A method for large depth-of-field holographic 3D display based on digital cone lenses

Abstract

This invention proposes a large depth-of-field holographic 3D display method based on a digital cone lens. The method includes the following steps: First, based on depth information, the 3D object to be recorded is segmented into different depth planes, and the wavefront information of each depth plane is extracted. Then, an improved 3D Fourier algorithm is used to obtain the phase distribution of the 3D object on the holographic plane, denoted as Φ. I The second step is to encode the optical cone lens into a digital cone lens using phase encoding, and denote the phase distribution of the digital cone lens as Φ. II The third step involves co-encoding the digital cone lens with the hologram of the 3D object, and then coherently superimposing the phase distribution Φ. I and Φ II The final large depth-of-field hologram is obtained. In the fourth step, the final large depth-of-field hologram is loaded onto the spatial light modulator, and the spatial light modulator is illuminated with a light source. Based on the 3D Fourier algorithm and the depth-of-focus characteristics of the cone lens, the large depth-of-field hologram of the 3D object is reconstructed.

Description

Technical Field

[0001] This invention relates to holographic 3D display technology, and more specifically, to a large depth-of-field holographic 3D display method based on a digital cone lens. Background Technology

[0002] With the rapid development of science and technology and the increasing demand for 3D displays, holographic 3D display technology has become a cutting-edge hot topic in the field of display technology, with broad application potential covering fields such as cultural entertainment, education and training, medical diagnosis, and industrial manufacturing. Unlike traditional binocular parallax or light field 3D display technologies, holographic 3D displays can completely record and reconstruct the wavefront information of objects, achieving true 3D reproduction with continuous parallax and full focusing characteristics, providing viewers with a more natural and comfortable stereoscopic visual experience. Existing holographic 3D display technologies typically rely on precise reconstruction depth control, meaning that imaging is limited to the focal plane, and image quality degrades rapidly outside the focal plane. However, the limited depth range hinders the further application of holographic 3D display technology. To address this issue, researchers have introduced special optical elements to adjust the reconstruction depth. However, the introduction of these special optical elements increases system complexity, limiting its further development. Therefore, achieving a large depth range holographic 3D display in a lightweight system remains an urgent challenge. Summary of the Invention

[0003] To achieve extended depth of field in holographic 3D displays, this invention proposes a method for large depth-of-field holographic 3D displays based on digital cone lenses. (See attached diagram) Figure 1 As shown, the method includes the following steps: First, based on the depth information, the 3D object to be recorded is segmented into different depth planes, and the wavefront information of each depth plane is extracted. Then, an improved 3D Fourier algorithm is used to obtain the phase distribution of the 3D object on the holographic plane, denoted as Φ. I The second step is to encode the optical cone lens into a digital cone lens using phase encoding, and denote the phase distribution of the digital cone lens as Φ. II The third step involves co-encoding the digital cone lens with the hologram of the 3D object, and then coherently superimposing the phase distribution Φ. I and Φ II The final large depth-of-field hologram is obtained. In the fourth step, the final large depth-of-field hologram is loaded onto the spatial light modulator, and the spatial light modulator is illuminated with a light source. Based on the 3D Fourier algorithm and the depth-of-focus characteristics of the cone lens, the large depth-of-field hologram of the 3D object is reconstructed.

[0004] In step one, before generating the hologram, the 3D object being recorded is first layered. Then, the 3D Fourier algorithm is used to calculate the hologram of the 3D object. The main process is as follows: First, based on the depth information of each layer, a suitable transform order p is selected, and a random initial phase distribution is assigned to obtain the initial complex amplitude distribution C on the target plane. obj-0 (x, y;z p Based on the fractional Fourier transform, the complex amplitude distribution C on the holographic plane is obtained. holo (u, v; z p ), represented as:

[0005] (1)

[0006] Where FRFT{·} denotes the fractional Fourier transform. This is achieved by analyzing the complex amplitude distribution C on the holographic plane. holo (u,v; z p By applying phase constraints, the phase distribution Φ on the holographic plane is obtained. holo , is represented as:

[0007] (2)

