All-domain dual-depth lens optimization method in integrated imaging 3D display system
By using a global dual-depth lens optimization method, the problem of uneven speckle size in traditional lens optimization methods is solved, which improves the spatial and angular resolution of the integrated imaging 3D display system and enhances the stereoscopic display effect.
Patent Information
- Application Number
- CN202511333731.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-18
- Publication Date
- 2025-12-05
AI Technical Summary
Traditional lens optimization methods only optimize for a specific field of view, resulting in uneven speckle size in integrated imaging 3D display systems, which affects the spatial resolution of 3D images and the stereoscopic viewing effect.
A global dual-depth lens optimization method is adopted. By constructing a global optimization function for the lens and an iterative optimization process, the surface parameters of the lens are optimized, the size of the blur spot is reduced, and the spatial resolution and angular resolution are improved.
It achieves simultaneous optimization of diffuse speckle across the entire viewing angle, improving the spatial and angular resolution of the 3D display system and enhancing the stereoscopic display effect.
Smart Images
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of integral imaging, and particularly relates to a lens optimization method for global double depth in an integral imaging three-dimensional (3D) system. BACKGROUND
[0002] Integral imaging is a true 3D display technology, which can collect the light field information of a real three-dimensional scene and reconstruct the real 3D scene through dense light beams. The reconstructed 3D image has true color, full parallax and real shadow, occlusion and other relationships, and no stereoscopic viewing visual fatigue. As a core element in the recording and reconstruction process of integral imaging, the imaging performance of the lens array determines the clarity of the reconstructed 3D image to some extent. The traditional lens optimization method usually only optimizes the spot size at the imaging plane under several special viewing angles, such as the center 0° viewing angle, 0.707 viewing angle, edge viewing angle or several random viewing angles manually set.
[0003] An ideal sub-pixel can be regarded as a rectangular gate function, and after nonlinear expansion by the lens, a diffused spot is formed on the imaging plane, as shown in FIG. 1. In the light field 3D display of dense viewpoints, the imaging plane is also called the central depth plane. The 3D voxel formed at the central depth plane is composed of tens or hundreds of reconstructed light rays under different lenses. Due to the existence of lens aberration, the light rays with different aperture angles emitted by the same sub-pixel in different image elements will form diffused spots with different sizes, as shown by the diffused spots V1, V2 and V3 in FIG. 2. The 3D voxel size is determined by the maximum diffused spot size, and is inversely proportional to the spatial resolution of the reconstructed 3D image. In addition, the viewpoint width at the viewing plane also affects the 3D viewing effect. When the viewpoint width is too wide, it is easy to cause viewpoint overlap and image crosstalk, which deteriorates the 3D stereoscopic perception and visual effect. Figure 1 Figure 1 SUMMARY
[0004] This invention proposes a global dual-depth lens optimization method for integrated imaging 3D display systems. This method includes two processes: constructing a global optimization function for the lens and iterative optimization of the lens. In the process of constructing the global optimization function, a two-dimensional analysis model is established based on the structural parameters of the integrated imaging 3D display system. The diffusion spot light field distribution of each sub-pixel covered by the lens at the corresponding viewing angle and the corresponding reconstruction plane is characterized by convolution using the sub-pixel gate function Rect and the lens point spread function PSF. For the light field distribution characteristics at different reconstruction planes, the full width at half maximum (FWHM) and one-tenth of the peak width are taken to numerically characterize the diffusion spot size. Then, performance curves of the diffusion spot peak width at the center depth plane and the viewing plane as a function of the global angle are constructed using cubic spline interpolation. Numerical quantization is performed by integral summation to obtain the global optimization function of the lens. During the iterative optimization of the lens, the surface parameters of the lens are input and the current optimization function value is calculated. In each iteration, new surface parameters are generated and a new optimization function value is calculated. The global optimization function values before and after optimization are compared. If the new optimization function value is smaller, it means that the size of the blur spot reconstructed by the current lens is smaller, and the new surface parameters are directly replaced. If the new optimization function value is larger, the new surface parameters are accepted with a certain probability. The number of iterations is accumulated until the optimization function value does not decrease significantly or the number of iterations reaches a set value, at which point the final lens structure is output.
