Large size holographic 3D display system and method without aliasing images

Abstract

The present application relates to a kind of large-size holographic 3D display system and method without aliasing image, belong to holographic display technical field.The method includes: holographic display system is composed of a spatial light modulator and a short focus flat convex lens, by regulating and controlling the position of three planes, the display range of imaging plane is expanded, including flat convex lens plane, focal plane of flat convex lens, imaging plane;Hologram design method first provides an initial light field distribution as initial hologram, the amplitude of the light field is unit amplitude, phase is random phase, in computer, according to the simulation of the initial hologram in the back and forth propagation between holographic surface and the plurality of object surfaces of the object to be displayed based on single fast fourier transform fresnel diffraction algorithm, in each round of iteration, aliasing error of fresnel diffraction algorithm is avoided by zero padding and non-uniform sampling operation, after iteration is completed, the design method can generate hologram of reproducible non-aliasing holographic 3D reconstruction image.

Description

Technical Field

[0001] This invention belongs to the field of holographic display technology and relates to a large-size holographic 3D display system and method without aliasing. Background Technology

[0002] Holographic display technology is hailed as the ideal technology for achieving true 3D display. With the continuous development of spatial light modulators (SLMs), SLMs are widely used in holographic display systems. They are typically used to load pure phase holograms to modulate incident light, and SLM-based holographic display technology has great potential in color, dynamic, and 3D holographic displays. However, current SLMs cannot meet the needs of large-size holographic displays. Since the pixel size of existing SLMs is generally between 6μm and 15μm, assuming a light source wavelength of 532nm and an SLM pixel size of 8μm, the diffraction angle of the SLM is only 1.9°. Although the size of the diffracted image will be larger than the size of the SLM as the propagation distance increases, the actual increase in the size of the diffracted image is very small due to the small diffraction angle.

[0003] Current methods for achieving large-size holographic displays include: stitching together reconstructed images from multiple spatial light modulators to achieve large-size holographic displays; however, this method makes the holographic display system structure more complex and requires precise optical paths to achieve seamless stitching; and using divergent spherical light to illuminate the SLM to physically increase the diffraction angle of the SLM to achieve large-size holographic displays. However, this type of method has certain limitations on the light source requirements, requiring divergent spherical beams with small radii, and the fact that the incident light is a spherical wave will cause uneven intensity and phase of the reconstructed image.

[0004] Furthermore, hologram design typically relies on Fresnel diffraction algorithms based on a single Fast Fourier Transform (FFT), as this algorithm only requires one FFT to obtain the calculation results. However, this algorithm has stringent usage conditions; the amplitude and phase calculations of the results often fail to simultaneously satisfy the sampling theorem, leading to aliasing errors in the imaging results. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a large-size holographic 3D display system and method without aliasing. The proposed holographic display system, combined with a hologram design method matching the system structure, achieves a large-size holographic 3D display without aliasing.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A large-size holographic 3D display system without aliasing, which includes a spatial light modulator (SLM) and a short-focal-length plano-convex lens;

[0008] The light transmission dimension L1 of the plano-convex lens is greater than the light transmission dimension L0 of the SLM;

[0009] L0 = NΔx0, where N is the number of SLM pixels and Δx0 is the SLM pixel interval;

[0010] L1 = λz1N / L0, where λ is the wavelength of light and z1 is the distance between the SLM and the plano-convex lens.

[0011] L1 = NΔx1, f is the focal length of the plano-convex lens, Δx1 is the sampling interval of the plano-convex lens plane, Δx1 = λz1 / L0.

[0012] To achieve holographic 3D display, the positions of the plane where the plano-convex lens is located, the focal plane of the plano-convex lens, and the imaging plane are adjusted. Specifically, the 3D image is divided into several 2D images through an iterative algorithm, the complex amplitude distribution of each 2D image on the hologram plane is calculated, all complex amplitude distributions are superimposed, and finally the phase of the superimposed complex amplitude is taken as the final generated hologram.

