Patent Publication Number: US-10330937-B2

Title: Near-eye display apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part of, and claims priority to, U.S. patent application Ser. No. 15/170,581 filed on Jun. 1, 2016, which is a continuation of, and claims priority to, U.S. patent application Ser. No. 14/729,899 (now U.S. Pat. No. 9,366,870) filed on Jun. 3, 2015, which in turn is a continuation of, and claims priority to, U.S. patent application Ser. No. 14/294,394 (now U.S. Pat. No. 9,052,505) filed on Jun. 3, 2014, which in turn is a continuation of, and claims priority to, PCT/CN2012/085987 filed on Dec. 6, 2012, which claims priority in part to CN 201110404197.1 filed on Dec. 6, 2011. The present application also claims priority to CN 201720172343.5 and CN 201710104603.X, both filed on Feb. 24, 2017. The disclosures of these applications are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     Display apparatuses are important parts of human-machine interfaces. Near-eye display apparatuses such as helmet-mounted displays are popular products in the display field. Helmet-mounted image display apparatuses used for virtual reality and display enhancement have gained rapid development. A helmet-mounted display apparatus can comprise three portions: a display image source, an optical system, and a support structure. Because users might wear the helmet-mounted display apparatus for a long time, the weight and compactness are important to the users&#39; comfort. 
     SUMMARY 
     In one aspect, the instant disclosure provides a display apparatus, including: a waveguide optical device; a projection optical system including an optical free-form surface; and a microdisplay device; wherein the projection optical system is coupled into the waveguide optical device through a tilted optical path. 
     In some embodiments, the waveguide device includes a planar waveguide optical element including: a rectangular prism input coupling end; a dichroic mirror array output coupling end; wherein parameters of the waveguide include: a plate thickness d; an angle θ between the dichroic mirror and a plane; a distance h1 between the input coupling end and the output coupling end; a distance h2 between dichroic mirrors of the array; a glass refractive index n; wherein of the waveguide device: the dichroic mirror array has mirrors parallel to each other; the angle satisfies 20°≤θ≤40°; the distance h2 between dichroic mirrors satisfies h2=d/tan(8); the refractive index n satisfies that 1.4≤n≤1.8; the thickness d satisfies that 1.4≤d≤3.6 mm. 
     In some embodiments, the planar waveguide optical element output coupling end comprises at least two parallel dichroic mirrors. 
     In some embodiments, the planar waveguide optical element input coupling end comprises a reflector or a triangular prism. 
     In some embodiments, the projection optical system comprises a light engine system and a free-form surface prism imaging system. 
     In some embodiments, the projection optical system comprises a prism having at least one optical free-form curved surface. 
     In some embodiments, the free-form surface prism comprises at least three free-form curved surfaces, of which the thicknesses are less than 5 mm and the widths are less than 10 mm, and the two orthogonal pupil exit positions may not coincide. 
     In some embodiments, the projection optical system overlaps with the input coupling end substantially, and the long exit pupil overlaps with the exit pupil of the waveguide device substantially. 
     In some embodiments, the light engine comprises a PBS beam splitter, a ¼ wave plate, a reflector, and an LED light source. 
     In some embodiments, if the input coupling end of the planar waveguide optical element comprises a reflector, and the input coupling end substantially overlaps with the free-form surface prism exit pupil, the following conditions can be satisfied to reduce stray light: 
     
       
         
           
             
               
                 
                   
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     wherein θ i  is the incident angle of light beam at the front or back surface of the waveguide optical element, ω y  is the largest field of view angle in the light pupil expansion direction, ω y ′ is the refractive angle of the largest field of view light beam in the light pupil expansion direction incident on the waveguide optical element. 
     In another aspect, the present disclosure provides a near-eye display system including a microdisplay apparatus, wherein the microdisplay apparatus comprises: a first and a second microdisplays, configured to display a closer and a farther observation image to the user&#39;s eyes, respectively, or display respectively a farther and a closer observation image to the user&#39;s eyes, respectively, wherein the first and second observation image have different distances to the user&#39;s eyes, but the fields of view areas covered are substantially the same. The first image is weighted toward rendering the objects with nearer depths in the three-dimensional scene, and the second image weighted toward rendering the objects with farther depths in the three-dimensional scene, wherein the projection optical system comprises: a first optical curved surface prism configured to magnify and place an image displayed by the first microdisplay at a distance relatively close to the user eye; a second optical curved surface prism configured to magnify and place an image displayed by the first microdisplay at a distance relatively far from the user eye; the first prism and the second prism include a pair of optical surfaces with same shape parameters but of opposite signs, i.e., the second optical surface of the first prism and the first optical surface of the second prism are glued together seamlessly, wherein the connection is coated with a half-permeable membrane to achieve the integration of two focal plane images. 
     In some embodiments, the first prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the second optical surface is a concave reflecting surface, a space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, the optical surfaces may include one of spherical surfaces, aspherical surfaces, or free-form surfaces such as complex curvature XY polynomial surfaces; light coming from the first microdisplay enters the first prism through the third optical surface, gets reflected by the first optical surface and is directed to the second optical surface, and gets reflected by the second optical surface before it enters the users&#39; eyes through the first optical surface. 
     In some embodiments, the second prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, the optical surfaces can be spherical surfaces, aspherical surfaces, free-form surfaces, or complex curvature XY polynomial surfaces; light coming from the second microdisplay enters the second prism through the third optical surface, gets reflected by the second optical surface and is directed to the first optical surface, and transmits through the first optical surface and then the first optical free-form surface before it enters the exit pupil of the near-eye display system. 
     In some embodiments, the first prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, a space surrounded by the three optical free-form surfaces is filled with glass or resin optical materials with a refractive index greater than 1.4, the optical surfaces may include one of spherical surfaces, aspherical surfaces, free-form surfaces, or complex curvature XY polynomial surfaces; light coming from the first microdisplay enters the first prism through the third optical surface, gets reflected by the first optical surface and is directed to the second optical surface, gets reflected by the second optical surface and then transmits through the first optical surface before it enters the users&#39; eyes. 
     In some embodiments, the second prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, the optical surfaces can be spherical surfaces, aspherical surfaces, free-form surfaces, or complex curvature XY polynomial surfaces; the light coming from the second microdisplay enters the second prism through the third optical surface, gets reflected by the first optical surface and is directed to the second optical surface, gets further reflected to the first optical surface for transmission, and transmits through the second and then the first optical surfaces of the first prism before it enters the exit pupil of the near-eye display system. 
     In some embodiments, the first prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, the optical surfaces can be spherical surfaces, aspherical surfaces, free-form surfaces, or complex curvature XY polynomial surfaces; the light coming from the first microdisplay enters the first prism through the third optical surface, gets reflected by the second optical surface and is directed to the first optical surface, gets reflected to the first optical surface by the second optical surface, and transmits through the first optical surface before it enters the exit pupil of the near-eye display system. 
     In some embodiments, the second prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, and the optical surfaces can be one or a plurality of spherical surfaces, aspherical surfaces, or free-form surfaces; the light coming from the second microdisplay enters the second prism through the third optical surface, gets reflected by the first optical surface and is directed to the second optical surface, gets further reflected to the first optical surface for transmission, and transmits through the second and then the first optical surfaces of the first prism before it enters the exit pupil of the near-eye display system. 
     In some embodiments, the first prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, and the optical surfaces can be one or a plurality of spherical surfaces, aspherical surfaces, or free-form surfaces; the light coming from the first microdisplay enters the first prism through the third optical surface, gets reflected by the second optical surface to the first optical surface, and transmits through the first optical surface before it enters the exit pupil of the near-eye display system. 
     In some embodiments, the second prism comprises three optical free-form surfaces, wherein: at least one light reflection occurs at one of the optical free-form surfaces, the space surrounded by the three optical free-form surfaces is filled with glass or resin optical material with a refractive index greater than 1.4, and the optical surfaces can be one or a plurality of spherical surfaces, aspherical surfaces, or free-form surfaces; the light coming from the second microdisplay enters the second prism through the third optical surface, gets reflected by the second optical surface to the first optical surface, and transmits through the second and then the first optical surfaces of the first prism before it enters the exit pupil of the near-eye display system. 
     In some embodiments, the tilted light path is a non-rectangular light path. 
     In another aspect, the present disclosure provides a near-eye display method, comprising the coupling of a projection optical system with a free-form optical surface to a waveguide optical element to form a waveguide optical device, using tilted optical path. The size of the display apparatus is much smaller because the two directions of the free-form curved surfaces&#39; exit pupil do not overlap. Meanwhile, the use of the optical waveguide element makes the optical element located in front of the users&#39; eyes to be very thin. 
     Various features will be described in details in the following different example embodiments, and will become apparent. 
     In another aspect, a planar waveguide optical element for a transmission-type near-eye display apparatus is provided, including a waveguide-type element structure configured to improve the field angle and reduce the thickness of the apparatus, by utilizing technologies of transmission-type near-eye display and splicing fields of views. 
     A transmission-type near-eye display (NED) is a small-sized photoelectric display apparatus worn in front of eyes of a user to provide visible virtual images for the wearer and meanwhile not to influence the user to observe the outside real scenes, the NED magnifying images from an image source through an optical system, and displaying the images in front of the user&#39;s eyes, the visual effects to be displayed varying from applications. In practical applications, to be ultrathin and light-weighted of such apparatus is the main goal to be pursued. However, the inventors of the present disclosure have recognized that it is difficult, if possible at all, for conventional rotationally-symmetric multiple-plates technologies to achieve transmission-type near-eye displays; furthermore, new designs such as free-form curved surfaces remain insufficient to satisfy users&#39; demand of being ultrathin; and additionally, and in the above technologies there still exist problems like smaller exit pupil diameter and smaller range of users&#39; eye movement (usually no greater than 8 mm), which affect users&#39; wearing experience. 
     The planar waveguide optical element may use total internal reflection transmission of light to significantly reduce thickness of the transmission-type near-eye device, and use a coupling exit end to achieve a larger exit pupil diameter. However, there are certain restrictions in the aspect of field angle. For example, some researchers note that due to influences exerted by geometric construction, ghost image and stray light, the beam-split surface array geometrically planar waveguide in existing technologies, such as that shown in  FIG. 15 , can have the largest field angle of about 40° when maintaining a relatively thin thickness. 
     Some embodiments of the present disclosure also provide a near-eye display apparatus using a waveguide optical element, and provides an optical solution by splicing waveguide optical elements to achieve an ultrathin profile, a large field of view, large exit pupil diameter and distance, and non-stray light. 
     In an aspect, a near-eye display apparatus is provided, including: a waveguide optical element comprising at least two waveguide plates with a light-transmission gap between the waveguide plates; a projection optical assembly configured to project image light emitted from an image source element onto the waveguide optical element so as to transmit the image light within the waveguide optical element. 
     In some embodiments, the projection optical assembly includes a free-form curved surface optical element. 
     In some embodiments, the free-form curved surface optical element is a prism at least comprising 3 XY polynomial free-form surfaces. 
     In some embodiments, the waveguide plates are arranged to overlap with each other in parallel with a predetermined air gap therebetween, each waveguide plate comprising two main surfaces parallel to each other, to transmit light coupled into said waveguide plates, in a predetermined direction by means of total internal reflection; and each of the waveguide plates comprises at least one partially reflective surface located inside each waveguide plate, said partially reflective surface is arranged within a space between said main surfaces as a beam-split surface at a predetermined angle with said main surfaces; the partially reflective surfaces inside said waveguide plates are distributed in different areas along the direction of said main surfaces. 
     In some embodiments, there are multiple partially reflective surfaces inside each waveguide plate, and the numbers of the partially reflective surfaces inside the waveguide plates are identical or different. 
     In some embodiments, the predetermined angle varies from the waveguide plates. 
     In some embodiments, the multiple partially reflective surfaces are distributed uniformly in a predetermined distribution area. 
     In some embodiments, the waveguide optical element also comprises coupling incidence portions integrated with or combined with each waveguide plate into a whole, the coupling incidence portions are used for refracting light beams into each waveguide plate so as to make light entering said each waveguide plate satisfy an incidence condition of total internal reflection. 
     In some embodiments, the coupling incidence portions are located on the same side of each waveguide plate, and protrude from waveguide plates in the same direction. 
     In some embodiments, the multiple partially reflective surfaces are configured to have different reflectivity to ensure that light exiting the waveguide plates has a substantially uniform intensity distribution in a predetermined area, the reflectivity of adjacent partially reflective surfaces satisfies the following formula: 
               R   N     =       R     N   -   1         1   -     R     N   -   1                 
wherein N is a sequence number of the partially reflective surface, R1 is reflectivity of the partially reflective surface closest to the coupling incidence portions.
 
