Non-iterative Fresnel pure phase hologram generation and multiplexing method, device and medium

Abstract

The present invention discloses a non-iterative Fresnel pure phase hologram generation and multiplexing method, device and medium, comprising the following steps: first, generating FS-OFRAPs of different planes using an iterative Fresnel method, then non-iteratively generating holograms corresponding to different layers in combination with a 3D object layering strategy, obtaining a final phase hologram by superposition or multiplexing, and finally reconstructing the multiplexed hologram to obtain a three-dimensional target object. The present invention can directly realize the rapid generation of pure phase holograms for three-dimensional holographic display. This method breaks through the limitations of the original OFRAP method on the size and position of the target amplitude fixed support in the spatial domain, and can realize the rapid generation of large-scale 3D CGH in a non-iterative manner. Numerical experiments and optical experiments verify the superiority of the 3D-FS-OFRAP method of the present invention.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional holography, and in particular to a method for generating and multiplexing a non-iterative Fresnel pure phase hologram. Background Art

[0002] Holography can record the three-dimensional (3D) information of light waves on a two-dimensional (2D) hologram and reproduce the three-dimensional information from the hologram. Compared with optical holographic display, computer-generated holographic three-dimensional projection display has significant advantages such as simple production, high efficiency, low cost and convenient storage and transmission of information. It can not only display static physical objects, but also virtual dynamic objects. The main challenge of three-dimensional computer holography is the huge computational cost required to simulate Fresnel diffraction for each object point in continuous three-dimensional space. At the same time, in many real-time dynamic holographic display systems, high-speed computing is required to generate computer generated holograms (CGH). Computational efficiency has become a bottleneck restricting the development of three-dimensional computer holography.

[0003] Currently, the commonly used three-dimensional CGH methods are: point cloud method, polygon method and layered method. In the point cloud method, 3D objects can be represented as a collection of independently acting self-luminous point light sources. Its main disadvantage is high computational complexity. Since the representation of solid shapes requires extremely fine sampling, the computational time may be unacceptable in some cases. The polygonal method uses planar primitive light sources to represent the surface of the object. Since the polygon plane is tilted relative to the hologram plane, the formula describing the propagation of the wave field between parallel planes is not directly applicable to the synthesis of CGH. A rotation transformation is required to associate the polygon plane with the plane parallel to the hologram, which increases the computational complexity. The layered method slices the 3D scene into layers according to different depth ranges, and then generates holograms for each layer. The final hologram is the sum of the contributions of the holograms of all layers, achieving a larger depth range.

[0004] The classic method for generating 3D phase holograms is the iterative Fresnel transform algorithm (IFrTA). This method is based on the Gerberch-Saxton (GS) algorithm proposed by Gerberch and Saxton. After replacing the Fourier transform in the GS algorithm with the Fresnel transform (Fresnel Transform, FrT), it is the so-called iterative Fresnel transform algorithm (IFrTA). However, IFrTA can only generate holograms for a single object. When this method is applied to three-dimensional holographic displays, it is necessary to iteratively generate holograms for each layer separately, which is very time-consuming. In 2021, Alejandro Velez Zea et al. proposed an optimized Fresnel random phase (Optimization Fresnel Random Phase, OFRAP) method for generating Fresnel pure phase holograms. Fresnel holograms have the advantage of allowing the selection of the reconstruction plane and can eliminate the need for lenses in the reconstruction system, thereby reducing its cost and complexity. OFRAP has the same support as the target window, but the size of the target support set and the parameters of the optical system cannot be changed. Otherwise, a new OFRAP needs to be generated. Summary of the Invention

[0005] The present invention proposes a non-iterative Fresnel pure phase hologram generation and multiplexing method, which can solve at least one of the above technical problems.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A non-iterative Fresnel pure phase hologram generation and multiplexing method comprises the following steps:

[0008] Firstly, the iterative Fresnel method is used to generate FS-OFRAPs in different planes. Then, the 3D object layering strategy is combined to non-iteratively generate holograms corresponding to different layers. The final phase hologram is obtained by superposition or multiplexing. Finally, the multiplexed hologram is reconstructed to obtain the three-dimensional target object.

[0009] Furthermore, the iterative Fresnel method is used to generate FS-OFRAPs in different planes, including first multiplying the full-support unit amplitude and the random phase mask and then performing an inverse Fresnel transform, and then following the iterative Fresnel algorithm to perform multiple iterations in a loop to generate FS-OFRAP.

[0010] Furthermore, the generation of FS-OFRAPs in different planes using the iterative Fresnel method also includes generating multiple FS-OFRAPs corresponding to each layer, that is, using the same input, passing through FS-OFRAP generation modules with different distance parameters z, and finally generating the FS-OFRAP corresponding to each layer.

