An optimization method for the simulation model of non-ideal volume holographic grating

Abstract

The present invention provides an optimization method for a non-ideal volume holographic grating simulation model, including a Fourier expansion of the volume holographic refractive index formula, sampling point selection, and asymmetric correction of the sampling points. The present invention enables accurate model calculation and simulation of non-ideal volume holographic gratings with grating tilt deviations. It optimizes existing calculation formulas for ideal gratings, making the simulation model more consistent with the actual grating parameters, significantly improving the accuracy and reliability of grating simulation.

Description

Technical Field

[0001] The invention relates to an optimization method for a non-ideal volume holographic grating simulation model and relates to the technical field of holographic display. Background Art

[0002] With the rapid development of augmented reality (AR) and virtual reality (VR) technologies, near-eye display technologies have attracted widespread attention in the market. Among these technologies, holographic waveguide display technology has made significant progress due to its ability to provide high-resolution and wide-field-of-view display effects.

[0003] In recent years, VHG has been widely used in holographic waveguide AR displays due to its excellent angle and wavelength selectivity and high diffraction efficiency. At the same time, domestic and foreign researchers have conducted extensive research on key technologies such as the influence mechanism of VHG diffraction characteristics on holographic waveguide imaging and the configuration of color, large-angle VHG diffraction waveguide near-eye display. Researchers often use the finite element method of COMSOL Multiphysics to simulate the diffraction characteristics of VHG gratings. This method can achieve high-precision numerical simulation. However, the above research is based on the simulation of the grating structure under ideal conditions, but there has been no related research on non-ideal VHG simulation models. In fact, in the post-processing process (drying and UV curing) of the volume holographic grating (VHG), the refractive index modulation of one grating period may be offset (the offset value cannot be accurately calculated). Optical path errors will also introduce grating tilt angle deviations, resulting in grating vector offsets. Therefore, there will be a large deviation between the measured grating efficiency curve and the theoretical calculation results of the ideal grating.

[0004] To accurately simulate VHG diffraction waveguide AR near-eye displays, a non-ideal VHG model must be established. Based on this model, near-eye display imaging optimization can be achieved. Therefore, simulation of non-ideal VHG gratings and their diffraction efficiency is crucial. On the other hand, commonly used optical simulation software such as Zemax and TracePro, while capable of designing, analyzing, optimizing, and performing other auxiliary functions for optical imaging systems, only supports the simulation of simple surface and volume gratings and lacks simulation models for non-ideal volume holographic gratings. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a calculation model and simulation method for a non-ideal volume holographic grating in order to overcome the shortcomings of the existing problems. The calculation model and simulation method of the volume holographic grating can overcome the problem of low accuracy of the calculation and simulation of the existing volume holographic grating, optimize the calculation model and simulation method of the volume holographic grating to improve the accuracy of the simulation model, and enable the grating simulation model to be better applied to the simulation optimization design of the volume holographic waveguide.

[0006] In order to solve the above problems, the technical solution adopted by the present invention is:

[0007] A calculation model and simulation method for a non-ideal volume holographic grating, including Fourier expansion of the volume holographic refractive index formula, selection of sampling points, and asymmetric correction of the sampling points; wherein

[0008] The Fourier expansion of the volume holographic refractive index formula is used to separate the stray sub-gratings in the volume holographic grating and express the refractive index of each stray sub-grating respectively.

[0009] To further express the refractive index of each stray sub-grating, the optimization formula is as follows:

[0010]

[0011] Where erp represents the refractive index of the volume holographic grating, dn i represents the refractive index modulation of the i-th individual holographic grating, KG i represents the grating vector of the i-th individual holographic grating, represents the grating tilt angle of the i-th volume holographic grating. During the VHG post-processing (drying and UV curing), the refractive index modulation of a grating period may shift (the displacement value cannot be accurately calculated). Optical path errors can also introduce grating tilt deviations, resulting in shifts in the grating vector. Therefore, the present invention performs a Fourier expansion on the volume holographic grating and selects i sampling points to optimize the volume holographic grating.

[0012] Furthermore, the i sampling points in the volume holographic grating are selected and divided equally into i harmonics within the confidence interval:

[0013] x i -x -i =4σ; scale=(x i -x -i ) / (i-1)

[0014] The refractive index modulation formula of each harmonic satisfies the following formula:

[0015]

[0016] The sum of the refractive index modulation of each harmonic is conserved, that is:

[0017]

[0018] Wherein, erp represents the refractive index of the volume holographic grating, and its value is fixed.

[0019] According to σ, i different sampling points are selected at equal intervals. These i points can approximately replace the normal distribution function f(x i ):

[0020] x0=KG0

[0021] x i =KG0+i*scale

[0022] x -i =KG0-i*scale

[0023] The dn corresponding to these i different sampling points i They are:

[0024] dn i =f(x i )*n0

[0025] Furthermore, the asymmetry of the sampling points in the volume holographic grating is corrected; after optimizing σ, thickness and refractive index modulation, the model is further optimized, and it is found that after moving the center position of the normal distribution to the left by a scale, the grating simulation curve and the actual curve are more closely matched.

