A fast hologram generation method based on high-frequency information extraction

Abstract

This invention proposes a fast hologram generation method based on high-frequency information extraction. The method includes the following three steps: First, preprocessing the object using a Gaussian filter to separate its high-frequency and low-frequency information, obtaining corresponding high-frequency and low-frequency images. Second, calculating the high-frequency image using a novel lookup table method to obtain the corresponding high-frequency hologram, and simultaneously calculating the low-frequency image using the angular spectrum method to obtain the corresponding low-frequency hologram. Third, superimposing the complex amplitude information of the high-frequency and low-frequency holograms to obtain the complex amplitude information of the final hologram, and extracting the phase information to obtain a pure phase hologram. The final pure phase hologram is then loaded onto a spatial light modulator for optical reconstruction. When coherent parallel light illuminates the spatial light modulator, the holographic image of the object is reconstructed. The method proposed in this invention reduces the number of object points involved in the calculation using the novel lookup table method, significantly improving the hologram calculation time.

Description

I. Technical Field

[0001] This invention relates to holographic display technology, and more specifically, to a method for rapid hologram generation based on high-frequency information extraction. II. Background Technology

[0002] In recent years, with the rapid development of computers, computational holographic 3D display technology has attracted widespread attention due to its flexibility. However, the enormous computational load affects the hologram generation speed, limiting the further development of dynamic holographic 3D displays. To improve computational speed, researchers have proposed different hologram generation algorithms based on different object description methods. Among them, the pixel method is a classic algorithm for hologram generation, which discretizes the object into individual ideal point light sources, calculates a sub-hologram for each point, and then superimposes all sub-holograms to obtain the final hologram, which can reconstruct the detailed information of the object very well. However, the number of pixels increases dramatically with the increase of object complexity, limiting the computational speed of hologram generation based on the pixel method. Some researchers have proposed different improved algorithms, such as novel lookup table methods, split lookup table methods, and compressed lookup table methods, but the computational speed is still difficult to meet the requirements of real-time dynamic holographic displays. Therefore, simplifying the calculation process to accelerate hologram calculation is an urgent problem to be solved in holographic 3D displays. III. Summary of the Invention

[0003] This invention proposes a fast hologram generation method based on high-frequency information extraction. (See attached diagram) Figure 1 As shown, the method includes the following three steps: First, the object is preprocessed based on a Gaussian filter to separate the high-frequency and low-frequency information of the object, obtaining corresponding high-frequency and low-frequency images. Second, the high-frequency image is calculated using a novel lookup table method, generating a sub-hologram corresponding to each pixel based on diffraction theory, and these sub-holograms are superimposed to obtain a high-frequency hologram. Simultaneously, the low-frequency image is calculated using the angular spectrum method to obtain the corresponding low-frequency hologram. Third, the complex amplitude information of the high-frequency and low-frequency holograms is superimposed to obtain the complex amplitude information of the final hologram, and the phase information is extracted to obtain a pure phase hologram. The final pure phase hologram is loaded onto a spatial light modulator for optical reconstruction. When coherent parallel light illuminates the spatial light modulator, the holographic image of the object is reproduced. The method proposed in this invention reduces the number of object points involved in the calculation using the novel lookup table method, significantly improving the hologram calculation time.

[0004] In step one, the image is preprocessed using a Gaussian filter to separate the high-frequency and low-frequency information, resulting in corresponding high-frequency and low-frequency information images. Gaussian filtering is a weighted average process of pixel values ​​in an image. The main steps are as follows: First, a two-dimensional matrix K is constructed as the convolution kernel, i.e., the Gaussian kernel. Then, for each pixel M in the image, the product of its neighboring pixels and the Gaussian kernel K is calculated. All the calculated neighboring pixel values ​​are summed to obtain the weighted value of pixel M. The weighted image is the low-frequency information image. Finally, the pixel difference between the original image and the low-frequency information image is analyzed to calculate the high-frequency information image.

