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全息技术能同时记录物体的振幅信息和相位信息,实现3维立体显示效果,被广泛应用于3维显示领域[1-8]。根据人眼视觉的需要,彩色动态3维全息必将是全息技术的最终目标[9-12]。彩色动态全息技术根据观察效果可分为彩色全息视频显示和彩色动感全息。由于彩色全息视频显示技术的光路复杂,对仪器设备要求高,需红、绿、蓝三色光同时再现,一般适合实验室观看。而利用彩虹全息技术制作的彩色动感全息,其采用二步法拍摄, 首先在菲涅耳线全息上记录一系列体视对,然后引入参考光与体视对再现重合像干涉,制得彩色彩虹全息图。彩色彩虹全息图通过人眼的水平移动将呈现出一系列动态效果, 其制作成本低、方便复制和携带。
为了进一步简化彩色动感全息的制作流程,提高再现像质量,本文中利用计算全息可以灵活地编码实际光波的相位和振幅,结合计算全息和光学全息技术,提出了一种计算编码制彩色动态3维全息图的方法。首先采集每个分动作对应的彩色物点;其次基于色度学原理,将各彩色物点分解为3个不同位置的分色物点,对应的位置由全息图的再现关系计算确定;再次在同一平面上记录各三分色物点所对应含体视对的3张线分色全息图,因分色物点位置已经过计算编码,所以线分色全息图经同一波长的共轭光再现后,各动作对应的三分色再现像可在同一平面完全重合;最后引入参考光与重合像干涉,记录彩色全息图。此彩色全息图经再现后,随着双眼位置的轻微移动,可见不同的动作像,从而实现彩色动态效果。本文中经理论分析和实验,验证了此方法的可行性。
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根据全息的基本原理,若用波长为λ的共轭平面光波再现分色全息图H1,r, H1,g, H1,b,它们的再现像位置与参考光、物点、再现光满足以下关系式[13]:
$ \left\{ \begin{array}{l} {x_{\rm{i}}} = {x_o} + \left( {{\lambda _{{\rm{r, g, b}}}}/\lambda - 1} \right){z_o}\tan \theta \\ {y_{\rm{i}}} = {y_o} + \left( {{\lambda _{r, g, b}}/\lambda - 1} \right){z_o}\tan \theta \\ {z_{\rm{i}}} = {\lambda _{{\rm{r, g, b}}}}{z_o}/\lambda \end{array} \right. $
(1) 式中,(xo, yo, zo)为物点的坐标;λr, g, b分别取λr, λg, λb,其为分色全息图对应H1, r, H1, g, H1, b的计算波长;(xi, yi, zi)是H1, r, H1, g, H1, b再现像中任意点的坐标;(yz, zz)和(yc, zc)分别为参考光源和再现光源在y轴及z轴上的坐标,tanθ=yz/zz=yc/zc。由(1)式可知,对同一位置的分色全息,它们的再现像位置不同。为了获取彩色像点,需三分色像的再现像位置完全相同,才能在空间重合,实现彩色效果。以往的很多文献中通过改变分色全息图放置的位置,从而使分色像重合的,但此方法操作麻烦,对光路要求高,且会带来一系列不必要的噪声。根据全息图物像关系,结合色度学原理,利用计算机等效编码,通过改变物点坐标,制作同一平面上不同位置的分色全息图,使它们能在同一平面再现时再现像完全重合。
对于空间坐标为(xo, yo, zo),颜色信息为(ro, go, bo)的彩色物点,可将其分解成红、绿、蓝3个分色物点[14],分别为(xo, r, yo, r, zo, r, ro),(xo, g, yo, g, zo, g, go)和(xo, b, yo, b, zo, b, bo)(如图 1所示)。并在同一平面上计算三分色物点Or, Og, Ob对应的物光波分布,分别引入平行光λr, λg, λb作为参考光,θr为平行光的入射角,记录两者干涉后的分色全息图H1, r, H1, g, H1, b[15-16]。根据(1)式可得,H1, r, H1, g, H1, b经波长为λ的光波再现后,三分色像点的坐标为:
$ \left\{ \begin{array}{l} \left\{ \begin{array}{l} {x_{\rm{r}}} = {x_{{\rm{o, r}}}} + \left( {{\lambda _{\rm{r}}}/\lambda - 1} \right){z_{{\rm{o, r}}}}\tan \theta \\ {y_{\rm{r}}} = {y_{{\rm{o, r}}}} + \left( {{\lambda _{\rm{r}}}/\lambda - 1} \right){z_{{\rm{o, r}}}}\tan \theta \\ {z_{\rm{r}}} = {\lambda _{\rm{r}}}{z_{{\rm{o, r}}}}/\lambda \end{array} \right.