A Method for Amplification and Quality Improvement of Optical Cylindrical Holographic Display

Abstract

The present invention proposes a method for magnification and quality improvement of optical cylindrical holographic display. The method includes three parts: improving the optical cylindrical holographic display scheme, optimizing the Fourier hologram by stochastic gradient descent, and hologram reconstruction. During the generation process of the method, first, a Fourier lens is added in the plane diffraction process of the optical cylindrical holographic display and the cylindrical diffraction process is cancelled. Then, using the stochastic gradient descent optimization Fourier algorithm proposed by the present invention, the randomly initialized hologram is reconstructed, and the loss value between the hologram and the target image is calculated. Then, its gradient is obtained. According to the backpropagation formula, the hologram is updated. The updated hologram is repeated the above operations until the set threshold is met, and the optimized hologram is obtained. Finally, the hologram is loaded for reconstruction. Compared with the optical cylindrical holographic display method before improvement, the hologram obtained by the method of the present invention can reconstruct a cylindrical image with higher quality and larger size, and has good application prospects in the cylindrical 360° display.

Description

Technical Field

[0001] The present invention relates to a holographic display technology, in particular to a method for magnifying and improving the quality of optically realizable cylindrical holographic displays. Background Art

[0002] Holographic display, as one of the most ideal true three-dimensional display technologies, has always received great attention. However, current planar holograms are limited by the too large pixel size of spatial light modulators and cannot reconstruct a sufficiently large field of view angle. Viewers can only view the holographic reconstruction image within a narrow angular range. In order to enable viewers to see the holographic reconstruction image in different directions, cylindrical holograms have been widely studied due to their 360° field of view region. However, the size and quality of current optical cylindrical holographic displays are not conducive to viewing. Compared with the existing large number of magnification and quality improvement methods in planar holograms, the magnification and quality improvement methods for optical cylindrical holographic displays have not been widely studied. Therefore, there is still great research potential for the magnification and quality improvement of optical cylindrical holographic displays. Summary of the Invention

[0003] This method aims at the problems of low quality and limited size of the above-mentioned optical cylindrical holographic display, and proposes a method for magnifying and improving the quality of optical cylindrical holographic displays. The proposed method replaces the planar diffraction process with a Fourier transform process, cancels the cylindrical propagation process, and uses stochastic gradient descent for hologram optimization. Compared with the existing optical cylindrical holographic display schemes, the hologram of the optical cylindrical holographic display obtained by this method can reconstruct an image with a larger size and higher quality.

[0004] The method for magnifying and improving the quality of the optical cylindrical holographic display is as Figure 1 and Figure 2 shown. The improved optical cylindrical holographic display scheme is specifically described as follows: adding a Fourier lens in the planar diffraction process of the optical cylindrical holographic display and canceling the cylindrical diffraction process; the process of using stochastic gradient descent for hologram optimization is specifically divided into six steps: ① Initialize a random phase as the Fourier hologram Ho, ② Reconstruct the initialized Fourier hologram Ho using the inverse Fourier algorithm to obtain the reconstructed image Ur, ③ Substitute the reconstructed image Ur and the target plane image Ue into the loss function to calculate the loss value, ④ Calculate the gradient of the calculated loss value and perform backpropagation to update the phase of the hologram, ⑤ Reconstruct the updated hologram Hi again, repeat operations ③ - ④ for optimization, ⑥ When the set number of optimization times is satisfied or a satisfactory reconstruction quality is obtained, obtain the final hologram; the reconstruction process is divided into three steps: ① Load the hologram, ② Use a conical mirror with a bottom angle of 45° to convert the reconstructed plane image to a cylinder, ③ Receive the holographic cylinder reconstruction image.

[0005] In the plane diffraction process of optical cylindrical holographic display, adding a Fourier lens and canceling the cylindrical diffraction process means replacing the angular spectrum diffraction process of the original cylindrical holographic display with Fourier transform. That is, replacing the originally finally generated angular spectrum hologram with a Fourier hologram and canceling the cylindrical diffraction process in the optical cylindrical holographic display scheme before improvement.

[0006] Initializing a random phase as the Fourier hologram Ho means generating a random phase distribution within the range of 0 - 2π using a random function as the initial Fourier hologram Ho.

[0007] Reconstructing the initialized Fourier hologram Ho using the inverse Fourier algorithm to obtain the reconstructed image Ur means reconstructing the Fourier hologram Ho using the inverse Fourier transform, expressed as Ur(x,y) = IFFT[FFT(Us(x,y))], where Us is the complex amplitude of the source field and Ur is the complex amplitude of the diffraction field.

[0008] Calculating the loss function between the reconstructed image Ur and the target image Uo means substituting the reconstructed complex amplitude image and the target image into the loss function for calculation to obtain the loss value Loss, as Figure 2 shown.