[0005] In step two, a novel lookup table method is used to calculate the high-frequency information image. The high-frequency information image is considered to be composed of a series of discrete points. Based on diffraction theory, the central fringe pattern is calculated, and the fringe patterns of other points are calculated using the principles of translation and superposition, thereby generating a high-frequency hologram. The complex amplitude distribution U of the high-frequency hologram... HF (x,y) is shown in the following formula:

[0006]

[0007]

[0008] Where N is the number of image points, k and λ represent the wavenumber and wavelength, respectively, and j is the imaginary unit. For the i-th point, A i and These are the corresponding amplitude and phase information, r i It is a point (x) on the holographic plane i ,y i ,z i The distance between (x, y, 0) and the sampling point (x, y, 0) is calculated. Simultaneously, the angular spectrum method is used to calculate the low-frequency information image, and the complex amplitude distribution U of the low-frequency hologram is calculated based on angular spectrum diffraction theory. LF (x,y) can be represented as:

[0009]

[0010] in, and Representing the Fourier transform and inverse Fourier transform respectively, A LF It is the amplitude of the low-frequency image, f x and f y y is the spatial frequency in the x and y directions, and z is the propagation distance.

[0011] In step three, the complex amplitude information on the final hologram plane is obtained by superimposing the complex amplitude information of the high-frequency hologram and the low-frequency hologram. Due to the different principles used in the calculation process, the amplitude differences in the complex amplitude distributions of the high-frequency and low-frequency holograms are significant, resulting in uneven brightness during the reconstruction of the high-frequency and low-frequency components. Therefore, the high-frequency complex amplitude distribution is recalculated based on angular spectrum diffraction theory, denoted as... Then, normalization is performed to obtain the optimized high-frequency complex amplitude distribution, denoted as .

[0012]

[0013] Where max|·| represents the function that maximizes the objective function. The final complex amplitude distribution U(x,y) of the hologram is expressed as:

[0014]

[0015] The phase information in the complex amplitude distribution U(x,y) is extracted to obtain a pure phase hologram.

[0016] In the holographic reconstruction process, the pure phase hologram generated in step three is loaded onto the spatial light modulator. When the spatial light modulator is illuminated by coherent parallel light, a holographic reconstruction image can be reconstructed.

[0017] The advantages of the method proposed in this invention are as follows: for complex objects, high-frequency information and low-frequency information are separated based on Gaussian filters. Only high-frequency information is calculated using a novel lookup table method, while low-frequency information is calculated using the angular spectrum method to improve the calculation speed. While ensuring that the detailed information of the object is completely reconstructed, the number of points involved in the calculation of the novel lookup table method is reduced, which greatly improves the calculation speed of holograms. IV. Description of the attached drawings

[0018] Appendix Figure 1 This is a schematic diagram of a fast hologram generation method based on high-frequency information extraction according to the present invention.

[0019] Appendix Figure 2 This diagram illustrates a comparison of the computation time between a fast hologram generation method based on high-frequency information extraction according to the present invention and a traditional novel lookup table method.

[0020] Appendix Figure 3 This is a reconstruction effect diagram of a fast hologram generation method based on high-frequency information extraction according to the present invention.

[0021] It should be understood that the above figures are only schematic and are not drawn to scale. V. Detailed Implementation Methods

[0022] The following detailed description of an embodiment of the fast hologram generation method based on high-frequency information extraction proposed in this invention further illustrates the invention. It is important to note that the following embodiments are for illustrative purposes only and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description still fall within the scope of protection of this invention.

