-
文中利用三维琼斯偏振光追迹矩阵[25-26]对人眼光学结构的偏振传输过程进行计算,从而建立人眼三维琼斯偏振感知模型。三维琼斯偏振光追迹矩阵是将传统的二维琼斯矩阵拓展至三维空间,描述了三维矢量光场中光学元件或系统对光束偏振态的改变,同时也表征了光学结构自身的偏振特性[27-28]。由于三维偏振追迹方法能精确计算三维矢量光场中光学系统或光学元件偏振态变化,非常适合用于人眼三维偏振感知模型的研究。人眼对线偏振光的偏振感知成像简化模型如图1所示。
图1中,E为入射人眼的偏振光场,O(0,0)为视野中直角坐标系中x-y平面中心,α为入射人眼的偏振光在x-y平面上的偏振角。黄斑的径向分布结构类似一个径向偏振片,对入射偏振光进行径向偏振调制,θ是黄斑x-y平面上采样点R(x,y)的方位角。
在三维琼斯偏振计算中,单一波长偏振光在空间某一点r处的振动状态可关于任意一组三维空间正交基底
$ \left( {{\eta _1},{\eta _2},{\eta _3}} \right) $ 进行三维投影,最终可表达为一个由三个分量所构成的3×1复数矢量,即$$ \vec E(t) = \left( {\begin{array}{*{20}{c}} {{\eta _x}(t)} \\ {{\eta _y}(t)} \\ {{\eta _z}(t)} \end{array}} \right) = {{\rm{e}}^{i(u(t) + {\beta _x}(t))}}\left( {\begin{array}{*{20}{c}} {{A_x}(t)} \\ {{A_y}(t){{\rm{e}}^{i({\beta _y}(t) - {\beta _x}(t))}}} \\ {{A_z}(t){{\rm{e}}^{i({\beta _z}(t) - {\beta _x}(t))}}} \end{array}} \right) $$ (1) 式中:
$ u(t) = \vec k \cdot (r/\left| r \right|) - \bar \omega t $ ,$ \vec k $ 为点r处的平均波矢量;${\eta _i}(t)(i = x,y,z)$ 为电场矢量的x、y和z三个正交的电场分量;${A_i}(t)$ 和${\beta _i}(t)(i = x,y,z)$ 分别为x、y和z电场分量的振度和位相。于是,对应的“三维瞬时琼斯矢量”可定义为:$$ \vec {{E}}(t) = \left( {\begin{array}{*{20}{c}} {{\eta _x}(t)} \\ {{\eta _y}(t)} \\ {{\eta _z}(t)} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {{A_x}(t)} \\ {{A_y}(t){{\rm{e}}^{i{\delta _y}(t)}}} \\ {{A_{{z}}}(t){{\rm{e}}^{i{\delta _z}(t)}}} \end{array}} \right) $$ (2) 式中:
${\delta _y}(t){\text{ = }}{\beta _y}(t){{ - }}{\beta _x}(t)$ ,${\delta _z}(t){\text{ = }}{\beta _z}(t){{ - }}{\beta _x}(t)$ 分别为y和z电场分量相对于x电场分量的位相差。公式(2)包含了任意一个电场矢量的三个电场分量振幅和位相信息,由于一般衡量的都是位相差,以${\delta _x}(t)$ 作为参考位相,只研究三个分量之间的相对位相差,避免了全局位相。同时,对于激发人眼偏振感知效应所使用的完全偏振光,任意时刻t的振动状态始终满足下列条件:$$ \left\{\begin{array}{l}\dfrac{{A}_{{y}}(t)}{{A}_{x}(t)}=常数\text{,}{\delta }_{y}(t)=常数\\ \dfrac{{A}_{z}(t)}{{A}_{x}(t)}=常数\text{,}{\delta }_{z}(t)=常数\end{array}\right. $$ (3) 由此可得,完全偏振光的三维琼斯矢量表达形式为:
$$ \vec {{E}} = \left( {\begin{array}{*{20}{c}} {{A_x}} \\ {{A_y}{{\rm{e}}^{i{\delta _y}}}} \\ {{A_z}{{\rm{e}}^{i{\delta _z}}}} \end{array}} \right) $$ (4) 为了计算入射人眼的三维琼斯偏振矢量经过人眼系统后所受到的影响,需要使用三维琼斯偏振光追迹中光线与光学界面作用的三维琼斯矩阵:
