Exposure method and apparatus for holographic two-dimensional gratings and calculation method for exposure beam.

Abstract

This invention discloses an exposure method and apparatus for a holographic two-dimensional grating, as well as a method for calculating the exposure beam, relating to the field of holographic two-dimensional grating technology. The method for calculating the exposure beam includes determining the wave vectors k1 and k2 of the exposure beam of the three-dimensional grating vector KG1 and the wave vectors k1 and k3 of the exposure beam of the three-dimensional grating vector KG2 based on the three-dimensional grating vector KG1 and the three-dimensional grating vector KG2. Wave vector k1 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG1 and KG2. An inclined vector is introduced and a vector triangle is constructed for rotation and iterative calculation, thereby realizing the single exposure of three beams of a holographic two-dimensional grating with two three-dimensional grating vectors. The exposure method and apparatus are set according to the parameters of the exposure beam obtained by the calculation method, solving the problem that the fabrication of a holographic two-dimensional grating requires multiple exposures with two beams, which is difficult to operate.

Description

Technical Field

[0001] This invention relates to the field of holographic two-dimensional grating technology, and more specifically, to an exposure method and apparatus for a holographic two-dimensional grating and a method for calculating the exposure beam. Background Technology

[0002] A holographic 2D grating is an optical element that forms a periodic micro-nano structure on a photosensitive material by recording an interference light field. In augmented reality (AR) or virtual reality (VR) devices, holographic 2D gratings can be used to improve visual display effects, achieve wider viewing angles and higher resolutions, and integrate the bending and coupling functions in the same area to achieve 2D pupil expansion. This avoids the bending grating occupying a large area, which helps to solve the limitation of the limited area of ​​the lens on the eye movement range and field of view. It is currently a research focus of AR or VR display elements.

[0003] The conventional method for exposing holographic two-dimensional gratings in existing technologies involves sequentially exposing two or more one-dimensional gratings on the same area and then cross-multiplexing them. The one-dimensional gratings required for holographic two-dimensional grating fabrication are created through dual-beam exposure, using prism coupling to sequentially expose multiple gratings. Because the surface orientation angles of the cross-multiplexed grating fringes differ, the prism needs to be rotated to align with the grating surface orientation after each exposure. This results in multiple dual-beam exposures and the need to reposition the prism each time, making the process complex. Furthermore, during multiple exposures, the grating fringes from successive exposures are prone to mutual interference, potentially damaging the integrity of the grating's periodic structure and thus affecting the optical performance stability of the holographic two-dimensional grating.

[0004] In summary, existing technologies for fabricating holographic two-dimensional gratings require multiple exposures using dual-beam arrays. This results in high prism positioning accuracy requirements, complex operations, long production cycles, and easy interference between grating fringes, leading to low production efficiency and increased manufacturing costs. These factors limit the large-scale production and market application of holographic two-dimensional gratings. Therefore, there is an urgent need for a technical solution that simplifies the exposure process, improves production efficiency, and ensures stable product performance. Summary of the Invention

[0005] The present invention aims to overcome at least one of the defects of the prior art and provides an exposure method and apparatus for holographic two-dimensional gratings and a method for calculating the exposure beam, which solves the problem that the fabrication of holographic two-dimensional gratings requires multiple exposures with dual beams, which is difficult to operate.

[0006] To solve the above-mentioned technical problems, the following technical solution is adopted:

[0007] Firstly, a method for calculating the exposure beam of a holographic two-dimensional grating is proposed. This method includes determining the wave vectors k1 and k2 of the exposure beam of the three-dimensional grating vector KG1, and the wave vectors k1 and k3 of the exposure beam of the three-dimensional grating vector KG2, based on the three-dimensional grating vector KG1 and the three-dimensional grating vector KG2. Wave vector k1 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG1 and KG2, specifically including:

[0008] Select a plane containing the three-dimensional grating vector KG1. Based on the amplitudes of the three-dimensional grating vector KG1 and the wave vectors k1 and k2 of the exposure beam, calculate the tilt vector S1 in the same plane. The three-dimensional grating vector KG1 and the wave vectors k1 and k2 form a vector triangle in the same plane. The line segment containing the tilt vector S1 is the perpendicular line to the side containing the three-dimensional grating vector KG1 in the vector triangle.

[0009] Set i=1 and execute the first loop;

[0010] The first cycle includes:

[0011] The tilt vector S i Rotate the three-dimensional grating vector KG1 by a preset angle α to obtain the tilt vector S. i+1 ;

[0012] Based on the three-dimensional grating vector KG1 and the tilt vector S i+1 A set of wave vectors k1 and k2 are calculated, and the wave vectors k1 and k2 satisfy: k1 = S i+1 +KG1 / 2, k2=S i+1 -KG 1 / 2;

[0013] Based on wave vector k1, determine wave vector k3 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k1 and k3 are equal to the XY components of the three-dimensional grating vector KG2.

