Method for rapidly suppressing speckle noise of computer-generated holographic reproductive image

Abstract

The invention provides a method for rapidly suppressing speckle noise of a computer-generated holographic reproductive image. A recorded object is regarded as a combination of discrete object points. The amplitude and phase information of any object point are recorded as a complex amplitude necessary interferogram with reduced size. And the complex amplitude necessary interferograms of all object points are superposed to generate the complex amplitude CGH. Pixels on the complex amplitude CGH are sequentially scanned, errors generated by an algorithm are diffused to four pixels which are adjacent to the pixel and are not processed for the pixel being processed, correction compensation of complex amplitude values of the pixels is achieved, a complex amplitude necessary interferogram is converted into a phase necessary interferogram, and finally a pure phase CGH is generated. When the pure phase CGH is reproduced, diffraction light boundaries of all phase necessary interferograms are respectively parallel, reproduced effective information in a watching visual area is not changed, and reproduced waste information outside the watching visual area is reduced. The speckle noise of the computer-generated holographic reproductive image is quickly suppressed by reducing recording of reproduction waste information and error diffusion processing of an algorithm.

Description

1. Technical Field

[0001] The present invention relates to the field of holographic display, and in particular to a method for rapidly suppressing speckle noise in computer-generated holographic reconstruction. 2. Background Technology

[0002] Speckle noise is one of the reasons that reduce the quality of computer-generated holographic reconstruction images. In order to improve the quality of the reconstructed image, a variety of methods for suppressing speckle noise have been proposed, such as the iterative method, the weak coherent light reconstruction method, the time averaging method, the pixel separation method and the error diffusion method. The iterative algorithm suppresses speckle noise through cyclic iterations, but as the number of iterations increases, the convergence of the algorithm deteriorates and the noise suppression effect is not obvious. The reconstruction optical system of the weak coherent light method needs to use a diffuser or multiple spatial light modulators (SLM) to reduce the coherence of the reconstructed light, which increases the complexity of the system. Both the time averaging method and the pixel separation method require the production of multiple computer-generated holograms (CGH), which not only increases the computational burden of the CGH, but also puts higher requirements on the refresh rate of the SLM, making it difficult to achieve dynamic holographic display.

[0003] The error diffusion algorithm calculates the complex amplitude CGH of the object through the Fresnel diffraction theory. In this process, for any object point, its amplitude and phase information is recorded as a complex amplitude interference pattern. The complex amplitude interference patterns of all object points are added together to form a complex amplitude CGH, which means that the amount of calculation is very large. Then, it processes each pixel on the complex amplitude CGH to generate a pure phase CGH, further increasing the amount of calculation. When using SLM for pure phase CGH reproduction, the size of the selected SLM is the same as the size of the complex amplitude interference pattern and the complex amplitude CGH. Let the center of the SLM be the coordinate origin, take a top view in the y direction, and the field of view distribution of the reproduced image is as shown in the attached figure. Figure 1 For simplicity, the x direction is used as an example to introduce the distribution of the viewing area. The y and z directions meet the same conditions. The size of the object and the reconstructed image is denoted by D x , the size of SLM is H x , the recording distance of CGH is L. According to the characteristics of the reconstructed image viewing area, at the viewing distance R, the viewer can only see the complete reconstructed image in the viewing area V. When the viewer is outside the viewing area at the upper V1 and lower V2 range, only part of the reconstructed image can be seen. The dimensions V, V1, and V2 satisfy formulas (1)-(2) respectively:

[0004] V=[H x (RL)-D x R] / L (1)

[0005] V1=V2=RD / L (2)

[0006] For the viewer, the diffracted light in the viewing area is the reproduction of effective information, and the diffracted light outside the viewing area is the reproduction of wasted information. However, the recording of wasted information occupies a certain amount of computation in CGH. Therefore, it is very meaningful to reduce the recording of wasteful information and quickly suppress the speckle noise of CGH reconstruction. III. Summary of the invention