$$ \begin{gathered} {\boldsymbol{ P}} = {{\boldsymbol{O}}_{{\rm{out}}}} \cdot {{\boldsymbol{W}}_r} \cdot {\boldsymbol{O}}_{{\rm{in}}}^{ - 1} =\\ \left( {\begin{array}{*{20}{c}} {\vec s'{_x}}&{\vec p'{_x}}&{\vec k'{_x}} \\ {\vec s'{_y}}&{\vec p'{_y}}&{\vec k'{_y}} \\ {\vec s'{_z}}&{\vec p'{_z}}&{\vec k'{_z}} \end{array}} \right) \cdot \left( {\begin{array}{*{20}{c}} {{t_{\rm{s}}}}&0&0 \\ 0&{{t_{\rm{p}}}}&0 \\ 0&0&1 \end{array}} \right) \cdot \left( {\begin{array}{*{20}{c}} {{{\vec s}_x}}&{{{\vec s}_y}}&{{{\vec s}_z}} \\ {{{\vec p}_x}}&{{{\vec p}_y}}&{{{\vec p}_z}} \\ {{{\vec k}_x}}&{{{\vec k}_y}}&{{{\vec k}_z}} \end{array}} \right) \\ \end{gathered} $$ (5) 式中:Wr为光线在光学界面上局部坐标系下的琼斯矩阵;ts和tp分别为s光和p光的振幅透射系数;Oout和Oin为酉矩阵,用来实现局部坐标系与全局坐标系之间的变换;
$ \vec k' $ 和$ \vec k $ 两列分别代表出射光和入射光波矢量;$ \left\{ {\overrightarrow s {'_x},\overrightarrow p {'_x}} \right\} $ 和$ \left\{ {{{\overrightarrow s }_x},{{\overrightarrow p }_x}} \right\} $ 分别对应入射光和出射光横截面上的正交偏振态。整个人眼系统的三维偏振光追迹矩阵Peye是由人眼各光学表面三维偏振光琼斯矩阵的级联:$$ \begin{gathered} {{\boldsymbol{P}}_{{\rm{eye}}}} = \prod\limits_{q = n, - 1}^1 {{{\boldsymbol{P}}_q}} = {{\boldsymbol{P}}_n} \cdot {{\boldsymbol{P}}_{n - 1}} \cdot \cdot \cdot {{\boldsymbol{P}}_2} \cdot {\boldsymbol{P}_1} = \\ \left( {{{\boldsymbol{O}}_{{\rm{out}},n}}{J_n}{\boldsymbol{O}}_{{\rm{in}},n}^{ - 1}} \right)\left( {{{\boldsymbol{O}}_{{\rm{out}},n - 1}}{{\boldsymbol{J}}_{n - 1}}{\boldsymbol{O}}_{{\rm{in}},n - 1}^{ - 1}} \right) \cdot \cdot \cdot \\ \cdot \cdot \cdot \left( {{{\boldsymbol{O}}_{{\rm{out}},2}}{{\boldsymbol{J}}_2}{\boldsymbol{O}}_{{\rm{in}},2}^{ - 1}} \right)\left( {{{\boldsymbol{O}}_{{\rm{out}},1}}{{\boldsymbol{J}}_1}{\boldsymbol{O}}_{{\rm{in}},1}^{ - 1}} \right) \\ \end{gathered} $$ (6) 只要给定入射人眼光学系统的偏振光的三维琼斯矢量
$ {\vec E_{{\rm{in}}}} $ 和人眼各光学表面的光追迹矩阵Peye,即可确定得出人眼中偏振光的三维琼斯矢量$ {\vec E_{{\rm{eye}}}} $ 为:$$ {\overrightarrow {{E}} _{{\rm{eye}}}} = {{\boldsymbol{P}}_{{\rm{eye}}}} \cdot {\overrightarrow {{E}} _{{\rm{in}}}} = {{\boldsymbol{P}}_{{\rm{eye}}}} \cdot \left( {\begin{array}{*{20}{c}} {{A_{x{\rm{in}}}}} \\ {{A_{y{\rm{in}}}}{{\rm{e}}^{i{\delta _{y{\rm{in}}}}}}} \\ {{A_{z{\rm{in}}}}{{\rm{e}}^{i{\delta _{z{\rm{in}}}}}}} \end{array}} \right) $$ (7) 由公式(7)还可以推导出人眼中的三维琼斯矢量光强为:
