WO2023015621A1 - 一种基于衍射模糊成像原理的无串扰全息3d显示方法 - Google Patents

一种基于衍射模糊成像原理的无串扰全息3d显示方法 Download PDF

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WO2023015621A1
WO2023015621A1 PCT/CN2021/115786 CN2021115786W WO2023015621A1 WO 2023015621 A1 WO2023015621 A1 WO 2023015621A1 CN 2021115786 W CN2021115786 W CN 2021115786W WO 2023015621 A1 WO2023015621 A1 WO 2023015621A1
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light field
diffraction
crosstalk
image
spatial spectrum
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王迪
庞应飞
王琼华
徐立军
李楠楠
李赵松
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北京航空航天大学
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    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/04—Processes or apparatus for producing holograms
    • G03H1/08—Synthesising holograms, i.e. holograms synthesized from objects or objects from holograms
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    • H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
    • H04N13/10—Processing, recording or transmission of stereoscopic or multi-view image signals
    • H04N13/106—Processing image signals
    • H04N13/122—Improving the 3D impression of stereoscopic images by modifying image signal contents, e.g. by filtering or adding monoscopic depth cues
    • H04N13/125—Improving the 3D impression of stereoscopic images by modifying image signal contents, e.g. by filtering or adding monoscopic depth cues for crosstalk reduction
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
    • H04N13/10—Processing, recording or transmission of stereoscopic or multi-view image signals
    • H04N13/106—Processing image signals
    • H04N13/128—Adjusting depth or disparity

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  • the present disclosure relates to holographic 3D display technology, and more specifically, the present disclosure relates to a crosstalk-free holographic 3D display method based on the principle of diffraction blur imaging.
  • holographic display can be divided into two steps of hologram recording and reproduction.
  • the principle of light interference is used to record the amplitude and phase information of the object in the form of interference fringes; in the reproduction process of the hologram, the principle of light diffraction is used to restore the same Wavefront information, thus providing all the depth information needed in human vision. Therefore, holographic display technology is considered to be one of the most ideal 3D display technologies.
  • holographic 3D display technology with complex images and full depth control is still difficult to realize. The fundamental reason is that when using 2D stored holograms to depict all the information required for complex 3D images, there is mutual influence between holographic projection images at different depths. .
  • the present disclosure proposes a crosstalk-free holographic 3D display method based on the principle of diffraction blur imaging.
  • the method includes three steps: the first step, for a 3D object, calculate the fuzzy light field distribution of the object according to Abbe's secondary imaging theory and the principle of Fresnel diffraction, and calculate the secondary Sub-diffraction fuzzy imaging conditions; the second step, based on the characteristics of secondary diffraction fuzzy imaging, establish the crosstalk relationship of light fields at different depths, calculate the crosstalk light field, and know that the crosstalk between one plane and another plane is actually the spatial spectrum of the plane The secondary diffraction blurred image on another plane; the third step, for the light field crosstalk between different depth planes, the spatial spectrum of the crosstalk light field forms the characteristics of a window matrix by superimposing the grating phase, so that the crosstalk light field takes the form of a window The form of the matrix is separated from the target light field, thereby generating a complex amplitude hologram, enabling the
  • step 1 the center of the object wave is located at the origin of the coordinates, and it propagates the light field along the z-axis direction
  • O( ⁇ , ⁇ ) represents the initial light field distribution of the object wave
  • O( ⁇ , ⁇ ) represents the initial light field distribution of the object wave
  • E(x k ,y k ,z k ) represents the distribution of the diffracted light field at a distance of z k after the object wave is superimposed on the lens.
  • E(x k ,y k ,z k ) and O( ⁇ , ⁇ ) is:
  • the spectrum image of the object wave is obtained when the object wave diffracts to the focal plane of the lens.
  • the spectral image is then re-diffracted as a new wave source.
  • the Fresnel diffraction image of the object wave is the blurred image of the object wave.
