A Color Spherical Holographic Display System Based on Conformal Diffraction Principle

Abstract

This invention proposes a color spherical holographic display system based on the principle of conformal diffraction. The system includes a color laser, a beam expander, lens I, a spatial light modulator, a semi-transparent mirror, lens II, an aperture, lens III, and a computer. The color laser, after passing through the beam expander and lens I, forms a collimated beam. The computer loads a color spherical hologram generated based on the principle of conformal diffraction onto the spatial light modulator. The incident collimated beam, after passing through the semi-transparent mirror, illuminates the spatial light modulator. The light wave modulated by the spatial light modulator, after passing through lens II, the aperture, and lens III, diffracts in space to form a holographic 3D reconstructed image with a natural spherical effect. The aperture is used to filter stray light. The system uses a computer to synchronously control the spatial light modulator and the color laser. When the color spherical hologram is loaded onto the spatial light modulator, red, green, and blue light beams illuminate the corresponding colored spherical holograms, ultimately displaying the color spherical holographic 3D reconstructed image.

Description

Technical Field

[0001] This invention relates to holographic display technology, and more specifically, to a color spherical holographic display system based on the principle of conformal diffraction. Background Technology

[0002] Holographic 3D displays have attracted widespread attention because they can completely record and reconstruct the wavefront information of 3D scenes, providing all the depth information required for human vision. An ideal holographic 3D display should possess characteristics such as a wide viewing angle, distortion-free operation, and dynamic color display. However, the pixel size and spatial bandwidth product of current spatial light modulators limit the viewing angle of holographic 3D displays. Common methods for expanding the viewing angle of holographic 3D displays include time-division multiplexing and space-division multiplexing. A wide-viewing-angle holographic 3D display system built using time-division multiplexing requires a high refresh rate for the spatial light modulator; a wide-viewing-angle holographic 3D display system built using space-division multiplexing requires multiple spatial light modulators, resulting in a complex system structure and high cost. In recent years, with the development of flexible materials, more and more researchers have extended the design of holograms from planes to curved or spherical surfaces to broaden the viewing angle of holographic 3D displays. However, due to the limitations of the shape of the spatial light modulator, it is currently difficult to achieve optical reproduction of curved or spherical holograms. Furthermore, when the holographic image is reconstructed on a curved or spherical screen, severe distortion will occur, affecting the viewing effect. Summary of the Invention

[0003] This invention proposes a color spherical holographic display system based on the principle of conformal diffraction. For example... Figure 1 As shown, the system includes a color laser, a beam expander, lens I, a spatial light modulator, a semi-transparent mirror, lens II, an aperture, lens III, and a computer. The color laser emits red, green, and blue light sequentially, which, after passing through the beam expander and lens I, forms a collimated beam. The computer loads a color spherical hologram generated based on conformal diffraction onto the spatial light modulator. The incident collimated beam, after passing through the semi-transparent mirror, illuminates the spatial light modulator. The light wave modulated by the spatial light modulator, after passing through lens II, the aperture, and lens III, diffracts in space to form a holographic 3D reconstructed image with a natural spherical effect. The aperture is used to filter out stray light. The system uses a computer to synchronously control the spatial light modulator and the color laser. When the color spherical hologram is loaded onto the spatial light modulator, the red, green, and blue light beams illuminate the corresponding colored spherical holograms, ultimately resulting in the observed color spherical holographic 3D reconstructed image.

[0004] The system proposed in this invention generates color spherical holograms based on the principle of conformal diffraction. The principle of holographic conformal diffraction is as follows: Figure 2 As shown, the radius of the sphere is R, and the mapping plane intersects with xO. yThe plane is parallel to the XY plane, and Q is an arbitrary point on the Z axis and not in the mapping plane. The coordinates of Q are (0, 0, z Q ). The coordinates of an arbitrary point B' on the plane are (x' B , y' B , z' B ), and the coordinates of the mapping point B of B' on the sphere are (x B , y B , z B ). According to the mapping relationship, the following is obtained:

[0005]

[0006] x B = rx' B (2)

[0007] y B = ry' B (3)

[0008]

[0009] wherein r is the mapping ratio.