     In some embodiments, the waveguide optical element also comprises coupling incidence portions integrated with or combined with each waveguide plate into a whole, the coupling incidence portions are used for refracting light beams into each waveguide plate so as to make light entering said each waveguide plate satisfy an incidence condition of total internal reflection, at least one of the coupling incidence portions comprises a wedge deflection element. 
     In some embodiments, the near-eye display apparatus further comprises an image source element configured to emit the image light to the projection optical assembly. 
     In another aspect, a display apparatus is provided, including: a waveguide optical element; a projection optical system having a free-form surface optical element; and a microdisplay; wherein the projection optical system is optically coupled to the waveguide optical element through an inclined optical path. 
     In some embodiments, the waveguide optical element comprises at least two waveguide plates with a light-transmission gap therebetween. 
     In some embodiments, the projection optical system comprises a prism having the optical free-form surface; wherein the prism comprises at least three free-form curved surfaces, has non-overlapping exit pupil positions in two orthogonal directions, a thickness ≤5 mm, and a width ≤10 mm. 
     In some embodiments, the waveguide plates are arranged to overlap with each other in parallel with a predetermined air gap therebetween, each waveguide plate comprising two main surfaces parallel to each other, to transmit light coupled into the waveguide plates, in a predetermined direction by means of total internal reflection; and each of the waveguide plates comprises at least one partially reflective surface located inside each waveguide plate, said partially reflective surface is arranged within a space between said main surfaces as a beam-split surface at a predetermined angle with said main surfaces; the partially reflective surface inside the waveguide plates are distributed in different areas along the direction of said main surfaces. 
     In some embodiments, there are multiple partially reflective surfaces inside each waveguide plate, and the numbers of the partially reflective surfaces inside the waveguide plates are identical or different. 
     In some embodiments, the waveguide optical element also comprises coupling incidence portions integrated with or combined with each waveguide plate into a whole, the coupling incidence portions are used for refracting light beams into the waveguide plates so as to make light entering said each waveguide plate satisfy an incidence condition of total internal reflection, the multiple partially reflective surfaces are configured to have different reflectivity to ensure that light exiting the waveguide plates has a substantially uniform intensity distribution in a predetermined area. 
     In some embodiments, the reflectivity of adjacent partially reflective surfaces satisfies the following formula: 
               R   N     =       R     N   -   1         1   -     R     N   -   1                 
wherein N is a sequence number of the partially reflective surfaces, R1 is reflectivity of the partially reflective surface closest to the coupling incidence portion.
 
     In another aspect, a method of displaying augmented reality (AR) or virtual reality (VR) images with a wearable display apparatus is provided, the method including: receiving images; projecting the images with a projection optical system including at least one free-form surface optical element; and coupling the projected images to an waveguide optical element through an inclined optical path, wherein the waveguide optical element comprises at least two waveguide plates with a light-transmission gap therebetween. 
     In some embodiments, the NED apparatus, through at least two layers of waveguide plates arranged to overlap, the beam-split surface arrays within each layer have different structure parameters, which can respectively influence fields of views of different angle ranges when combined with a projection optical assembly having free-form surfaces, and also guarantee a larger field angle, an image within effective field of view to have a relatively uniform intensity of light, less stray light, and an exit pupil diameter at least to be up to over 10 mm under the circumstance that the thickness gets only a limited increase relative to a single layer waveguide, thereby acquiring a better AR experience while the overall weight is lighter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a structural diagram of a conventional planar waveguide display system; 
         FIG. 2  is a diagram of internal optical paths of a conventional planar waveguide display system; 
         FIG. 3  is a structure diagram of a free-form surface projection optical system; 
         FIG. 4  is a diagram of a planar waveguide display system according to some embodiments; 
         FIG. 5  is an illustration of the relative relationship between the entrance pupil and the exit pupil of a projection system; 
         FIG. 6  is a schematic of optical paths inside the waveguide according to some embodiments; 
         FIG. 7  is a top view of the light propagation inside the waveguide; 
         FIG. 8  is a structural diagram of the free-form surface optical waveguide in a helmet implementation; 
         FIG. 9  is an illustration of the relationships between light output efficiency and reflectivity of each of the half-mirrors; 
         FIG. 10  is an illustration of the focal plane division of optical systems in existing technologies; 
         FIG. 11  is a synthetic diagram of the optical system according to the first embodiment; 
         FIG. 12  is a synthetic diagram of the optical system according to the second embodiment; 
         FIG. 13  is a synthetic diagram of the optical system according to the third embodiment; 
         FIG. 14  is a synthetic diagram of the optical system according to the fourth embodiment; 
         FIG. 15  is a structural diagram of a beam-split surface array geometrically planar waveguide in the prior art; 
         FIG. 16  is a diagram of an NED apparatus and optical path according to some embodiments of the present disclosure; 
         FIG. 17  illustrates a first waveguide plate “A” and a second waveguide plate “B” of the structure according to  FIG. 16 ; and 
         FIG. 18  is a diagram of a projection optical element of the NED apparatus according to  FIG. 16 . 
     
    
    
     DETAILED DESCRIPTION 
     The following description, with reference to the accompanying drawings, describes some embodiments of the display devices, systems, and methods. Similar reference numerals are used to denote similar parts when applicable. 
     It can be difficult for conventional spherical optical technologies to achieve optical see-through functionalities. Even if the see-through functionality is achieved, the systems can also get bulky in size, have small fields of views, and have low resolutions, etc. The field of view is limited by the lens thickness. In general, the larger the field of view, the greater the thickness of the optical system is. 
     One embodiment disclosed herein uses a free-form surface optical technology to realize diffraction-reflection and off-axis structure design for a light weighted helmet-mounted optical see-through display system with a large field of view. The thickness of the part located in front of the eyes can still be limited by the structure, and is normally greater than 1 cm. Another embodiment uses a waveguide technology, allowing the thickness of the optical element located in front of the eyes to be reduced to a few millimeters, and thus realizes the optical see-through functionality. The optical waveguide component does not generate optical power, and the virtual imaging portion has low optical energy utilization and may need projection magnification by a projection optical system, so the two portions need to be coupled appropriately. When the conventional waveguide element is used for the helmet mounted display system, a light engine may be needed to generate highly bright display images. The projection system and the light engine can be bulky and heavy, thereby affecting the volume and weight of the helmet display system. In addition, the conventional waveguide element used for helmet display system can have problems such as a small field of view, and stray light interferences. 
     For example, the input coupling end of the conventional waveguide optical element may use a tilted reflector, and it causes a fairly amount of stray light between the reflector and interface of the waveguide&#39;s front and back surfaces. To reduce the stray lights, the projection optical system&#39;s exit pupil needs to be coupled with the entrance pupil without fully using the coupling reflector. Therefore, alignment precision and exit pupil diameter of the projection optical system are highly demanded in the conventional waveguide elements. In addition, the conventional coupling method also limits the volume miniaturization of the overall size of the display system. Because the projection system is located behind or in front of the waveguide, reflectors are needed for folding. 
       FIG. 1  is a schematic structural view of a conventional planar waveguide display system. A waveguide element comprises a plane reflector input-coupling end and a plane reflector output coupling end. Light coming from the micro display  4 , gets collimated by the projection optical system  6 , transmits through the front surface of the waveguide plate, propagates in the waveguide after being coupled by the reflector  8  of the input coupling end and reaches the output-coupling end  12 . The light leaves the front surface and reaches the users&#39; eyes  14  after being reflected by the output coupling end. This can be considered a prototype waveguide helmet mounted display system. However, because there is only one reflector at the output-coupling end, and the light is reflected directly to the output coupling end from the input-coupling end, the field of view of the waveguide optics element and the thickness are greatly restricted. The thickness T of the waveguide components increases substantially with an increasing field of view. 
     Although this structure is simple, it may have multiple disadvantages, among which the main one is the largest field of view is severely restricted by the glass plane thickness. As can be seen from the drawing, the slab waveguide has a maximum allowable angle of: 
                       α   max     =     arctan   ⁡     (       T   -     d   eye         2   ⁢   l       )         ,           (   2   )               
wherein T is the thickness of the slab waveguide, d eye  is the exit pupil diameter of the waveguide optical system, and l is the distance between the two reflective surfaces. If the angle is greater than α max , the light will be reflected at the front and back surfaces of the waveguide slab before it reaches the second reflective surface, and ghost images may be formed by the stray light caused from multiple light reflections. Therefore, the maximum angle of field of view of this type of structure can be obtained as follows:
 
FOV max ≈2 vα   max   (3)
 
wherein v is the refractive index of the planar glass, typically between 1.5-1.6. Because the human eye pupils&#39; diameters are in the range of 2-6 mm, in order to adjust to the eye movements, the minimum acceptable value of the planar waveguide system exit pupil diameter is about 8 mm. For most people, l is between 40-60 mm. Therefore, even if the field of viewing angle is only 8°, the system may need a thickness of the glass plane to be up to 12 mm.
 
       FIG. 2  is a schematic diagram illustrating internal optical paths of a conventional planar waveguide display system. To overcome the restrictions on the field of view due to the single-reflective-surface-coupling output in the geometric planar waveguide system, multiple-reflective-surface-coupling output geometry of the waveguide is used, shown in  FIG. 2 . In this configuration, the output coupling portion utilizes a series combination of half-transmission-half-reflection lenses to solve the limitation of the field of view along the light propagation direction. 
     The input-coupling reflective surface is illuminated by light emitted from the image source after being collimated. The reflective surface couples the incident light to the waveguide to ensure the light is confined within the waveguide, and internal reflections occur inside the glass plane. After multiple reflections, the light reaches the transflective surface used for output coupling. On the transflective surface, part of the light leaves the waveguide and enters the users&#39; eyes, and the other part of the light transmits through the surface and continues to propagate to the next transflective lens. The maximum field angle allowed in this structure is: 
     
       
         
           
             
               
                 
                   
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     It is known from the formula of the field of the output coupling set comprising a series of transflective lenses can overcome the limit on the maximum field of view allowed, which is rather small. The field of view angle can be infinitely expanded as long as there is enough number of transflective lenses. However, considering that as the number of transflective lenses increases, the energy carried by the light decreases rapidly after passing through these lenses, it is reasonable to use 4-6 such lenses. When N equals 4, the coupling surface inclination angle is 30°, the required thickness of the glass plane for the field of view angle of 15° and 30° is merely 5.3 mm and 8.2 mm, respectively. Compared to the conventional structure of the single reflective output coupling, the thickness of the glass plane is greatly reduced. 
     Considering the field of view in X-direction of the waveguide, the maximum field of view in X-direction is not related to the size and number of the transflective lenses, but is dependent on the range of the light beam perpendicular to the waveguide. The maximum field of view is 
                       FOV   max     ≈         D   η     -     d   eye           R   eye     +     l   /     (     v   ⁢           ⁢   sin   ⁢           ⁢     α   in       )             ,           (   5   )               
wherein v is the refractive index of the waveguide, typically between 1.5 and 1.6, l is the distance between the input coupling central axis and output coupling central axis, about 40-60 mm, D η  is the range of the input light beam in the direction perpendicular to the waveguide.
 