  • step 2 the two projected light fields on z s and z k planes are denoted as E(x s ,y s ,z s ) and E(x k ,y k ,z k ) respectively, and the projected light field E (x s ,y s ,z s ) will further propagate to the z k plane, and get a crosstalk light field
  • step 3 in order to eliminate the influence of the secondary diffraction blurred image of the spatial spectrum light wave on the target light field, a grating phase is added to the projected light field for convolution, so that the target light field only contains high-frequency signals, and the target light field uses the following expression:
  • I(x s , y s , z s ) represents the light intensity distribution of the projected light field
  • df x and df y represent the sampling intervals of f x and f y respectively
  • M and N represent the resolution of the hologram
  • ⁇ represents the Dirac function. Used to cancel the secondary phase envelope generated on the diffraction surface during Fresnel diffraction, It is a grating phase that convolves a large number of low-frequency signals in the projected light field into the high-frequency region, so that its spatial spectrum forms the characteristics of a window matrix.
  • the spatial spectrum information of the projected light field is transferred to a position away from the center of the spectrum, there is no spatial spectrum information at the position of the middle window, so the fuzzy image of the secondary diffraction of the spatial spectrum light wave is mainly distributed at the position away from the center of the projection surface, and it is not in the The target light field at the center of the projection surface produces crosstalk.
  • I(x b ,y b ,z b )
  • 2 is the light intensity distribution of the target light field, Represents the summation symbol. exist and Under the combined action of , the crosstalk light field is separated from the target light field in the form of a window matrix. When the reproduced light illuminates the hologram, a holographic 3D display effect without crosstalk is realized.
  • Figure 1 is a schematic flowchart of a crosstalk-free holographic 3D display method based on the principle of diffraction blur imaging according to the present disclosure.
  • FIG. 3 is the simulation comparison result diagram of the crosstalk-free holographic 3D display of the present disclosure.
