Low-noise color hologram calculation method based on fractional order discrete convolution

Abstract

The invention proposes a low-noise color holographic 3D display method based on fractional order discrete convolution, and the method comprises the following three steps: 1, extracting the three-channel information of a color 3D object, taking the image center of the intensity information of a single channel as an original point, expanding zero elements at the periphery, and superposing a secondary phase, and obtaining the initial complex amplitude distribution of an object plane; and 2, calculating complex amplitude distribution of the holographic surface by using fractional order discrete convolution, applying double constraints of amplitude and secondary phase to the object plane, performing loop iterative calculation, and stopping iteration until the phase distribution of the holographic surface is converged to a local optimal value. And a third step of obtaining the low-noise color hologram of the 3D object by superposing the phase holograms with different depths. According to the method, free control over the size of a reproductive image is achieved through fractional order discrete convolution transformation, the problem of chromatic aberration of magnification is solved, speckle noise is suppressed by optimizing the phase of a hologram through double constraints, and low-noise color holographic 3D display is achieved.

Description

1. Technical Field

[0001] The present invention relates to a computer generated holographic display technology, and more specifically, to a method for calculating a low-noise color hologram based on fractional-order discrete convolution. 2. Background Technology

[0002] As one of the most ideal 3D display technologies, holographic display technology has important applications in the fields of medicine, education, military, entertainment, etc. In order to obtain a more realistic viewing experience, high-quality color holographic 3D display technology is necessary. However, due to the influence of factors such as laser coherence, there are problems such as speckle noise and chromatic aberration in color holographic 3D display, which greatly affects the viewing experience. Some researchers use blazed gratings with high-pass filters to eliminate zero-order light and stray light to obtain high-quality color holographic 3D reproduction images. However, the offset of the blazed grating is discrete, resulting in a low degree of freedom in the position offset of the reproduced image. In addition, some researchers eliminate magnification chromatic aberration by pre-compensating the original image of the recorded object. However, pre-compensating the original image of the recorded object will make the resolution gap between the red, green and blue channel images too large, limiting the practicality of color holographic display. So far, although color holographic 3D display has made great progress in all aspects, it is still far from application. How to achieve low-noise color holographic 3D display while eliminating magnification chromatic aberration has become one of the key issues that need to be urgently solved in the current holographic display technology. III. Summary of the invention

[0003] The present invention proposes a low-noise color hologram calculation method based on fractional-order discrete convolution, as shown in the attached Figure 1As shown, the method includes the following three steps: the first step is to extract the intensity and depth map information of the red, green and blue channels of the color 3D object respectively, and expand the zero elements around the image center of the intensity information of a single channel as the origin to obtain the initial amplitude information of a single channel, wherein the position of the original channel information is the original image interval, and the position of the expanded zero element is the expanded interval. In addition, the secondary phase is superimposed on the original image interval in the initial amplitude information to obtain the initial complex amplitude distribution of the object plane. The second step is to perform a fractional-order discrete convolution transformation on the initial complex amplitude distribution of the object plane to obtain the complex amplitude distribution of the holographic surface, extract the phase information of the complex amplitude distribution of the holographic surface and perform a fractional-order discrete convolution inverse transformation to obtain the complex amplitude distribution of the object plane. At the same time, the dual constraints of amplitude and secondary phase are applied to the original image interval of the complex amplitude distribution of the object plane to complete the first iteration, and then the object plane complex amplitude distribution after the dual constraint optimization replaces the initial complex amplitude distribution of the object plane to start the next round of cyclic iteration until the phase distribution of the holographic surface converges to the local optimal value, and the iterative cycle is stopped. The third step is to extract and output the single-channel phase hologram. According to the depth map information extracted in step one, the corresponding fractional-order discrete convolution transform order is calculated. By superimposing single-channel phase holograms of different depths, a low-noise phase hologram of a single-channel 3D object can be obtained. The same iterative cycle operation is performed on the information of the red, green and blue channels to obtain a three-channel low-noise color hologram. The three-channel low-noise color hologram is reproduced in a time-division multiplexing or space-division multiplexing manner to achieve a low-noise color holographic 3D display.

