A Color Metasurface Holographic 3D Display Method Based on Fresnel Near-Field Diffraction Algorithm

Abstract

This invention proposes a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm, comprising the following four steps: First, the 3D object is discretized into a set of independent points with depth information. A sub-hologram of each point on the holographic surface is calculated according to Fresnel near-field diffraction conditions to eliminate magnification chromatic aberration in the reconstructed image. Second, the sub-holograms of all points of the 3D object are coherently superimposed to obtain the complex amplitude information of the holographic surface. Third, the phase is extracted from the complex amplitude information in step two to obtain the final phase hologram. The obtained phase hologram information is then encoded using a metasurface to obtain the final metasurface hologram. Fourth, the obtained metasurface hologram is processed to prepare a metasurface structure. The unit cells of the metasurface structure are set to subwavelength dimensions, and axial chromatic aberration is eliminated under Fresnel near-field diffraction. When the metasurface structure is irradiated by a laser, a color metasurface holographic 3D image without chromatic aberration is reconstructed.

Description

I. Technical Field

[0001] This invention relates to holographic display technology, and more specifically, to a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm. II. Background Technology

[0002] Metasurface structures, composed of nanoarrays of subwavelength units, offer more flexible control over light waves, bringing new opportunities for the development of holography. However, the reconstruction distance of metasurface holographic 3D displays depends on the wavelength of the light source. Reconstructed images at different wavelengths have different sizes and positions, resulting in axial and magnification chromatic aberration, affecting reconstruction quality and limiting the development of color metasurface holographic 3D displays. To eliminate chromatic aberration in color metasurface holography, some researchers have reduced its impact on the reconstructed image by adjusting the incident angle of the optical path. While this method can eliminate axial chromatic aberration to some extent, it requires high precision in optical path alignment. Some researchers have adjusted the reconstructed object size separately by encoding holograms of three colors, allowing the reconstructed images of red, green, and blue to overlap at the same position, thus eliminating magnification chromatic aberration. However, this method requires three metasurface holograms to reconstruct the color hologram. Some researchers have used polarization-sensitive metasurface structures, utilizing the polarization selectivity of the metasurface structure to achieve separate reconstruction of red, green, and blue colors; however, achieving color overlap remains difficult. In addition, some researchers have proposed wavelength-sensitive composite metasurface structures. When different colors of light illuminate the metasurface structure, the red, green, and blue units within the structure can independently modulate the holograms of red, green, and blue colors, thereby achieving color difference compensation. However, this method places high demands on the selection of metasurface materials. Currently, how to achieve color difference-free color metasurface holographic 3D displays remains an urgent problem to be solved. III. Summary of the Invention

[0003] This invention proposes a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm. (See attached diagram) Figure 1As shown, the method includes the following four steps. First, the 3D object is discretized into a set of independent points with depth information. A sub-hologram of each point on the holographic surface is calculated based on Fresnel near-field diffraction conditions to eliminate magnification chromatic aberration in the reconstructed image. Second, the sub-holograms of all points of the 3D object are coherently superimposed to obtain the complex amplitude information of the holographic surface. Third, the phase is extracted from the complex amplitude information in step two to obtain the final phase hologram. The obtained phase hologram information is then encoded using a metasurface to obtain the final metasurface hologram. Fourth, the obtained metasurface hologram is processed to prepare a metasurface structure. The unit cells of the metasurface structure are set to subwavelength dimensions, and axial chromatic aberration is eliminated under Fresnel near-field diffraction. When the metasurface structure is irradiated with a laser, a colorless metasurface holographic 3D image is reconstructed.

[0004] In step one, the 3D object is first discretized into a set of independent object points with depth information. Each object point is treated as an independent point light source, and the complex amplitude distribution of each object point to the holographic surface is calculated, thereby generating a sub-hologram. The complex amplitude of any object point m on the holographic surface is... The distribution is as follows:

[0005]

[0006] in H(k) is the complex amplitude distribution of point m on the object plane. x ,k y ;z) is the spatial frequency transfer function, and z represents the diffraction distance. and These are the Fourier transform and the inverse Fourier transform, k x and k y These are the spatial frequencies in the x and y directions, respectively.