[0014] Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k1 and k3, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG2 is less than a preset threshold. If so, record the set of wave vectors k1, k2 and k3. If not, discard the set of wave vectors k1, k2 and k3.

[0015] Determine if i ≥ 2π / α is true; if yes, output the recorded m sets of wave vectors k1, k2 and k3; if no, set i = i + 1 and execute the first loop.

[0016] The above calculation method determines the vector relationship based on the wave vectors of two three-dimensional grating vectors and their common exposure beam, and the amplitude of the wave vector of the exposure beam. It introduces tilt vectors for rotation iteration, and uses the threshold of the difference of the Z-axis components to screen the effective wave vector group, thus determining the wave vector group of the exposure beam of the two three-dimensional grating vectors. This ensures that the output wave vector group can accurately reproduce the target three-dimensional grating vector, providing reliable parameter support for the synchronous exposure of three beams, avoiding ghosting, ensuring the formation of complete and regular interference fringes, reducing the difficulty of operation, and improving the stability of optical performance.

[0017] Preferably, the above calculation method further includes determining the wave vectors k2 and k4 of the exposure beam based on the three-dimensional grating vector KG3, wherein the XY components of the three-dimensional grating vector KG2 and the three-dimensional grating vector KG3 are equal but the Z components are different, and the wave vector k2 is the wave vector of the common exposure beam of the three-dimensional grating vector KG1 and the three-dimensional grating vector KG3, specifically including:

[0018] Let n=1, then execute the second loop;

[0019] The second cycle includes:

[0020] Select the nth group of wave vectors k1, k2, and k3;

[0021] Calculate the wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k2 and k4 are equal to the XY components of the three-dimensional grating vector KG3.

[0022] Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG3 is less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4.

[0023] Determine if n=m is true; if yes, output the recorded wave vectors k1, k2, k3 and k4; if no, set n=n+1 and execute the second loop.

[0024] Preferably, the above calculation method further includes determining the wave vectors k3 and k4 of the exposure beam based on the three-dimensional grating vector KG4, wherein the XY components of the three-dimensional grating vector KG1 and the three-dimensional grating vector KG4 are equal but the Z components are different, and the wave vector k3 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG2 and KG4, specifically including:

[0025] Let n=1, then execute the third loop;

[0026] The third cycle includes:

[0027] Select the nth group of wave vectors k1, k2, and k3;

[0028] Calculate the wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k3 and k4 are equal to the XY components of the three-dimensional grating vector KG4.

[0029] Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG4 is less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4.

[0030] Determine if n=m is true; if yes, output the recorded wave vectors k1, k2, k3 and k4; if no, set n=n+1 and execute the third loop.

[0031] The above calculation method calculates wave vector k4 based on three three-dimensional grating vectors and a selected set of wave vectors that meet the threshold conditions. By iteratively substituting the selected set of wave vectors into the calculation, the threshold of the difference in the Z-axis component is used to select the effective set of wave vectors. This determines the set of wave vectors for the exposure beams of the three three-dimensional grating vectors, providing reliable parameter support for the synchronous exposure of four beams.

[0032] Preferably, the above calculation method further includes determining the wave vectors k2 and k4 of the exposure beam of the three-dimensional grating vector three KG3 and the three-dimensional grating vector four KG4 based on the three-dimensional grating vector three KG3 and the three-dimensional grating vector four KG4. The three-dimensional grating vector two KG2 and the three-dimensional grating vector three KG3 have equal XY components but different Z components. The three-dimensional grating vector one KG1 and the three-dimensional grating vector four KG4 have equal XY components but different Z components. Wave vector k2 is the wave vector of the common exposure beam of the three-dimensional grating vector one KG1 and the three-dimensional grating vector three KG3. Wave vector k3 is the wave vector of the common exposure beam of the three-dimensional grating vector two KG2 and the three-dimensional grating vector four KG4. Wave vector k4 is the wave vector of the common exposure beam of the three-dimensional grating vector three KG3 and the three-dimensional grating vector four KG4. The calculation steps are as follows:

[0033] Let n=1, then execute the fourth loop;

[0034] Select the nth group of wave vectors k1, k2, and k3;

[0035] Calculate wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k2 and k4 are equal to the XY components of the three-dimensional grating vector KG3, and make the XY components of the holographic grating vector exposed by the interference of wave vectors k3 and k4 equal to the XY components of the three-dimensional grating vector KG4.

[0036] Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4, and the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4;

[0037] Determine whether the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4 and the Z-axis component of the three-dimensional grating vector KG3, and the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4 and the Z-axis component of the three-dimensional grating vector KG4, are all less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4.

[0038] Determine if n=m is true; if yes, output the recorded wave vectors k1, k2, k3 and k4; if no, set n=n+1 and execute the fourth loop.

