Color hologram generation method based on approximate secondary phase mask

Abstract

The invention relates to the technical field of holography, in particular to a color hologram generation method based on an approximate secondary phase mask. The method comprises the following steps: constructing an approximate secondary phase; extracting an optimized approximate secondary phase mask from a spatial domain or a frequency domain according to the approximate secondary phase; and decomposing a target image into RGB three-channel amplitudes, and combining the optimized approximate secondary phase mask with the three-channel amplitudes to obtain a color hologram. According to the method, the calculation efficiency can be improved, a hybrid optimization strategy is provided, a high-quality initial phase is quickly generated through an approximate secondary phase mask, the phase distribution is refined by combining limited GS iteration (10-30 times), the single frame generation time is compressed to be within 5 seconds, the efficiency is improved by more than 50% compared with that of a traditional GS algorithm, high-frequency noise is inhibited through regular phase distribution, and the calculation efficiency is improved. The phase uniformity is improved in combination with double-domain optimization, so that the PSNR value of the reconstructed image exceeds 28dB, the SSIM value exceeds 0.9, and the noise power is reduced by more than 30% compared with a random phase method.

Description

Technical Field

[0001] The present invention relates to the technical field of holography, and in particular to a method for generating a color hologram based on an approximate quadratic phase mask. Background Art

[0002] Holographic display technology can fully restore the three-dimensional appearance of an object by recording and reconstructing the amplitude and phase information of light waves, and has become a research hotspot in the field of display technology. Traditional hologram generation methods are mainly divided into two categories: iterative algorithms and non-iterative algorithms. The iterative algorithm is represented by the Gerchberg-Saxton (GS) algorithm, which gradually optimizes the phase distribution by repeatedly performing Fourier transform and inverse transform between the object plane and the hologram plane. Although the GS algorithm can generate high-quality holograms, its computational complexity is extremely high, and the generation time of a single frame is usually more than 10 seconds (50-100 iterations), which cannot meet the needs of real-time dynamic display. In addition, the GS algorithm is prone to falling into local minima, resulting in artifacts and speckle noise in the reconstructed image, which may obscure key details in scenarios with strict image quality requirements such as medical imaging.

[0003] Non-iterative algorithms, represented by random phase mask methods (such as the ORAP method), rapidly generate holograms by introducing a random phase. Although such methods reduce the single-frame generation time to less than 0.5 seconds, the uncontrollable nature of the random phase results in high noise power in the reconstructed image (PSNR < 20dB) and severe loss of detail (SSIM < 0.8). In recent years, researchers have proposed optimizing random phase masks (such as the FS-ORAP method), which improves the adaptability of the phase distribution through a fully supported window design. However, there are still limitations on the target size and position. For example, when the target image size is adjusted from 512×512 to 1024×1024, traditional ORAP needs to regenerate the mask, resulting in wasted computing resources and reduced efficiency.

[0004] In terms of color holographic display, existing methods usually simply superimpose RGB three-channel holograms. However, the differences in RGB laser wavelengths (such as 671nm for red laser, 532nm for green laser, and 473nm for blue laser) will cause longitudinal scaling (error > 10%) and lateral offset (error > 5%) of the reconstructed image, seriously damaging color consistency. Although some studies have attempted to adjust the phase by wavelength ratio, the correction accuracy is insufficient and the cumulative effect of chromatic aberration caused by changes in target position in dynamic scenes is not considered. In addition, existing methods have poor adaptability to dynamic 3D targets, and the efficiency of layered processing and multiplexing strategies is low, making it difficult to achieve real-time refresh (frame rate < 10fps).

[0005] In summary, the existing technology has significant defects in hologram generation efficiency, image quality and dynamic adaptability. Summary of the Invention

[0006] In view of the above-mentioned shortcomings of the prior art, the object of the present invention is to provide a color hologram generation method based on an approximate quadratic phase mask, which realizes efficient, high-quality and highly flexible color hologram generation.

[0007] To achieve the above-mentioned and other related objectives, the present invention provides a method for generating a color hologram based on an approximate quadratic phase mask, comprising:

[0008] S1, construct an approximate quadratic phase;

[0009] S2. extracting an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase;

[0010] S3. Decompose the target image into RGB three-channel amplitudes, and combine the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to obtain a color hologram.

