical system  400  for projecting images at a single depth plane.  FIG.  7    depicts another optical system  400 ′, which includes a light source  420 , three LOEs  490 , and three respective in-coupling gratings  492 . The optical system  400 ′ also includes three beam-splitters or dichroic mirrors  462  (to direct light to the respective LOEs) and three LC shutters  464  (to control when the LOEs are illuminated). When the system  400 ′ is in use, the light beam from the light source  420  is split into three sub-beams/beamlets by the three-beam-splitters  462 . The three beam-splitters also redirect the beamlets toward respective in-coupling gratings  492 . After the beamlets enter the LOEs  490  through the respective in-coupling gratings  492 , they propagate along the LOEs  490  by substantially TIR where they interact with additional optical structures resulting in display to an eye of a user. The surface of in-coupling gratings  492  on the far side of the optical path can be coated with an opaque material (e.g., aluminum) to prevent light from passing through the in-coupling gratings  492  to the next LOE  490 . In some embodiments the beam-splitters  462  can be combined with wavelength filters to generate red, green and blue beamlets. In such an embodiment, three LOEs  490  are required to display a color image at a single depth plane. In another embodiment, LOEs  490  may each present a portion of a larger, single depth-plane image area angularly displaced laterally within the user&#39;s field of view, either of like colors, or different colors (“tiled field of view”). 
       FIG.  8    depicts still another optical system  400 ″, having six beam-splitters  462 , six LC shutters  464  and six LOEs  490 , each having a respective ICG  492 . As explained above during the discussion of  FIG.  7   , three LOEs  490  are required to display a color image at a single depth plane. Therefore, the six LOEs  490  of this system  400 ″ are able to display color images at two depth planes. 
       FIG.  10    depicts a LOE  490  having an ICG  492 , an orthogonal pupil expander  494  (“OPE”), and an exit pupil expander  496  (“EPE”). 
     As shown in  FIGS.  4 - 9   , as the number of depth planes, field tiles, or colors generated increases (e.g., with increased MR scenario quality), the numbers of LOEs  490  and ICGs  492  increases. For example, a single RGB color depth plane requires at least three LOEs  490  with three ICGs  492 . As a result, any image defects (e.g., blurring from limited beam diameter) are also multiplied with additional opportunities to detract from MR scenario quality. Thus, the increasing number of optical elements required to generate an acceptable MR scenario exacerbates image quality problems. 
     The LOEs  490  discussed above can additionally function as exit pupil expanders  496  (“EPE”) to increase the numerical aperture of a light source  420 , thereby increasing the resolution of the system  400 . Since the light source  420  produces light of a small diameter/spot size, the EPE  496  expands the apparent size of the pupil of light exiting from the LOE  490  to increase the system resolution. In other embodiments of the MR system  400 , the system may further comprise an orthogonal pupil expander  494  (“OPE”) in addition to an EPE  496  to expand the light in both the X and Y directions. More details about the EPEs  496  and OPEs  494  are described in the above-referenced U.S. Utility patent application Ser. No. 14/555,585 and U.S. Utility patent application Ser. No. 14/726,424, the contents of which have been previously incorporated by reference. 
       FIG.  10    depicts an LOE  490  having an ICG  492 , an OPE  494  and an EPE  496 .  FIG.  10    depicts the LOE  490  from a top view that is similar to the view from a user&#39;s eyes. The ICG  492 , OPE  494 , and EPE  496  may be any type of DOE, including volumetric or surface relief. 
     The ICG  492  is a DOE (e.g., a linear grating) that is configured to admit light from a light source  420  for propagation by TIR. In the embodiment depicted in  FIG.  10   , the light source  420  is disposed to the side of the LOE  490 . 
     The OPE  494  is a DOE (e.g., a linear grating) that is slanted in the lateral plane (i.e., perpendicular to the light path) such that a light beam that is propagating through the system  400  will be deflected by 90 degrees laterally. The OPE  494  is also partially transparent and partially reflective along the light path, so that the light beam partially passes through the OPE  494  to form multiple (e.g.,  11 ) beamlets. In some embodiments, the light path is along an X axis, and the OPE  494  configured to bend the beamlets to the Y axis. 
     The EPE  496  is a DOE (e.g., a linear grating) that is slanted in the axial plane (i.e., parallel to the light path or the Y direction) such that the beamlets that are propagating through the system  400  will be deflected by 90 degrees axially. The EPE  496  is also partially transparent and partially reflective along the light path (the Y axis), so that the beamlets partially pass through the EPE  496  to form multiple (e.g.,  7 ) beamlets. The EPE  496  is also slated in a Z direction to direction portions of the propagating beamlets toward a user&#39;s eye. 
     The OPE  494  and the EPE  496  are both also at least partially transparent along the Z axis to allow real-world light (e.g., reflecting off real-world objects) to pass through the OPE  494  and the EPE  496  in the Z direction to reach the user&#39;s eyes. In some embodiments, the ICG  492  is at least partially transparent along the Z axis also at least partially transparent along the Z axis to admit real-world light. 
       FIG.  11 A  shows a first light beam  610  entering an eye  600  and being focused by a lens  602  to a small spot  612  on the retina  604 . Preferably, the small spot  612  is approximately the size of a photoreceptor on the retina  604 . The first image or first portion of an image corresponding to the first light beam  610  is in focus, as shown by the energy distribution curve  614  corresponding to the first light beam  610  in the graph in  FIG.  11 B .  FIG.  11 A  also depicts a second light beam  620  entering the eye  600  and being focused by the lens  602  to a larger spot  622  on the retina  604 . The second image or second portion of an image corresponding to the second light beam  620  (with the larger spot  622 ) is less in focus (e.g., out of focus), as shown by the energy distribution curve  624  corresponding to the second light beam  620 , in the graph in  FIG.  11 B .  FIG.  11 B  depicts the energy distribution patterns of two real-world light beams as focused by a lens onto a retina. 
       FIG.  12 A  shows an eye  700  with a lens  702  that is accommodated so that the second light beam  720  is focused to a small spot  722  on the retina  704 . Consequently, a second image or second portion of an image corresponding to the second light beam  710  is in focus, as shown by the energy distribution curve  724  corresponding to the second light beam  720  in the graph in  FIG.  12 B . However, in  FIG.  12 A , the first light beam  710  is focused to a larger spot  712  on the retina  704 , resulting in a larger spot  712  on the retina  704 . The first image or first portion of an image corresponding to the first light beam  710  (with the larger spot  712 ) is less in focus (e.g., out of focus), as shown by the energy distribution curve  714  corresponding to the first light beam  710 , in the graph in  FIG.  12 B .  FIG.  12 B  depicts the energy distribution patterns of two real-world light beams as focused by a lens onto a retina. 
     The size of a beam spot on the retina affects the resolution of an image as follows. The function of an eye is to collect light information related to a “3-D” scene, which is comprised of a plurality of point sources of light (e.g., emitted or reflected). For instance, a tree may include millions of point sources of light that reflect light from the sun. The eye (e.g., the lens therein) bends light beams to a spot on the retina. Ideally, the beam spot on the retina is the size of a photoreceptor. An eye that is well focused on an object will focus light beams from that object on as small a spot on the retina as possible. When an eye is out of focus relative to an object, the light beams will be brought into focus in front of or behind retina, and the spot resembles a circle instead of a point. A wider circular spot may impinge on several photoreceptors on the retina resulting in a blurred image as interpreted by the optical cortex of the viewer. Further, smaller beam spots (e.g., from 2-3 mm diameter beams) will change spot size (i.e., blur or focus) with lens accommodation more quickly. On the other hand, larger beam spots (e.g., from a 0.5 mm diameter beam) will not change spot size (i.e., blur or focus) with lens accommodation. 
       FIG.  13 A  shows an eye  800  with a lens  802  that is accommodated so that the first and second light beams  810 ,  820  are focused to respective larger spots  812 ,  822  on the retina  804 . Consequently, the first and second images or first and second portions of one or more images corresponding to the first and second light beams  810 ,  820  are less in focus (e.g., out of focus) compared to an in focus image, as shown by the energy distribution curves  814 ,  824  corresponding to the first and second light beams  810 ,  820 , in the graph in  FIG.  13 B .  FIG.  13 B  depicts the energy distribution patterns of two real-world light beams as focused by a lens onto a retina. As shown in  FIGS.  11 A- 13 B , the anatomy of a single lens eye renders it difficult to concurrently focus two light beams having different angles of incidence. When one beam is in focus, the other beam will be out of focus. Attempting to accommodate the lens to an intermediate focus of two light beams, as shown in  FIGS.  13 A and  13 B , may result in two out of focus images or portions of one or more images. As a result of anatomical limitations, when a single lens eyes bring a light beam or portion of a field of view (“FOV”) into focus, other light beams or portions of the FOV will be out of focus. 
     Compounding this image focus limitation are various other optical, anatomical, and technological limitations. Image resolution is a function of beam diameter and beam angle (“optical invariant”), which is tied to the number of resolvable spots (e.g., as in the laser scanner industry). The optical invariant is related to a numerical aperture collected by pixels multiplied by the number of pixels. Larger light beam diameters result in higher image resolutions. Smaller light beam diameters result in the ability to conserve increasing light beam angles to maximize the FOV. These optical limitations render beam diameter optimization difficult, because beam diameter affects both image resolution and light beam angle, resulting in a tradeoff between image quality and FOV size. 
       FIGS.  14 A to  14 B  demonstrate the relationship between light beam diameter and image resolution. As shown in  FIG.  14 A , a light beam  910  having a maximally sized beam diameter  916  (e.g., sufficient to fill an entire pupil of the eye  900  or about 2-3 mm) generates the smallest spot size  912  for the given eye  900 . The small spot size  912  results in a corresponding in focus image or portion thereof as shown in the energy distribution curve  914  in  FIG.  14 B .  FIG.  14 B  depicts the energy distribution patterns of a real-world light beam as focused by a lens onto a retina. The larger diameter of light beam  910  allows the eye  900  to focus the light beam  900  by changing the shape of the lens  902 . The ability to focus maximally sized light beams results in increased image resolution. However, a light beam  1010  having a smaller beam diameter  1016  (e.g., about 0.5 mm) generates a larger spot size  1012 , as shown in  FIG.  15 A . Larger spot size  1012  results in a corresponding out of focus image or portions thereof as shown in the energy distribution curve  1014  in  FIG.  15 B .  FIG.  15 B  depicts the energy distribution patterns of a real-world light beam as focused by a lens onto a retina. 
     Further, if a light beam diameter is around 0.5 mm, open loop accommodation with some eyes, as a result of which everything will appear to be at the same poor level of focus. As in pin-hole cameras, the entire FOV will be equally and poorly focused, because the retina space is too small to resolve larger spots displayed thereon, as shown in  FIGS.  15 A and  15 B . Moreover, if a light beam diameter is around 0.5 mm, the pupil may become fully open, resulting in optical aberrations such as halos around point light sources. 
     As described above, various other optical, anatomical, and technological limitations result in performance limitations of head-worn displays. For instance, light beams with smaller diameters (e.g., around 0.5 mm) compared to light beams with larger diameters (e.g., around 2-3 mm) will result in lower image resolution and optical aberrations. On the other hand, light beams with larger diameters (e.g., around 2-3 mm) compared to light beams with smaller diameters (e.g., around 0.5 mm) will result in narrower FOVs. Balancing image resolution with FOV results in sub-optimal image resolution and FOVs. 
     The following disclosure describes various embodiments of systems and methods for simulating a larger diameter light beam using a plurality (e.g., an array) of smaller diameter light beams. These beam multiplier systems and methods generate bundles of interrelated, interacting, cloned beamlets  1116  that pass through the pupil to impinge on the retina  1104 , as shown in  FIG.  16 A . A combination of a beam array, relative spacing, and beam diameter can generate compact energy images at the retina  1104  (see  FIG.  16 B ).  FIG.  16 B  depicts the energy distribution patterns of an array of real-world light beams as focused by a lens  1102  onto a retina  1104  including optical interactions of the light beams with each other. By eliminating energy in side-lobes (at constant power) through interference and other optical properties of beam arrays (e.g., coherency, phase uniformity, etc.), light energy (e.g., irradiance, peak intensity, etc.) is concentrated in the middle of the graph as shown by the energy distribution curve  1114  corresponding to the beamlets  1116  in the graph in  FIG.  16 B . This focused light energy, in turn, generates a more focused image with higher image resolution. For example, coherency and phase uniformity across the beamlets  1116  may correspond to energy distributions having relatively high peak values and attenuated side-lobes, and thus may serve to yield images that are relatively focused and sharp in appearance. In effect, the array of cloned smaller diameter beamlets  1116  generates a smaller spot  1112  on the retina  1104  with a sharp point spread function  1114  that approximates the sharp point spread function  914  generated by a larger diameter beam  910  (see  FIGS.  14 A and  14 B ). The array of smaller diameter beamlets  1116  allows the system to overcome the beam diameter limitation (resulting from diffraction and/or device size limitations). At the same time, the system&#39;s use of smaller diameter light beams results in a wider FOV. 
     The plurality/array of beamlets (each with a smaller diameter) simulates the light energy from a much larger diameter light beam, increasing image resolution while maintaining the wider FOV based on the smaller beam diameter. 
       FIG.  17 A  schematically depicts an LOE  490  that generates an array of beamlets  1216  from a single incoming light beam  1210  (see beam multipliers described below). Some of the beamlets  1216  pass through a pupil  1206  formed by an iris  1208  to be focused by a lens  1202 . While  FIG.  17 A  depicts a plurality of beamlets  1216 ,  FIG.  17 A  does not illustrate the two dimensional array of beamlets according to some embodiments.  FIG.  17 B  schematically depicts select beamlets  1206  from a beamlet array passing through a pupil  1206  formed by an iris  1208 . 
     The spacing of beamlet spots can also affect image quality. As shown in  FIG.  18 A , beamlet spots  1316  on a retina may be overlapping, with each beamlet spot  1316  covering more than one photoreceptor. When coherent and in-phase, the distribution pattern of beamlet spots  1316  depicted in  FIG.  18 A  may yield images that appear in focus and sharp. However, when each beamlet spot  1316  impinges on more than one photoreceptor, or when there is a phase disparity of multiple beamlet spots impinging on a single photoreceptor, the resulting images may not be as sharp in appearance.  FIGS.  18 B and  18 C  depict other beamlet spot  1316  distribution patterns on a retina, where each beamlet spot  1316  may approximately cover one photoreceptor. Generally, these distribution patterns may result in images that appear fairly in focus and sharp, as they may be less impacted by coherency and phase uniformity than that of  FIG.  18 A . Accordingly, beam array architecture, relative beam/beamlet spacing, and beam/beamlet diameter are factors that may affect the resolution/sharpness of images at a retina. 
       FIG.  19    depicts beam multiplier  1430  (i.e., a thin beam multiplier), which may be a light guiding optical element, such as an OPE  494  and/or an EPE  496  of an LOE  490  (see  FIG.  67   ). An input beam  1410  enters the beam multiplier  1430  (e.g., via an ICG or other entry portion) and travels down the beam multiplier  1430  by substantially TIR. As the input beams  1410  travel down the beam multiplier  1430 , each time the input beams  1410  interact with an out-coupling grating (“OCG”)  1498 , a portion of the input beams  1410  exits the beam multiplier  1430  via the OCG  1498 . The OCG  1498  is configured to allow a portion of a light beam to exit the beam multiplier  1430  while another portion of the light beam propagates along the beam multiplier  1430  via substantially TIR. The OCG  1498  may be a diffractive optical element of any type, including volumetric or surface relief. The beam multiplier  1430  clones a single input beam  1410  into three output beamlets  1416 , which each encode the same pixel information as the input beam  1410 . 
     While the beam multiplier  1430  is depicted inside view in  FIG.  19   , the beam multiplier  1430  may have a length and a width like the OPE  494  and/or the EPE  496  shown in  FIG.  67   . Further, while the input beams  1410  are depicted as propagating in a generally left to right direction, the beam multiplier  1430  may be configured to direct light beams in a variety of patterns, including but not limited to zigzag patterns that generate an array of beamlets  1416  (see e.g.,  FIG.  18 B ). 
     As shown in  FIG.  20   , only some (i.e., one) of the beamlets  1516  exiting from the beam multiplier  1530  pass through the pupil  1506  defined by the iris  1508  to be focused by the lens  1502 . Therefore, even with beam multiplication, spacing of beamlets  1516  can affect the actual number of beams perceived by a user.  FIG.  20    also shows that the number of bounces of the input beams  1510  per length of the beam multiplier  1530  determines the number of beamlets  1516  exiting from a given length the beam multiplier  1530 . 
       FIG.  21    depicts a thinner beam multiplier  1630 ′ according to some embodiments. A thicker beam multiplier  1630  is also depicted for comparison. Over approximately the same length, each input light beam  1610  (which angle of incidence preserve between the two the multipliers) bounces more times in the thinner beam multiplier  1630 ′ compared to the thicker beam multiplier  1630 . The input light beam  1610  bounces back and forth a higher spatial frequency because there is less distance to traverse before the beam  1610  encounters each surface of the thinner beam multiplier  1630 ′. Accordingly, a higher density of beamlets emerge from the thinner beam multiplier  1630 ′ compared to the thicker beam multiplier  1630 . For instance, each input light beam  1610  bounces 13 times in the thinner beam multiplier  1630 ′, while a similar input light beam  1610  bounces only three times in the thicker beam multiplier  1630 . A thinner beam multiplier  1630 ′ provides more beam multiplication (i.e., cloning) per length of beam multiplier compared to a thicker beam multiplier  1630 . Further, when this linear increase in cloning efficiency is multiplied over two dimensions (e.g., length and width) the increase in cloning efficiency from reduced beam multiplier thickness is exponential. The respective spacing between multiplied beamlets into two dimensions are not necessarily the same (although symmetry is preferred). Moreover, a thinner beam multiplier  1630 ′ may decrease during even with increased beam overlap through coherent interactions. 