[0039] The above calculation method calculates wave vector k4 based on four three-dimensional grating vectors and a selected set of wave vectors that meet the threshold conditions. By iteratively substituting the selected set of wave vectors into the calculation, the threshold of the difference between the two sets of Z-axis components is used to select the effective set of wave vectors, thus determining the set of wave vectors for the exposure beams of the four three-dimensional grating vectors, providing reliable parameter support for the synchronous exposure of four beams.

[0040] Secondly, an exposure method for a holographic two-dimensional grating is proposed. This exposure method uses three beams corresponding to the wave vectors k1, k2, and k3 calculated by the above calculation method to simultaneously expose the holographic photosensitive material once, thereby obtaining a holographic two-dimensional grating with two three-dimensional grating vectors.

[0041] The exposure method also includes simultaneously exposing the holographic photosensitive material once with four beams corresponding to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method, to obtain a holographic two-dimensional grating with three three-dimensional grating vectors.

[0042] The exposure method also includes simultaneously exposing the holographic photosensitive material once with four beams corresponding to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method, to obtain a holographic two-dimensional grating with four three-dimensional grating vectors.

[0043] The above exposure method utilizes the wave vector group selected by the above calculation method to achieve single exposure of multiple beams of holographic photosensitive material. More specifically, it can realize single exposure of two-dimensional gratings with two gratings intersecting and two-dimensional gratings with four gratings multiplexed, reducing the complexity of operation, avoiding the problem of long production cycle caused by repeated rotation and positioning of prisms during multiple exposures, and the problem of easy mutual interference of grating stripes, improving the integrity of holographic two-dimensional grating structure, increasing production efficiency while reducing costs.

[0044] Thirdly, an exposure device for a holographic two-dimensional grating is proposed. The exposure device includes three light sources, the emission angles of which are set according to the wave vectors k1, k2, and k3 calculated by the above calculation method. The three beams emitted by the light sources simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes, thus obtaining a holographic two-dimensional grating with two three-dimensional grating vectors.

[0045] The exposure device may also include four light sources. The emission angles of the four light sources are set according to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method. The three beams emitted by them simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with three three-dimensional grating vectors.

[0046] The exposure device may also include four light sources. The emission angles of the four light sources are set according to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method. The three beams emitted by them simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with four three-dimensional grating vectors.

[0047] The aforementioned device utilizes a light source to emit multiple beams corresponding to the wave vector group selected by the aforementioned calculation method, thereby achieving a single exposure of multiple beams of holographic photosensitive material. Optionally, combinations that are easy to construct exposure optical paths can be selected based on the wave vector group, ensuring that the output wave vector group can accurately reproduce the target three-dimensional grating vector, providing reliable parameter support for the synchronous exposure of three beams, avoiding ghosting phenomena, ensuring the formation of complete and regular interference fringes, reducing the difficulty of operation, and improving the stability of optical performance.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] This invention innovatively proposes a single-exposure method for holographic two-dimensional gratings using multiple beams. It provides a method for calculating the exposure beam of the holographic two-dimensional grating. By determining the wave vector of the three-dimensional grating vector through the vector relationship between the three-dimensional grating vector and the wave vector of the exposure beam, the exposure process of holographic two-dimensional grating fabrication is simplified, reducing operational difficulty and improving production efficiency. The single-exposure operation avoids the problem of mutual interference of grating fringes caused by multiple exposures, which affects the integrity of the periodic structure of the holographic two-dimensional grating. This enables the holographic two-dimensional grating to accurately transmit the image beam without ghosting, ensuring the stability of the optical performance of the holographic two-dimensional grating. Attached Figure Description

[0050] Figure 1 This invention relates to a method for calculating the exposure beam of a holographic two-dimensional grating with two three-dimensional grating vectors.

[0051] Figure 2 This is the vector triangle that constitutes the three-dimensional grating vector of the present invention.

[0052] Figure 3 This is a schematic diagram of the K-vector sphere calculation of the present invention.

[0053] Figure 4 This invention relates to a method for calculating the exposure beam of a holographic two-dimensional grating with three three-dimensional grating vectors.

[0054] Figure 5 This invention provides another method for calculating the exposure beam of a holographic two-dimensional grating with three three-dimensional grating vectors.

[0055] Figure 6 This is the K-domain diagram of the holographic two-dimensional grating of the present invention.

[0056] Figure 7 This is a diagram showing the correspondence between the XY components of the four three-dimensional grating vectors of the present invention and the wave vectors of the four exposure beams.