$$ {I_{{\rm{eye}}}} = {\vec {{E}}_{{\rm{eye}}}} \cdot \vec {{E}}_{{\rm{eye}}}^\dagger $$ (8) 式中:上标
$ \dagger $ 符号表示对琼斯矢量求复共轭转置。此外,由于人眼偏振像差表征了人眼光学系统的偏振特性,对偏振光进行追迹是获得人眼偏振像差函数的主要计算方法,因此对公式(6)进行坐标变化,得到人眼光瞳的二维琼斯光瞳:$$ \begin{gathered} {\boldsymbol{J}}\left( {H,\rho ,\lambda } \right) = {\left\{ {{{\boldsymbol{O}}_{{\rm{out}},2}}{{\boldsymbol{P}}_{{\rm{total}}}}{\boldsymbol{O}}_{{\rm{in}},1}^{ - 1}} \right\}_{2 \times 2}}= \\ \left( {\begin{array}{*{20}{c}} {{{\boldsymbol{J}}_{xx}}\left( {\boldsymbol{H},\boldsymbol\rho ,\lambda } \right)}&{{{\boldsymbol{J}}_{xy}}\left( {\boldsymbol{H},\boldsymbol\rho ,\lambda } \right)} \\ {{{\boldsymbol{J}}_{yx}}\left( {\boldsymbol{H},\boldsymbol\rho ,\lambda } \right)}&{{{\boldsymbol{J}}_{yy}}\left( {\boldsymbol{H},\boldsymbol\rho ,\lambda } \right)} \end{array}} \right) \\ \end{gathered} $$ (9) 式中:H表示光线的物坐标矢量;ρ表示光瞳坐标矢量;
$\lambda $ 为波长。即偏振像差函数表征了光学系统的偏振特性与波长、光瞳坐标以及物坐标变化规律,利用公式(9)即可实现人眼光瞳偏振波前的仿真。其中琼斯矩阵所表达的物理意义相当晦涩,而奇异值(SVD)分解能清晰地展现出琼斯矩阵中包含的偏振信息,公式(9)的奇异值分解为:$$ {\boldsymbol{J}} = {\boldsymbol{UDV}}{^\dagger } = \left( {{\boldsymbol{UDU}}{^\dagger }} \right)\left( {{\boldsymbol{UV}}{^\dagger }} \right) $$ (10) 式中:U、V为酉矩阵;D为对角阵,其对角元素为奇异值;
${\boldsymbol{UD}}{{\boldsymbol{U}}^\dagger }$ 为Hermitian矩阵,与二向衰减相对应,表征了光学系统对入射光偏振态的选择性;${\boldsymbol{U}}{{\boldsymbol{V}}^\dagger }$ 为酉矩阵,代表了琼斯矩阵中的延迟部分,表征了光学系统对入射光两个正交偏振态之间的位相差异。对公式(10)进一步演化:$$ {\boldsymbol{J}} = t \cdot {{\rm{e}}^{i\phi }} \cdot {{\boldsymbol{J}}_D}\left( {d,\theta } \right) \cdot {{\boldsymbol{J}}_R}\left( {\phi ,\beta } \right) $$ (11) 式中:t为光瞳切趾,表征了两个正交偏振态分量的平均透过率;
$ {{\rm{e}}^{i\phi }} $ 为标量波前,表征了两个正交偏振态的位相变化量的平均值,光瞳切趾和标量波前是与偏振无关的标量函数;JD为二向衰减,JR为位相延迟。由公式(11)可知,琼斯矩阵的奇异值分解不仅包含了光瞳的矢量特性,还包含了标量特性,通过公式(5)~(11)可以对人眼光瞳的二向衰减和位相延迟进行计算和评价,不仅能建立更全面的人眼系统偏振评价方法,还能对人眼光瞳处的偏振感知图像进行仿真分析。 -