[0004] In step one, after extracting the intensity information of the three channels, taking a single channel as an example, the channel information is set as the original channel information. In order to avoid crosstalk in the iterative operation in step two, the size of the original channel information is expanded, that is, information with zero intensity is added around the original image to obtain the initial amplitude information, where the position of the original channel information is the original image interval, and the position of the information with zero intensity is the expansion interval. Combined with the depth information extracted from the channel, the corresponding expansion interval range is set by calculating the order of the fractional discrete convolution transform corresponding to the depth. If the depth of the original channel information is z and the corresponding transformation order is a, then the size of the initial amplitude information is enlarged by a factor g compared to the size of the original channel information, expressed as:

[0005]

[0006] In addition, the secondary phase is superimposed on the original image interval in the initial amplitude information The initial complex amplitude distribution of the object plane is obtained, where the superimposed secondary phase is expressed as:

[0007]

[0008] Among them, X and Y represent the horizontal and vertical coordinates of the secondary phase respectively, and m and n represent the horizontal and vertical resolutions of the original image interval respectively.

[0009] In step 2, the complex amplitude distribution D1(X,Y) of the holographic surface obtained by performing fractional-order discrete convolution transformation on the initial complex amplitude distribution of the object plane is expressed as:

[0010]

[0011] Where D0(X,Y) represents the initial complex amplitude distribution in the object plane, i represents an imaginary number, λ is the wavelength of the incident light, and f e is the standard focal length, dx and du are the sampling intervals of the object plane and the holographic plane respectively, and DCT represents discrete convolution transform. The formula of discrete convolution transform is expressed as:

[0012]

[0013] In the formula,

[0014] g(x,y)*h(ux,vy)=IFFT{FFT[g(x,y)]×FFT[h(ux,vy)]} (5)

[0015]

[0016] h(ux,vy)=exp(iπs[(ux) 2 +(vy) 2 ]) (7)

[0017]

[0018] Among them, f is the focal length of the lens, (x, y) is the object plane coordinate, (u, v) is the holographic surface coordinate, (x0, y0) is the center point coordinate of the object plane, (u0, v0) is the center point coordinate of the holographic surface, FFT and IFFT are Fourier transform and inverse Fourier transform respectively. By setting the center point position of the object plane and the holographic surface image in the discrete convolution transform calculation, the overlap of the holographic reconstruction image with the zero-order light and stray light is avoided, and there is no need to use a discrete blazed grating, which improves the freedom of the position of the reconstruction image. In addition, the sampling rate of the object plane and the holographic surface in the discrete convolution transform calculation is free. By adjusting the sampling rate value, the size of the holographic reconstruction image can be freely controlled, solving the problem of the need to pre-compensate the original image due to magnification chromatic aberration.

[0019] Extract the phase information of the complex amplitude distribution D1(X,Y) of the holographic surface And perform the inverse fractional-order discrete convolution transform to obtain the object plane complex amplitude distribution D2(X,Y):

[0020]

[0021] Applying dual constraints of amplitude and quadratic phase to the original image interval of D2(X,Y) yields the optimized complex amplitude distribution D3(X,Y) in the object plane:

[0022]

[0023] Among them, S and N represent the original image interval and the extended interval respectively, and RD(X,Y) represents the initial amplitude information of the original channel. and A2 represent the phase and amplitude of the complex amplitude distribution in the object plane, respectively. Through double-constrained optimization, the phase distribution of the hologram converges to the local optimal value, which can effectively suppress the speckle noise in the holographic reconstruction image.

