A near-eye display system design method based on free-form geometric phase optical elements

Abstract

The application discloses a near-eye display system design method based on a free-form geometric phase optical element. The method comprises the following steps: firstly, calculating an initial phase function of the free-form geometric phase optical element; secondly, preliminarily designing a near-eye display system and an exposure system of the free-form geometric phase optical element according to the phase function; thirdly, jointly optimizing the near-eye display system, the exposure system and a Bragg period of the free-form geometric phase optical element to obtain the near-eye display system and the exposure system with good image quality and high diffraction efficiency; fourthly, exposing and preparing the free-form geometric phase optical element by using the exposure system according to the joint optimization result; and finally, assembling the near-eye display system based on the free-form geometric phase optical element. The near-eye display system based on the free-form geometric phase optical element designed according to the method proves that the method can preferably complete the design of the near-eye display system based on the free-form geometric phase optical element, and the method is simple, fast and the designed system has excellent performance.

Description

Technical Field

[0001] This invention relates to the field of near-eye display technology, and in particular to a design method for a near-eye display system based on a free geometric phase optical element. Background Technology

[0002] Augmented Reality (AR) display technology is a method of overlaying digital information onto the real world to create mixed reality experiences. Users can view virtual images and interact with the external physical environment through AR devices such as AR glasses and head-mounted displays. It has enormous market application value in multimedia entertainment, as well as in military, industrial, and medical fields.

[0003] To make AR devices thinner and lighter and provide a more comfortable user experience, holographic optical elements (HOEs) are introduced into AR optical system designs as couplers or aberration correction elements. HOEs are diffractive optical elements made using the principles of holography. During the exposure stage, the interference of reference and object light records the phase on a photosensitive material, enabling large-angle, high-efficiency light deflection with a thin and light-weight design during the reconstruction stage.

[0004] Currently, based on the different photosensitive materials used, HOEs can be divided into photopolymer holographic optical elements (PPHOEs) and geometric phase optical elements (Pancharatnam–Berry optical elements, PBOEs). PPHOEs are optical devices that achieve specific functions through the periodic refractive index distribution of photopolymers. PBOEs, on the other hand, are optical devices that achieve specific functions through the geometric phase of anisotropic media. Currently used anisotropic media include nematic liquid crystals and cholesteric liquid crystals. Nematic liquid crystals can be regarded as waveplates, with the geometric phase added to the transmitted orthogonally circularly polarized light, and the diffraction efficiency is the highest at half-wave. For cholesteric liquid crystals, the geometric phase is added to the same chiral circularly polarized light reflected by the CLC, and the diffraction efficiency increases with increasing thickness until saturation. Cholesteric PBOEs include liquid crystal polarizer gratings and liquid crystal polarizer lenses.

[0005] Currently, all methods for preparing HOEs have their own limitations. The design and preparation methods for PPHOEs are more mature, but due to the limitations of the materials themselves, their spectral and angular bandwidths are relatively small. PBOEs have larger spectral and angular bandwidths, but almost all current design processes and examples use plane waves and spherical waves for exposure, resulting in poor aberration correction capabilities. Methods that do not use interferometric exposure but instead use laser direct writing or polarization projection imaging can theoretically freely control the exposure wavefront, but due to limitations such as the minimum control unit size of components like laser direct writing probes and spatial light modulators, the resolution and smoothness of the obtained optical phase patterns are limited, and it is impossible to prepare components with submicron-level periods. Summary of the Invention

[0006] To address the shortcomings of FPPHOE in terms of spectral and angular bandwidth, the disadvantages of currently fabricated PBOE in aberration correction capabilities, and the low phase pattern resolution and smoothness of PBOEs prepared by methods such as laser direct writing and polarization projection imaging, this invention provides a design method for a near-eye display system based on a free geometric phase optical element. The near-eye display system includes an image source and several beam control elements, including the free geometric phase element. Light generated by the image source is transmitted through the beam control element in the optical system to the free geometric phase optical element, where it is diffracted and enters the eye for imaging. Due to the Bragg diffraction condition and polarization selectivity of the element, most of the external light directly passes through the free geometric phase optical element to enter the eye for imaging.