\\ \left\{ \begin{array}{l} {x_{\rm{g}}} = {x_{{\rm{o, g}}}} + \left( {{\lambda _{\rm{g}}}/\lambda - 1} \right){z_{{\rm{o, g}}}}\tan \theta \\ {y_{\rm{g}}} = {y_{{\rm{o, g}}}} + \left( {{\lambda _{\rm{g}}}/\lambda - 1} \right){z_{{\rm{o, g}}}}\tan \theta \\ {z_{\rm{g}}} = {\lambda _{\rm{g}}}{z_{{\rm{o, g}}}}/\lambda \end{array} \right.\\ \left\{ \begin{array}{l} {x_{\rm{b}}} = {x_{{\rm{o, b}}}} + \left( {{\lambda _{\rm{b}}}/\lambda - 1} \right){z_{{\rm{o, b}}}}\tan \theta \\ {y_{\rm{b}}} = {y_{{\rm{o, b}}}} + \left( {{\lambda _{\rm{b}}}/\lambda - 1} \right){z_{{\rm{o, b}}}}\tan \theta \\ {z_{\rm{b}}} = {\lambda _{\rm{b}}}{z_{{\rm{o, b}}}}/\lambda \end{array} \right. \end{array} \right. $
(2) 为了实现真正的原彩色物体再现,需三分色像在空间上完全重合,即:
$ \left\{ \begin{array}{l} {x_{\rm{r}}} = {x_{\rm{g}}} = {x_{\rm{b}}}\\ {y_{\rm{r}}} = {y_{\rm{g}}} = {y_{\rm{b}}}\\ {z_{\rm{r}}} = {z_{\rm{g}}} = {z_{\rm{b}}} \end{array} \right. $
(3) 因此需调整计算全息图H1, r, H1, g, H1, b的参量设置,将三分色物点空间坐标调整如下:
$ \left\{ \begin{array}{l} \left\{ \begin{array}{l} {z_{{\rm{o, z}}}} = \lambda {z_{\rm{o}}}/{\lambda _{\rm{r}}}\\ {x_{{\rm{o, r}}}}{\rm{ = }}{x_{\rm{o}}}\\ {y_{{\rm{o, r}}}} = {y_{\rm{o}}} \end{array} \right.\\ \left\{ \begin{array}{l} {z_{{\rm{o, g}}}} = \lambda {z_{\rm{o}}}/{\lambda _{\rm{g}}}\\ {x_{{\rm{o, g}}}} = {x_{\rm{o}}} + \left( {1/{\lambda _{\rm{g}}} - 1/{\lambda _{\rm{r}}}} \right)\lambda {z_{\rm{o}}}\tan \theta \\ {y_{{\rm{o, g}}}} = {y_{\rm{o}}} + \left( {1/{\lambda _{\rm{g}}} - 1/{\lambda _{\rm{r}}}} \right)\lambda {z_{\rm{o}}}\tan \theta \end{array} \right.\\ \left\{ \begin{array}{l} {z_{{\rm{o, b}}}} = \lambda {z_{\rm{o}}}/{\lambda _b}\\ {x_{{\rm{o, b}}}} = {x_{\rm{o}}} + \left( {1/{\lambda _b} - 1/{\lambda _{\rm{r}}}} \right)\lambda {z_{\rm{o}}}\tan \theta \\ {y_{{\rm{o, b}}}} = {y_{\rm{o}}} + \left( {1/{\lambda _b} - 1/{\lambda _{\rm{r}}}} \right)\lambda {z_{\rm{o}}}\tan \theta \end{array} \right. \end{array} \right. $
(4) 将(4)式代入(2)式可知,经编码调整后的三分色物点,若在同一平面记录其全息图,并用共轭光Rλ*再现,它们的再现像能在空间上完全重合(如图 2所示),从而实现真正的彩色再现。
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设计分色全息图时,需在分色全息图上设置一系列全息体视对,使全息图再现时,能看到一系列动态再现像,从而实现动态效果[17]。因为人眼瞳孔的大小一般为3mm,所以直接将分色全息图设置成宽度为3mm~5mm的线形全息图,这样可以大大减少计算时间和计算量。此时线全息图除了具有分色全息图功能,还兼具了狭缝的作用[18-19]。一个体视对左右体视窗的距离取人眼两瞳孔之距6.5cm,依次记录线全息图上的所有体视全息对(如图 3所示), 图中, L1,L2,L3分别对应第1, 2, 3个体视对的左视窗,R1,R2,R3分别对应第1, 2, 3个体视对的右视窗。彩色全息图再现时,随着人眼的快速移动能看见不同动作对应的视窗,能够产生动态效果。