[0057] Figure 8 This invention relates to a method for calculating the exposure beam of a holographic two-dimensional grating with four three-dimensional grating vectors. Detailed Implementation

[0058] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the invention. To better illustrate the following embodiments, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions; it is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0059] Example 1

[0060] This example provides a method for calculating the exposure beam of a holographic two-dimensional grating, which can calculate the exposure beam of a holographic two-dimensional grating with two, three, or four three-dimensional grating vectors.

[0061] like Figure 1 The diagram illustrates a method for calculating the exposure beam of a holographic two-dimensional grating with two three-dimensional grating vectors. This method includes determining the wave vectors k1 and k2 of the exposure beam of the three-dimensional grating vector KG1, and the wave vectors k1 and k3 of the exposure beam of the three-dimensional grating vector KG2, based on the first three-dimensional grating vector KG1 and the second three-dimensional grating vector KG2. Wave vector k1 is the wave vector of the common exposure beam of the first three-dimensional grating vector KG1 and the second three-dimensional grating vector KG2. Specifically, it includes:

[0062] Step S100: Select a plane where the three-dimensional grating vector KG1 is located, and calculate the tilt vector S1 on the same plane based on the amplitude of the three-dimensional grating vector KG1 and the wave vectors k1 and k2 of the exposure beam.

[0063] like Figure 2 As shown, the three-dimensional grating vector KG1, along with wave vectors k1 and k2, forms a vector triangle in the same plane, with the vector relationship satisfying: KG1 = k1 - k2. A perpendicular line is drawn from the vertex of the vector triangle (the intersection of k1 and k2) to its opposite side (KG1), and the intersection of this perpendicular line with the opposite side is the foot of the perpendicular. For ease of description, this paper defines the vector pointing from the intersection of the wave vectors to the foot of the three-dimensional grating vector as the tilted vector S1, and the line segment containing the tilted vector S1 is the perpendicular line to the side containing the three-dimensional grating vector KG1 in the vector triangle. The amplitudes of wave vectors k1 and k2 are the wavenumber n / λ of the exposure beam in the medium, where n is the average refractive index of the medium and λ is the wavelength in vacuum. Therefore, given the three-dimensional grating vector KG1, and the wave vectors k1 and k2 lying in a defined plane, the tilted vector S1 perpendicular to it can be calculated.

[0064] Step S200: Let i=1 and execute the first loop.

[0065] The first cycle includes steps S310 to S340.

[0066] Step S310: Set the tilt vector S i Rotate the three-dimensional grating vector KG1 by a preset angle α to obtain the tilt vector S. i+1 .

[0067] Step S320: Based on the three-dimensional grating vector KG1 and the tilt vector S i+1 A set of wave vectors k1 and k2 are calculated.

[0068] Given a three-dimensional grating vector KG1, the tilt vector S1 can rotate around KG1 in countless different planes. Different wave vectors k1 and k2 can be obtained on these different planes using the calculation method described above. These wave vectors can all interfere with the exposure recording to form a holographic two-dimensional grating with the same three-dimensional grating vector KG1. If it is necessary to create a holographic two-dimensional grating with both KG1 and KG2, the wave vectors k1, k2, and k3 of the exposure beam can be found. Wave vector k1 is the common exposure beam wave vector of both KG1 and KG2, and it can interfere with the other two wave vectors k2 and k3 to form KG1 and KG2 respectively.

[0069] Step S330: Determine wave vector k3 based on wave vector k1, such that the XY components of the holographic grating vector exposed by the interference of wave vectors k1 and k3 are equal to the XY components of the three-dimensional grating vector KG2.

[0070] Step S340: Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k1 and k3, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG2 is less than a preset threshold. If so, record the set of wave vectors k1, k2 and k3. If not, discard the set of wave vectors k1, k2 and k3.

[0071] By ensuring that the XY components of the holographic grating vector exposed by the interference of wave vectors k1 and k3 are equal to the XY components of the three-dimensional grating vector KG2, and by determining whether the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k1 and k3 and the Z-axis component of the three-dimensional grating vector KG2 is less than a preset threshold, it is ensured that the output wave vector group can accurately reproduce the target three-dimensional grating vector, providing reliable parameter support for the synchronous exposure of three beams, avoiding ghosting, ensuring the formation of complete and regular interference fringes, reducing the difficulty of operation and improving the stability of optical performance.

[0072] Step S410: Determine whether i≥2π / α is true.

[0073] Step S420: If yes, output the recorded m sets of wave vectors k1, k2 and k3.

[0074] Step S430: If not, let i = i + 1 and execute the first loop.

