Cylindrical Holographic Speckle Suppression Method Based on Directional Gradient Update

Abstract

The present invention proposes a method for suppressing cylindrical holographic speckles based on directional gradient update. Aiming at the problem of speckle suppression in cylindrical holographic reconstruction, a method for suppressing cylindrical holographic speckles based on directional gradient update is proposed. The proposed method regards the generation process of the cylindrical hologram as an optimization process, and uses the directional gradient update method to optimize the hologram. It is a novel algorithm for improving the reconstruction quality of cylindrical holograms, and can effectively suppress the speckle noise during the reconstruction of cylindrical holograms. Compared with the traditional cylindrical self-diffraction iteration method, the hologram obtained by the method of the present invention can reconstruct images of higher quality. Through the directional gradient update method, its convergent peak signal-to-noise ratio is much higher than that of the traditional self-diffraction iteration method, and it will have good application prospects in 360° cylindrical display.

Description

Technical Field

[0001] The present invention relates to a holographic display technology, in particular to a method for improving the reproduction quality of cylindrical holograms. Background Art

[0002] As an ideal true three-dimensional display technology, holographic display has always received great attention. However, current planar holograms are limited by the too large pixel size of the spatial light modulator and cannot reconstruct a sufficiently large viewing angle. Viewers can only view the holographic reproduction image within a narrow angle range. In order to enable viewers to see the holographic reproduction image in different directions, researchers have proposed cylindrical holograms. However, in the current cylindrical hologram generation algorithm, its reproduction quality is not satisfactory. Compared with the large number of existing reproduction quality improvement algorithms for planar holograms, the method for improving the reproduction quality of cylindrical holograms has not been widely studied. Among them, the largest factor causing quality degradation is speckle noise. Therefore, aiming at the problem of improving the quality of cylindrical holograms, the problem of speckle suppression in cylindrical hologram reproduction needs to be solved urgently. Summary of the Invention

[0003] In view of the above-mentioned speckle suppression problem in cylindrical hologram reproduction, the present invention proposes a method for suppressing cylindrical hologram speckles based on directional gradient update. The proposed method regards the process of generating a cylindrical hologram as an optimization process and uses the directional gradient update method to optimize the generation of the cylindrical hologram. It is a novel algorithm for improving the reproduction quality of cylindrical holograms and can effectively suppress the speckle noise during the reproduction of cylindrical holograms.

[0004] This method includes two parts: the generation and reconstruction of the cylindrical hologram; the process of generating the cylindrical hologram based on the directional gradient update method is as Figure 1 shown, and the process of generating the cylindrical hologram is specifically described as:

[0005] (1) Iterative loop. At the t-th loop, the cylindrical phase hologram is The reconstructed diffraction field is z t , in the result of the previous loop at the (t - 1)-th time, the cylindrical phase hologram is The reconstructed diffraction field is z t-1 , and the cylindrical diffraction algorithm adopts the angular spectrum algorithm of cylindrical waves. The reconstruction process is expressed as z t = IFT{FT[H t × TF CFP}, and the hologram generation process is expressed as where j is the imaginary unit, H t is the complex amplitude distribution of the diffraction field on the holographic plane, and TF CFP is the transfer function of the forward propagation model.

[0006] (2) Initialization: Use a random function to generate a random phase distribution within the range of 0 - 2π as the initial cylindrical hologram. Then, the cylindrical hologram is reconstructed using the cylindrical diffraction algorithm to obtain the initialized reconstructed complex amplitude distribution z0.

[0007] (3) Directional gradient update: Calculate the phase gradient error at the t-th iteration through directional gradient calculation. The specific calculation process is as follows. Among them, Re() represents the real part operation, conj() represents the conjugate operation, · represents the vector dot product, I is the original intensity image, and then the result phase hologram of the previous (t - 1)-th iteration is superimposed with it to obtain the phase hologram at the t-th iteration, denoted as

[0008] (4) Iterative loop termination: When the number of iterative optimizations meets the set number or the reconstruction quality reaches the set threshold, stop the iterative process and retain the phase hologram of the previous loop iteration as the optimized final phase hologram.

[0009] The reconstruction process of the cylindrical hologram is specifically described as follows: Step 1, load the cylindrical hologram onto the corresponding modulator; Step 2, receive the reconstructed image of the cylindrical hologram at the corresponding diffraction distance.

