A high-quality holographic 3D display method based on interlayer edge optimization

Abstract

The application provides a high-quality holographic 3D display method based on interlayer edge optimization, which comprises three steps: in the first step, a 3D scene is subjected to layering treatment, and the 3D object is subjected to equidistant layering in the axial direction according to the depth distribution range of the 3D object; in the second step, a forward propagation model based on the layered slices is constructed according to the angular spectrum diffraction theory, so that each layer image is subjected to weighted calculation with the initial image, and a mask is established to separate the effective area and the background area. Then, the initial complex amplitude distribution of the hologram plane is established, the loss function of the target complex amplitude distribution is calculated layer by layer, the complex amplitude distribution of the hologram plane is optimized based on the stochastic gradient descent algorithm, then the complex amplitude of the hologram plane is diffraction propagated to the image plane according to the angular spectrum diffraction theory to obtain the image plane complex amplitude distribution, and the optimized hologram plane complex amplitude distribution is obtained; in the third step, the optimized hologram plane complex amplitude distribution is subjected to nonlinear phase compensation, and the phase information is extracted to generate a pure phase hologram, so that when a coherent light source irradiates the pure phase hologram, the high-quality holographic 3D display based on interlayer edge optimization is realized.

Description

Technical Field

[0001] This invention relates to holographic display technology, and more specifically, to a high-quality holographic 3D display method based on interlayer edge optimization. Background Technology

[0002] Holographic 3D display technology, with its ability to completely record and reconstruct the wavefront information of 3D scenes, has shown broad application potential in various fields such as education and healthcare. In current hologram generation methods, to reconstruct realistic 3D scenes with depth cues, it is typically necessary to divide the 3D object into multiple discrete planes along the axial direction. However, since the edges of 3D objects usually correspond to locations of abrupt changes in depth or intensity in the scene, the light field exhibits strong amplitude jumps and phase discontinuities. The diffracted light from adjacent planes coherently superimposes in this region, forming significant edge crosstalk. To improve edge reconstruction quality, some researchers have optimized the sampling interval between multiple planes or introduced random phase diffusion to break the constructive interference of coherent light, thereby reducing crosstalk. However, the introduction of random phase introduces random speckle noise, affecting the quality of holographic displays. Some researchers have used convolutional neural networks to predict multi-plane holograms. Through end-to-end network training, they have suppressed crosstalk between adjacent planes to some extent. However, due to the strong nonlinear characteristics and drastic gradient changes in light intensity in the edge regions, the network's generalization ability at the edges is poor, easily producing artifacts. Therefore, how to achieve high-quality edge reconstruction of multi-planar 3D objects has become an urgent problem to be solved in holographic 3D display. Summary of the Invention

[0003] This invention proposes a high-quality holographic 3D display method based on inter-layer edge optimization. (See attached diagram) Figure 1 As shown, the method includes three steps: First, the 3D scene is layered, and the 3D objects are divided into equally spaced layers along the axial direction according to their depth distribution range. Second, based on angular spectral diffraction theory, a forward propagation model based on layered slices is constructed, and each layer image is weighted and calculated with the initial image. A mask is established to separate the effective region and the background region. Then, an initial complex amplitude distribution of the hologram plane is established, and the loss function of the target complex amplitude distribution is calculated layer by layer. The complex amplitude distribution of the hologram plane is optimized based on the stochastic gradient descent algorithm. Subsequently, according to angular spectral diffraction theory, the complex amplitude of the hologram plane is diffracted and propagated to the image plane to obtain the complex amplitude distribution of the image plane, resulting in the optimized complex amplitude distribution of the hologram plane. Third, nonlinear phase compensation is performed on the optimized complex amplitude distribution of the hologram plane to extract phase information and generate a pure phase hologram. When a coherent light source illuminates the pure phase hologram, a high-quality holographic 3D display with optimized inter-layer edges is achieved.