  • Figures 3(a)-(b) are the crosstalk-free holographic 3D display results of the present disclosure
  • Figures 3(c)-(d) are holographic 3D display results when random phases are superimposed.
  • the crosstalk light field has been completely separated from the target light field, which means that under the action of the grating phase, the spatial spectrum of the projected image is changed, so that the crosstalk as a blurred image of the spatial spectrum will also change accordingly, and finally the crosstalk is realized. Separation of the light field from the target image. Therefore, using the method proposed in the present disclosure can effectively eliminate the influence of crosstalk, and the average standard error value of the two planes is about 0.06.
  • a group of control groups is set up to compare the simulation effect with the present disclosure.
  • the present disclosure provides a crosstalk-free holographic 3D display method based on the principle of diffraction fuzzy imaging, which can eliminate light field crosstalk between images of different depths, and achieve high-quality holographic 3D display effects without crosstalk, thereby improving The quality of the holographic 3D display.

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Abstract

一种基于衍射模糊成像原理的无串扰全息3D显示方法，包括三个步骤：第一步，对于一个3D物体，根据阿贝二次成像理论和菲涅尔衍射原理计算出物体的模糊光场分布，并计算物体的二次衍射模糊成像条件；第二步，基于二次衍射模糊成像特点建立不同深度面光场的串扰关系，计算出串扰光场；第三步，对不同深度面之间的光场串扰，通过叠加光栅相位使串扰光场的空间频谱形成窗口矩阵的特点，使串扰光场以窗口矩阵的形式与目标光场分离，从而生成复振幅全息图，实现无串扰的全息3D显示效果。

Description

一种基于衍射模糊成像原理的无串扰全息3D显示方法
相关申请的交叉引用
本公开要求于2021年8月13日提交中国专利局的申请号为2021109300001、名称为“一种基于衍射模糊成像原理的无串扰全息3D显示方法”的中国专利申请的优先权，其全部内容通过引用结合在本公开中。
技术领域
本公开涉及全息3D显示技术，更具体地说，本公开涉及一种基于衍射模糊成像原理的无串扰全息3D显示方法。
背景技术
根据全息技术的基本原理，全息显示可分为全息图的记录和再现两个步骤。在全息图的记录过程中，利用了光的干涉原理，以干涉条纹的形式记录物体的振幅和相位信息；在全息图的再现过程中，利用了光的衍射原理，恢复出与被记录物体相同的波前信息，从而提供了人眼视觉里所需要的全部深度信息。因此，全息显示技术被认为是最理想的3D显示技术之一。然而，复杂图像与全深度控制的全息3D显示技术依然难以实现，其根本原因在于当使用2D存储的全息图描绘复杂3D图像所需的所有信息时，不同深度的全息投影图像之间存在相互影响。由于激光具有很高的相干性，在全息重建过程中，单个像点会以艾里斑的形式重建出来，而相邻像点之间则存在一定的重叠区域，这部分区域会发生干涉从而引入串扰光，影响观看效果。虽然国内外学者提出了不少降低串扰的方法，如波前整形法和/或添加随机相位因子等，但这些方法只能在一定程度上提高全息3D显示的质量，无法完全消除不同深度图像之间的串扰。
发明内容
本公开提出一种基于衍射模糊成像原理的无串扰全息3D显示方法。如附图1所示，该方法包括三个步骤：第一步，对于一个3D物体，根据阿贝二次成像理论和菲涅尔衍射原理计算出物体的模糊光场分布，并计算物体的二次衍射模糊成像条件；第二步，基于二次衍射模糊成像特点建立不同深度面光场的串扰关系，计算出串扰光场，得知一个平面对另一个平面的串扰其实是该平面的空间频谱在另一个平面上的二次衍射模糊像；第三步，对不同深度面之间的光场串扰，通过叠加光栅相位使串扰光场的空间频谱形成窗口矩阵的特点，使串扰光场以窗口矩阵的形式与目标光场分离，从而生成复振幅全息图，使目标光场 实现无串扰的全息3D显示效果。
