Holographic 3D display system based on polymer liquid crystal scattering film

Abstract

The application discloses a holographic 3D display system based on a polymer liquid crystal scattering film, combines a spatial light modulator (SLM) with ML-PDLCs, calculates holograms of different layers of an object to be displayed first, then reproduces the holograms through the SLM, places ML-PDLCs at the reproduction image positions, and the reproduction images of different layers correspond to the ML-PDLC film layers one by one. The ML-PDLCs are used as a projection two-dimensional image receiving screen of the SLM, all the film layers of the ML-PDLCs are in a transparent state under power supply at the beginning, when an image of a layer is reproduced, the corresponding film layer is in a scattering state under power-off, and the reproduction image is displayed on the film layer. All the broken layer holograms are displayed one by one, the corresponding ML-PDLC film layers are sequentially powered on and powered off, and the reproduction image is sequentially displayed on the corresponding film layers. Assuming that the object is decomposed into N layers, the ML-PDLCs are used as the projection two-dimensional image receiving screen of the SLM, the projection frame frequency of the SLM and the power-on time sequence of the ML-PDLC film layers are controlled, different two-dimensional images can be projected to different ML-PDLC film layers for display, and a complete three-dimensional image with continuous depth can be seen.

Description

Technical Field

[0001] This invention belongs to the field of holographic three-dimensional display technology, specifically relating to a holographic 3D display system based on a polymer liquid crystal scattering film. Background Technology

[0002] Holographic 3D display can reproduce the light wavefront carrying information about a 3D object exactly as it is displayed. It is a display technology based on wavefront reconstruction, and therefore it is considered the most ideal true 3D display technology at present.

[0003] The earliest holograms were optical holograms, which used a laser as a light source to illuminate an object. After transmission or reflection (scattering) by the object, an object light wave (W) was formed. When this object light wave (W) met another light wave (C) called a reference light wave, interference fringes were formed. By recording these interference fringes using a photosensitive material, a hologram was obtained. The information of the object light wave was encoded into the hologram. When the hologram was illuminated by a laser, due to diffraction, the outgoing light wave would contain the original object light wave, thus allowing the image of the object to be reconstructed.

[0004] Computer-generated holography does not require the actual existence of an object. It only requires inputting the mathematical description of the object's light wave into a computer, which encodes it to obtain a digital hologram. This hologram can then be output as an optically reproducible hologram using a plotter or a dedicated computational hologram miniaturization system. Alternatively, it can be output to a spatial light modulator for direct display. Computational holograms can not only comprehensively record the amplitude and phase of actual light waves but also synthesize the wavefronts of objects that do not exist in the real world, thus possessing unique advantages and great flexibility. Computer-generated holograms are digital and can be processed through printing and other methods to become actual transparent sheets, similar to optical holograms. Figure 1 Similarly, light waves can be reproduced using laser illumination. Alternatively, they can be directly transmitted to optoelectronic display devices for display. A spatial light modulator is a device that modulates the spatial distribution of light waves. Under the control of an electrically driven signal, it changes the amplitude or intensity, phase, polarization state, etc., of the light distribution in space. By inputting a computer-generated hologram into a spatial light modulator, an image can be reproduced when illuminated by a laser. Spatial light modulators have a high refresh rate, thus enabling dynamic holographic displays, which is impossible with optical holograms.

[0005] Currently, holographic 3D display has made some encouraging progress. A recent notable achievement is the report by the German company SeeReal in 2017. [1] A holographic display with a field of view of 300 mm * 200 mm was realized using very low resolution SLM (pixel spacing of 135 μm, vertical spacing of 35 μm), holographic optical elements, and window tracking technology, but it is only for one person to observe; its principle is based on the concept of tomographic holography. [2]和[3]The 3D object O is considered to be composed of multiple cross-sections, each of which is a two-dimensional image, similar to a CT scan. The Fresnel holograms of each two-dimensional image are calculated one by one. Figure 1 It uses the optical path of tomographic holography recording principle to decompose the target (object 1 to be displayed) into two-dimensional images (Lay0, Lay1...Lay ... n For each image layer, its hologram is recorded (calculated). The distance Z between different image layers and the hologram plane Q varies depending on their relative positions. n They are also different. Let the distance between adjacent layers be ΔZ. l Then the nth layer slice Lay n The distance from the hologram plane Q is:

[0006] Z n =Z0+n△Z l (0-1)

[0007] Holograms of each layer are sequentially input into a spatial light modulator (SLM) according to a specific time sequence. The SLM is then illuminated with a beam-expanding laser. As each hologram is input, the SLM reconstructs its image at the corresponding spatial position, forming a longitudinal scan of the image plane. If the SLM's frame rate is fast enough, such that the total scanning time of all sections is less than the visual persistence time of the human eye (approximately 0.1-0.4 seconds), a complete three-dimensional image will be formed. However, due to the relatively low spatial resolution of current SLMs, the divergence angle of the reconstructed image points is very small, meaning that the two eyes cannot simultaneously see the same image point. Figure 2 In the holographic reconstruction, the cone angle of the cone-shaped beam emitted from point A of the holographic image is ω (field of view angle FOV), which is much smaller than the minimum angle Ω required for binocular stereoscopic vision. Although the holographic reconstruction image is three-dimensional, the human eye cannot obtain the feeling of a three-dimensional image by using visual axis convergence.

[0008] Therefore, expanding the field of view of the holographic image is one of the most critical technologies that needs to be overcome in holographic display.

[0009] [1]R. Y.GRITSAI,E.ZSCHAU,R.MISSBACH,H.SAHM,M.STOCK,ANDH.STOLLE, Large real-time holographic 3D displays:enabling components and results, Applied Optics, 56(13), 2017.