[0007] The Freeform Geometric Phase Optical Element (FPBOE) refers to a PBOE that obtains a freeform wavefront by inserting a freeform lens into the exposure optical path. It requires exposure using orthogonally circularly polarized light and is fabricated by spin-coating liquid crystal onto a photo-alignment layer. The Freeform Geometric Phase Optical Element of this invention includes a photo-alignment layer and a liquid crystal layer. The photo-alignment layer is used to align the director of the liquid crystal layer, and the liquid crystal layer is used to introduce geometric phase.

[0008] The design method for a near-eye display system based on a free geometric phase optical element proposed in this invention includes the following steps:

[0009] 1) Based on the near-eye display system parameters and the exposure system wavelength, obtain the position and corresponding phase function of the object light source and the reference light source considering the central field of view imaging effect;

[0010] 2) The phase function of the free geometric phase optical element, excluding the phases corresponding to the object light source and the reference light source, is obtained by the least squares method. This phase function is expressed in the form of an XY polynomial.

[0011] 3) The free geometric phase optical element is a geometric phase element that uses a free-form surface wavefront for exposure during the exposure process. Its phase function is composed of the phase function formed by the interference of the object light point source and the reference light point source in space and the phase function represented by the XY polynomial in step 2). The near-eye display system is initially designed based on the phase function of the free geometric phase optical element.

[0012] 4) Preliminary design of the exposure system for the free-geometric phase optical element;

[0013] 5) Through joint optimization of the near-eye display system, the exposure system, and the Bragg period of the free geometric phase element, a near-eye display system with good image quality and high diffraction efficiency, as well as an exposure system for exposing the free geometric phase optical element, are finally obtained.

[0014] 6) Based on the results of joint optimization, a free geometric phase element is fabricated using an exposure system, and finally, a near-eye display system based on the free geometric phase optical element is assembled.

[0015] Compared with the prior art, the beneficial effects of the present invention include:

[0016] (1) This invention proposes a design method for a near-eye display system based on a free geometric phase element. Based on this method, a near-eye display system based on a free geometric phase element is designed, the free geometric phase element is fabricated, and the near-eye display system is assembled. This invention describes a method for establishing the initial structure of the near-eye display system and a method for selecting the initial structure of the exposure system. In the optimization stage, imaging quality, diffraction efficiency, and the obstruction of different elements are considered simultaneously. In the fabrication stage, environmental factors, element positioning factors, and the influence of multiple reflections of light are considered. The designed geometric phase optical element has continuous phase change, strong aberration correction capability, and high and uniform diffraction efficiency. It can provide a complete design method and process for a free geometric phase optical system with high imaging quality and high diffraction efficiency.

[0017] (2) The present invention uses a photo-alignment layer and a liquid crystal layer as materials for preparing HOE, which overcomes the shortcomings of small spectral bandwidth and angular bandwidth compared with PPHOE.

[0018] (3) The present invention introduces a freeform wavefront into the exposure optical path of the PBOE by using a freeform lens. Compared with the traditional polarization holographic preparation method that only uses spherical waves and plane waves for exposure, the phase function of the prepared PBOE has a higher degree of freedom to meet the needs of non-zero optical extension optical systems. Compared with preparation methods such as laser direct writing and polarization projection imaging, the preparation method of the present invention overcomes the limitation of the minimum control unit size and can prepare PBOEs with submicron periods. Compared with the introduction of freeform wavefront by using a freeform mirror, the polarization state of the exposure beam is better maintained.

[0019] (4) This invention jointly optimizes the Bragg period of the near-eye display system, the exposure system, and the free geometric phase optical element. It comprehensively considers the aberrations and efficiency of the near-eye display system and the consistency between the phase function of the designed FPBOE in the near-eye display system and the actual exposed FPBOE, providing a larger solution space for obtaining a near-eye display system with good image quality and high diffraction efficiency, as well as an exposure system for exposing free geometric phase optical elements. Attached Figure Description

[0020] Figure 1 This is a longitudinal schematic diagram of the liquid crystal molecule arrangement in a liquid crystal polarization grating.