     The beam multipliers depicted in  FIGS.  19 - 21    include two opposing reflective surfaces that reflect light in substantially opposite directions to enable substantially TIR. In other embodiments, beam multipliers include more than two reflective surfaces. For instance, the multi-surface beam multiplier  1730  depicted in  FIG.  22 A  includes first and second light guiding optical sub-elements (“LOS”)  1730 A,  1730 B. The first LOS  1730 A is similar to the beam multiplier  1530  depicted in  FIG.  20    in that it has two (i.e., first and second) opposing reflective surfaces  1732 ,  1734 . The second LOS  1730 B depicted in  FIG.  22 A  has a third reflective surface  1736  that reflects light in substantially the same direction as the second reflective surface  1734  in the first LOS  1730 A. 
     The second LOS  17306  is disposed over the first LOS  1730 A such that an incoming light beam  1710  at least partially passes through the first LOS  1730 A and enters the second LOS  1730 B. As an incoming light beam  1710  passes through the first LOS  1730 A, a portion thereof is partially reflected by the second reflective surface  1734 . The portion of the incoming light beams  1710  that passes through the second LOS  1730 B is reflected by the third reflective surface  1736  in substantially the same direction as the portion of the incoming light beam  1710  that is reflected by the second reflective surface  1734 . The result of the addition of the second LOS  17306  and its third reflective surface  1736  is a multiplication of the number of beamlets  1716  propagating along the first and second LOSs  1730 A,  1730 B by substantially TIR. 
     The thickness of the second LOS  1730 B depicted in  FIG.  22 A  is such that some of beamlets  1716  reflecting off of the third reflective surface  1736  substantially overlap with the beamlets  1716  reflecting off of the second reflective surface  1734 . For situations in which some of the beamlets  1716  are out of phase with one another, such overlap can serve to amplify the effects of destructive interference between phase-mismatched beamlets. In addition, high levels of overlap can serve to minimize the degree of multiplication of the number of beamlets  1716 . For instance, while the first bounce off of the second and third reflective surfaces  1734 ,  1736  multiplies the number of beams  1710 /beamlets  1716  from 1 to 2, the second bounce only multiplies the number of beamlets  1716  from 2 to 3. The extent to which at least some of beamlets  1716  overlap can be controlled by adjusting the input beam  1710  diameter and/or the input beam  1710  separation, both of which are substantially conserved during substantially TIR. For example, the distance between the edges of two adjacent beamlets, from among the number of beamlets  1716 , may be increased by reducing the diameter of the input beam  1710 . 
     The beam multiplier  1730  depicted in  FIG.  22 B  includes first and second LOSs  1730 A,  1730 B, like the beam multiplier  1730  depicted in  FIG.  22 A . However, the thickness of the second LOS  1730 B has been tuned/selected such that the beamlets  1716  reflecting off of the third reflective surface  1736  do not overlap with the beamlets  1716  reflecting off of the second reflective surface  1734 . Consequently, the beam multiplier  1730  depicted in  FIG.  22 B  has a higher degree of beamlet multiplication than the beam multiplier  1730  depicted in  FIG.  22 A . For instance, while the first bounce off of the second and third reflective surfaces  1734 ,  1736  multiplies the number of beams  1710 /beamlets  1716  from 1 to 2, the second bounce multiplies the number of beamlets  1716  from 2 to 4. Continuing with this pattern, each bounce off of the second and third reflective surfaces  1734 ,  1736  doubles the number of beamlets  1716  in substantially exponential growth. 
     The beam multiplier  1830  depicted in  FIG.  23    includes first and second LOSs  1830 A,  1830 B, like the beam multiplier  1730  depicted in  FIG.  22 A . A difference between the beam multipliers  1730 ,  1830  is that the second LOS  1830 B depicted in  FIG.  23    has a fourth reflective surface  1838  in addition to the third reflective surface  1836 . The third and fourth reflective surfaces  1836 ,  1838  are disposed on opposing sides of the second LOS  1830 B, and reflect light in substantially opposite directions. 
     The second LOS  1830 B is disposed over the first LOS  1830 A such that an incoming light beam  1810  at least partially passes through the first LOS  1830 A and enters the second LOS  1830 B. As an incoming light beam  1810  passes through the first LOS  1830 A, a portion thereof is partially reflected by the second reflective surface  1834 . The portion of the incoming light beams  1810  that passes through the second LOS  1830 B is reflected by the third reflective surface  1836  in substantially the same direction as the portion of the incoming light beam  1810  that is reflected by the second reflective surface  1834 . Before the reflected beamlet  1816  exits the second LOS  1830 B, a portion of the reflected beamlet  1816  is reflected by the fourth reflective surface  1838  back toward the third reflective surface  1836 . The result of the addition of the fourth reflective surfaces  1838  in the second LOS  18306  is a further multiplication of the number of beamlets  1816  propagating along the first and second LOSs  1830 A,  1830 B by substantially TIR even compared to the beam multiplier  1730  depicted in  FIG.  22 A . As shown in  FIG.  23   , the addition of the fourth reflective surface  1838  results in an additional bounce for each light beam  1810 /beamlet  1816 , thereby multiplying the number of beamlets produced at each interaction with the first and second LOSs  1830 A,  1830 B (i.e., the light multiplier  1830 ). 
     The beam multiplier  1930  depicted in  FIG.  24    includes first and second LOSs  1930 A,  1930 B, like the beam multiplier  1830  depicted in  FIG.  23   . A difference between the beam multipliers  1830 ,  1930  is that the beam multiplier  1930  depicted in  FIG.  24    includes a third LOS  1930 C. Like the second LOS  1930 B, the third LOS  1930 C includes a b of opposing reflective surfaces (i.e., fifth and sixth reflective surfaces  1940 ,  1942 ) that reflect light in substantially opposite directions. The fifth and sixth reflective surfaces  1940 ,  1942  are disposed on opposing sides of the third LOS  1930 C. 
     The third LOS  1930 C is disposed over the second LOS  19306  (and therefore the first LOS  1930 A) such that an incoming light beam  1910  at least partially passes through the first and second LOSs  1930 A,  19306  and enters the third LOS  1930 C. As an incoming light beam  1910  passes through the first LOS  1930 A, a portion thereof is partially reflected by the second reflective surface  1934 . Similarly, as an incoming light beam  1910  passes through the second LOS  1930 B, a portion thereof is partially reflected by the third reflective surface  1936 . The portion of the incoming light beams  1910  that passes through the second LOS  1930 B is reflected by the third reflective surface  1936  in substantially the same direction as the portion of the incoming light beam  1910  that is reflected by the second reflective surface  1934 . Similarly, The portion of the incoming light beams  1910  that passes through the third LOS  1930 C is reflected by the fifth reflective surface  1940  in substantially the same direction as the portions of the incoming light beam  1910  that are respectively reflected by the second and third reflective surfaces  1934 ,  1936 . 
     Before the reflected beamlet  1916  exits the second LOS  1930 B, a portion of the reflected beamlet  1916  is reflected by the fourth reflective surface  1938  back toward the third reflective surface  1936 . Similarly, before the reflected beamlet  1916  exits the third LOS  1930 C, a portion of the reflected beamlet  1916  is reflected by the sixth reflective surface  1942  back toward the fifth reflective surface  1940 . The result of the addition of the third LOS  1930 C and its fifth and sixth reflective surfaces  1940 ,  1942  is a further multiplication of the number of beamlets  1916  propagating along the first, second, and third LOSs  1930 A,  1930 B,  1930 C by substantially TIR. As shown in  FIG.  24   , the addition of the third LOS  1930 C results in an additional pair of bounces for each light beam  1910 /beamlet  1916 , thereby multiplying the number of beamlets produced at each interaction with the first, second, and third LOSs  1930 A,  1930 B,  1930 C (i.e., the light multiplier  1930 ). 
     Multi-surface beam multipliers can be fabricated using a lamination process. In some embodiments, a second substrate (e.g., a second LOS) having a second thickness is laminated onto a first substrate (e.g., a first LOS) having a first thickness. The interface between the two substrates may be partially reflective (e.g., a metallic coating/half-silvered mirror, a thin film coating, a dichroic mirror, a dielectric interface, a diffraction grating, a diffractive element, etc.) In another embodiment, separate waveguides/LOEs can be laminated together with a partially-reflective interface. 
     Further, the ratio of thicknesses of first and second LOSs (and various sub combinations of any plurality of LOSs in a system) can affect beamlet multiplication by beamlet overlap. If the respective thicknesses are whole number multiples or quotients (i.e., factors), then cloned beamlets may overlap when they exit the first and second LOSs, reducing the degree of beamlet multiplication. Therefore, in some embodiments (see  FIG.  22 B ) the first thickness of the first LOS may be a non-even factor of the second thickness of the second LOS. For instance, the first thickness may be 0.3256 times the second thickness (instead of e.g., 0.2 or 0.5). Quasi-random beamlet arrays with multiple LOSs may be insensitive to angle or imperfections in LOS thicknesses. 
     Beam multipliers can also be tuned by varying the degree of reflectiveness/transmittance of various surfaces (e.g., other than 50/50). Using this and other techniques, the multipliers can be tuned to have an even distribution of energy across the beamlets. For moderate amounts of beam multiplication (e.g., sufficient to fill the pupils of the eyes), the beam multiplier(s) can be two to ensure that beamlets (and groups thereof) have the same amounts of energy, as the eye sweeps across different sets of beamlets. Equalizing the amount of energy across beamlets minimizes dropouts in intensity (artifacts; winking) as the user&#39;s eyes sweep the FOV. With an exponentially increasing number of beamlets, beamlets will eventually randomly overlap, thereby reducing intensity artifacts. 
       FIG.  25    depicts a beam multiplier  2030  that is tuned/optimized to produce the most light (e.g., with an optimal beam diameter/energy distribution) for beamlets  2016  that are directed toward the center  2044  of an FOV. For instance, the beam multiplier  2030  can be tuned to vary the light intensity/energy as a function of the angle of the beamlets  2016  that will be emerging from the beam multiplier  2030 . Beamlets  2016  directed toward the center  2044  of an FOV  10  to be more perpendicular/orthogonal to the surface of the beam multiplier  2030  (i.e., have a smaller angle of incidence). This design minimizes artifacts at the center  2044  of the FOV where some users&#39; eyes will be directed most of the time, while at the same time controlling the amount of energy required to display an image. As a trade-off, the beam multiplier  2030  has been less tuned/optimized for more eccentric beamlets  2016  at the peripheral portions of the FOV. 
     A FOV may be expanded with kaleidoscopically tuned beam multipliers. The relative reflectivity of surfaces can be tuned such that the beam multiplier has dense beam multiplication in optically important regions (e.g., center of an FOV) and sparse beam multiplication in optically less important regions (e.g., periphery of an FOV). The FOV can be determined to various types of eye tracking, including but not limited to interpupillary distance measurement and pupil motion tracking. 
     The OPE  494  and EPE  496  depicted in  FIG.  67    do not cover/overlie each other. However, if an OPE overlies an EPE or a portion thereof, there is an increased opportunity for multiple reflections of beams (i.e., mirrored beams) that may exit the LOE  490  toward the user&#39;s eye. The mirrored beams may be shifted in phase resulting in artifact (e.g., bull&#39;s eye or Fresnel zone artifacts “FZA”). One method of reducing FZAs is by reducing mirrored beams using anti-reflective coatings. Another method of reducing FZAs is to separate a thin waveguide OPE from the EPE. The thickness of a thin waveguide OPE can also be tuned such that FZAs are minimized because the thin waveguide OPE brings the beamlets back into phase for one wavelength (e.g., using a two pi thickness relationship). The relative phase difference between beamlets is a function of wavelength and scan angle. The thickness of a thin waveguide OPE can be tuned to minimize FZAs with green light, for which the human eye is most sensitive. For instance, a thin waveguide OPE can be tuned for 515 nm-540 nm, 520 nm (green), or 532 nm (green). In other embodiments, a thin waveguide OPE can be tuned to minimize FZAs with 475 nm (blue) light or 650 nm (red) light. Because the human eye is more able to discern blue light in an annular region around the fovea, certain FZAs are more detrimental to blue light, and minimizing those FZAs for blue light can greatly improve image quality. Accordingly, a thin waveguide OPE can overlie an EPE while reducing FZAs if the thickness of the thin waveguide OPE is tuned to have a two pi thickness relationship. 
       FIGS.  26 A and  26 B  depict a beam multiplier  2600  having a refractive index gap (e.g., air gap)  2602  that ensures light will propagate by substantially TIR at the interface (with the refractive index gap) rather than be partially transmitted into the adjacent layer. The light path through the beam multiplier begins with entry into OPE 1   2604  (e.g., a thicker LOS), out of OPE 1   2604  via an OCG  2606 , into OPE 2   2608  via an ICG  2610 , and through OPE 2   2608  (e.g., a thinner LOS). The refractive index gap  2602  controls light flow through this beam multiplier  2600  allowing light to pass between OPE 1   2604  and OPE 2   2608  only via the OCG  2606  and ICG  2610 . By varying the thicknesses of OPE 1   2604  and OPE 2   2608 , different periodic relationships can be achieved for OPE 1   2604  and OPE 2   2608 . This can be tuned to generate different spatial frequency for beamlet cloning. While the varied optical (light modifying) characteristic described above is LOE thickness, other optical characteristics (such as diffractive index) can also be varied to achieve effects similar to those described herein. 
     There are two exit edges  2612 ,  2614  for OPE 1   2604  (see  FIG.  26 B ). In some embodiments, both exits edges are coupled to OPE 2   2608 . In another embodiment, the diffraction efficiency of OPE 1   2604  can be varied in various portions of OPE 1   2604  to guide the majority of the light to one exit edge (e.g.,  2606 ), which is coupled into OPE 2   2608 . 
     Using such a system, the OPE (as a separate element) can be removed from the LOE  490  (e.g., see  FIG.  10   ) and stretched into a separate layer  494  that covers the entire eyepiece or a significant portion thereof. Light is coupled into the LOE  490  and enters the separate large OPE  494  for multiplication as a controlled interface between the two optical elements. The light beam can stair-step through the OPE  494  and be multiplied on multiple interactions with elements of the OPE  494 . Exit beamlets from the OPE  494  are not single beams, but rather multiple, superimposed beamlets from the beam splitting by the OPE  494 . 
     Using this design can also create a large region including a smaller region in which all or most of the information/light energy is contained. Such a system can use depth switching mechanisms to route light to different layers (e.g., multiple depth plane layers). The layers can be polymer dispersed liquid crystal (“PDLC”) switchable layers. Alternatively, the layers can be waveguides with respective LC shutters. Such a system can use TIR based structures from a main LOE to generate multiple exit ports for redundant optical information that can be selected by LC shutter or PDLC swatches. In some embodiments, a single OPE can feed light/optical information to multiple EPE layers (e.g., EPEs corresponding to red, green, and blue light). 
       FIG.  27    depicts a beam multiplier  2700  wherein a single OPE  2702  feeds light/optical information to 2 EPE layers  2704 ,  2706  using 2 spatially displaced OCGs  2708 ,  2710 . OCG 1   2708  couples the OPE  2702  to EPE 1   2704  through ICG 1   2712 . OCG 2   2710  couples the OPE  2702  to EPE 2   2706  through ICG 2   2714 . The OCGs  2708 ,  2710  can be PDLC, which can be turned on or off. Alternatively, an LC shutter layer (not shown) can be interposed between the OPE  2702  and the EPE layers  2704 ,  2706 . In some embodiments, the number of EPE layers can be set to correspond to the number of multiple depth layers for an MR system. In alternative embodiments, a single OCG can be divided into multiple windows with shutters or switches to selectively feed light/optical information to a plurality of EPE layers. In another embodiment  2800  ( FIG.  28   ), the OCGs  2808 ,  2810  can be formed at or from two exit edges of the OPE  2802 . 
       FIG.  29    depicts a beam multiplier  2900  with an OPE  2902  designed similar to a “hall of mirrors”. In this independent, large OPE module  2902 , an input/primary beam  2904  is multiplied by the OPE  2902  and multiplied beamlets exit the OPE  2902  via one or more OCGs  2906 . Three of the four OPE edges  2908 ,  2910 ,  2912  may be polished and coated with aluminum to render them reflective. Two opposing mirrors  2908 ,  2912  reflect the beams and beamlets propagating through the OPE  2902 , generating additional beamlets (with the same optical information) as the reflected beamlets interact with the OPE  2902 . Such an OPE  2902  can be tuned to have a low diffraction efficiency toward the OCG  2906 , but beam multiplication will be greatly increased with multiple passes through the OPE  2902 . Optionally, the OPE  2902  may have one or more regions of relatively higher diffraction efficiency  2914  to facilitate beam multiplication by increasing the beam length through the OPE  2902  before beams/beamlets exit through the OCG  2906 . 
     In a similar embodiment  3000  depicted in  FIG.  30   , only two of the edges  3010 ,  3012  (perpendicular edges) and a small portion of a third edge  3008  of the OPE  3002  are polished and coated with aluminum to render them reflective. This treatment results in reduced beamlet multiplication, but doubles the amount of area for exits  3016  (e.g., for OCGs (not shown)). This design increases the surface area  3016  for out-coupling. 
     For both of the embodiments depicted in  FIGS.  29  and  30   , the OPE  2902 ,  3002  can be optimized/tuned with variable diffraction efficiency. For instance, the upper left of regions in both of these embodiments can be tuned to diffract light in an up-and-down direction and to minimize light reflected back toward the ICG  2918 ,  3018 , which may unintentionally couple out of the OPE  2902 ,  3002 . 
     The beam multiplier  3100  depicted in  FIG.  31    includes an OPE  3102  that is shared across wavelengths. A first OCG  3104  is tuned to out-couple green light with a blue and red light absorber  3106  coupled to the OCG  3104 . A second OCG  3108  is tuned to out-couple blue and red (i.e., magenta) light with a green light absorber  3110  coupled to the OCG  3108 . 