[0075] The tilt vector S i Rotate the three-dimensional grating vector KG1 by a preset angle α until one revolution is completed. Calculate and record the wave vector sets k1, k2, and k that meet the threshold condition. 3， Among the final output sets of wave vectors k1, k2, and k3, combinations that are easy to build an exposure optical path can be further selected based on the beam angle. The aforementioned sets of wave vectors k1, k2, and k3 are wave vectors within the grating medium, and the incident angle is the angle between the wave vector and the z-axis normal to the grating surface. If the incident angle corresponding to one of the wave vectors is too large and exceeds the critical angle for total internal reflection, then a prism coupling method needs to be used in the optical path to couple the beam in the air into the grating medium. Since the more beams that need to be coupled by prisms, the higher the cost and the more difficult the optical path debugging becomes, the selection principle is: select the smallest possible three beam angles to avoid using prism coupling, ensuring low exposure costs while reducing operational difficulty; if at least one beam inevitably needs to be coupled by prisms, then select the wave vector set with the fewest beams that need to be coupled by prisms.

[0076] like Figure 3As shown, more intuitively, the above calculation method can be aided by a K-vector sphere established in three-dimensional space. The radius of the K-vector sphere is the wavenumber n / λ of the exposure beam in the medium, that is, the amplitude of wave vectors k1 and k2. On the K-vector sphere, a pair of parallel circles (red) represent the trajectory of the two endpoints of the three-dimensional grating vector KG1 rotating 360° around the center, and another pair of parallel circles (blue) represent the trajectory of the two endpoints of the three-dimensional grating vector KG2 rotating 360° around the center. The starting point of the tilt vector S1 and the wave vectors k1, k2 and k3 coincides with the center and rotates around the center. Each time it rotates to a specific position (i.e., the position where the red circle intersects the blue circle), a set of wave vectors k1, k2 and k3 that can simultaneously expose KG1 and KG2 is determined.

[0077] like Figure 4 The diagram illustrates a method for calculating the exposure beam of a holographic two-dimensional grating with three three-dimensional grating vectors. This includes determining the wave vectors k2 and k4 of the exposure beam based on the three-dimensional grating vector KG3. The three-dimensional grating vector KG2 and KG3 have equal XY components but different Z components. Wave vector k2 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG1 and KG3. Specifically, this includes:

[0078] Steps S100 to S430 are consistent with the above-described method for calculating the exposure beam of a holographic two-dimensional grating with two three-dimensional grating vectors.

[0079] Step S500: Let n=1 and execute the second loop.

[0080] The second cycle includes steps S610 to S630.

[0081] Step S610: Select the nth group of wave vectors k1, k2 and k3.

[0082] Step S620: Calculate the wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k2 and k4 are equal to the XY components of the three-dimensional grating vector KG3.

[0083] Step S630: Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG3 is less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4.

[0084] Step S710: Determine whether n=m is true.

[0085] Step S720: If yes, output the recorded wave vectors k1, k2, k3 and k4.

[0086] Step S730: If not, let n = n + 1 and execute the second loop.

[0087] Substitute the wave vector sets k1, k2, and k3 that meet the threshold condition one by one into the calculation and record the wave vector sets k1, k2, k3, and k that meet the threshold condition. 4， From the final output of several sets of wave vectors k1, k2, k3, and k4, combinations that are easy to build an exposure optical path can be further selected based on the beam angle.

[0088] like Figure 5 The diagram illustrates another method for calculating the exposure beam of a holographic two-dimensional grating with three three-dimensional grating vectors. This includes determining the wave vectors k3 and k4 of the exposure beam based on the three-dimensional grating vector KG4. The XY components of the three-dimensional grating vector KG1 and the three-dimensional grating vector KG4 are equal, but their Z components are different. The wave vector k3 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG2 and KG4. Specifically, it includes:

[0089] Steps S100 to S430 are consistent with the above-described method for calculating the exposure beam of a holographic two-dimensional grating with two three-dimensional grating vectors.

[0090] Step S50: Let n=1 and execute the third loop.

[0091] The third cycle includes steps S61 to S63.

[0092] Step S61: Select the nth group of wave vectors k1, k2 and k3.

[0093] Step S62: Calculate the wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k3 and k4 are equal to the XY components of the three-dimensional grating vector KG4.

[0094] Step S63: Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG4 is less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4.

[0095] Step S71: Determine whether n=m is true.

[0096] Step S72: If yes, output the recorded wave vectors k1, k2, k3 and k4.

[0097] Step S73: If not, let n = n + 1 and execute the second loop.

[0098] Substitute the wave vector sets k1, k2, and k3 that meet the threshold condition one by one into the calculation and record the wave vector sets k1, k2, k3, and k that meet the threshold condition. 4， From the final output of several sets of wave vectors k1, k2, k3, and k4, combinations that are easy to build an exposure optical path can be further selected based on the beam angle.