在步骤一中，如附图2所示，物波的中心位于坐标原点处，其沿z轴方向进行光场传播，O(ξ,η)代表物波的初始光场分布，接着在物波上叠加焦距为z s的透镜相位信息
Figure PCTCN2021115786-appb-000001
E(x k,y k,z k)表示物波叠加了透镜之后在距离为z k的衍射光场分布，根据菲涅尔衍射原理，E(x k,y k,z k)与O(ξ,η)的关系为：
Figure PCTCN2021115786-appb-000002
其中j表示虚数符号，λ表示波长，
Figure PCTCN2021115786-appb-000003
表示衍射距离为z＝z k的菲涅尔正衍射。当衍射距离为透镜的焦距，即z k＝z s时，菲涅尔衍射像是聚焦的；当z k≠z s时，菲涅尔衍射像是离焦的，此时E(x k,y k,z k)为O(ξ,η)的模糊像。
在焦距为z s的透镜相位的作用下，物波衍射到透镜的焦面时得到物波的频谱图像。然后该频谱图像作为新的波源会发生二次衍射。将物波O(ξ,η)的高度记为L H＝md ξ，其中，m和d ξ分别表示物波在ξ方向的像素数和像素尺寸，根据衍射计算得出二次衍射模糊成像条件为：当
Figure PCTCN2021115786-appb-000004
时，z∈[z m,∞)且z≠z s；当
Figure PCTCN2021115786-appb-000005
时，z∈[z m,z′ m]且z≠z s。其中，
Figure PCTCN2021115786-appb-000006
Figure PCTCN2021115786-appb-000007
当衍射距离z满足上述两个条件中的任意一个条件，则物波的菲涅尔衍射图像就是该物波的模糊像。
在步骤二中，将两个位于z s和z k平面的投影光场分别记为E(x s,y s,z s)和E(x k,y k,z k)，投影光场E(x s,y s,z s)会进一步传播到z k面，得到一个串扰光场
Figure PCTCN2021115786-appb-000008
Figure PCTCN2021115786-appb-000009
其中，
Figure PCTCN2021115786-appb-000010
表示在衍射距离为z s时的菲涅尔逆衍射。与此同时，受到光场
Figure PCTCN2021115786-appb-000011
的串扰，z k面上的重建光场E′(x k,y k,z k)表示成：
Figure PCTCN2021115786-appb-000012
此时的
Figure PCTCN2021115786-appb-000013
为z s面对z k面的光场串扰。反过来，z k面对z s面也会造成光场串扰，表示为
Figure PCTCN2021115786-appb-000014
根据计算可得出：
Figure PCTCN2021115786-appb-000015
式中
Figure PCTCN2021115786-appb-000016
表示傅里叶逆变换，空间频谱坐标f x和f y满足关系：f x＝ξ/λz s,f y＝η /λz s。使用O s(f x,f y)表示光场
Figure PCTCN2021115786-appb-000017
的空间频谱，公式(6)则表达为：
Figure PCTCN2021115786-appb-000018
其中，O s(-f x,-f y)是光场
Figure PCTCN2021115786-appb-000019
的空间频谱O s(f x,f y)的倒立像，因此，串扰
Figure PCTCN2021115786-appb-000020
其实是投影光场的空间频谱叠加上焦距为z s的透镜相位后在衍射距离为z＝z k处的菲涅尔衍射光场，即串扰
Figure PCTCN2021115786-appb-000021
其实是空间频谱光波的二次衍射模糊像。
在步骤三中，为了消除空间频谱光波的二次衍射模糊像对目标光场的影响，在投影光场上添加光栅相位进行卷积，使得目标光场只含高频信号，目标光场用下式表示：
Figure PCTCN2021115786-appb-000022
Figure PCTCN2021115786-appb-000023
Figure PCTCN2021115786-appb-000024
其中，I(x s,y s,z s)表示投影光场的光强分布，df x和df y分别表示f x和f y的采样间隔，M和N表示全息图的分辨率，-M≤m≤M,-N≤n≤N。δ表示Dirac函数。
Figure PCTCN2021115786-appb-000025
用于抵消菲涅尔衍射时在衍射面上产生的二次相位包络，
Figure PCTCN2021115786-appb-000026
是一个光栅相位，将投影光场中的大量低频信号卷积到高频区域内，从而使其空间频谱形成窗口矩阵的特点。由于投影光场的空间频谱信息被转移到偏离频谱中心的位置，使得中间窗口位置处无空间频谱信息，因此空间频谱光波的二次衍射模糊像主要分布在偏离投影面中心的位置，其不对位于投影面中心的目标光场产生串扰。