     The beam multiplier  3200  depicted in  FIG.  32    includes an OPE  3202  with three output regions  3204 ,  3206 ,  3208 . The three output regions  3204 ,  3206 ,  3208  are tuned to respectively out-couple red  3204 , green  3206 , and blue  3208  light using OCGs  3204 ,  3206 ,  3208  with matching absorbers  3210 ,  3212 ,  3214 . The DOEs  3216  in the OPE  3202  form a “V” shape  3218  with an approximately 90 degree angle, but the DOEs may form other shapes with different angles in other embodiments (e.g., to modify beamlet density (not shown)). 
     The beam multipliers  3300  depicted in  FIGS.  33 A- 33 I  illustrate various “quilts” of different OPE  3302  regions that allow tuning of OPEs  3302  for various out-coupling patterns. In all of these OPEs  3302 , a single input/primary beam  3304  is multiplied, diffracted, and/or reflected by various components of the OPEs  3302  to form various multiplied beams/beamlets  3306  having a variety of out-coupling patterns. For example,  FIG.  33 A  depicts an OPE  3302  including three sections  3308 ,  3310 ,  3312  having different diffractive properties. The three sections may be independently switchable PDLC components (e.g., to change the out-coupling pattern) or they may be static components.  FIG.  33 C  depicts an OPE  3302  having a diffractive section  3314  and first and second PDLC components  3316 ,  3318  (e.g., to change the out-coupling pattern).  FIG.  33 G  depicts an OPE  3302  having DOEs  3320  in the OPE  3302  form a “V” shape  3322  similar to the OPE  3202  in  FIG.  32   . 
     Referring now to  FIGS.  34 - 36   , one specific embodiment of the display screen  110  will be described. As shown in  FIG.  34   , the waveguide  172  is a single unitary substrate or plane of an optically transparent material, such as, e.g., glass, fused silica, acrylic, or polycarbonate, although in alternative embodiments, the waveguide  172  may be composed of separate distinct substrates or panes of optically transparent material that are bonded together in the same plane or in different planes. The IC element  168  may be closely associated with (e.g., embedded in) the face  180   b  of the waveguide  172  for receiving the collimated light beam  250  from the image projection assembly  108  into the waveguide  172  via the face  180   b , although in alternative embodiments, the IC element  168  may be associated with (e.g., embedded in) the other face  180   a  or even the edge of the waveguide  172  for coupling the collimated light beam  250  into the waveguide  172  as an in-coupled light beam. The DOE(s)  174  are associated with the waveguide  172  (e.g., incorporated within the waveguide  172  or abutting or adjacent one or more of the faces  180   a ,  180   b  of the waveguide  172 ) for, as briefly discussed above, two-dimensionally expanding the effective entrance pupil of the collimated light beam  250 . 
     To this end, the DOE(s)  174  comprises an orthogonal pupil expansion (OPE) element  186  closely associated with (e.g., embedded in) the face  180   b  of the waveguide  172  for splitting the in-coupled light beam  252  into orthogonal light beamlets  254 , and an exit pupil expansion (EPE) element  188  closely associated with (e.g., embedded in) the face  180   b  of the waveguide  172  for splitting the orthogonal light beamlets  254  into a set of out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172  towards the eye(s)  52  of the end user  50 . In the alternative embodiment where the waveguide  172  is composed of distinct panes, the OPE element(s)  174  and EPE element  188  may be incorporated into different panes of the waveguide  172 . 
     The OPE element  186  relays light along a first axis (horizontal or x-axis in  FIG.  34   ), and expands the effective pupil of light along a second axis (vertical or y-axis in  FIG.  34   ). In particular, as best shown in  FIG.  35   , the IC element  168  optically in-couples the collimated light beam  250  for propagation as an in-coupled light beam within the waveguide  172  via TIR along an internally reflective optical path parallel to an axis  262  (in this case, along the vertical or y-axis), and in doing so, repeatedly intersects the OPE element  186 . In the illustrated embodiment, the OPE element  186  has a relatively low diffraction efficiency (e.g., less than 50%), and comprises a series of diagonal diffractive elements (forty-five degrees relative to the x-axis), such that, at each point of intersection with the OPE element  186 , a portion (e.g., greater than 90%) of the in-coupled light beam  252  continues to propagate within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis), and the remaining portion (e.g., less than 10%) of the in-coupled light beam  252  is diffracted as an orthogonal light beamlet  254  (shown as being dashed in  FIG.  35   ) that propagates within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  264  (in this case, along the horizontal or x-axis) toward the EPE element  188 . It should be appreciated that although the axis  264  is described as being perpendicular or orthogonal to the axis  262  (y-axis), the axis  264  may alternatively be obliquely oriented with respect to axis  262  (y-axis). 
     In a similar fashion, at each point of intersection with the OPE element  186 , a portion (e.g., greater than 90%) of each orthogonal light beamlet  254  continues to propagate in the waveguide  172  via TIR along the respective internally reflective optical path parallel to the axis  264  (x-axis), and the remaining portion (e.g., less than 10%) of the respective orthogonal light beamlet  254  is diffracted as secondary light beamlets  256  that propagate within the waveguide  172  via TIR along respective internally reflective optical paths (shown by dashed lines) parallel to the axis  262  (y-axis). In turn, at each point of intersection with the OPE element  186 , a portion of (e.g., greater than 90%) of each secondary light beamlet  256  continues to propagate in the waveguide  172  via TIR along a respective internally reflective optical path parallel to the axis  262  (y-axis), and the remaining portion (e.g., less than 10%) of the respective secondary light beamlet  256  is diffracted as tertiary light beamlets  258  that combine in phase with the orthogonal light beamlets  254  and propagate within the waveguide  172  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     Thus, by dividing the in-coupled light beam  252  into multiple orthogonal light beamlets  254  that propagate within the waveguide  172  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis), the entrance pupil of the collimated light beam  250  in-coupled into the display screen  110  is expanded vertically along the y-axis by the OPE element  186 . 
     The EPE element  188 , in turn, further expands the light&#39;s effective exit pupil along the first axis (horizontal x-axis in  FIG.  36   ). In particular, as best shown in  FIG.  36   , the EPE element  188 , like the OPE element  186 , has a relatively low diffraction efficiency (e.g., less than 50%), such that, at each point of intersection with the EPE element  188 , a portion (e.g., greater than 90%) of each orthogonal light beamlet  254  continues to propagate within the waveguide  172  respectively along an respective internally reflective optical path parallel to the axis  264  (x-axis), and the remaining portion of each orthogonal light beamlet  254  is diffracted as an out-coupled light beamlet  256  that exits the face  180   b  of the waveguide  172  (along the z-axis), as illustrated in  FIG.  36   . That is, every time a light beamlet hits the EPE element  188 , a portion of it will be diffracted toward the face  180   b  of the waveguide  172 , while the remaining portion will continue to propagate within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  264  (x-axis). 
     Thus, by dividing each orthogonal light beamlet  254  into multiple out-coupled light beamlets  256 , the entrance pupil of the collimated light beam  250  is further expanded horizontally along the x-axis by the EPE element  188 , resulting in a two-dimensional array of out-coupled light beamlets  256  that resemble a larger version of the original in-coupled light beam  252 . 
     Although the OPE element  186  and EPE element  188  are illustrated in  FIG.  34    as non-overlapping in the x-y plane, the OPE element  186  and EPE element  188  may overlap each other in the x-y plane, as illustrated in  FIG.  39   , or may partially overlap each other in the x-y plane, as illustrated in  FIG.  38   . In both cases, like in the embodiment illustrated in  FIG.  34   , the OPE element  186  will split the in-coupled light beam  252  that propagates within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis) into orthogonal light beamlets  254  that propagate within the waveguide  172  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). In these cases, the OPE element  186  and EPE element  188  will need to be respectively disposed on opposite faces  180   a ,  180   b  of the waveguide  172 . 
     In addition to the function of out-coupling the light beamlets  256  from the face  180   b  of the waveguide  172 , the EPE element  188  serves to focus the output set of light beamlets  256  at along a given focal plane, such that a portion of an image or virtual object is seen by end user  50  at a viewing distance matching that focal plane. For example, if the EPE element  188  has only a linear diffraction pattern, the out-coupled light beamlets  256  exiting the face  180   b  of the waveguide  172  toward the eye(s)  52  of the end user  50  will be substantially parallel, as shown in  FIG.  39 A , which would be interpreted by the brain of the end user  50  as light from a viewing distance (focal plane) at optical infinity. However, if the EPE element  188  has both a linear diffraction pattern component and a radially symmetric diffraction pattern component, the out-coupled light beamlets  256  exiting the face  180   b  of the waveguide  172  will be rendered more divergent from the perspective of the eye(s)  52  of the end user  50  (i.e., a convex curvature will be imparted on the light wavefront), and require the eye(s)  52  to accommodate to a closer distance to bring the resulting image into focus on the retina and would be interpreted by the brain of the end user  50  as light from a viewing distance (e.g., four meters) closer to the eye(s)  52  than optical infinity, as shown in  FIG.  39 B . The out-coupled light beamlets  256  exiting the face  180   b  of the waveguide  172  can be rendered even more divergent from the perspective of the eye(s)  52  of the end user  50  (i.e., a more convex curvature will be imparted on the light wavefront), and require the eye(s)  52  to accommodate to an even closer distance to bring the resulting image into focus on the retina and would be interpreted by the brain of the end user  50  as light from a viewing distance (e.g., 0.5 meters) closer to the eye(s)  52 , as shown in  FIG.  39 C . 
     Although the waveguide apparatus  170  has been described herein as having only one focal plane, it should be appreciated that multiple planar optical waveguides  172  with associated OPEs  176  and EPEs  178  can be used to simultaneously or sequentially generate images at multiple focal planes, as discussed in U.S. Patent Publication Nos. 2015/0309264 and 2015/0346490, which are expressly incorporated herein by reference. 
     As previously described, it is desirable to increase the saturation or in-fill of the exit pupil of the display screen  110 . Without modification, the exit pupil of the display screen  110  may not be optimally saturated. For example, as illustrated in  FIG.  40 A , the pupil of the collimated light beam  250  may be expanded to an exit pupil  300   a  of a 3×3 array of out-coupled light beamlets  256 , which are relatively sparse in nature (i.e., the gaps between the out-coupled light beamlets  256  are relatively large). However, the display screen  110  may be enhanced with beam-multiplication features, such that the pupil of the collimated light beam  250  is expanded to an exit pupil  300   b  of a more saturated 9×9 array of out-coupled light beamlets  256 , as illustrated in  FIG.  40 B . 
     For example, in some embodiments, two OPEs  186  are employed to double the number of orthogonal light beamlets  254  obtained from the in-coupled light beam  252 , and thus, double the saturation of the two-dimensional array of out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172 . 
     In particular, as shown in  FIGS.  41 - 43   , a waveguide apparatus  170   a  is similar to the waveguide apparatus  170  described, with the exception that the waveguide apparatus  170   a  comprises a first OPE element  186   a  disposed adjacent (e.g., on) the first face  180   a  of the waveguide  172  for splitting the in-coupled light beam  252  propagating within the waveguide  172  via TIR along an internally reflecting optical path parallel to the axis  262  (y-axis) into a first set of orthogonal light beamlets  254   a  for propagation within the waveguide  172  via TIR along respective internally reflecting optical paths parallel to the axis  264  (x-axis) (best shown in  FIG.  41   ), and a second OPE element  186   b  disposed adjacent (e.g., on) the second face  180   b  of the waveguide  172 , for splitting the in-coupled light beam  252  propagating within the waveguide  172  via TIR along an internally reflecting optical path parallel to the axis  262  (y-axis) into a second set of orthogonal light beamlets  254   b  for propagation within the waveguide  172  via TIR along respective internally reflecting optical paths parallel to the axis  264  (x-axis). As best shown in  FIG.  41   , the first and second sets of orthogonal light beamlets  254   a ,  254   b  alternate with each other. 
     That is, because the in-coupled light beam  252  propagating within the waveguide  172  via TIR along the internally reflective optical path parallel to the axis  262  (y-axis) alternately intersects the first and second OPE elements  186   a ,  186   b  on the opposite faces  180   a ,  180   b  of the waveguide  172 , portions of the in-coupled light beam  252  are respectively diffracted as the first and second primary sets of light beamlets  254   a ,  254   b  for propagation within the waveguide  172  via TIR along alternating internally reflective optical paths parallel to the axis  264  (x-axis). Secondary light beamlets  256   a ,  256   b  (shown in  FIGS.  41  and  42   ) are also respectively generated from the beamlets  254   a ,  254   b , which further creates tertiary light beamlets  258   a ,  258   b  (shown only in  FIG.  41   ) that respectively combine in phase with the orthogonal light beamlets  254   a ,  254   b . In turn, the first and second primary sets of light beamlets  254   a ,  254   b  intersect the EPE element  188  on the face  180   b  of the waveguide  172 , portions of which are respectively diffracted as a first set of out-coupled light beamlets  256   a  and a second set of out-coupled light beamlets  256   b  that exit the face  180   b  of the waveguide  172 . Thus, the doubling of the orthogonal light beamlets  254  correspondingly increases the saturation of the exit pupil  300   a  expanded by the display screen  110  (shown in  FIG.  40 B ). 
     In another embodiment, partially reflective interfaces are incorporated into the waveguide  172  to increase the number of light beamlets propagating within the waveguide  172 , and thus, increase the saturation of the two-dimensional array of out-coupled light beamlets  256  exiting the face  180   b  of the waveguide  172 . In the embodiments illustrated below, the waveguide  172  comprises a plurality of layered substrates having at least one pair of adjacent substrates and a semi-reflective interface between each of the pair(s) of adjacent substrates, such that a light beam that intersects each semi-reflective interface is split into multiple beamlets that propagate within the waveguide  172  via TIR, thereby increasing the density of the out-coupled light beamlets exiting the face  180   b  of the waveguide  172 . It should be noted that the adjacent substrates described below are not drawn to scale and are illustrated as being multiples of each other for purposes of simplicity. However, adjacent substrates may be, and preferably are, non-multiples of each other, such that the density of the in-fill of out-coupled light beamlets exiting the face of the waveguide is maximized. 
     In particular, and with reference to  FIGS.  44 - 46   , a waveguide apparatus  170   b  is similar to the waveguide apparatus  170  described, with the exception that the waveguide  172  is a composite substrate composed of a primary waveguide  172   a  and secondary waveguide  172   b . The waveguide apparatus  170   b  further comprise a semi-reflective interface  190  disposed between the primary waveguide  172   a  and secondary waveguide  172   b.    
     In some embodiments, the semi-reflective interface  190  takes the form of a semi-reflective coating, such as one composed of, e.g., a metal, such as gold, aluminum, silver, nickel-chromium, chromium, etc., a dielectric, such as oxides, fluorides, sulfides, etc., a semiconductor, such as silicon, germanium, etc., and/or a glue or adhesive with reflective properties can be disposed between the primary waveguide  172   a  and secondary waveguide  172   b  via any suitable process, such as physical vapor deposition (PVD), ion-assisted deposition (IAD), ion beam sputtering (IBS), etc. The ratio of reflection to transmission of the semi-reflective coating  190  may be selected or determined based at least in part upon the thickness of the coating  190 , or the semi-reflective coating  190  may have a plurality of small perforations to control the ratio of reflection to transmission. In an alternative embodiment, the primary waveguide  172   a  and secondary waveguide  172   b  are composed of materials having different indices of refraction, such that the interface between the waveguides  172   a ,  172   b  are semi-reflective for light that is incident on the semi-reflective interface of less than a critical angle (i.e., the incidence angle at which a portion of the light is transmitted through the semi-reflective interface, and the remaining portion of the light is reflected by the semi-reflective interface). The semi-reflective interface  190  is preferably designed, such that the angle of a light beam incident on the semi-reflective interface  190  is preserved. 
     In any event, as best shown in  FIG.  45   , the IC element  168  couples the collimated light beam  250  into the planar optical waveguide  172  as an in-coupled light beam  252 , which propagates within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis). The semi-reflective interface  190  is configured for splitting the in-coupled light beam  252  into multiple in-coupled light beamlets. 
     In particular, the semi-reflective interface  190  is configured for splitting the in-coupled light beam  252  into two primary in-coupled light beamlets (in this case, a first primary in-coupled light beamlet  252   a  (shown by a solid line) and a second primary in-coupled light beamlet  252   b  (shown by a dashed line) that propagate within the primary waveguide  172   a  along an internally reflective optical path parallel to the axis  262  (y-axis). As shown in  FIG.  45   , the semi-reflective interface  190  generates a secondary in-coupled light beamlet  252 ′ that propagates within the secondary waveguide  172   b  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis), and from which the second primary in-coupled light beamlet  252   b  is created. 
     It should be appreciated that, because the thickness of the primary waveguide  172  is a multiple of the thickness of the secondary waveguide  172   b  (in this case, exactly twice as thick), only two primary in-coupled light beamlets  252   a ,  252   b  are generated due to recombination of light beamlets. However, in the preferred case where the thickness of the primary waveguide  172   a  is a non-multiple of the thickness of the secondary waveguide  172   b , an additional primary in-coupled light beamlet  252  is generated at each point of intersection between a secondary in-coupled light beamlet  252 ′ and the semi-reflective interface  190 , and likewise, an additional secondary in-coupled light beamlet  252 ′ is generated at each point of intersection between a primary in-coupled light beamlet  252  and the semi-reflective interface  190 . In this manner, the number of primary in-coupled light beamlets  252  geometrically increases from the ICO  168  along the axis  262 . 