[0023] One embodiment of the present invention uses a collimated light source with a wavelength of 532nm as the coherent light source. The spatial light modulator is a reflective pure phase spatial light modulator with a pixel pitch of 6.4μm and a resolution of 1920×1080, addressable grayscale levels of 256, a phase modulation capability of 2π, and a refresh rate of 60Hz. First, a set of images of "flowers" with resolutions of 300×300, 400×400, 500×500, and 600×600 are used as the recorded objects, with a reconstruction distance of 20cm. When using the traditional novel lookup table method for calculation, the hologram generation times are 617s, 1096s, 1709s, and 2456s, respectively. The calculation time increases significantly with the increase in the resolution of the recorded object. When using the method of this invention for calculation, high-frequency and low-frequency information images of the "flower" are extracted based on a Gaussian filter. A novel lookup table method and angular spectrum method are used to calculate the high-frequency and low-frequency holograms respectively. These are then superimposed and processed to obtain the final pure phase hologram. The generation times of the final pure phase holograms are 211s, 375s, 570s, and 774s, respectively. A comparison of the calculation times is attached. Figure 2 As shown. Compared with the traditional novel lookup table method, the calculation speed is improved by 65.81%, 65.79%, 66.65%, and 68.49%, respectively. The method of this invention can improve the generation speed of holograms by more than 60%, and the speed improvement is more significant with the increase of image resolution. When the pure phase hologram calculated by this invention at a resolution of 600×600 for the "flower" is loaded onto a spatial light modulator, the reconstructed image is shown in the attached figure when the reconstruction light illuminates the spatial light modulator. Figure 3 As shown in the figure. The results indicate that the method of the present invention can achieve correct reconstruction of the reconstructed image.

Claims

1. A fast hologram generation method based on high-frequency information extraction, characterized by, The method comprises the following three steps: first, based on a Gaussian filter, the object is pre-processed to separate the high-frequency information and the low-frequency information of the object, and the corresponding high-frequency image and low-frequency image are obtained; second, the high-frequency image is calculated by using a new lookup table method, the corresponding sub-hologram of each pixel point is generated according to the diffraction theory, and the high-frequency hologram is obtained by superposition, and the low-frequency image is calculated by using an angular spectrum method to obtain the corresponding low-frequency hologram; third, the complex amplitude information of the high-frequency hologram and the low-frequency hologram is superposed to obtain the complex amplitude information of the final hologram, and the phase information is extracted to obtain a pure phase hologram. In step two, a new look-up table method is used to calculate the high-frequency information image. The high-frequency information image is regarded as a series of discrete points. Based on the diffraction theory, the central fringe pattern is calculated. The fringe patterns of other points are calculated through the translation and superposition principle, thereby generating a high-frequency hologram. The complex amplitude distribution U of the high-frequency hologram is as follows: HF (x, y) = U(x, y) e where N is the number of image points, k and λ represent the wave number and wavelength, respectively, and j is the imaginary unit; for the i-th point, A i and are the corresponding amplitude and phase information, respectively, r i is the distance between the point (x i , y i , z i ) on the holographic plane and the sampling point (x, y, 0); at the same time, the angular spectrum method is used to calculate the low-frequency information image, and the complex amplitude distribution U LF (x, y) of the low-frequency hologram calculated based on the angular spectrum diffraction theory is represented as: wherein and represent the Fourier transform and the inverse Fourier transform, respectively, A LF is the amplitude of the low-frequency image, f x and f y are the spatial frequencies in the x and y directions, respectively, and z is the propagation distance; In step three, the complex amplitude information on the final hologram plane is obtained by superimposing the complex amplitude information of the high frequency hologram and the low frequency hologram; due to the difference in the principle used in the calculation process, the amplitude difference of the complex amplitude distribution of the high frequency and the low frequency hologram is large, which leads to the uneven brightness when the high frequency and the low frequency are reconstructed; therefore, the high frequency complex amplitude distribution is calculated again based on the angular spectrum diffraction theory, denoted as Then, the normalized processing is performed to obtain the optimized high frequency complex amplitude distribution, denoted as Wherein, max|·| represents a function of obtaining the maximum value of the target function; the complex amplitude distribution U(x, y) of the final hologram is represented as: The phase information in the complex amplitude distribution U(x, y) is extracted to obtain a pure phase hologram.

2. The method for generating a quick hologram based on high frequency information extraction according to claim 1, characterized in that, For a complex object, based on the Gaussian filter, the high-frequency information and the low-frequency information are separated, only the high-frequency information is calculated by using the new lookup table method, and the low-frequency information is calculated by using the angular spectrum method to improve the calculation speed, the number of point elements participating in the calculation of the new lookup table method is reduced while ensuring that the detailed information of the object is completely reconstructed, and the calculation speed of the hologram is greatly improved.

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