[0099] like Figure 6 As shown, in the K-domain diagram of the holographic two-dimensional grating, K0 is the XY component of the three-dimensional grating vector in the coupling region, i.e., the surface component. K1, K2, K3, and K4 are the XY components of the four three-dimensional grating vectors KG1, KG2, KG3, and KG4 in the turning and coupling regions, respectively. To ensure the holographic two-dimensional grating accurately transmits the image beam without ghosting, K1 and K4 need to be equal, and K2 and K3 need to be equal. K1 and K2 cause the beam to bend within the holographic two-dimensional grating, while K3 and K4 cause the beam to couple out of the holographic two-dimensional grating. Since the tilt angles of the Bragg surfaces matched for the turning and coupling functions are different, the XY components of three-dimensional grating vector one (KG1) and three-dimensional grating vector four (KG4) are equal, but their Z components are different. Similarly, the XY components of three-dimensional grating vector two (KG2) and three-dimensional grating vector three (KG3) are equal, but their Z components are different.

[0100] like Figure 7 The diagram illustrates the correspondence between the XY components K1, K2, K3, and K4 of the four three-dimensional grating vectors and the wave vectors k1, k2, k3, and k4 of the four exposure beams. For a holographic two-dimensional grating with four three-dimensional grating vectors, a single exposure requires four beams. If the XY components of two three-dimensional grating vectors are equal but their Z components are unequal, for example, three-dimensional grating vector one KG1 and three-dimensional grating vector four KG4, and three-dimensional grating vector two KG2 and three-dimensional grating vector three KG3, then the two sets of dual-beam wave vectors that produce these two three-dimensional grating vectors do not share a common exposure beam wave vector; that is, four completely different exposure beam wave vectors are required. The argument is proved by contradiction: Assume that the XY components of two 3D grating vectors are equal, but their Z components are unequal. Furthermore, there exists a shared wave vector for the exposure beam, while the wave vectors of the other two exposure beams are different. Since the XY components of the 3D grating vector are equal, the XY components of the wave vectors of the other two exposure beams are also equal. Since the amplitude of the wave vector of an exposure beam is always equal to the wavenumber n / λ, the Z components of the wave vectors of the other two exposure beams are also equal. That is, if the wave vectors of the other two exposure beams are equal, the Z components of the resulting 3D grating vector must also be equal, violating the premise. Therefore, only a shared wave vector exists. Figure 7 This is the correspondence shown.

[0101] like Figure 8The diagram illustrates a method for calculating the exposure beam of a holographic two-dimensional grating with four three-dimensional grating vectors. The method includes determining the wave vectors k2 and k4 of the exposure beam of the three-dimensional grating vector KG3 and the three-dimensional grating vector KG4 based on the three-dimensional grating vector KG3 and KG4. The three-dimensional grating vector KG2 and KG3 have equal XY components but different Z components. The three-dimensional grating vector KG1 and KG4 have equal XY components but different Z components. Wave vector k2 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG1 and KG3. Wave vector k3 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG2 and KG4. Wave vector k4 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG3 and KG4. The calculation steps are as follows:

[0102] Steps S100 to S430 are consistent with the above-described method for calculating the exposure beam of a holographic two-dimensional grating with two three-dimensional grating vectors.

[0103] Step S5: Set n=1 and execute the fourth loop.

[0104] The fourth cycle includes steps S81 to S84.

[0105] Step S81: Select the nth group of wave vectors k1, k2 and k3.

[0106] Step S82: Calculate wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k2 and k4 are equal to the XY components of the three-dimensional grating vector KG3, and make the XY components of the holographic grating vector exposed by the interference of wave vectors k3 and k4 equal to the XY components of the three-dimensional grating vector KG4.

[0107] Step S83: Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4, and the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4.

[0108] Step S84: Determine whether the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4 and the Z-axis component of the three-dimensional grating vector KG3, and the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4 and the Z-axis component of the three-dimensional grating vector KG4, are all less than a preset threshold; if so, record the set of wave vectors k1, k2, k3 and k4; if not, discard the set of wave vectors k1, k2, k3 and k4.

[0109] Step S91: Determine whether n=m is true.

[0110] Step S92: If yes, output the recorded wave vectors k1, k2, k3 and k4.

[0111] Step S93: If not, let n = n + 1 and execute the fourth loop.

[0112] Substitute the wave vector sets k1, k2, and k3 that meet the threshold condition one by one into the calculation and record the wave vector sets k1, k2, k3, and k that meet the threshold condition. 4， From the final output of several sets of wave vectors k1, k2, k3, and k4, combinations that are easy to build an exposure optical path can be further selected based on the beam angle.

[0113] Example 2

[0114] This embodiment proposes an exposure method for a holographic two-dimensional grating. The exposure method uses three beams corresponding to the wave vectors k1, k2 and k3 calculated by the above calculation method to simultaneously expose the holographic photosensitive material once, thereby obtaining a holographic two-dimensional grating with two three-dimensional grating vectors.

[0115] The exposure method also includes simultaneously exposing the holographic photosensitive material once with four beams corresponding to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method, to obtain a holographic two-dimensional grating with three three-dimensional grating vectors.