     If the field of view required in the X direction is 30°, with the parameters given above, the width of the light beam width in the X direction will be approximately 42 mm. The width in the horizontal direction is given by the equation S Z =T tan(α in ). Therefore, the width of the light beam width in the horizontal direction is about approximately S Z =6.8 mm, which indicates the aspect ratio of the incident light beam to be 6. This may require the numerical aperture of the collimating optical system to be very large, making it difficult to make a compact and portable system. 
       FIG. 3  is a structural diagram of a free-form curved surface projection optical system. It can be used in augmented reality transmission-type imaging optical system. In  FIG. 3 , light coming from microdisplay  5  transmits through optical surface  4  of the free-form curved surface prism, has a total reflection on optical surface  2  and reaches towards the concave reflective surface  3 . After the reflection off the reflective surface  3 , the light enters the user&#39;s eyes through optical surface  2 . In augmented reality transmissive helmet, the optical structure of the internal channel does not change Optical surface  3  uses a transflective structure. The energy of the external light loses ½ of its energy when it is incident on the optical surface  3 , and a portion transmits through optical surface  3  and optical surface  2  to enter the user&#39;s pupil. 
       FIG. 4  is a diagram of a planar waveguide display system according to some embodiments; it comprises waveguide optical elements and a projection optical system. The projection optical system further includes an illumination light engine system. The conventional projection system may use a spherical lens or a conventional aspherical lens. A bulky projection system can cause difficulties in reducing the weight and volume of the waveguide helmet system. 
       FIG. 5  is a schematic diagram illustrating the relative relationship between the exit pupil and the entrance pupil of the projection system; if the exit pupils of the projection system in two directions are the same and they located in the input coupling end of the waveguide optical element, at the exit pupil position of the system, light beams of different fields of views in the direction perpendicular to the exit expansion direction may separate, making it impossible for the user&#39;s eyes to see the full image simultaneously. If the exit pupil in the direction perpendicular to the exit pupil expansion direction is located in the entrance pupil position of the optical waveguide element, the position of the exit pupil of the system can form a superimposed and expanded exit pupil. 
     The exit pupil of the projection optical system may need to be matched to the entrance pupil of the optical waveguide element appropriately, so as to effectively eliminate unnecessary stray light. So in order to reduce stray light generated by the waveguide optical element entrance coupling end, the exit pupil of the projection optical system may need to be matched to the entrance pupil of the optical waveguide element appropriately. 
       FIG. 6  is a schematic diagram of the optical path inside the waveguide according to some embodiments; the entrance pupil of the waveguide optical element may comprise a triangular prism, and an optical surface of which coincides with the surface of the waveguide optical element. Light can transmit through the prism slanted surface directly and is coupled into the waveguide optical element without reflection, reducing possible stray light generated at the input coupling end of the conventional waveguide optical element. Meanwhile, the projection system can be realized using a free-form optical system. 
       FIG. 7  is a diagram of light propagation inside the projection optical system; it includes a three-dimensional view, a top view (XZ), and a side view (YZ). As can be seen from the drawing, the exit pupil positions at the two directions of the free-form curved surface projection system do not overlap, and the exit pupil distance in the XZ plane is greater than the projection distance within the YZ plane. 
       FIG. 8  is a schematic diagram of the optical path structure of the free-form curved surface waveguide helmet according to some embodiments; it uses the waveguide optical element illustrated in  FIG. 6  and the free-form curved surface projection optical system illustrated in  FIG. 7 . As a result of using the free-form curved surface, the simplification of the projection optical system can be maximized, allowing the bulky projection system to be miniaturized with reduced weight and volume, thereby reduces weight and volume of the entire system. 
       FIG. 9  illustrates the relationship between the light output efficiency and the reflectivity of each transflective lens. In order to ensure the consistency of real transmittance of light through the waveguide system, and to simplify the processing and coating of each beam splitter, various beam splitter surfaces can be coated with the same film. Each curve shown in the drawing illustrates the light beam curve of the output coupling efficiency of the reflector as a function of the transmittance at different positions. As such, the reflectivity of each beam splitter coating cannot be too high, otherwise the output coupling light efficiency of the beam splitter located at the waveguide entrance output coupling end will have an overly low efficiency, which results in large differences in the overall image brightness and affects the overall wholeness and viewing effect of the image. The light output coupling efficiency formula can be expressed as:
 
 E   ri   =T   r   i-1 ×(1− T   r ),  (6)
 
where T is the transmittance of the beam splitter, and i represents the i-th beam splitter.
 
     As shown in  FIG. 9 , in the case that each beam splitter has the same reflectivity, the output coupling efficiency of the light energy of each reflector varies with a changing transmission. When the transmittance is 1, the light energy output coupling efficiency is 0. As can be seen from the figure, the transmission of each beam splitter control may be preferably controlled to be between 0.65 and 0.85. 
     Some embodiments disclosed herein provide a free-form curved surface prism helmet display, realizes a large field of view, reduces or eliminates stray lights, and has relatively high light energy utilization efficiency. 
     Some embodiments disclosed herein use a new coupling method, to further fold the system, thereby realizes a more compact display system. Using tilted optical paths, the system thickness is greatly reduced. Optical gratings can also be used as the coupling component besides the prism mentioned above. 
     Compared with conventional helmet display technology, some embodiments disclosed herein use free-form curved surface technology and waveguide technology to fully promote and utilize their advantages, and thereby reduce the volume and weight of the helmet display system. 
     Some embodiments provide a waveguide near-eye display apparatus that is particularly suitable for outdoor and mobile augmented reality display systems. Development of helmet display optical system has evolved from a coaxial rotationally-symmetric transmission-type structure into a catadioptric structure. In order to achieve the see-though function, light weight, and a glasses-type display effect, the helmet display technologies use an off-axis catadioptric structure, free-form curved surfaces, holographic diffraction, and waveguide technologies. Existing helmet displays have disadvantages such as small field of view, large size, and heavy weight. The embodiments described below use free-form curved surface optics in conjunction with waveguide technologies, to overcome the disadvantages of traditional helmet displays, reduces the size and weight of near-eye helmet displays, increases the field of view, and reduces stray light. 
     In some of the following embodiments, the coordinate system may be specified as a right-handed coordinate system, for example: the direction horizontally to the right is the Z-axis direction, the direction upward perpendicular to the Z-axis direction is the Y-axis, and the direction inward perpendicular to the paper plane YOZ is the X-axis. The light comes from the light source, goes through the light engine, the free-form surface projection system, the planar waveguide, and reaches the user&#39;s eyes. 
     In the following, with reference to the attached drawings, embodiment of the free-form surface prisms helmet display optical system is provided. Imaging optical path of the microdisplay  5  and the imaging quality of the optical imaging system are described in detail. The optical path may include an internal channel, and an external channel to observe the outside world. 
     As shown in  FIG. 8 , the free-form surface projection optical system can include a free-form surface prism and an illumination light engine. The light engine may include a light source, a polarization beam splitter (PBS), a reflector, and a ¼ slide. It can achieve high energy utilization efficiency and uniform illumination over the image source. The free-form surface prism can comprise one of a plurality of free-form curved surfaces, such as a few free-form curved surfaces or non-spherical surfaces, using catadioptric projection optical path mode to enable system miniaturization. 
     As shown in  FIG. 8 , the planar waveguide optical element can comprise a series of semi-reflective/semi-transparent prisms, including an input-coupling portion and an output-coupling portion. The input-coupling portion can include a rectangular prism and a plate, and the output coupling portion can include an array of semi-reflective/semi-transparent lenses bonded together. 
     The projection optical system can include a free-form surface prism, an illumination light engine, and a microdisplay. The illumination light engine can project the light uniformly onto the image source after collimating the light source. The illuminated images can be further collimated and magnified by the free-form surface prism optical element, forming an output pupil in the two perpendicular directions of the exit end of the free-form surface prism. The nearer exit pupil overlaps with the input coupling end of the planar waveguide optical element substantially and the farther exit pupil overlaps with the exit pupil of the planar waveguide optical element substantially. The parallel light beam, after collimated by the projection optical system, can be incident on the input prism according to a specified method, and then coupled into the waveguide. The light beam&#39;s incidence angle at the front and back surfaces of the planar waveguide are greater than the respective critical angles. After transmitting in the waveguide through multiple total reflections between the front and back surfaces, the light beam can then propagate through the output-coupling end of the planar waveguide as the output, couples into the air, and eventually reaches the user&#39;s eyes. 
     According to some embodiments, interactions between the waveguide and the free-form surface can reduce the pupil diameter. For example, the diameters can be reduced from 6-8 mm down to 3-4 mm; the sagittal direction of the free-form curved surface can be extended; the free-form surface prism exit pupil distance can also reduced. In particular, the improvements on the overall system from the free-form curved surfaces may include: a more compact size, lighter weight, less stray light, such as little or no stray light at the input-coupling end. 
     Referring to  FIG. 8 : the light coming from the LED light source gets reflected by a beam splitter PBS, goes through a ¼ slide, undergoes a polarization state rotation by 45 degrees, gets reflected by a reflector and goes through the ¼ slide again, undergoes a polarization state rotation by 45 degrees again, changes from p light to s light, and is incident on the beam splitter PBS. The light goes through the beam splitter PBS and reaches the LCOS display chip. After illuminating the LCOS, the light is reflected to the PBS beam splitter. The LCOS changes the polarization state of the light by 90 degrees. At this point the light is reflected by the PBS and it enters the free-form surface prism projection system. The free-form surface prism projection system collimates and magnifies the light beam, which is coupled into the waveguide optical element through the exit pupil. The light further propagates in the waveguide, and eventually reaches the user&#39;s eyes through the output-coupling portion. 
     Table A lists  10  groups of preferred parameters of the waveguide structure, wherein Theta is the angle between the half-transmission-half-reflection lens and the waveguide plane, d is the thickness of the optical waveguide element, H1 is the distance between the input-coupling end and the output-coupling end, index is the material refractive index of the optical waveguide. PV lists PV values of the ratio between the stray light and the useful light, AVE is the average value, RMS is the root mean square value, EPDY is the exit pupil diameter of the system in the Y direction. The above parameters are for the case where the exit pupil distance is 20 mm. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE A 
               
               
                   
               
               