[0010] After completing the conformal mapping process of the recorded object and the sphere, the complex amplitude distribution of the spherical object on the spatial light modulator plane is calculated using the angular spectrum diffraction method. The angular spectrum A(f x , f y ) of the object is represented as:

[0011]

[0012] wherein represents the Fourier transform, U(x, y) is the complex amplitude distribution of the spherical object, f x and f y represent spatial frequencies, and j is an imaginary number. The angular spectrum distribution A''(f x , f y ) on the spatial light modulator plane is calculated using the angular spectrum propagation formula as:

[0013]

[0014] wherein λ is the wavelength, k is the wave number, k = 2π / λ, z0 is the distance from the sphere center to the spatial light modulator plane, and z(x', y') is the depth distribution of the spherical object. Through conformal mapping and angular spectrum propagation, the complex amplitude distribution U''(x, y) of the spherical object on the spatial light modulator plane is obtained and represented as:

[0015]

[0016] The system provided by the present application realizes color spherical holographic display by the following method: firstly, information of red, green and blue color channels of a recorded object is extracted; then, the information of the three color channels is calculated respectively according to corresponding wavelengths, and complex amplitude distributions of the three colors are obtained based on formulas (1)-(7); then, phase optimization is performed on the complex amplitude distributions of the three colors by an error diffusion algorithm, and finally, spherical holograms of three different colors are obtained. When the color spherical hologram is loaded onto a spatial light modulator, the spatial light modulator reads the spherical holograms of the red, green and blue channels in time sequence. At T0 moment, the spherical hologram of the red channel is read by the spatial light modulator, and at the same time, a laser is driven to emit red light, so that the reconstruction of the spherical hologram of the red channel is realized; at T1 moment, the spherical hologram of the green channel is read by the spatial light modulator, and at the same time, the laser is driven to close the red light and emit green light, so that the reconstruction of the spherical hologram of the green channel is realized; at T2 moment, the spherical hologram of the blue channel is read by the spatial light modulator, and at the same time, the laser is driven to close the green light and emit blue light, so that the reconstruction of the spherical hologram of the blue channel is realized, and the cycle continues from T0 moment. When the switching time is fast enough, according to the visual persistence effect of the human eye, color spherical holographic 3D display effect is observed. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 FIG. 1 is a structural schematic diagram of a color spherical holographic display system based on the conformal diffraction principle of the present application.

[0018] Figure 2 FIG. 2 is a schematic diagram of the holographic conformal diffraction principle of the present application.

[0019] Figure 3 FIG. 3 is a schematic diagram of the color spherical holographic display effect of the present application.

[0020] The illustration numbers in the above figures are as follows:

[0021] (1) color laser, (2) beam expander, (3) lens I, (4) spatial light modulator, (5) half-transmission half-reflection mirror, (6) lens II, (7) diaphragm, (8) lens III, (9) computer, (10) spherical reconstruction image.

[0022] It should be understood that the above figures are only schematic and are not drawn to scale. DETAILED DESCRIPTION

[0023] The following will be described in detail the embodiment of the color spherical holographic display system based on the conformal diffraction principle, and further describe the present application. It is necessary to point out here that the following embodiments are only used for further description of the present application, and can not be understood as limiting the scope of the present application, the skilled in the art can make some non-essential improvements and adjustments according to the above description of the present application, still belong to the protection scope of the present application.

[0024] The system embodiment of the present application is: in the experimental system, the red light wavelength of the color laser is 638nm, the green light wavelength is 520nm, and the blue light wavelength is 450nm. The spatial light modulator is a reflective pure phase spatial light modulator, the pixel pitch and resolution thereof are 4.5μm and 1920×1080 respectively, the refresh rate is 180Hz, and the phase modulation capacity is 2π. The focal length of lens I, lens II and lens III is all 20cm. The object "BUAA" is used as the recorded object, the resolution thereof is 1080×1080, the reconstruction distance is 15cm, and the reconstruction spherical radius is 4mm. The spherical holograms of the red, green and blue channels of the object are generated based on the conformal diffraction principle, and the resolution of the spherical holograms is all 1920×1080. The color spherical hologram is loaded onto the spatial light modulator, the spatial light modulator is synchronously controlled to read the spherical holograms of the red, green and blue channels, and the color laser is synchronously controlled to emit light waves of the corresponding color channel, so as to finally realize the color spherical holographic display effect as shown in Figure 3 .