[0013] The hologram plane is the plane on which the spatial light modulator is located, and the hologram is loaded onto the spatial light modulator.

[0014] Furthermore, the iterative algorithm includes a forward calculation process and a backward calculation process;

[0015] The forward calculation process is as follows: first, calculate the light field distribution of the front plane of the plano-convex lens based on the light field distribution of the hologram; then, calculate the light field distribution of the focal plane of the plano-convex lens based on the light field distribution of the rear plane of the plano-convex lens; and finally, calculate the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens.

[0016] The reverse calculation process is the opposite;

[0017] The initial number of samples for the hologram is N×N. The hologram is padded with zeros to M×M so that the size of the hologram in the calculation is L0=MΔx0=L1;

[0018] After the iteration is completed, the phase of the middle N×N points of the iteration output is taken as the final generated hologram.

[0019] Furthermore, in the calculation of the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens, the Fast Fourier Transform (FFT) in the Fresnel diffraction algorithm based on a single Fast Fourier Transform is replaced with Non-Uniform Fast Fourier Transform (NUFFT) to adjust the sampling interval of the imaging plane and use all sampling points for the area occupied by the image.

[0020] A method for large-size holographic 3D display without aliasing includes the following steps: placing a spatial light modulator (SLM) and a short-focal-length plano-convex lens side by side, and satisfying the following conditions;

[0021] The light transmission dimension L1 of the plano-convex lens is greater than the light transmission dimension L0 of the SLM;

[0022] L0 = NΔx0, where N is the number of SLM pixels and Δx0 is the SLM pixel interval;

[0023] L1 = λz1N / L0, where λ is the wavelength of light and z1 is the distance between the SLM and the plano-convex lens.

[0024] L1 = NΔx1, f is the focal length of the plano-convex lens, Δx1 is the sampling interval of the plano-convex lens plane, Δx1 = λz1 / L0.

[0025] To achieve holographic 3D display, the positions of the plane where the plano-convex lens is located, the focal plane of the plano-convex lens, and the imaging plane are adjusted. Specifically, the 3D image is divided into several 2D images through an iterative algorithm, the complex amplitude distribution of each 2D image on the hologram plane is calculated, all complex amplitude distributions are superimposed, and finally the phase of the superimposed complex amplitude is taken as the final generated hologram.

[0026] The hologram plane is the plane on which the spatial light modulator is located, and the hologram is loaded onto the spatial light modulator.

[0027] Furthermore, the iterative algorithm includes a forward calculation process and a backward calculation process;

[0028] The forward calculation process is as follows: first, calculate the light field distribution of the front plane of the plano-convex lens based on the light field distribution of the hologram; then, calculate the light field distribution of the focal plane of the plano-convex lens based on the light field distribution of the rear plane of the plano-convex lens; and finally, calculate the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens.

[0029] The reverse calculation process is the opposite;

[0030] The initial number of samples for the hologram is N×N. The hologram is padded with zeros to M×M so that the size of the hologram in the calculation is L0=MΔx0=L1;

[0031] After the iteration is completed, the phase of the middle N×N points of the iteration output is taken as the final generated hologram.

[0032] Furthermore, in the calculation of the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens, the Fast Fourier Transform (FFT) in the Fresnel diffraction algorithm based on a single Fast Fourier Transform is replaced with Non-Uniform Fast Fourier Transform (NUFFT) to adjust the sampling interval of the imaging plane and use all sampling points for the area occupied by the image.

[0033] The beneficial effects of this invention are as follows:

[0034] 1. Compared to traditional holographic display systems, large-size holographic 3D displays can be achieved by simply introducing a short-focal-length plano-convex lens and adjusting the positions of the lens plane, focal plane, and imaging plane.

[0035] 2. In the hologram design method, the traditional Fresnel diffraction algorithm based on single fast Fourier transform is improved by zero-padding and non-uniform sampling operations for different calculation steps. This avoids the sampling error and constant sampling interval problems in the traditional algorithm, eliminates the aliasing of the holographic reconstructed image, and improves the visual quality.