[0007] H(k) x ,k y The inverse Fourier transform of (x, y, z) is set as the spatial impulse response function h(x, y, z) in the Fourier domain, expressed as follows:

[0008]

[0009] Where k0 is the wave vector of the recorded light, and λ is the wavelength of the recorded light, when the coordinates of the object point in space are (h, w; 0), the complex amplitude distribution of any object point m on the holographic surface is expressed as:

[0010]

[0011] In the holographic reconstruction process, a plane wave is used as the reconstruction light to illuminate the hologram, and the complex amplitude distribution of the reconstruction light is... for:

[0012]

[0013] Where k r This is the wave vector of the reconstructed light. When the wavelength of the reconstructed light is the same as that of the recording light, the wave vectors of the reconstructed and recording light are also the same, i.e., k. r =k0. At this point, when the sub-hologram of any object point m is illuminated by the reconstructed light, the complex amplitude distribution of the reconstructed image... for:

[0014]

[0015] Where z r This indicates the axial position of the reconstructed image, * indicates convolution, and ∝ is the proportionality sign. The part following the proportionality sign determines the position, depth, and shape of the reconstructed image. Based on Fresnel near-field diffraction analysis, this part is represented as:

[0016]

[0017] Let the above formula and The coefficient is 0, leaving only the linear term. This occurs when the wavelengths of the reference light and the recording light are exactly the same, i.e., k. r When k = 0, the following conditions must be met:

[0018]

[0019] That is, when the reference light and the preset wavelength are the same, the axial position of the reconstructed image is the same as the diffraction distance of the object point. At this point, we obtain:

[0020]

[0021] Therefore, the reconstructed image corresponding to object point m is located at a distance z from the hologram. r At a distance where the position coordinates satisfy x = -h and y = -w. For 3D objects, when the reference light has the same wavelength as the preset light, the reconstruction distance of the holographic image is the same as the diffraction distance, and the reconstructed image has no magnification chromatic aberration.

[0022] When the reference light wavelength is different from the preset wavelength, then:

[0023]

[0024] At this point, the recurrence distance is:

[0025]

[0026] Where λ rThis is the wavelength of the reconstructed light. When the wavelengths of the reference light and the recording light are not the same, the axial displacement of the reconstructed image is determined by the wavelengths of the recording light and the reference light, and is proportional to z. In this case, the complex amplitude distribution of the reconstructed image at point m is:

[0027]

[0028] Combining formulas (11) and (12), we get:

[0029]

[0030] At this point, the coordinates of the reconstructed image corresponding to object point m are x = -h and y = -w. Therefore, when the wavelengths of the reference light and the recording light are different, the spatial position of the reconstructed image corresponding to the object point will not change, that is, no magnification chromatic aberration will be introduced.

[0031] In step two, the sub-holograms of all object points of the 3D object are coherently superimposed based on formulas (1)-(4) to obtain the complex amplitude information of the 3D object on the holographic surface.

[0032] In step three, the phase is extracted from the complex amplitude information obtained in step two to obtain the final phase hologram. The obtained phase hologram information is then encoded using a metasurface to obtain the final metasurface hologram. Metasurface encoding is based on a geometrically phase-controlled transmissive medium metasurface unit. The geometric phase is entirely determined by the polarization state of the incident light and the orientation angle of the metasurface unit, and is independent of wavelength. This ensures that the metasurface holography can be controlled across the entire visible light range to achieve color holographic reconstruction. The units of the metasurface structure are set to subwavelength dimensions. Because the reconstruction distance of the metasurface holography is very close, axial chromatic aberration is eliminated under Fresnel near-field diffraction. When white light directly illuminates the metasurface structure, a color holographic 3D image without magnification chromatic aberration or axial chromatic aberration is reconstructed. IV. Description of the attached drawings

[0033] Appendix Figure 1 This is a schematic diagram of the process of a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm according to the present invention.

[0034] Appendix Figure 2 This is a top view of the metasurface structure of a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm according to the present invention.

[0035] Appendix Figure 3 This is a schematic diagram illustrating the reconstruction effect of a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm according to the present invention. Figure 3 (a) Color reconstruction effect when "V" focused; Figure 3 (b) Color reconstruction effect when “N” is focused.

[0036] It should be understood that the above figures are only schematic and are not drawn to scale. V. Detailed Implementation Methods

[0037] The following detailed description of an embodiment of a color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm proposed in this invention further illustrates the invention. It is necessary to point out that the following embodiments are only used for further explanation of this invention and should not be construed as limiting the scope of protection of this invention. Any non-essential improvements and adjustments made to this invention by those skilled in the art based on the above description still fall within the scope of protection of this invention.

[0038] One embodiment of the present invention involves selecting the letters "N" and "V" located at two different depth planes as 3D objects with a resolution of 5000×5000. The diffraction distances of "N" and "V" are set to 3mm and 20mm, respectively. The complex amplitude distribution of the 3D objects is calculated based on the Fresnel near-field diffraction algorithm, phase information is extracted, and a metasurface hologram with a resolution of 5000×5000 is generated. Then, the metasurface units are fabricated. The fabricated metasurface is a transmission-type dielectric metasurface based on geometric phase. The substrate of the metasurface units is sapphire, on which single-crystal silicon is etched. The metasurface structure has a resolution of 5000×5000 and a period of 350nm, as shown in the attached figure. Figure 2 The image shown is a top view of the metasurface structure captured by a scanning electron microscope. Red, green, and blue lasers were used as the reconstructed light to illuminate the metasurface structure, with wavelengths of 671 nm, 532 nm, and 473 nm, respectively. The reconstructed images are shown in the attached figure. Figure 3 As shown, when the diffraction distance is 20 mm, a focused color holographic reconstruction of the letter "V" can be seen. When the diffraction distance is 3 mm, a focused color holographic reconstruction of the letter "N" can be seen. Experimental results show that under colored light illumination, the metasurface hologram achieves aberration-free color holographic reconstruction at both depths. The experiment verifies that the method of this invention can achieve aberration-free color metasurface holographic 3D display.