[0026] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0027] The present invention provides an optimization method for a non-ideal volume holographic grating model, which can accurately calculate and simulate the volume holographic grating model. The optimization is based on the calculation formula of the current ideal volume holographic grating simulation model. The non-ideal volume holographic grating model of the present invention introduces variables such as refractive index modulation, harmonics, grating inclination angle, and grating thickness, so that the simulation results of the grating model are more consistent with the actual grating measurement results, greatly improving the accuracy of the grating simulation, thereby improving the reliability of the grating simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a grating SEM image.

[0029] Figure 2 This is the raster distribution diagram of eleven sampling points.

[0030] Figure 3 This is the preliminary simulation result after considering the normal distribution.

[0031] Figure 4 The figure shows the simulation results of different grating thicknesses within the 95% confidence interval.

[0032] Figure 5 The simulation results of different refractive index modulation degrees within the 95% confidence interval are shown.

[0033] Figure 6 The simulation results for different standard deviations within the 95% confidence interval are shown in Figure 2.

[0034] Figure 7 The figure shows the simulation results of different numbers of harmonics within the 95% confidence interval.

[0035] Figure 8 This is a simulation image of the grating without asymmetric correction.

[0036] Figure 9 This is a simulation image of the grating after asymmetric correction. DETAILED DESCRIPTION

[0037] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0038] A calculation model and simulation method for a non-ideal volume holographic grating, including Fourier expansion of the volume holographic refractive index formula, selection of sampling points, and asymmetric correction of the sampling points; wherein

[0039] The Fourier expansion of the volume holographic refractive index formula is used to separate the stray sub-gratings in the volume holographic grating and express the refractive index of each stray sub-grating respectively.

[0040] like Figure 2 The refractive index of each stray sub-grating is expressed as shown in the figure, and the optimization formula is as follows:

[0041]

[0042] Wherein, erp represents the refractive index of the volume holographic grating, dn1 represents the refractive index modulation of the first individual holographic grating, dn2 represents the refractive index modulation of the second individual holographic grating, dn3 represents the refractive index modulation of the third individual holographic grating, dn4 represents the refractive index modulation of the fourth individual holographic grating, dn5 represents the refractive index modulation of the fifth individual holographic grating, dn6 represents the refractive index modulation of the sixth individual holographic grating, dn7 represents the refractive index modulation of the seventh individual holographic grating, dn8 represents the refractive index modulation of the eighth individual holographic grating, dn9 represents the refractive index modulation of the ninth individual holographic grating, and dn 10 represents the refractive index modulation of the 10th individual holographic grating, dn 11 represents the refractive index modulation degree of the 11th individual holographic grating, KG1 represents the grating vector of the 1st individual holographic grating, KG2 represents the grating vector of the 2nd individual holographic grating, KG3 represents the grating vector of the 3rd individual holographic grating, KG4 represents the grating vector of the 4th individual holographic grating, KG5 represents the grating vector of the 5th individual holographic grating, KG6 represents the grating vector of the 6th individual holographic grating, KG7 represents the grating vector of the 7th individual holographic grating, KG8 represents the grating vector of the 8th individual holographic grating, KG9 represents the grating vector of the 9th individual holographic grating, and KG 10 The grating vector of the 10th individual holographic grating, KG 11 represents the grating vector of the 11th individual holographic grating, represents the grating inclination angle of the first individual holographic grating; represents the grating inclination angle of the second individual holographic grating; represents the grating inclination angle of the third individual holographic grating; represents the grating inclination angle of the fourth individual holographic grating; represents the grating inclination angle of the fifth individual holographic grating; represents the grating inclination angle of the sixth individual holographic grating; represents the grating inclination angle of the 7th individual holographic grating; represents the grating inclination angle of the 8th individual holographic grating; represents the grating inclination angle of the 9th individual holographic grating; represents the grating inclination angle of the 10th individual holographic grating; represents the grating inclination angle of the 11th individual holographic grating.

[0043] During the VHG post-processing (drying and UV curing), the refractive index modulation of a grating period may shift (the shift value cannot be accurately calculated). Optical path errors can also introduce grating tilt deviations, resulting in grating vector offsets. Therefore, this embodiment performs Fourier expansion on the volume holographic grating and selects 11 sampling points to optimize the volume holographic grating.

[0044] Furthermore, 11 sampling points are selected in the volume holographic grating and divided equally into 5 harmonics within the confidence interval:

[0045] x5-x -5 =4σ; scale = (x5-x -5 ) / (5-1)

[0046] like Figure 2 As shown, x0 is the 0th sampling point, x1 is the 1st forward sampling point, and x -1 is the first negative sampling point, x2 is the second positive sampling point, and x -2 is the second negative sampling point, x3 is the third positive sampling point, and x -3 is the third negative sampling point, x4 is the fourth positive sampling point, x -4 is the 4th negative sampling point, x5 is the 5th positive sampling point, x -5 is the 5th negative sampling point; x5 and x -5 The difference is 4 standard deviations; scale is the width of each harmonic.