[0005] The process of constructing the global optimization function for the lens is shown in the appendix. Figure 2 As shown, the origin is the intersection of the central axis of the lens unit and the plane containing the sub-pixels on the display screen. The direction along the display screen is the X-axis, and the direction perpendicular to the display screen is the Y-axis. Let i be the index of the sub-pixel under the lens unit, and let θ be the aperture angle formed by the i-th sub-pixel and the optical center of the lens. i The light field distribution at an axial depth *l* after the sub-pixel rays are modulated by the lens is represented by the lens's point spread function *PSF(θ,l)*. (See attached image.) Figure 3 As shown, the lens point spread function curves for the first and eleventh sub-pixels at the center depth plane and viewing plane, respectively, are presented. An ideal sub-pixel can be considered as a rectangular gate function, and the light field distribution modulated by the lens can be expressed as the convolution of the gate function and the lens point spread function, as shown in the appendix. Figure 4 As shown. Therefore, the light field distribution U formed by the i-th sub-pixel at an axial depth l under the lens unit can be expressed as:
[0006]
[0007] In the formula, A represents the luminance of the sub-pixel; p sThe subpixel size is represented by rect(·); rect(·) represents the rectangular function; * represents the convolution operation; in the point spread function (PSF) of the lens, i represents the subpixel index, i∈{0,1,2,3…i-1}; l represents the axial depth, l∈{l... CDP ,l VP}; c represents the vertex curvature of the lens, k represents the conic coefficient of the lens, and α represents the aspherical coefficient of the lens. The light field distribution U comprehensively characterizes the reconstruction quality and light field distribution characteristics of the blur spot. When l = l CDP When U represents the light field distribution of the diffuse spot at the central depth plane, when l = l VP At that time, U represents the light field distribution of the diffuse spot at the viewing plane. Let x i Let x be the X-axis coordinate of the i-th sub-pixel. i = (i-1)×p s Characterization points (x) of the global angular diffuse spot light field distribution at the central depth plane and the viewing plane are constructed. i ,w i (See attached) Figure 5 As shown, where w i Let U be the peak width of the diffuse spot light field distribution U of the i-th sub-pixel at the corresponding plane. Piecewise interpolation of the diffuse spot characterization points on the center depth plane and the viewing plane using cubic spline curves yields the performance curve S3(x) characterizing the reconstruction of the diffuse spot at continuous angles across the entire domain. Its piecewise interpolation formula can be expressed as:
[0008] S3(x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 (2)
[0009] In the formula, S3(x) represents the performance curve constructed after cubic spline interpolation, and a i b i c i d i The coefficients to be determined are obtained through piecewise slopes and multiple derivatives. Ultimately, the global optimization function F(x) of the lens can be expressed as:
[0010]
[0011] In the formula, N{·} represents the normalization operation, and γ1 and γ2 are the optimization weight values.
[0012] Preferably, in order to accurately characterize the spot size at the center depth plane and the viewing plane, the full width at half maximum of the light field distribution is usually taken to characterize the spot size of the 3D voxel, i.e., w i = FWHM[U(l CDP )], where FWHM[·] represents the operation of taking the full width at half maximum, as shown in the accompanying Figure 6 Since the spot at the viewing plane has a wide spread characteristic, and the part below 10% of the maximum brightness is relatively weak in stimulating the human eye, the spot size of the viewing plane is characterized by the tenth of the peak width, corresponding to w i = FWTM[U(l VP )], where FWTM[·] represents the operation of taking the tenth of the peak width, as shown in the accompanying Figure 7
[0013] The iterative optimization process of the lens, as shown in the accompanying Figure 8 The initial lens surface parameters are first input, the global optimization function value of the current lens structure is calculated according to the global optimization function construction process of the lens, new surface parameters c', k', a' are generated, and the global optimization function value of the new parameters is calculated. If the new optimization function value is smaller, the new surface parameters are directly replaced. If the new optimization function is larger, the new surface parameters are accepted with a certain probability. The acceptance probability can be represented as
[0014] P = exp{m / [F m (c, k, a) - F m (c', k', a')]} (4)
[0015] where P represents the probability of accepting new parameters, m represents the number of iterations, c, k, a represent the original surface parameters, and c', k', a' represent the new surface parameters. According to the above iterative optimization process, new surface parameters c', k', a' are continuously generated for surface optimization, and the number of iterations m is accumulated until the optimization function value is not significantly reduced or the number of iterations reaches a set value. In the initial stage of iterative optimization, a large probability is allowed to accept a worse solution, so as to escape from the local optimal value. As the number of iterations increases, the method is more inclined to fine-tune in the local, and finally finds the global minimum result of the optimization function.