[0010] [2]Trester S.Computer-simulated Fresnel holography[J].EuropeanJournal of Physics,21(4),2000,

[0011] [3] Cao Xuemei, Sang Xinzhu, Computational holograms of complex 3D scenes based on 2D color images and depth maps, Chinese Journal of Lasers, 41(6), 2014. Summary of the Invention

[0012] This invention addresses the technical problem that the human eye cannot distinguish 3D reconstructed images from SLM (Spatial Light Modulator) reconstructions. It combines a Spatial Light Modulator (SLM) with Multilayer Photomultiplexed Cartridges (ML-PDLCs). First, holograms of different layers of the object to be displayed are calculated. Then, these are reconstructed using the SLM. ML-PDLCs are placed at the locations of the reconstructed images, with each layer corresponding to a specific ML-PDLC film. ML-PDLCs serve as the receiving screen for the 2D image projected by the SLM. Initially, all layers of the ML-PDLCs are electrically conductive and transparent. When reconstructing an image of a specific layer, the corresponding layer is de-energized and scatters light, thus displaying the reconstructed image on that layer. This process achieves the goal of creating a complete tomographic hologram. Figure 1 As the corresponding ML-PDLCs film layers are switched on and off sequentially, the reconstructed image will be displayed on the corresponding film layers in turn. Assuming the object is decomposed into N layers, and the time required for the SLM to display all N layers of hologram is ΔT, using ML-PDLCs as the receiving screen for the SLM projection of two-dimensional images, by controlling the SLM projection frame rate and the power-on sequence of the ML-PDLCs film layers, different two-dimensional images can be projected onto different film layers of the ML-PDLCs for display, forming a longitudinal scan of the two-dimensional image. If ΔT is less than the visual persistence time of the human eye, a complete three-dimensional image with continuous depth will be seen.

[0013] The present invention provides a holographic 3D display system based on a polymer liquid crystal scattering film, comprising:

[0014] A computer is used to create Fresnel holograms of n-layer two-dimensional images with data encoding. The n-layer two-dimensional images correspond one-to-one with the n-layer parallel cross-sections of the three-dimensional image of a 3D object, which are decomposed layer by layer from the back end plane to the front end plane.

[0015] The spatial light modulator modulates the illumination light emitted by the light source module and reconstructs the reconstructed images of each layer of holograms in the reconstruction light field according to the loading sequence, so that the position of the n-layer reconstructed images corresponds to the position of the two-dimensional image of the reconstructed image in the three-dimensional image, and the size of the reconstructed image is consistent with the three-dimensional image of the 3D object.

[0016] The diffusion laminate consists of M parallel polymer scattering liquid crystal films, where n ≤ M ≤ 10. The positions of the n reconstructed images from the rear end plane to the front end plane in the reconstructed light field coincide one-to-one with the positions of the n polymer scattering liquid crystal films in the diffusion laminate. These n polymer scattering liquid crystal films are controlled by a computer. When the reconstructed image of the nth hologram is reconstructed, the polymer scattering liquid crystal films that coincide with the position of the reconstructed image of that layer are in a scattering state, scattering the reconstructed image into a three-dimensional image, while the remaining polymer scattering liquid crystal films are in a transparent state, allowing the reconstructed image to pass through without interference.

[0017] An aperture, placed at the end face of the output window of the diffusion laminate, is used to block the zero-order term and conjugate image of the diffracted light;

[0018] The response time of the polymer scattering liquid crystal film is T, the frequency frame of the spatial light modulator is at least 1 / T Hz, and the pixel spacing of the spatial light modulator is d. slm Satisfy the following formula: d slm ≤λZ o / 2L o L o The planar dimensions of the reconstructed image, λ being the wavelength of the illuminating light, and Z... o To reproduce the distance between the image and the spatial light modulator, the planar dimension of the diffuse laminate is not less than L. o The response time refers to the total time it takes for the polymer scattering liquid crystal film to go from the scattering state when the power is off to the transparent state when the power is on, and then back to the scattering state when the power is off again.

[0019] Furthermore, the response time refers to the total time for the polymer scattering liquid crystal film to go from a scattering state with a transmittance of no more than 20% when the power is off to a transparent state after the power is on, and then back to a scattering state with a transmittance of no more than 20% when the power is off again.

[0020] Furthermore, the polymer scattering liquid crystal film takes 10ms to go from a scattering state with a transmittance of no more than 20% when the power is off to a transparent state after the power is on, and takes 100ms to go from a scattering state with a transmittance of no more than 20% after the power is on and then off.

[0021] Furthermore, the polymer scattering liquid crystal film takes 10ms to go from a scattering state with a transmittance of no more than 20% when the power is off to a transparent state after the power is on, and takes 60ms to go from a scattering state with a transmittance of no more than 20% after the power is on and off.

[0022] Furthermore, the frequency frame of the spatial light modulator is at least 25nHz, n is not greater than 19, and the response time of the polymer scattering liquid crystal film is not greater than 1 / 25n seconds.

[0023] Furthermore, the holographic 3D display system based on polymer liquid crystal scattering film also includes: a lens L1, an aperture and lens L1 are arranged sequentially along the normal G of the reconstructed image on the side of the spatial light modulator facing the diffusion laminate, the n-layer reconstructed image is located within the frame of the aperture, and the 0th layer reconstructed image closest to lens L1 among the n-layer reconstructed images is more than one focal length away from lens L1, the imaging optical path of the n-layer polymer scattering liquid crystal film lens L1 closest to lens L1 in the diffusion laminate is more than one focal length away from lens L1, lens L1 magnifies the n-layer reconstructed image and images it into the diffusion laminate, the n-layer magnified real image coincides with the position of the n-layer polymer scattering liquid crystal film in the diffusion laminate one by one, and the planar size of the real image is not larger than the planar size of the diffusion laminate.

[0024] Furthermore, if the layer spacing of the reconstructed image from layer n' to n'+1 is Δl n’ Then the interlayer spacing of the n' to n'+1th polymer scattering liquid crystal layers Z Ha Let ΔZ be the distance between the nth layer of the reproduced image and the input-side focal point of lens L1. Hn’ f1 is the distance between the nth layer reconstructed image and the n'th layer reconstructed image, and f1 is the focal length of lens L1.

[0025] Furthermore, the center-to-center distance Δl' between adjacent polymer-scattered liquid crystal films in the diffusion laminate is... n’ Equal, Δl' n’ =Δl'1, and △l1 is the spacing between the reconstructed images of layers 0 to 1. When the computer creates the hologram, it transforms the spatial coordinates of the original objects in the holograms of different layers to compensate for the deformation caused by imaging through lens L1, so that lens L1 enlarges the reconstructed images proportionally onto the corresponding polymer scattering liquid crystal films arranged at equal intervals in the diffusion laminate.