[0021] Figure 2 This refers to the molecular arrangement on the surface of a free geometric phase optical element.

[0022] Figure 3 Optical path diagram of a near-eye display system provided as an example of the present invention;

[0023] Figure 4 This is an MTF curve diagram of an example of the present invention.

[0024] Figure 5 This is a distortion curve diagram of an example of the present invention.

[0025] Figure 6 Efficiency diagrams at different fields of view in this invention example

[0026] Figure 7 This is a schematic diagram of the exposure system for the free geometric phase optical element in an example of the present invention.

[0027] Figure 8 A schematic diagram of the process for preparing free geometric phase optics. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0029] A longitudinal schematic diagram of a liquid crystal polarizer grating is shown below. Figure 1 As shown, the transverse period of the bulk grating is determined by the angle and wavelength of the incident orthogonally polarized light, while the Bragg period is determined by the concentration of doped chiral molecules. For a freeform surface wavefront exposed FPBE, the grating period and direction are different at each location on its transverse surface. A schematic diagram of the liquid crystal molecule arrangement at nine points on the FPBE surface is shown below. Figure 2 As shown.

[0030] This embodiment provides a design method for a near-eye display system based on a free geometric phase optical element. The free geometric phase optical element includes a light alignment layer and a liquid crystal layer. The light alignment layer is used to align the director of the liquid crystal layer, and the liquid crystal layer is used to introduce geometric phase. This embodiment specifically includes the following steps:

[0031] 1) Based on the near-eye display system parameters and the exposure system wavelength, obtain the position and corresponding phase function of the object light source and the reference light source considering the central field of view imaging effect;

[0032] 2) The phase function of the free geometric phase optical element, excluding the phases corresponding to the object light source and the reference light source, is obtained by the least squares method. This phase function is expressed in the form of an XY polynomial.

[0033] 3) The free geometric phase optical element is a geometric phase element that uses a free-form surface wavefront for exposure during the exposure process. Its phase function is composed of the phase function formed by the interference of the object light point source and the reference light point source in space and the phase function represented by the XY polynomial in step 2). The near-eye display system is initially designed based on the phase function of the free geometric phase optical element.

[0034] 4) Preliminary design of the exposure system for the free-geometric phase optical element;

[0035] 5) Through joint optimization of the near-eye display system, the exposure system, and the Bragg period of the free geometric phase element, a near-eye display system with good image quality and high diffraction efficiency, as well as an exposure system for exposing the free geometric phase optical element, are finally obtained.

[0036] 6) Based on the results of joint optimization, a free geometric phase element is fabricated using an exposure system, and finally, a near-eye display system based on the free geometric phase optical element is assembled.

[0037] The steps of this invention will be described in detail below:

[0038] The near-eye display system parameters mentioned in step 1) include: image source parameters, object-side field of view, pupil position, and exit pupil distance. Specifically, step 1) involves: determining the position of the free geometric phase optical element based on the pupil position and exit pupil distance; determining the position of the reference light source based on the relative position of the object-side center field of view and the free geometric phase optical element; determining the position of the object light source based on the relative position of the image source center point and the free geometric phase optical element; and calculating the optical path difference between the object light source and the reference light source on the free geometric phase element to obtain the phase functions corresponding to the object light source and the reference light source.

[0039] Based on the near-eye display system parameters obtained in step 1), the position coordinates of the object beam and reference beam that result in ideal imaging of the central field of view can be calculated. At this point, other field points fail to be imaged at their ideal positions and cannot be used as initial structures for subsequent optimization. However, the complex wavefront representation capabilities provided by the XY polynomial can correct the imaging conditions of other field points.

[0040] Since rays from different fields of view may strike the same point on the FPBOE, and even rays striking the same point may have different ideal exit ray directions, the phase function of the FPBOE cannot guarantee that all incident rays reach their ideal positions. Therefore, we must assign weights to each ray in each field of view, defining the deviation between the x and y cosines of the actual exit ray and the x and y cosines of the ideal exit ray as the error function. We then use the least squares method to find the phase function of the FPBOE that minimizes this error function.