[0007] The present invention proposes a method for rapidly suppressing speckle noise of a computer-generated holographic reconstruction image, wherein the recorded object is regarded as a combination of discrete object points. The amplitude and phase information of any object point are recorded as a complex amplitude necessary interference pattern with a reduced size. The complex amplitude necessary interference patterns of all object points are superimposed to generate a complex amplitude CGH. The pixels on the complex amplitude CGH are sequentially scanned and processed, and for a pixel being processed, the error generated by the algorithm is diffused to the four adjacent and unprocessed pixels to achieve correction and compensation of their complex amplitude values, and the complex amplitude necessary interference pattern is converted into a phase necessary interference pattern, and finally a pure phase CGH is generated. When the pure phase CGH is reproduced, the diffraction light boundaries of all the phase necessary interference patterns are parallel, the reproduced effective information in the viewing area remains unchanged, and the reproduced waste information outside the viewing area is reduced. The present invention rapidly suppresses the speckle noise of the computer-generated holographic reconstruction image by reducing the recording of the reproduced waste information and the error diffusion processing of the algorithm.

[0008] The method for rapidly suppressing speckle noise of a computer generated holographic reconstruction image of the present invention comprises three steps: generating a complex amplitude CGH, generating a pure phase CGH and reproducing the pure phase CGH. The process is shown in the attached figure. Figure 2 As shown. Let the center of the CGH and SLM studied in the present invention be the origin of the coordinates. For simplicity, during the CGH recording and reproduction process, the present invention takes a top view in the y direction and takes the x direction as an example for introduction. The y and z directions meet the same conditions.

[0009] Step 1: Generation of complex amplitude CGH. The recorded object is considered as a combination of discrete points. The size of the recorded object is D x , using Fresnel diffraction theory to record the amplitude and phase information of all object points, the recording distance is L, and one object point generates a complex amplitude necessary interference pattern. The starting point position of the complex amplitude necessary interference pattern corresponding to any object point m(x,-L) on the x-axis is x1, the end point position is x2, and the size is S x , they satisfy formulas (3)-(5) respectively:

[0010]

[0011] S x =x1-x2=H x -D x (5)

[0012] Among them, Hx The size of the SLM used in the present invention. The size of the complex amplitude necessary interference pattern is reduced to be smaller than the size of the SLM, which is determined by the size of the object to be recorded and the size of the SLM. The complex amplitude necessary interference patterns of all object points are added together to generate the complex amplitude CGH.

[0013] Step 2: Generation of pure phase CGH. For the complex amplitude CGH in step 1, the present invention scans it from left to right and from top to bottom starting from the first pixel. For the pixel in the kth row and lth column on the complex amplitude CGH being processed, its light field complex amplitude is recorded as h(k, l). The present invention sets the amplitude value of the pixel in the kth row and lth column to 1, takes the phase term of the complex amplitude to obtain the pure phase value p(k, l), which satisfies formula (6):

[0014] p(k,l)=arg(h(k,l)) (6)

[0015] Among them, arg() is the phase value operation of taking the complex amplitude. Therefore, the complex amplitude value of the pixel in the kth row and lth column is converted into a pure phase value p(k,l), and the error e(k,l) between p(k,l) and the original complex amplitude value h(k,l) satisfies formula (7):

[0016] e(k,l)=h(k,l)-p(k,l) (7)

[0017] Then, the present invention diffuses the error e(k, l) to four pixels adjacent to the currently processed pixel and not scanned, that is, to the right (kth row, (l+1) column), lower left ((k+1)th row, (l-1) column), lower ((k+1)th row, l column) and lower right ((k+1)th row, (l+1) column) pixels, then the complex amplitude values ​​h(k, l+1), h(k+1, l-1), h(k+1, l), h(k+1, l+1) of the right, lower left, lower and lower right pixels are updated respectively, and they satisfy formula (8):

[0018]