在光学领域中,人眼是一个复杂的三维结构光学系统,从角膜至眼底视网膜前的每一界面和折射率都具有各向异性,并且由于人眼中近视、远视和散光是最常见、最广泛存在的晶状体屈光度变化,为了精确地对人眼内的海丁格尔刷效应进行分析,文中使用具有四个改进型球面的“Navarro光学模型眼 [29-30] ”对人眼进行光学建模,通过改变晶状体在自适应调节过程中屈光度的增加量对人眼在不同屈光度情况下的成像进行计算,从而实现对近视、远视和散光等情况的偏振像差计算研究[31]。文中所采用的理想、近视和散光Navarro人眼模型光学结构示意图如图2所示。
图 2 理论、理想、近视和散光Navarro人眼模型光学结构
Figure 2. Tangential structure of theory, ideal, astigmatism and myopia Navarro schematic eye
在图2(a)为由角膜、房水、晶状体和玻璃体构成的四层人眼理论模型,图2 (b)为介质折射率均匀的理想Navarro人眼模型,其结构参数如表1所示,图2(c)为由于晶状体屈光度改变引起的−2D近视Navarro人眼模型,图2(d)为由于晶状体子午、弧矢面屈光度不一致导致的单纯−5D散光Navarro人眼模型。
表 1 理想Navarro人眼光学模型参数
Table 1. Parameters of ideal Navarro schematic eye
Parameter Radius of curvature/mm Quadric coefficient k Thickness/mm Refractive index(n) Anterior corneal 7.72 −0.26 0.55 1.367 Posterior corneal 6.5 0 Atria − − 3.05 1.337 Anterior lens 10.2 −3.13 4.0 1.42 Posterior lens −6.0 −1.0 Vitreum − − 16.4 1.336 Retina −12.3 0 − − 从图2(c)~(d)中可以看出,当人眼中晶状体面型改变时,屈光度会改变,导致进入人眼内光线的焦点位置发生移动,造成人眼出现近视和散光等现象。不同屈光度晶状体面型参数变化以及各自的像面位置变化如表2所示。
表 2 不同屈光度晶状体和像面的参数变化
Table 2. Parameter changes of lens and image plane with different diopters
Parameter Anterior lens Radius/mm Thickness/mm Image plane position/mm Ideal eye Symmetry 10.2 4 24 −2D myopia Symmetry 8.07 4.05 24.05 −5D astigmatism Tangential 10.2 4.14 24 Sagittal 5.9 24.14 为了分析人眼系统中因晶状体面型差异所导致的屈光度改变对海丁格尔刷效应造成的影响,文中以人眼黄斑敏感的460 nm波长线正入射线偏振光为基础,利用偏振光追迹方法精确计算人眼系统中任意一条光线的偏振像差函数[25,32],再根据公式(6)~(10)对理想人眼(0D)、[−5D,+5D]近、远视人眼和[−5D,+5D]单纯性散光人眼的偏振像差进行仿真计算,获取整个光瞳处的二向衰减和位相延迟大小,从而分析人眼晶状体屈光度变化对海丁格尔刷效应的影响。值得注意的是,由于人眼系统透射系数由菲涅耳公式计算得出,公式(5)中ts和tp为两个实数,导致虚数表示的位相延迟JR几乎为0,所以在人眼介质均匀的情况下,由晶状体屈光度差异引起的偏振像差以实数表示的JD二向衰减为主。眼瞳中理想人眼(0 D)与[−5D,+5D]近/远视和[−5D,+5D]单纯性散光人眼的二向衰减仿真结果如图3所示。
图 3 理想人眼、近/远视和单纯性散光人眼的二向衰减仿真
Figure 3. Diattenuation simulation of ideal, myopic/hyperopic and astigmatic eyes
从图3(a1)~(e1)中可以看出,圆环上从内到外二向衰减数值逐渐增大,这是由于随着光瞳半径增大,偏振光线的入射角逐渐增大,使s光和p光反射振幅比增大,导致二向衰减增加,圆环由内向外呈现递增趋势。由近视和远视造成的晶状体屈光度改变也导致二向衰减发生变化,当偏振光线靠近光瞳外围时影响最为剧烈。从图3(a2)~(e2)中可以看出,在单纯性散光人眼中由于晶状体弧矢面和子午面的屈光度不一致,晶状体的非对称面型影响了眼瞳上二向衰减的分布,造成二向衰减呈现微弱的椭圆形分布。这种差异证明了人眼结构面型的差异会影响人眼光瞳的二向衰减的数值和分布。为了更直观地对比图3中的数据,对不同屈光度人眼的二向衰减的最大值和均方根(RMS)进行比较,数据如图4所示。
图 4 理想人眼、近/远视和单纯性散光人眼的二向衰减仿真结果的最大值和均方根值比较