[0041] Step 2) of this invention involves obtaining the phase function of the free geometric phase optical element, excluding the phases corresponding to the object light source and the reference light source, using the least squares method. In a preferred embodiment of this invention, step 2) specifically involves:

[0042] The phase function of the free geometric phase optical element is expressed by XY polynomial, excluding the phase formed by the interference between the object light source and the reference light source. The phase function in XY polynomial form is used as the optimization variable. The loss function is the wave vector deviation between the ideal and actual outgoing rays at a certain point of the free geometric phase optical element at different fields of view and pupils, minus the grating vector formed by the interference between the object light source and the reference light source as described in step 1. The optimization is performed by least squares method to obtain the optimized phase function.

[0043] The XY polynomial is represented as follows:

[0044]

[0045] Where 1≤t≤10, 0≤n≤10, and t and n are integers; m=tn, m≥0, and m is an even number; j=((m+n) 2 +m+3n) / 2,λ e The wavelength used in the exposure system, (x,y) are the coordinates on the plane of the free geometric phase optical element, (x o ,y o ,z o (x) represents the coordinates of the object light point source, (x) r ,y r ,z r () represents the coordinates of the reference light source.

[0046] A free-form geometric phase optical element is a geometric phase element that uses a free-form surface wavefront for exposure during the exposure process. Its phase function consists of the phase function formed by the interference of the object light source and the reference light source in space, and the phase function represented by the XY polynomial described in step 2). The phase function of the FPBOE obtained in the above steps... Optimizing the initial structure of the near-eye display system yields a near-eye display system with good imaging performance based on FPBOE. Specifically, the near-eye display system includes an image source and several beam control elements, including free geometric phase optical elements. Using the near-eye display system parameters described in step 1) and the phase function of the free geometric phase optical elements obtained in steps 1) and 2) as the initial structure, the aberrations of the near-eye display system as the error function, and the longitudinal distance between the pupil and the image source as the constraint, optimization is performed to obtain the preliminary design of the near-eye display system.

[0047] Next, we need to design the exposure system in step 4) to prepare the FPBOE with the corresponding phase function. For the FPBOE exposure system, since the mirror introduces a significant change in polarization state, we need to use a freeform lens to generate a freeform wavefront for exposure. The field of view of the exposure system is set to a single field of view, and the final outgoing light should be parallel or converge to a single point.

[0048] In a specific embodiment of the present invention, step 4) specifically comprises: the exposure system includes a beam control element and a free geometric phase optical element to be exposed; the beam control element is disposed in the object light path and / or the reference light path, and is used to modulate the light of the corresponding light path into a free curve wavefront, and the modulated object light wavefront and the reference light wavefront interfere on the surface of the free geometric phase optical element to be exposed to form the phase function of the free geometric phase optical element;

[0049] In the initial design of the exposure system, the exposure system is regarded as a single-field imaging system, with the reference wavefront / object wavefront as the object-side field of view and the object wavefront / reference wavefront as the image-side field of view. The positive and negative diffraction orders of the free geometric phase optical element are set, and the aperture of the beam control element is changed to meet the design requirements. The beam control element should be a refractive freeform lens to reduce the influence on the polarization state of the exposure beam.

[0050] To achieve simultaneous control of image quality and efficiency in near-eye display systems, the near-eye display system and the corresponding FPBOE exposure system need to be jointly optimized as one of multiple zoom structures.

[0051] The criterion for joint optimization is to minimize the error function while satisfying custom constraints. The error function includes the lateral ray aberration of the near-eye display system and the lateral ray aberration of the exposure system. The lateral ray aberration of the near-eye display system determines the image quality of the near-eye display system, while the lateral ray aberration of the exposure system determines the consistency between the phase function of the FPBE generated by the exposure system and the phase function of the FPBE designed in the near-eye display system. The custom constraints are the average efficiency and the root mean square value of the field efficiency across all fields of view.

