A Fast Phase Hologram Generation Method Based on Weighted Phase Reuse WGS Algorithm

Abstract

This invention discloses a fast phase hologram generation method based on the weighted, phase-reused WGS algorithm. The method involves inputting parameters related to hologram calculation, along with a normalized weight term *w* and a phase random term *θ*, into the phase value calculation. The values ​​of the weight term *w* and the phase random term *θ* are updated using the calculated amplitude distribution. This iterative process is repeated until the generated hologram converges to its optimal value. After completing the WGS algorithm process, the weight term *w* and the phase term *θ* obtained from the iterative phase hologram are reused. This invention effectively reduces the number of iterations and improves the calculation speed during real-time phase hologram calculation, avoiding the problems of increased iterations and longer response times caused by complex calculations. It is a method for achieving high-quality, real-time reconstruction of complex light fields with fewer iterations and lower time costs.

Description

Technical Field

[0001] This invention relates to the field of phase hologram computation technology, and in particular to a fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm. Background Technology

[0002] Based on a holographic phase map loaded onto the target surface of a spatial light modulator, the incident light wavefront can be flexibly modulated, thereby allowing for flexible changes to the three-dimensional spatial position, number, and beam type of the diffracted spots at the Fourier surface after wavefront modulation, i.e., in the reconstructed light field. This wavefront modulation technique based on phase holograms has attracted considerable attention in recent years. However, slow computation speed, long response time for real-time reconstructed light field control, and low quality of the reconstructed light field (i.e., low uniformity of diffracted spot intensity) have always been the main problems limiting wavefront modulation and real-time light field reconstruction based on spatial light modulators. To obtain a high-quality reconstructed light field, researchers have proposed various iterative algorithms, such as the GS algorithm, WGS algorithm, and GAA algorithm. These algorithms improve the quality of the reconstructed light field by introducing relevant parameters into the iteration. WGS, as a highly representative iterative algorithm, is widely used in phase hologram calculations due to its high quality of reconstructed light field. However, the WGS algorithm requires multiple iterations to converge to the optimal value, resulting in slow computation speed and long response time in real-time phase hologram calculations. As the complexity of the reconstructed light field increases, the computational speed of the WGS algorithm decreases sharply, while the response time for generating the phase hologram increases significantly. This is because, during the computational reconstruction of the light field, the WGS algorithm needs to recalculate and iterate based on all input parameters. This process greatly affects the response time of phase hologram generation, limiting the efficiency of diffraction light field reconstruction and restricting the real-time performance of light field reconstruction. Therefore, research on real-time holographic phase image generation algorithms with fast computation speed, short response time, and high-quality reconstructed light field remains highly promising. Summary of the Invention

[0003] To overcome the aforementioned problems in the existing technology, this invention proposes a fast phase hologram generation method based on the weighted, phase-reused WGS algorithm.

[0004] To address the issues of the aforementioned WGS algorithm requiring multiple iterations to converge to the optimal value, resulting in slow real-time phase hologram computation and a sharp increase in phase hologram generation response time with increasing modulation optical field complexity, a fast phase hologram generation method based on a weighted, phase-reuse WGS algorithm is proposed. The specific technical solution includes: a fast phase hologram generation method based on a weighted, phase-reuse WGS algorithm, comprising the following steps:

[0005] Step 1: Convert the pixel size and arrangement on the spatial light modulator into a two-dimensional grid.

[0006] Step 2: Using the distribution grid and diffraction spot parameters of the spatial light modulator from Step 1, calculate the exponential term of the phase value applied to each pixel coordinate of the spatial light modulator. And calculate the coordinates of the center of all diffraction spots at the Fourier leaf surface. A set;

[0007] Step 3, based on the exponential term of different spot center coordinates The phase value Φ at different pixel coordinates of the spatial light modulator is obtained. j WGS ;

[0008] Step 4, via Φ j WGS Calculate the amplitude distribution V at different diffraction spots on the Fourier leaf surface. m The values ​​of the normalized weight term w and the phase term θ are updated using the obtained amplitude distribution;

[0009] Step 5: Repeat the iterative process of steps 3-4 to calculate the phase value Φ. j WGS The generated hologram converges to the optimal value, and a phase hologram is plotted and the phase term θ is output. m and normalized weight term w m ;

[0010] Step 6, output phase term θ m and normalized weight term w m The data is processed and then reused.