[0016] The present application proposes a lens optimization method for global double depth in an integrated imaging 3D display system. In the global optimization function construction process of the lens, the sub-pixel gate function rect and the lens point spread function PSF convolution are used to represent the spot light field distribution of each sub-pixel at the corresponding field of view angle and the corresponding reconstruction plane under the lens; different peak widths w i The method involves numerically characterizing the size of the blur spot; then constructing the final global optimization function for the lens through cubic spline interpolation and integration; during the iterative optimization of the lens, the conic coefficient, vertex curvature, and aspherical coefficient are optimized; by comparing the global optimization function values before and after optimization and controlling the number of iterations, the global angular blur spot at both the central depth plane and the viewing plane is simultaneously optimized, ultimately yielding better lens structure parameters. This method can simultaneously optimize the blur spot at both the central depth plane and the viewing plane within the global angular range, thereby improving both the spatial and angular resolution of the 3D display system and achieving high-quality stereoscopic display effects. Attached Figure Description
[0017] Appendix Figure 1 This is a schematic diagram illustrating the light field display principle of integrated imaging.
[0018] Appendix Figure 2 This is a schematic diagram of a global angle speckle analysis model.
[0019] Appendix Figure 3 This is a schematic diagram of the lens point diffusion function curves of sub-pixels at different positions in the center depth plane and the viewing plane.
[0020] Appendix Figure 4 This is a schematic diagram of sub-pixel speckle analysis.
[0021] Appendix Figure 5 A schematic diagram showing the speckle characterization points and speckle performance curves at the center depth plane and the viewing plane.
[0022] Appendix Figure 6 This is a schematic diagram of the full width at half maximum (FWHM) of the light field distribution of the sub-pixel diffuse spot.
[0023] Appendix Figure 7 This is a schematic diagram showing one-tenth of the peak width of the light field distribution of the sub-pixel diffuse spot.
[0024] Appendix Figure 8 This is a schematic diagram of the iterative optimization process for the lens.
[0025] Appendix Figure 9 The diffusion function curve is shown at the lens point of 3.71 degrees at CDP.
[0026] Appendix Figure 10 A comparison of performance curves representing the size of the dispersion spot at the center depth plane before and after optimization.
[0027] Appendix Figure 11 A comparison of performance curves representing the size of the diffusion spot at the viewing plane before and after optimization.
[0028] The figure labels in the above figures are:
[0029] 1 micro image array, 2 lens array, 3 center depth plane, 4 voxel, 5 viewing plane, 6 view point, 7 imagelet, 8 all-angle reconstruction ray, 9 reconstructed 3D image, 10 sub-pixel on display screen, 11 point spread function of first sub-pixel under lens at center depth plane, 12 point spread function of first sub-pixel under lens at viewing plane, 13 point spread function of eleventh sub-pixel under lens at center depth plane, 14 point spread function of eleventh sub-pixel under lens at viewing plane, 15 rectangular function representing sub-pixel light emitting surface, 16 point spread function of lens, 17 airy disk light field distribution function, 18 sub-pixel light emitting surface, 19 blur caused by lens point spread function, 20 sub-pixel airy disk, 21 convolution operation symbol, 22 airy disk representation point of sub-pixel at different positions under lens at center depth plane, 23 airy disk representation point of sub-pixel at different positions under lens at viewing plane, 24 performance curve representing size of airy disk at center depth plane after interpolation, 25 performance curve representing size of airy disk at viewing plane after interpolation, 26 X axis representing physical coordinates of sub-pixel, 27 Y axis representing peak width of sub-pixel airy disk light field distribution, 28 full width at half maximum of airy disk light field distribution at center depth plane, 29 one-tenth peak width of airy disk light field distribution at viewing plane, 30 performance curve representing size of airy disk at center depth plane before optimization, 31 performance curve representing size of airy disk at center depth plane after optimization, 32 performance curve representing size of airy disk at viewing plane before optimization, 33 performance curve representing size of airy disk at viewing plane after optimization.