                 No. 
                 Theta 
                 d 
                 H1 
                 Index 
                 PV 
                 AVE 
                 RMS 
                 EPDY 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 29.6 
                 3.2 
                 17 
                 1.78 
                 0.04655 
                 0.02613 
                 0.02962 
                 13.34 
               
               
                 2 
                 29.6 
                 3.0 
                 16 
                 1.78 
                 0.04750 
                 0.02622 
                 0.02974 
                 11.96 
               
               
                 3 
                 29.6 
                 2.8 
                 15 
                 1.78 
                 0.04836 
                 0.02631 
                 0.02988 
                 10.67 
               
               
                 4 
                 29.6 
                 2.6 
                 14 
                 1.74 
                 0.04852 
                 0.02682 
                 0.03045 
                 9.24 
               
               
                 5 
                 29.6 
                 2.6 
                 14 
                 1.78 
                 0.04900 
                 0.02639 
                 0.03030 
                 9.29 
               
               
                 6 
                 29.6 
                 2.8 
                 15 
                 1.74 
                 0.04952 
                 0.02675 
                 0.03034 
                 10.56 
               
               
                 7 
                 29.6 
                 2.4 
                 13 
                 1.78 
                 0.04995 
                 0.02646 
                 0.03010 
                 7.98 
               
               
                 8 
                 29.6 
                 2.4 
                 13 
                 1.74 
                 0.05017 
                 0.02694 
                 0.03063 
                 7.88 
               
               
                 9 
                 29.6 
                 2.4 
                 13 
                 1.70 
                 0.05108 
                 0.02741 
                 0.03113 
                 7.85 
               
               
                 10 
                 29.6 
                 3.0 
                 16 
                 1.74 
                 0.05130 
                 0.02674 
                 0.03033 
                 11.93 
               
               
                   
               
            
           
         
       
     
     The following embodiments do not include the waveguide portion so as to mainly describe the advantages brought by the free-form surfaces. 
     Some embodiments disclosed herein provide a realistic three-dimensional bifocal monocular helmet display device, comprising a first optical curved surface prism and a second optical curved surface prism. The optical surface may be in the form of a spherical, an aspheric or a free-form surface. Each prism may comprise a first optical surface, a second optical surface, and a third optical surface. The first optical curved surface prism and the second optical curved prism include a pair of curved surfaces with the same surface shape. The curved surface on the first optical surface is coated with a half-transmissive-half-reflective membrane, and the first and second optical curved surface prisms can be boned together; together there are display components, including the first and second microdisplays. The first optical curved surface prism and the first microdisplay form the first display focal plane, and the second optical curved surface prism and the second microdisplay form the second display focal plane. The first and second display focal planes each generates a viewing screen closer and farther from the user&#39;s eyes, respectively, or each generates a viewing screen closer and farther from the user&#39;s eyes, respectively. When rendering images, according to the depths of objects in the scene, depth filters may be applied respectively to the two microdisplays, thereby generate the observed images with realistic three-dimensional views. The bifocal monocular helmet display device according to some embodiments of the disclosure is compact, and light weighted. In particular, for stereoscopic helmet display device, the embodiments provide helmet mount display devices that are in line with the human eye&#39;s natural stereoscopic vision. It solves or improves the problems in traditional stereoscopic helmet display devices where the focus and vergence are not consistent, and it improves comfort level as well as relieves visual fatigue. 
     Embodiments of the present disclosure provide a free-form curved surface prism helmet mount display device optical system, in particular, an optical system that can, with a monocular design, generate a real stereoscopic effect with a compact bifocal helmet mount display. 
     Factors contributing to the three-dimensional vision of the human eyes include: the size of the object, the clarity of the object, and the binocular parallax for the object. Typically the human eyes&#39; focus and vergence correlation provides information for a sense of depth. However, the focus and vergence information provided by the traditional binocular helmet mount display device may not be consistent. Because light may come from a single focal plane, and for human eyes to see the object clearly, they need to focus on a fixed focal plane. A stereoscopic image is usually of a certain depth, i.e., located in front of and behind the focal plane. The stronger the sensation of being stereoscopic, the larger the differences between the focus and the vergence are. This has led to the inconsistency in the human eyes between focus and vergence, and more likely caused eye fatigue of the user. 
     To reduce the contradiction caused by the inconsistency between the focus and the vergence at the user&#39;s eyes, some solutions such as focal-plane-zoomable HMDs and multi-focal-plane HMDs are studied. The main approaches of focal-plane-zoomable HMDs can be summarized in two categories: changing the image plane position, and changing the position of the optical system. The multi-focal-plane HMD solutions can include time-division multiplexing or spatial multiplexing display solutions. Spatial multiplexing can be achieved by placing stacked microdisplays in front of the visual optical element, and displaying images of different depths in different microdisplays to generate depth information. However, due to the fact that the image from the back travels through a number of microdisplays, the brightness of the image cannot be guaranteed. The integration of multiple light paths can be achieved by using multi-optical beam splitters. The system comprises a plurality of focal planes, and the focal depth information generated from different focal planes can be different. However, such systems are bulky, not easy to be light weighted, and also difficult to be head mounted, as shown in  FIG. 10 . Time-division multiplexing multiple-focal-plane HMDs use liquid lenses, deformable mirror or lenses, or birefringence lenses to adjust the system&#39;s focus, thereby change the distances observed by the system at different times. Such systems may have high requirements on refresh rate of the microdisplays and critical optical components. If more focal planes are constructed, the minimum refresh rate of the system may have even higher requirements. 
     Some embodiments disclosed herein use spatial multiplexing multi-focal-plane technologies and free curved surface optical technologies to realize compact and light weighted bi-focal-plane HMD. Users can observe three-dimensional images using only a monocular visual optical system, and it is consistent with the natural human eye vision. Light weighted freeform surface bifocal monocular HMD optical system is also suitable for wearing on user&#39;s head, and three-dimensional display is produced in line with the natural visual characteristics of the human eye, thereby helps avoiding visual fatigues caused by traditional three-dimensional HMDs. 
     One embodiment of the optical system uses a reverse optical path design, i.e., tracing light from the eyes to the microdisplay. For the convenience of description, ray tracing direction starts from the position of the exit pupil, through the optical system, and eventually reaches the microdisplay. 
     Some of the embodiments use spherical and aspheric surface shapes to describe curved surfaces, which can be described by a toric XY polynomial (AXYP) surface. In the surface type column of the following table, sph represents spherical surface, asp represents aspherical surface, and the default is AXYP surface. 
     In some embodiments, the aspherical surface can be expressed as the equation: 
                   z   =         cx   2       1   +       [     1   -       (     1   +   k     )     ⁢     c   2     ⁢     x   2         ]       1   /   2           +     Ax   4     +     Bx   6     +     Cx   8     +     Dx   10               (   7   )               
wherein, c is an apex radius of curvature of the surface, k is the coefficient of the secondary surface, and A, B, C, D are aspherical 4th, 6th, 8th, 10th aspheric coefficients, respectively.
 
     Some embodiments use an Anamorphic Aspherical Surface (AAS). An AAS may also be referred as a complex aspherical surface, which has a radius of curvature in two directions, but can be different. The curved surface is a plane of symmetry, which has two planes of symmetry, each on yoz and xoz planes of symmetry. The advantages include easy control of optimization and fast optimization convergence rate. The AAS can be described as: 
                   z   =             C   x     ⁢     x   2       +       C   y     ⁢     y   2           1   +       {     1   -       (     1   +     K   x       )     ⁢     C   x   2     ⁢     x   2       -       (     1   +     K   y       )     ⁢     C   y   2     ⁢     y   2         }       1   /   2           +       ∑     i   =   1     n     ⁢       A   i     ⁢       {         (     1   -     P   i       )     ⁢     x   2       +       (     1   +     P   i       )     ⁢     y   2         }       i   +   1                     (   8   )               
wherein, C x  is the radius of curvature of the curved surface of X direction in the XZ plane, C y  is the radius of curvature of the curved surface of Y direction in the YZ plane, K x  is the conic coefficient of the curved surface in X direction, K y  is the conic
     coefficient of surface in Y direction, A i  is 4, 6, 8, 10, . . . 2n-order aspheric coefficients, and is rotational symmetric on the Z-axis, P i  is 4, 6, 8, 10, . . . 2n-order non-rotationally symmetric coefficients.   

     Some embodiments use XY polynomial surface (XYP). XYP surface equation can be described as: 
                     z   ⁡     (     x   ,   y     )       =       c   1     +       c   2     ⁢   y     +       c   3     ⁢   x     +       c   4     ⁢     y   2       +       c   5     ⁢   yx     +       c   6     ⁢     x   2       +       c   7     ⁢     y   3       +       c   8     ⁢     y   2     ⁢   x     +       c   9     ⁢     yx   2       +       c   10     ⁢     x   3       +       c   11     ⁢     y   4       +       c   12     ⁢     y   3     ⁢   x     +       c   13     ⁢     y   2     ⁢     x   2       +       c   14     ⁢     yx   3       +       c   15     ⁢     x   4       +       c   16     ⁢     y   5       +       c   17     ⁢     y   4     ⁢   x     +       c   18     ⁢     y   3     ⁢     x   2       +       c   19     ⁢     y   2     ⁢     x   3       +       c   20     ⁢     yx   4       +       c   21     ⁢     x   5       +       c   22     ⁢     y   6       +       c   23     ⁢     y   5     ⁢   x     +       c   24     ⁢     y   4     ⁢     x   2       +       c   25     ⁢     y   3     ⁢     x   3       +       c   26     ⁢     y   2     ⁢     x   4       +       c   27     ⁢     yx   5       +       c   28     ⁢     x   6       +       c   29     ⁢     y     7   ⁢                 +       c   30     ⁢     y   6     ⁢   x     +       c   31     ⁢     y   5     ⁢     x   2       +       c   32     ⁢     y   4     ⁢     x   3       +       c   33     ⁢     y   3     ⁢     x   4       +       c   34     ⁢     y   2     ⁢     x   5       +       c   35     ⁢     yx   6       +       c   36     ⁢     x   7       +   …             (   9   )               
By appropriately selecting the power of XYP, the surface can be made symmetric on the yoz plane, or symmetric on the xoz plane. The surface shape can provide more freedom, but the ray tracing and optimization may be slower. In one embodiment, this type of surface can be controlled to be a curved surface with only one plane of symmetry.
 
     Some embodiments use an AXYP curved surface equation: 
                     z   =             c   x     ⁢     x   2       +       c   y     ⁢     y   2           1   +       (     1   -       (     1   +     k   x       )     ⁢     c   x   2     ⁢     x   2       -       (     1   +     k     y   ⁢                 )     ⁢     c   y   2     ⁢     y   2         )       1   /   2           +       ∑     m   =   0     p     ⁢       ∑     n   =   0     p     ⁢       C     (     m   ,   n     )       ⁢     x   m     ⁢     y   n               ⁢     
     ⁢           ⁢     1   ≤     m   +   n     ≤   p             (   10   )               
wherein, c x , c y  respectively are the radii of curvature of the vertex of the surface in the meridional direction and the sagittal direction, k x , k y  are the conic constants of the surface of the meridional and sagittal directions, respectively, C (m, n)  is the coefficient of the polynomial x m y n , and p is the highest number of power of the polynomial.
 