[0004] Preferably, in step two, for the image of each depth layer, the complex amplitude distribution propagated to the corresponding target plane is calculated using forward angular spectrum propagation. The target complex amplitude for each layer is:

[0005]

[0006] Among them, F, F -1 Let f(x,y) represent the Fast Fourier Transform and Inverse Fast Fourier Transform functions, respectively, where (x,y) are the target plane coordinates, (x,y) are the object plane coordinates, and (f(x,y)) are the object plane coordinates. x , f y ) represents the spatial frequency, U t (X,Y) represents the complex amplitude distribution of the target light field, U(x,y) represents the complex amplitude distribution of the object light field, and H(f x , f y Let be the angular spectrum propagation function, and its expression is:

[0007]

[0008] Where j represents the imaginary unit, k represents the wave number, and z i Let λ be the diffraction distance on the i-th plane, and λ be the wavelength.

[0009] Next, masks are extracted from the original images of each plane. The mask for each layer is calculated by weighted superposition of the intensity distribution of the corresponding original image and the complex amplitude of the target plane obtained in step one, and the expression is:

[0010]

[0011] Among them, Mask i (x,y) is the mask of the i-th plane, w1 and w2 are preset weight coefficients, satisfying w1+w2=1, I i (x, y) represents the original image intensity distribution on the i-th plane. This weighted mask is used to distinguish the effective region from the background region on each plane. Pixels within the effective region participate in optimization, while pixels in the background region are suppressed. The weighted mask preserves the edge sharpness and clarity of the original image and reduces crosstalk caused by the superposition of light fields in the edge regions between different planes.

[0012] An initial complex amplitude distribution is defined on the holographic plane. The amplitude component is set to a constant 1, representing a uniform light intensity distribution across the entire plane, while the phase component is randomly selected, ranging from 0 to 2π. This initial complex amplitude distribution is propagated backward to the target plane using an angular spectrum backpropagation algorithm, resulting in a reconstructed complex amplitude distribution on the target plane. The reconstructed complex amplitude is compared with the target complex amplitude, and the loss function is calculated. The loss function expression is:

[0013]

[0014] Where L sum Let L be the total loss value, q be the number of planes, and L be the total loss value. i Let L be the in-plane loss value of the i-th plane. inter This represents the crossover loss value between each plane. L i The loss value for each plane is calculated independently to evaluate the reconstruction quality of that plane itself, unaffected by other planes. Specifically, it is calculated as the mean square error between the target complex amplitude distribution and the reconstructed complex amplitude distribution.

[0015]

[0016] Where MSE(·) is the average of the squared deviations between the predicted and actual values. A r and Φ r These are the amplitude and phase distributions of the reconstructed plane, A. t and Φ t These represent the amplitude and phase distributions of the target plane, respectively. p is the weighting coefficient for the background region, and U... rbg and U tbg These are the reconstructed amplitude distribution and the target amplitude distribution in the background region, respectively. inter The expression is:

[0017]

[0018] Where [0] is the tensor distribution of all zeros, Mask m It is the mask of the m-th layer, U n Let be the complex amplitude distribution of the nth layer. The crosstalk intensity is evaluated by calculating the energy distribution of the light field of the nth layer in the effective region of the mth layer. When the light field from a non-current layer leaks into the effective region of the current layer, this loss increases, thereby guiding stochastic gradient descent to optimize active crosstalk suppression.

[0019] Based on the obtained total loss function, the complex amplitude distribution of the hologram plane is used as a trainable parameter and iteratively updated through stochastic gradient descent.

[0020] Repeat the loss function calculation and stochastic gradient descent update steps above until the loss function of the complex amplitude distribution in the hologram plane tends to converge, and finally obtain the optimized complex amplitude distribution.