Figure 4. Comparison of MAX and RMS simulation diattenuation in ideal, myopic, hyperopic and astigmatism eyes
从图4(a)中可以看出,人眼瞳上二向衰减随人眼晶状体的屈光度变化而变化,−5D近视人眼的二向衰减最为明显,其最大值为0.728%,均方根值为0.353%。从图4(b)中可以看出,散光人眼因晶状体的角膜子午面和弧矢面屈光度不一致,导致子午面和弧矢面的二向衰减存在差异,−5D单纯近视散光人眼的二向衰减最为明显,其最大值为0.725%,均方根值为0.351%,与普通−5D近视眼相比略小,但5D单纯远视散光眼的二向衰减最大值为0.667%,均方根值为0.329%,大于普通5D远视眼的最大值0.661%和均方根值0.321%。眼瞳上二向衰减差异对比表明,文中所提出的人眼偏振感知模型可以精确分析由人眼内由晶状体屈光度差异造成的偏振相差,同时也说明由人眼内结构和屈光度差异所产生的偏振像差需要根据人眼实际面型变化进行具体计算。此外,由人眼偏振像差结果的数量级可知,因[−5D,5D]屈光度差异引起的人眼二向衰减小于1%,证明在人眼中折射率均匀、结构没有损伤且黄斑健康的情况下,因晶状体屈光度变化所产生的二向衰减变化不大,对入射偏振光所产生的退偏效应很小。所以近视、远视及散光等屈光度变化的人眼和理想人眼一样都具有对偏振光进行感知的能力,这从偏振像差的角度证明了海丁格尔刷效应图像检测作为黄斑疾病检测的手段具有一定的泛用性。
-
从对人眼的偏振像差分析可知,不同晶状体屈光度的人眼都具有感知海丁格尔刷效应的可能性。为了对海丁格尔刷效应的图像进行成像仿真,利用所建立的人眼三维琼斯偏振感知模型,给定入射人眼线偏振光的三维琼斯矢量
$ {\vec {{E}}_{in}} $ ,利用人眼黄斑的琼斯三维径向调制矩阵Pmacula:$$ {{\boldsymbol{P}}}_{{\rm{macula}}}=\left(\begin{array}{ccc}{\mathrm{cos}}^{2}\theta & \dfrac{\mathrm{sin}2\theta }{2}& 0\\ \dfrac{\mathrm{sin}2\theta }{2}& {\mathrm{sin}}^{2}\theta & 0\\ 0& 0& 1\end{array}\right) $$ (12) 式中:θ为黄斑上采样点R(x,y)相对于黄斑中心点O的方位角。再结合公式(7)即可得出黄斑感知的线偏振光的三维琼斯矢量
${\vec {{E}}_{{\rm{macula}}}}$ 为:$$ {\vec {{E}}_{{\rm{macula}}}} = {{\boldsymbol{P}}_{{\rm{macula}}}} \cdot {{\boldsymbol{P}}_{{\rm{eye}}}} \cdot {\vec{{ E}}_{{\rm{in}}}} $$ (13) 通过公式(8)和公式(13)就可计算出不同偏振态的线偏振光在人眼光瞳处所生成的海丁格尔刷效应的强度图像。同时,考虑到人眼在进行偏振光感知时的光危害防护问题[33],以人眼黄斑敏感的460 nm波长线偏振光为例,偏振光源的辐射亮度应小于2 mW/(sr·cm2)[34]。由人眼黄斑素的光谱吸收特性可知,此时海丁格尔刷效应图像会变成一个强度随入射偏振角变化的暗色图案。以x-y平面上偏振角为45º(α1=45º)和−45º(α2=−45º)正入射的线偏振光为例,对传统刷子、棋盘和网格等几种海丁格尔刷效应图像进行仿真。人眼光瞳处的理想人眼、−5D近视人眼和−5D单纯近视散光人眼海丁格尔刷效应的入射偏振光场和感知图像如图5所示。
图 5 理想人眼、−5D近视人眼和-5D单纯近视散光人眼海丁格尔刷效应强度图像
Figure 5. Haidinger’s brushes intensity images of ideal eye, −5D myopic eye and -5D astigmatism eye
从图5(a1)~(d1)普通海丁格尔刷强度图像、图5(a2)~(d2)偏振棋盘强度图像和图5(a3)~(d3)偏振网格强度图像对比中可以看出,在相同的入射线偏振光场情况下,海丁格尔刷效应图像中的强度变化与入射线偏振光偏振角和黄斑径向结构有关,由屈光度差异造成的影响主要在眼瞳边缘的灰度分布上。证明文中所提出的人眼三维偏振感知模型可以针对不同入射线偏振光场、人眼屈光度和面型对人眼感知的海丁格尔刷效应进行精确仿真成像。