[0010] During the generation process of the cylindrical hologram, the cylindrical diffraction algorithm adopts the cylindrical convolution diffraction algorithm. The feature of this method is that it considers the diffraction process between two concentric cylindrical surfaces as a space-invariant system in the cylindrical coordinate system. The holographic plane diffraction field distribution U2 is the convolution of the object light field U1 and the point spread function h of this space-invariant system, expressed as: U2 = U1 * h, where * is the convolution operation. The cylindrical convolution diffraction algorithm based on the fast Fourier transform is expressed as U2 = IFFT[FFT(U1) × FFT(h)], where FFT and IFFT represent the fast Fourier transform and the inverse transform respectively.

[0011] The beneficial effect of this method is that the proposed method for suppressing speckle in cylindrical hologram reconstruction is an iterative algorithm based on directional gradient update. Compared with the traditional cylindrical self-diffraction iterative algorithm, this method has better convergence effect. The obtained cylindrical hologram can reproduce an image with better quality, maintaining a relatively high value of peak signal-to-noise ratio and far superior to the traditional method. Description of the Drawings

[0012] Att Figure 1 is the algorithm flow chart of the proposed method.

[0013] AttFigure 2 This is the speckle suppression effect diagram of the present invention. Detailed implementation manners

[0014] The following details a typical embodiment of a cylindrical holographic speckle suppression method based on directional gradient update of the present invention, and further specifically describes this method. It is necessary to point out here that the following embodiments are only used to further illustrate this method and cannot be construed as limiting the protection scope of this method. Those skilled in the art make some non-essential improvements and adjustments to this method according to the content of this method above, and still fall within the protection scope of the present invention.

[0015] The present invention proposes a cylindrical holographic speckle suppression method based on directional gradient update. This method includes two parts: the generation and reconstruction of a cylindrical hologram; the process of generating a cylindrical hologram by the directional gradient update method is as Figure 1 shown, and the generation process of the cylindrical hologram is specifically described as:

[0016] (1) Iterative loop. At the t-th loop, the cylindrical phase hologram is The reconstructed diffraction field is z t , and in the result of the (t - 1)-th loop of the previous round, the cylindrical phase hologram is The reconstructed diffraction field is z t-1 , and the cylindrical diffraction algorithm uses the angular spectrum algorithm of cylindrical waves. The reconstruction process is expressed as z t = IFT{FT[H t × TF CFP}, and the hologram generation process is expressed as where j is the imaginary unit, H t is the complex amplitude distribution of the diffraction field on the holographic plane, and TF CFP is the transfer function of the forward propagation model.

[0017] (2) Initialization. Use a random function to generate a random phase distribution within the range of 0 - 2π as the initial cylindrical hologram Then, reconstruct the cylindrical hologram using the cylindrical diffraction algorithm to obtain the initialized reconstructed complex amplitude distribution z0.

[0018] (3) Directional gradient update. Calculate the phase gradient error at the t-th loop through directional gradient calculation The specific calculation process is as follows, where Re() represents the real part operation, conj() represents the conjugate operation, · represents the dot product of vectors, I is the original intensity image, and then the phase hologram of the result of the (t - 1)-th loop of the previous round Superimposed with it, the phase hologram of the t-th cycle is obtained, denoted as,

[0019] (4) The iterative loop terminates. When the number of iterative optimizations meets the set number or the reconstruction quality reaches the set threshold, the iterative process is stopped, and the phase hologram of the previous loop iteration is retained as the optimized final phase hologram.

[0020] The reconstruction process of the cylindrical hologram is specifically described as follows: Step 1, load the cylindrical hologram onto the corresponding modulator; Step 2, at the corresponding diffraction distance, receive the reconstructed image of the cylindrical hologram.

[0021] In the generation process of the cylindrical hologram, for the cylindrical diffraction algorithm, the cylindrical convolution diffraction algorithm is adopted. It is characterized in that this method considers that the diffraction process between two concentric cylindrical surfaces is a space-invariant system in the cylindrical coordinate system, and the diffraction field distribution U2 of the holographic surface is the convolution of the object light field U1 and the point spread function h of this space-invariant system, denoted as: U2 = U1 * h, where * is the convolution operation. The cylindrical convolution diffraction algorithm based on the fast Fourier transform is expressed as U2 = IFFT[FFT(U1) × FFT(h)], where FFT and IFFT respectively represent the fast Fourier transform and the inverse transform.