[0030] It should be understood that the above-mentioned figures are only schematic and not drawn to scale. DETAILED DESCRIPTION
[0031] A typical embodiment of the lens optimization method for full global dual depth in the integrated imaging 3D display system of the present application is described in detail below, and the present application is further described in detail. It is necessary to point out here that the following embodiment is only used to further illustrate the present application and cannot be understood as a limitation on the protection scope of the present application. Those skilled in the art can make some non-essential improvements and adjustments to the present application according to the above content of the present application, and still belong to the protection scope of the present application.
[0032] This invention proposes a global dual-depth lens optimization method for integrated imaging 3D display systems. This method includes two processes: constructing the global optimization function of the lens and iterative optimization of the lens. In the process of constructing the global optimization function, a two-dimensional analysis model is established based on the structural parameters of the integrated imaging 3D system. The light field distribution of the blur spot at the center depth plane and the viewing plane of each sub-pixel covered by the lens is characterized using the sub-pixel gate function Rect and the lens point spread function PSF convolution as theoretical foundations. For the light field distribution characteristics at different planes, the full width at half maximum (FWHM) and one-tenth of the peak width are taken to numerically characterize the blur spot size. Then, performance curves of the blur spot peak width at the center depth plane and the viewing plane as a function of the global angle are constructed using cubic spline interpolation. Finally, numerical quantization is performed by integral summation to obtain the global optimization function of the lens. During the iterative optimization of the lens, the surface parameters of the lens are input, and the current optimization function value is calculated according to the global optimization function construction process. In each iteration, new surface parameters are generated and a new optimization function value is calculated. The global optimization function values before and after optimization are compared. If the new optimization function value is smaller, it means that the size of the reconstructed blur spot of the current lens is smaller, and the new surface parameters are directly replaced. If the new optimization function value is larger, the new surface parameters are accepted with a certain probability. The number of iterations is accumulated until the optimization function value does not decrease significantly or the number of iterations reaches a set value, at which point the final lens structure is output.
[0033] The process of constructing the global optimization function for the lens is shown in the appendix. Figure 2 As shown, a two-dimensional coordinate system is established with the intersection of the central axis of the lens unit and the plane containing the sub-pixels on the display screen as the origin, the direction along the display screen as the X-axis, and the direction perpendicular to the display screen as the Y-axis. The sub-pixel size is 15.75 μm, and the lens pitch is 0.36 mm. A rectangular function for the sub-pixel is constructed based on the sub-pixel size and luminous intensity. In Zemax OpticStudio 2022 software, the initial structure of the lens is set: pitch 0.36 mm, material refractive index 1.56, and initial surface parameters: c = -1.65, k = 0, α = 0. The field of view angles corresponding to each sub-pixel under the lens are also set: 0.31°, 0.93°, 1.62°, 2.34°, 3.05°, 3.71°, 4.42°, 5.17°, 5.82°, 6.53°, 7.21°, and 8°. Based on the current initial lens structure, the lens point spread function PSF(θ,l) at the center depth plane and the viewing plane under the global field of view is obtained, as shown in the appendix. Figure 9 As shown, the diffuse spot light field distribution function U of the corresponding sub-pixel is obtained according to formula (1).
[0034]
[0035] The light field distribution U comprehensively characterizes the reconstruction quality and light field distribution characteristics of the diffuse spot. When l = lCDP When U represents the diffuse spot light field distribution at the central depth plane, when l = l VP When U represents the diffuse spot light field distribution at the viewing plane, let x i Let x be the X-axis coordinate of the i-th sub-pixel. i = (i-1)×p s Characterization points (x) of the global angular diffuse spot light field distribution at the central depth plane and the viewing plane are constructed. i ,w i (See attached) Figure 5 As shown, where w i Let U be the peak width of the diffuse spot light field distribution U of the i-th sub-pixel at the corresponding plane. Piecewise interpolation of the diffuse spot characterization points on the center depth plane and the viewing plane using cubic spline curves yields the performance curve S3(x) characterizing the reconstruction of the diffuse spot at continuous angles across the entire domain. Its piecewise interpolation formula can be expressed as:
[0036] S3(x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i )3 (2)
[0037] In the formula, S3(x) represents the performance curve constructed after cubic spline interpolation, and a i b i c i d i The coefficients to be determined are obtained through piecewise slopes and multiple derivatives. Ultimately, the global optimization function F(x) of the lens can be expressed as:
[0038]
[0039] Preferably, considering the different sensitivities of the human eye to spatial resolution and angular resolution in 3D displays, optimization weights of γ1:γ2 = 3:1 are assigned to the blur spots at the center depth plane and the viewing plane, respectively. Based on the above-described global optimization function construction process and the initial lens surface parameters, the initial global optimization function value is 5.32.