计算全息图时,线全息图上的每一个体视全息对可视为动态物点上发出的光波在传播过程中被两个孔径所限制而形成的。
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彩色全息图的拍摄采用光学方法拍摄,整个彩色动态全息图的制作流程如图 4所示。He-Ne激光器发出波长为λr=632.8nm的激光经分束镜分成两路,一路经滤波准直后为平行光,用于共轭再现H1(含H1, r, H1, g, H1, b);另一路同样经滤波准直后为平行光,充当参考光,在H1再现像重合平面上,两光束干涉后,用光学方法记录彩色全息图H2。
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为了实验验证,获取了彩色物体的两个分动作的颜色信息F(i, j, k)和空间信息(i, j, k),对于分动作的任一彩色物点,经分色处理后,基色物点的颜色信息分别为fr(i, j, k), fg(i, j, k), fb(i, j, k),空间信息经等效计算编码后,三基色物点的等效空间坐标为(ir, jr, kr), (ig, jg, kg), (ib, jb, kb),则各分色全息图平面上(x, y, z)的模拟物光分布为[20]:
$ \left\{ \begin{array}{l} {o_{\rm{r}}}\left( {x,y,z} \right) = \sum\limits_{i,j,k}^{I,J,K} {{f_{\rm{r}}}\left( {i,j,k} \right)\exp \left\{ {{\rm{i}}\frac{{2\pi }}{{{\lambda _{\rm{r}}}}}\frac{{{{\left( {x - {i_{\rm{r}}}\Delta {x_{\rm{o}}}} \right)}^2} + {{\left( {y - {j_{\rm{r}}}\Delta {y_{\rm{o}}}} \right)}^2} + {{\left( {z - {k_{\rm{r}}}\Delta {z_{\rm{o}}}} \right)}^2}}}{{{{\left[ {{z_{{\rm{o,r}}}} + h\left( {{i_{\rm{r}}},{j_{\rm{r}}},{k_{\rm{r}}}} \right)} \right]}^2}}}} \right.} \\ {o_{\rm{g}}}\left( {x,y,z} \right) = \sum\limits_{i,j,k}^{I,J,K} {{f_{\rm{g}}}\left( {i,j,k} \right)\exp \left\{ {{\rm{i}}\frac{{2\pi }}{{{\lambda _{\rm{g}}}}}\frac{{{{\left( {x - {i_{\rm{g}}}\Delta {x_{\rm{o}}}} \right)}^2} + {{\left( {y - {j_{\rm{g}}}\Delta {y_{\rm{o}}}} \right)}^2} + {{\left( {z - {k_{\rm{g}}}\Delta {z_{\rm{o}}}} \right)}^2}}}{{{{\left[ {{z_{{\rm{o,g}}}} + h\left( {{i_{\rm{g}}},{j_{\rm{g}}},{k_{\rm{g}}}} \right)} \right]}^2}}}} \right.} \\ {o_{\rm{b}}}\left( {x,y,z} \right) = \sum\limits_{i,j,k}^{I,J,K} {{f_{\rm{b}}}\left( {i,j,k} \right)\exp \left\{ {{\rm{i}}\frac{{2\pi }}{{{\lambda _{\rm{b}}}}}\frac{{{{\left( {x - {i_{\rm{b}}}\Delta {x_{\rm{o}}}} \right)}^2} + {{\left( {y - {j_{\rm{b}}}\Delta {y_{\rm{o}}}} \right)}^2} + {{\left( {z - {k_{\rm{b}}}\Delta {z_{\rm{o}}}} \right)}^2}}}{{{{\left[ {{z_{{\rm{o,b}}}} + h\left( {{i_{\rm{b}}},{j_{\rm{b}}},{k_{\rm{b}}}} \right)} \right]}^2}}}} \right.} \end{array} \right. $