     The OPE element  186  is configured for respectively splitting the primary in-coupled light beamlets  252   a ,  252   b  into two sets of primary orthogonal light beamlets. In particular, the primary in-coupled light beamlets  252   a ,  252   b  intersect the OPE element  186  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary in-coupled light beamlets  252   a ,  252   b  are diffracted as two sets of primary orthogonal light beamlets  254   a ,  254   b  that propagate within the waveguide  172  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     As best shown in  FIG.  46   , the semi-reflective interface  190  is configured for splitting the two sets of orthogonal light beamlets  254   a ,  254   b  into four sets of orthogonal light beamlets. In particular, the semi-reflective interface  190  splits the set of primary orthogonal light beamlets  254   a  into two sets of primary orthogonal light beamlets  254   a  (in this case, a first set of primary orthogonal light beamlets  254   a ( 1 ) (shown by a solid line) and a second set of primary orthogonal light beamlets  254   a ( 2 ) (shown by a dashed line) that propagate within the primary waveguide  172   a  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). As shown in  FIG.  46   , the semi-reflective interface  190  generates a set of secondary orthogonal light beamlets  252 ′ that propagate within the secondary waveguide  172   b  via TIR along respective internally reflective optical paths parallel to the axis  264 ′ (x-axis), and from which the second set of primary orthogonal light beamlets  254   a ( 2 ) is created. Similarly, the semi-reflective interface  190  splits the set of orthogonal light beamlets  254   b  into two more sets of primary orthogonal light beamlets (not shown) that propagate within the primary waveguide  172   a  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     It should be appreciated that, because the thickness of the primary waveguide  172   a  is a multiple of the thickness of the secondary waveguide  172   b  (in this case, exactly twice as thick), only two primary orthogonal light beamlets  254  are generated from each orthogonal light beamlet  254 . However, in the preferred case where the thickness of the primary waveguide  172   a  is a non-multiple of the thickness of the secondary waveguide  172   b , an additional primary orthogonal light beamlet  254  is generated at each point of intersection between a secondary orthogonal light beamlet  254 ′ and the semi-reflective interface  190 , and likewise, an additional secondary orthogonal light beamlet  254 ′ is generated at each point of intersection between a primary in-coupled light beamlet  254  and the semi-reflective interface  190 . In this manner, the number of primary orthogonal light beamlets  254  geometrically increases from the ICO  168  along the axis  264  (x-axis). 
     The EPE element  188  is configured for splitting each of the orthogonal light beamlets into the set of out-coupled light beamlets  256 . For example, the sets of primary orthogonal light beamlets  254  (only the sets of primary orthogonal light beamlets  254   a ( 1 ) and  254   a ( 2 ) shown) intersect the EPE element  188  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary orthogonal light beamlets  254  are diffracted as the set of out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172 . Thus, the increase in the number of the in-coupled light beamlets  252  and the number of orthogonal light beamlets  254  correspondingly increases the saturation of the exit pupil  300   a  expanded by the display screen  110  (shown in  FIG.  40 B ). 
     Referring to  FIGS.  47 A- 47 D , the manner in which the semi-reflective interface  190  multiplies a light beam (in this case, the in-coupled light beam  252 , although the same technique can be applied to the orthogonal beam  254  as well) into multiple beamlets  252  (in this case, two light beamlets  252   a  and  252   b ) will now be described. In the example of  FIGS.  47 A- 47 D , the primary waveguide  172   a  is a multiple of the secondary waveguide  172   b , and therefore, the primary light beamlet  252  and secondary light beamlet  252 ′ may share several intersection points at the semi-reflective interface  190 . However, as briefly discussed above, the primary waveguide  172   a  is preferably a non-multiple of the secondary waveguide  172   b , such that the number of common intersection points at the semi-reflective interface  190  is minimized, thereby generating additional light beamlets  252  and maximizing the in-fill of out-coupled beamlets. 
     At the first point of intersection P 1  with the semi-reflective interface  190 , a portion of the light beam  252  is transmitted through the semi-reflective interface  190  into the secondary waveguide  172   b  as the secondary light beamlet  252 ′, which is reflected by the face  180   a  of the waveguide  172  back to a second point of intersection P 2  of the semi-reflective interface  190 , while a portion of the light beam  252  is reflected by the semi-reflective interface  190  back into the primary waveguide  172   a  as the primary light beamlet  252   a , which is reflected by the face  180   b  of the waveguide  172  back to a third point of intersection P 3  of the semi-reflective interface  190  ( FIG.  47 A ). 
     At the second point of intersection P 2  with the semi-reflective interface  190 , a portion of the secondary light beamlet  252 ′ is transmitted through the semi-reflective interface  190  into the primary waveguide  172   b  as the primary light beamlet  252   b , which is reflected by the face  180   a  of the waveguide  172  back to a fourth point of intersection P 4  of the semi-reflective interface  190 , while a portion of the secondary light beamlet  252 ′ is reflected by the semi-reflective interface  190  back into the secondary waveguide  172   b  as the secondary light beamlet  252 ′, which is reflected by the face  180   a  of the waveguide  172  back to the third point of intersection P 3  of the semi-reflective interface  190  ( FIG.  47 B ). 
     At the third point of intersection P 3  with the semi-reflective interface  190 , a portion of the primary light beamlet  252   a  is transmitted through the semi-reflective interface  190  into the secondary waveguide  172   b , and a portion of the secondary light beamlet  252 ′ is reflected by the semi-reflective interface  190  back into the secondary waveguide  172   b , which portions happen to combine together as the secondary light beamlet  252 ′ and reflected by the face  180   b  of the waveguide  172  back to the fourth point of intersection P 4  ( FIG.  47 C ). Of course, the primary light beamlet  252   a  and the secondary light beamlet  252 ′ may not have a common point of intersection P 3 , in which case, an additional secondary light beamlet  252 ′ may be generated. Furthermore, at the third point of intersection P 3  with the semi-reflective interface  190 , a portion of the secondary light beamlet  252 ′ is transmitted through the semi-reflective interface  190  into the primary waveguide  172   a , and a portion of the primary light beamlet  252   a  is reflected by the semi-reflective interface  190  back into the primary waveguide  172   a , which portions may combine together as the primary light beamlet  252   a , which is reflected by the face  180   b  of the waveguide  172  back to a fifth point of intersection P 5  of the semi-reflective interface  190  ( FIG.  47 C ). Of course, the secondary light beamlet  252 ′ and the primary light beamlet  252   a  may not have a common point of intersection P 3 , in which case, an additional primary light beamlet  252  may be generated. 
     At the fourth point of intersection P 4  with the semi-reflective interface  190 , a portion of the primary light beamlet  252   b  is transmitted through the semi-reflective interface  190  into the secondary waveguide  172   b , and a portion of the secondary light beamlet  252 ′ is reflected by the semi-reflective interface  190  back into the secondary waveguide  172   b , which portions may combine together as the secondary light beamlet  252 ′ and reflected by the face  180   b  of the waveguide  172  back to the fifth point of intersection P 5  ( FIG.  47 D ). Of course, the primary light beamlet  252   b  and the secondary light beamlet  252 ′ may not have a common point of intersection P 4 , in which case, an additional secondary light beamlet  252 ′ may be generated. Furthermore, at the fourth point of intersection P 4  with the semi-reflective interface  190 , a portion of the secondary light beamlet  252 ′ is transmitted through the semi-reflective interface  190  into the primary waveguide  172   a , and a portion of the primary light beamlet  252   b  is reflected by the semi-reflective interface  190  back into the primary waveguide  172   a , which portions combine together as the primary light beamlet  252   b , which is reflected by the face  180   b  of the waveguide  172  back to a sixth point of intersection P 6  of the semi-reflective interface  190  ( FIG.  47 D ). Of course, the secondary light beamlet  252 ′ and the primary light beamlet  252   b  may not have a common point of intersection P 4 , in which case, an additional primary light beamlet  252  may be generated. 
     Thus, it can be appreciated from the foregoing that light energy is transferred between the primary waveguide  172   a  and secondary waveguide  172   b  to generate and propagate two light beamlets  252   a ,  252   b  within the waveguide apparatus  170 . 
     Significantly, the thicknesses of the layered substrates, in coordination with the expected incident angles of the light beams on each semi-reflective interface, are selected, such that there is no gap between the edges of adjacent out-coupled beamlets  256 . 
     For example, in the embodiment illustrated in  FIGS.  44 - 46   , the thickness of the secondary waveguide  172   b  is less than the thickness of the primary waveguide  172   a , with the thickness Δt of the secondary waveguide  172   b  being selected such that the spacings between the centers of adjacent ones of the resulting out-coupled light beamlets  256  are equal to or less than the width w of the collimated light beamlet  250 . Of course, if the primary waveguide  172   a  is not a multiple of the secondary waveguide  172   b , the spacings between the centers of adjacent ones of the resulting out-coupled light beamlets  256  may be greater than the width w of the collimated light beamlet  250 . 
     It should be noted that the width w of the collimated light beam  250  relative to the size of the IC element  168  has been exaggerated for purposes of illustration. In reality, the width w of the collimated light beam  250  will be much smaller than the size of the IC element  168 , which needs to be large enough to accommodate all scan angles of the collimated light beam  250 . In the preferred embodiment, the average spacing between adjacent out-coupled light beamlets  256  is minimized for the worst-case scan angle. For example, for the worst-case scan angle, although there may be gaps between some of the adjacent out-coupled light beamlets  256 , there will be no gaps between most of the adjacent out-coupled light beamlets  256 . 
     Thus, the thickness Δt of the secondary waveguide  172   b  may be selected based on the worst-case scan angle to minimize the spacings between adjacent out-coupled beamlets  256 . It should be noted that the worst-case scan angle is one that results in the smallest angle of incidence of the in-coupled light beam  252  on the semi-reflective interface  190 . Of course, if the primary waveguide  172   a  is not a multiple of the secondary waveguide  172   b , more out-coupled beamlets  256  will be generated, thereby naturally decreasing the average spacing between adjacent out-coupled beamlets  256 . In this case, it may be beneficial to select the thickness values t and Δt to have a least common multiple that is relatively high. For example, in selecting the thickness values t and Δt, one may seek to maximize the least common multiple of the thickness values t and Δt to maximize the quantity of out-coupled beamlets  256  for the worst-case scan angle. Furthermore, selecting the thickness values t and Δt may also yield an uneven/complex distribution of out-coupled beamlets  256  that may minimize adverse effects created by coherent light interactions between adjacent out-coupled beamlets  256 . 
     For example, if it is assumed that the worst-case angle of incidence between the in-coupled light beam  252  and the semi-reflective interface  190  is sixty degrees, and the thickness t of the primary waveguide  172   a  is exactly twice the thickness Δt of the secondary waveguide  172   b , the thickness Δt of the secondary waveguide  172   b  should be √{square root over (3)}/2 the width w of the in-coupled light beam  252 , so that, as illustrated in  FIG.  48   , the adjacent primary in-coupled light beamlets  252  will have no gaps therebetween, and as illustrated in  FIG.  49   , the adjacent primary orthogonal light beamlets  254  will have no gaps therebetween, and thus, the adjacent out-coupled light beamlets  256  will have no gaps therebetween. 
     It should be appreciated that, for purposes of simplicity in explanation, no refraction of light transmitted through the semi-reflective interface  190  is assumed. However, in the case where substantial refraction of the transmitted light through the semi-reflective interface  190  occurs, the angle of transmission of the light due to such refraction must be taken into account when selecting the thickness Δt of the secondary waveguide  172   b . For example, the greater the refraction of the light, such that the angle of the transmitted light relative to the semi-reflective interface  190  decreases, the more the thickness Δt of the secondary waveguide  172   b  must be decreased to compensate for such refraction. 
     It should also be appreciated from the foregoing that the generation of the primary in-coupled light beamlets  252  propagating within the primary waveguide  172   a  via TIR along the internally reflective optical paths parallel to the axis  262  (y-axis), and then the generation of the primary out-coupled light beamlets  256  propagating within the primary waveguide  172   a  along the internally reflective optical paths parallel to the axis  264  (x-axis), assuming an appropriate thickness Δt of the secondary waveguide  172   b , will completely in-fill the exit pupil of the display screen  110 . 
     In the case where it is desirable to decrease the thickness Δt of the secondary waveguide  172   b  to further decrease the average spacing between the adjacent primary in-coupled light beamlets  252 , primary orthogonal light beamlets  254 , and out-coupled light beamlets  256 , the thickness t of the primary waveguide  172   a  may be much greater than the thickness Δt of the secondary waveguide  172   b , e.g., greater than three, four, five, or even more times the thickness Δt of the secondary waveguide  172   b.    
     For example, as illustrated with respect to the waveguide apparatus  170   c  in  FIGS.  50  and  51   , the thickness t of the primary waveguide  172   a  is three times the thickness Δt of the secondary waveguide  172   b . As best shown in  FIG.  50   , the IC element  168  couples the in-coupled light beam  252  into the waveguide  172 , which propagates within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis). The semi-reflective interface  190  is configured for splitting the in-coupled light beam  252  into three in-coupled light beamlets. In particular, the semi-reflective interface  190  splits the in-coupled light beam  252  into three primary in-coupled light beamlets  252  (a first primary in-coupled light beamlet  252   a  (shown by a solid line) and two more primary in-coupled light beamlets  252   b ,  252   c  (shown by dashed lines)) that propagate within the primary waveguide  172   a  along respective internally reflective optical paths parallel to the axis  262 . As shown in  FIG.  50   , the semi-reflective interface  190  generates a secondary in-coupled light beamlet  252 ′ that propagates within the secondary waveguide  172   b  via TIR along an internally reflective optical path parallel to the axis  264 ′ (x-axis), and from which the two primary in-coupled light beamlet  252   b ,  252   c  are created. 
     It should be appreciated that, because the thickness of the primary waveguide  172   a  is a multiple of the thickness of the secondary waveguide  172   b  (in this case, exactly three times as thick), only three primary in-coupled light beamlets  252   a ,  252   b ,  252   c  are generated due to recombination of light beamlets. However, in the preferred case where the thickness of the primary waveguide  172   a  is a non-multiple of the thickness of the secondary waveguide  172   b , an additional primary in-coupled light beamlet  252  is generated at each point of intersection between a secondary in-coupled light beamlet  252 ′ and the semi-reflective interface  190 , and likewise, an additional secondary in-coupled light beamlet  252 ′ is generated at each point of intersection between a primary in-coupled light beamlet  252  and the semi-reflective interface  190 . In this manner, the number of primary in-coupled light beamlets  252  geometrically increases from the ICO  168  along the axis  262  (y-axis). 
     The OPE element  186  is configured for respectively splitting the primary in-coupled light beamlets  252   a - 252   c  into three sets of primary orthogonal light beamlets. In particular, the primary in-coupled light beamlets  252   a - 252   c  intersect the OPE element  186  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary in-coupled light beamlets  252   a - 252   c  are diffracted as three sets of primary orthogonal light beamlets  254   a - 254   c  that propagate within the waveguide  172  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     As best shown in  FIG.  51   , the semi-reflective interface  190  is configured for splitting the three sets of orthogonal light beamlets  254   a - 254   c  into nine sets of orthogonal light beamlets. In particular, the semi-reflective interface  190  splits the set of primary orthogonal light beamlets  254   a  into three sets of primary orthogonal light beamlets  254   a  (a first set of primary in-coupled light beamlets  254   a  (shown by a solid line) and two more sets of primary in-coupled light beamlets  254   b ,  254   c  (shown by dashed lines)) that propagate within the primary waveguide  172   a  via TIR along a respective internally reflective optical path parallel to the axis  264  (x-axis). As shown in  FIG.  51   , the semi-reflective interface  190  generates a set of secondary in-coupled light beamlets  252 ′ that propagates within the secondary waveguide  172   b  via TIR along respective internally reflective optical paths parallel to the axis  262 ′ (y-axis), and from which the two sets of primary in-coupled light beamlets  254   b ,  254   c  are created. Similarly, the semi-reflective interface  190  splits the set of orthogonal light beamlets  254   b  into three more sets of primary orthogonal light beamlets (not shown) and the set of orthogonal light beamlets  254   c  into three more set of primary orthogonal light beamlets (not shown) that propagate within the primary waveguide  172   a  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     It should be appreciated that, because the thickness of the primary waveguide  172   a  is a multiple of the thickness of the secondary waveguide  172   b  (in this case, exactly three times as thick), only three primary sets of orthogonal light beamlets  254   a ,  254   b ,  254   c  are generated due to recombination of light beamlets. However, in the preferred case where the thickness of the primary waveguide  172   a  is a non-multiple of the thickness of the secondary waveguide  172   b , an additional set of primary orthogonal light beamlets  254  is generated at each point of intersection between a set of secondary orthogonal light beamlets  254 ′ and the semi-reflective interface  190 , and likewise, an additional set of secondary orthogonal light beamlets  254 ′ is generated at each point of intersection between a primary set of orthogonal light beamlet  254  and the semi-reflective interface  190 . In this manner, the number of primary orthogonal light beamlets  254  geometrically increases from the ICO  168  along the axis  264  (x-axis). 
     The EPE element  188  is configured for splitting the nine sets of orthogonal light beamlets into the set of out-coupled light beamlets  256 . In particular, as shown in FIG.  51 , the sets of primary orthogonal light beamlets  254  (only the sets of primary orthogonal light beamlets  254   a ( 1 )- 254   a ( 3 ) shown) intersect the EPE element  188  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary orthogonal light beamlets  254  are diffracted as the set of out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172 . Thus, the increase in the number of the in-coupled light beamlets  252  and the number of orthogonal light beamlets  254  correspondingly increases the saturation of the exit pupil  300   a  expanded by the display screen  110  (shown in  FIG.  40 B ). 