[0011] The fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm described above, specifically includes step 1: the grid coordinate distribution of pixels in the X direction is (-p min ,p max ,R x ), where p min p max R represents the minimum and maximum pixel coordinates in the X direction, respectively. x The resolution in the X direction of the spatial light modulator;

[0012] The grid coordinate distribution of the pixels in the Y direction is (-q) min ,q max ,R y ), where q min ,q max R represents the minimum and maximum pixel coordinates in the Y direction, respectively. y Let x be the resolution in the Y direction of the spatial light modulator. m ,y m ,z m ,θ m ,wm , where x m ,y m ,z m θ represents the three-dimensional coordinates (x, y, z) of the center of the m-th diffraction spot in the reconstructed optical field at the Fourier surface of the incident beam after wavefront modulation by the holographic phase diagram; m Let w be a phase term with values ​​in the range [0, 2π]. m The weights are normalized terms.

[0013] The above-described fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm, in step 2, the exponential term... The calculation formula is:

[0014]

[0015] Among them, z m Let λ represent the Z-axis coordinate of the center of the m-th diffraction spot in the reconstructed light field, λ represent the incident light wavelength, and f represent the effective focal length of the optical system. j ,y j () represents the coordinates of the j-th pixel in the spatial light modulator, x m The x-axis coordinate of the center of the m-th diffraction spot in the reconstructed light field is represented by y. m This represents the Y-axis coordinate of the center of the m-th diffraction spot in the reconstructed light field.

[0016] In the fast phase hologram generation method based on the weighted, phase reuse (WGS) algorithm described above, the phase value Φ at different pixel coordinates in step 3... j WGS The calculation formula is:

[0017]

[0018] in, The exponential term representing the coordinates of different light spot centers; θ m This represents a phase term whose value ranges from [0, 2π]; w m The weights represent the normalized weights; i represents the imaginary unit; and n represents the number of iterations.

[0019] The fast phase hologram generation method based on the weighted, phase-multiplexed WGS algorithm described above, in step 4, involves the amplitude distribution V at different diffraction spots on the Fourier surface. m The calculation formula is:

[0020]

[0021] Where N represents the total number of pixels in the spatial light modulator, Φ j This represents the phase value at different pixel coordinates. The exponential term represents the coordinates of the centers of different light spots.

[0022] The aforementioned fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm, specifically involves the following process in step 6: When using the fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm for the first time, the phase term θ... m For random values ​​in [0, 2π], the normalized weight term w m Take w m =1 / m;

[0023] In the second and subsequent use of the fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm, the normalized weight term w obtained in the previous holographic phase hologram generation process is adjusted according to the changes in the reconstructed light field. m and phase term θ m Perform data processing and output normalized weight terms. and phase term

[0024] The beneficial effects of this invention are that it effectively improves the calculation speed of phase holograms, achieving high-quality real-time optical field reconstruction; and it greatly reduces the response time when calculating complex phase holograms, avoiding the problem of increased iterations and longer response times caused by complex calculations. The phase hologram generation method of this invention is a method that achieves high-quality real-time, complex optical field reconstruction with fewer iterations and lower time costs, effectively improving the real-time performance of wavefront modulation. Compared with the traditional WGS algorithm, it can effectively reduce the response time of holographic phase map calculation without sacrificing the quality of the reconstructed optical field, and greatly improve the calculation speed when reconstructing complex optical fields. Attached Figure Description

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0026] Figure 1 This is a schematic diagram of the process for generating phase holograms according to the present invention;

[0027] Figure 2 This is a schematic diagram illustrating the parameter calculation for generating the phase hologram of the present invention;

[0028] Figure 3 The diagram shows the correspondence between the computation time required to achieve 95% light intensity uniformity at the Fourier surface under different WGS algorithm, weighted WGS algorithm, and phase multiplexing WGS algorithm conditions. From left to right, the diagram shows the correspondence between the computation time required to move one, two, and three focal positions at the Fourier surface and the focal positions.

[0029] Figure 4This invention presents the relationship between the computation time required to achieve 95% light intensity uniformity under WGS algorithm, weighted WGS algorithm, and phase multiplexing WGS algorithm, and the distance between the newly added focal point and the nearest focal point.

[0030] Figure 5 This invention presents the relationship between the computation time required to achieve 95% light intensity uniformity and the number of focal points to be eliminated under the WGS algorithm, weighted WGS algorithm, and phase multiplexing WGS algorithm respectively. Detailed Implementation

[0031] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] This invention proposes a fast phase hologram generation method based on the weighted and phase-reused WGS algorithm. The method includes two parts: hologram phase value, weight and phase calculation, and weight and phase reuse.