[0024] In step 3, the corresponding fractional discrete convolution transform order is calculated based on the depth information extracted previously. The corresponding relationship between the fractional discrete convolution transform order is shown in the attached figure. Figure 2 As shown, xy is the object plane, uv is the holographic surface, and a is the transformation order. In the fractional-order discrete convolution transform, the relationship between z and a is expressed as:

[0025]

[0026] Preferably, the value range of a is (0,2). When a=1, the position of the reconstructed image is at the focal length of the imaging lens; when a<1, the reconstructed image is located before the focal plane of the lens, and the smaller a is, the farther from the focal plane of the lens; when a>1, the reconstructed image is located after the focal plane of the lens, and the larger a is, the farther from the focal plane of the lens. By superimposing holograms calculated with different a, a holographic 3D display with different depths of the reconstructed image can be achieved. IV. Description of the drawings

[0027] Attached Figure 1 The present invention is a flowchart of a method for calculating a low-noise color hologram based on fractional-order discrete convolution.

[0028] Attached Figure 2 It is a schematic diagram of the corresponding relationship of the fractional-order discrete convolution transform orders of the present invention.

[0029] Attached Figure 3 This is a comparison chart of the holographic 3D display effects of a low-noise hologram calculation method based on fractional-order discrete convolution of the present invention and a traditional Gerchberg-Saxton hologram calculation method. Figure 3 (a)-(b) are the reconstruction results of the traditional Gerchberg-Saxton algorithm. Figure 3 (c)-(d) are the reconstruction effects of the algorithm proposed in this invention.

[0030] It should be understood that the above drawings are only schematic and are not drawn to scale. V. Specific implementation methods

[0031] The following is a detailed description of an embodiment of a low-noise color hologram calculation method based on fractional-order discrete convolution proposed by the present invention, and further describes the present invention. It is necessary to point out that the following embodiments are only used to further illustrate the present invention and cannot be understood as limiting the scope of protection of the present invention. Personnel skilled in the art in this field may make some non-essential improvements and adjustments to the present invention based on the above invention content, which still fall within the scope of protection of the present invention.

[0032] An embodiment of the present invention is: In order to verify the feasibility of the proposed method, lasers with wavelengths of 473nm, 532nm and 671nm are used as color reconstruction light sources, and a reflective pure phase spatial light modulator is used to load the hologram. The pixel pitch and resolution of the spatial light modulator are 3.6μm and 3840×2160, respectively. The phase modulation capability is 2π, and the refresh rate is 120Hz. The images of "Magic Cube" and "Flower" are used as the recorded color 3D objects with a resolution of 500×500. The reconstruction distances of "Magic Cube" and "Flower" are set to 20cm and 26.2cm, respectively. In the process of fractional-order discrete convolution transformation, the order a of "Magic Cube" and "Flower" are set to 1 and 1.2, respectively. In order to verify the effect of the method proposed in the present invention, the traditional Gerchberg-Saxton algorithm and the method proposed in the present invention are used to calculate the pure phase hologram of the color 3D object and perform holographic reconstruction. The corresponding holographic reconstruction image results are shown in the attached figure. Figure 3 As shown. Figure 3 (a)-(b) show the focusing effects of the “magic cube” and “flower” respectively when using the traditional Gerchberg-Saxton algorithm. Figure 3 (c)-(d) are the focusing effects of the "magic cube" and "flower" respectively when the method proposed in the present invention is used. The speckle noise suppression effect is evaluated by calculating the speckle noise contrast. The noise contrast of the traditional algorithm is 0.0810 and 0.5701 respectively, and the noise contrast of the proposed method is 0.0520 and 0.1297 respectively. The results show that the method proposed in the present invention can effectively suppress speckle noise and improve the quality of color holographic 3D reproduction images.