     According to one embodiment of the disclosure, the structure of the bifocal monocular three-dimensional HMD apparatus is shown in  FIG. 11 . It includes two optical surface prisms and two microdisplays, forming two different observation planes of different depths, respectively. When rendering the images on the microdisplays, appropriate light intensity filters need to be used. This can allow users to feel the observed images between screen  109  and  110 , thereby produces the three-dimensional display effect with a certain depth. 
     An optical system including the first focal plane can have its optical path formed as follows. The optical path of the first focal plane can include optical surfaces  101 ,  102  and  103 , the inside cavity can be filled with glass or other materials. According to the description of reverse ray tracing, the light starts from the user&#39;s eyes located at the exit pupil, travels from the front surface of the optical surface  101  and transmits through it, and arrives at the optical surface  102 . Because a semi-permeable membrane is coated on optical surface  102 , the light splits into two beams. After the light beam reflection occurs, it is incident on this surface again from the back of optical surface  101 . The light undergoes a total reflection, reaches optical surface  103 , eventually leaves the wedge prism through transmission, and arrives at micro-display  106 . The viewing screen corresponding to the image plane  107  is located at the position  110 . Table 1 lists the eccentricity and inclination angles of each optical surface for generating the focal plane in a first embodiment. Table 3 lists the parameters of all surfaces according to the first embodiment. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 Eccentricity 
                 Eccentricity 
                   
               
               
                   
                 Surface 
                 in Y 
                 in Z 
                 Inclination on 
               
               
                   
                 No. 
                 direction 
                 direction 
                 the X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 101 
                 −4.000 
                 28.660 
                 11.500 
               
               
                   
                 102 
                 1.000 
                 36.840 
                 −13.900 
               
               
                   
                 103 
                 18.050 
                 31.000 
                 87.000 
               
               
                   
                 106 
                 22.555 
                 36.352 
                 56.858 
               
               
                   
                   
               
            
           
         
       
     
     The optical path of the optical system including the second focal plane can be formed as follows. The optical path of the second view screen can include optical surfaces  101 ,  102 ,  104 , and  105 . The light coming from the human eye transmits through optical surface  101 , undergoes a reflection on optical surface  104 , the reflected light transmits through optical surface  105 , and reaches the second image plane  107 . The viewing screen corresponding to the image plane  107  is located at position  109 . Table 2 lists the eccentricity and inclination values of each optical for generating the second focal plane of the optical path according to the first embodiment. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 Eccentricity 
                 Eccentricity 
                   
               
               
                   
                 Surface 
                 in Y 
                 in Z 
                 Inclination on 
               
               
                   
                 No. 
                 direction 
                 direction 
                 the X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 101 
                 −4.000 
                 28.660 
                 11.500 
               
               
                   
                 102 
                 1.000 
                 36.840 
                 −13.900 
               
               
                   
                 104 
                 8.447 
                 44.853 
                 37.003 
               
               
                   
                 105 
                 −10.000 
                 32.484 
                 99.327 
               
               
                   
                 107 
                 −14.893 
                 34.122 
                 26.580 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Coefficient 
                 101 
                 102 
                 103 
                 104 
                 105 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius in YZ 
                 −3.16E+02 
                 −6.30E+01 
                 −8.35E+02 
                 −6.33E+01 
                 −1.63E+01 
               
               
                 plane (cuy) 
               
               
                 Conic constant 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 in X (Kx) 
               
               
                 Conic constant 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 in Y (Ky) 
               
               
                 Radius in XZ 
                 −3.62E+02 
                 −4.79E+01 
                 −6.26E+02 
                 −4.89E+01 
                 −2.72E+01 
               
               
                 plane (cux) 
               
               
                 x 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 
                 7.95E−08 
                 7.13E−09 
                 −8.26E−12 
                 0 
                 0 
               
               
                 x2 
                 −6.69E−04 
                 −8.71E−04 
                 −4.43E−04 
                 0 
                 0 
               
               
                 xy 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y2 
                 −1.53E−09 
                 3.25E−04 
                 3.14E−03 
                 0 
                 0 
               
               
                 x3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y 
                 1.96E−10 
                 −3.87E−06 
                 −1.91E−04 
                 0 
                 0 
               
               
                 xy2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y3 
                 3.42E−10 
                 6.10E−05 
                 3.33E−04 
                 0 
                 0 
               
               
                 x4 
                 −7.44E−06 
                 −2.89E−06 
                 6.85E−05 
                 −8.89E−07 
                 1.17E−05 
               
               
                 x3y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y2 
                 −9.63E−06 
                 8.85E−07 
                 1.15E−04 
                 −1.58E−06 
                 −5.61E−05 
               
               
                 xy3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y4 
                 −3.12E−06 
                 2.35E−06 
                 6.07E−05 
                 −7.02E−07 
                 6.73E−05 
               
               
                 x5 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y 
                 −2.23E−13 
                 1.83E−07 
                 −7.16E−06 
                 0 
                 0 
               
               
                 x3y2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y3 
                 1.35E−12 
                 −6.00E−09 
                 9.25E−06 
                 0 
                 0 
               
               
                 xy4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y5 
                 −1.07E−11 
                 −1.24E−07 
                 −1.09E−05 
                 0 
                 0 
               
               
                 x6 
                 7.64E−09 
                 4.32E−09 
                 −9.13E−07 
                 −1.92E−17 
                 3.18E−08 
               
               
                 x5y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y2 
                 2.15E−08 
                 −2.91E−09 
                 1.62E−06 
                 2.71E−14 
                 −1.33E−07 
               
               
                 x3y3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y4 
                 2.02E−08 
                 −1.49E−08 
                 −7.35E−07 
                 −1.28E−11 
                 1.85E−07 
               
               
                 xy5 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y6 
                 6.33E−09 
                 −1.42E−08 
                 −1.08E−06 
                 2.00E−09 
                 −8.56E−08 
               
               
                 x7 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y 
                 −4.09E−16 
                 −4.63E−10 
                 2.22E−07 
                 0 
                 0 
               
               
                 x5y2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y3 
                 1.79E−15 
                 −3.87E−10 
                 −2.23E−07 
                 0 
                 0 
               
               
                 x3y4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y5 
                 2.55E−15 
                 6.10E−10 
                 −1.54E−07 
                 0 
                 0 
               
               
                 xy6 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y7 
                 −2.52E−14 
                 2.10E−11 
                 8.47E−08 
                 0 
                 0 
               
               
                 x8 
                 6.74E−12 
                 −5.03E−12 
                 8.29E−09 
                 −4.18E−12 
                 −6.03E−09 
               
               
                 x7y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y2 
                 1.98E−11 
                 1.80E−11 
                 −2.83E−08 
                 −1.56E−12 
                 1.02E−08 
               
               
                 x5y3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y4 
                 2.19E−11 
                 −1.28E−11 
                 1.09E−08 
                 −2.17E−13 
                 −6.51E−09 
               
               
                 x3y5 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y6 
                 1.07E−11 
                 2.86E−11 
                 −9.24E−09 
                 −1.35E−14 
                 1.84E−09 
               
               
                 xy7 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y8 
                 1.97E−12 
                 3.95E−11 
                 1.06E−08 
                 −3.14E−16 
                 −1.95E−10 
               
               
                 x9 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x8y 
                 2.01E−19 
                 9.48E−13 
                 −1.82E−09 
                 0 
                 0 
               
               
                 x7y2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y3 
                 −6.37E−19 
                 4.17E−12 
                 2.58E−09 
                 0 
                 0 
               
               
                 x5y4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y5 
                 −6.59E−19 
                 −3.63E−12 
                 −6.26E−10 
                 0 
                 0 
               
               
                 x3y6 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y7 
                 3.53E−18 
                 1.01E−12 
                 1.54E−09 
                 0 
                 0 
               
               
                 xy8 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y9 
                 7.18E−19 
                 1.42E−12 
                 −1.14E−09 
                 0 
                 0 
               
               
                 x10 
                 −4.00E−15 
                 4.19E−20 
                 1.63E−20 
                 −4.08E−18 
                 −3.83E−15 
               
               
                 x9y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x8y2 
                 −2.37E−14 
                 −2.89E−20 
                 9.01E−21 
                 −9.25E−17 
                 7.11E−14 
               
               
                 x7y3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y4 
                 −5.63E−14 
                 9.02E−20 
                 6.85E−20 
                 −8.38E−16 
                 −5.27E−13 
               
               
                 x5y4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y6 
                 −6.67E−14 
                 −1.07E−19 
                 1.94E−20 
                 −3.80E−15 
                 1.96E−12 
               
               
                 x3y7 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y8 
                 −3.96E−14 
                 7.06E−20 
                 2.90E−20 
                 −8.61E−15 
                 −3.63E−12 
               
               
                 xy9 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y10 
                 −9.39E−15 
                 −3.36E−20 
                 2.88E−20 
                 −7.80E−15 
                 2.69E−12 
               
               
                   
               
               
                 * xmyn: indicates that the term is the m-th power term of x multiplied by the n-th power term of y 
               
            
           
         
       
     
     According to some embodiments, the structure of the bifocal monocular three-dimensional HMD apparatus is shown in  FIG. 12 . It includes two optical surface prisms and two microdisplays, forming two viewing planes of different depths, respectively. 
     The optical system including the first focal plane can have its optical path formed as follows. The optical path of the first focal plane can include optical surfaces  201 ,  202  and  203 , the inside cavity formed therefrom can be filled with glass or other materials. According to the description for the reverse ray tracing, the light starts from the users&#39; eye located at the exit pupil, travels from the front surface of the optical surface  201 , transmits through it, and arrives at the optical surface  202 . Because a semi-permeable membrane is coated on optical surface  202 , the light splits into two beams. After the light beam reflection occurs, it is incident on this surface again from the back of optical surface  201 . The light undergoes a total reflection, then is incident on optical surface  203 , leaves the wedge prism through transmission, and eventually arrives at microdisplay  206 . The viewing screen corresponding to the image plane  207  is located at position  210 . Table 4 lists the eccentricity and inclination angles of each optical surface for the first focal plane of the optical path according to a second embodiment. Table 6 lists the parameters of all surfaces according to the second embodiment. 
     The optical path of the optical system including the second focal plane can be formed as follows. The optical path of the second view screen can include optical surfaces  201 ,  202 ,  204 , and  205 . The light coming from the human eye transmits through the optical surface  201 , has a reflection on surface  204 . The reflected light transmits through optical surface  205  and reaches the second image plane  207 . The viewing screen corresponding to the image plane  207  is located at position  209 . Table 5 lists the eccentricity and inclination angles of each optical surface for the second focal plane of the optical path according to the second embodiment. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                   
                 Eccentricity 
                 Eccentricity 
                   
               
               
                   
                 Surface 
                 in Y 
                 in Z 
                 Inclination on 
               
               
                   
                 No. 
                 direction 
                 direction 
                 X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 201 
                 4.610 
                 27.313 
                 11.900 
               
               
                   
                 202 
                 −3.810 
                 35.625 
                 −20.874 
               
               
                   
                 203 
                 18.300 
                 28.482 
                 87.285 
               
               
                   
                 206 
                 22.185 
                 34.983 
                 61.351 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                   
                 Eccentricity 
                 Eccentricity 
                   
               
               
                   
                 Surface 
                 in Y 
                 in Z 
                 Inclination on 
               
               
                   
                 No. 
                 direction 
                 direction 
                 X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 201 
                 4.610 
                 27.313 
                 11.900 
               
               
                   
                 202 
                 −3.810 
                 35.625 
                 −20.874 
               
               
                   
                 204 
                 −13.695 
                 45.936 
                 −8.107 
               
               
                   