[0033] The fast phase hologram generation process based on the weighted, phase-reusing WGS algorithm is as follows: Figure 1 As shown, the parameter calculation process is as follows: Figure 2 As shown, the generation process consists of five steps: 1. Converting the pixel size and arrangement on the spatial light modulator into a two-dimensional distributed grid; 2. Using the distributed grid and diffraction spot parameters of the spatial light modulator in step 1, calculating the exponential term of the phase value loaded onto each pixel coordinate of the spatial light modulator. And calculate the coordinates of the center of all diffraction spots at the Fourier leaf surface. 3. The exponential term based on the coordinates of different light spot centers. The phase value Φ at different pixel coordinates of the spatial light modulator is obtained. j WGS 4. Through Φ j WGS Calculate the amplitude distribution V at different diffraction spots on the Fourier leaf surface. m 5. Update the values ​​of the normalized weight term w and the phase term θ using the obtained amplitude distribution; 6. Repeat the iterative process described in 3 and 4 to calculate the phase value Φ. j WGS The generated hologram converges to the optimal value, and a phase hologram is plotted and the phase term θ is output. m and normalized weight term w m For the output phase term θ m and normalized weight term w m Data is processed and reused based on the actual situation.

[0034] The pixel size and arrangement on the spatial light modulator are transformed into a two-dimensional grid, and the exponential term of the phase value loaded at each pixel coordinate of the spatial light modulator is calculated. This refers to the grid coordinate distribution of pixels in the X direction as (-p) min ,p max ,R x );p min p max R represents the minimum and maximum pixel coordinates in the X direction, respectively. x Let be the resolution in the X direction of the spatial light modulator; similarly, the grid coordinate distribution of the pixels in the Y direction is (-q min ,q max ,R y ). q min ,q max R represents the minimum and maximum pixel coordinates in the Y direction, respectively. y Let be the resolution in the Y direction of the spatial light modulator.

[0035] Based on the distribution grid and diffraction spot parameters, calculate the exponential term of the phase value at each pixel coordinate of the spatial light modulator. And calculate the coordinates of the center of all diffraction spots at the Fourier leaf surface. The set refers to the set with parameter x. m ,y m ,z m ,θ m ,w m ;where x m ,y m ,z m θ represents the three-dimensional coordinates (x, y, z) of the center of the m-th diffraction spot in the reconstructed optical field at the Fourier surface of the incident beam after wavefront modulation by the holographic phase diagram; m Let w be a phase term with values ​​in the range [0, 2π]. m For the normalized weight terms, according to the formula Calculate the exponential term of the phase value at each pixel coordinate of the spatial light modulator. In the formula, λ represents the incident light wavelength, f represents the effective focal length of the optical system, (x j ,y j () represents the coordinates of the j-th pixel of the spatial light modulator; and calculates all the coordinates based on the number and coordinate positions of the diffraction spot centers. A set of.

[0036] Based on the exponential term of different spot center coordinates The phase value Φ at different pixel coordinates of the spatial light modulator is obtained. j WGS This refers to the exponential term of the coordinates of different light spot centers. Separately and phase random terms θ mSummation, multiplying the sum by the imaginary unit i, taking the exponent e, and multiplying the result by the weight term w. m Summing and taking the tilt angle gives the phase value at different pixel coordinates of the spatial light modulator, i.e. Where n represents the number of iterations.

[0037] Through Φ j WGS Calculate the amplitude distribution V at different diffraction spots on the Fourier leaf surface. m The value of the normalized weight term w and the phase term θ is updated by the obtained amplitude distribution, which means that through Φ j WGS According to the formula Calculate the amplitude distribution of different diffraction spots at the Fourier surface, where N represents the total number of pixels in the spatial light modulator. Based on the calculated amplitude distribution V... m According to the formula Substitute into the iterative process to recalculate and update the weight terms. and phase term The value of .

[0038] Repeat the above iterative process to calculate the phase value Φ. j WGS The generated hologram converges to the optimal value, and a phase hologram is plotted and the phase term θ is output. m and normalized weight term w m This refers to repeating the above iterative process until the desired target optical field uniformity is achieved, and then outputting Φ based on the iteratively optimized result. j WGS The phase hologram is drawn, and the corresponding phase term θ is output. m and normalized weight term w m For the output phase term θ m and normalized weight term w m Data reuse based on actual conditions refers to reusing the normalized weight term w obtained during the previous holographic phase map generation process, according to the changes in the reconstructed light field. m and phase term θ m Perform the appropriate data processing and output the normalized weights. and phase term The weights obtained from reuse in the above process and phase term In subsequent calculations to reconstruct the diffraction field, the random term θ introduced in the initial calculation is replaced. m and normalized weight term w m Repeat the calculation of phase values ​​at different pixel coordinates of the spatial light modulator and the WGS iteration process.