[0011] Furthermore, the non-iterative generation of holograms corresponding to different layers in combination with the 3D object layering strategy specifically includes:

[0012] The three-dimensional object is layered at equal intervals along the depth direction, and the two-dimensional cross-sectional image after layering is synthesized with the complex amplitude of the FS-OFRAP at the corresponding distance. The inverse Fresnel transform is performed to generate the pure phase hologram of each layer non-iteratively.

[0013] Furthermore, the final phase hologram is obtained by superposition or multiplexing, including converting the phase holograms generated by each layer into complex amplitudes for superposition or multiplexing to generate the phase hologram of the 3D target.

[0014] Furthermore, the multiplexing methods include overlay multiplexing and space division multiplexing.

[0015] Furthermore, the superposition multiplexing method is to directly add the complex amplitudes of the holograms to generate a multiplexed hologram; if there are N complex amplitudes of the holograms, the superposition multiplexing method formula is as follows:

[0016]

[0017] Among them, F j (x,y)=exp[iφ j (x,y)], represents the complex amplitude corresponding to the jth hologram, φ j (x, y) is the jth phase hologram, and the phase of the superimposed complex amplitude M(x, y) is finally extracted to obtain the multiplexed hologram.

[0018] Furthermore, space division multiplexing is to divide the space for multiplexing; first, the SLM is divided into N areas, and each area is placed with the complex amplitude of each layer of the hologram, and the placement position corresponds to the position of the selected placement area in the original hologram complex amplitude; each sub-sample is placed at their respective relative original positions.

[0019] On the other hand, the present invention discloses a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the above method.

[0020] On the other hand, the present invention further discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above method.

[0021] It can be seen from the above technical solution that since traditional three-dimensional holographic display mainly generates holograms through iteration, the generation time is long and the reconstruction quality is poor. The present invention combines the full support optimized Fresnel random phase (FS-OFRAP) and the three-dimensional object layering idea to propose a three-dimensional non-iterative phase hologram full support optimized Fresnel random phase method (Three-dimensional full support optimization Fresnel random phase, 3D-FS-OFRAP). First, the iterative Fresnel method is used to generate FS-OFRAPs of different planes, and then the 3D object layering strategy is combined to non-iteratively generate holograms corresponding to different layers, and finally the final phase hologram is obtained by superposition or multiplexing. The effectiveness of the 3D-FS-OFRAP method of the present invention is verified by numerical experiments and optical experiments.

[0022] This paper proposes a three-dimensional fully supported optimized Fresnel random phase (3D-FS-OFRAP) method that can directly and rapidly generate pure phase holograms for 3D holographic displays. This method overcomes the limitations of the original OFRAP method in the size and position of the target amplitude fixed support in the spatial domain and enables the rapid generation of large-scale 3D CGHs in a non-iterative manner. Numerical and optical experiments validate the superiority of the 3D-FS-OFRAP method. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of three-dimensional hologram generation;

[0024] Figure 2 Schematic diagram of the Fresnel diffraction zone and the Fraunhofer diffraction zone

[0025] Figure 3 is a flow chart for generating phase holograms using OFRAP;

[0026] Figure 4 This is a flowchart of generating phase holograms using FS-OFRAP FS-WA (Full support window amplitude);

[0027] Figure 5 It is a schematic diagram of the phenomenon of “near is small and far is big”;

[0028] Figure 6 is a schematic diagram of the FS-OFRAP generation module;

[0029] Figure 7 This is the flow chart of FS-OFRAP generation with different distance parameters;

[0030] Figure 8It is the hologram generation module of each layer; AH (Amplitude hologram), PH (Phase hologram);

[0031] Figure 9 (a) is a schematic diagram of superposition multiplexing in this embodiment; (b) is a schematic diagram of space division multiplexing in this embodiment;

[0032] Figure 10 This is the overall flow chart of 3D-FS-OFRAP according to an embodiment of the present invention. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0034] like Figure 10 As shown, the non-iterative Fresnel pure phase hologram generation and multiplexing method described in this embodiment includes the following steps:

[0035] Firstly, the iterative Fresnel method is used to generate FS-OFRAPs in different planes. Then, the 3D object layering strategy is combined to non-iteratively generate holograms corresponding to different layers. The final phase hologram is obtained by superposition or multiplexing. Finally, the multiplexed hologram is reconstructed to obtain the three-dimensional target object.

[0036] The following are respectively described in combination with the existing technology:

[0037] 3D CGH

[0038] The holographic display process can be divided into two steps: wavefront recording and wavefront reconstruction. Wavefront recording and wavefront reconstruction are the core of holography. Figure 1 shown.