     Notably, such saturation of the exit pupil  300   a  by the waveguide apparatus  170   c  of  FIGS.  50 - 51    is equivalent to the saturation of the exit pupil  300   a  by the waveguide apparatus  170   b  of  FIGS.  45 - 46    if the width w of the collimated light beam  250  in-coupled in the waveguide apparatus  170   c  is ⅔ smaller than the width w of the collimated light beam  250  in-coupled in the waveguide apparatus  170   b . That is, the thickness Δt of the secondary waveguide  172   b  need only be scaled downed to be commensurate with the decrease in the width w of the collimated light beam  250  in-coupled in the waveguide apparatus  170   b . For example, assuming the same worst-case angle of incidence between the in-coupled light beam  252  and the semi-reflective interface  190  to be sixty degrees, the thickness Δt of the secondary waveguide  172   b  can be scaled down to √{square root over (3)}/2 the width w of the in-coupled light beam  252 , so that, as illustrated in  FIG.  52   , the edges of the adjacent primary in-coupled light beamlets  252  will have no gaps therebetween, and as illustrated in  FIG.  53   , the edges of the adjacent primary orthogonal light beamlets  254  will have no gaps therebetween, and thus, the edges of the adjacent out-coupled light beamlets  256  will have no gaps therebetween. 
     It can be appreciated from the foregoing that, while the thickness t of the primary waveguide  172   a  may be much larger than the width w of the collimated light beam  250  in-coupled into the waveguide apparatuses  170   b ,  170   c , illustrated in  FIGS.  44 - 53   , the thickness Δt of the secondary waveguide  172   b  may be smaller than the width w of the collimated light beam  250 . However, if the thickness Δt of the secondary waveguide  172   b  required to eliminate spacings between the centers of adjacent ones of the resulting out-coupled light beamlets  256 , given the worst-case scanning angle, is too small for manufacturability purposes, the thickness of the secondary waveguide  172   b  may alternatively be selected, such that the difference in the thicknesses between the primary waveguide  172   a  and secondary waveguide  172   b  is equal to a difference thickness Δt, as illustrated in the waveguide apparatus  170   d  of  FIGS.  54  and  55   . 
     Thus, in this case, the thickness of the secondary waveguide  172   b  may be selected to be slightly less than the thickness t of the primary waveguide  172   a , i.e., t-Δt. As best shown in  FIG.  54   , the IC element  168  couples the in-coupled light beam  252  into the waveguide  172 , which propagates within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis). The semi-reflective interface  190  is configured for splitting the in-coupled light beam  252  into three in-coupled light beamlets. In particular, the semi-reflective interface  190  splits the in-coupled light beam  252  into three primary in-coupled light beamlets  252  (a first primary in-coupled light beamlet  252   a  (shown by a solid line) and two more primary in-coupled light beamlets  252   b ,  252   c  (shown by dashed lines)) that propagate within the primary waveguide  172   a  along respective internally reflective optical paths parallel to the axis  262 . As shown in  FIG.  54   , the semi-reflective interface  190  generates two secondary in-coupled light beamlets  252 ( 1 )′ and ( 2 )′ that propagate within the secondary waveguide  172   b  via TIR along respective internally reflective optical paths parallel to the axis  262 ′ (y-axis), and from which the two primary in-coupled light beamlet  252   b ,  252   c  are created. 
     The OPE element  186  is configured for respectively splitting the primary in-coupled light beamlets  252   a - 252   c  into three sets of primary orthogonal light beamlets. In particular, the primary in-coupled light beamlets  252   a - 252   c  intersect the OPE element  186  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary in-coupled light beamlets  252   a - 252   c  are diffracted as three sets of primary orthogonal light beamlets  254   a - 254   c  that propagate within the waveguide  172  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     As best shown in  FIG.  55   , the semi-reflective interface  190  is configured for splitting the three sets of orthogonal light beamlets  254   a - 254   c  into nine sets of orthogonal light beamlets. In particular, the semi-reflective interface  190  splits the set of primary orthogonal light beamlets  254   a  into three sets of primary orthogonal light beamlets  254   a  (a first set of primary in-coupled light beamlets  254   a  (shown by a solid line) and two more sets of primary in-coupled light beamlets  254   b ,  254   c  (shown by dashed lines)) that propagate within the primary waveguide  172  along respective internally reflective optical paths parallel to the axis  264  (x-axis). As shown in  FIG.  55   , the semi-reflective interface  190  generates two sets of secondary in-coupled light beamlets  254 ( 1 )′ and  254 ( 2 )′ that propagate within the secondary waveguide  172   b  via TIR along respective internally reflective optical paths parallel to the axis  264 ′ (x-axis), and from which the two sets of primary in-coupled light beamlets  254   b ,  254   c  are created. Similarly, the semi-reflective interface  190  splits the set of orthogonal light beamlets  254   b  into three more sets of primary orthogonal light beamlets (not shown) and the set of orthogonal light beamlets  254   c  into three more set of primary orthogonal light beamlets (not shown) that propagate within the primary waveguide  172   a  along respective internally reflective optical paths parallel to the axis  264  (x-axis). 
     The EPE element  188  is configured for splitting the nine sets of orthogonal light beamlets into the set of out-coupled light beamlets  256 . In particular, as shown in  FIG.  55   , the sets of primary orthogonal light beamlets  254  (only the sets of primary orthogonal light beamlets  254   a ( 1 )- 254   a ( 3 ) shown) intersect the EPE element  188  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary orthogonal light beamlets  254  are diffracted as the set of out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172 . Thus, the increase in the number of the in-coupled light beamlets  252  and the number of orthogonal light beamlets  254  correspondingly increases the saturation of the exit pupil  300   a  expanded by the display screen  110  (shown in  FIG.  40 B ). 
     In the same manner that the thickness Δt of the secondary waveguide  172   b  is selected above with respect to the waveguide apparatuses  170   b  and  170   c  of  FIGS.  44 - 53   , the difference in thickness Δt between the primary waveguide  172   a  and the secondary waveguide  172   b  in the embodiment of  FIGS.  54 - 55    is selected, such that assuming the same worst-case angle of incidence between the in-coupled light beam  252  and the semi-reflective interface  190  to be sixty degrees, the difference thickness Δt may be selected to be √{square root over (3)}/2 the width w of the in-coupled light beam  252 , so that the adjacent primary in-coupled light beamlets  252  and the edges of the adjacent primary orthogonal light beamlets  254  will have no gaps therebetween, and thus, the edges of the adjacent out-coupled light beamlets  256  will have no gaps therebetween. Thus, in this case, the thickness of the secondary waveguide  172   b  will be greater than the width w of the in-coupled light beam  252 . 
     Although the previous waveguide apparatuses  170   a - 170   d  illustrated in  FIGS.  44 - 55    have been described as comprising only one secondary waveguide  172   b , it should be appreciated that waveguide apparatus  170  may have multiple secondary waveguides  172   b . For example, referring to  FIGS.  56  and  57   , a waveguide apparatus  170   e  comprises two secondary waveguides  172   b  disposed on the primary waveguide  172   a , and four semi-reflective interfaces  190 , one of which is disposed between the primary waveguide  172   a  and one of the secondary waveguides  172   b , and the remaining one of which is disposed between the respective secondary waveguides  172   b.    
     As best shown in  FIG.  56   , the IC element  168  couples the in-coupled light beam  252  into the waveguide  172 , which propagates within the waveguide  172  via TIR along an internally reflective optical path parallel to the axis  262  (y-axis). The semi-reflective interface  190  is configured for splitting the in-coupled light beam  252  into three in-coupled light beamlets. In particular, the semi-reflective interfaces  190  split the in-coupled light beam  252  into three primary in-coupled light beamlets  252  (a first primary in-coupled light beamlet  252   a  (shown by a solid line) and two more primary in-coupled light beamlets  252   b ,  252   c  (shown by dashed lines)) that propagate within the primary waveguide  172   a  along respective internally reflective optical paths parallel to the axis  262  (y-axis). As shown in  FIG.  56   , the semi-reflective interface  190  generates two secondary in-coupled light beamlets  252 ′ that propagate within the respective two secondary waveguides  172   b  via TIR along respective internally reflective optical paths parallel to the axis  262 ′ (y-axis), and from which the two primary in-coupled light beamlet  252   b ,  252   c  are created. 
     The OPE element  186  is configured for respectively splitting the primary in-coupled light beamlets  252   a - 252   c  into three sets of primary orthogonal light beamlets. In particular, the primary in-coupled light beamlets  252   a - 252   c  intersect the OPE element  186  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary in-coupled light beamlets  252   a - 252   c  are diffracted as three sets of primary orthogonal light beamlets  254   a - 254   c  that propagate within the waveguide  172  via TIR along internally reflective optical paths parallel to the axis  264  (x-axis). 
     As best shown in  FIG.  57   , the semi-reflective interfaces  190  are configured for splitting the three sets of orthogonal light beamlets  254   a - 254   c  into nine sets of orthogonal light beamlets. In particular, the semi-reflective interfaces  190  split the set of primary orthogonal light beamlets  254   a  into three sets of primary orthogonal light beamlets  254   a  (a first set of primary orthogonal light beamlets  254   a  (shown by a solid line) and two more sets of primary orthogonal light beamlets  254   b ,  254   c  (shown by dashed lines)) that propagate within the primary waveguide  172   a  via TIR along respective internally reflective optical paths parallel to the axis  264  (x-axis). As shown in  FIG.  57   , the semi-reflective interface  190  generates two sets of secondary in-coupled light beamlets  252 ′ that propagate within the respective two secondary waveguides  172   b  via TIR along respective internally reflective optical paths parallel to the axis  264 ′ (x-axis), and from which the two primary orthogonal light beamlet  252   b ,  252   c  are created. Similarly, the semi-reflective interface  190  splits the set of orthogonal light beamlets  254   b  into three more sets of primary orthogonal light beamlets (not shown) and the set of orthogonal light beamlets  254   c  into three more set of primary orthogonal light beamlets (not shown) that propagate within the primary waveguide  172   a  along respective internally reflective optical paths parallel to the axis  264  (x-axis). In some embodiments, the two secondary waveguides  172   b  may be different thicknesses. In addition, for reasons similar to those having been described above with reference to  FIGS.  44 - 55   , in some examples, these different thicknesses may be non-multiples of each other. It also follows that the thickness of the primary waveguide  172   a  may be a non-multiple of one or both of the two different thicknesses of the two secondary waveguides  172   b . In other embodiments, the two secondary waveguides  172   b  may be of equal thickness. 
     The EPE element  188  is configured for splitting the nine sets of orthogonal light beamlets into the set of out-coupled light beamlets  256 . In particular, as shown in FIG.  57 , the sets of primary orthogonal light beamlets  254  (only the sets of primary orthogonal light beamlets  254   a ( 1 )- 254   a ( 3 ) shown) intersect the EPE element  188  adjacent the face  180   b  of the waveguide  172 , such that portions of the primary orthogonal light beamlets  254  are diffracted as the set of out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172 . Thus, the increase in the number of the in-coupled light beamlets  252  and the number of orthogonal light beamlets  254  correspondingly increases the saturation of the exit pupil  300   a  expanded by the display screen  110  (shown in  FIG.  40 B ). Although the waveguide apparatus  170   e  illustrated in  FIGS.  56  and  57    has been described above as comprising two secondary waveguides  172   b , it should be appreciated that waveguide apparatus  170   e  and others described herein may have at least two (e.g., three, four, five, or more) secondary waveguides  172   b.    
     In the prior embodiments, the entrance pupil of the collimated light beam output by the collimation element  154  is expanded only by the combination of the OPE element  186  and EPE element  188  of the display screen  110 , and includes features in close association with the OPE element  186  and EPE element  188  for increasing the saturation of the exit pupil of the display screen  110 . In the embodiments of a display subsystem  104 ′ subsequently described herein, the image projection assembly  108  further includes a pre-pupil expansion (PPE)  192 , which in the embodiment illustrated in  FIG.  58   , is disposed between the collimation element  166  and the IC element  168  of the display screen  110 . 
     The PPE  192  represents the first pupil expansion stage, and is designed to use one or more beam-multiplication techniques to pre-expand the entrance pupil of the collimated light beam  250  to an intermediate exit pupil  300   a  of a set (in this case, a two-dimensional 3×3 array) of initial out-coupled light beamlets  256 ′ prior to in-coupling into the waveguide apparatus  170  of the display screen  110  (which emulates inputting a conventional collimated light beam having a larger pupil size as illustrated in  FIG.  59 A ), and the display screen  110  represents the second pupil expansion stage, which further expands, in a conventional manner, the pupil size of the collimated light beam  250  to a final exit pupil  300   b  of a set (in this case, a two-dimensional 9×9 array) of final out-coupled light beamlets  256 , as illustrated in  FIG.  59 B . 
     In alternative embodiments, the display screen  110  may further expand the pupil size of the collimated light beam  250  to an exit pupil of an even more saturated set of final out-coupled light beamlets  256  using the aforementioned enhanced beam multiplication techniques. However, it should be appreciated that the use of the PPE  192  lends itself well to miniature-scale image devices that output relatively small pupil sized light beams that can be expanded to normal pupil sized light beams for input into a conventional PE for expansion to an exit pupil commensurate with the entrance pupil size of the eye(s)  52  of the end user  50 . For example, the PPE  192  may expand the entrance pupil of a collimated beam to a pre-expanded pupil that is at least ten times larger (e.g., at least 0.5 mm pupil) than the entrance pupil (e.g., 50 mil pupil size), and the waveguide apparatus  170  of the display screen  110  may further expand the pre-expanded pupil of the collimated light beam  250  to an exit pupil that is at least ten times larger (e.g., at least 5 mm pupil) than the pre-expanded pupil of the collimated light beam  250 . By utilizing a multi-stage pupil expansion system, manufacturing constraints associated with expanding the relatively small pupil of a collimated beam to a relatively large and saturated exit pupil need not be imposed on just one pupil expansion device, but rather can be distributed amongst multiple expansion devices, thereby facilitating manufacture of the entire system. 
     Referring now to  FIGS.  60 - 63   , some embodiments of the display subsystem  104 ′ utilize a conventional PE that comprises the afore-described waveguide apparatus  170  illustrated in  FIGS.  34 - 36    and a PPE  192   a  that, in the illustrated embodiment, takes the form of a mini-version of the waveguide apparatus  170  that is mounted to the IC element  168 . 
     To this end, the PPE  192   a  takes the form of a waveguide apparatus  170 ′ having a size commensurate with the size of the IC element  168  of the primary waveguide apparatus  170 . As with the primary waveguide apparatus  170  of the display screen  110 , the mini-waveguide apparatus  170 ′ comprises a planar optical waveguide  172 ′ that takes the form of a single unitary substrate or plane of optically transparent material (as described above with respect to the waveguide  172 ) and one or more DOEs  174 ′ associated with the waveguide  172 ′ for two-dimensionally pre-expanding the effective exit pupil of a collimated light beam  250  optically coupled into the waveguide  172 ′. The PPE  192   a  further comprises an IC element  168 ′ disposed on the face  180   b ′ of the waveguide  172 ′ for receiving the collimated light beam  250  from the collimation element  166  into the waveguide  172 ′ via the face  180   b ′, although in alternative embodiments, the IC element  168 ′ may be disposed on the other face  180   a ′ or even the edge of the waveguide  172 ′ for coupling the collimated light beam  250  into the waveguide  172  as an in-coupled light beam. The DOE(s)  174 ′ are associated with the waveguide  172 ′ (e.g., incorporated within the waveguide  172 ′ or abutting or adjacent one or more of the faces  180   a ′,  180   b ′ of the waveguide  172 ′) for, as briefly discussed above, two-dimensionally pre-expanding the effective entrance pupil of the collimated light beam  250  optically coupled into the waveguide  172 ′. 
     To this end, the DOE(s)  174  comprise an orthogonal pupil expansion (OPE) element  186  for splitting the in-coupled light beam  252  into a set of initial orthogonal light beamlets  254 ′, and an exit pupil expansion (EPE) element  188 ′ for splitting each initial orthogonal light beamlet  254 ′ into a set of initial out-coupled light beamlets  256 ′ that exit the face  180   b ′ of the waveguide  172 ′. In the particular embodiment illustrated in  FIGS.  60 - 63   , the OPE element  186 ′ and EPE element  188 ′ completely overlap each other in the x-y plane, and thus, the OPE element  186 ′ is disposed on the face  180   a  of the waveguide  172 ′ and the EPE element  188 ′ is disposed on the face  180   b  of the waveguide  172 ′. Alternatively, the OPE element  186 ′ and EPE element  188 ′ may not overlap at all in the x-y plane, in which case, both the OPE element  186 ′ and EPE element  188 ′ may be disposed on the same face  180   b  of the waveguide  172 ′. 
     The OPE element  186 ′ relays light along a first axis (horizontal or x-axis in  FIG.  60   ), and pre-expands the effective exit pupil of light along a second axis (vertical or y-axis in  FIG.  60   ). In particular, as best shown in  FIG.  61   , the IC element  168 ′ optically in-couples the collimated light beam  250  as an in-coupled light beam  252 ′ for propagation within the waveguide  172 ′ via TIR along an internally reflective optical path  262  (in this case, along the vertical or y-axis), and in doing so, repeatedly intersects the OPE element  186 ′. In the illustrated embodiment, the OPE element  186 ′ has a relatively low diffraction efficiency (e.g., less than 50%), and comprises a series of diagonal diffractive elements (forty-five degrees relative to the x-axis), such that, at each point of intersection with the OPE element  186 ′, a portion (e.g., greater than 90%) of the in-coupled light beam  252 ′ continues to propagate within the waveguide  172 ′ via TIR along an internally reflective optical path parallel to the axis  262  (y-axis), and the remaining portion (e.g., less than 10%) of the in-coupled light beam  252 ′ is diffracted as an initial orthogonal light beamlet  254 ′ (shown as being dashed in  FIG.  61   ) that propagates within the waveguide  172 ′ via TIR along an internally reflective optical path parallel to the axis  264  (in this case, along the horizontal or x-axis) toward the EPE element  188 ′. It should be appreciated that although the axis  264  is described as being perpendicular or orthogonal to the axis  262  (y-axis), the axis  264  may alternatively be obliquely oriented with respect to the axis  262 . 