[0036] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0038] Figure 1 This is a structural diagram of a traditional holographic display system.

[0039] Figure 2 This is a system structure diagram of the present invention;

[0040] Figure 3 This is a schematic diagram illustrating the use of NUFFT in the method of the present invention;

[0041] Figure 4 shows the simulation reconstruction results. Figure 4(a) is the reference image, Figure 4(b) is the reconstruction result of the hologram designed according to the conventional method using the system of the present invention, and Figure 4(c) is the reconstruction result of the hologram designed by the method of the present invention. Detailed Implementation

[0042] The following specific examples illustrate the implementation of the present invention. 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, and various details in this specification can 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 illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0043] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0044] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0045] Traditional holographic display systems rely on a single SLM for holographic image reconstruction, such as... Figure 1 As shown, due to the small diffraction angle of the SLM, the size of the reconstructed image is also small. The holographic display system of this invention consists of an SLM and a short-focal-length plano-convex lens, as shown... Figure 2 As shown, the incident light is an ideal plane wave. The reconstructed image is enlarged by controlling the distance between the SLM and the short-focal-length plano-convex lens, as well as the property of the plano-convex lens to focus and then diffuse the light. Specifically, large-size holographic 3D displays are achieved by adjusting the position of the plano-convex lens, the position of its focal plane, and the position of the imaging plane.

[0046] According to Fresnel diffraction theory, the light transmission dimension L0 of the SLM and the light transmission dimension L1 of the plano-convex lens satisfy the following:

[0047] L0L1=λz1N (1)

[0048] Where λ is the wavelength, z1 is the distance between the SLM and the plano-convex lens, and N is the number of pixels of the SLM.

[0049] The light transmission dimension L1 of the plano-convex lens and the dimension L of the focal plane of the plano-convex lens f satisfy:

[0050] L1L f =λfN (2)

[0051] Where f is the focal length of the plano-convex lens.

[0052] The size L of the focal plane of the plano-convex lens f The image plane size L2 satisfies:

[0053] L f L2=λ(zf)N (3)

[0054] Where zf is the distance between the focal plane of the plano-convex lens and the imaging plane.

[0055] According to equations (1)-(3), the larger L1 is, the larger L is. f The smaller the value, the larger the size of L2 becomes. Specifically,

[0056] L0 = NΔx0, where Δx0 is the pixel size of the SLM. At this time, it is possible to make L1 > L0. The focal length f of the plano-convex lens needs to be relatively small, satisfying... (Δx1 is the sampling interval on the plane of the plano-convex lens). Ultimately, large-size holographic 3D displays can be achieved.

[0057] In the hologram design method of this invention, a 3D object is considered as a combination of multiple 2D images at depth locations. The hologram of each 2D image is calculated and then superimposed to obtain the hologram of the 3D object. The hologram of each 2D image is obtained through an iterative algorithm, and one iteration can be divided into 6 steps:

[0058] S1: Given an initial random phase of the holographic plane Let the amplitude distribution be A0 = 1, then the light field distribution on the holographic plane is as follows: The hologram has a size of L0 and a sampling number of N×N. Zero-padding is applied to the hologram to make its size equal to the light-passing size L1 of the plano-convex lens plane, thus improving computational accuracy. The light field distribution U1 in front of the plano-convex lens is obtained using a Fresnel diffraction algorithm based on a single fast Fourier transform, i.e.:

[0059]

[0060]

[0061] S2: The light field distribution on the back plane of the plano-convex lens is as follows The light field distribution U of the focal plane of the plano-convex lens was obtained using a Fresnel diffraction algorithm based on fast single Fourier transform. f .