[0011] In one embodiment of the present invention, constructing the approximate quadratic phase in step S1 includes:

[0012] In the bandwidth range (-f x ,f x ) and (-f y ,f y ) samples i frequency points, where i<M and i<N, M and N are the number of pixels of the target image in the horizontal and vertical directions respectively;

[0013] By formula f p =repmat{linspace(-f x ,f x ,i),M / i} and f q =repmat{linspace(-f y ,f y ,i),N / i} to get f p and f q , f p and f q are the frequency components in the x and y directions generated by discrete sampling, which are used to approximate the quadratic phase distribution;

[0014] According to f p and f q The approximate quadratic phase expression is obtained Δp and Δq represent the sampling intervals in the x-direction and y-direction, respectively, to construct an approximate quadratic phase.

[0015] In one embodiment of the present invention, extracting an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase in step S2 includes:

[0016] S21, creating a fully supported rectangular window of the same size as the target image, multiplying the approximate quadratic phase by the amplitude of the fully supported rectangular window, and then performing an inverse Fourier transform to obtain an initial phase;

[0017] S22. Optimizing the initial phase by a finite number of iterations using an improved Gerchberg-Saxton algorithm to obtain a complex amplitude in the hologram plane;

[0018] S23, performing adaptive constraint adjustment on the complex amplitude of the hologram plane, dynamically optimizing the phase distribution, and extracting the optimized approximate quadratic phase mask from the spatial domain or the frequency domain.

[0019] In one embodiment of the present invention, step S3 decomposes the target image into RGB three-channel amplitudes, and combines the optimized approximate quadratic phase mask with the three-channel amplitudes to obtain a color hologram, including:

[0020] S31, decomposing the target image into RGB three-channel amplitudes, combining the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to perform IFT and extract a pure phase hologram;

[0021] S32, according to the difference in wavelength of RGB laser r ,λ g ,λ b ,Through frequency domain scaling and spatial translation, a three-channel pure phase hologram is obtained;

[0022] S33, superimposing the three-channel pure phase holograms according to the signal-to-noise ratio weights to generate a color hologram.

[0023] In one embodiment of the present invention, performing a finite number of iterative optimizations on the initial phase includes performing Fourier transform on the object plane complex amplitude to obtain the hologram plane complex amplitude.

[0024] In one embodiment of the present invention, the termination condition of the iterative optimization of the improved Gerchberg-Saxton algorithm is that a preset number of iterations, i.e., 10-30 times, is reached, or the PSNR value of the reconstructed image is ≥28dB.

[0025] In one embodiment of the present invention, the frequency domain scaling and spatial translation include: the red channel phase scaling factor is λ b / λ r , the green channel phase scaling factor is λ b / λ g ; lateral offset Δx=k(λ b -λ r ), where k is the ratio of pixel pitch to wavelength.

[0026] The present invention also provides a color hologram generation system based on an approximate quadratic phase mask, comprising:

[0027] An approximate quadratic phase construction module, used to construct an approximate quadratic phase;

[0028] An approximate quadratic phase mask extraction module is used to extract an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase;

[0029] The color hologram acquisition module is used to decompose the target image into RGB three-channel amplitudes, and combine the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to obtain a color hologram.

[0030] As described above, the color hologram generation method based on the approximate quadratic phase mask of the present invention has the following beneficial effects:

[0031] (1) The color hologram generation method based on the approximate quadratic phase mask of the present invention can improve computational efficiency. The traditional GS algorithm is computationally time-consuming due to the high number of iterations, while the non-iterative method is fast but the quality is unstable. The present invention proposes a hybrid optimization strategy, which quickly generates high-quality initial phases by approximating the quadratic phase mask, and then refines the phase distribution by combining a limited number of GS iterations (10-30 times), compressing the single-frame generation time to less than 5 seconds, which is more than 50% more efficient than the traditional GS algorithm.

[0032] (2) The color hologram generation method based on the approximate quadratic phase mask of the present invention can enhance image quality. The approximate quadratic phase mask suppresses high-frequency noise through regular phase distribution, and combines dual-domain optimization to improve phase uniformity, so that the PSNR value of the reconstructed image exceeds 28dB and the SSIM value exceeds 0.9, which is more than 30% lower than the noise power of the random phase method.

[0033] (3) The color hologram generation method based on the approximate quadratic phase mask of the present invention can eliminate the chromatic aberration effect. Based on the wavelength difference of RGB lasers, a dynamic chromatic aberration correction algorithm is designed. Through the strategy of combining frequency domain scaling and spatial translation, the longitudinal size error is controlled within 3% and the lateral offset error is reduced to less than 2%.