[0019] Wherein "←" indicates that the variable on the right is used to update the variable on the left, a, b, c and d are called error diffusion coefficients, and a = 7 / 16, b = 3 / 16, c = 5 / 16, d = 1 / 16. Therefore, the complex amplitude values ​​of the pixels in the (l+1)th row, (k+1)th row, (l-1)th row, (k+1)th row, and (l+1)th row are corrected and compensated according to the error of the current pixel in the kth row and lth column. After the present invention completes the processing of all pixels on the complex amplitude CGH, a pure phase light field distribution p(k, l) is obtained, that is, a pure phase CGH is formed. In the process of pixel scanning processing of the complex amplitude CGH, the complex amplitude necessary interference pattern on the complex amplitude CGH is converted into a phase necessary interference pattern.

[0020] Step 3: Reconstruction of pure phase CGH. Load the pure phase CGH onto the SLM for reconstruction. The distribution of the viewing area of ​​the reconstructed image is as follows: Figure 3 As shown. According to the geometric relationship, the diffraction light boundaries of all phase necessary interference patterns are parallel, and their overlapping area is the viewing area of ​​the reconstructed image. The area outside the viewing area is the reconstructed waste information. At the viewing distance R, the viewing area size V' of the reconstructed image, the waste information V1'' and V2' respectively satisfy the formulas (9)-(10):

[0021] V'=[H x (RL)-D x R] / L (9)

[0022] V1'=V2'=D (10)

[0023] Compared with formulas (9) and (10) and formulas (1) and (2), the present invention reduces the recording size of the necessary interference pattern of the complex amplitude during the generation of the complex amplitude CGH, so that the effective information in the viewing area remains unchanged during the reproduction process, and the waste information outside the viewing area is reduced. In addition, in the generation of the pure phase CGH, the correction and compensation of the complex amplitude value is performed through error diffusion, and finally the rapid suppression of the speckle noise of the computer-generated holographic reproduction image is achieved. IV. Description of the drawings

[0024] The foregoing and additional aspects and advantages of the present invention will be further clarified and easily understood from the following detailed description in conjunction with the accompanying drawings and embodiments, in which:

[0025] Attached Figure 1 Schematic diagram of the viewing area distribution of the holographic reconstruction image using the error diffusion algorithm.

[0026] Attached Figure 2 It is a schematic diagram of the process of the present invention.

[0027] Attached Figure 3 Schematic diagram of the viewing area distribution of the holographic reconstruction image according to the method of the present invention.

[0028] The diagram numbers in the above drawings are:

[0029] 1 recorded object, 2 SLM, 3 CGH reconstruction image, 4 necessary phase interference pattern of object point m.

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

[0031] A typical embodiment of a method for rapidly suppressing speckle noise in computer-generated holographic reconstruction using the present invention is described in detail below to further describe the present invention.

[0032] The invention discloses a method for rapidly suppressing speckle noise in computer generated holographic reconstruction, including three steps: generating a complex amplitude CGH, generating a pure phase CGH, and reproducing the pure phase CGH. The center of the CGH and SLM studied by the invention is set as the origin of the coordinates. For simplicity, during the CGH recording and reproducing process, the invention takes a top view in the y direction, and takes the x direction as an example for introduction. The y and z directions satisfy the same situation.

[0033] Step 1: Generation of complex amplitude CGH. The recorded object is regarded as a combination of discrete object points. The size of the recorded object is 4 mm. The amplitude and phase information of all object points are recorded using Fresnel diffraction theory. The recording distance is 300 mm. One object point generates a complex amplitude necessary interference pattern. The size of the SLM used in the present invention is 15.36 mm. The starting point position of the complex amplitude necessary interference pattern corresponding to the object point m (0, -300 mm) on the x-axis is x1, the end point position is x2, and the size is S x , they satisfy

[0034] S x =5.68mm-(-5.68mm)=11.36mm. The size of the complex amplitude necessary interference pattern is reduced to be smaller than the size of the SLM, which is determined by the size of the object being recorded and the size of the SLM. The complex amplitude necessary interference patterns of all object points are added together to generate the complex amplitude CGH.