[0009] Calculating the gradient of the calculated loss and performing backpropagation to update the phase of the hologram means calculating the gradient of the calculated loss value with respect to the phase of the hologram Ho to obtain its gradient According to the backpropagation formula Hi = Ho - lr * Grad, the updated phase of the hologram Hi is obtained, where lr is the learning rate.

[0010] Reconstructing the updated hologram Hi again and repeating steps ④ - ⑤ for optimization means replacing the original Fourier hologram with the updated Fourier hologram and continuing the previous two steps to calculate the loss value loss and the gradient, and performing backpropagation to continuously optimize the phase of the hologram.

[0011] When the set number of optimization times is met or a satisfactory reconstruction quality is obtained, obtaining the final hologram means stopping the optimization process when the number of optimization times meets the set number or the reconstruction quality reaches the set threshold, and retaining the hologram of the previous iteration as the finally optimized hologram.

[0012] Loading the hologram means loading the hologram onto a planar phase - type spatial light modulator.

[0013] Using a conical mirror with a bottom angle of 45° to convert the reconstructed planar image to a cylindrical image means converting the reconstructed planar image into a cylindrical image through a conical mirror with a bottom angle of 45°.

[0014] The received holographic reconstruction image mentioned above refers to the cylindrical image reconstructed on a cylindrical receiver.

[0015] The present invention greatly improves the display effect of optical cylindrical holographic display. In the improved optical cylindrical holographic display scheme, the size of the reconstructed image is significantly increased, and the quality of the reconstructed image is also significantly improved. Brief Description of the Drawings

[0016] Appendix Figure 1 is the implementation model of the proposed method.

[0017] Appendix Figure 2 is the proposed optimization method.

[0018] Appendix Figure 3 is the relationship between the optimization iteration times of the proposed method and the reconstruction quality.

[0019] Appendix Figure 4 is the simulation reconstruction results of the proposed method and the method before improvement. (b), (e), (h) are the simulation reconstruction results of the optical cylindrical holographic display before improvement, and (c), (f), (i) are the simulation reconstruction results after the improvement of the present invention.

[0020] Appendix Figure 5 is the optical reconstruction results of the proposed method and the method before improvement. (a), (d) are the optical reconstruction results of the optical cylindrical holographic display before improvement, and (b), (c), (e), (f) are the optical reconstruction results of the optical cylindrical holographic display after the improvement of the present invention.

[0021] Appendix Figure 6 is the detailed optical reconstruction results of the proposed method and the method before improvement.

[0022] Note: The above drawings are only schematic and are not drawn to scale. Detailed Embodiment

[0023] A typical embodiment of a method for magnifying and improving the quality of an optical cylindrical holographic display according to the present invention will be described in detail below to further specifically describe the method. It is necessary to point out here that the following embodiments are only used to further illustrate the method and cannot be construed as limiting the protection scope of the method. Those skilled in the art can make some non-essential improvements and adjustments to the method according to the content of the method above, and still fall within the protection scope of the present invention.

[0024] The present invention proposes a method for magnifying and improving the quality of an optical cylindrical holographic display, which includes three parts: improving the optical cylindrical holographic display scheme, optimizing the Fourier hologram by stochastic gradient descent, and hologram reconstruction.

[0025] The method for magnification and quality improvement of the optical cylindrical holographic display is as follows Figure 1 and Figure 2 shown. The improved optical cylindrical holographic display scheme is specifically described as follows: adding a Fourier lens in the plane diffraction process of the optical cylindrical holographic display and canceling the cylindrical diffraction process; the hologram optimization process using stochastic gradient descent is specifically divided into six steps: ① Initialize a random phase as the Fourier hologram Ho, ② Reconstruct the initialized Fourier hologram Ho using the inverse Fourier algorithm to obtain the reconstructed image Ur, ③ Substitute the reconstructed image Ur and the target plane image Ue into the loss function to calculate the loss value, ④ Calculate the gradient of the calculated loss value and perform backpropagation to update the phase of the hologram, ⑤ Reconstruct the updated hologram Hi again, repeat operations ③ - ④ for optimization, ⑥ When the set number of optimization times is met or a satisfactory reconstruction quality is obtained, the final hologram is obtained. The reconstruction process is divided into three steps: ① Load the hologram, ② Use a conical mirror with a bottom angle of 45° to convert the reconstructed plane image to a cylinder, ③ Receive the holographic cylindrical reconstruction image.

[0026] Adding a Fourier lens in the plane diffraction process of the optical cylindrical holographic display and canceling the cylindrical diffraction process means replacing and canceling the angular spectrum diffraction process of the original cylindrical holographic display and using Fourier transform instead, that is, replacing the originally finally generated angular spectrum hologram with a Fourier hologram and canceling the cylindrical diffraction process in the optical cylindrical holographic display scheme before improvement.

[0027] Initializing a random phase as the Fourier hologram Ho means using a random function to generate a random phase distribution within the range of 0 - 2π as the initial Fourier hologram Ho.