从图5(b1)~(b3)理想人眼海丁格尔刷效应强度图、图5(c1)~(c3)近视人眼海丁格尔刷效应强度图和图5(d1)~(d3)散光人眼海丁格尔刷效应强度图对比中可以看出,虽然人眼所感知的海丁格尔刷效应图像的强度分布与入射线偏振光场和黄斑径向结构有关,但相对于均匀线偏振光场(图5(a1))所能产生的传统刷子图像,由非均匀线偏振光场(图5(a2)~(a3))所产生的偏振棋盘和网格图像的灰度变化更剧烈,具有更多的细节信息,图像中的突发性亮度变化和不连续边能刺激人眼空间灵敏度特性,克服特罗克斯勒消逝效应,从而增强人眼对线偏振光的感知效果。此外,通过结合人眼的特性,如黄斑素密度、时空敏感度特性和眼内双折射效应等,对海丁格尔刷效应图像进行量化分析,不仅能提升人眼对线偏振光的感知质量,还能对人眼内的黄斑结构和黄斑素特性进行定性分析。利用偏振光场的海丁格尔刷效应感知效果和成像情况反映出人眼黄斑结构性质和病变情况;量化黄斑随年龄老化、病变或功能退化引起的海丁格尔刷效应变化规律,最终实现对黄斑的健康情况的分析,有助于提升海丁格尔刷效应在医学和临床中对黄斑变性和病变的检测能力,促进海丁格尔刷效应对于人眼黄斑疾病的医学应用。
Modeling and analysis of Haidinger’s brushes polarization perception in human eyes (Invited)
-
摘要: 海丁格尔刷效应是一种人眼对线偏振光进行感知的内视效应,可用于判断人眼黄斑疾病的病变情况。针对现有海丁格尔刷效应图像存在难以精确仿真和分析的问题,通过三维琼斯矩阵和矢量对人眼的偏振感知效应进行计算,建立了一种人眼偏振感知模型,对理想、近/远视和散射等形式的人眼进行了偏振像差分析。结果表明:在人眼内介质均匀的情况下,人眼光瞳上正入射的460 nm波长线偏振光因晶状体[−5D,+5D]屈光度差异所产生的二向衰减小于1%。基于所建立的人眼偏振感知模型,利用入射偏振光的三维琼斯矢量对人眼光瞳上不同入射光场和屈光度的海丁格尔刷效应强度图像进行仿真计算,为海丁格尔刷效应的研究提供有效理论依据,扩大海丁格尔刷效应在人眼黄斑病变检测中的应用。Abstract: Haidinger’s brushes is a kind of inward vision phenomenon that human eyes perceive linearly polarized light, which can be used in the detection of macular disease. It was difficule to simulate and analyze accurately for Haidinger's brushes images, that the polarization perception of human eyes was calculated based on the three-dimensional (3-D) Jones matrix and vector to establish a polarization perception model of human eyes. The polarization aberration of ideal, myopic, hyperopic and astigmatic eyes was analyzed by using the 3-D Jones polarization perception model. The results show that the diattenuation of normal incident linearly polarized light at 460 nm caused by the diopter difference of [−5D, +5D] is less than 1% when the medium in human eye is uniform. Based on the established 3-D Jones polarization perception model of human eyes, the 3-D Jones vector of incident linearly polarized light is used to simulate the Haidinger’s brushes images of different incident light fields and human eye diopters. The objective is to provide effective theoretical basis for the study of Haidinger’s brushes and expand the application of Haidinger’s brushes in the detection of human macular disease.