[0035] Step 2: Generation of pure phase CGH. For the complex amplitude CGH in step 1, the present invention scans it from left to right and from top to bottom starting from the first pixel. For the pixel in the kth row and lth column on the complex amplitude CGH being processed, its light field complex amplitude is recorded as h(k,l). The present invention sets the amplitude value of the pixel in the kth row and lth column to 1, takes the phase term of the complex amplitude to obtain the pure phase value p(k,l), satisfying p(k,l)=arg(h(k,l)), where arg() is the operation of taking the phase value of the complex amplitude. Therefore, the complex amplitude value of the pixel in the kth row and lth column is converted into a pure phase value p(k,l), and the error e(k,l) between p(k,l) and the original complex amplitude value h(k,l) satisfies e(k,l)=h(k,l)-p(k,l). Then, the present invention diffuses the error e(k,l) to four pixels adjacent to the currently processed pixel and not scanned, that is, to the right (kth row, (l+1) column), lower left ((k+1)th row, (l-1) column), lower ((k+1)th row, l column) and lower right ((k+1)th row, (l+1) column) pixels, then the complex amplitude values ​​h(k,l+1), h(k+1,l-1), h(k+1,l), h(k+1,l+1) of the right, lower left, lower and lower right pixels are updated respectively, and they satisfy Wherein "←" indicates that the variable on the right is used to update the variable on the left, a, b, c and d are called error diffusion coefficients, and a = 7 / 16, b = 3 / 16, c = 5 / 16, d = 1 / 16. Therefore, the complex amplitude values ​​of the pixels in the (l+1)th row, (k+1)th row, (l-1)th row, (k+1)th row, and (l+1)th row are corrected and compensated according to the error of the current pixel in the kth row and lth column. After the present invention completes the processing of all pixels on the complex amplitude CGH, a pure phase light field distribution p(k, l) is obtained, that is, a pure phase CGH is formed. In the process of pixel scanning processing of the complex amplitude CGH, the complex amplitude necessary interference pattern on the complex amplitude CGH is converted into a phase necessary interference pattern.

[0036] Step 3: Reconstruction of pure phase CGH. Load the pure phase CGH onto the SLM for reconstruction. According to the geometric relationship, the diffraction light boundaries of all necessary phase interference patterns are parallel, and their overlapping area is the viewing area of ​​the reconstructed image. The area outside the viewing area is the reconstructed waste information. At a viewing distance of 500mm, the viewing area size V' of the reconstructed image, the waste information V1'' and V2' respectively satisfy V'=[15.36mm*(500mm-300mm)-4mm*500mm] / 300mm=3.57mm, V1'=V2'=4mm. In the error diffusion algorithm, the size of the complex amplitude interference pattern is 15.36mm, and the viewing area size of the reconstructed image is V=[15.36mm*(500mm-300mm)-4mm*500mm] / 300mm=3.57mm, V1=V2=500mm*4mm / 300mm=6.67mm.

[0037] By comparison, it can be seen that in the process of complex amplitude CGH generation, the present invention reduces the recording size of the necessary interference pattern of the complex amplitude, so that the effective information in the viewing area remains unchanged during the reproduction process, and the waste information outside the viewing area is reduced. In addition, in the process of generating pure phase CGH, the correction and compensation of the complex amplitude value is performed through error diffusion, and finally the rapid suppression of the speckle noise of the computer-generated holographic reproduction image is achieved.