[0034] (4) The color hologram generation method based on the approximate quadratic phase mask of the present invention can improve scene adaptability, adopt a full-support window design and a layered multiplexing strategy, support dynamic adjustment of the target image size (256×256 to 1024×1024) and position, and do not need to repeatedly generate masks. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flowchart of a method for generating a color hologram based on an approximate quadratic phase mask provided in an embodiment of the present application.

[0036] Figure 2 A flow chart of an approximate quadratic phase mask optimization algorithm for a color hologram generation method based on an approximate quadratic phase mask provided in an embodiment of the present application.

[0037] Figure 3 A color phase hologram generation flow chart of a color hologram generation method based on an approximate quadratic phase mask provided in an embodiment of the present application.

[0038] Figure 4 Schematic diagram of an experimental setup for a color hologram generation method based on an approximate quadratic phase mask provided in an embodiment of the present application. DETAILED DESCRIPTION

[0039] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other unless they conflict.

[0040] This section will describe in detail the specific embodiments of the present invention. The preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the accompanying drawings is to supplement the description of the text part of the specification with graphics, so that people can intuitively and vividly understand each technical feature and the overall technical solution of the present invention, but it should not be understood as a limitation on the scope of protection of the present invention.

[0041] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", etc., indicating positions or positional relationships, are based on the positions or positional relationships shown in the accompanying drawings and are only for the convenience of describing the present invention and simplifying the description. They do not indicate or imply that the devices or components referred to must have a specific position, be constructed and operated in a specific position. Therefore, they should not be understood as limiting the present invention. The terms "installed", "connected", and "connected" should be understood in a broad sense. For example, they can be fixed connections, detachable connections, or integral connections; they can be mechanical connections or electrical connections; they can be direct connections, indirect connections through an intermediate medium, or internal connections between two components. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0042] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0043] See also Figure 1 , Figure 1 This is a workflow diagram of a method for generating a color hologram based on an approximate quadratic phase mask provided in an embodiment of the present application. The present invention provides a method for generating a color hologram based on an approximate quadratic phase mask, comprising:

[0044] Step S1: construct an approximate quadratic phase.

[0045] Specifically, constructing the approximate quadratic phase in step S1 includes:

[0046] In the bandwidth range (-f x ,f x ) and (-f y ,f y ) samples i frequency points, where i<M and i<N, M and N are the number of pixels of the target image in the horizontal and vertical directions respectively;

[0047] By formula f p =repmat{linspace(-f x ,f x ,i),M / i} and f q =repmat{linspace(-f y ,f y ,i),N / i} to get f p and f q , f p and f q are the frequency components in the x and y directions generated by discrete sampling, which are used to approximate the quadratic phase distribution;

[0048] According to f p and f q The approximate quadratic phase expression is obtained Δp and Δq represent the sampling intervals in the x-direction and y-direction, respectively, to construct an approximate quadratic phase.

[0049] Step S2: extracting an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase.

[0050] Specifically, extracting the optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase in step S2 includes:

[0051] S21, creating a fully supported rectangular window of the same size as the target image, multiplying the approximate quadratic phase by the amplitude of the fully supported rectangular window, and then performing an inverse Fourier transform to obtain an initial phase;

[0052] S22. Optimizing the initial phase by a finite number of iterations using an improved Gerchberg-Saxton algorithm to obtain a complex amplitude in the hologram plane;

[0053] S23, performing adaptive constraint adjustment on the complex amplitude of the hologram plane, dynamically optimizing the phase distribution, and extracting the optimized approximate quadratic phase mask from the spatial domain or the frequency domain.

[0054] Step S3: decompose the target image into RGB three-channel amplitudes, and combine the optimized approximate quadratic phase mask with the three-channel amplitudes to obtain a color hologram.

[0055] Specifically, in step S3, the target image is decomposed into RGB three-channel amplitudes, and the optimized approximate quadratic phase mask is combined with the three-channel amplitudes to obtain a color hologram, including:

[0056] S31, decomposing the target image into RGB three-channel amplitudes, combining the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to perform IFT and extract a pure phase hologram;

[0057] S32, according to the difference in wavelength of RGB laser r ,λ g ,λ b ,Through frequency domain scaling and spatial translation, a three-channel pure phase hologram is obtained;

[0058] S33, superimposing the three-channel pure phase holograms according to the signal-to-noise ratio weights to generate a color hologram.