[0021] Preferably, in step three, the phase distribution corresponding to the optimized hologram planar complex amplitude distribution obtained in step two is extracted. To simulate and compensate for the nonlinear distortion in the photoelectric response of the spatial light modulator, a nonlinear gamma correction mechanism is introduced. Specifically, the extracted phase is first linearly mapped to the interval between 0 and 1, and then a power transformation is performed using a set correction factor to simulate the nonlinear mapping characteristics between the input grayscale and the output phase modulation. After nonlinear correction, the corresponding phase distribution is extracted to generate a pure phase hologram. The pure phase hologram is loaded onto the spatial light modulator, and a collimated laser beam illuminates the working area of ​​the spatial light modulator to achieve optical holographic reconstruction. Attached Figure Description

[0022] Appendix Figure 1 This is a flowchart illustrating a high-quality holographic 3D display method based on interlayer edge optimization according to the present invention.

[0023] Appendix Figure 2 Figure 1 shows the reconstruction effect of a high-quality holographic 3D display method based on interlayer edge optimization according to the present invention. Figure 2(a) shows the reconstruction effect at a reconstruction distance of 22cm, Figure 3(b) shows the reconstruction effect at a reconstruction distance of 24cm, and Figure 4(c) shows the reconstruction effect at a reconstruction distance of 26cm.

[0024] It should be understood that the above figures are only schematic and are not drawn to scale. Detailed Implementation

[0025] The following will describe in detail, with reference to the accompanying drawings and embodiments, a high-quality holographic 3D display method based on interlayer edge optimization proposed in this invention. It should be noted that the following embodiments are only for further illustration of this invention and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description are still within the scope of protection of this invention.

[0026] One embodiment of the present invention is as follows: To verify the feasibility of the proposed method, three mosaic images are selected as the recorded objects, with a resolution of 500×500. The upper left, lower left, and lower right mosaic images are located on depth planes of 22cm, 24cm, and 26cm, respectively, and the incident light wavelength is 532nm. The hologram has a resolution of 1920×1080 and a pixel spacing of 6.4μm. The loss function is calculated based on the layering of the multi-plane image, and the hologram is iteratively optimized using the stochastic gradient descent method, where the number of iterations for loss function calculation and stochastic gradient descent is set to 200. The obtained hologram is loaded onto a spatial light modulator, and holographic reconstruction can be achieved under collimated laser beam illumination, as shown in the attached figure. Figure 2 As shown. Among them, the appendix Figure 2(a) shows the holographic reconstruction effect when the top left image is focused. Figure 2 (b) shows the holographic reconstruction effect when the lower left mosaic is focused. Figure 2 (c) shows the holographic reconstruction effect when the bottom right mosaic is focused. The holographic reconstructed image generated by the method has clear edges and no significant diffraction artifacts, realizing the ability to reconstruct high-quality multi-planar 3D objects.

Claims

1. A high-quality holographic 3D display method based on inter-layer edge optimization, characterized in that, The method includes three steps: First, the 3D scene is layered by dividing it into equal-interval layers along the axis according to the depth distribution range of the 3D objects. The second step is to construct a forward propagation model based on layered slices, according to the angular spectrum diffraction theory, so that each layer of image is weighted and calculated with the initial image, and the effective area and background area are separated by establishing a mask. Then, an initial complex amplitude distribution in the hologram plane is established, and the loss function of the target complex amplitude distribution is calculated layer by layer. The complex amplitude distribution in the hologram plane is optimized based on the stochastic gradient descent algorithm. Subsequently, according to the angular spectrum diffraction theory, the complex amplitude of the hologram plane is diffracted and propagated to the image plane to obtain the complex amplitude distribution in the image plane, thus obtaining the optimized complex amplitude distribution in the hologram plane. In the third step, nonlinear phase compensation is performed on the optimized complex amplitude distribution in the hologram plane to extract phase information and generate a pure phase hologram. When the pure phase hologram is illuminated by a coherent light source, a high-quality holographic 3D display with optimized interlayer edges is achieved.