[0052] Specifically, this invention employs step 5) for joint optimization. During joint optimization, the Bragg period that maximizes the diffraction efficiency of the principal ray in the central field of view is first calculated as the initial value. The near-eye display system initially designed in step 3), the exposure system initially designed in step 4), and the initial value of the Bragg period are used as inputs. The weighted sum of the error functions of the near-eye display system and the exposure system is used as the total error function. The constraints of the near-eye display system, the exposure system, and the efficiency constraint are used as the total constraints. Joint optimization is then performed to obtain a near-eye display system with good image quality and high diffraction efficiency, as well as an exposure system for exposing free geometric phase optical elements.

[0053] For calculating the efficiency of a single ray, the efficiency formula of coupled-wave theory is used, and its efficiency η is:

[0054]

[0055] ΔK=k out,z -k in,z -K G,z

[0056]

[0057]

[0058] Where ΔK is the phase adaptation factor, κ is the coupling coefficient, t is the medium thickness, and k out,z Let k be the z-axis component of the wave vector of the outgoing ray. in,z K represents the z-axis component of the incident ray wave vector. G,z n is the z-component of the grating vector. d Let λ be the refractive index modulation of the liquid crystal, k0 be the magnitude of the wave vector mode in the liquid crystal, and λ be the wavelength of the incident light.

[0059] For m fields of view, n rays are sampled for each field of view, and the average efficiency η for each field of view is... i for:

[0060]

[0061] The average efficiency η across all fields of viewtotal for:

[0062]

[0063] The root mean square value of the field of view efficiency η rms for:

[0064]

[0065] By jointly optimizing the near-eye display system and the exposure system, a near-eye display system with good image quality and high diffraction efficiency can be obtained, as well as an exposure system that ensures high consistency between the exposed FPBOE phase function and the FPBOE phase function designed in the near-eye display system.

[0066] After obtaining the joint optimization results in step 5), it is necessary to proceed to step 6) to prepare the near-eye display system. This involves using an exposure system to prepare a free geometric phase element and finally assembling the near-eye display system based on the free geometric phase optical element.

[0067] The specific steps are as follows: First, adjust the liquid crystal mixture according to the Bragg period of the freely geometrically phased optical element obtained through joint optimization. Second, set the exposure system according to the parameters of the exposure system obtained through joint optimization. Third, expose the substrate with a spin-coated photo-alignment layer using the exposure system. Then, spin-coat the exposed photo-alignment layer with the liquid crystal mixture, followed by curing. Repeat the spin-coating and curing process until a sufficient thickness is achieved to obtain the freely geometrically phased optical element. Finally, assemble the near-eye display system based on the freely geometrically phased optical element according to the parameters of the near-eye display system obtained through joint optimization. Note that when exposing the substrate with the spin-coated photo-alignment layer, a prism should be placed on the back side of the substrate to avoid multiple interferences caused by reflection of the exposure beam, which would affect the exposure effect.

[0068] In a specific embodiment of the present invention, a schematic diagram of the exposure system corresponding to the FPBOE used in the near-eye display system is shown below. Figure 7 As shown, the coherent light emitted by the 457nm laser 03 is split into two beams by the NPBS 04. The object beam passes through the filter and expander 05 from above and reaches the reflector 06. It then becomes linearly polarized by the linear polarizer 07, circularly polarized by the quarter-wave plate 08, and becomes a freeform wavefront by the freeform lens 09. Finally, it is incident on the optical alignment layer of the sample 15. The reference beam changes direction from below by the reflector 10, passes through the filter and expander 11, and becomes circularly polarized by the linear polarizer 12 and the quarter-wave plate 13. Finally, it is directly incident on the optical alignment layer of the sample 15.

[0069] In the fabrication process of an FPBOE element in a specific embodiment, we selected reactive mesocrystalline RM257 as the host liquid crystal material. For the chiral agent, we chose R5011, which has a large torsional force (HTP) (HTP≈10⁸ / μm). The overall fabrication process of the FPBOE element is as follows: Figure 8 As shown,

[0070] (1) Clean the glass substrate;

[0071] (2) Dry the glass substrate at 120°C for 30 minutes;

[0072] (3) Prepare the photoalignment layer solution and liquid crystal mixture;

[0073] (4) Spin-coating a photo-alignment layer solution onto a glass substrate;

[0074] (5) Use Figure 7 Exposure system shown is used for exposure

[0075] (6) Spin-coating a liquid crystal mixture onto the photoalignment layer after exposure;

[0076] (7) After heat annealing at 80℃ for 5 minutes, the product is placed in an environment of ultraviolet light and nitrogen for curing.