[0039] When the observation plane and the aperture plane are in the Fresnel diffraction region, that is, the distance z between the observation plane and the aperture plane satisfies At this time, Fresnel diffraction can be used to calculate the field distribution of the object light wave propagating in the Fresnel diffraction zone; when the distance z between the observation plane and the aperture plane satisfies This is the Fraunhofer diffraction region. Figure 2 The relationship between the Fresnel diffraction zone and the Fraunhofer diffraction zone is shown.

[0040] Fresnel diffraction:

[0041]

[0042] Where λ is the wavelength, k is the wave number, z is the distance between the object plane and the recording medium, and U0(x0,y0) is the object light wave. However, the calculation using formula (1) is cumbersome and time-consuming, so the present invention uses the Fresnel diffraction-double Fourier calculation method (D-FFT):

[0043]

[0044] in and are Fourier transform and inverse Fourier transform respectively.

[0045] OFRAP

[0046] To generate an OFRAP, a window is first created that corresponds to the support size of the target for which the phase hologram is desired. A random phase mask is multiplied by this window, and then an inverse Fresnel transform (IFrT) is performed. After each IFrT, the resulting amplitude is replaced by the target amplitude corresponding to each plane, i.e., the amplitude of the previously created target window. After each IFrT, the resulting amplitude is replaced by a uniform amplitude equal to the size of the SLM area, and the OFRAP is generated after several iterations.

[0047] The amplitude target whose phase hologram you wish to generate is multiplied by this OFRAP. IFrT is then applied to the target, and the resulting amplitude is set to a constant, generating a pure phase hologram of the target. After FrT, the desired target can be reconstructed. Figure 3 Flowchart for generating phase holograms using OFRAP.

[0048] This method offers the speed advantage of random phase hologram generation while achieving reconstruction quality close to that of the IFrTA algorithm. However, the initially created window corresponds to the support dimensions of the desired phase hologram target, determining the size and position of the generated hologram. Therefore, this method can only generate holograms of a specific size and position. Holograms of other sizes and positions require replacing the window and regenerating the hologram. This can be time-consuming in applications requiring the generation of multiple holograms of varying sizes or positions.

[0049] The following are the main contents of the present invention, namely FS-OFRAP;

[0050] To solve the problems of OFRAP in practical applications, the present invention uses the fully supported optimized Fresnel random phase method (FS-OFRAP). Unlike OFRAP, FS-OFRAP creates a fully supported unit amplitude with the same size as the SLM plane. Figure 4 Flowchart for generating phase holograms using FS-OFRAP.

[0051] In addition to sharing the advantages of OFRAP, FS-OFRAP requires only a single FS-OFRAP generation for applications requiring the generation of holograms of multiple targets of varying sizes or positions. This single FS-OFRAP can then be used to generate holograms of any target. FS-OFRAP is fully supported, enabling the generation of holograms of targets of arbitrary size and position, significantly reducing the time required to generate multiple holograms of varying sizes and positions, and offering exceptional flexibility.

[0052] 3D-FS-OFRAP

[0053] When the light source emits light outward, the light beam becomes wider and wider during the propagation process. Therefore, when receiving light on a certain plane, the farther the projection surface is, the greater the light received. Figure 5 This is a schematic diagram illustrating the aforementioned "near smaller, far larger" phenomenon. This phenomenon also applies to hologram reconstruction: projection surfaces closer to the hologram receive a smaller image than those farther away. However, the OFRAP method can only generate holograms for objects of fixed size and position, lacking flexibility for varying distances and supports. Therefore, the present invention utilizes the FS-OFRAP method, which supports objects of arbitrary size and position, meeting the required requirements.

[0054] The present invention combines the layering method with the FS-OFRAP method to propose a 3D-FS-OFRAP method. First, a window is created. This window is a fully supported unit amplitude, which supports generating holograms for targets of any size and position. A random phase mask is multiplied by this window, and then an inverse Fresnel transform is performed. After several iterations of the GS cycle, the FS-OFRAP is generated. The process is modularized, and the FS-OFRAP generation module is as follows: Figure 6 shown.

[0055] Secondly, since the distance between each layer and the hologram plane is different after the target 3D object is layered, multiple FS-OFRAPs corresponding to each layer should be generated. Using the same input, the FS-OFRAP generation modules with different distance parameters z are used to finally generate the FS-OFRAP corresponding to each layer. Figure 7 shown.

[0056] Next, the three-dimensional object is layered at equal intervals along the depth direction, and the two-dimensional cross-sectional images after layering are synthesized with the FS-OFRAP at the corresponding distance to generate complex amplitudes, and then the inverse Fresnel transform is performed to generate the pure phase hologram of each layer non-iteratively. The process is modularized, and the hologram generation modules of each layer are as follows: Figure 8 shown.