Claims

1. A color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm, characterized in that, The method includes the following four steps: First, the 3D object is discretized into a set of independent object points with depth information, and the sub-hologram of each object point on the holographic surface is calculated according to the Fresnel near-field diffraction condition to eliminate the magnification chromatic aberration in the reconstructed image; Second, the sub-holograms of all object points of the 3D object are coherently superimposed to obtain the complex amplitude information of the holographic surface. The third step is to extract the phase from the complex amplitude information in step two to obtain the final phase hologram. By encoding the obtained phase hologram information with a metasurface, the final metasurface hologram is obtained. The fourth step is to process and prepare the obtained metasurface hologram to obtain a metasurface structure. The unit of the metasurface structure is set to a subwavelength size. The axial chromatic aberration is eliminated under Fresnel near-field diffraction. When the metasurface structure is irradiated by a laser, a color metasurface holographic 3D image without chromatic aberration is reproduced. In step one, the 3D object is first discretized into a set of independent object points with depth information. Each object point is considered as an independent point light source. The complex amplitude distribution of each object point to the holographic surface is calculated, thereby generating a sub-hologram. The complex amplitude distribution of any object point m on the holographic surface is then calculated. for: in H(k) is the complex amplitude distribution of object point m on the object plane. x ,k y ; z) is the spatial frequency transfer function, where z represents the diffraction distance, and These are the Fourier transform and the inverse Fourier transform, k x and k y These are the spatial frequencies in the x and y directions, respectively; H(k) x ,k y The inverse Fourier transform of (x, y, z) is set as the spatial impulse response function h(x, y, z) in the Fourier domain, expressed as follows: Where k0 is the wave vector of the recorded light, and λ is the wavelength of the recorded light, when the coordinates of the object point in space are (h, w; 0), the complex amplitude distribution of any object point m on the holographic surface is expressed as: In the holographic reconstruction process, a plane wave is used as the reconstruction light to illuminate the hologram, and the complex amplitude distribution of the reconstruction light is... for: Where k r It is the wave vector of the reconstructed light. When the wavelength of the reconstructed light is the same as that of the recording light, the wave vectors of the reconstructed light and the recording light are also the same, i.e., k. r =k0, at this point, when the sub-hologram of any object point m is illuminated by the reconstruction light, the complex amplitude distribution of the reconstructed image is... for: Where z r This indicates the axial position of the reconstructed image, * indicates convolution operation, and ∝ is the proportionality sign. The part after the proportionality sign determines the position, depth, and shape of the reconstructed image. Based on Fresnel near-field diffraction analysis, this part is represented as: Let the above formula and The coefficient is 0, leaving only the linear term. This occurs when the wavelengths of the reference light and the recording light are exactly the same, i.e., k. r When k = 0, the following conditions must be met: That is, when the reference light and the preset wavelength are the same, the axial position of the reconstructed image is the same as the diffraction distance of the object point, at which point we obtain: For 3D objects, when the reference light has the same wavelength as the preset light, the reconstruction distance of the holographic image is the same as the diffraction distance, and the reconstructed image has no magnification chromatic aberration. When the wavelengths of the reference light and the recording light are not the same, the axial displacement of the reconstructed image is determined by the wavelengths of the recording light and the reference light, and is proportional to z. In this case, the complex amplitude distribution of the reconstructed image at point m is: in, The spatial position of the reproduced image corresponding to the object point will not change, that is, no magnification chromatic aberration will be introduced.

2. The color metasurface holographic 3D display method based on Fresnel near-field diffraction algorithm according to claim 1, characterized in that, In step three, the phase is extracted from the complex amplitude information in step two to obtain the final phase hologram. The obtained phase hologram information is then encoded using a metasurface to obtain the final metasurface hologram. Metasurface encoding is based on a transmissive medium metasurface unit with geometric phase modulation. The geometric phase is completely determined by the polarization state of the incident light and the orientation angle of the metasurface unit, and is independent of the wavelength. This ensures that the metasurface hologram can be modulated throughout the visible light range to achieve color holographic reconstruction. The unit of the metasurface structure is set to a subwavelength size. Since the reconstruction distance of the metasurface hologram is very close, the axial chromatic aberration is eliminated under Fresnel near-field diffraction. When white light directly illuminates the metasurface structure, a color holographic 3D image without magnification chromatic aberration and axial chromatic aberration is reproduced.

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