[0077] (8) Repeat spin coating and curing until sufficient thickness is achieved.

[0078] In one specific embodiment of the present invention, a near-eye display system based on a free geometric phase optical element was designed according to the above design method. This near-eye display system consists of an image microdisplay and a free geometric phase optical element.

[0079] The optical path diagram of the designed near-eye display system is as follows: Figure 3 As shown, the image signal light generated by the image microdisplay 01 is incident on the free geometric phase optical element 02, and after being diffracted, it enters the human eye for imaging. At the same time, due to the Bragg diffraction condition and polarization selectivity of the element, most of the ambient light directly passes through the free geometric phase optical element and enters the human eye for imaging.

[0080] The exposure system of the free geometric phase optical element 02 uses a barrel to fix a freeform lens, ensuring the relative positional relationship between the freeform lens and the sample to reduce errors. The exit of the barrel acts as an aperture to limit the size of the exposure area on the sample.

[0081] MTF images of near-eye display systems, such as Figure 4 As shown, the MTF values ​​in the meridional and sagittal directions for all 15 fields of view are greater than 0.1 at 20 lp / mm. The distortion image of the near-eye display system is shown below. Figure 5 As shown, the distortion in all 15 fields of view is less than 15%. The efficiency of the near-eye display system is as follows: Figure 6 As shown, the average efficiency is greater than 97.15%, and the root mean square value is less than 0.53%.

[0082] Depend on Figures 3-6 As can be seen, the near-eye display system based on the free geometric phase optical element designed according to this method proves that this method can successfully realize the design of a near-eye display system based on the free geometric phase optical element. The designed geometric phase optical element has continuous phase change, strong aberration correction capability, and high and uniform diffraction efficiency, which can provide a complete design method and process for a free geometric phase optical system with high imaging quality and high diffraction efficiency.

[0083] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A design method for a near-eye display system based on a free geometric phase optical element, wherein the free geometric phase optical element comprises a light alignment layer and a liquid crystal layer, the light alignment layer is used to align the director of the liquid crystal layer, and the liquid crystal layer is used to introduce geometric phase, characterized in that, The design method includes the following steps: 1) Based on the near-eye display system parameters and the exposure system wavelength, obtain the position and corresponding phase function of the object light source and the reference light source considering the central field of view imaging effect; 2) The phase function of the free geometric phase optical element, excluding the phases corresponding to the object light source and the reference light source, is obtained by the least squares method. This phase function is expressed in the form of an XY polynomial. 3) The free geometric phase optical element is a geometric phase element that uses a free-form surface wavefront for exposure during the exposure process. Its phase function is composed of the phase function formed by the interference of the object light point source and the reference light point source in space and the phase function represented by the XY polynomial in step 2). The near-eye display system is initially designed based on the phase function of the free geometric phase optical element. 4) Preliminary design of the exposure system for the free-geometric phase optical element; 5) Through joint optimization of the near-eye display system, the exposure system, and the Bragg period of the free geometric phase element, a near-eye display system with good image quality and high diffraction efficiency, as well as an exposure system for exposing the free geometric phase optical element, are finally obtained. 6) Based on the results of joint optimization, a free geometric phase element is fabricated using an exposure system, and finally, a near-eye display system based on the free geometric phase optical element is assembled.

2. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: The near-eye display system parameters mentioned in step 1) include: image source parameters, object field of view, pupil position, and exit pupil distance; Step 1) specifically involves: determining the position of the free geometric phase optical element based on the pupil position and exit pupil distance; determining the position of the reference light source based on the relative position of the object center field of view and the free geometric phase optical element; determining the position of the object light source based on the relative position of the image source center point and the free geometric phase optical element; and calculating the optical path difference between the object light source and the reference light source on the free geometric phase element to obtain the phase function corresponding to the object light source and the reference light source.

3. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: Step 2) specifically refers to: The phase function of the free geometric phase optical element, excluding the phase formed by the interference between the object light source and the reference light source, is expressed by an XY polynomial. The phase function in XY polynomial form is used as the optimization variable. The loss function is the wave vector deviation between the ideal and actual outgoing rays at a certain point of the free geometric phase optical element at different fields of view and pupils, minus the grating vector formed by the interference between the object light source and the reference light source as described in step 1). The optimization is performed by least squares method to obtain the optimized phase function. The XY polynomial is represented as follows: Where 1≤t≤10, 0≤n≤10, and t and n are integers; m=tn, m≥0, and m is an even number; j=((m+n) 2 +m+3n) / 2,λ e The wavelength used in the exposure system, (x,y) are the coordinates on the plane of the free geometric phase optical element, (x o ,y o ,z o (x) represents the coordinates of the object light point source, (x) r ,y r ,z r () represents the coordinates of the reference light source.

4. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: Step 3) specifically refers to: The near-eye display system includes an image source and several beam control elements, including free geometric phase optical elements. Using the near-eye display system parameters described in step 1) and the phase function of the free geometric phase optical elements obtained in steps 1) and 2) as the initial structure, the aberrations of the near-eye display system as the error function, and the longitudinal distance between the pupil and the image source as the constraint, optimization is performed to obtain the preliminary design of the near-eye display system.

5. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: Step 4) specifically refers to: The exposure system includes a beam control element and a free geometric phase optical element to be exposed; the beam control element is disposed in the object light path and / or the reference light path, and is used to modulate the light of the corresponding light path into a free curve wavefront. The modulated object light wavefront and the reference light wavefront interfere on the surface of the free geometric phase optical element to be exposed to form the phase function of the free geometric phase optical element. In the initial design of the exposure system, the exposure system is regarded as a single field of view imaging system, with the reference wavefront and object wavefront as the object-side field of view, and the object wavefront and reference wavefront as the image-side field of view; by setting the positive and negative diffraction orders of the free geometric phase optical element, the aperture of the beam control element is changed to meet the design requirements. The beam control element should be a refractive freeform lens to reduce its influence on the polarization state of the exposure beam.

6. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: Step 5) specifically refers to: The Bragg period, which maximizes the diffraction efficiency of the principal ray in the central field of view, is calculated as the initial value. The near-eye display system (preliminary design in step 3), the exposure system (preliminary design in step 4), and the initial value of the Bragg period are used as inputs. The weighted sum of the error functions of the near-eye display system and the exposure system is used as the total error function. The constraints of the near-eye display system, the exposure system, and the efficiency constraint are used as the total constraints. Joint optimization is performed to obtain a near-eye display system with good image quality and high diffraction efficiency, as well as an exposure system for exposing free geometric phase optical elements. The error functions of both the near-eye display system and the exposure system are aberrations. The lateral ray aberration of the near-eye display system determines the imaging quality of the near-eye display system, while the lateral ray aberration of the exposure system determines the consistency between the phase function of the free geometric phase optical element generated by the exposure system and the phase function of the free geometric phase optical element designed in the near-eye display system. The efficiency constraints are the average efficiency of all fields of view and the root mean square value of the field efficiency.

7. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: Step 6) specifically refers to: Based on the Bragg period of the free geometric phase optical element obtained through joint optimization, the liquid crystal mixture is prepared, and the exposure system is set according to the parameters of the exposure system obtained through joint optimization. The substrate with a spin-coated light alignment layer is exposed using the exposure system, and the liquid crystal mixture is spin-coated on the exposed light alignment layer. Then, a curing operation is performed, and the spin-coating and curing are repeated until a sufficient thickness is obtained to obtain the free geometric phase optical element. Finally, the near-eye display system based on the free geometric phase optical element is assembled according to the near-eye display system parameters obtained through joint optimization.

8. The design method for a near-eye display system based on a free geometric phase optical element as described in claim 1, characterized in that: When exposing a substrate with a spin-coated photoalignment layer, a prism should be placed on the back of the substrate to avoid multiple interferences caused by reflection of the exposure beam, which would affect the exposure effect.

Images