     Thus, by dividing the in-coupled light beam  252 ′ into multiple initial orthogonal light beamlets  254 ′ that propagate along parallel internally reflective optical paths  264 , the entrance pupil of the collimated light beam  250  in-coupled into the mini-waveguide apparatus  170 ′ is pre-expanded vertically along the y-axis by the OPE element  186 ′. 
     The EPE element  188 ′, in turn, further pre-expands the light&#39;s effective pupil along the first axis (horizontal x-axis in  FIG.  62   ). In particular, the EPE element  188 ′, like the OPE element  186 ′, has a relatively low diffraction efficiency (e.g., less than 50%), such that, at each point of intersection with the EPE element  188 ′, a portion (e.g., greater than 90%) of each initial orthogonal light beamlet  254 ′ continues to propagate along a respective internally reflective optical path parallel to the axis  264  (x-axis), and the remaining portion of each initial orthogonal light beamlet  254 ′ is diffracted as an initial out-coupled light beamlet  256 ′ that exits the face  180   b ′ of the waveguide  172 ′ (along the z-axis), as illustrated in  FIG.  62   . That is, every time a light beamlet hits the EPE element  188 ′, a portion of it will be diffracted toward the face  180   b  of the waveguide  172 ′, while the remaining portion will continue to propagate along a respective internally reflective optical path parallel to the axis  264  (x-axis). 
     Thus, by dividing each initial orthogonal light beamlet  254 ′ into multiple initial out-coupled light beamlets  256 ′, the exit pupil of the in-coupled light beam  252  is further pre-expanded horizontally along the x-axis by the EPE element  188 ′, resulting in a two-dimensional array of initial out-coupled light beamlets  256 ′ that resemble a larger version of the original in-coupled light beam  252 . 
     In the same manner as described above with respect to  FIGS.  34 - 36   , the primary waveguide apparatus  170  further two-dimensionally expands the pupil of the collimated light beam  250 . That is, the initial out-coupled light beamlets  256 ′ are input into the IC element  168  of the primary waveguide apparatus  170  as in-coupled light beamlets  252 ( 1 )- 252 ( 4 ), which are in turn, split by the OPE element  186  into four sets of orthogonal light beamlets  254 ( 1 )- 254 ( 4 ), which are further split by the EPE element  188  into final out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172  towards the eye(s)  52  of the end user  50 . 
     Thus, as illustrated in  FIG.  63   , a single collimated light beam  250  is split into a one-dimensional array of four initial orthogonal light beamlets  254 ′ by the OPE element  186 ′, which is further split into a two-dimensional 4×4 array of initial out-coupled light beamlets  256 ′ by the EPE element  188 ′, which is further split into a two-dimensional 4×16 array of orthogonal light beamlets  254  by the OPE element  174 ′, which is further split into a 16×16 array of final out-coupled light beamlets  256 . As can be appreciated, the use of the PPE  192   a  (i.e., the mini-waveguide apparatus  170 ′) increases the saturation of the exit pupil of the display screen  110  from a 4×4 array of final out-coupled light beamlets  256  to a 16×16 array of final out-coupled light beamlets  256 . Of course, the PPE  192   a  can be designed to create smaller or larger arrays of initial out-coupled light beamlets  256 ′, e.g., a 2×2 array, 3×3 array, 5×5 array, etc., and can even be designed to create a non-square matrix of initial out-coupled light beamlets  256 ′, e.g., a 2×3 array, 3×2 array, 3×4 array, 4×3 array, etc. Significantly, the thickness of the waveguide  172  of the primary waveguide apparatus  170  will be greater than the thickness of the waveguide  172 ′ of the mini-waveguide apparatus  170 ′. In this case, for purposes of simplicity in illustration, the thickness of the primary waveguide  172  is four times the thickness of the secondary waveguide  172 ′. However, it should be appreciated that, as discussed above with respect to the embodiments of  FIGS.  44 - 57   , it may be beneficial to maximize the least common multiple of the respective thickness values of the waveguides  172 ,  172 ′, thereby maximizing the quantity of exit pupils yielded for the widest scan angle, and furthermore, yielding an uneven/complex distribution of out-coupled beamlets  256  that may minimize adverse effects created by coherent light interaction between adjacent out-coupled beamlets  256 . 
     Referring now to  FIGS.  64 - 66   , another embodiment of a display subsystem  104 ′ utilizes a conventional PE that comprises the afore-described waveguide apparatus  170  illustrated in  FIGS.  34 - 36    and a PPE  192   b  that, like the PPE  192   a , two-dimensionally pre-expanding the effective entrance pupil of a collimated light beam  250  optically coupled into the PPE  192   b , but unlike the PPE  192   a , is not a waveguide, but rather takes the form of an adapter. 
     In particular, the PPE  192   b  comprises a diffractive beam splitter  194  that utilizes a single DOE that splits the collimated light beam  250  into a set of initial out-coupled light beamlets  256 ′. As best shown in  FIGS.  65  and  66   , the diffractive beam splitter  194  comprises an optical planar substrate  196  having opposing first and second faces  196   a ,  196   b  and a diffraction grating  198  associated with the one of the faces  196   a ,  196   b , and in this case, the face  196   b  of the substrate  196 . The diffraction grating  198  splits the collimated light beam  250  entering the face  196   a  of the substrate  196  into a set of diverging light beamlets  254 ′ that exit the face  196   b  of the substrate  196  at diverging angles. 
     The diffraction grating  198  can be designed to generate an odd number of diverging light beamlets  254 ′ from the single collimated light beam  250  or an even number of diverging light beamlets  254 ′ from the single collimated light beam  250 . Significantly, when the collimated light beam  250  intersects the diffraction grating  198 , beamlets are created at different diffraction orders. For example, as illustrated in FIG.  67 A, one diffraction grating  198 ′ is designed to split the collimated light beam  250  into five diverging light beamlets  254 ′ respectively corresponding to five diffraction orders (−2, −1, 0, +1, +2), each diverging light beamlet  254 ′ being separated from an adjacent diverging light beamlet  254 ′ by a separation angle θ s . As illustrated in  FIG.  67 B , another diffraction grating  198 ″ is designed to split the collimated light beam  250  into four diverging light beamlets  254 ′ respectively corresponding to four diffraction orders (−3, −1, +1, +3), each diverging light beamlet  256 ′ being separated from an adjacent diverging light beamlet  256 ′ by a separation angle 2θ s . 
     The diffraction grating  198  may either split the collimated light beam  250 ′ into a one-dimensional array of diverging light beamlets  254 ′ or a two-dimensional (M×N) array of diverging light beamlets  254 ′. In the embodiment illustrated in  FIGS.  64 - 66   , the diffraction grating splits the collimated light beam  250  into a 4×4 array of diverging light beamlets  254 ′. Of course, the PPE  192   b  can be designed to create smaller or larger arrays of diverging light beamlets  254 ′, e.g., a 1×2 array, 2×1 array, 2×2 array, 3×3 array, 5×5 array, etc., and can even be designed to create non-square two-dimensional arrays of diverging light beamlets  254 ′, e.g., a 2×3 array, 3×2 array, 3×4 array, 4×3 array, etc. 
     Significantly, the PPE  192   b  applies an angle preserving expansion to the collimated light beam  250 . That is, the PPE  192   b  bends the set of diverging light beamlets  254 ′ exiting the face  196   b  of the substrate  196  back to the original angle of the collimated light beam  250 ′. To this end, the PPE  192   b  comprises a lens  200 , and in this embodiment a diffractive lens, that refocuses the diverging light beamlets  254 ′ as the set of initial out-coupled light beamlets  256 ′ back to the original angle of the collimated light beam  250 ′. Although the diffractive lens  200  is illustrated as being separate from the IC element  168 , the function of the diffractive lens  200  can be incorporated into the IC element  168 . 
     It can be appreciated from the foregoing that the PPE  192   b  two-dimensionally pre-expands the effective entrance pupil of the collimated light beam  250 . In the same manner as described above with respect to  FIGS.  34 - 36   , the primary waveguide apparatus  170  further two-dimensionally expands the pupil of the collimated light beam  250 . That is, the 4×4 array of initial out-coupled light beamlets  256 ′ are input into the IC element  168  of the primary waveguide apparatus  170  as a 4×4 array of in-coupled light beamlets  252  (only  252 ( 1 )- 252 ( 4 ) shown), which are in turn, split by the OPE element  186  into a 4×4 array of orthogonal light beamlets  254  (only  254 ( 1 )- 254 ( 4 ) shown), which are further split by the EPE element  188  into final out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172  towards the eye(s)  52  of the end user  50 , as illustrated in  FIGS.  64 - 66   . Notably, the separation angle θ s  in the embodiment of  FIG.  67 A  or the separation angle 2θ s , in  FIG.  67 B  will be selected, such that the separation distance s between adjacent initial out-coupled light beamlets  256 ′ at the intersection with the lens  200  will be equal to the desired spacings of the final out-coupled light beamlets  256  exiting the primary waveguide apparatus  170 . 
     Referring now to  FIGS.  68 - 73   , still another embodiment of a display subsystem  104  utilizes a conventional PE that comprises the afore-described waveguide apparatus  170  illustrated in  FIGS.  34 - 36    and a PPE  192   c  that, like the PPE  192   a , two-dimensionally pre-expands the effective exit pupil of a collimated light beam  250  optically coupled into the PPE  192   c , but unlike the PPE  192   a , is not a waveguide, but rather takes the form of a prism. 
     As best shown in  FIGS.  71 - 73   , the PPE  192   c  comprises an optically transparent prism body  202 , which, in the illustrated embodiment, takes the form of cuboid having a first face  202   a  and a second face  202   b , and a plurality of prism planes  204  disposed in the interior of the prism body  202 . The plurality of prism planes  204  comprises a first set of parallel prism planes  204   a  disposed at an oblique angle to the first face  202   a  (in this case, at a forty-five degree angle) and a second set of parallel prism planes  204   b  at an oblique angle to the second face  202   b  (in this case, at a forty-five degree angle). In the illustrated embodiment, the first set of parallel prism planes  204   a  consists of two prism planes  202   a ( 1 ) and  202   a ( 2 ), and the second set of parallel prism planes  204   b  consists of two prism planes  202   b ( 1 ) and  202   b ( 2 ), although in alternative embodiments, each set of parallel prism planes  204  may consist of more than two prism planes. 
     The prism body  202  comprises prism sections  206   a - 202   f  that are bonded together to create the whole of the prism body  202 . The prism plane  204   a ( 1 ) is formed at the interface between the prism sections  206   a  and  206   b ; the prism plane  204   a ( 2 ) is formed at the interface between the prism sections  206   b  and  206   c ; the prism plane  204   b ( 1 ) is formed at the interface between the prism sections  206   d  and  206   e ; and the prism plane  204   b ( 2 ) is formed at the interface between the prism sections  206   e  and  206   f.    
     The prism planes  204  are configured for splitting a collimated light beam  250  entering the first face  202   a  of the prism body  202  into a set of initial out-coupled light beamlets  256 ′ (and in this case, a 2×2 array of light beamlets  256 ′) that exit the second face  202   b  of the prism body  202 . 
     To this end, each of the prism planes  204   a ( 1 ) and  204   b ( 1 ) is formed of a semi-reflective coating, such as one composed of, e.g., a metal, such as gold, aluminum, silver, nickel-chromium, chromium, etc., a dielectric, such as oxides, fluorides, sulfides, etc., a semiconductor, such as silicon, germanium, etc., and/or a glue or adhesive with reflective properties, which can be disposed between adjacent prism sections  206  via any suitable process, such as physical vapor deposition (PVD), ion-assisted deposition (IAD), ion beam sputtering (IBS), etc. The ratio of reflection to transmission of the semi-reflective coating may be selected or determined based at least in part upon the thickness of the coating, or the semi-reflective coating may have a plurality of small perforations to control the ratio of reflection to transmission. Thus, each of the prism planes  204   a ( 1 ) and  204   b ( 1 ) will split a light beam by reflecting a portion of the light beam and transmitted the remaining portion of the light beam. In contrast, each of the prism planes  204   a ( 2 ) and  204   b ( 2 ) is preferably formed of a completely reflective coating, which may be composed of the same material as the semi-reflective coating. However, the thickness of the coating may be selected, such that the prism planes  204   a ( 2 ) and  204   b ( 2 ) are completely reflective. 
     In an alternative embodiment, adjacent prism sections  206  may be composed of materials having different indices of refraction, such that the prism plane  204  between the respective prism sections  206  is semi-reflective (in the case of prism planes  204   a ( 1 ) or  204   b ( 1 )) or completely reflective (in the case of prism planes  204   a ( 2 ) and  204   b ( 2 )) for light that is incident on the semi-reflective interface at less than a critical angle. In any event, each prism plane  204  is preferably designed, such that the angle of a light beam incident on the prism plane  204  is preserved. 
     As best shown in  FIG.  72   , the first set of prism planes  204   a  relay light along a first axis (horizontal or x-axis), and pre-expands the effective exit pupil of light along a second axis (vertical or y-axis). In particular, the first set of prism planes  204   a  split the collimated light beam  250  entering the first face  202   a  of the prism body  202  into two orthogonal light beamlets  254 ( 1 )′ and  254 ( 2 )′, and reflects these light beamlets  254 ′ toward the second set of prism planes  204   b  in a first direction. That is, a portion of the collimated light beam  250  is reflected by the prism plane  204   a ( 1 ) as the orthogonal light beamlet  254 ( 1 )′, and the remaining portion of the collimated light beam  250  is transmitted by the prism plane  204   a ( 1 ) to the prism plane  204   a ( 2 ) for reflection as the orthogonal light beamlet  254 ( 2 )′. 
     As best shown in  FIG.  73   , the second set of prism planes  204   b , in turn, further pre-expand the light&#39;s effective exit pupil along the second axis (horizontal or x-axis). In particular, the second set of prism planes  204   b  split each of the orthogonal light beamlets  254 ′ into two initial out-coupled light beamlets  256 ′, and reflects these initial out-coupled light beamlets  256 ′ out of the second face  202   b  of the prism body  202  in a second direction orthogonal to the first direction, although the second direction may be non-orthogonal to the first direction. That is, a portion of the orthogonal light beamlet  254 ( 1 )′ is reflected by the prism plane  204   b ( 1 ) as an initial out-coupled light beamlet  256 ( 1 )′, and the remaining portion of the orthogonal light beamlet  254 ( 1 )′ is transmitted by the prism plane  204   b ( 1 ) to the prism plane  204   b ( 2 ) for reflection as an initial out-coupled light beamlet  256 ( 2 )′. Likewise, a portion of the orthogonal light beamlet  254 ( 2 )′ is reflected by the prism plane  204   b ( 1 ) as an initial out-coupled light beamlet  256 ( 3 )′, and the remaining portion of the orthogonal light beamlet  254 ( 2 )′ is transmitted by the prism plane  204   b ( 1 ) to the prism plane  204   b ( 2 ) for reflection as an initial out-coupled light beamlet  256 ( 4 )′. Thus, a 2×2 array of initial out-coupled light beamlets  256 ′ exit the second face  202   b  of the prism body  202 . 
     It can be appreciated from the foregoing that the PPE  192   c  two-dimensionally pre-expands the effective entrance pupil of the collimated light beam  250 . In the same manner as described above with respect to  FIGS.  34 - 36   , the primary waveguide apparatus  170  further two-dimensionally expands the pupil of the collimated light beam  250 . That is, the initial out-coupled light beamlets  256 ′ are input into the IC element  168  of the primary waveguide apparatus  170  as a 2×2 array of in-coupled light beamlets (only  252 ( 1 )- 252 ( 2 ) shown), which are in turn, split by the OPE element  186  into four sets of orthogonal light beamlets (only  254 ( 1 )- 254 ( 2 ) shown), which are further split by the EPE element  188  into final out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172  towards the eye(s)  52  of the end user  50 , as illustrated in  FIGS.  68 - 70   . 
     The distance d between the prism planes  204  are preferably selected, such that the distance s between adjacent initial out-coupled light beamlets  256 ′ will be equal to the desired spacings of the final out-coupled light beamlets  256  exiting the primary waveguide apparatus  170 . In the illustrated embodiment, the prism planes  204  are oriented at forty-five degree angle to the faces  202   a ,  202   b  of the prism body  202 , and thus, the distance d can be expressed as a function of the distance s, as follows: d=s*sin 45°. The thickness of the waveguide  172  in the primary waveguide apparatus  170  can be multiples of the distance d between the prism planes  204  in each set of parallel prism planes  204  of the PPE  192   c  (in this case, two times the distance d between the parallel prism planes  204 ), such that the in-fill of final out-coupled light beamlets  256  is facilitated. 
     It should be appreciated that larger arrays of initial out-coupled light beamlets  256 ′ may be created by decreasing the distance between the prism planes  204  in each set of parallel prism planes  204  of the PPE  192   c  relative to the size of the prism body  202 , as illustrated in  FIGS.  74  and  75   . 
     For example, as illustrated in  FIG.  74   , the first set of prism planes  204   a  may split the collimated light beam  250  entering the first face  202   a  of the prism body  202  into three orthogonal light beamlets  254 ( 1 )′- 254 ( 3 )′, and reflects these light beamlets  254 ′ toward the second set of prism planes  204   b . That is, a portion of the collimated light beam  250  is reflected by the prism plane  204   a ( 1 ) as the orthogonal light beamlet  254 ( 1 )′, and the remaining portion of the collimated light beam  250  is transmitted by the prism plane  204   a ( 1 ) to the prism plane  204   a ( 2 ), where it is repeatedly reflected between the prism plane  204   a ( 1 ) and  204   a ( 2 ), portions of which will be transmitted back through the prism plane  204   a ( 1 ) as the orthogonal light beamlets  254 ( 2 )′ and  254 ( 3 )′. 