[0026] Furthermore, when calculating the hologram, the coordinates x of the actual object point are plotted on the n'-th layer two-dimensional image plane. on Transform using the following formula: The coordinates x of the n'th layer of the two-dimensional image of the actual object along the normal G direction are... on Transform using the following formula:

[0027] Furthermore, the holographic 3D display system based on polymer liquid crystal scattering film also includes a lens L2, which is arranged along the normal C of the real image on the side of the diffusion laminate facing away from the lens L1. The lens L2 magnifies and images the n-layer three-dimensional image layer scattered by the diffusion laminate, and the interval between adjacent image layers after magnification is less than the resolution limit of the human eye along the normal C direction. The distance between the lens L2 and the n-th three-dimensional image layer in the diffusion laminate is more than one focal length.

[0028] Furthermore, the layer spacing of the reconstructed images from layer n' to n'+1 is Δl. n’ , The distance between the nth three-dimensional image layer and the focal point of lens L2 is z. ia , z e f1 is the observation distance, which is the distance between the human eye and the magnified image of lens L2, and f2 is the focal length of lens L2.

[0029] The beneficial effects of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0030] This invention first reduces the digitized 3D model to match the maximum lateral size of the image that the spatial light modulator can reproduce. Then, based on the size of the stacked ML-PDLCs and the film layer spacing, the focal length of lens L1 and the optical path are selected to ensure that the size of the holographic image magnified into a real image is less than or equal to the size of the ML-PDLCs. Furthermore, the distance between n=0 and the adjacent layer (n=1) real image is equal to the ML-PDLCs film layer spacing Δl'1, and the corresponding adjacent layer spacing of the reproduced image is Δl1. The relationship between Δl1 and Δl'1 is as follows: The 3D object is layered, with each layer spaced by Δl1. To avoid longitudinal nonlinear amplification caused by L1 imaging from the lens head, the layer spacing of the 3D object is transformed when calculating the hologram. In this way, the reconstructed images of each layer of the hologram are not equidistant, but after L1 imaging, the spacing of each layer of real images will become equidistant, all being Δl'1, thus corresponding to the layers of ML-PDLCs. Attached Figure Description

[0031] Figure 1 Schematic diagram for recording tomographic holograms;

[0032] Figure 2 The field of view for holographic reconstruction;

[0033] Figure 3 To expand the field of view of the holographic reconstruction image using PDLC;

[0034] Figure 4 For direct projection of holographic image point diffusion;

[0035] Figure 5 Schematic diagram of the astigmatism principle of ML-PDLCs;

[0036] Figure 6 This is a diagram of the polymer liquid crystal structure;

[0037] Figure 7 Reconstructing the optical path pattern from a hologram;

[0038] Figure 8 The PDLC membrane's "on-off" time response curve;

[0039] Figure 9 This is a schematic diagram showing the expanded viewing angle of the PDLC film's image point.

[0040] Figure 10 Optical path diagram for holographic three-dimensional display imaging based on stacked PDLCs films;

[0041] Figure 11 This is a schematic diagram of a holographic three-dimensional display system based on stacked PDLCs films. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] Example 1

[0044] Figure 3 One embodiment of the present invention includes: a light source module, a spatial light modulator (SLM), a diffusion laminate (ML-PDLCs), an aperture (AP), and a computer. The computer decomposes the three-dimensional image of the 3D object layer by layer from the rear plane to the front plane into a two-dimensional image set composed of n equidistant parallel cross-sections, and calculates the Fresnel hologram of each layer of the two-dimensional image. The spatial light modulator loads the Fresnel holograms sequentially into the computer according to the loading sequence, modulates the illumination light emitted by the light source module, and sequentially emits the reconstructed images of the n-layer holograms in the G direction according to the loading sequence, so that the n-layer reconstructed images are sequentially reconstructed in the reconstructed light field, and the position of the n-layer reconstructed images corresponds to the position of the two-dimensional image of the reconstructed image in the three-dimensional image. The reconstructed images are the same size as the three-dimensional image of the 3D object. All n-layer reconstructed images are perpendicular to the G direction, and the M-layer polymer scattering liquid crystal film... A diffusion laminate is arranged sequentially along the G direction, with n≤M≤19. The spacing between adjacent layers in the M-layer polymer scattering liquid crystal film is equal to the spacing between adjacent decomposed layers in the three-dimensional image of the 3D object. The M-layer polymer scattering liquid crystal film is positioned such that the positions of the n-layer reconstructed images from the rear end plane to the front end plane in the reconstructed light field coincide one-to-one with the positions of the n-layer polymer scattering liquid crystal films in the diffusion laminate. These n-layer polymer scattering liquid crystal films are controlled by a computer so that when the spatial light modulator emits the reconstructed image of the n-layer hologram, the polymer scattering liquid crystal film whose position coincides with that layer's reconstructed image is in a scattering state, while the remaining polymer scattering liquid crystal films are in a transparent state. When in the scattering state, the reconstructed image is scattered into a three-dimensional image; when in the transparent state, the reconstructed image is allowed to pass through without interference. The front end face of the diffusion laminate away from the spatial light modulator is placed within the frame of the aperture.

[0045] In operation, holograms of different layers are sequentially input into the SLM (Synthetic Laser Mediator) and illuminated with a laser. A layered polymer scattering liquid crystal film (ML-PDLC) is placed in the holographic reconstruction area, with each layer's reconstruction image position corresponding one-to-one with the PDLC position. When the nth layer hologram is reconstructed at a certain moment, its reconstructed image is located on the nth layer of the ML-PDLC. At this time, the film is de-energized, and the reconstructed image is scattered, making it visible to the eye. Once the SLM has completed the reconstruction of all layers of holograms, the reconstructed images of all layers complete one scan along the scanning direction shown in the diagram. Figure 4 The intermediate AP is an aperture used to block the zeroth-order term and conjugate image of the diffracted light.