[0022] In the example of the present invention, in the cylindrical wave angular spectrum algorithm, the transfer function of the forward propagation model is specifically expressed as TF CFP = H n (1) (k r , r) / H n (1) (k r , a), where k r =(k 2 - k y 2 ) 1 / 2 , k = 2π / λ is the wave vector, λ is the wavelength, k y = N k y , k y = H n (1) 2π / y, H n (1) is the first kind of Hankel function, y is the height of the cylinder, a is the object surface radius of the cylinder, and r is the holographic surface cylinder radius.

[0023] In the example of the present invention, in the cylindrical convolution diffraction algorithm, the point spread function is specifically expressed as, h = exp(jkd) / (jkd)cosa, where j is the imaginary unit, k is the wave vector, cosa is the tilt factor, and d is the distance between the source point and the target point.

[0024] In an example of the present invention, the resolution of the original object image is 1024x1024, the inner diameter of the cylinder is 10 mm, the outer diameter of the cylinder is 100 mm, the height of the cylinder is 100 mm, and the wavelength is 180 um. The hologram generated by the optimization method of the present invention has a reproduction result as Figure 2 shown, with high reconstruction quality and significant speckle noise suppression effect. Therefore, the method of the present invention has great application prospects in three-dimensional display.

Claims

1. A method for suppressing cylindrical holographic speckles based on directional gradient update, characterized in that The method includes two parts: the generation and reconstruction of a cylindrical hologram; the generation process of the cylindrical hologram is specifically described as follows: (1) Iterative loop. At the t-th loop, the cylindrical phase hologram is The reconstructed diffraction field is z t , in the result of the (t - 1)-th loop of the previous round, the cylindrical phase hologram is The reconstructed diffraction field is z t-1 , and the cylindrical diffraction algorithm adopts the angular spectrum algorithm of cylindrical waves. The reconstruction process is expressed as z t = IFT{FT[H t ×TF CFP}, and the hologram generation process is expressed as where j is the imaginary unit, H t is the complex amplitude distribution of the diffraction field on the holographic plane, and TF CFP is the transfer function of the forward propagation model; (2) Initialization. A random phase distribution within the range of 0 - 2π is generated using a random function as the initial cylindrical hologram Then, the cylindrical hologram is reconstructed using the cylindrical diffraction algorithm to obtain the initialized reconstructed complex amplitude distribution z0; (3) Directional gradient update. The phase gradient error of the t-th loop is calculated through directional gradient calculation The specific calculation process is as follows, where Re() represents the real part operation, conj() represents the conjugate operation, · represents the vector dot product, I is the original intensity image, and then the phase hologram of the result of the (t - 1)-th loop of the previous round is superimposed on it to obtain the phase hologram of the t-th loop, expressed as, (4) Iterative loop termination. When the number of iterative optimizations meets the set number or the reconstruction quality reaches the set threshold, the iterative process is stopped, and the phase hologram of the previous loop iteration is retained as the optimized final phase hologram; the reconstruction process of the cylindrical hologram is specifically described as follows: Step 1, load the cylindrical hologram onto the corresponding modulator; Step 2, receive the reconstructed image of the cylindrical hologram at the corresponding diffraction distance.

2. In the method for suppressing cylindrical holographic speckles based on directional gradient update described in claim 1, during the generation process of the cylindrical hologram, for the cylindrical diffraction algorithm, the cylindrical convolution diffraction algorithm is adopted, characterized in that This method considers that the diffraction process between two concentric cylindrical surfaces is a space-invariant system in the cylindrical coordinate system. The diffraction field distribution U2 on the holographic plane is the convolution of the object light field U1 and the point spread function h of this space-invariant system, expressed as: U2 = U1 * h, where * represents the convolution operation. The cylindrical convolution diffraction algorithm based on the fast Fourier transform is expressed as U2 = IFFT[FFT(U1) × FFT(h)], where FFT and IFFT represent the fast Fourier transform and the inverse transform respectively.

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