对公式(5)进行逆菲涅尔变换，求得重建光场的菲涅尔全息图，最终所得到的全息图复 振幅分布H表示为：
Figure PCTCN2021115786-appb-000027
其中I(x b,y b,z b)＝|E(x b,y b,z b)| 2就是目标光场的光强分布，
Figure PCTCN2021115786-appb-000028
表示求和符号。在
Figure PCTCN2021115786-appb-000029
和
Figure PCTCN2021115786-appb-000030
的共同作用下，串扰光场以窗口矩阵的形式与目标光场分离。当再现光照射全息图时，实现无串扰的全息3D显示效果。
附图说明
附图1为本公开的一种基于衍射模糊成像原理的无串扰全息3D显示方法的流程示意图。
附图2为本公开的物体的模糊成像过程示意图。
附图3为本公开的无串扰全息3D显示的仿真对比结果图。附图3(a)-(b)为本公开的无串扰全息3D显示结果，附图3(c)-(d)为叠加随机相位时的全息3D显示结果。
上述各附图中的图示标号为：
(1)叠加透镜相位后的物波；(2)透镜的焦平面；(3)模糊像。
应该理解上述附图只是示意性的，并没有按比例绘制。
具体实施方式
下面详细说明本公开提出的一种基于衍射模糊成像原理的无串扰全息3D显示方法的实施例，对本公开进行进一步的描述。有必要在此指出的是，以下实施例只用于本公开做进一步的说明，不能理解为对本公开保护范围的限制，该领域技术熟练人员根据上述发明内容对本公开做出一些非本质的改进和调整，仍属于本公开的保护范围。
为了实现无串扰的全息3D显示，使用位于两个不同深度平面的两幅图像“美女”和“猩猩”作为被记录物体，其分辨率均为200×200，对应的投影深度分别为7.68cm和18.44cm。接着，将这两幅投影图像的复振幅信息提取出来，并分别叠加透镜相位。令m＝M＝1000，n＝M＝1000，设置光波的波长为532nm，叠加光栅相位使两个投影深度面的目标光场与其串扰光场相互分离，根据公式(11)生成分辨率为1000×1000的全息图，全息图的像素大小为d ξ＝d η＝6.4μm。当使用平面波照射该全息图时，其在深度为7.68cm和18.44cm处的仿真重建结果分别如附图3(a)和附图3(b)所示，可以看到，对应深度面的再现像被清晰地重现出来。此时的串扰光场已经完全和目标光场分离开，这说明在光栅相位的作用下，投影图像的空间频谱被改变，从而作为空间频谱模糊像的串扰也会随之改变，最终实现了串扰光 场与目标图像的分离。因此，采用本公开所提出的方法能有效地消除串扰的影响，两个平面的平均标准误差值约为0.06。同时，为了进一步说明本公开中消除光场串扰的效果，设置了一组对照组与本公开进行了仿真效果对比。当给每个投影图像施加一个随机相位，即
Figure PCTCN2021115786-appb-000031
为随机相位时，串扰被离散成了随机散斑，其在深度为7.68cm和18.44cm处的结果如附图3(c)和附图3(d)所示，此时的两个平面的平均标准误差值约为0.44。因此，当
Figure PCTCN2021115786-appb-000032
为随机相位时，重建光场会受到串扰的影响。因此，本公开的方法能实现高质量的全息3D显示效果。
工业实用性
综上所述，本公开提供了一种基于衍射模糊成像原理的无串扰全息3D显示方法，其能够消除不同深度图像之间的光场串扰，实现无串扰高质量的全息3D显示效果，从而提高全息3D显示的质量。

Claims (4)

  1. 一种基于衍射模糊成像原理的无串扰全息3D显示方法，其特征在于，所述方法包括三个步骤：第一步，对于一个3D物体，根据阿贝二次成像理论和菲涅尔衍射原理计算出物体的模糊光场分布，并计算物体的二次衍射模糊成像条件；第二步，基于二次衍射模糊成像特点建立不同深度面光场的串扰关系，计算出串扰光场，得知一个平面对另一个平面的串扰其实是所述平面的空间频谱在另一个平面上的二次衍射模糊像；第三步，对不同深度面之间的光场串扰，通过叠加光栅相位使串扰光场的空间频谱形成窗口矩阵的特点，使串扰光场以窗口矩阵的形式与目标光场分离，从而生成复振幅全息图，使目标光场实现无串扰的全息3D显示效果。
  2. 根据权利要求1所述的一种基于衍射模糊成像原理的无串扰全息3D显示方法，其特征在于，在步骤一中，物波的中心位于坐标原点处，其沿z轴方向进行光场传播，O(ξ,η)代表物波的初始光场分布，接着在物波上叠加焦距为z s的透镜相位信息
    Figure PCTCN2021115786-appb-100001
    E(x k,y k,z k)表示物波叠加了透镜之后在距离为z k的衍射光场分布，根据菲涅尔衍射原理，E(x k,y k,z k)与O(ξ,η)的关系为：
    Figure PCTCN2021115786-appb-100002
    其中j表示虚数符号，λ表示波长，
    Figure PCTCN2021115786-appb-100003
    表示衍射距离为z＝z k的菲涅尔正衍射，当衍射距离为透镜的焦距，即z k＝z s时，菲涅尔衍射像是聚焦的；当z k≠z s时，菲涅尔衍射像是离焦的，此时E(x k,y k,z k)为O(ξ,η)的模糊像；
    在焦距为z s的透镜相位的作用下，物波衍射到透镜的焦面时得到物波的频谱图像，然后所述频谱图像作为新的波源会发生二次衍射，将物波O(ξ,η)的高度记为L H＝md ξ，其中，m和d ξ分别表示物波在ξ方向的像素数和像素尺寸，根据衍射计算得出二次衍射模糊成像条件为：当