                 205 
                 −12.464 
                 35.094 
                 −90.674 
               
               
                   
                 207 
                 −15.081 
                 37.723 
                 −84.415 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 Coefficient 
                 201 
                 202 
                 203 
                 204 
                 205 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Radius in YZ 
                 8.34E+17 
                 −5.60E+01 
                 −1.63E+02 
                 −3.55E+01 
                 −2.98E+01 
               
               
                 plane (cuy) 
               
               
                 Conic constant 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 in X (Kx) 
               
               
                 Conic constant 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 in Y (Ky) 
               
               
                 Radius in XZ 
                 −1.91E+02 
                 −6.31E+01 
                 −1.23E+02 
                 −3.32E+01 
                 −1.11E+02 
               
               
                 plane (cux) 
               
               
                 x 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 
                 −6.08E−03 
                 4.01E−09 
                 2.68E−10 
                 −3.93E−02 
                 −6.59E−11 
               
               
                 x2 
                 −5.88E−03 
                 −2.13E−03 
                 1.53E−02 
                 6.28E−04 
                 9.02E−03 
               
               
                 xy 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y2 
                 −2.97E−03 
                 −4.04E−04 
                 −7.21E−03 
                 3.39E−03 
                 2.57E−10 
               
               
                 x3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y 
                 8.51E−05 
                 1.15E−04 
                 1.04E−03 
                 −1.88E−05 
                 5.56E−12 
               
               
                 xy2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y3 
                 −2.01E−05 
                 6.52E−05 
                 −1.80E−03 
                 −1.12E−04 
                 −1.51E−13 
               
               
                 x4 
                 −3.24E−06 
                 −1.51E−06 
                 4.39E−05 
                 −1.16E−07 
                 1.84E−07 
               
               
                 x3y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y2 
                 −6.04E−06 
                 −8.26E−06 
                 3.25E−04 
                 1.04E−05 
                 2.55E−06 
               
               
                 xy3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y4 
                 −5.11E−06 
                 −5.66E−06 
                 −2.15E−05 
                 2.36E−06 
                 −2.29E−11 
               
               
                 x5 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y 
                 −4.49E−07 
                 −4.49E−09 
                 1.60E−05 
                 2.50E−08 
                 −8.37E−14 
               
               
                 x3y2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y3 
                 1.05E−06 
                 4.31E−07 
                 5.09E−06 
                 −3.76E−07 
                 −1.30E−13 
               
               
                 xy4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y5 
                 −5.56E−08 
                 8.95E−08 
                 9.67E−06 
                 4.68E−08 
                 1.65E−14 
               
               
                 x6 
                 3.82E−08 
                 6.32E−09 
                 −4.05E−07 
                 1.04E−08 
                 7.41E−12 
               
               
                 x5y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y2 
                 −4.74E−08 
                 −1.03E−08 
                 −1.23E−07 
                 −1.03E−08 
                 2.07E−10 
               
               
                 x3y3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y4 
                 5.25E−08 
                 2.30E−09 
                 −1.83E−06 
                 −7.32E−09 
                 1.44E−09 
               
               
                 xy5 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y6 
                 −2.10E−10 
                 8.79E−09 
                 4.54E−06 
                 −1.16E−09 
                 6.53E−13 
               
               
                 x7 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y 
                 3.56E−16 
                 −5.41E−10 
                 2.97E−07 
                 −3.54E−10 
                 6.04E−16 
               
               
                 x5y2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y3 
                 3.57E−17 
                 8.41E−10 
                 −2.00E−07 
                 4.86E−10 
                 1.94E−15 
               
               
                 x3y4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y5 
                 −1.88E−16 
                 −7.22E−10 
                 2.27E−07 
                 1.20E−10 
                 7.15E−16 
               
               
                 xy6 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y7 
                 1.30E−15 
                 1.17E−09 
                 9.45E−07 
                 −2.53E−11 
                 −4.28E−17 
               
               
                 x8 
                 −1.65E−16 
                 7.48E−12 
                 2.63E−09 
                 −4.68E−11 
                 9.82E−16 
               
               
                 x7y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y2 
                 4.44E−17 
                 8.04E−12 
                 1.18E−08 
                 −1.29E−11 
                 1.61E−14 
               
               
                 x5y3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y4 
                 −3.28E−17 
                 −6.70E−11 
                 1.08E−08 
                 2.17E−11 
                 2.15E−13 
               
               
                 x3y5 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y6 
                 −2.48E−16 
                 −9.94E−11 
                 5.95E−08 
                 2.24E−11 
                 9.90E−13 
               
               
                 xy7 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y8 
                 3.17E−16 
                 −1.18E−10 
                 8.32E−08 
                 7.25E−13 
                 −7.49E−15 
               
               
                 x9 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x8y 
                 3.80E−20 
                 −2.99E−13 
                 −6.68E−09 
                 8.90E−13 
                 −1.11E−18 
               
               
                 x7y2 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y3 
                 6.89E−19 
                 2.39E−12 
                 1.90E−09 
                 2.54E−12 
                 −7.36E−18 
               
               
                 x5y4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y5 
                 1.28E−18 
                 1.65E−12 
                 2.47E−09 
                 −7.41E−13 
                 −8.11E−18 
               
               
                 x3y6 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y7 
                 4.26E−19 
                 5.65E−12 
                 2.57E−09 
                 6.36E−13 
                 −2.00E−19 
               
               
                 xy8 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y9 
                 −4.08E−19 
                 2.11E−12 
                 2.60E−09 
                 3.07E−14 
                 −3.97E−19 
               
               
                 x10 
                 −7.39E−19 
                 −1.02E−20 
                 −1.54E−18 
                 1.13E−13 
                 −1.93E−18 
               
               
                 x9y 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x8y2 
                 −5.90E−20 
                 7.04E−20 
                 −7.96E−19 
                 4.71E−14 
                 −3.02E−19 
               
               
                 x7y3 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x6y4 
                 7.75E−19 
                 −9.30E−20 
                 −1.08E−18 
                 −1.22E−13 
                 2.98E−17 
               
               
                 x5y4 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x4y6 
                 3.23E−20 
                 1.49E−20 
                 −8.84E−19 
                 −1.25E−14 
                 2.91E−16 
               
               
                 x3y7 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 x2y8 
                 −1.16E−19 
                 3.81E−20 
                 1.77E−18 
                 −4.88E−14 
                 1.02E−15 
               
               
                 xy9 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y10 
                 −5.26E−19 
                 4.05E−19 
                 −1.63E−18 
                 −3.77E−15 
                 2.98E−17 
               
               
                   
               
            
           
         
       
     
     According to one embodiment of the disclosure, the structure of the bifocal monocular three-dimensional HMD apparatus is shown in  FIG. 13 . It includes two optical surface prisms and two microdisplays, forming two viewing planes of different depths, respectively. 
     The optical system including the first focal plane can have its optical path formed as follows. The optical path of the first focal plane can include optical surfaces  301 ,  302  and  303 , the inside cavity can be filled with glass or other materials. According to the description of the reverse ray tracing, the light starts from the exit pupil, travels from the front surface of optical surface  301 , transmits through it, and arrives at the optical surface  302 . Because a semi-permeable membrane is coated on optical surface  302 , the light splits into two beams. One beam undergoes a reflection and it is incident on optical surface  303 . It transmits through optical surface  303 , leaves the wedge prism, and arrives at the microdisplay  306 . The viewing screen corresponding to the microdisplay  306  is located at the position  308 . Table 7 lists the eccentricity and inclination angles of each optical surface for the first focal plane of the optical path according to the third embodiment. Tables 9 and 10 list the parameters of all surfaces according to the third embodiment. 
     The optical system including the second focal plane can have its optical path formed as follows. The optical path of the second view screen can include optical surfaces  301 ,  302 ,  304 , and  305 . The light coming from the human eye transmits through optical surface  301  and it is incident on the optical surface  302  before it has another transmission. It travels to optical surface  304  before it has a reflection. The reflected light passes optical surface  302  and is reflected again before it reaches optical surface  305 , it transmits through, and eventually reaches the microdisplay  307 . The viewing screen corresponding to the microdisplay  307  is located at position  309 . Table 8 lists the eccentricity and inclination angles of each optical surface for the second focal plane of the optical path according to the third embodiment. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Surface 
                 Eccentricity 
                 Eccentricity 
                 Inclination on 
               
               
                   
                 No. 
                 Y direction 
                 Z direction 
                 the X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 301 
                 0.000 
                 17.413 
                 0.000 
               
               
                   
                 302 
                 0.000 
                 26.665 
                 −35.631 
               
               
                   
                 303 
                 10.757 
                 24.903 
                 −69.446 
               
               
                   
                 306 
                 22.903 
                 27.997 
                 −56.746 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 Surface 
                 Eccentricity 
                 Eccentricity 
                 Inclination on 
               
               
                   
                 No. 
                 Y direction 
                 Z direction 
                 the X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 301 
                 0.000 
                 17.413 
                 0.000 
               
               
                   
                 302 
                 0.000 
                 26.665 
                 −35.631 
               
               
                   
                 304 
                 4.279 
                 33.618 
                 24.825 
               
               
                   
                 305 
                 −7.989 
                 29.319 
                 83.401 
               
               
                   
                 307 
                 −12.220 
                 27.168 
                 88.299 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 9 
               
             
            
               
                   
                   
               
               
                   
                 Surface No. 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 301 
                 302 
                 304 
                 305 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Radius of 
                 40 
                 −84.1856 
                 −84.1856 
                 −25.498 
               
               
                   
                 curvature 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 10 
               
               
                   
                   
               
               
                   
                 Coefficient 
                 303 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Radius in YZ plane (cuy) 
                 1.95E+01 
               
               
                   
                 Conic constant in X (Kx) 
                 0 
               
               
                   
                 Conic constant in Y (Ky) 
                 0 
               
               
                   