[0059] In one embodiment of the present invention, the approximate quadratic phase is constructed:

[0060] Generation of approximate quadratic phase: According to the formula Generate an approximate quadratic phase mask. In actual operation, we must first reasonably select the bandwidth range (-f x ,f x ) and (-f y ,f y) and the number of sampling points k. For example, for a target image with a resolution of 512×512, after multiple experiments, it has been verified that when k=128, it can effectively reduce the impact of high-frequency noise while ensuring computational efficiency and improve the quality of the reconstructed image. Use linspace(x1,x2,i) to generate i evenly spaced points between (x1,x2), and then repeat the operation with the repmat(array,j) function to obtain f p and f q , the specific calculation process is as follows:

[0061] f p =repmat{linspace(-f x ,f x ,i),M / i}

[0062] f q =repmat{linspace(-f y ,f y ,i),N / i}

[0063] Combining the above two equations, we can get the approximate quadratic phase.

[0064] Optimized approximate quadratic phase mask generation:

[0065] After the initial phase is generated, the improved GS algorithm is used for finite-time iterative optimization. First, a fully supported rectangular window of the same size as the target image is created (with 1 inside the window and 0 outside), multiplied by the approximate quadratic phase mask, and then an inverse Fourier transform (IFT) is performed to obtain the initial complex amplitude A0(x,y). Then, an iterative loop is entered:

[0066] Fourier transform: complex amplitude A in the object plane k (x,y) is Fourier transformed (FT) to obtain the complex amplitude B of the hologram plane k (u,v).

[0067] Adaptive constraint adjustment: Dynamically adjust the amplitude constraint conditions based on the target image characteristics. For example, strict amplitude constraints are applied to signal areas to preserve details, while relaxed constraints are applied to non-signal areas to accelerate convergence.

[0068] Inverse Fourier transform: transform the adjusted complex amplitude B k ′(u,v) performs inverse Fourier transform (IFT) to update the object plane complex amplitude A k+1 (x,y)

[0069] The iteration termination condition is either reaching a preset number of iterations (e.g., 20) or the PSNR of the reconstructed image exceeds 28dB. An optimized approximate quadratic phase mask of the holographic plane is obtained. Compared with the traditional GS algorithm, this method reduces the number of iterations from 50 to 20 by introducing initial phase optimization, while also improving the average PSNR by 15%.

[0070] Dual-domain optimization strategy:

[0071] To further improve the flexibility and efficiency of phase generation, this paper introduces a dual-domain optimized random phase method. The core of this method is to extract the optimized phase from the spatial domain (SD-ORAP) or the frequency domain (FD-ORAP). The specific process includes:

[0072] Initialization: Generate a random phase of the full-support window and obtain the dual-domain phase distribution through GS iterative optimization.

[0073] Phase extraction: Choose between SD-ORAP and FD-ORAP based on target requirements. Spatial domain phase (SD-ORAP) directly extracts the phase of the plane of the extract and is suitable for high-resolution targets; frequency domain phase (FD-ORAP) extracts the phase of the hologram plane and is suitable for fast generation. Experiments show that SD-ORAP achieves a 2dB higher PSNR than FD-ORAP at 512×512 resolution, while FD-ORAP increases generation speed by 20%.

[0074] Dynamic Cropping: For objects of varying sizes, the required region is cropped from a pre-generated large-scale dual-domain optimized random phase, avoiding repeated computations. For example, cropping a 512×512 region from a 1024×1024 mask only increases the time by 5%.

[0075] Multi-channel chromatic aberration correction and synthesis:

[0076] Aiming at the wavelength difference of RGB three-color laser, the present invention proposes a dynamic chromatic aberration correction algorithm. First, the target image is decomposed into three channels of R, G, and B amplitude A r (x,y),A g (x,y),A b (x,y), and are combined with the optimized phase mask to generate pure phase holograms for each channel. Chromatic aberration correction is divided into two steps:

[0077] Frequency domain scaling: according to wavelength ratio λ r ,λ g ,λ b The phase of the R and G channels is scaled in the frequency domain with the scaling factors being λ b / λ r and λ b / λ g For example, when λ r =671nm,λb =473nm, the R channel scaling factor is 0.705.

[0078] Spatial translation: Calculate the lateral offset Δx = k(λ b -λ r ), where k is the scale factor, and the three-channel images are aligned by translation operation.