[0046] like Figure 5 This diagram illustrates how multiple PDLCs are stacked in the holographic reconstruction region to form ML-PDLCs. Five PDLCs are shown in the diagram, denoted as PDLC1, PDLC2, PDLC3, PDLC4, and PDLC5. PDLC1, PDLC2, PDLC3, and PDLC5 are energized, while PDLC4 is de-energized. A thin parallel light beam A is incident on the ML-PDLCs. Since PDLC1, PDLC2, and PDLC3 are energized and transparent, the light passes directly through. Because PDLC4 is in a scattering state, when the light strikes point B on PDLC4, scattering occurs, forming a cone-shaped beam with B as its vertex. The scattered light continues to pass directly through PDLC5, and a point of light can be seen at point B by the human eye.

[0047] "Multi-layer polymer-dispersed liquid crystal films" (ML-PDLCs) are composed of multiple polymer liquid crystal (PDLC) scattering films (e.g., Figure 6PDLC films are characterized by being transparent and scattering under energized and de-energized conditions, respectively. The principle is that liquid crystals are dispersed in micron-sized droplets within a solid organic polymer matrix. Because the optical axes of these droplets are freely oriented, their refractive indices do not match the matrix's. When light passes through the matrix, it is strongly scattered by the droplets, resulting in an opaque, milky-white or semi-transparent state. Applying a voltage adjusts the optical axis orientation of the liquid crystal droplets; when their refractive indices match, the film becomes transparent. Removing the electric field restores the droplets to their initial scattering state. This embodiment utilizes this characteristic to scatter image points at different cross-sections, thereby expanding the viewing angle. Clearly, the performance of the PDLC film directly affects the success of this embodiment. Table 1 shows the performance parameters of commercially available PDLC films. The following application analysis shows that the time response of current PDLC films is far from meeting requirements. This is because light undergoes energy attenuation upon entering ML-PDLCs, resulting in two main causes of light loss: surface reflection and internal absorption. The outermost layer of the PDLC film is made of PET material. Assuming its refractive index is approximately n, for one-sided reflection, approximately r = [(n-1) / (n+1)]. 2 Energy is reflected. Let the transmittance of a single PDLC film in the open state be T, and its absorptivity be α (absorption coefficient is not used here because the PDLC film is not uniform). Let the energy of the incident light be 1. For a single PDLC film, the energy loss of the reflected light at the point of incidence is r, the energy of the light incident into the film is 1-r, the energy loss of the light absorbed at the interface is (1-r)α, the energy of the light reaching the exit interface is 1-(1-r)α, and the energy loss of the light upon exiting is...

[0048] [1-(1-r)α]r, the total energy loss is:

[0049] ε=r+(1-r)α+[1-(1-r)α]r=2r+(1-r) 2 α = 1 - T (1-1)

[0050] Therefore, the absorption rate can be calculated as follows:

[0051] Table 1 Typical Technical Parameters of Ordinary PDLC Membranes

[0052] Optical transmittance power ups Approximately 80% (+ / - 3%) Haze power ups <7.5％ Power outage >90％ Viewing angle power ups Approximately 150° Electricity power adapter power ups 65VAC Response time Power on-power off 100 milliseconds Power off - power on 10 milliseconds Power consumption power ups Approximately 50,000 RMB per square meter thickness Approximately 0.4 mm

[0053] Assuming ML-PDLCs consist of N layers, and that the bonding between each PDLC sheet is tight (or that there is no emission between the PET surfaces of the layers within the stack and the air interface), then the reflection and absorption losses of each layer, as well as the total transmittance, are:

[0054] First layer reflection loss: σ ri =r

[0055] First layer absorption loss: σ1=(1-r)α

[0056] Second layer absorption loss: σ²=[1-r-(1-r)α]α=(1-r)(1-α)α

[0057] Third-layer absorption loss: σ3=[1-r-(1-r)α-(1-r)(1-α)α]α=(1-r)(1-α) 2 α

[0058] Fourth layer absorption loss: σ4=[1-r-(1-r)α-(1-r)(1-α)α-(1-r)(1-α)] 2 α]α=(1-r)(1-α) 3 α

[0059] The absorption loss σ of the Nth layer N =(1-r)(1-α) N-1 α

[0060] Total absorption of N layers:

[0061] Last layer reflection loss:

[0062] Total energy loss: σ = σ ri +σ α +σ re

[0063] Transmitted energy:

[0064] Transmittance:

[0065] Currently, the maximum transmittance of PDLC products under open conditions can reach T = 82%. The refractive index of PET is approximately 1.6. Assuming ML-PDLCs have 30 layers, calculations using the above formula yield τ ≈ 6.8%, indicating significant energy loss and very weak emitted light. If the ML-PDLCs have 10 layers, τ ≈ 38%. Therefore, in this embodiment, 10 layers of ML-PDLCs are preferred. If the ML-PDLCs have 19 layers, τ ≈ 17.6%. The emitted light is still relatively weak; using a high-power laser as the reconstruction light source can increase the brightness of the reconstructed image to some extent. Therefore, in this embodiment, 19 layers of ML-PDLCs are optionally chosen.

[0066] Furthermore, based on the principle of layered 3D display using stacked liquid crystal modulator films, a high refresh rate is required for the spatial light modulator (SLM) to obtain a continuous dynamic 3D image. Assuming the target to be displayed has N layers, all N layers must be scanned once to display "one frame" of the object. According to the time resolution requirements of the human eye, at least 25-30 frames per second are needed for continuous dynamic display. This requires the SLM's refresh rate to be at least 25-30 NHz. If N = 10, the required frame rate is 250-300 Hz. If N = 19, the required frame rate is 475-570 Hz.

[0067] Although this design can meet the frame rate requirements using existing SLMs, the time response of current ordinary PDLC films is very slow. According to Table 1, the film's response time from the scattering state to the transparent state is 10ms, while the time from the transparent state to the scattering state is 100ms, which is insufficient. The refresh rate is in the millisecond range. In fact, research shows that the entire response time of a PDLC membrane from off to on to on to off can reach the millisecond level, or even the microsecond level. [4] .