                 Radius in XZ plane (cux) 
                 1.03E+01 
               
               
                   
                 x 
                 0 
               
               
                   
                 y 
                 0 
               
               
                   
                 x2 
                 0 
               
               
                   
                 xy 
                 0 
               
               
                   
                 y2 
                 0 
               
               
                   
                 x3 
                 0 
               
               
                   
                 x2y 
                 0 
               
               
                   
                 xy2 
                 0 
               
               
                   
                 y3 
                 0 
               
               
                   
                 x4 
                 −2.58E−04 
               
               
                   
                 x3y 
                 0 
               
               
                   
                 x2y2 
                 −4.37E−04 
               
               
                   
                 xy3 
                 0 
               
               
                   
                 y4 
                 −1.85E−04 
               
               
                   
                 x5 
                 0 
               
               
                   
                 x4y 
                 0 
               
               
                   
                 x3y2 
                 0 
               
               
                   
                 x2y3 
                 0 
               
               
                   
                 xy4 
                 0 
               
               
                   
                 y5 
                 0 
               
               
                   
                 x6 
                 −1.70E−06 
               
               
                   
                 x5y 
                 0 
               
               
                   
                 x4y2 
                 −8.64E−07 
               
               
                   
                 x3y3 
                 0 
               
               
                   
                 x2y4 
                 −1.47E−07 
               
               
                   
                 xy5 
                 0 
               
               
                   
                 y6 
                 −8.30E−09 
               
               
                   
                 x7 
                 0 
               
               
                   
                 x6y 
                 0 
               
               
                   
                 x5y2 
                 0 
               
               
                   
                 x4y3 
                 0 
               
               
                   
                 x3y4 
                 0 
               
               
                   
                 x2y5 
                 0 
               
               
                   
                 xy6 
                 0 
               
               
                   
                 y7 
                 0 
               
               
                   
                 x8 
                 2.64E−08 
               
               
                   
                 x7y 
                 0 
               
               
                   
                 x6y2 
                 6.12E−08 
               
               
                   
                 x5y3 
                 0 
               
               
                   
                 x4y4 
                 5.32E−08 
               
               
                   
                 x3y5 
                 0 
               
               
                   
                 x2y6 
                 2.06E−08 
               
               
                   
                 xy7 
                 0 
               
               
                   
                 y8 
                 2.99E−09 
               
               
                   
                 x9 
                 0 
               
               
                   
                 x8y 
                 0 
               
               
                   
                 x7y2 
                 0 
               
               
                   
                 x6y3 
                 0 
               
               
                   
                 x5y4 
                 0 
               
               
                   
                 x4y5 
                 0 
               
               
                   
                 x3y6 
                 0 
               
               
                   
                 x2y7 
                 0 
               
               
                   
                 xy8 
                 0 
               
               
                   
                 y9 
                 0 
               
               
                   
                 x10 
                 −2.55E−10 
               
               
                   
                 x9y 
                 0 
               
               
                   
                 x8y2 
                 −6.35E−10 
               
               
                   
                 x7y3 
                 0 
               
               
                   
                 x6y4 
                 −6.32E−10 
               
               
                   
                 x5y4 
                 0 
               
               
                   
                 x4y6 
                 −3.14E−10 
               
               
                   
                 x3y7 
                 0 
               
               
                   
                 x2y8 
                 −7.82E−11 
               
               
                   
                 xy9 
                 0 
               
               
                   
                 y10 
                 −7.78E−12 
               
               
                   
                   
               
            
           
         
       
     
     According to some embodiments, the structure of the bifocal monocular three-dimensional HMD apparatus is shown in  FIG. 14 . It includes two optical surface prisms and two microdisplays, forming two viewing planes of different depths, respectively. 
     The optical system including the first focal plane can have its optical path formed as follows. The optical path of the first focal plane can include optical surfaces  401 ,  402  and  403 . The inside cavity can be filled with glass or other materials. In accordance with description of the reverse ray tracing, the light starts from the exit pupil, travels from the front surface of optical surface  401 , transmits through it, and arrives at optical surface  402 . Because a semi-permeable membrane is coated on optical surface  302 , the light splits into two beams. One light beam undergoes a reflection, and it is incident on optical surface  403 . It transmits through optical surface  403 , leaves the wedge prism, and arrives at microdisplay  406 . The viewing screen corresponding to microdisplay  406  is located at a position  408 . Table 11 lists the eccentricity and inclination angles for each optical surface for the first focal plane of the optical path according to the fourth embodiment. Tables 13 and 14 list the parameters of all surfaces according to the fourth embodiment. 
     The optical system including the second focal plane can have its optical path formed as follows. The optical path of the second view screen can include optical surfaces  401 ,  402 ,  404 , and  405 . The light coming from the human eyes transmits through the optical surface  401  before it is incident on optical surface  402  and has a reflection. The reflected light passes through optical surface  405  and reaches the second image plane  407 . The viewing screen corresponding to the image plane  407  is located at position  409 . Table 12 lists the eccentricity and inclination angles of the optical path for the second focal plane of the optical path according to the fourth embodiment. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 11 
               
               
                   
                   
               
               
                   
                   
                 Eccentricity 
                 Eccentricity 
                   
               
               
                   
                 Surface 
                 in Y 
                 in Z 
                 Inclination on 
               
               
                   
                 No. 
                 direction 
                 direction 
                 the X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 401 
                 0.000 
                 17.413 
                 0.000 
               
               
                   
                 402 
                 0.000 
                 26.665 
                 −35.631 
               
               
                   
                 403 
                 10.757 
                 24.903 
                 −69.446 
               
               
                   
                 406 
                 22.903 
                 27.997 
                 −56.746 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 12 
               
               
                   
                   
               
               
                   
                   
                 Eccentricity 
                 Eccentricity 
                   
               
               
                   
                 Surface 
                 in Y 
                 in Z 
                 Inclination on 
               
               
                   
                 No. 
                 direction 
                 direction 
                 the X-axis 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 401 
                 0.000 
                 17.413 
                 0.000 
               
               
                   
                 402 
                 0.000 
                 26.665 
                 −35.631 
               
               
                   
                 404 
                 4.723 
                 34.715 
                 23.246 
               
               
                   
                 405 
                 −7.578 
                 27.366 
                 86.117 
               
               
                   
                 407 
                 −13.777 
                 26.116 
                 31.371 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                   
                 TABLE 13 
               
             
            
               
                   
                   
               
               
                   
                 Surface No. 
               
            
           
           
               
               
               
               
            
               
                   
                 401 
                 402 
                 405 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Surface 
                 sph 
                 sph 
                 asp 
               
               
                   
                 type 
               
               
                   
                 Radius of 
                 40 
                 −84.1856 
                 −18.53256112 
               
               
                   
                 curvature 
               
               
                   
                 K 
                   
                   
                 0 
               
               
                   
                 A4 
                   
                   
                 −6.71E−05 
               
               
                   
                 A6 
                   
                   
                 −6.19E−08 
               
               
                   
                 A8 
                   
                   
                 −2.30E−09 
               
               
                   
                 A10 
                   
                   
                 −1.90E−11 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 14 
               
               
                   
                   
               
               
                   
                 Coefficient 
                 403 
                 404 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Radius in YZ plane (cuy) 
                 19.46217052 
                 −50.37825638 
               
               
                   
                 Conic constant in X (Kx) 
                 0 
                 0 
               
               
                   
                 Conic constant in Y (Ky) 
                 0 
                 0 
               
               
                   
                 Radius in XZ plane (cux) 
                 24.16525332 
                 −45.84629567 
               
               
                   
                 x 
                 0 
                 0 
               
               
                   
                 y 
                 −6.23E−11 
                 −0.169265848 
               
               
                   
                 x2 
                 1.37E−12 
                 −0.000189081 
               
               
                   
                 xy 
                 0 
                 0 
               
               
                   
                 y2 
                 −5.67E−12 
                 0.001687998 
               
               
                   
                 x3 
                 0 
                 0 
               
               
                   
                 x2y 
                 −2.17E−13 
                 3.85E−06 
               
               
                   
                 xy2 
                 0 
                 0 
               
               
                   
                 y3 
                 3.29E−12 
                 9.66E−06 
               
               
                   
                 x4 
                 −0.00025809 
                 6.83E−06 
               
               
                   
                 x3y 
                 0 
                 0 
               
               
                   
                 x2y2 
                 −0.00043699 
                 −8.09E−06 
               
               
                   
                 xy3 
                 0 
                 0 
               
               
                   
                 y4 
                 −0.000184974 
                 7.19E−06 
               
               
                   
                 x5 
                 0 
                 0 
               
               
                   
                 x4y 
                 3.19E−14 
                 5.32E−07 
               
               
                   
                 x3y2 
                 0 
                 0 
               
               
                   
                 x2y3 
                 −4.12E−14 
                 4.59E−07 
               
               
                   
                 xy4 
                 0 
                 0 
               
               
                   
                 y5 
                 −4.20E−14 
                 1.52E−06 
               
               
                   
                 x6 
                 −1.70E−06 
                 −1.73E−07 
               
               
                   
                 x5y 
                 0 
                 0 
               
               
                   
                 x4y2 
                 −8.64E−07 
                 2.41E−07 
               
               
                   
                 x3y3 
                 0 
                 0 
               
               
                   
                 x2y4 
                 −1.47E−07 
                 −5.23E−08 
               
               
                   
                 xy5 
                 0 
                 0 
               
               
                   
                 y6 
                 −8.30E−09 
                 2.63E−08 
               
               
                   
                 x7 
                 0 
                 0 
               
               
                   
                 x6y 
                 −1.93E−16 
                 1.51E−09 
               
               
                   
                 x5y2 
                 0 
                 0 
               
               
                   
                 x4y3 
                 −2.24E−16 
                 −1.42E−08 
               
               
                   
                 x3y4 
                 0 
                 0 
               
               
                   
                 x2y5 
                 7.68E−16 
                 −7.97E−09 
               
               
                   
                 xy6 
                 0 
                 0 
               
               
                   
                 y7 
                 1.00E−16 
                 −6.48E−09 
               
               
                   
                 x8 
                 2.64E−08 
                 1.84E−09 
               
               
                   
                 x7y 
                 0 
                 0 
               
               
                   
                 x6y2 
                 6.12E−08 
                 −2.10E−09 
               
               
                   
                 x5y3 
                 0 
                 0 
               
               
                   
                 x4y4 
                 5.32E−08 
                 −1.95E−09 
               
               
                   
                 x3y5 
                 0 
                 0 
               
               
                   
                 x2y6 
                 2.06E−08 
                 7.12E−10 
               
               
                   
                 xy7 
                 0 
                 0 
               
               
                   
                 y8 
                 2.99E−09 
                 −1.80E−10 
               
               
                   
                 x9 
                 0 
                 0 
               
               
                   
                 x8y 
                 1.13E−18 
                 −2.67E−11 
               
               
                   
                 x7y2 
                 0 
                 0 
               
               
                   
                 x6y3 
                 −5.67E−18 
                 8.29E−11 
               
               
                   
                 x5y4 
                 0 
                 0 
               
               
                   
                 x4y5 
                 9.47E−18 
                 −1.02E−10 
               
               
                   
                 x3y6 
                 0 
                 0 
               
               
                   
                 x2y7 
                 −7.50E−18 
                 1.12E−10 
               
               
                   
                 xy8 
                 0 
                 0 
               
               
                   
                 y9 
                 7.77E−19 
                 1.58E−11 
               
               
                   
                 x10 
                 −2.55E−10 
                 −7.07E−12 
               
               
                   
                 x9y 
                 0 
                 0 
               
               
                   
                 x8y2 
                 −6.35E−10 
                 7.67E−12 
               
               
                   
                 x7y3 
                 0 
                 0 
               
               
                   
                 x6y4 
                 −6.32E−10 
                 4.63E−12 
               
               
                   
                 x5y4 
                 0 
                 0 
               
               
                   
                 x4y6 
                 −3.14E−10 
                 −2.06E−12 
               
               
                   
                 x3y7 
                 0 
                 0 
               
               
                   
                 x2y8 
                 −7.82E−11 
                 3.42E−12 
               
               
                   
                 xy9 
                 0 
                 0 
               
               
                   
                 y10 
                 −7.78E−12 
                 6.00E−13 
               
               
                   
                   
               
            
           
         
       