[0116] The exposure method also includes simultaneously exposing the holographic photosensitive material once with four beams corresponding to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method, to obtain a holographic two-dimensional grating with four three-dimensional grating vectors.

[0117] The above exposure method utilizes the wave vector group selected by the above calculation method to achieve single exposure of multiple beams of holographic photosensitive material. More specifically, it can realize single exposure of two-dimensional gratings with two gratings intersecting and two-dimensional gratings with four gratings multiplexed, reducing the complexity of operation, avoiding the problem of long production cycle caused by repeated rotation and positioning of prisms during multiple exposures, and the problem of easy mutual interference of grating stripes, improving the integrity of holographic two-dimensional grating structure, increasing production efficiency while reducing costs.

[0118] Example 3

[0119] This embodiment proposes an exposure device for a holographic two-dimensional grating. The exposure device includes three light sources. The emission angles of the three light sources are set according to the wave vectors k1, k2 and k3 calculated by the above calculation method. The three beams emitted by them simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with two three-dimensional grating vectors.

[0120] The exposure device may also include four light sources. The emission angles of the four light sources are set according to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method. The three beams emitted by them simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with three three-dimensional grating vectors.

[0121] The exposure device may also include four light sources. The emission angles of the four light sources are set according to the wave vectors k1, k2, k3 and k4 calculated by the above calculation method. The three beams emitted by them simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with four three-dimensional grating vectors.

[0122] The aforementioned device utilizes a light source to emit multiple beams corresponding to the wave vector group selected by the aforementioned calculation method, thereby achieving a single exposure of multiple beams of holographic photosensitive material. Optionally, combinations that are easy to construct exposure optical paths can be selected based on the wave vector group, ensuring that the output wave vector group can accurately reproduce the target three-dimensional grating vector, providing reliable parameter support for the synchronous exposure of three beams, avoiding ghosting phenomena, ensuring the formation of complete and regular interference fringes, reducing the difficulty of operation, and improving the stability of optical performance.

[0123] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solution of the present invention, and are not intended to limit the specific implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for calculating the exposure beam of a holographic two-dimensional grating, characterized in that, This includes determining the wave vectors k1 and k2 of the exposure beam of the three-dimensional grating vector KG1 and the three-dimensional grating vector KG2 based on the three-dimensional grating vector KG1 and the three-dimensional grating vector KG2, and the wave vectors k1 and k3 of the exposure beam of the three-dimensional grating vector KG2, wherein the wave vector k1 is the wave vector of the common exposure beam of the three-dimensional grating vector KG1 and the three-dimensional grating vector KG2, specifically including: A plane containing the three-dimensional grating vector KG1 is selected. Based on the amplitudes of the three-dimensional grating vector KG1 and the wave vectors k1 and k2 of the exposure beam, the tilt vector S1 in the same plane is calculated. The three-dimensional grating vector KG1 and the wave vectors k1 and k2 form a vector triangle in the same plane. The line segment containing the tilt vector S1 is the perpendicular line to the side containing the three-dimensional grating vector KG1 in the vector triangle. Set i=1 and execute the first loop; The first loop includes: The tilt vector S i Rotate the three-dimensional grating vector KG1 by a preset angle α to obtain the tilt vector S. i+1 ; Based on the three-dimensional grating vector KG1 and the tilt vector S i+1 A set of wave vectors k1 and k2 are calculated, wherein the wave vectors k1 and k2 satisfy: k1 = S i+1 +KG1 / 2, k2=S i+1 -KG 1 / 2; Based on the wave vector k1, determine the wave vector k3 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k1 and k3 are equal to the XY components of the three-dimensional grating vector KG2. Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k1 and k3, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG2 is less than a preset threshold. If so, record the set of wave vectors k1, k2 and k3. If not, discard the set of wave vectors k1, k2 and k3. Determine if i ≥ 2π / α is true; if yes, output the recorded m sets of wave vectors k1, k2 and k3; if no, set i = i + 1 and execute the first loop.

2. The method for calculating the exposure beam of a holographic two-dimensional grating according to claim 1, characterized in that, It also includes determining the wave vectors k2 and k4 of the exposure beam based on the three-dimensional grating vector KG3, wherein the three-dimensional grating vector KG2 and the three-dimensional grating vector KG3 have equal XY components but different Z components, and the wave vector k2 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG1 and KG3, specifically including: Let n=1, then execute the second loop; The second cycle includes: Select the nth group of wave vectors k1, k2, and k3; Calculate wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k2 and k4 are equal to the XY components of the three-dimensional grating vector KG3; Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG3 is less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4. Determine if n=m is true; if yes, output the recorded wave vectors k1, k2, k3 and k4; if no, set n=n+1 and execute the second loop.