Claims

1. A method for rapidly suppressing speckle noise in a computer generated holographic reconstruction includes three steps: generating a complex amplitude CGH, generating a pure phase CGH, and reproducing the pure phase CGH. The center of the CGH and SLM studied in the present invention is taken as the origin of the coordinates. For simplicity, during the CGH recording and reproducing process, the present invention takes a top view in the y direction and takes the x direction as an example for introduction. The y and z directions meet the same conditions. Step 1: Generation of complex amplitude CGH. The recorded object is regarded as a combination of discrete points. The size of the recorded object is D x , using Fresnel diffraction theory to record the amplitude and phase information of all object points, the recording distance is L, and one object point generates a complex amplitude necessary interference pattern. The starting point position of the complex amplitude necessary interference pattern corresponding to any object point m(x,-L) on the x-axis is x1, the end point position is x2, and the size is S x , they satisfy S x =x1-x2=H x -D x , where H x For the size of the SLM used in the present invention, the size of the complex amplitude necessary interference pattern is reduced to be smaller than the size of the SLM, which is determined by the size of the object to be recorded and the size of the SLM, and the complex amplitude necessary interference patterns of all object points are added to generate the complex amplitude CGH; Step 2: Generation of pure phase CGH. For the complex amplitude CGH in step 1, the present invention scans it from left to right and from top to bottom starting from the first pixel. For the pixel in the kth row and lth column on the complex amplitude CGH being processed, its light field complex amplitude is recorded as h(k,l). The present invention sets the amplitude value of the pixel in the kth row and lth column to 1, takes the phase term of the complex amplitude to obtain the pure phase value p(k,l), satisfying p(k,l)=arg(h(k,l)), where, arg() is an operation to obtain the phase value of the complex amplitude. Therefore, the complex amplitude value of the pixel in the kth row and lth column is converted into a pure phase value p(k,l). The error e(k,l) between p(k,l) and the original complex amplitude value h(k,l) satisfies e(k,l)=h(k,l)-p(k,l). Then, the present invention diffuses the error e(k,l) to the four pixels adjacent to the currently processed pixel and not scanned, that is, to its right (kth row and (l+1) column), lower left ((k+1) row and (l-1) column), lower ((k+1) row and (l+1) column) and lower right ((k+1) row and (l+1) column) pixels. Then, the complex amplitude values ​​h(k,l+1), h(k+1,l-1), h(k+1,l), h(k+1,l+1) of the right, lower left, lower and lower right pixels are updated respectively, and they satisfy Wherein "←" indicates that the variable on the right is used to update the variable on the left, a, b, c and d are called error diffusion coefficients, and a=7 / 16, b=3 / 16, c=5 / 16, d=1 / 16, therefore, the complex amplitude values ​​of the pixels in the (l+1)th row, (k+1)th row, (l-1)th row, (k+1)th row, and (l+1)th row are corrected and compensated according to the error of the pixel in the current kth row, and (l+1)th column. After the present invention completes the processing of all pixels on the complex amplitude CGH, a pure phase light field distribution p(k,l) is obtained, that is, a pure phase CGH is formed. In the process of pixel scanning processing of the complex amplitude CGH, the complex amplitude necessary interference pattern on the complex amplitude CGH is converted into a phase necessary interference pattern; Step 3: Reconstruction of pure phase CGH. Load the pure phase CGH onto the SLM for reconstruction. According to the geometric relationship, the diffraction light boundaries of all necessary phase interference patterns are parallel. Their overlapping area is the viewing area of ​​the reconstructed image. The area outside the viewing area is the reconstructed waste information. At the viewing distance R, the viewing area size V' of the reconstructed image, the waste information V1" and V2' respectively satisfy V'=[H x (RL)-D x R] / L, V1'=V2'=D. In the process of complex amplitude CGH generation, the present invention reduces the recording size of the necessary interference pattern of the complex amplitude, so that the effective information reproduced in the viewing area remains unchanged during the reproduction process, and the waste information reproduced outside the viewing area is reduced. In addition, in the process of generating pure phase CGH, the complex amplitude value is corrected and compensated through error diffusion, ultimately achieving rapid suppression of speckle noise in the computer-generated holographic reproduction image.

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