Claims

1. A low-noise color hologram calculation method based on fractional-order discrete convolution, characterized in that: The method includes the following three steps: In the first step, the intensity and depth map information of the red, green and blue channels of the color 3D object are extracted respectively. For the extracted intensity information, taking a single channel as an example, the channel information is set as the original channel information. In order to avoid crosstalk in the iterative operation in step 2, the size of the original channel information is expanded, that is, information with zero intensity is added around the original image to obtain the initial amplitude information of a single channel. The position of the original channel information is the original image interval, and the position of the information with zero intensity is the expansion interval. Combined with the depth information extracted from the channel, the corresponding expansion interval range is set by calculating the fractional discrete convolution transform order corresponding to the depth. If the depth of the original channel information is z and the corresponding transform order is a, the size of the initial amplitude information is enlarged by a factor g compared to the size of the original channel information as follows: In addition, the secondary phase is superimposed on the original image interval in the initial amplitude information The initial complex amplitude distribution D0(X,Y) of the object plane is obtained, and the superimposed secondary phase is expressed as: Among them, X and Y represent the horizontal and vertical coordinates of the secondary phase, respectively, and m and n represent the horizontal and vertical resolutions of the original image interval, respectively; In the second step, the initial complex amplitude distribution D0(X,Y) of the object plane is transformed by fractional discrete convolution to obtain the complex amplitude distribution D1(X,Y) of the holographic surface, which is expressed as: Where i represents an imaginary number, λ is the wavelength of the incident light, and f e is the standard focal length, dx and du are the sampling intervals of the object plane and the holographic plane respectively, DCT represents discrete convolution transform, and the formula of discrete convolution transform is expressed as: In the formula, g(x,y)*h(ux,vy)=IFFT{FFT[g(x,y)]×FFT[h(ux,vy)]}, h(u-x,v-y)=exp(iπs[(u-x) 2 +(v-y) 2 ]), Among them, f is the focal length of the lens, (x, y) is the object plane coordinate, (u, v) is the holographic surface coordinate, (x0, y0) is the center point coordinate of the object plane, (u0, v0) is the center point coordinate of the holographic surface, FFT and IFFT are Fourier transform and inverse Fourier transform respectively. By setting the center point position of the object plane and the holographic surface image in the discrete convolution transform calculation, the overlap of the holographic reconstruction image with the zero-order light and stray light is avoided, and there is no need to use a discrete blazed grating, which improves the freedom of the position of the reconstruction image. In addition, the sampling rate of the object plane and the holographic surface in the discrete convolution transform calculation is free. By adjusting the sampling rate value, the size of the holographic reconstruction image can be freely controlled, and the problem of magnification chromatic aberration requiring pre-compensation of the original image is solved; Next, extract the phase information of the holographic surface complex amplitude distribution D1(X,Y) And perform the inverse fractional-order discrete convolution transform to obtain the object plane complex amplitude distribution D2(X,Y): In addition, the dual constraints of amplitude and quadratic phase are imposed on the original image interval of D2(X,Y) to obtain the optimized object plane complex amplitude distribution D3(X,Y): Among them, S and N represent the original image interval and the extended interval respectively, and RD(X,Y) represents the initial amplitude information of the original channel. and A2 represent the phase and amplitude of the complex amplitude distribution of the object plane, respectively. Through dual-constraint optimization, the phase distribution of the hologram converges to the local optimal value, which can effectively suppress the speckle noise in the holographic reconstruction image. Finally, the object plane complex amplitude distribution D3 (X, Y) after dual-constraint optimization replaces the initial complex amplitude distribution D0 (X, Y) of the object plane to start the next round of iteration until the phase distribution of the holographic surface converges to the local optimal value, and the iteration cycle is stopped; The third step is to extract and output a single-channel phase hologram. The corresponding fractional-order discrete convolution transform order is calculated according to the depth map information extracted in step 1. In the fractional-order discrete convolution transform, the relationship between the depth z and the order a is expressed as: Among them, the value range of a is (0,2), when a=1, the position of the reconstructed image is at the focal length of the imaging lens, when a<1, the reconstructed image is located in front of the focal plane of the lens, the smaller a is, the farther away from the focal plane of the lens, when a>1, the reconstructed image is located behind the focal plane of the lens, and the larger a is, the farther away from the focal plane of the lens. By superimposing single-channel phase holograms of different depths, a low-noise phase hologram of a single-channel 3D object can be obtained, and the same iterative cycle operation is taken for the information of the red, green and blue channels to obtain a three-channel low-noise color hologram. Finally, the three-channel low-noise color hologram is reproduced in a time-division multiplexing or space-division multiplexing manner to achieve a low-noise color holographic 3D display.

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