-
表 1 理想Navarro人眼光学模型参数
Table 1. Parameters of ideal Navarro schematic eye
Parameter Radius of curvature/mm Quadric coefficient k Thickness/mm Refractive index(n) Anterior corneal 7.72 −0.26 0.55 1.367 Posterior corneal 6.5 0 Atria − − 3.05 1.337 Anterior lens 10.2 −3.13 4.0 1.42 Posterior lens −6.0 −1.0 Vitreum − − 16.4 1.336 Retina −12.3 0 − − 表 2 不同屈光度晶状体和像面的参数变化
Table 2. Parameter changes of lens and image plane with different diopters
Parameter Anterior lens Radius/mm Thickness/mm Image plane position/mm Ideal eye Symmetry 10.2 4 24 −2D myopia Symmetry 8.07 4.05 24.05 −5D astigmatism Tangential 10.2 4.14 24 Sagittal 5.9 24.14 -
[1] Haidinger W. Ueber das directe Erkennen des polarisirten Lichts und der Lage der Polarisationsebene [J]. Annalen Der Physik, 1844, 139(9): 29-39. (in German [2] Peddie W. Helmholtz's treatise on physiological optics [J]. Nature, 1924, 114(2877): 887-889. [3] Gábor Horváth. Polarized Light and Polarization Vision in Animal Sciences[M]. Berlin: Springer, 2014. [4] Zhevandrov N D. Polarisation physiological optics [J]. Physics-Uspekhi, 1995, 38(10): 1147. doi: 10.1070/PU1995v038n10ABEH000115 [5] Floch A L, Ropars G, Enoch J, et al. The polarization sense in human vision [J]. Vision Research, 2010, 50(20): 2048-2054. doi: 10.1016/j.visres.2010.07.007 [6] Temple S E, Roberts N W, Misson G P. Haidinger's brushes elicited at varying degrees of polarization rapidly and easily assesses total macular pigmentation [J]. Journal of the Optical Society of America A, 2019, 36(4): B123. doi: 10.1364/JOSAA.36.00B123 [7] Bernstein P S, Delori F C, Richer S, et al. The value of measurement of macular carotenoid pigment optical densities and distributions in age-related macular degeneration and other retinal disorders [J]. Vision Research, 2010, 50(7): 716-728. doi: 10.1016/j.visres.2009.10.014 [8] Naylor E J, Stanworth A. The measurement and clinical significance of the Haidinger effect[J]. Transactions Ophthalmological Society of the United Kingdom, 1955, 75: 67-79. [9] Bone R A, Landrum J T. Macular pigment in Henle fiber membranes: A model for Haidinger's brushes [J]. Vision Research, 1984, 24(2): 103-108. doi: 10.1016/0042-6989(84)90094-4 [10] Müller P L, Müller S, Gliem M, et al. Perception of Haidinger brushes in macular disease depends on macular pigment density and visual acuity [J]. Investigative Ophthalmology & Visual Science, 2016, 57(3): 1448-1456. [11] Stockman A. The spectral sensitivity of the human short-wavelength sensitive cones derived from thresholds and color matches [J]. Vision Research, 1999, 39(17): 2901-2927. doi: 10.1016/s0042-6989(98)00225-9 [12] Misson G P, Anderson S J. The spectral, spatial and contrast sensitivity of human polarization pattern perception[J]. Scientific Reports, 2017, 7(1): 16571. [13] Naylor E J, Stanworth A. Retinal pigment and the Haidinger effect [J]. The Journal of Physiology, 1954, 124(3): 543-552. doi: 10.1113/jphysiol.1954.sp005127 [14] Goldschmidt M. A new test for function of the macula lutea [J]. Archives of Ophthalmology, 1950, 44(1): 129-135. doi: 10.1001/archopht.1950.00910020132008 [15] Forster H W. The clinical use of the Haidinger's brushes phenomenon [J]. American Journal of Ophthalmology, 1954, 38(5): 661-665. doi: 10.1016/0002-9394(54)90291-3 [16] Perenin M T, Vadot E. Macular sparing investigated by means of Haidinger brushes. [J]. British Journal of Ophthalmology, 1981, 65(6): 429. doi: 10.1136/bjo.65.6.429 [17] Ozyurt A, Kocak N, Akan