     As illustrated in  FIG.  75   , the second set of prism planes  204   b  split each of the orthogonal light beamlets  254 ′ into three initial out-coupled light beamlets  256 ′, and reflects these initial out-coupled light beamlets  256 ′ out of the second face  202   b  of the prism body  202 . Thus, a 3×3 array of initial out-coupled light beamlets  256 ′ exit the second face  202   b  of the prism body  202 . That is, a portion of each orthogonal light beamlet  254  is reflected by the prism plane  204   b ( 1 ) as an initial out-coupled light beamlet  256 ( 1 )′, and the remaining portion of this orthogonal light beamlet  254 ′ is transmitted by the prism plane  204   b ( 1 ) to the prism plane  204   b ( 2 ), where it is repeatedly reflected between the prism plane  204   b ( 1 ) and  204   b ( 2 ), portions of which will be transmitted back through the prism plane  204   b ( 1 ) as the initial out-coupled light beamlets  256 ( 2 )′ and  256 ( 3 )′. 
     Again, the distance d between the prism planes  204  are preferably selected, such that the distance s between adjacent initial out-coupled light beamlets  256 ′ will be equal to the desired spacings of the final out-coupled light beamlets  256  exiting the primary waveguide apparatus  170 . In the illustrated embodiment, the prism planes  204  are oriented at forty-five degree angle to the faces  202   a ,  202   b  of the prism body  202 , and thus, the distance d can be expressed as a function of the distance s, as follows: d=s*sin 45°. 
     Thus, for each orthogonal light beamlet  254 , three initial out-coupled light beamlets  256 ′ will be generating, thereby creating a 3×3 array of initial out-coupled light beamlets  256 ′ exit the second face  202   b  of the prism body  202 . Of course, the PPE  192   c  can be designed to create even larger arrays of initial out-coupled light beamlets  256 ′, e.g., a 4×4 array, a 5×5 array, etc., by further decreasing the distance between the prism planes  204  in each set of parallel prism planes  204  of the PPE  192   c  relative to the size of the prism body  202 . 
     Although the PPE  192   c  has been described as generated square arrays of initial out-coupled light beamlets  256 ′, the PPE  192   c  can alternatively be designed to generate non-square arrays of initial out-coupled light beamlets  256 ′, e.g., a 2×3 array, 3×2 array, 2×3 array, 3×2 array, etc., by making the distance between the prism planes  204   a ( 1 ) and  204   a ( 2 ) different from the distance between the prism planes  204   b ( 1 ) and  204   b ( 2 ). Furthermore, although the PPE  192   c  has been described as creating two-dimensional arrays of initial out-coupled light beamlets  256 ′, the PPE  192   c  can be designed to create one-dimensional arrays of initial out-coupled light beamlets  256 ′, e.g., 1×2 array, 1×3 array, etc., by designing the PPE  192   c  with only one set of parallel prism planes  204 . 
     Furthermore, although the PPE  192   c  has been described as generating initial out-coupled light beamlets  256 ′ that exit the prism body  202  at an orthogonal angle to the face  202   b  of the prism body  202 , the PPE  192   c  can be designed, such that the initial out-coupled light beamlets  256 ′ exit the prism body  202  at an oblique angle to the face  202   b  of the prism body  202  by changing the orientations of one or both of the sets of prism planes  204  relative to the face  202   b  of the prism body  202 . 
     Referring now to  FIGS.  76 - 79   , yet another embodiment of a display subsystem  104 ′ utilizes a conventional PE that comprises the afore-described waveguide apparatus  170  illustrated in  FIGS.  34 - 36    and a PPE  192   e  that, like the PPE  192   c , takes the form of a prism, but unlike the PPE  192   c , utilizes a cavity prism, as opposed to a solid prism, that one-dimensionally pre-expands the effective entrance pupil of a collimated light beam  250  optically coupled into the PPE  192   e.    
     As best shown in  FIG.  79   , the PPE  192   e  comprises an optically transparent cavity prism  208 , which includes a first triangular prism section  210   a  and a second triangular prism section  210   b . The prism sections  210   a ,  210   b  are spaced from each other to create an open space  212  therebetween that is bound on one side by a prism plane  212   a  of the prism section  210   a  and on the other side by a prism plane  212   b  of the prism section  210   b , with the prism planes  212   a ,  212   b  being parallel to each other. The first prism section  210   a  has a first face  214   a  and a second face  214   b  opposite the prism plane  212   a . The prism plane  212   a  is disposed at an oblique angle to the first and second faces  214   a ,  214   b  (in this case, at a forty-five degree angle). 
     The prism planes  212  are configured for splitting a collimated light beam  250  entering the first face  202   a  of the prism section  210  into a set of initial light beamlets  256 ′ (in this case, a 1×4 array of initial out-coupled light beamlets  256 ′) that exit the second face  214   b  of the first prism section  210   a . To this end, the first prism plane  212   a  is designed to be partially reflective, whereas the second prism plane  212   b  is designed to be completely reflective in the same manner that the prism planes  204  of the PPE  192   c  described above are designed to be partially reflective or completely reflective. Each prism plane  212  is preferably designed, such that the angle of a light beam incident on the prism plane  212  is preserved. 
     As best shown in  FIG.  79   , the PPE  192   c  one-dimensionally pre-expands the effective exit pupil of light along a first axis (horizontal or x-axis). In particular, the set of prism planes  212  splits the collimated light beam  250  into four initial out-coupled light beamlets  256 ′, and reflects these initial out-coupled light beamlets  256 ′ out of the second face  214   b  of the prism section  210   b . Thus, a 1×4 array of initial out-coupled light beamlets  256 ′ exit the second face  214   b  of the prism body  210 . That is, a portion of the collimated light beam  250  is reflected by the prism plane  212   a  as an initial out-coupled light beamlet  256 ( 1 )′, and the remaining portion of the collimated light beam  250  is transmitted by the prism plane  212   b  to the prism plane  212   a , where it is repeatedly reflected between the prism plane  212   a  and prism plane  212   b , portions of which will be transmitted back through prism plane  212   a  as initial out-coupled light beamlets  256 ( 2 )′- 256 ( 4 )′. Of course, the PPE  192   e  can be designed to create smaller or larger one-dimensional arrays of initial out-coupled light beamlets  256 ′, e.g., a 1×2 array, a 1×3 array, 1×5 array, etc., by decreasing or increasing the distance between the prism planes  212  relative to the size of the prism  208 . 
     It can be appreciated from the foregoing that the PPE  192   e  one-dimensionally pre-expands the effective entrance pupil of the collimated light beam  250 . In the same manner as described above with respect to  FIGS.  34 - 36   , the primary waveguide apparatus  170  further two-dimensionally expands the pupil of the collimated light beam  250 . That is, the initial out-coupled light beamlets  256 ′ are input into the IC element  168  of the primary waveguide apparatus  170  as a 1×4 array of in-coupled light beamlets  252 ( 1 )- 252 ( 4 ), which are in turn, split by the OPE element  186  into a 1×4 array of orthogonal light beamlets  254 ( 1 )- 254 ( 4 ), which are further split by the EPE element  188  into final out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172  towards the eye(s)  52  of the end user  50 , as illustrated in  FIGS.  76 - 78   . 
     The distance d between the prism planes  212  are preferably selected, such that the distance s between adjacent initial out-coupled light beamlets  256 ′ will be equal to the desired spacings of the final out-coupled light beamlets  256  exiting the primary waveguide apparatus  170 . In the illustrated embodiment, the prism planes  212  are oriented at forty-five degree angle to the faces  214   a ,  214   b  of the prism body  202 , and thus, the distance d can be expressed as a function of the distance s, as follows: d=s*sin 45°. Significantly, the thickness of the waveguide  172  in the primary waveguide apparatus  170  will be multiples of the distance d between the prism planes  212  of the PPE  192   e  (in this case, two times the distance d between the prism planes  212 ), such that the in-fill of the final out-coupled light beamlets  256  is facilitated. 
     It should be appreciated that the because the distance d between the prism planes  212  is set merely by locating the prism planes  212  relative to each other, the spacings between the final out-coupled light beamlets  256  may be arbitrarily set without concern for manufacturing limitations. That is, since the PPE  192   e  does not utilize an optical substrate between the prism planes  212 , but rather utilizes a cavity between the prism planes  212 , one need not be concerned with the limitations related to the minimum thickness of such optical substrate. 
     Referring now to  FIGS.  80 - 89   , some embodiments of a display subsystem  104  utilize a conventional PE that comprises the afore-described waveguide apparatus  170  illustrated in  FIGS.  34 - 36    and a PPE  192   f  that, in the illustrated embodiment, takes the form of a multi-layered mini-waveguide apparatus  220  mounted to the IC element  168 . 
     The mini-waveguide apparatus  220  has a size commensurate with the size of the IC element  168  of the primary waveguide apparatus  170 . The mini-waveguide apparatus  220  comprises a plurality of waveguide assemblies  222 , and in this case, a top waveguide assembly  222   a  and a bottom waveguide assembly  222   b . Each waveguide assembly  222  is configured for splitting each of one or more collimated beams or beamlets (collimated light beam  250  in the bottom waveguide assembly  222   b  and out-coupled light beamlets  256 ′ in the top waveguide assembly  222   b ) a two-dimensional array (in this case, a 4×4 array) of out-coupled light beamlets  256 ′, as will be described in further detail below. 
     In the particular mini-waveguide apparatus  220  described herein, the bottom waveguide assembly  222   b  functions to split a single collimated light beam  250  into a two-dimensional array of out-coupled light beamlets  256 ′, whereas the top waveguide assembly  222   a  functions to split the two-dimensional array of out-coupled light beamlets  256 ′ from the bottom waveguide assembly  222   b  into multiple two-dimensional arrays of out-coupled light beamlets  256 ″, as illustrated in  FIG.  83   . To this end, the top waveguide assembly  222   a  and bottom waveguide assembly  222   b  are disposed relative to each other, such that the top waveguide assembly  222   a  receives the out-coupled light beamlets  256 ′ from the bottom waveguide assembly  222   b . For example, as will be illustrated below, the top surface  224   a  of the bottom waveguide assembly  222   b  is affixed to the bottom surface  224   b  of the top waveguide assembly  222   a.    
     Referring further to  FIGS.  84  and  85 A- 85 B , each waveguide assembly  222  comprises a pair of orthogonal waveguide units configured as a top orthogonal waveguide unit  226   a  and a bottom orthogonal waveguide unit  226   b , with the bottom surface  228   b  of the top orthogonal waveguide unit  226   a  being affixed to the top surface  228   a  of the bottom orthogonal waveguide unit  226   b . The orthogonal waveguide units  226  are identical to each other, the only difference being that they are orthogonally oriented relative to each other. Each orthogonal waveguide unit  226  comprises a planar optical waveguide  230  taking the form of a single unitary substrate or plane of optically transparent material (as described above with respect to the waveguide  172 ). The planar optical waveguides  230  of the respective orthogonal waveguide units  226  are identically dimensioned, each having top and bottom faces  230   a ,  230   b . Each orthogonal waveguide unit  226  further comprises an IC element  232  associated with (e.g., disposed on) the bottom face  230   b  of the respective planar optical waveguide  230 , and an EPE  234  respectively associated with (e.g., disposed on) the top face  230   a  of the planar optical waveguide  230 . 
     Each IC element  232  is configured for in-coupling one or more light beams or beamlets into the respective planar optical waveguide  230  for propagation via TIR along an internally reflective optical path ( 236   a  in the case of the top orthogonal waveguide unit  226   a , and  236   b  in the case of the bottom orthogonal waveguide unit  226   b ), and in doing so, repeatedly intersects the EPE element  234 . In the same manner as described above with respect to the EPE element  188  of the primary waveguide apparatus  170 , the EPE element  234  has a relatively low diffraction efficiency (e.g., less than 50%), such that, at each point of intersection with the EPE element  234 , a portion (e.g., greater than 90%) of each light beam or beamlet continues to propagate along the respective internally reflective optical path  236 , and the remaining portion of each light beam or beamlet is diffracted as an initial out-coupled light beamlet  256 ′ that exits the top face  230   a  of the respective planar optical waveguide  230 . In the illustrated embodiment, the sizes of the IC element  232  and EPE element  234  are equal to each other and are commensurate to the size of the respective planar optical waveguide  230  with which the IC element  232  and EPE element  234  are associated, such that pupil expansion of the collimated light beam  250  is maximized, while also facilitating in-coupling of two-dimensional arrays of out-coupled light beamlets  256 ′ from the bottom orthogonal waveguide unit  226   b  to the top orthogonal waveguide unit  226   a , as will be described in further detail below. 
     The IC elements  232  of the orthogonal waveguide units  226  are oriented orthogonally to each other, such that each light beam or beamlet ( 250  or  256 ′) that is in-coupled into the bottom face  224   b  of a respective waveguide assembly  222  is split into a two-dimensional array of initial out-coupled light beamlets  256 ′ (or  256 ″) that exit the top face  224   a  of the waveguide assembly  222 , as illustrated in  FIG.  84   . 
     In particular, the IC elements  232  of each waveguide assembly  222  are oriented orthogonally relative to each other, such that the IC element  232  associated with the bottom orthogonal waveguide unit  226   b  in-couples light for propagation via TIR along an internally reflective optical path parallel to a first axis  262  (in this case, along the y-axis), such that the light is expanded by the corresponding EPE element  234  along the first axis  262  (see  FIG.  85 B ), while the IC element  232  associated with the top orthogonal waveguide unit  226   a  in-couples each light beam or beamlet for propagation via TIR along internally reflective optical path parallel to a second axis  264  (in this case, along the x-axis) orthogonal to the first axis  264 , such that the light is expanded by the corresponding EPE element  234  along that second axis  264  (see  FIG.  85 A ). 
     As briefly discussed above with respect to  FIG.  83   , the bottom face  224   b  of the top waveguide assembly  222   a  is affixed to the top surface  224   a  of the bottom waveguide assembly  222   b , such that the output of the bottom waveguide assembly  222   a  is provided as an input to the top waveguide assembly  222   a , thereby generating multiple arrays of out-coupled light beamlets  256 ″ from a single collimated light beam  250 . 
     In particular, with further reference to  FIGS.  86 A and  86 B , the bottom waveguide assembly  222   b  receives the collimated light beam  250  from the collimation element  166  and splits the collimated light beam  250  into a two-dimensional array of initial out-coupled light beamlets  256 ′ that exit the top face  224   a  of the bottom waveguide assembly  222   b.    
     That is, the IC element  224  associated with the bottom orthogonal waveguide unit  226   b  of the bottom waveguide assembly  222   b  optically couples the collimated light beam  250  as an initial in-coupled light beam  252 ′ for propagation within the respective planar optical waveguide  230  via TIR along the first internally reflective optical path parallel to the axis  262  (y-axis), and the EPE element  226  associated with the bottom orthogonal waveguide unit  226   b  of the bottom waveguide assembly  222   b  splits the collimated light beam  250  into a one-dimensional array of initial out-coupled light beamlets  256 ′ that exit the top face  228   a  of the respective bottom orthogonal waveguide unit  226   b.    
     In turn, the IC element  224  associated with the top orthogonal waveguide unit  226   a  of the bottom waveguide assembly  222   b  optically couples the one-dimensional array of initial out-coupled light beamlets  256 ′ as initial orthogonal light beamlets  254 ′ for propagation within the respective planar optical waveguide  230  via TIR along respective second internally reflective optical paths parallel to the axis  264  (x-axis) that are orthogonal to first internally reflective optical path parallel to the axis  262  (y-axis), and the EPE element  226  associated with the top orthogonal waveguide unit  226   a  of the bottom waveguide assembly  222   b  splits the initial orthogonal light beamlets  254 ′ into a two-dimensional array of initial out-coupled light beamlets  256 ′ that exit the top face  228   a  of the respective top orthogonal waveguide unit  226   a.    
     The top waveguide assembly  222   a  receives the two-dimensional array of initial out-coupled light beamlets  256 ′ from the bottom waveguide assembly  222   b  and splits this two-dimensional array of initial out-coupled light beamlets  256 ′ into a plurality of two-dimensional arrays of intermediate out-coupled light beamlets  256 ″ that exit the top face  224   a  of the top waveguide assembly  222   a.    
     That is, the IC element  224  associated with the bottom orthogonal waveguide unit  226   b  of the top waveguide assembly  222   a  optically couples the two-dimensional array of initial out-coupled light beamlets  256 ′ as intermediate sets of in-coupled light beams  252 ″ for propagation within the respective planar optical waveguide  230  via TIR along the first internally reflective optical path parallel to the axis  262  (y-axis), and the EPE element  226  associated with the bottom orthogonal waveguide unit  226   b  of the top waveguide assembly  222   a  splits the intermediate sets of in-coupled light beamlets  252 ″ into two-dimensional arrays of intermediate out-coupled light beamlets  256 ″ of initial out-coupled light beamlets  256 ′ that exit the top face  228   a  of the respective bottom orthogonal waveguide unit  226   b.    
     In turn, the IC element  224  associated with the top orthogonal waveguide unit  226   a  of the top waveguide assembly  222   a  optically couples the two-dimensional arrays of intermediate out-coupled light beamlets  256 ″ as intermediate orthogonal light beamlets  254 ″ for propagation within the respective planar optical waveguide  230  via TIR along respective second internally reflective optical paths  264  (x-axis) that are orthogonal to first internally reflective optical path parallel to the axis  262  (y-axis), and the EPE element  226  associated with the top orthogonal waveguide unit  226   a  of the top waveguide assembly  222   a  splits the intermediate orthogonal light beamlets  254 ″ into two-dimensional arrays of intermediate out-coupled light beamlets  256 ″ that exit the top face  228   a  of the respective top orthogonal waveguide unit  226   a.    