2. The high-quality holographic 3D display method based on inter-layer edge optimization according to claim 1, characterized in that, In step two, for the image of each depth layer, the complex amplitude distribution propagated to the corresponding target plane is calculated using forward angular spectrum propagation; the target complex amplitude for each layer is: Among them, F, F -1 Let f(x,y) represent the Fast Fourier Transform and Inverse Fast Fourier Transform functions, respectively, where (x,y) are the target plane coordinates, (x,y) are the object plane coordinates, and (f(x,y)) are the object plane coordinates. x , f y ) represents the spatial frequency, U t (X,Y) represents the complex amplitude distribution of the target light field, U(x,y) represents the complex amplitude distribution of the object light field, and H(f x , f y Let be the angular spectrum propagation function, and its expression is: Where j represents the imaginary unit, k represents the wave number, and z i Let λ be the diffraction distance of the i-th plane, and λ be the wavelength. Next, masks are extracted from the original images of each plane. The mask for each layer is calculated by weighted superposition of the intensity distribution of the corresponding original image and the complex amplitude of the target plane obtained in step one, and the expression is: Among them, Mask i (x,y) is the mask of the i-th plane, w1 and w2 are preset weight coefficients, satisfying w1+w2=1, I i (x,y) represents the original image intensity distribution of the i-th plane; this weighted mask is used to distinguish the effective region from the background region of each plane. Pixels in the effective region participate in optimization, while pixels in the background region are suppressed; the weighted mask preserves the edge clarity and sharpness of the original image and reduces crosstalk caused by the superposition of light fields in the edge regions between different planes. An initial complex amplitude distribution is set on the holographic plane, where the amplitude component is set to a constant 1, representing a uniform light intensity distribution across the entire plane, and the phase component is randomly selected, ranging from 0 to 2π. This initial complex amplitude distribution is then propagated backward to the target plane using an angular spectrum backpropagation algorithm to obtain the reconstructed complex amplitude distribution on the target plane. The reconstructed complex amplitude is compared with the target complex amplitude, and the loss function is calculated. The expression for the loss function is: Where L sum Let q be the total loss value, q be the number of planes, and L be the total loss value. i Let L be the in-plane loss value of the i-th plane. inter L represents the crossover loss value between each plane; i The loss value for each plane is calculated independently to evaluate the reconstruction quality of that plane itself, unaffected by other planes. Specifically, it is calculated as the mean square error between the target complex amplitude distribution and the reconstructed complex amplitude distribution. Where MSE(·) is the average of the squared deviations between the predicted and actual values; A r and Φ r These are the amplitude and phase distributions of the reconstructed plane, A. t and Φ t These represent the amplitude and phase distributions of the target plane, respectively; p is the weighting coefficient of the background region, and U... rbg and U tbg These are the reconstructed amplitude distribution and the target amplitude distribution in the background region, respectively; L inter The expression is: Where [0] is the tensor distribution of all zeros, Mask m It is the mask of the m-th layer, U n Let be the complex amplitude distribution of the nth layer; the crosstalk intensity is evaluated by calculating the energy distribution of the light field of the nth layer in the effective region of the mth layer. When the light field of a non-current layer leaks into the effective region of the current layer, this loss increases, thereby guiding stochastic gradient descent to optimize active crosstalk suppression. Based on the obtained total loss function, the complex amplitude distribution of the hologram plane is used as a trainable parameter and iteratively updated through stochastic gradient descent. Repeat the loss function calculation and stochastic gradient descent update steps above until the loss function of the complex amplitude distribution in the hologram plane tends to converge, and finally obtain the optimized complex amplitude distribution.

3. The high-quality holographic 3D display method based on inter-layer edge optimization according to claim 1, characterized in that, In step three, the phase distribution corresponding to the optimized hologram planar complex amplitude distribution is extracted. To simulate and compensate for the nonlinear distortion of the spatial light modulator in the photoelectric response, a nonlinear gamma correction mechanism is introduced. Specifically, the extracted phase is first linearly mapped to the interval between 0 and 1, and then a power transformation is performed on it using a set correction factor to simulate the nonlinear mapping characteristics between the input gray level and the output phase modulation amount. After nonlinear correction, the corresponding phase distribution is extracted to generate a pure phase hologram. The pure phase hologram is loaded onto the spatial light modulator, and the working area of ​​the spatial light modulator is illuminated by a collimated laser beam to achieve optical holographic reconstruction.

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