[0079] The corrected three-channel hologram is synthesized using a weighted superposition strategy, with weights dynamically assigned based on the signal-to-noise ratio of each channel. Experiments show that this algorithm reduces chromatic aberration error from 12% to 4.7% and significantly improves its adaptability to dynamic targets.

[0080] See also Figure 2 、 Figure 3 , Figure 2 A flow chart of an approximate quadratic phase mask optimization algorithm for a color hologram generation method based on an approximate quadratic phase mask provided in an embodiment of the present application. Figure 3 A color phase hologram generation flow chart of a color hologram generation method based on an approximate quadratic phase mask provided in an embodiment of the present application. A fully supported rectangular window of the same size as the target image is padded with zeros as the input amplitude, and an approximate quadratic phase is superimposed to obtain the initial input complex amplitude of the object plane. For example: the resolution of the target image is N×N, first create a fully supported rectangular window with the same resolution as the target image, fill this rectangular aperture window with zeros to a size of 2N×2N, and then superimpose the approximate quadratic phase on this rectangular window to obtain the initial input complex amplitude A0(x,y) of the object plane. The complex amplitude A of the object plane k (x,y) is Fourier transformed (FT) to obtain the complex amplitude B of the hologram plane k (u,v). The amplitude of the hologram plane is adaptively constrained and adjusted, and the phase remains unchanged. The adjusted complex amplitude B k ′(u,v) performs inverse Fourier transform (IFT) to update the object plane complex amplitude A k+1 (x, y). Perform multiple forward and inverse Fourier transforms on the complex amplitude of the object plane to obtain the optimized approximate quadratic phase mask of the holographic plane. Decompose the target image into three channels of R, G, and B amplitude A r (x,y),A g (x,y),A b (x, y), and are combined with the optimized approximate quadratic phase mask to generate the pure phase hologram of each channel. Finally, the pure phase holograms of the three channels are combined to generate a color hologram.

[0081] See also Figure 4 , Figure 4A schematic diagram of an experimental setup for a color hologram generation method based on an approximate quadratic phase mask provided in an embodiment of the present application. The schematic diagram of the experimental setup includes: a three-color laser light source, an attenuation plate, a spatial filter, a reflector, a dichroic mirror, a beam expander, a collimating lens, a beam splitter, a spatial light modulator, a 4-f system, and a camera; the axes of the laser light source, attenuation plate, and spatial filter are in a straight line. The reflector and dichroic mirror adjust the red, green, and blue lasers to a straight line, which passes through the beam expander, collimating lens, and beam splitter to the spatial light modulator. The spatial light modulator is connected to a computer. The 4-f system is used to eliminate the influence of zero-order light generated by the spatial light modulator. The camera is used to capture and reconstruct images.

[0082] Green lasers with wavelengths of 532 nm, 635 nm, and 445 nm were used as light sources. These lasers were directed through an attenuator and spatial filter onto a reflector and dichroic mirror, respectively. The red, green, and blue lasers were aligned by the reflector and dichroic mirror, then passed through a beam expander, collimating lens, and beam splitter prism to the spatial light modulator. The experiment used an 8-bit reflective, pure-phase SLM with a sampling interval of 6.4 μm × 6.4 μm and a resolution of 1920 × 1080. The focal length of the lens was 40 cm, and the target image size was 512 × 512, which was upscaled to 1024 × 1024 using zero padding. A 4-f system consisting of two lenses was used to eliminate the influence of zero-order light generated by the SLM. A Cannon EOS 450D camera with a 55 mm lens was used to capture the reconstructed images.

[0083] Similar in principle to the color hologram generation method based on an approximate quadratic phase mask of the present invention, the present invention also provides a color hologram generation system based on an approximate quadratic phase mask, comprising:

[0084] An approximate quadratic phase construction module, used to construct an approximate quadratic phase;

[0085] An approximate quadratic phase mask extraction module is used to extract an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase;

[0086] The color hologram acquisition module is used to decompose the target image into RGB three-channel amplitudes, and combine the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to obtain a color hologram.

[0087] In summary, the present invention's color hologram generation method based on an approximate quadratic phase mask can improve computational efficiency. Traditional GS algorithms are computationally time-consuming due to their high number of iterations, while non-iterative methods are fast but offer inconsistent quality. This invention proposes a hybrid optimization strategy that rapidly generates high-quality initial phases using an approximate quadratic phase mask. This strategy then refines the phase distribution using a limited number of GS iterations (10-30). This reduces the single-frame generation time to less than 5 seconds, achieving an efficiency improvement of over 50% compared to traditional GS algorithms.