[0057] Next, the phase holograms generated by each layer are converted into complex amplitudes and superimposed or multiplexed to generate a phase hologram of the 3D object. Synthesizing multiple holograms to obtain a single 2D hologram is called hologram multiplexing. Multiplexing can be used to combine holograms of objects at different positions in 3D space to recreate an extended scene with depth. Therefore, the multiplexing method is based on the generation of layer-based 3D holograms, and the generated multiplexed hologram can be used to reconstruct the complete 3D object. Common multiplexing methods include superposition multiplexing and space division multiplexing.

[0058] The superposition multiplexing method is to directly add the complex amplitudes of the holograms to generate a multiplexed hologram. Suppose there are N complex amplitudes of the holograms, then the superposition multiplexing method formula is as follows:

[0059]

[0060] Among them, F j (x,y)=exp[iφ j (x,y)], represents the complex amplitude corresponding to the jth hologram, φ j (x, y) is the jth phase hologram, and the phase of the superimposed complex amplitude M(x, y) is finally extracted to obtain the multiplexed hologram.

[0061] Space division multiplexing is to divide the space for multiplexing. First, the SLM is divided into N areas, and each area is placed with the complex amplitude of each layer of hologram. The placement position corresponds to the position of the selected placement area in the original hologram complex amplitude. Each sub-sample is placed at its respective relative original position. Two multiplexing methods are as follows: Figure 9 shown.

[0062] Finally, the multiplexed hologram is reconstructed to obtain the three-dimensional target object. The overall flow chart of 3D-FS-OFRAP is as follows: Figure 10 As shown in Figure 2, the computational process for generating the final 3D target hologram is non-iterative. This method reduces the amount of computation while improving computational speed and efficiency, effectively ensuring reconstruction quality. The advantages of this method are that the reconstruction plane can be selected during Fresnel hologram generation and the need for lenses in the reconstruction system can be eliminated, thereby reducing hardware cost and complexity.

[0063] In another aspect, the present invention further discloses a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the steps of any of the above methods.

[0064] On the other hand, the present invention further discloses a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of any of the above methods.

[0065] In another embodiment provided by the present application, a computer program product including instructions is also provided, which, when executed on a computer, enables the computer to execute the steps of any one of the methods in the above embodiments.

[0066] It is understandable that the system provided by the embodiment of the present invention corresponds to the method provided by the embodiment of the present invention, and the explanation, examples and beneficial effects of the relevant contents can refer to the corresponding parts of the above method.

[0067] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0068] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0069] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A non-iterative Fresnel pure phase hologram generation and multiplexing method, characterized in that: The following steps are included: First, an iterative Fresnel method is used to generate FS-OFRAPs in different planes. Then, a 3D object layering strategy is combined to non-iteratively generate holograms corresponding to different layers. The final phase hologram is obtained by superposition or multiplexing. Finally, the multiplexed hologram is reconstructed to obtain the 3D target object. The method of generating FS-OFRAPs of different planes using the iterative Fresnel method includes: first, multiplying the fully supported unit amplitude by the random phase mask and then performing an inverse Fresnel transform; then, following the iterative Fresnel algorithm and performing multiple iterations to generate the FS-OFRAP; generating multiple FS-OFRAPs corresponding to each layer, that is, using the same input and passing through the FS-OFRAP generation modules with different distance parameters z, and finally generating the FS-OFRAP corresponding to each layer; The 3D object layering strategy is then combined with non-iterative generation of holograms corresponding to different layers. Specifically, the 3D object is layered at equal intervals along the depth direction, the layered 2D cross-sectional image is combined with the FS-OFRAP at the corresponding distance for complex amplitude synthesis, and an inverse Fresnel transform is performed to non-iteratively generate a pure phase hologram for each layer. The final phase hologram is obtained by superposition or multiplexing, including converting the phase holograms generated by each layer into complex amplitudes for superposition or multiplexing to generate the phase hologram of the 3D target; The multiplexing methods include overlay multiplexing and space division multiplexing.

2. The non-iterative Fresnel pure phase hologram generation and multiplexing method according to claim 1, characterized in that: The superposition multiplexing method is to directly add the complex amplitudes of the holograms to generate a multiplexed hologram. If there are N complex amplitudes of the holograms, the superposition multiplexing method formula is as follows: (2) in, , indicating the j The complex amplitude corresponding to the hologram is For the j phase holograms, and finally extract the superimposed complex amplitude The phase of the multiplexed hologram is obtained.

3. The non-iterative Fresnel pure phase hologram generation and multiplexing method according to claim 1, characterized in that: Space division multiplexing is to divide the space for multiplexing; first, the SLM is divided into N areas, and the complex amplitude of each layer of the hologram is placed in each area. The placement position corresponds to the position of the selected placement area in the original hologram complex amplitude; each sub-sample is placed in their respective relative original positions.

4. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 3.

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