Claims

1. A color spherical holographic display system based on the principle of conformal diffraction, characterized in that, The system comprises a color laser, a beam expander, a lens I, a spatial light modulator, a half-transmission half-reflection mirror, a lens II, a diaphragm, a lens III and a computer; wherein the color laser emits red light, green light and blue light in time sequence, forms a collimated light beam after the beam expander and the lens I, the computer loads the color spherical hologram generated based on the conformal diffraction principle to the spatial light modulator, the incident collimated light beam irradiates the spatial light modulator after the half-transmission half-reflection mirror, the light wave modulated by the spatial light modulator forms a holographic 3D reconstruction image with natural spherical effect in space after the lens II, the diaphragm and the lens III, the diaphragm is used for filtering stray light, the computer is used for synchronously controlling the spatial light modulator and the color laser in the system, when the color spherical hologram is loaded to the spatial light modulator, the light beams of red, green and blue colors irradiate the spherical hologram of corresponding color respectively, and finally a color spherical holographic 3D reconstruction image is observed; The color spherical hologram is generated based on a conformal diffraction principle. In the holographic conformal diffraction principle, the radius of the sphere is R, a mapping plane is parallel to the xOy plane, a Q point is an arbitrary point on the z axis and is not in the mapping plane, coordinates of the Q point are (0, 0, z Q ), coordinates of an arbitrary point B' on the plane are (x' B , y' B , z' B ), and coordinates of a mapping point B of the point B' on the sphere are (x B , y B , z B ). According to the mapping relationship, the following is obtained: x B = rx' B y B = ry' B Wherein r is a mapping ratio; After the conformal mapping process of the recorded object and the sphere is completed, the complex amplitude distribution of the spherical object on the spatial light modulator plane is calculated using the angular spectrum diffraction method, and the angular spectrum A(f x ,f y ) of the object is represented as: wherein denotes the Fourier transform, U(x,y) is the complex amplitude distribution of the spherical object, f x and f y denotes the spatial frequency, j is the imaginary unit, the angular spectrum distribution A"(f x ,f y ) on the plane of the spatial light modulator is calculated using the angular spectrum propagation formula Wherein λ is a wavelength, k is a wave number, k=2π / λ, z0 is a distance from a spherical center to a spatial light modulator plane, z(x', y') is a depth distribution of a spherical object, a complex amplitude distribution U''(x, y) of the spherical object on the spatial light modulator plane is obtained through conformal mapping and angular spectrum propagation, and is expressed as:

2. The color spherical holographic display system based on the principle of conformal diffraction according to claim 1, characterized in that, The proposed system realizes color spherical holographic display through the following method: firstly, information of red, green and blue color channels of a recorded object is extracted; then, the information of the three color channels is calculated according to corresponding wavelengths to obtain complex amplitude distributions of the three colors; then, the complex amplitude distributions of the three colors are optimized in phase through an error diffusion algorithm, and finally spherical holograms of the three different colors are obtained; when the color spherical hologram is loaded to the spatial light modulator, the spatial light modulator reads the spherical holograms of the red, green and blue channels in time sequence, at T0 moment, the red channel spherical hologram is read by the spatial light modulator, and the laser is driven to emit red light at the same time, so that the reconstruction of the red channel spherical hologram is realized; at T1 moment, the green channel spherical hologram is read by the spatial light modulator, and the laser is driven to emit green light at the same time, so that the reconstruction of the green channel spherical hologram is realized; at T2 moment, the blue channel spherical hologram is read by the spatial light modulator, and the laser is driven to emit blue light at the same time, so that the reconstruction of the blue channel spherical hologram is realized; the cycle continues at T0 moment, and when the switching time is fast enough, the color spherical holographic display effect is observed according to the visual persistence effect of the human eye. Wherein r is a mapping ratio; Wherein λ is a wavelength, k is a wave number, k=2π / λ, z0 is a distance from a spherical center to a spatial light modulator plane, z(x', y') is a depth distribution of a spherical object, a complex amplitude distribution U''(x, y) of the spherical object on the spatial light modulator plane is obtained through conformal mapping and angular spectrum propagation, and is expressed as: The proposed system realizes color spherical holographic display through the following method: firstly, information of red, green and blue color channels of a recorded object is extracted; then, information of the three color channels is calculated according to corresponding wavelengths to obtain complex amplitude distributions of the three colors; then, the complex amplitude distributions of the three colors are optimized in phase through an error diffusion algorithm, and finally spherical holograms of the three different colors are obtained; when the color spherical hologram is loaded to the spatial light modulator, the spatial light modulator reads the spherical holograms of the red, green and blue channels in time sequence, at T0 moment, the red channel spherical hologram is read by the spatial light modulator, and the laser is driven to emit red light at the same time, so that the reconstruction of the red channel spherical hologram is realized; at T1 moment, the green channel spherical hologram is read by the spatial light modulator, and the laser is driven to emit green light at the same time, so that the reconstruction of the green channel spherical hologram is realized; at T2 moment, the blue channel spherical hologram is read by the spatial light modulator, and the laser is driven to emit blue light at the same time, so that the reconstruction of the blue channel spherical hologram is realized; the cycle continues at T0 moment, and when the switching time is fast enough, the color spherical holographic display effect is observed according to the visual persistence effect of the human eye.

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