[0088] The technical principles of the present invention have been described above with reference to specific embodiments. These descriptions are intended solely to illustrate the principles of the present invention and are not to be construed in any way as limiting the scope of protection of the present invention. Based on the explanations herein, those skilled in the art will be able to devise other specific embodiments of the present invention without inventive effort, and such equivalent variations or substitutions are intended to be encompassed within the scope of the claims of this application.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A color hologram generation method based on an approximate quadratic phase mask, characterized in that: include: S1, construct an approximate quadratic phase; S2. extracting an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase; S3. Decompose the target image into RGB three-channel amplitudes, and combine the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to obtain a color hologram.

2. The method for generating a color hologram based on an approximate quadratic phase mask according to claim 1, wherein: The construction of the approximate quadratic phase in step S1 includes: In the bandwidth range (-f x ,f x ) and (-f y ,f y ) samples i frequency points, where i<M and i<N, M and N are the number of pixels of the target image in the horizontal and vertical directions respectively; By formula f p =repmat{linspace(-f x ,f x ,i),M / i} and f q =repmat{linspace(-f y ,f y ,i),N / i} to get f p and f q , f p and f q are the frequency components in the x and y directions generated by discrete sampling, which are used to approximate the quadratic phase distribution; According to f p and f q The approximate quadratic phase expression is obtained Δp and Δq represent the sampling intervals in the x-direction and y-direction, respectively, to construct an approximate quadratic phase.

3. The method for generating a color hologram based on an approximate quadratic phase mask according to claim 2, wherein: Extracting an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase in step S2 includes: S21, creating a fully supported rectangular window of the same size as the target image, multiplying the approximate quadratic phase by the amplitude of the fully supported rectangular window, and then performing an inverse Fourier transform to obtain an initial phase; S22. Optimizing the initial phase by a finite number of iterations using an improved Gerchberg-Saxton algorithm to obtain a complex amplitude in the hologram plane; S23, performing adaptive constraint adjustment on the complex amplitude of the hologram plane, dynamically optimizing the phase distribution, and extracting the optimized approximate quadratic phase mask from the spatial domain or the frequency domain.

4. The method for generating a color hologram based on an approximate quadratic phase mask according to claim 3, wherein: In step S3, the target image is decomposed into RGB three-channel amplitudes, and the optimized approximate quadratic phase mask is combined with the three-channel amplitudes to obtain a color hologram. S31, decomposing the target image into RGB three-channel amplitudes, combining the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to perform IFT and extract a pure phase hologram; S32, according to the difference in wavelength of RGB laser r ,λ g ,λ b ,Through frequency domain scaling and spatial translation, a three-channel pure phase hologram is obtained; S33, superimposing the three-channel pure phase holograms according to the signal-to-noise ratio weights to generate a color hologram.

5. The method for generating a color hologram based on an approximate quadratic phase mask according to claim 3, wherein: The finite number of iterative optimizations of the initial phase includes Fourier transforming the object plane complex amplitude to obtain the hologram plane complex amplitude.

6. The method for generating a color hologram based on an approximate quadratic phase mask according to claim 3, wherein: The termination condition of the iterative optimization of the improved Gerchberg-Saxton algorithm is that a preset number of iterations is reached, i.e., 10-30 times, or the PSNR value of the reconstructed image is ≥28dB.

7. The method for generating a color hologram based on an approximate quadratic phase mask according to claim 4, wherein: The frequency domain scaling and spatial translation include: the red channel phase scaling factor is λ b / λ r , the green channel phase scaling factor is λ b / λ g ; lateral offset Δx=k(λ b -λ r ), where k is the ratio of pixel pitch to wavelength.

8. A color hologram generation system based on an approximate quadratic phase mask, characterized in that: include: An approximate quadratic phase construction module, used to construct an approximate quadratic phase; An approximate quadratic phase mask extraction module is used to extract an optimized approximate quadratic phase mask from the spatial domain or the frequency domain according to the approximate quadratic phase; The color hologram acquisition module is used to decompose the target image into RGB three-channel amplitudes, and combine the optimized approximate quadratic phase mask with the three-channel amplitudes respectively to obtain a color hologram.

Images