     Thus, the bottom waveguide assembly  222   b  splits the collimated light beam  250  into a two-dimensional array of initial out-coupled light beamlets  256 ′, and the top waveguide assembly  222   a  splits the two-dimensional array of out-coupled light beamlets  256 ′ into several two-dimensional arrays of intermediate out-coupled light beamlets  256 ″. The two-dimensional array of initial out-coupled light beamlets  256 ′, as well as each of the two-dimensional arrays of intermediate out-coupled light beamlets  256 ″, have an inter-beamlet spacing s 1 , and the two-dimensional array of intermediate out-coupled light beamlets  256 ″ have an inter-array spacing s 2  different from the inter-beamlet spacing s 1  of the two-dimensional arrays of initial out-coupled light beamlets  256 ′ and intermediate out-coupled light beamlets  256 ″ (see, e.g.,  FIGS.  89 A and  89 B ). The inter-array spacing s 2  and the inter-beamlet spacing s 1  are non-multiples of each other, so that the light beamlets  256 ″ are distributed in a manner that maximizes the density of the in-fill of the exit pupil of the PPE  192   f , and thus, the exit pupil of the display screen  110 , as will be described in further detail below. 
     Notably, the inter-beamlet spacing s 1  is dictated by the respective thicknesses of the waveguides  230  of the bottom waveguide assembly  222   b . Similarly, the inter-array spacing s 2  is dictated by the respective thicknesses of the waveguides  240  of the top waveguide assembly  222   a . The thicknesses of the waveguides  230  of the top and bottom waveguide assemblies  222  may be strategically selected based on the diameter of the collimated light beam  250 . In some examples, the inter-beamlet spacing s 1  and inter-array spacing s 2 , although different from each other, may each be a multiple of the diameter of the collimated light beam  250  to maximize the in-fill of the exit pupil of the PPE  192   f.    
     Thus, the inter-beamlet spacing s 1  may be a multiple (“m”) of the diameter of the collimated light beam  250  (“d”), such that s 1 =m×d. Using this value of s 1 , the inter-array spacing s 2  may be described by: s 2 =s 1 +d. That is, s 1  and s 2  may be consecutive multiples of the diameter of the collimated light beam  250 , such that s 2 =(m+1)×d. For example, the inter-beamlet spacing s 1  may be three times the diameter of the diameter of the collimated light beam  250 . Using this value of s 1 , the inter-array spacing s 2  may be four times the diameter of the collimated light beam  250 . As exemplified in the illustrated embodiment below, this results in the inter-array spacing s 2  being 1.33 times the inter-beamlet spacing s 1 . 
     The first and second planar optical waveguide assemblies  222   a ,  222   b  respectively have unequal thicknesses t 1 , t 2 , as illustrated in  FIG.  83   , with such thicknesses being set by the thicknesses of the respective planar optical waveguides  230  incorporated into the respective orthogonal waveguide units  226   a ,  226   b  of the optical waveguide assemblies  222   a ,  222   b . For example, as illustrated in  FIGS.  86 A and  86 B , the thicknesses of the planar optical waveguides  230  incorporated into the top planar optical waveguide assembly  222   a  are greater than the thicknesses of the planar optical waveguides  230  incorporated into the bottom planar optical waveguide assembly  222   b . Preferably, the first and second inter-beamlet spacing s 1 , s 2 , and thus, the thicknesses t 1 , t 2  of the first and second planar optical waveguide assemblies  222   a ,  222   b , are non-multiples of each other to ensure that the multiple arrays of the intermediate out-coupled light beamlets  252 ″ are generated from the single array of initial out-coupled light beamlets  252 ′. 
     As briefly discussed above, the bottom waveguide assembly  222   b  splits the collimated light beam  250  into a two-dimensional array of initial out-coupled light beamlets  256 ′, and the top waveguide assembly  222   a  splits the two-dimensional array of out-coupled light beamlets  256 ′ into several two-dimensional arrays of intermediate out-coupled light beamlets  256 ″. In other words, the bottom waveguide assembly  222   b  and top waveguide assembly  222   a  respectively generate two transfer functions that are convolved to produce the desired pattern of intermediate out-coupled light beamlets  252 ″. 
     For example, as illustrated in  FIG.  87 A , the bottom waveguide assembly  222   b  (as the first expander) has a first transfer function h 1 , such that y=x*h 1 , where x is the optical input (a light beam of diameter a) into the bottom waveguide assembly  222   b , and y is the optical output from the bottom waveguide assembly  222   b . In this example, the transfer function h 1  results in a 4×4 array of light beamlets of a diameter a, spaced apart from each other by a distance of 3a. Similarly, as illustrated in  FIG.  87 B , the top waveguide assembly  222   a  (as the second expander) has a second transfer function h 2 , such that y=x*h 2 , where x is the optical input (a light beam of diameter a) into the top waveguide assembly  222   a , and y is the optical output from the bottom waveguide assembly  222   a . In this example, the transfer function h 2  results in a 4×4 array of light beamlets of a diameter a, spaced apart from each other by a distance of 4a. As illustrated in  FIG.  87 C , the transfer functions h 1  and h 2  can be convolved, such that y=h 1 *h 2 . Thus, the collimated light beam  250  (as the optical input x) may be input into the bottom waveguide assembly  222   b , which applies the transfer function h 1  to the collimated light beam  250 , thereby generating a two-dimensional array of intermediate out-coupled light beamlets  256 ′ that have the beam pattern illustrated in  FIG.  87 A . The two-dimensional array of intermediate out-coupled light beamlets  256 ′ output by the bottom waveguide assembly  222   b  may be input into the top waveguide assembly  222   a , which applies the transfer function h 2  to the two-dimensional array of intermediate out-coupled light beamlets  256 ′, thereby generating multiple two-dimensional arrays of intermediate out-coupled light beamlets  256 ″, the composite of which creates the light beamlet pattern illustrated in  FIG.  87 C . 
     Referring now to  FIGS.  88  and  89 A- 89 H , multiple generations of intermediate out-coupled light beamlets  256 ″ proliferate as the two-dimensional array of initial out-coupled light beamlets  256 ′ propagates through the top optical waveguide assembly  222   a . As a result, the density of intermediate out-coupled light beamlets  256 ″ progressively increase from left to right and from up to down across the top face  224   a  of the top planar optical waveguide assembly  222   a  through several generations of beam splitting until an N×N array of completely filled in out-coupled light beamlets  258 ′ is generated, which in this case, is a 10×10 array of out-coupled light beamlets  258 ′ (shown in  FIG.  89 H ). In the illustrated embodiment, seven generations of beam splitting that generate sixteen two-dimensional arrays (in this case, 4×4 arrays) of intermediate out-coupled light beamlets  256 ( 1 )″- 256 ( 16 )″ results in the densely saturated 10×10 array of out-coupled light beamlets  258 ′. As there shown, the beamlets designated with “0” are those of the two-dimensional array of initial out-coupled light beamlets  256 ′, whereas the beamlets designated with “ 1 ”-“ 16 ” are respectively those of the sixteen two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 1 )″- 256 ( 16 )″. Notably, a lettering scheme is used in  FIGS.  89 A- 89 H  to make it easier to understand the initial out-coupled light beamlets  256 ′ to which the intermediate out-coupled light beamlets  256 ″ correspond. Under this lettering scheme, each beamlet in the 4×4 array of beamlets  256 ′ that is output by the bottom waveguide assembly  222   b  (the first expander) illustrated in  FIG.  87 A , and is input into the top waveguide assembly  222   a  (the second expander) illustrated in  FIG.  87 B  corresponds to a different alphabetical letter (“A” through “P”). In this manner, each beamlet  256 ″ that is output by top waveguide assembly  222   a  (the second expander) can be seen as corresponding to both a specific two-dimensional array of intermediate out-coupled light beamlets  256 ( 1 )″- 256 ( 16 )″ and a family of related beamlets (“A” through “P”). 
     In particular, the two-dimensional array of intermediate out-coupled light beamlets  256 ( 1 )″ is generated directly from the two-dimensional array of initial out-coupled light beamlets  256 ′ (see  FIG.  89 A ). At the first generation, the two-dimensional array of intermediate out-coupled light beamlets  256 ( 1 )″ spawns a two-dimensional array of intermediate out-coupled light beamlets  256 ( 2 )″ and a two-dimensional array of intermediate out-coupled light beamlets  256 ( 3 )″ respectively along the x-axis and the y-axis (see  FIG.  89 B ). 
     At the second generation, the two-dimensional array of intermediate out-coupled light beamlets  256 ( 2 )″ spawns a two-dimensional array of intermediate out-coupled light beamlets  256 ( 4 )″ along the x-axis; both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 2 )″ and  256 ( 3 )″ combine to spawn the two-dimensional array of intermediate out-coupled light beamlets  256 ( 5 )″ respectively along the x-axis and the y-axis; and the two-dimensional array of intermediate out-coupled light beamlets  256 ( 3 )″ spawns a two-dimensional array of intermediate out-coupled light beamlets  256 ( 6 )″ along the y-axis (see  FIG.  89 C ). 
     At the third generation, the two-dimensional array of intermediate out-coupled light beamlets  256 ( 4 )″ spawns a two-dimensional array of intermediate out-coupled light beamlets  256 ( 7 )″ along the x-axis; both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 4 )″ and  256 ( 5 )″ combine to spawn the two-dimensional array of intermediate out-coupled light beamlets  256 ( 8 )″ respectively along the x-axis and the y-axis; both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 5 )″ and  256 ( 6 )″ combine to spawn the two-dimensional array of intermediate out-coupled light beamlets  256 ( 9 )″ respectively along the x-axis and the y-axis; and the two-dimensional array of intermediate out-coupled light beamlets  256 ( 6 )″ spawns a two-dimensional array of intermediate out-coupled light beamlets  256 ( 10 )″ along the y-axis (see  FIG.  89 D ). 
     At the fourth generation, both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 7 )″ and  256 ( 8 )″ combine to spawn a two-dimensional array of intermediate out-coupled light beamlets  256 ( 11 )″ respectively along the x-axis and the y-axis; both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 8 )″ and  256 ( 8 )″ combine to spawn a two-dimensional array of intermediate out-coupled light beamlets  256 ( 12 )″ respectively along the x-axis and the y-axis; and both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 9 )″ and  256 ( 10 )″ combine to spawn a two-dimensional array of intermediate out-coupled light beamlets  256 ( 13 )″ respectively along the x-axis and the y-axis (see  FIG.  89 E ). 
     At the fifth generation, both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 11 )″ and  256 ( 12 )″ combine to spawn a two-dimensional array of intermediate out-coupled light beamlets  256 ( 14 )″ respectively along the x-axis and the y-axis; and both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 12 )″ and  256 ( 13 )″ combine to spawn a two-dimensional array of intermediate out-coupled light beamlets  256 ( 15 )″ respectively along the x-axis and the y-axis (see  FIG.  89 F ). 
     At the sixth generation, the both the two-dimensional arrays of intermediate out-coupled light beamlets  256 ( 14 )″ and  256 ( 15 )″ combine to spawn a two-dimensional array of intermediate out-coupled light beamlets  256 ( 16 )″ respectively along the x-axis and the y-axis (see  FIG.  89 G ). 
     It can be appreciated that all of the intermediate out-coupled light beamlets  256 ″ designated with a specific letter in the light beamlet pattern illustrated in  FIG.  89 H  can be traced back to the corresponding initial out-coupled light beamlet with the same specific letter in the two-dimensional array of initial out-coupled light beamlets  256 ′ illustrated in  FIG.  89 A . For example, it can be seen in  FIG.  90 A  that a 4×4 array of intermediate out-coupled light beamlets  256 ″ designated with the letter “A” can be derived from the single initial out-coupled light beamlet  256   a  designed with the letter “A.” As another example, it can be seen from  FIG.  90 B  that a 4×4 array of intermediate out-coupled light beamlets  256 ″ designated with the letter “D” can be derived from the single initial out-coupled light beamlet  256   a  designed with the letter “D.” As still another example, it can be seen from  FIG.  90 C  that a 4×4 array of intermediate out-coupled light beamlets  256 ″ designated with the letter “M” can be derived from the single initial out-coupled light beamlet  256   a  designed with the letter “M.” As yet another example, it can be seen from  FIG.  90 D  that a 4×4 array of intermediate out-coupled light beamlets  256 ″ designated with the letter “P” can be derived from the single initial out-coupled light beamlet  256   a  designed with the letter “P”. 
     It can be appreciated from the foregoing that the PPE  192   f  two-dimensionally pre-expands the effective entrance pupil of the collimated light beam  250 . In the same manner as described above with respect to  FIGS.  34 - 36   , the primary waveguide apparatus  170  further two-dimensionally expands the pupil of the collimated light beam  250 . That is, the intermediate out-coupled light beamlets  256 ″ are input into the IC element  168  of the primary waveguide apparatus  170  as in-coupled light beamlets  252 , which are in turn, split by the OPE element  186  into orthogonal light beamlets  254 , which are further split by the EPE element  188  into final out-coupled light beamlets  256  that exit the face  180   b  of the waveguide  172  towards the eye(s)  52  of the end user  50 , as illustrated in  FIGS.  80 - 82   . Notably, although the PPE  192   f  generates many two-dimensional arrays of out-coupled beamlets  256 ″ that conceivably provides an exit pupil greater than the saturated 10×10 two-dimensional array of out-coupled beamlets  258 ′, the primary waveguide apparatus  170  may be designed to assume that the PPE  192   f  has an exit pupil consisting of only the 10×10 two-dimensional array of out-coupled beamlets  258 ′. 
     It should be noted that, although the multi-layered mini-waveguide apparatus  220  lends itself for use as a PPE  192   f , a larger version of the multi-layered waveguide apparatus  220  can be used as the primary waveguide apparatus  170  in order to expand the entrance pupil of a collimated light beam  250  (unexpanded or pre-expanded) in-coupled into the primary waveguide apparatus  170 . 
     While beam multipliers have been described above as OPEs and EPEs, beam multipliers according to the embodiments described herein can be disposed anywhere in an LOE. For instance, beam multipliers described herein can be disposed as a separate multiplication stage/region between various parts of an LOE (e.g., between ICG and OPE). Further, beam multipliers described herein can function as ICGs. 
     While certain numbers of beams and beamlets are depicted in some of the figures, it should be appreciated that this is for clarity. Each single beam or beamlet depicted in the figures may represent a plurality of beams or beamlets carrying related information and having similar trajectories. 
     While certain numbers of LOSs and reflective surfaces are depicted in some of the figures, other embodiments may include other combinations of LOSs and reflective surfaces. 
     The above-described MR systems are provided as examples of various optical systems that can benefit from more selectively reflective optical elements. Accordingly, use of the optical systems described herein is not limited to the disclosed MR systems, but rather applicable to any optical system. 
     Various exemplary embodiments of the disclosure are described herein. Reference is made to these examples in a non-limiting sense. They are provided to illustrate more broadly applicable aspects of the disclosure. Various changes may be made to the disclosure described and equivalents may be substituted without departing from the true spirit and scope of the disclosure. In addition, many modifications may be made to adapt a particular situation, material, composition of matter, process, process act(s) or step(s) to the objective(s), spirit or scope of the present disclosure. Further, as will be appreciated by those with skill in the art that each of the individual variations described and illustrated herein has discrete components and features which may be readily separated from or combined with the features of any of the other several embodiments without departing from the scope or spirit of the present disclosure. All such modifications are intended to be within the scope of claims associated with this disclosure. 
     The disclosure includes methods that may be performed using the subject devices. The methods may comprise the act of providing such a suitable device. Such provision may be performed by the end user. In other words, the “providing” act merely requires the end user obtain, access, approach, position, set-up, activate, power-up or otherwise act to provide the requisite device in the subject method. Methods recited herein may be carried out in any order of the recited events which is logically possible, as well as in the recited order of events. 
     Exemplary aspects of the disclosure, together with details regarding material selection and manufacture have been set forth above. As for other details of the present disclosure, these may be appreciated in connection with the above-referenced patents and publications as well as generally known or appreciated by those with skill in the art. The same may hold true with respect to method-based aspects of the disclosure in terms of additional acts as commonly or logically employed. 
     In addition, though the disclosure has been described in reference to several examples optionally incorporating various features, the disclosure is not to be limited to that which is described or indicated as contemplated with respect to each variation of the disclosure. Various changes may be made to the disclosure described and equivalents (whether recited herein or not included for the sake of some brevity) may be substituted without departing from the true spirit and scope of the disclosure. In addition, where a range of values is provided, it is understood that every intervening value, between the upper and lower limit of that range and any other stated or intervening value in that stated range, is encompassed within the disclosure. 
     Also, it is contemplated that any optional feature of the inventive variations described may be set forth and claimed independently, or in combination with any one or more of the features described herein. Reference to a singular item, includes the possibility that there are plural of the same items present. More specifically, as used herein and in claims associated hereto, the singular forms “a,” “an,” “said,” and “the” include plural referents unless the specifically stated otherwise. In other words, use of the articles allow for “at least one” of the subject item in the description above as well as claims associated with this disclosure. It is further noted that such claims may be drafted to exclude any optional element. As such, this statement is intended to serve as antecedent basis for use of such exclusive terminology as “solely,” “only” and the like in connection with the recitation of claim elements, or use of a “negative” limitation. 
     Without the use of such exclusive terminology, the term “comprising” in claims associated with this disclosure shall allow for the inclusion of any additional element—irrespective of whether a given number of elements are enumerated in such claims, or the addition of a feature could be regarded as transforming the nature of an element set forth in such claims. Except as specifically defined herein, all technical and scientific terms used herein are to be given as broad a commonly understood meaning as possible while maintaining claim validity. 
     The breadth of the present disclosure is not to be limited to the examples provided and/or the subject specification, but rather only by the scope of claim language associated with this disclosure. 
     In the foregoing specification, the disclosure has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the disclosure. For example, the above-described process flows are described with reference to a particular ordering of process actions. However, the ordering of many of the described process actions may be changed without affecting the scope or operation of the disclosure. The specification and drawings are, accordingly, to be regarded in an illustrative rather than restrictive sense. 
     In the foregoing specification, the disclosure has been described with reference to specific embodiments thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the disclosure. For example, the above-described process flows are described with reference to a particular ordering of process actions. However, the ordering of many of the described process actions may be changed without affecting the scope or operation of the disclosure. The specification and drawings are, accordingly, to be regarded in an illustrative rather than restrictive sense.