3. The method for calculating the exposure beam of a holographic two-dimensional grating according to claim 1, characterized in that, It also includes determining the wave vectors k3 and k4 of the exposure beam based on the three-dimensional grating vector KG4, wherein the three-dimensional grating vector KG1 and the three-dimensional grating vector KG4 have equal XY components but different Z components, and the wave vector k3 is the wave vector of the common exposure beam of the three-dimensional grating vectors KG2 and KG4, specifically including: Let n=1, then execute the third loop; The third cycle includes: Select the nth group of wave vectors k1, k2, and k3; Calculate wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k3 and k4 are equal to the XY components of the three-dimensional grating vector kG4. Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4, and determine whether the difference between it and the Z-axis component of the three-dimensional grating vector KG4 is less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4. Determine if n=m is true; if yes, output the recorded wave vectors k1, k2, k3 and k4; if no, set n=n+1 and execute the third loop.

4. The method for calculating the exposure beam of a holographic two-dimensional grating according to claim 1, characterized in that, The method also includes determining the wave vectors k2 and k4 of the exposure beam of the three-dimensional grating vector three KG3 and the three-dimensional grating vector four KG4 based on the three-dimensional grating vector three KG3 and the three-dimensional grating vector four KG4. The three-dimensional grating vector two KG2 and the three-dimensional grating vector three KG3 have equal XY components but different Z components. The three-dimensional grating vector one KG1 and the three-dimensional grating vector four KG4 have equal XY components but different Z components. The wave vector k2 is the wave vector of the common exposure beam of the three-dimensional grating vector one KG1 and the three-dimensional grating vector three KG3. The wave vector k3 is the wave vector of the common exposure beam of the three-dimensional grating vector two KG2 and the three-dimensional grating vector four KG4. The wave vector k4 is the wave vector of the common exposure beam of the three-dimensional grating vector three KG3 and the three-dimensional grating vector four KG4. The calculation steps are as follows: Let n=1, then execute the fourth loop; Select the nth group of wave vectors k1, k2, and k3; Calculate wave vector k4 such that the XY components of the holographic grating vector exposed by the interference of wave vectors k2 and k4 are equal to the XY components of the three-dimensional grating vector KG3, and make the XY components of the holographic grating vector exposed by the interference of wave vectors k3 and k4 equal to the XY components of the three-dimensional grating vector KG4. Calculate the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4, and the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4; Determine whether the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k2 and k4 and the Z-axis component of the three-dimensional grating vector KG3, and the difference between the Z-axis component of the holographic grating vector exposed by the interference of wave vectors k3 and k4 and the Z-axis component of the three-dimensional grating vector KG4, are all less than a preset threshold. If so, record the set of wave vectors k1, k2, k3 and k4. If not, discard the set of wave vectors k1, k2, k3 and k4. Determine if n=m is true; if yes, output the recorded wave vectors k1, k2, k3 and k4; if no, set n=n+1 and execute the fourth loop.

5. An exposure method for a holographic two-dimensional grating, characterized in that, The three beams corresponding to the wave vectors k1, k2 and k3 calculated by the method described in claim 1 are simultaneously used to expose the holographic photosensitive material once to obtain a holographic two-dimensional grating with two three-dimensional grating vectors.

6. A method for exposing a holographic two-dimensional grating, characterized in that, The four beams corresponding to the wave vectors k1, k2, k3 and k4 calculated by any one of claims 2 to 3 are used to simultaneously expose the holographic photosensitive material once to obtain a holographic two-dimensional grating with three three-dimensional grating vectors.

7. An exposure method for a holographic two-dimensional grating, characterized in that, The four beams corresponding to the wave vectors k1, k2, k3 and k4 calculated by the method described in claim 4 are used to simultaneously expose the holographic photosensitive material once, thereby obtaining a holographic two-dimensional grating with four three-dimensional grating vectors.

8. An exposure apparatus for a holographic two-dimensional grating, characterized in that, It includes three light sources, the emission angles of which are set according to the wave vectors k1, k2 and k3 calculated by the method according to claim 1. The three beams emitted by the light sources simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with two three-dimensional grating vectors.

9. An exposure apparatus for a holographic two-dimensional grating, characterized in that, It includes four light sources, the emission angles of which are set according to the wave vectors k1, k2, k3 and k4 calculated by the method according to any one of claims 2 to 3. The three beams emitted by the light sources simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with two three-dimensional grating vectors.

10. An exposure apparatus for a holographic two-dimensional grating, characterized in that, It includes four light sources, the emission angles of which are set according to the wave vectors k1, k2, k3 and k4 calculated by the method according to claim 4. The three beams emitted by the light sources simultaneously illuminate the holographic photosensitive material and interfere on the holographic photosensitive material. The holographic photosensitive material records the interference fringes to obtain a holographic two-dimensional grating with two three-dimensional grating vectors.

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