[0068] Currently, the selected ordinary PDLC film can achieve the effect of using visual persistence to create the illusion of a complete 3D static image composed of 10 layers of three-dimensional images.

[0069] When selecting a spatial light modulator (SLM), if only the resolution of the image is considered, the more pixels the better. If the size of the reproduced image is also considered, the smaller the pixels the better. For dynamic display, the higher the frame rate the better. In this embodiment, when N=10, the frame rate is required to be at least 250Hz. In this embodiment, when N=19, the frame rate is required to be at least 475Hz.

[0070] When selecting an SLM, the pixel interval d of the SLM is... slm Given the following requirement, let N be the number of pixels in the horizontal direction of the SLM. slm The number of pixels in the vertical direction is M. slm Then its maximum spatial frequency is The display size is L horizontally. hx =d slm N slm Longitudinal L hy =d slm M slm See also Figure 7 Let the lateral width of the reproduced image I1 be L. o The wavelength of the reconstructed image light is λ, and the distance between the reconstructed image and the SLM is z. o If a lensless Fourier transform holography is used, then in order to ensure the separation of the holographic reconstructed image from the zero-order light, the spatial frequencies of the interference fringes of the hologram must satisfy the following:

[0071]

[0072] In order to reproduce the image using SLM, f is required. h ≤f slm ,Right now

[0073] Image size that can be reproduced:

[0074] According to Rayleigh's criterion, the resolvable pixel size of a holographic reconstruction is:

[0075] Based on the magnification factor M of the final SLM output image and the size of the final image presented to the observer, the planar width of the reconstructed image I1 can be deduced to be L. o For color display using SLM, let the wavelengths of the reproduced three primary color lasers be λ. R =0.65×10 -3 mm, λ G =0.53×10 -3 mm, λ B =0.46×10 -3 mm, if L0 = 21.5 mm, according to equation (1-6), the relationship between SLM pixel spacing, image distance, and reconstructed image size is as follows:

[0076]

[0077] To ensure that the reproduced images of the three primary color images are all of sufficient size, the smallest image must be used, i.e. Calculate based on z. o =350mm. That is, the maximum SLM pixel spacing corresponding to a sufficiently large reconstructed image is d. slm =3.74×10 -3 mm.

[0078] Example 2

[0079] Although the design of Example 1 can meet the frame rate requirements using existing SLMs, the time response of conventional PDLC films is currently very slow. According to Table 1, the film's response time from the scattering state to the transparent state is 10 ms, while the time from the transparent state to the scattering state is 100 ms, which is insufficient. The refresh rate is per second.

[0080] Currently, the selected ordinary PDLC film can achieve the effect of using visual persistence to create the illusion of a complete 3D static image composed of 19 layers of three-dimensional images.

[0081] In this embodiment, the PDLCs are primarily in an "on" state during operation. That is, if no reconstructed image appears, all layers of the PDLCs are transparent. When an image of a layer reconstructed from a hologram in the SLM is projected onto a PDLC layer, that layer is in an "off" state, thus scattering the image. When the next image appears, its corresponding layer is in an "off" state, while the layer corresponding to the previous image is in an "on" state, and so on. Based on the existing characteristics of PDLC films, the time required for the on / off state of consecutive images is 110 milliseconds. To accommodate the response speed of the PDLC film, the time for the SLM to display each hologram layer is also set to 110 milliseconds. If the PDLCs consist of 19 layers, the time required to complete one refresh is 2.09 seconds. This means that 19 images appear sequentially in the field of view within 2.09 seconds. Utilizing the persistence of vision, the human eye can perceive a complete 3D static image composed of 19 images.

[0082] According to Table 1, the response time of the film from the scattering state to the transparent state is 10ms, while the response time from the transparent state to the scattering state is 100ms, for a total response time of 110ms. The 3D display frame rate is determined based on the PDLC response time using the formula... At this point, if N=19, for a PDLC with a response time of T=110ms, the frame rate for 3D display using the spatial light modulator (SLM) is determined by... The calculated value is approximately 0.4785, or 2.09 seconds to display one frame, achieving the effect of a 3D still image.

[0083] Preferably, reducing the off-state time can improve the response speed. The 100ms on-off response time refers to the time required for the PDLC film to transition from a transparent to a fully scattering state. Reducing this time will decrease the scattering of the PDLC film. Figure 8 This is a time response curve of a PDLC film during the "on-off" state. It shows that as the off-state time increases, the transmittance gradually decreases, accompanied by a gradual increase in scattering. From 1400 ms to 1520 ms, a time of 120 ms, the PDLC film reaches its maximum scattering. At 1460 ms, the transmittance has already dropped to 20%, with most of the energy scattered. If the scattering angle at the image point at this point is sufficient for human vision, 1460 ms can be taken as the cutoff point for the off state, thus reducing the "on-off" response time to only 60 ms.

[0084] According to Table 1, the total response time of the film from the scattering state to the transparent state and back to the scattering state is 60ms. The 3D display frame rate is determined based on the PDLC response time using the formula... At this point, if N=19, for a PDLC with a response time of T=60ms, the frame rate for 3D display using the spatial light modulator (SLM) is... The calculated value is approximately 0.87719, meaning it takes about 1.14 seconds to display one frame, achieving the effect of a 3D still image.

[0085] If the spatial light modulator selected in Example 1 is RSLM-4K70-P, which has a maximum frame rate of only 480Hz, it has a large number of pixels and the pixel size is less than 3.74μm, which meets the requirement of clear static display of 19-layer three-dimensional image.

[0086] Comparative Example 1

[0087] Considering the interdependence between computational holography and the parameters of SLM and ML-PDLCs, the lens imaging method used in Embodiment 1 or Embodiment 2 can increase the degree of freedom in parameter selection. That is, the holographic image reconstructed by the SLM is imaged onto the ML-PDLCs through a lens L1, such as... Figure 10 This is another embodiment of the present invention.