[0047] The refractive index modulation formula of each harmonic satisfies the following formula:

[0048]

[0049] where Δn iis the refractive index modulation of the i-th grating, i is the i-th sampling point, Δn0 represents the refractive index modulation amplitude at the center point, σ is the standard deviation of the normal distribution, μ is the mean of the distribution, and x i is the position of the i-th sampling point.

[0050] like Figure 3 These are the preliminary simulation results after considering the normal distribution.

[0051] According to the comparison, it can be found that the standard deviation σ in the normal distribution refractive index model, the number of samples n within the 95% confidence interval, and the refractive index modulation degree dn have a great influence on the accuracy of the simulation model.

[0052] like Figure 4 The simulation results for different grating thicknesses d within the 95% confidence interval are shown.

[0053] The figure shows that thickness has a significant impact on the simulation results. The greater the thickness, the smaller the angular bandwidth, while the opposite is true, the larger the diffraction angular bandwidth. It can be observed that when d = 22 μm, the simulation results are consistent with the measured results, so 22 μm is selected as the thickness for the rest of this article.

[0054] like Figure 5 is the refractive index modulation degree d within the 95% confidence interval n The simulation results are shown in Figure 2.

[0055] It can be seen from the figure that different d n It has a great influence on the simulation results. It can be observed that when d n =0.015, the simulation results are consistent with the measured results, so the following d n Select 0.015.

[0056] like Figure 6 These are the simulation results for different standard deviations σ within the 95% confidence interval.

[0057] It can be seen from the figure that the thickness has a great influence on the simulation results. It can be observed that when σ = 1e5, the simulation results are consistent with the measured results. Therefore, σ is selected as 1e5 later.

[0058] like Figure 7 The simulation results for different numbers of harmonics within the 95% confidence interval are shown.

[0059] As can be seen from the figure, to ensure the accuracy of the simulation model, at least two harmonic components need to be considered; the simulation results corresponding to the five harmonics are closest to the measured data;

[0060] Therefore, according to the above data, select d = 22um; d n =0.015; σ=1e5; the experimental data model of 5 harmonics is closest to the actual results.

[0061] like Figure 8 As shown in the figure, the simulation results show that the sampling points on the left and right sides obey the normal distribution, the amplitude of the sampling points on the left is lower than that on the right, and the diffraction angle bandwidth is asymmetric on the left and right;

[0062] Therefore, make Figure 9 By modifying the normal distribution center to the left by a scale, we can see that the simulation results have a better fit with the test data and are closer to the measured data.

[0063] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for optimizing a non-ideal volume holographic grating simulation model, characterized in that: The steps include: Step 1: Perform Fourier expansion on the volume holographic refractive index formula, the formula is as follows: Where, erp represents the refractive index of the volume holographic grating, dn i represents the refractive index modulation of the i-th daughter holographic grating, KG i represents the grating vector of the i-th daughter holographic grating, represents the grating inclination angle of the i-th daughter holographic grating, and (x, y) represents the coordinates of the grating cross section; Step 2: Divide the harmonics into i types of harmonics within the confidence interval according to the number i of daughter holographic gratings; x i -x -i =4σ;scale=(x i -x -i ) / (i-1) The refractive index modulation formula of each harmonic satisfies the following formula: σ represents the standard deviation of the normal distribution, and scale is the width of each harmonic; Step 3: Select the number of daughter volume holographic gratings, the volume holographic grating thickness, the refractive index modulation, and the standard deviation of the normal distribution as optimization parameters, and use the control variable method to obtain the volume holographic grating refractive index simulation diagram under different optimization parameters; Step 4: Compare the simulated refractive index images of the volume holographic grating under different optimization parameters with the measured refractive index images of the volume holographic grating, and select the value of the optimized parameter corresponding to the simulated refractive index image of the volume holographic grating that is closest to the measured image; Step 5: Substitute the values of the optimized parameters selected in step 1 into the formula in step 1, calculate the reflectivity, and draw the refractive index curve of the volume holographic grating; Step 6: Move the center position of the normal distribution of the volume holographic grating refractive index curve drawn in step 5 to the left by a scale distance to obtain the final volume holographic grating refractive index curve.

2. The method for optimizing a non-ideal volume holographic grating according to claim 1, wherein: The thickness is selected as 22um.

3. The method for optimizing a non-ideal volume holographic grating according to claim 1, wherein: The number of daughter holographic gratings is chosen to be 11.

4. The method for optimizing a non-ideal volume holographic grating according to claim 1, wherein: σ is chosen to be 1e5.

5. The method for optimizing a non-ideal volume holographic grating according to claim 1, wherein: The refractive index modulation degree is selected as 0.015.

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