[0040] The iterative optimization process of the lens is as follows: Figure 8As shown, according to the initial lens surface profile parameters c = -1.65, k = 0, a = 0 input above, new surface profile parameters c' = -1.32, k' = -2.33, a' = 2.31 are generated, and the global optimization function value of the new parameters is calculated to be 4.73, which is smaller than the old global optimization function value 5.32, so the new optimization function value is directly replaced by the new parameters. Conversely, if the new optimization function value is larger, then the new surface profile parameters are accepted with a certain probability. The acceptance probability can be expressed as
[0041] P = exp{m / [F m (c,k,α)-F m (c',k',a')]} (4)
[0042] In the formula, P represents the probability of accepting new parameters, m is the number of iterations, c, k, a and c', k', a' represent the original surface profile parameters and the new surface profile parameters respectively. According to the above iterative optimization process of the lens, new surface profile parameters c', k', a' are continuously generated for surface profile optimization, and the number of iterations m is accumulated until the optimization function value is not significantly reduced or the number of iterations reaches a set value, and the optimization process is ended. In the initial stage of iterative optimization, a higher probability is allowed to accept worse solutions, so as to escape from the local optimal value. As the number of iterations increases, the method is more inclined to fine-tune in the local. Finally, after multiple iterations of optimization, the final output lens surface profile parameters are c = -0.66, k = 6.023, a = -4.95. As shown in the attached Figure 10 and attached Figure 11 As shown, the performance curves of the diffraction spot at the central depth plane and the viewing plane after optimization are significantly better than before optimization, which is manifested as the corresponding diffraction spot size of each field angle is smaller.
Claims
1. A method for lens optimization for global dual depth in an integral imaging 3D display system, characterized in that, The method comprises two processes of a global optimization function construction of the lens and an iterative optimization of the lens; in the global optimization function construction of the lens, a two-dimensional analysis model is established according to structural parameters of an integral imaging 3D display system, a sub-pixel gate function Rect and a lens point spread function PSF convolution are used to represent the distribution of a diffraction spot light field of each sub-pixel covered by the lens at a corresponding field of view angle and a corresponding reconstruction plane, a full width at half maximum and a tenth peak width are respectively taken for numerical representation of the diffraction spot size according to the light field distribution characteristics at different reconstruction planes, a performance curve of the peak width of the diffraction spot at the central depth plane and the viewing plane changing with the global angle is constructed through cubic spline interpolation, and numerical quantization is performed through integral summation to obtain the global optimization function of the lens; In the iterative optimization process of the lens, the surface profile parameters of the lens are input and the current function value is calculated, new surface profile parameters are generated and the new global optimization function value is calculated in each iteration process, the global optimization function values before and after optimization are compared, if the new optimization function value is smaller, it indicates that the diffraction spot size reconstructed by the current lens is smaller, and the new surface profile parameters are directly replaced, if the new optimization function value is larger, the new surface profile parameters are accepted with a certain probability, and the iteration number is accumulated until the optimization function value is not obviously reduced or the iteration number reaches a set value, and the finally optimized lens structure is output.