[0008] Among them, Cons Φ The [·] symbol represents a phase constraint, and its main operation is to extract phase information from the complex amplitude distribution. At this point, the obtained phase distribution is not yet optimized, making it difficult to achieve high reconstruction quality. Therefore, the fractional-order inverse Fourier transform is used to calculate the complex amplitude distribution C of each layer on the object plane. obj (x, y; z p ), represented as:

[0009] (3)

[0010] Where IFRFT{·} denotes the fractional-order inverse Fourier transform. Subsequently, the complex amplitude distribution C on the object plane... obj (x,y; z p By applying amplitude constraints, the optimized complex amplitude distribution C can be obtained. obj-c (x, y; z p ):

[0011] (4)

[0012] Where Cons A [·] indicates amplitude constraint, which means replacing the amplitude information with the initial amplitude distribution.

[0013] In step two, a cone lens is introduced and its parameters are designed. It is then encoded into a digital cone lens using phase encoding. The structure of the cone lens is shown in the attached figure. Figure 2 As shown, it consists of a cylinder and a cone, which together produce an approximately non-diffractive Bessel beam. Unlike Gaussian beams, which gradually diverge with increasing propagation distance, Bessel beams exhibit non-diffractive properties, maintaining their intensity distribution over a relatively long depth range. Therefore, the cone lens keeps the beam focused throughout its focal depth. The focal depth of the cone lens is determined by its incident radius R, refractive index n, and vertex angle α. By selecting appropriate parameters such as the focal depth and radius of the cone lens and performing phase encoding, its conversion into a digital cone lens is achieved. The phase distribution of the digital cone lens is expressed as:

[0014] (5)

[0015] Where, d m Representing radial coordinates, f0 and z DOF These represent the focal length and depth of focus of the digital conical lens, respectively. Compared to traditional optical conical lenses, the phase encoding method of digital conical lenses allows for flexible adjustment of the phase distribution, thereby improving system flexibility and reducing experimental costs.

[0016] Finally, the phase distribution Φ of the digital cone lens II Phase distribution Φ of the holographic surface of the 3D object I The images are then superimposed to generate the final large depth-of-field hologram. Because this hologram carries the phase distribution of a digital cone lens, the light beam remains focused within a certain depth range. By loading this hologram onto a spatial light modulator, large depth-of-field holographic 3D reconstruction can be achieved. Attached Figure Description

[0017] Appendix Figure 1 This is a flowchart illustrating a large depth-of-field holographic 3D display method based on a digital cone lens according to the present invention.

[0018] Appendix Figure 2 This is a schematic diagram of the structure of the cone lens of the present invention.

[0019] Appendix Figure 3 This is the result of the large depth-of-field 3D reconstruction of the present invention. Among them, Figure 3 (a)-(c) show the reconstruction effect of the "butterfly" focus. Figure 3 (d)-(f) show the reconstruction effect of the "flower" focus.

[0020] It should be understood that the above figures are only schematic and are not drawn to scale. Detailed Implementation

[0021] The following detailed description of an embodiment of the large depth-of-field holographic 3D display method based on a digital cone lens proposed in this invention further illustrates the invention. It is necessary to point out that the following embodiments are only used to further illustrate the invention and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to the invention by those skilled in the art based on the above description still fall within the scope of protection of this invention.

[0022] One embodiment of the present invention is as follows: To verify the feasibility of the proposed method, a 532 nm wavelength laser was used as the reconstruction light source. A reflective pure phase spatial light modulator was used to load the hologram. The pixel pitch and resolution of the spatial light modulator were 6.4 µm and 1920 × 1080, respectively, with a phase modulation capability of 2π and a refresh rate of 60 Hz. A 3D object composed of a "butterfly" and a "flower" was selected as the recorded object, both with a resolution of 1000 × 1000. The transformation order p of the "butterfly" and the "flower" were set to 0.9 and 1.0, respectively. The digital cone lens had a focal length of 40 cm, a depth of focal length of 20 cm, and R = 0.1. The calculated hologram was then loaded into the spatial light modulator for optical reconstruction experiments, and reconstructed images were obtained at different depth planes. (See attached image) Figure 3 As shown in (a)-(c), the "butterfly" remains clear within a depth range of 23 cm to 25 cm, while the "flower" is blurred. Conversely, as shown in the attached image... Figure 3 As shown in (d)-(f), within a depth range of 29 cm to 31 cm, the "flower" is clearly focused, while the "butterfly" becomes blurred. The experimental results verify the effectiveness of the large depth-of-field holographic 3D display method based on a digital cone lens of the present invention.