[0088] The holographic image I0 reconstructed by the SLM is located near the aperture AP, and then magnified into a real image by the lens L1. ML-PDLCs are placed at the real image location to perform layered divergence angle expansion on the reconstructed image. The 0th layer of the n-layer reconstructed image closest to the lens L1 is more than one focal length from the lens L1. The imaging optical path of the n-layer polymer scattering liquid crystal film lens L1, which is closest to the lens L1 in the diffusion laminate, is also more than one focal length from the lens L1. The lens L1 magnifies the n-layer reconstructed image and projects it into the diffusion laminate. The magnified real image of the n layers sequentially coincides with the positions of the n-layer polymer scattering liquid crystal films in the diffusion laminate, and the planar size of the real image is no larger than the planar size of the diffusion laminate.

[0089] As can be seen from the figure, the horizontal and vertical magnifications of the images in different layers are different due to their different positions relative to lens L1. This will cause distortion of the overall three-dimensional image, which must be corrected.

[0090] For holograms, the more pixels there are, the more information can be reproduced. In practical applications, the amount of information in a 3D reproduced image is mainly reflected in the image size, field of view, and color. Given a certain amount of information, these three factors can be selected based on the needs.

[0091] like Figure 9 As shown. The computer-generated hologram is input into the spatial light modulator (SLM), and the reconstruction light C illuminates the SLM. The reconstructed image I of the nth layer hologram is generated. Hn Near the aperture AP plane, the front end of the entire reconstructed image layer is a. H The backend is b H Let z Ha and z Hb They are a H Point and b HLet z be the distance between the point and the focal point F1 on the input side of lens L1. Ha -z Hb =D H D H To reproduce the longitudinal depth (depth of field) of the image, lens L1 is used with respect to lens I. Hn The image is located outside the focal point F1′ on the output side of lens L1, and is a magnified real image I. Pn The front and back ends of all real image layers after imaging are a, respectively. P With b P Let a P b P The distances from the focus F1′ are z Pa z Pb The depth of field of the real image is D. P =z Pa -z Pb .

[0092] Let I be the reconstructed image of the n'-th layer hologram. Hn’ The plane and the front end a H The distance is △z Hn’ The distance to the focus F1 is: z Hn’ =z Ha +△z Hn’ (2-1)

[0093] Further set I Hn’ Real image I Pn’ The plane and a P The distance between them in the plane is △z Pn’ The distance to the focus F1′ is: z Pn’ =z Pa -△z Pn’ (2-2)

[0094] The horizontal magnification of the n'th layer image is:

[0095] 1≤n'≤n, where n' is the front end a of the image layer closest to lens L1 from the point of complete image reconstruction. H Plays the role of backend b H The number of layers between them, f1 is the distance from the center of lens L1 to the output side focal point F1′.

[0096] According to Newton's formula for an ideal imaging system, we can obtain: z Hn’ z Pn’ =f1 2 (2-4)

[0097] Right now

[0098] Let I Hn’ With adjacent reconstructed image I Hn’+1The layer spacing is Δl n’ Then for I Hn’+1 After L1 imaging, we have:

[0099]

[0100] In the formula △l′ n’ This is the distance between adjacent real image layers after imaging through the lens. Subtracting (2-6) from equation (2-5) yields:

[0101]

[0102] From this, we can obtain the vertical magnification:

[0103]

[0104] ΔZ Hn′ When = 0,

[0105] The above analysis shows that after the reconstructed image is imaged by the lens, the horizontal and vertical magnification of the image increases with the object depth Δz. Hn As the image changes, the real image IP will be distorted. In particular, the spacing between adjacent real image layers (Equation 2-7) is no longer equal. If the film layers in ML-PDLCs are arranged at equal intervals, then the image layer and the film layer cannot correspond one-to-one.

[0106] Example 3

[0107] Since the equidistant arrangement of PDLC films in ML-PDLCs is relatively easy to fabricate, in order to achieve a one-to-one correspondence between the image layer and the film layer, it is desirable for the image formed by lens L1 to be proportionally magnified to the original object. To achieve this, when adopting the arrangement of scale 1, the spatial coordinates of the original object in different layers of the hologram can be transformed during hologram calculation to compensate for the distortion caused by imaging through lens L1. Then, these coordinates are sequentially input into the SLM, illuminated by a laser, and projected onto the corresponding PDLC films equidistantly arranged in ML-PDLCs.

[0108] Transformation of the original object's horizontal coordinates:

[0109] Let Z be the distance between the front end face of the original object and the holographic recording plane. ao The distance between the nth layer of the object and the front face of the object is Δz. on The distance between this surface and the holographic recording plane is:

[0110] Z on =Z ao -△z on (2-9)

[0111] Let the n'th level Ion The coordinates of a certain point on the ground are x o According to equation (2-3), the coordinates of its image are:

[0112]

[0113] When △z Hn When = 0, that is, the coordinates of a certain point x on the front surface of the original object are 0. o After being imaged by lens L1, the coordinates of the conjugate point on the front plane ap of image I1 are x. Pn0 , With △z Hn’ Increase, with coordinates x at different levels on Image coordinates x Pn Gradually getting smaller. In order to make When calculating a hologram, the x-coordinates of the actual object point are shifted horizontally. on Transform using the following formula:

[0114] Transformation of the original object's longitudinal coordinates:

[0115] For the longitudinal interval, according to equation (2-7), when Δz Hn’ When = 0, In order to magnify the image formed by L1 proportionally to the original object, let the corresponding aperture contain the image-reproducing plane (i.e., a). H The interval Δl1 between a surface (n'=0) and its adjacent surface (n'=1) is a fixed value, representing the interlayer spacing between layers 0 and 1 of the 3D object.

[0116] To ensure that the interval between different adjacent image planes remains constant According to equation (2-7), let:

[0117]

[0118] If the spacing between adjacent PDLC films in ML-PDLCs is determined to be Δl′ n , Equation (2-11) can be written as:

[0119]

[0120]

[0121] make:

[0122]

[0123] The above equation can be simplified to (z) Han’ +△l n’ ) 2 =△l n’ z l0

[0124]

[0125] Solving the above equations, we finally obtain the layer spacing when calculating the hologram:

[0126]

[0127] The sign of the above formula is determined based on the actual parameters. For example, let Δl1 = 0.3 mm, z Ha =30mm, object depth of field is D H =30mm For n = 2, z Ha2 =z Ha +△l1=30.3mm

[0128]

[0129] When the value is negative, Δl2 = 0.3124 mm; when the value is positive, Δl2 = 2939.1 mm. Clearly, taking the negative sign aligns with the actual situation.