2. The method of claim 1, wherein the lens optimization is performed for a global dual depth in an integral imaging 3D display system. The global optimization function construction process of the lens, taking the intersection of the axis in the lens unit and the plane of the sub-pixel on the display screen as the origin, the direction of the display screen as the X axis, and the direction perpendicular to the display screen as the Y axis, let i be the index of the sub-pixel under the lens unit, the aperture angle formed by the i-th sub-pixel and the lens optical center is represented as θ i The light field distribution of the sub-pixel light ray passing through the lens modulation at the axial depth l is represented by the point spread function PSF(θ, l) of the lens, the ideal sub-pixel is regarded as a rectangular gate function, the light field distribution after passing through the lens modulation is represented as the convolution of the sub-pixel gate function and the lens point spread function, and the light field distribution U formed by the i-th sub-pixel under the lens unit at the axial depth l is represented as: where A represents the luminous intensity of a sub-pixel, p s represents the size of a sub-pixel, rect(·) represents a rectangular function, * represents a convolution operation, in the point spread function PSF of a lens, i represents the index of a sub-pixel, i ∈ {0, 1, 2, 3…i-1}, l represents the axial depth, l ∈ {l CDP ,l VP}, c represents the vertex curvature of a lens, k represents the conic coefficient of a lens, a represents the aspheric coefficient of a lens, the light field distribution U comprehensively characterizes the reconstruction quality of a diffraction spot and the light field distribution characteristics, when l = l CDP , U represents the light field distribution of a diffraction spot at a central depth plane, when l = l VP , U represents the light field distribution of a diffraction spot at a viewing plane, let x i be the X-axis coordinate of the i-th sub-pixel, i.e., x i = (i-1) × p s , construct the representation points (x i , w i ) of the full-angle diffraction spot light field distribution at the central depth plane and the viewing plane, where w i is the peak width of the i-th sub-pixel in the diffraction spot light field distribution U at the corresponding plane, and perform piecewise interpolation on the diffraction spot representation points at the central depth plane and the viewing plane by using a cubic spline curve to obtain a performance curve S3(x) representing the reconstruction of a full-angle continuous diffraction spot, and the piecewise interpolation formula can be represented as S3(x) = a i + b i (x - x i ) + c i (x - x i ) 2 + d i (x - x i ) 3 , where S3(x) represents the performance curve constructed by cubic spline interpolation, a i , b i , c i , d i are undetermined coefficients determined by piecewise slope and multiple derivatives, finally, the global optimization function F(x) of the lens can be represented as In the formula, N{·} represents a normalization operation, and γ1 and γ2 are optimization weight values.
3. The method of claim 2, wherein the lens optimization is performed for a global dual depth in an integral imaging 3D display system. To precisely characterize the diffraction spot size at the central depth plane and at the viewing plane, for the diffraction spot at the central depth plane, the full width at half maximum of the light field distribution is taken to characterize the diffraction spot size of the 3D voxel, i.e., w i = FWHM [U(l CDP )], where FWHM [·] denotes the full width at half maximum operation; for the diffraction spot at the viewing plane, the tenth of the peak width is taken to characterize the diffraction spot size of the viewing plane at the viewpoint, i.e., w i = FWTM [U(l VP )], where FWTM [·] denotes the tenth of the peak width operation.
4. The method of claim 1, wherein the lens optimization is for a global dual depth in an integral imaging 3D display system. In the iterative optimization process of the lens, the surface profile parameters of the lens are input and the current function value is calculated, new surface profile parameters are generated and the new global optimization function value is calculated in each iteration process, the global optimization function values before and after optimization are compared, if the new optimization function value is smaller, it indicates that the diffraction spot size reconstructed by the current lens is smaller, and the new surface profile parameters are directly replaced, if the new optimization function value is larger, the new surface profile parameters are accepted with a certain probability, and the iteration number is accumulated until the optimization function value is not obviously reduced or the iteration number reaches a set value, and the finally optimized lens structure is output. P = exp{m / [F m (c, k, a) - F m (c', k', a')]} In the formula, P represents the probability of accepting the new parameters, m represents the iteration number, c, k, and a represent the original surface profile parameters, c', k', and a' represent the new surface profile parameters, according to the above iterative optimization process, new surface profile parameters c', k', and a' are continuously generated for surface profile optimization, the iteration number m is accumulated, and the optimization process is ended when the optimization function value is not obviously reduced or the iteration number reaches a set value, in the initial stage of the iterative optimization, a larger probability is allowed to accept a worse solution, so as to escape from a local optimal value, with the increase of the iteration number, the method is more inclined to fine optimization in the local, and finally the global minimum result of the optimization function is found.