[0028] Reconstructing the initialized Fourier hologram Ho using the inverse Fourier algorithm to obtain the reconstructed image Ur means reconstructing the Fourier hologram Ho using the inverse Fourier transform, expressed as Ur(x,y) = IFFT[FFT(Us(x,y))], where Us is the complex amplitude of the source field and Ur is the complex amplitude of the diffraction field.

[0029] Calculating the loss function with the reconstructed image Ur and the target image Uo means substituting the reconstructed complex amplitude image and the target image into the loss function for calculation to obtain the loss value Loss, as Figure 2 shown.

[0030] Calculating the gradient of the calculated loss and performing backpropagation to update the phase of the hologram means calculating the gradient of the calculated loss value with respect to the phase of the hologram Ho to obtain its gradient According to the backpropagation formula Hi = Ho - lr * Grad, the updated hologram phase Hi is obtained, where lr is the learning rate.

[0031] The operation of reconstructing the updated hologram Hi again and repeating steps ④ - ⑤ for optimization means replacing the original Fourier hologram with the updated Fourier hologram, and then continuing the previous two steps to calculate the loss value loss and the gradient, and performing backpropagation to continuously optimize the hologram phase.

[0032] When the set number of optimization times is satisfied or a satisfactory reconstruction quality is obtained, obtaining the final hologram means that when the number of optimization times meets the set number or the reconstruction quality reaches the set threshold, the optimization process is stopped, and the hologram of the previous iteration is retained as the finally optimized hologram.

[0033] The operation of loading the hologram means loading the hologram onto a planar phase - type spatial light modulator.

[0034] The operation of using a conical mirror with a bottom angle of 45° to convert the reconstructed planar image into a cylindrical image means that the reconstructed planar image is converted into a cylindrical image through a conical reflecting mirror with a bottom angle of 45°.

[0035] The operation of receiving the holographic reconstruction image means receiving the reconstructed cylindrical image on a cylinder.

[0036] In the example of the present invention, using Figure 2 the method of optimizing the Fourier hologram by means of the schematic random gradient descent to generate a Fourier hologram with a resolution of 1080×1080.

[0037] Applying the generated hologram described above in Figure 1 the optimized optical cylindrical holographic display shown. From Figure 3 the relationship between the reconstructed cylindrical image and the number of iterations shown, it can be seen that as the number of iterations progresses, the quality of the reconstructed image rapidly rises and converges. The simulation results of the cylindrical display implemented by the present invention are as shown in Figure 4 (b), (e), (f) are the simulation results of the optical cylindrical holographic display before improvement, and (c), (h), (i) are the simulation results of the improved optical cylindrical holographic display of the present invention. The number of all optimization times is 500 times. From the comparison between (b) and (c), (e) and (f), (h) and (i), the present invention has achieved a prominent effect of quality improvement.

[0038] Figure 5These are the optical experimental results for realizing optical cylindrical holographic display in the present invention, using Fourier lenses with focal lengths of 250 mm and 300 mm respectively. The results of the optical cylindrical holographic display before improvement are shown in rows (a) and (d). The experimental results of the improved optical cylindrical holographic display using a 250-mm Fourier lens in the present invention are shown in rows (b) and (e). The experimental results of the improved optical cylindrical holographic display using a 300-mm Fourier lens in the present invention are shown in rows (c) and (f). Figure 6 (h), (i), and (j) highlight the details of the experimental pictures. Figure 6 (i) and (j) are the experimental results after improvement in the present invention using Fourier lenses with focal lengths of 250 mm and 300 mm respectively. It can be seen that significant quality improvement and magnification effects have been achieved in the improved optical cylindrical holographic display of the present invention. The magnification effect increases with the increase in the focal length of the Fourier lens.

Claims

1. A method for magnification and quality improvement of optical cylindrical holographic display, characterized in that The method includes three parts: improving the optical cylindrical holographic display scheme, optimizing the Fourier hologram by stochastic gradient descent, and hologram reconstruction. The improvement of the optical cylindrical holographic display scheme is specifically described as follows: adding a Fourier lens during the plane diffraction process of the optical cylindrical holographic display and canceling the cylindrical diffraction process. The optimization of the Fourier hologram by stochastic gradient descent is specifically described as follows: Step 1, initialize a random phase as the Fourier hologram Ho; Step 2, reconstruct the initialized Fourier hologram Ho using the inverse Fourier algorithm to obtain the reconstructed image Ur; Step 3, substitute the reconstructed image Ur and the target plane image Ue into the loss function to calculate the loss value; Step 4, calculate the gradient of the calculated loss value and perform backpropagation to update the phase of the hologram; Step 5, reconstruct the updated hologram Hi again, repeat the operations of Step 3 and Step 4 for optimization; Step 6, when the set number of optimization times is satisfied or a satisfactory reconstruction quality is obtained, obtain the final hologram. The hologram reconstruction is specifically described as follows: Step 1, load the hologram; Step 2, use a conical mirror with a bottom angle of 45° to convert the reconstructed plane image to a cylinder; Step 3, receive the holographic cylindrical reconstruction image.

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