[0130]

[0131] or

[0132] The above calculation is quite complex and can be performed using a computer recursive method, i.e.:

[0133]

[0134]

[0135]

[0136] Substituting ΔZ into equation (2-13) Hn′ It can then be transformed into When calculating a hologram, the coordinates x of the nth layer of the actual object are plotted vertically. on The above formula is used to transform the image to compensate for the distortion caused by imaging through lens L1. This ensures that when the PDLC films in ML-PDLCs are arranged at equal intervals, the tomographic hologram reconstructed by the SLM is magnified proportionally to the original object after passing through L1, achieving a one-to-one correspondence between the image layer and the film layer. Furthermore, the center-to-center distance Δl'1 between adjacent polymer scattering liquid crystal films in the diffused laminate is equal, and... △l1 is the spacing between the reconstructed images of layers 0 to 1.

[0137] Example 4

[0138] To obtain a larger field of view for 3D display, the 3D image captured by the ML-PDLCs in Example 3 needs to be further magnified, as will be explained below. Figure 10 The optical path illustrates the imaging process. The diagram shows lens L2 imaging the three-dimensional image layers scattered by ML-PDLCs. Lens L2 is positioned along the normal C of the real image on the side of the diffuse laminator facing away from lens L1. Lens L2 magnifies and images the n-layer three-dimensional image layers scattered by the diffuse laminator, and the spacing between adjacent image layers after magnification is less than the resolving limit of the human eye along the normal C. Lens L2 is more than one focal length away from the nth three-dimensional image layer in the diffuse laminator. s The spacing between adjacent three-dimensional image layers is determined by equation (2-12). Let z be the distance between the nth image layer and the focal point F2. in After L2 imaging, the longitudinal magnification is:

[0139]

[0140] The interval between the corresponding magnified image layers is:

[0141]

[0142] The above equation shows that, with other parameters remaining constant, the closer the three-dimensional image layer is to the focal point F2 (i.e., z... in The smaller the value, the better. in The larger it is, the closer the three-dimensional image layer to F2 is to the very front of the object, a. p Let z be the distance between the foremost 3D image layer and the focal point F2. ia Then the maximum spacing between the magnified image layers is:

[0143]

[0144] When displaying three-dimensional images using tomography, the longitudinal variation can be considered continuous when the interval between adjacent magnified image layers is less than the longitudinal resolution limit of the human eye. The longitudinal resolution limit of the human eye. [5] yes:

[0145] ε is the angle that the human eye can resolve, and its limit is ε = 2.9 × 10⁻⁶. -4 rad, in practical applications ε can be taken as 4 × 10 - 4 rad,

[0146] L e ≈65mm is the interpupillary distance, z e This is the observation distance, that is, the distance between the human eye and the image. The above formula can be written as:

[0147] △z e =6.7×10 -6 z e 2 (3-5)

[0148] To ensure that the image layers are continuous when the human eye observes a magnified image, the following condition must be met: Δl′ imax <△z e ,Right now

[0149]

[0150] Equation (3-5) serves as the basis for parameter selection when designing the overall display system.

[0151] For example: Let z Ha =30mm, f1=50mm, z ia =10mm, f2=70mm,

[0152] z e =1500mm, the calculation yields the following layer spacing for the object's reconstructed image when calculating the hologram:

[0153]

[0154] The spacing between adjacent three-dimensional image layers in ML-PDLCs

[0155]

[0156] Referring to equation (2-12), the final horizontal magnification of the image is:

[0157] During the design process, parameters should be selected based on the actual condition of the device.

[0158] Example 5

[0159] Figure 11 This is a preferred embodiment of the present invention: a holographic 3D display system based on a polymer liquid crystal scattering film, comprising: a computer, a spatial light modulator, a diffusion laminate, an aperture, lenses L1 and L2, a first semi-reflecting mirror, and a second semi-reflecting mirror. The spatial light modulator and the diffusion laminate are arranged as in Embodiment 1 or Embodiment 2, and the PDLC films within the diffusion laminate are arranged at equal intervals. The aperture, lenses L1, and L2 are arranged similarly to those in Embodiment 4. The computer, following the method of Embodiment 3, transforms the spatial coordinates of the original objects in different layers of the hologram when calculating the hologram to compensate for the deformation caused by imaging through lens L1. The layer interval between the n' to n'+1th reconstructed images is Δl. n’ , The distance between the nth three-dimensional image layer and the focal point of lens L2 is z.ia , z e f1 is the observation distance, i.e., the distance between the human eye and the magnified image of lens L2, and f2 is the focal length of lens L2. The corresponding interval between adjacent three-dimensional image layers in ML-PDLCs is...

[0160] The scattering angle of the image points is expanded using a polymer liquid crystal scattering film (PDLC). The tomographic hologram I1, displayed by a color SLM, is imaged by lens L1 and then reflected by a semi-reflective mirror to form a real image I2. A diffusion laminate is placed at I2. The position of each real image layer in the tomographic hologram corresponds sequentially to the position of each PDLC scattering film layer in the diffusion laminate. When a real image layer is reproduced, the corresponding PDLC is in a scattering state, while the other layers are transparent. This one-to-one correspondence is achieved through synchronous control. If the time required to reproduce all layers is less than the visual persistence time of the human eye, a complete three-dimensional image with continuous depth will be seen. Lens L2 is used to image I2 again to adjust the image size and realism. Figure 11 The image given is a virtual image I3 formed after L2 imaging. To facilitate observation, a semi-reflecting mirror is used to reflect the image onto I3. 3’ This allows for through-see 3D display.

[0161] [4] Zheng Jihong, Zhong Yangwan, et al. Study on electro-controlled polymer-dispersed liquid crystal holographic lens and its properties. Acta Physica Sinica, 59(3), 2010

[0162] [5] Wang Hui. Wavefront Reconstruction 3D Display. Beijing: Science Press, 2016: 11.