Claims

1. A method for large depth-of-field holographic 3D display based on a digital cone lens, characterized in that, The method includes the following steps: First, based on depth information, the 3D object to be recorded is segmented into different depth planes, and the wavefront information of each depth plane is extracted. Then, an improved 3D Fourier algorithm is used to obtain the phase distribution of the 3D object on the holographic plane, denoted as Φ. I The second step is to encode the optical cone lens into a digital cone lens using phase encoding, and denote the phase distribution of the digital cone lens as Φ. II The third step involves co-encoding the digital cone lens with the hologram of the 3D object, and then coherently superimposing the phase distribution Φ. I and Φ II The final large depth-of-field hologram is obtained; the fourth step is to load the final large depth-of-field hologram onto the spatial light modulator, illuminate the spatial light modulator with a light source, and reconstruct the large depth-of-field hologram of the 3D object based on the 3D Fourier algorithm and the focal depth characteristics of the cone lens.

2. The method for large depth-of-field holographic 3D display based on a digital cone lens according to claim 1, characterized in that, Before generating the hologram, the 3D object being recorded is first layered. Then, the 3D Fourier algorithm is used to calculate the hologram of the 3D object. The main process is as follows: First, based on the depth information of each layer, an appropriate transform order p is selected, and a random initial phase distribution is assigned to obtain the initial complex amplitude distribution C on the target plane. obj-0 (x, y; z p Based on the fractional Fourier transform, the complex amplitude distribution C on the holographic plane is obtained. holo (u, v; z p ), represented as: Where FRFT{·} denotes the fractional Fourier transform, which is obtained by transforming the complex amplitude distribution C on the holographic plane. holo (u, v;z p By applying phase constraints, the phase distribution Φ on the holographic plane is obtained. holo , is represented as: Among them, Cons Φ [·] denotes phase constraint, and its main operation is to extract phase information from the complex amplitude distribution. At this point, the obtained phase distribution is not yet optimized, making it difficult to achieve high reconstruction quality. Therefore, the fractional-order inverse Fourier transform is used to calculate the complex amplitude distribution C of each layer on the object plane. obj (x, y; z p ), represented as: Where IFRFT{·} denotes the fractional-order inverse Fourier transform, and subsequently, the complex amplitude distribution C on the object plane... obj (x, y;z p By applying amplitude constraints, the optimized complex amplitude distribution C is obtained. obj-c (x, y; z p ): Where Cons A [·] indicates amplitude constraint, which means replacing the amplitude information with the initial amplitude distribution.

3. The method for large depth-of-field holographic 3D display based on a digital cone lens according to claim 1, characterized in that, A conical lens is introduced and its parameters are designed. It is then encoded into a digital conical lens using phase encoding. The conical lens consists of a cylinder and a cone, which together produce an approximately non-diffractive Bessel beam. Unlike a Gaussian beam that gradually diverges with increasing propagation distance, a Bessel beam exhibits non-diffraction characteristics and can maintain its intensity distribution over a relatively long depth range. Therefore, the conical lens keeps the beam focused throughout its focal depth. The focal depth of the conical lens is determined by the incident radius R, refractive index n, and vertex angle α. By selecting appropriate parameters such as the focal depth and radius of the conical lens and performing phase encoding, its conversion into a digital conical lens is achieved. The phase distribution of the digital conical lens is expressed as: Where, d m Representing radial coordinates, f0 and z DOF These represent the focal length and depth of focus of the digital cone lens, respectively.

4. The method for large depth-of-field holographic 3D display based on a digital cone lens according to claim 1, characterized in that, The phase distribution Φ of the digital cone lens II Phase distribution Φ of the holographic surface of the 3D object I The images are superimposed to generate a final large depth-of-field hologram. Because the hologram carries the phase distribution of a digital cone lens, the light beam remains focused within a certain depth range. By loading the hologram onto a spatial light modulator, large depth-of-field holographic 3D reconstruction is achieved.

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