(5) 式中, h(i, j, k)为离记录面最近的物点到记录面的距离; Δx0, Δy0, Δz0分别为3维物体的取样间隔; zo, r, zo, g, zo, g分别为分色物点的等效记录距离,zo, r=400μm, zo, g=491.97μm, zo, b=552.78μm。根据(5)式计算全息记录面上所有体视对区域对应的物光波分布并与参考光干涉,获得三分色菲涅耳全息图H1, r, H1, g, H1, b。其中H1, r, H1, g, H1, b的计算波长为λr=632.8nm, λg=514.5nm, λb=457.9nm,全息图的采样间隔为0.0015mm,参考光角度为4°, H1, r, H1, g, H1, b的尺寸为3mm×30mm,单个体视窗长度为3mm,体视对间距为6.5cm,H1, r, H1, g, H1, b的记录波长为λ=632.8nm。H1, r, H1, g, H1, b经共轭光再现后,与参考光干涉,记录彩色全息图H2。图 5a、图 5b为原彩色物体的两个动作,图 5c、图 5d为H2的彩色再现像。
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通过研究全息图的物像关系,利用计算全息可编码物光波的灵活性,提出了一种计算编码制彩色动态全息的方法。此方法不仅能有效解决彩色动态全息图再现像难重合,对光路拍摄要求高的问题;另外,此方法有效避免了一些不必要的噪声,提高了再现像的质量;并且该方法简单易行、方便操作。经实验验证,该方法切实可行,在3维显示方面具有较好的应用价值。
编码法制彩色动态全息
Making color dynamic holograms by the coding method
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摘要: 为了获取高质量的彩色动态全息,采用计算机编码的方法,提出了一种制彩色动态全息的新方法。根据色度学和采样原理, 将任一分动作物点分解为红、绿、蓝三基色物点,计算编码调整三基色物点的位置,使它们对应的含体视对的3张分色全息图放置在同一平面上, 经共轭光再现后,所有体视对的再现像能在空间上完全重合,并记录重合像与参考光干涉后的彩色全息图。结果表明,彩色全息图经再现后,随着人眼位置的移动,可见不同的动作像,从而实现彩色动态效果。此方法能有效解决彩色动态全息图再现像难重合、对实验条件要求高的问题;且操作简单易行,能有效避免一些不必要的噪声,在3维显示方面具有较好的应用价值。Abstract: In order to make a nice hologram, a new method to create a color dynamic hologram by computer coding was proposed. According to the colorimetry principles and the sampling principle, an object point of every behaves can be resolved into three primary color objects as red, blue and green, whose coordinate data are coded by the computer in order to let their monochromatic stereoscopic holograms have a pefect overlap when they are placed in a plane and reappeared by conjugate light. The overlapping images interferenced with the reference light to form a dynamic color hologram. The experiment shows that a dynamin visual can be seen with the movement of the position of the eyes when the color hologram is reproduced. This method can effectively solve the problem that difficult overlap of images with low experimental conditions, which also avoid some unnecessary noise with simple operation, and has good application value in 3-D display.
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Key words:
- information optics /
- dynamic hologram /
- coding method /
- colorimetric principle
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