Claims

1. A holographic 3D display system based on a polymer liquid crystal scattering film, characterized in that, include: A computer is used to create Fresnel holograms of n-layer two-dimensional images with data encoding. The n-layer two-dimensional images correspond one-to-one with the n-layer parallel cross-sections of the three-dimensional image of a 3D object, which are decomposed layer by layer from the back end plane to the front end plane. The spatial light modulator modulates the illumination light emitted by the light source module and reconstructs the reconstructed images of each layer of holograms in the reconstruction light field according to the loading sequence, so that the position of the n-layer reconstructed images corresponds to the position of the two-dimensional image of the reconstructed image in the three-dimensional image, and the size of the reconstructed image is consistent with the three-dimensional image of the 3D object. The diffusion laminate consists of M parallel polymer scattering liquid crystal films, where n≤M≤19. The positions of the n reconstructed images from the rear end plane to the front end plane in the reconstructed light field coincide one-to-one with the positions of the n polymer scattering liquid crystal films in the diffusion laminate. These n polymer scattering liquid crystal films are controlled by a computer. When the reconstructed image of the nth hologram is reconstructed, the polymer scattering liquid crystal films that coincide with the position of the reconstructed image of that layer are in a scattering state, scattering the reconstructed image into a three-dimensional image, while the remaining polymer scattering liquid crystal films are in a transparent state, allowing the reconstructed image to pass through without interference. An aperture, placed at the end face of the output window of the diffusion laminate, is used to block the zero-order term and conjugate image of the diffracted light; The response time of the polymer scattering liquid crystal film is T, the frame rate of the spatial light modulator is at least 1 / T Hz, and the pixel spacing of the spatial light modulator is... d slm Satisfy the following formula: d slm ≤ λZ o / 2L o , L o To reproduce the planar dimensions of the image, λ The wavelength of the illumination light, Z o To reproduce the distance between the image and the spatial light modulator, the planar dimensions of the diffuse laminate are not less than [specific dimensions to be filled in]. L o ， The response time refers to the total time for the polymer scattering liquid crystal film to go from the scattering state when the power is off to the transparent state when the power is on, and then back to the scattering state when the power is off again. Lens L1, aperture, and lens L1 are arranged sequentially along the normal G of the reconstructed image on the side of the spatial light modulator facing the diffusion laminate. The n-layer reconstructed image is located within the frame of the aperture, and the 0th layer reconstructed image, which is closest to lens L1 among the n-layer reconstructed images, is more than one focal length away from lens L1. The imaging optical path of the n-layer polymer scattering liquid crystal film lens L1, which is closest to lens L1 among the diffusion laminates, is more than one focal length away from lens L1. Lens L1 magnifies and images the n-layer reconstructed image into the diffusion laminate. The magnified real image of the n layers coincides with the position of the n-layer polymer scattering liquid crystal film in the diffusion laminate one by one, and the planar size of the real image is not larger than the planar size of the diffusion laminate. If the layer interval of the reconstructed image from layer n' to n'+1 is Δ l n’ Then the interlayer spacing of the n' to n'+1th polymer scattering liquid crystal layers ,in Let be the distance between the nth layer of the reproduced image and the input-side focal point of lens L1. For the nth layer reconstructed image and the nth layer n 'Distance of the image reproduced by the layer' Let L be the focal length of lens L1.

2. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 1, characterized in that, The response time refers to the total time it takes for the polymer scattering liquid crystal film to go from a scattering state with a transmittance of no more than 20% when the power is off to a transparent state after the power is on, and then back to a scattering state with a transmittance of no more than 20% when the power is off again.

3. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 2, characterized in that, The polymer scattering liquid crystal film takes 10ms to go from a scattering state with a transmittance of no more than 20% when the power is off to a transparent state after the power is on, and takes 100ms to go from a scattering state with a transmittance of no more than 20% after the power is on to a scattering state after the power is off.

4. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 2, characterized in that, The polymer scattering liquid crystal film takes 10ms to go from a scattering state with a transmittance of no more than 20% when the power is off to a transparent state after the power is on, and takes 60ms to go from a scattering state with a transmittance of no more than 20% after the power is on to a scattering state after the power is off.

5. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 2, characterized in that, The frame rate of the spatial light modulator is at least 25nHz, n is not greater than 19, and the response time of the polymer scattering liquid crystal film is not greater than 1 / 25n seconds.

6. The holographic 3D display system based on a polymer liquid crystal scattering film according to any one of claims 1 to 5, characterized in that, The center-to-center distance of adjacent polymer-scattering liquid crystal films in the diffusion laminate equal, ,and , The spacing between the reconstructed images of layers 0 to 1 is such that when the computer creates the hologram, it transforms the spatial coordinates of the original objects in the holograms of different layers to compensate for the deformation caused by imaging by lens L1, so that lens L1 magnifies the reconstructed images proportionally onto the corresponding polymer scattering liquid crystal films that are equally spaced in the diffusion laminate.

7. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 6, characterized in that, When calculating a hologram, the coordinates of the actual object point are plotted on the n'-th layer two-dimensional image plane. Transform using the following formula: And the coordinates of the n'th layer of the two-dimensional image of the actual object along the normal G direction. Transform using the following formula: , .

8. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 7, characterized in that, It also includes a lens L2, which is arranged along the normal C of the real image on the side of the diffusion laminate facing away from the lens L1. The lens L2 magnifies and images the n-layer three-dimensional image layer scattered by the diffusion laminate, and the interval between adjacent image layers after magnification is less than the resolution limit of the human eye along the normal C direction. The distance between the lens L2 and the n-th three-dimensional image layer in the diffusion laminate is more than one focal length.

9. The holographic 3D display system based on a polymer liquid crystal scattering film according to claim 8, characterized in that, The layer interval between the n' and n'+1 layers of the reconstructed image is Δ ln’ , The distance between the nth three-dimensional image layer and the focal point of lens L2 is Z. iα Z e It refers to the observation distance, that is, the distance between the human eye and the magnified image of lens L2. Let L be the focal length of lens L2.

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