[0039] In the example used in this invention, real-time optical field reconstruction is performed based on a 9*9 diffraction spot array at the Fourier surface, involving focus movement, addition, and elimination. The correspondence between different types of real-time optical path reconstruction and the number of iterations is discussed. This example is completed using GPU parallel computing. A phase-type spatial light modulator with a spatial resolution of 1920*1080 and a pixel size of 8µm is used to modulate the incident light field by loading a phase hologram. Specifically, a grid with coordinates [-7680, 7680, 1920] is created in the X direction, and similarly, a grid with coordinates [-4320, 4320, 1080] is created in the Y direction. The parameter x is then substituted. m ,y m ,z m ,θ m ,w m A 9x9 diffraction pattern array is generated at the Fourier surface. Since m = 81, 81 sets of x-beams are needed. m ,y m ,z m The coordinates of θ are composed of 81 random numbers between [0, 2π]. m Array, 81 w m =1 / 81 of the composition w m The array is used to calculate the phase value Φ at different pixel coordinates of the spatial light modulator. j WGS .

[0040] According to Φ j WGS Calculate the amplitude distribution V of different diffraction spots at the Fourier surface. m And according to V m Recalculate and update the weights. and phase term The value of Φ is calculated. The above iterative process is repeated to calculate the phase value Φ. j WGS The generated hologram converges to the optimal value, and a phase hologram is plotted and the phase term θ is output. m and normalized weight term w m .

[0041] w m and θ m Perform the corresponding data processing and output the normalized weights required for reuse. and phase term This data processing involves two cases: changes in the position and number of diffraction spots at the Fourier surface. In the first case, the weighting terms of the phase holograms obtained from the two optical field reconstructions... and phase term If the number of elements in an array is the same, it can be directly reused in the generation of a new phase hologram.

[0042] Figure 3 This paper presents the correspondence between the computation time required to achieve 95% light intensity uniformity at the Fourier transform surface and the focal position under different WGS algorithm, weighted WGS algorithm, and phase-multiplexed WGS algorithm conditions. From left to right, the figures show the correspondence between the computation time required to move one, two, and three focal positions at the Fourier transform surface and the focal position. Real-time optical field reconstruction based on changes in focal position and number is performed using a 9*9 focal array at the Fourier transform surface. Figure 3 As shown, when reconstructing the light field by moving the focal positions at points 1 to 3 on the Fourier surface using this method, the number of iterations is 2 to 5. Since the computation time for each iteration is roughly the same, compared to the traditional WGS algorithm which generates a reconstructed light field with similar uniformity through 19-21 iterations, this method improves the computation speed by 2.5-5 times, or equivalently, reduces the computation time by 60%-80%; in the second case, the weight term w in the two light field reconstruction calculations... m and phase term θ m If the number of elements in the array is different, then the original weight term w needs to be adjusted. m and phase term θ m The array is reused after subtracting existing items or adding corresponding items to ensure that the number of elements in the array is the same. When reconstructing the light field generated by a single focus within the Fourier plane, since the initial phase term is a random number within the range [0, 2π], the average value π is chosen as the new phase term and incorporated into the reuse process. The normalized value of the corresponding number of focuses is used as a new weight term and incorporated into the reuse process; for example, when m = 81, 81 w... m =1 / 81 of the composition w m The array is used for reuse.

[0043] Figure 4 This diagram illustrates the relationship between the computation time required to achieve 95% light intensity uniformity under different WGS algorithms (with and without weighting or phase reuse) and the distance between the newly added focal point and the nearest focal point. Real-time light field reconstruction of the newly added focal point is performed based on a 9x9 focal array at the Fourier surface. For example... Figure 4 As shown, when reconstructing the light field generated by a single focus within the Fourier surface using this method, the number of iterations is 3 to 5. Since the computation time for each iteration is roughly the same, compared to the traditional WGS algorithm which generates a reconstructed light field with similar uniformity through 19-21 iterations, this method improves the computation speed by 3-4 times, or equivalently, reduces the computation time by 60%-80%. When reconstructing the light field by eliminating the focus within the Fourier surface, the corresponding elements in the weight and phase term arrays are deleted and then incorporated into the reuse process. Figure 5This paper presents the correlation between the computation time required to achieve 95% light intensity uniformity and the number of focal points to be eliminated under the WGS algorithm, weighted WGS algorithm, and phase-reused WGS algorithm, respectively. Real-time light field reconstruction for focal point removal is based on a 9*9 focal array at the Fourier surface.