     
     As illustrated in  FIGS. 16-18 , the near-eye display apparatus  161  according to some embodiments the present disclosure includes a projection optical assembly  100  for projecting light emitted from an image source element onto a waveguide optical element so as to transmit the light within the waveguide optical element. Specifically, two layers of waveguide plates  11  and  121  are superposed to form the waveguide optical element, each waveguide plate  11 ,  121  comprising two main surfaces  11   s ,  12   s  parallel to each other; the first waveguide plate  11  comprises six coupling exit beam-split surfaces and is attached with a coupling incidence portion  13 ; likewise, the second waveguide plate  121  is attached with a coupling incidence portion  14 , and comprises six coupling exit beam-split surfaces; the main surfaces of the first and the second waveguide plates are parallel to each other, and a tiny air layer  15  exists between adjacent main surfaces of the first waveguide plate  11  and the second waveguide plate  121  to act as a light-transmission gap. Those skilled in the art can understand that other light-transmission media or vacuum, if meeting the requirement of achieving total reflection of light within respective waveguide plates, can also be placed between the two waveguide plates. A microdisplay  16  which can be LCD, OLED, LCoS or DLP is used as an image source element of the first waveguide plate and the second waveguide plate. The image light coming from the image source element enters the coupling incidence portion  13  attached (e.g. by means of adhesion) to one side of the main surface of the first waveguide plate  11  as well as the coupling incidence portion  14  attached to one side of the main surface of the second waveguide plate  121 , through the projection optical assembly, wherein the coupling incidence portions  13  and  14  have a substantially triangular section. 
     In one example mode, vertex angles of the coupling incidence portions are oriented in the same direction, namely, the coupling incidence portions being on the same side of the two waveguide plates and protruding from the waveguide plates in the same direction, thereby making image light (usually parallel light) existing through the projection optical assembly able to be coupled through the coupling incidence portions respectively into the first waveguide plate  11  and the second waveguide plate  121  for transmission, further arriving at the beam-split surfaces after several times of total reflection, wherein the beam-split surface is a partially reflective surface forming a predetermined angle (e.g., characteristic angle of the beam-split surface) with the main surface, the image light subsequently is coupled to exit through the coupling exit beam-split surfaces  11   a - 11   f  and  12   a - 12   f  (some reference signs not shown in the drawings) inside each waveguide plate, and finally reaches the exit pupil position EP to enter human eyes of a user and form an image. 
     Because it may need to rely on multiple coupling exit beam-split surfaces for coupling and exit of light, in the present example, in order to achieve uniformity of exit images, the beam-split surfaces are distributed at a regular interval in the distribution area, wherein each beam-split surface is coated with beam-split membrane, and reflectivity of each beam-split membrane increases as the position of the beam-split surface is gradually away from the coupling incidence portion. This may effectively improve uniformity of illumination brightness within exit pupil range, and the reflectivity R of membranes on the adjacent beam-split surfaces can be expressed as equation (11): 
                     R   N     =       R     N   -   1         1   -     R     N   -   1                   (   11   )               
wherein N is a sequence number for beam-split membranes, for example, R 1  is reflectivity of a beam-split membrane of the beam-split surface closest to the coupling incidence portion.
 
     The distribution of beam-split surfaces in two waveguide plates can be defined according to a distance between distribution boundary points of beam-split surfaces on the waveguide plates. Point A indicates an upper distribution boundary point of the beam-split surface within the first waveguide plate  11  (corresponding to the beam-split surface  11   a ), and Point B indicates a lower boundary point within the second waveguide plate  121  (corresponding to the beam-split surface  12   f ). Under the distribution feature of beam-split surfaces in this example, distance P AB  between Points A and B satisfy equation (12): 
                     P   AB     ≥     EPD   +     2   ⁢   ERF   ×     tan   ⁡     (     FOV   /   2     )         +       d   n     ⁢     tan   ⁡     (     FOV   /   2     )                   (   12   )               
wherein EPD is the exit pupil diameter, ERF is the exit pupil distance, FOV is the field angle which can be achieved by the waveguide optical element, n is the refractivity of the waveguide plate, and d is the thickness of the waveguide optical element.
 
     Because the distribution area of the beam-split surfaces within two waveguide plates fail to coincide along the direction of main surfaces (i.e., the direction of light transmission), the image light from the microdisplay is separately coupled and exited to different areas of field of view, thereby achieving image lights exiting from different waveguide plates to complete the splicing and display at the exit pupil position, which may remarkably increase the effective field angle and resolution ratio of image. 
     In the example, the characteristic angle θ 1  of the beam-split surfaces within the first waveguide plate is relatively large, responsible for light beams within the field of view [0, FOV/2], while the characteristic angle θ 2  of the beam-split surfaces within the second waveguide plate is relatively small, responsible for light beams within the field of view [−FOV/2, 0], and in this situation, two layers of waveguide plates respectively have a thickness of 1.92 mm and 1.25 mm, see, e.g.,  FIG. 17  “A1;” or, alternatively, thicknesses of two layers of waveguide plates are changed to 1.30 mm and 1.88 mm, respectively, see, e.g.,  FIG. 17  “B1,” and in this situation, the characteristic angle θ 1  of the beam-split surface within the first waveguide plate is relatively small, responsible for light beams within the field of view [−FOV/2, 0], while the characteristic angle θ 2  of the beam-split surface within the second waveguide plate is relatively large, responsible for light beams within the field of view [0, FOV/2]. As shown in  FIG. 17 , “A1” and “B1” portions, the coupling incidence portions of the waveguide optical elements is positioned on the same side of the waveguide plates, but of opposite orientation. 
     Structure parameters of the dual waveguide elements according to the example are illustrated in Table 1-1. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 1-1 
               
               
                   
                   
               
               
                   
                 Thickness 
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                 of 
               
               
                   
                 waveguide 
                   
                   
                 air 
               
               
                   
                 plate 
                 θ 
                 n 
                 gap 
                 n 
                 ERF 
                 EPD 
                 FOV 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 FIG. 
                 1st 
                 1.92 mm 
                 27° 
                 1.7 
                 0.03 
                 3.2 mm 
                 18 mm 
                 10.5 mm 
                 64° 
               
               
                 17 
                 waveguide 
               
               
                 A1 
                 plate 
               
               
                   
                 2nd 
                 1.25 mm 
                 19° 
                 1.7 
               
               
                   
                 waveguide 
               
               
                   
                 plate 
               
               
                 FIG. 
                 1st 
                 1.30 mm 
                 19° 
                 1.7 
                 0.02 
               
               
                 17 
                 waveguide 
               
               
                 B1 
                 plate 
               
               
                   
                 2nd 
                 1.88 mm 
                 27° 
                 1.7 
               
               
                   
                 waveguide 
               
               
                   
                 plate 
               
               
                   
               
            
           
         
       
     
       FIG. 18  illustrates a projection optical assembly  100  including the abovementioned waveguide optical element, specifically the projection optical assembly comprising a free-form-surface prism comprising three optical surfaces  102 ,  103 , and  104 , all being XY polynomial free-form surfaces, a microdisplay  16  acting as an image source element, images shown thereon are incident on the surface  102  through the surface  104  and there occurs a total reflection, subsequently being incident on the surface  103 , the light beams travelling through the surface  102  again after the reflection on the surface  103 , exiting and entering the exit pupil position  1101  of the projection optical assembly. 
     Parameters of each optical surface can be indicated in Tables 1-2 and 1-3 as below. 
                                                 TABLE 1-2                               Eccentricity   Eccentricity   Eccentricity           Surface   Surface           in X   in Y   in Z   Alpha       No.   type   Radius   Material   direction   direction   direction   inclination                                                                102   XY   284.480   PMMA   0.000   60.612   1.500   0.000           polynomial       103   XY   −74.545   PMMA   0.000   −14.082   5.937   −22.855           polynomial       104   XY   27.342       0.000   20.975   4.147   38.922           polynomial       image   spherical   ∞       0.000   22.362   9.231   57.233       surface                    
wherein the XY polynomial free-form surface is described as equation (13), each coefficient of which is listed in Table 1-3:
 
     
       
         
           
             
               
                 
                   
                     z 
                     = 
                     
                       
                         
                           cr 
                           2 
                         
                         
                           1 
                           + 
                           
                             
                               1 
                               - 
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     k 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   c 
                                   2 
                                 
                                 ⁢ 
                                 
                                   r 
                                   2 
                                 
                               
                             
                           
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             2 
                           
                         
                         ⁢ 
                         
                           
                             C 
                             j 
                           
                           ⁢ 
                           
                             x 
                             m 
                           
                           ⁢ 
                           
                             y 
                             n 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     j 
                     = 
                     
                       
                         
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   m 
                                   + 
                                   n 
                                 
                                 ) 
                               
                               2 
                             
                             + 
                             m 
                             + 
                             
                               3 
                               ⁢ 
                               n 
                             
                           
                           ] 
                         
                         / 
                         2 
                       
                       + 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1-3 
               
               
                   
                   
               
               
                   
                 Surface 102 
                 Surface 103 
                 Surface 104 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 K 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C1 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C2 
                 0.293 
                 −5.234e−002 
                 −0.281 
               
               
                   
                 C3 
                 7.219e−003 
                  −3135e−003 
                 3.452e−002 
               
               
                   
                 C4 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C5 
                 2.123e−003 
                   5.940e−003 
                 3.362e−002 
               
               
                   
                 C6 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C7 
                 9.212e−006 
                 −4.559e−005 
                 −5.451e−003 
               
               
                   
                 C8 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C9 
                 −2.312e−005 
                   8.344e−006 
                 3.633e−003 
               
               
                   
                 C10 
                 1.323e−006 
                 −1.453e−007 
                 −4.329e−004 
               
               
                   
                 C11 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C12 
                 4.880e−007 
                   9.914e−007 
                 1.440e−004 
               
               
                   
                 C13 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C14 
                 −1.294e−007 
                 −2.000e−006 
                 −4.380e−004 
               
               
                   
                 C15 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C16 
                 −4.083e−009 
                 −1.130e−008 
                 −1.793e−005 
               
               
                   
                 C17 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C18 
                 −1.150e−009 
                   4.899e−009 
                 1.113e−005 
               
               
                   
                 C19 
                 0.000 
                 0.000 
                 0.000 
               
               
                   
                 C20 
                 −3.151e−011 
                 −3.441e−009 
                 −3.392e−005 
               
               
                   
                   
               
            
           
         
       
     
     Although two waveguide plates are used in the NED apparatus according to the abovementioned example of the present disclosure, thickness of each waveguide plate is further reduced as compared with that of a structure only using one waveguide plate, and the overall thickness gets a limited increase but the field angle significantly expands. Two layers of waveguide plates mutually use the same projection optical assembly, thereby simplifying the overall structure, and putting the coupling incidence portions of the two waveguide plates on the same side. By this, light beams within the range of field of view [0, FOV] in the projection optical assembly need to be deflected through a wedge deflection element  17  and then enters the first waveguide plate  11 , thereby meeting the requirement that the coupling incidence portion  13  of the first waveguide plate  11  makes for optical coupling angle. Besides, the wedge deflection element  17  may introduce certain wedge plate chromatic aberration. 
     Further, the waveguide optical element also can be used with a projection optical assembly comprising conventional spherical/aspherical lens to make up a near-eye display apparatus, or different waveguide plates correspond to a single projection optical assembly and a single image source element, and in this situation, adaptive modification on design is needed for each projection optical assembly, so as to achieve the requirement of maximizing field angle, without using the wedge deflection element  17 . 
     Although specific embodiments have been described above in detail, the description is merely for purposes of illustration. It should be appreciated, therefore, that many aspects described above are not intended as required or essential elements unless explicitly stated otherwise. Various modifications of, and equivalent acts corresponding to, the disclosed aspects of the embodiments, in addition to those described above, can be made by a person of ordinary skill in the art, having the benefit of the present disclosure, without departing from the spirit and scope of the disclosure defined in the following claims, the scope of which is to be accorded the broadest interpretation so as to encompass such modifications and equivalent structures.