P, et al. Comparison of macular pigment optical density in patients with dry and wet age-related macular degeneration[J]. Indian Journal of Ophthalmology, 2017, 65(6): 477. [18] Wu J, Cho E, Willett W C, et al. Intakes of lutein, zeaxanthin, and other carotenoids and age-related macular degeneration during 2 decades of prospective follow-up [J]. Jama Ophthalmology, 2015, 133(12): 1-10. [19] Salim Lahmiri, Amir Shmuel. Variational mode decomposition based approach for accurate classification of color fundus images with hemorrhages [J]. Optics & Laser Technology, 2017, 96: 243-248. [20] Kumar S, Adarsh A, Kumar B, et al. An automated early diabetic retinopathy detection through improved blood vessel and optic disc segmentation [J]. Optics & Laser Technology, 2020, 121: 105815. [21] Misson G P. A Mueller matrix model of Haidinger's brushes [J]. Ophthalmic & Physiological Optics the Journal of the British College of Ophthalmic Opticians, 2010, 23(5): 441-447. [22] Misson G P, Timmerman B H, Bryanston-Cross P J. Human perception of visual stimuli modulated by direction of linear polarization [J]. Vision Research, 2015, 115: 48-57. doi: 10.1016/j.visres.2015.08.004 [23] Wang Q, Bryanston-Cross P J, Timmerman B H, et al. Spatial frequency sensitivity analysis of polarized light perception on the human macular with 3D Stokes vector [J]. Optics & Laser Technology, 2020, 130: 106323. [24] Wang Q, Bryanston-Cross P, Timmerman B H, et al. Simulation and application of a 3D Stokes model to the human polarized light perception optical phenomena [C]//Conference on Optical Sensing and Imaging Technology, 2020. [25] Yun G, Crabtree K, Chipman R A. Three-dimensional polarization ray-tracing calculus I: Definition and diattenuation [J]. Appl Opt, 2011, 50(18): 2855-2865. doi: 10.1364/AO.50.002855 [26] He W, Fu Y, Zheng Y, et al. Polarization properties of a corner-cube retroreflector with three-dimensional polarization ray-tracing calculus [J]. Appl Opt, 2013, 52(19): 4527-4535. doi: 10.1364/AO.52.004527 [27] He Wenjun, Jia Wentao, Feng Wentian, et al. Three-dimensional polarization aberration of deep ultraviolet lithographic projection lens [J]. Infrared and Laser Engineering, 2018, 47(8): 0818006. (in Chinese) [28] He Wenjun, Jia Wentao, Li Yahong, et al. Polarization control method of vector light field based on S-wave plate and double retarders [J]. Infrared and Laser Engineering, 2018, 47(12): 1207001. (in Chinese) [29] Navarro R, Santamaría J, Bescós J. Accommodation-dependent model of the human eye with aspherics [J]. Journal of the Optical Society of America A, 1985, 2(8): 1273-1280. doi: 10.1364/JOSAA.2.001273 [30] Kong Meimei, Gao Zhishan, Chen Lei, et al. Research and development of the optical model of human eyes [J]. Laser Technology, 2008, 32(4): 370-373. (in Chinese) [31] 孔梅梅, 高志山, 陈磊, 等. 基于人眼光学模型建立的角膜模型[J]. 光学精密工程, 2009, 17(4). Kong Meimei, Gao Zhishan, Chen Lei, et al. Corneal model based on human eye optical models[J]. Optics and Precision Engineering, 2009, 17(4): 707-712. [32] Yun G, Mcclain S C, Chipman R A. Three-dimensional polarization ray-tracing calculus II: Retardance [J]. Applied Optics, 2011, 50(18): 2866-2874. doi: 10.1364/AO.50.002866 [33] 激光产品的安全第9部分: 非相干光辐射最大允许照射量. GB/T 7247.9—2016 [S]. 北京: 国家市场监督管理总局, 2016. [34] Ophthalmic instruments - Fundamental requirements and test methods - Part 2: Light hazard protection. ISO15004—2: 2007 [S]. Switzerland: International Organization for Standardization, 2007.