[0044] like Figure 5 As shown, when eliminating focal positions 0 to 5 on the Fourier surface in the reconstructed light field using this method, the number of iterations is 2 to 6. Real-time light field reconstruction after focal point removal is based on a 9*9 focal array on the Fourier surface. Since the computation time for each iteration is roughly the same, compared to the traditional WGS algorithm which generates a reconstructed light field with similar uniformity through 18-21 iterations, this method improves computation speed by 2-4.5 times, or equivalently, reduces computation time by 70%-90%.

[0045] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. The scope of protection of the present invention is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within its spirit and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of the present invention.

Claims

1. A fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm, characterized in that, The steps include: Step 1: Convert the pixel size and arrangement on the spatial light modulator into a two-dimensional grid. Step 2: Using the distribution grid and diffraction spot parameters of the spatial light modulator from Step 1, calculate the exponential term of the phase value applied to each pixel coordinate of the spatial light modulator. And calculate the coordinates of the center of all diffraction spots at the Fourier leaf surface. A set; Step 3, based on the exponential term of different spot center coordinates The phase value Φ at different pixel coordinates of the spatial light modulator is obtained. j WGS ; Step 4, via Φ j WGS Calculate the amplitude distribution V at different diffraction spots on the Fourier leaf surface. m The values ​​of the normalized weight term w and the phase term θ are updated using the obtained amplitude distribution; Step 5: Repeat the iterative process of steps 3-4 to calculate the phase value Φ. j WGS The generated hologram converges to the optimal value, and a phase hologram is plotted and the phase term θ is output. m and normalized weight term w m ; Step 6, output phase term θ m and normalized weight term w m The data is processed and then reused.

2. The fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm according to claim 1, characterized in that, Step 1 specifically includes: the grid coordinate distribution of pixels in the X direction is (-p min ,p max ,R x ), where p min p max R represents the minimum and maximum pixel coordinates in the X direction, respectively. x The resolution in the X direction of the spatial light modulator; The grid coordinate distribution of the pixels in the Y direction is (-q) min ,q max ,R y ), where q min ,q max R represents the minimum and maximum pixel coordinates in the Y direction, respectively. y Let x be the resolution in the Y direction of the spatial light modulator. m ,y m ,z m ,θ m ,w m , where x m ,y m ,z m θ represents the three-dimensional coordinates (x, y, z) of the center of the m-th diffraction spot in the reconstructed optical field at the Fourier surface of the incident beam after wavefront modulation by the holographic phase diagram; m Let w be a phase term with values ​​in the range [0, 2π]. m The weights are normalized terms.

3. The fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm according to claim 1, characterized in that, The index term in step 2 The calculation formula is: Among them, z m Let λ represent the Z-axis coordinate of the center of the m-th diffraction spot in the reconstructed light field, λ represent the incident light wavelength, and f represent the effective focal length of the optical system. j ,y j (x) represents the coordinates of the j-th pixel in the spatial light modulator. m The x-axis coordinate of the center of the m-th diffraction spot in the reconstructed light field is represented by y. m This represents the Y-axis coordinate of the center of the m-th diffraction spot in the reconstructed light field.

4. The fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm according to claim 1, characterized in that, The phase value Φ at different pixel coordinates in step 3 j WGS The calculation formula is: in, The exponential term representing the coordinates of different light spot centers; θ m This represents a phase term whose value ranges from [0, 2π]; w m The weights represent the normalized weights; i represents the imaginary unit; and n represents the number of iterations.

5. The fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm according to claim 1, characterized in that, In step 4, the amplitude distribution V at different diffraction spots on the Fourier surface m The calculation formula is: Where N represents the total number of pixels in the spatial light modulator, Φ j This represents the phase value at different pixel coordinates. The exponential term represents the coordinates of the centers of different light spots.

6. The fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm according to claim 1, characterized in that, The specific process of reuse in step 6 is as follows: When using the fast phase hologram generation method based on weighted, phase reuse WGS algorithm for the first time, the phase term θ m For random values ​​in [0, 2π], the normalized weight term w m Take w m =1 / m; In the second and subsequent use of the fast phase hologram generation method based on the weighted, phase-reusing WGS algorithm, the normalized weight term w obtained in the previous holographic phase hologram generation process is adjusted according to the changes in the reconstructed light field. m and phase term θ m Perform data processing and output normalized weight terms. and phase term

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