    Figure PCTCN2021115786-appb-100004
    时，z∈[z m,∞)且z≠z s；当
    Figure PCTCN2021115786-appb-100005
    时，z∈[z m,z′ m]且z≠z s；其中，
    Figure PCTCN2021115786-appb-100006
    Figure PCTCN2021115786-appb-100007
    当衍射距离z满足上述两个条件中的任意一个条件，则物波的菲涅尔衍射图像就是所述物波的模糊像。
  3. 根据权利要求1所述的一种基于衍射模糊成像原理的无串扰全息3D显示方法，其特征在于，在步骤二中，将两个位于z s和z k平面的投影光场分别记为E(x s,y s,z s)和E(x k,y k,z k)，投影光场E(x s,y s,z s)会进一步传播到z k面，得到一个串扰光场
    Figure PCTCN2021115786-appb-100008
    Figure PCTCN2021115786-appb-100009
    其中，
    Figure PCTCN2021115786-appb-100010
    表示在衍射距离为z s时的菲涅尔逆衍射，与此同时，受到光场
    Figure PCTCN2021115786-appb-100011
    的串扰，z k面上的重建光场E′(x k,y k,z k)表示成：
    Figure PCTCN2021115786-appb-100012
    此时的
    Figure PCTCN2021115786-appb-100013
    为z s面对z k面的光场串扰，反过来，z k面对z s面也会造成光场串扰，表示为
    Figure PCTCN2021115786-appb-100014
    根据计算得出：
    Figure PCTCN2021115786-appb-100015
    式中
    Figure PCTCN2021115786-appb-100016
    表示傅里叶逆变换，空间频谱坐标f x和f y满足关系：f x＝ξ/λz s,f y＝η/λz s，使用O s(f x,f y)表示光场
    Figure PCTCN2021115786-appb-100017
    的空间频谱，上式则表达为：
    Figure PCTCN2021115786-appb-100018
    其中，O s(-f x,-f y)是光场
    Figure PCTCN2021115786-appb-100019
    的空间频谱O s(f x,f y)的倒立像，因此，串扰
    Figure PCTCN2021115786-appb-100020
    其实是投影光场的空间频谱叠加上焦距为z s的透镜相位后在衍射距离为z＝z k处的菲涅尔衍射光场，即串扰
    Figure PCTCN2021115786-appb-100021
    其实是空间频谱光波的二次衍射模糊像。
  4. 根据权利要求1所述的一种基于衍射模糊成像原理的无串扰全息3D显示方法，其特征在于，在步骤三中，为了消除空间频谱光波的二次衍射模糊像对目标光场的影响，在投影光场上添加光栅相位进行卷积，使得目标光场只含高频信号，目标光场用下式表示：
    Figure PCTCN2021115786-appb-100022
    Figure PCTCN2021115786-appb-100023
    Figure PCTCN2021115786-appb-100024
    其中，I(x s,y s,z s)表示投影光场的光强分布，df x和df y分别表示f x和f y的采样间隔，M和N表示全息图的分辨率，-M≤m≤M,-N≤n≤N，δ表示Dirac函数，
    Figure PCTCN2021115786-appb-100025
    用于抵消菲涅尔衍射时在衍射面上产生的二次相位包络，
    Figure PCTCN2021115786-appb-100026
    是一个光栅相位，将投影光场中的大量低频信号卷积到高频区域内，从而使其空间频谱形成窗 口矩阵的特点，由于投影光场的空间频谱信息被转移到偏离频谱中心的位置，使得中间窗口位置处无空间频谱信息，因此空间频谱光波的二次衍射模糊像主要分布在偏离投影面中心的位置，其不对位于投影面中心的目标光场产生串扰；
    最终所得到的全息图复振幅分布H表示为：
    Figure PCTCN2021115786-appb-100027
    其中I(x b,y b,z b)＝|E(x b,y b,z b)| 2就是目标光场的光强分布，
    Figure PCTCN2021115786-appb-100028
    表示求和符号，在
    Figure PCTCN2021115786-appb-100029
    和
    Figure PCTCN2021115786-appb-100030
    的共同作用下，串扰光场以窗口矩阵的形式与目标光场分离，当再现光照射全息图时，实现无串扰的全息3D显示效果。
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