[0062] S3: The light field distribution U2 of the imaging plane is obtained by the Fresnel diffraction algorithm based on a single non-uniform fast Fourier transform. The amplitude distribution of U2 is replaced with the amplitude of the target image to obtain U'2. The Fresnel diffraction algorithm based on a single non-uniform fast Fourier transform replaces the FFT in equation (4) with the non-uniform fast Fourier transform (NUFFT) to perform non-uniform sampling in the spatial frequency domain. The NUFFT algorithm is mainly improved to address the weakness of the traditional FFT algorithm, which can only process data distributed on a uniform grid. It describes the fast Fourier transform relationship between data distributed on uniform grid nodes and data distributed on non-uniform grid nodes, effectively solving the problem that when calculating data distributed on a non-uniform grid, only discrete Fourier transform can be used for long-term calculation. NUFFT is used to control the calculation area of ​​the imaging plane, such as Figure 3 As shown, the size of the light field varies for the reconstructed image plane at different depths; the farther away from the hologram, the larger the size and the larger the sampling interval. However, the Fresnel diffraction algorithm based on Fast Single Fourier Transform can only calculate the light field within the entire plane, meaning all sampling points are used for the entire plane. As the distance increases, the number of sampling points in the actual area occupied by the reconstructed image further back decreases, with the remaining sampling points used for the background region, which is detrimental to accurate calculation. In contrast, the Fresnel diffraction algorithm based on Single Non-Uniform Fast Fourier Transform can readjust the sampling interval to make the actual calculation size consistent with the reconstructed image size, using all sampling points for the area occupied by the image, thus improving calculation accuracy.

[0063] S4: Perform reverse propagation and obtain the light field distribution U' of the focal plane of the plano-convex lens using a Fresnel diffraction algorithm based on a single non-uniform fast Fourier transform. f .

[0064] S5: Obtain the light field distribution U' on the back plane of the plano-convex lens using a Fresnel diffraction algorithm based on a single fast Fourier transform. 1' .

[0065] S6: Obtain the light field distribution U'0 in the SLM plane using a Fresnel diffraction algorithm based on a single fast Fourier transform. Set the amplitude of U'0 to 1 to form a new U0 and begin the next iteration.

[0066] When the root mean square error between the amplitude of U2 and the amplitude of the target image reaches a given accuracy or the maximum number of iterations, the phase of the N×N points in the middle of U0 at this point is taken as the hologram. In this hologram design method, zero-padding and non-uniform sampling operations can avoid aliasing in the final holographic reconstructed image.

[0067] Example 1:

[0068] In the actual experiment, a pure phase SLM was used, with a pixel size of 8μm, and the hologram had 11024×1024 pixels. Therefore, the size of the hologram was 8.192mm×8.192mm. The laser wavelength was 532nm. Figure 1 The structure of a single SLM has a propagation range of 400mm, and according to equation (1), the size of the imaging plane is only 26.6mm × 26.6mm. According to the present invention... Figure 2 The structure of the SLM is the same as above. The distance between the SLM and the plano-convex lens is 174.917 mm. The focal length of the plano-convex lens is 50 mm. Similarly, it propagates 400 mm behind the plano-convex lens. According to formulas (1) to (3), the size of the imaging plane is 81.424 mm × 81.424 mm.

[0069] Example 2:

[0070] According to the present invention Figure 2 The structure and parameters are the same as in Example 1. In the design process of the hologram, the reference image is Figure 4(a). Without zero padding and non-uniform sampling, that is, the number of samples is always 1024×1024. The simulation reconstruction result is shown in Figure 4(b). The reconstructed image has aliasing interference, which affects the visual perception. In the hologram design method proposed in this invention, 1024×1024 is zero-padded to 1454×1454, and all samples are used for the area occupied by the image. The simulation reconstruction result is shown in Figure 4(c), which eliminates aliasing.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A large-size holographic 3D display system without aliasing, characterized in that: The system includes a spatial light modulator (SLM) and a short-focal-length plano-convex lens; The light transmission size of the plano-convex lens Larger than the light transmission size of an SLM L 0; , For SLM pixel count, For SLM pixel spacing; N / The wavelength of light The distance between the SLM and the plano-convex lens. ; , f The focal length of the plano-convex lens is... The sampling interval is the plane of the plano-convex lens. , ; To achieve holographic 3D display, the positions of the plane where the plano-convex lens is located, the focal plane of the plano-convex lens, and the imaging plane are adjusted. Specifically, the 3D image is divided into several 2D images through an iterative algorithm, the complex amplitude distribution of each 2D image on the hologram plane is calculated, all complex amplitude distributions are superimposed, and finally the phase of the superimposed complex amplitude is taken as the final generated hologram. In this context, the hologram plane is the plane where the spatial light modulator is located, and the hologram is loaded onto the spatial light modulator. The iterative algorithm includes a forward calculation process and a backward calculation process; The forward calculation process is as follows: first, calculate the light field distribution of the front plane of the plano-convex lens based on the light field distribution of the hologram; then, calculate the light field distribution of the focal plane of the plano-convex lens based on the light field distribution of the rear plane of the plano-convex lens; and finally, calculate the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens. The reverse calculation process involves calculating the light field distribution of the plano-convex lens focal plane based on the light field distribution of the imaging plane, then calculating the light field distribution of the plano-convex lens rear plane based on the light field distribution of the plano-convex lens focal plane, and finally calculating the light field distribution of the hologram based on the light field distribution of the plano-convex lens front plane. The initial number of samples for the hologram is N × N Zero-padding the hologram to... M × M This makes the size of the hologram in the calculation... ; After the iteration is complete, take the middle value of the iteration output. N × N The phase of each point is the final generated hologram.

2. The large-size holographic 3D display system without aliasing as described in claim 1, characterized in that: In the calculation of the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens, the Fast Fourier Transform (FFT) in the Fresnel diffraction algorithm based on a single Fast Fourier Transform is replaced with Non-Uniform Fast Fourier Transform (NUFFT) to adjust the sampling interval of the imaging plane and use all sampling points for the area occupied by the image.

3. A method for large-size holographic 3D display without aliasing, characterized in that: The method includes the following steps: placing a spatial light modulator (SLM) and a short-focal-length plano-convex lens side by side, and satisfying the following conditions; The light transmission size of the plano-convex lens Larger than the light transmission size of an SLM L 0; , For SLM pixel count, For SLM pixel spacing; N / The wavelength of light The distance between the SLM and the plano-convex lens. ; , f The focal length of the plano-convex lens is... The sampling interval is the plane of the plano-convex lens. , ; To achieve holographic 3D display, the positions of the plane where the plano-convex lens is located, the focal plane of the plano-convex lens, and the imaging plane are adjusted. Specifically, the 3D image is divided into several 2D images through an iterative algorithm, the complex amplitude distribution of each 2D image on the hologram plane is calculated, all complex amplitude distributions are superimposed, and finally the phase of the superimposed complex amplitude is taken as the final generated hologram. In this context, the hologram plane is the plane where the spatial light modulator is located, and the hologram is loaded onto the spatial light modulator. The iterative algorithm includes a forward calculation process and a backward calculation process; The forward calculation process is as follows: first, calculate the light field distribution of the front plane of the plano-convex lens based on the light field distribution of the hologram; then, calculate the light field distribution of the focal plane of the plano-convex lens based on the light field distribution of the rear plane of the plano-convex lens; and finally, calculate the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens. The reverse calculation process is the opposite; The initial number of samples for the hologram is N × N Zero-padding the hologram to... M × M This makes the size of the hologram in the calculation... ; After the iteration is complete, take the middle value of the iteration output. N × N The phase of each point is the final generated hologram.

4. The method for large-size holographic 3D display without aliasing as described in claim 3, characterized in that: In the calculation of the light field distribution of the imaging plane based on the light field distribution of the focal plane of the plano-convex lens, the Fast Fourier Transform (FFT) in the Fresnel diffraction algorithm based on a single Fast Fourier Transform is replaced with Non-Uniform Fast Fourier Transform (NUFFT) to adjust the sampling interval of the imaging plane and use all sampling points for the area occupied by the image.

Images