lesson_09_asphereical_lens_design.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 抗偏位非球面人工晶体设计简介\n",
    "\n",
    "**非球面平衡曲线？ABC曲线？高次非球面？轴向渐进非球面？非恒定像差？**\n",
    "\n",
    "这些到底是什么？\n",
    "\n",
    "**Ray Tracing？光路追迹**\n",
    "\n",
    "这些又是什么？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定理\n",
    "\n",
    "“当你需要深入了解时，一定在眼科书里找不到详细。”\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 工具\n",
    "\n",
    "* 工业用光学设计软件：\n",
    "    * Zemax: 专业工具，人工晶体设计厂商常用，昂贵\n",
    "    * OSLO EDU：教学版本免费，一些功能受到限制\n",
    "\n",
    "此次演示使用Python，一种开源的计算机语言，我们从0开始，演示如何建一个轮子。\n",
    "\n",
    "* 需要的知识：\n",
    "    * 高数：求微分\n",
    "    * 线性代数：向量乘法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "from lmfit import minimize, Parameters\n",
    "\n",
    "#matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 非球面的表示法\n",
    "\n",
    "$$\n",
    "z(r)=\\frac{r^{2}}{R\\left(1+\\sqrt{1-(1 + \\kappa) \\frac{r^{2}}{R^{2}}}\\right)}+\\alpha_{4} r^{4}+\\alpha_{6} r^{6}+\\cdots\n",
    "$$\n",
    "\n",
    "* r 曲面到光轴的距离，假定是轴对称的曲面，r只有偶数次幂级数\n",
    "\n",
    "## 描述一个非球面镜的参数：\n",
    "* R：曲率半径\n",
    "* $\\kappa$\n",
    "    * 眼科常使用Q来代替$\\kappa$\n",
    "    \n",
    "|$\\kappa$ | 意义|\n",
    "|:---|:---|\n",
    "|$\\kappa$ < -1|双曲线|\n",
    "|$\\kappa$ = -1|抛物线|\n",
    "|-1 < $\\kappa$ < 0| 椭圆（prolate spheroid)|\n",
    "|$\\kappa$ = 0| 圆|\n",
    "|$\\kappa$ > 0| 椭圆 （oblate spheroid）|\n",
    "\n",
    "* 高次项系数：$\\alpha_{4},\\alpha_{6},\\alpha_{8},\\alpha_{10},\\cdots$\n",
    "* 镜面中心顶点的位置\n",
    "* 镜面两侧介质的折射率\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def z(r,surface_parameter):\n",
    "    R=surface_parameter[\"R\"]\n",
    "    kappa=surface_parameter[\"kappa\"]\n",
    "    a=surface_parameter['a']\n",
    "    partA = r**2 / (R*(1+np.sqrt(1-(1+kappa)*(r**2)/(R**2))))\n",
    "    partB = 0\n",
    "    for i in range(len(a)):\n",
    "        partB += a[i]*(r**(i*2+2))\n",
    "    return partA+partB \n",
    "\n",
    "def surface(r, surface_parameter):\n",
    "    (z0,r0)=surface_parameter[\"apex\"]\n",
    "    return z(r-r0, surface_parameter)+z0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ABC曲线图示：\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对函数z(r)上每一点的曲率半径：\n",
    "$$\n",
    "Radius=\\frac{\\left|z^{\\prime \\prime}(r)\\right|}{\\left(1+z^{\\prime 2}(r)\\right)^{3 / 2}}\n",
    "$$\n",
    "换算成屈光度\n",
    "$$\n",
    "Power=\\frac{N_2-N_1}{Radius} \\\\\n",
    "Power = \\frac{(N_2-N_1)\\left(1+z^{\\prime 2}(r)\\right)^{3 / 2}}{\\left|z^{\\prime \\prime}(r)\\right|}\n",
    "$$\n",
    "其中$N_1,N_2$是镜面两侧的折射率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "已知:\n",
    "\n",
    "$$\n",
    "z(r)=\\frac{r^{2}}{R\\left(1+\\sqrt{1-(1 + \\kappa) \\frac{r^{2}}{R^{2}}}\\right)}+\\alpha_{4} r^{4}+\\alpha_{6} r^{6}+\\cdots\n",
    "$$\n",
    "\n",
    "一阶导数: \n",
    "$$\n",
    "z^{\\prime}=\\frac {\\partial z}{\\partial r} = \\frac{r}{R \\sqrt{1-\\frac{r^{2}(1+\\kappa)}{R^{2}}}} + 4 a_4 r^{3}+6 a_6 r^{5}+ \\cdots\n",
    "$$\n",
    "二阶导数：\n",
    "\n",
    "$$\n",
    "z^{\\prime \\prime}=\\frac {\\partial ^2 z}{\\partial r^2} =\\frac{R^{3} \\sqrt{1-\\frac{r^{2}(1+\\kappa)}{R^{2}}}}{\\left(R^{2}-r^{2}(1+\\kappa)\\right)^{2}}+12 a_4 r^{2}+30 a_6 r^{4}+ \\cdots\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dz(r,surface_parameter):\n",
    "    R=surface_parameter[\"R\"]\n",
    "    kappa=surface_parameter[\"kappa\"]\n",
    "    a=surface_parameter['a']\n",
    "    # z'\n",
    "    dz_partA= r/(R* np.sqrt(1-(1+kappa)*r**2/R**2)) \n",
    "    dz_partB = 0\n",
    "    for i in range(len(a)):\n",
    "        dz_partB +=(i*2+2) * a[i]*(r**(i*2+1))\n",
    "    return dz_partA+dz_partB\n",
    "\n",
    "def dz2(r,surface_parameter):\n",
    "    R=surface_parameter[\"R\"]\n",
    "    kappa=surface_parameter[\"kappa\"]\n",
    "    a=surface_parameter['a']\n",
    "    dz2_partA= R**3 * np.sqrt(1-r**2 * (1+kappa)/R**2) / ((R**2-r**2 * (1+kappa))**2)\n",
    "    dz2_partB = 0\n",
    "    for i in range(len(a)):\n",
    "        dz2_partB +=(i*2+2)*(i*2+1) * a[i]*(r**(i*2))\n",
    "    return dz2_partA+dz2_partB\n",
    "    \n",
    "def surface_power(r,surface_parameter):\n",
    "    (n1,n2)=surface_parameter['refractive_index']\n",
    "    d1=dz(r,surface_parameter)\n",
    "    d2=dz2(r,surface_parameter)\n",
    "    power=(n2-n1)*(1+d1**2)**(3/2)/ np.abs(d2)\n",
    "    return power\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 测试绘图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_surface(r, surface_parameter, ax):\n",
    "    ax.plot(surface(r,surface_parameter),r)\n",
    "    ax.scatter(surface_parameter['apex'][0],surface_parameter['apex'][1])\n",
    "    return ax\n",
    "def draw_power(r, surface_parameter, ax):\n",
    "    ax.plot(r,surface_power(r,surface_parameter))\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "surface_0={\n",
    "    \"R\":10,\n",
    "    \"kappa\": +0.5, # 𝜅  > 0\t椭圆 （oblate spheroid）\n",
    "    \"a\":[0,0,0,0],\n",
    "    'apex':[0,0],\n",
    "    'refractive_index':[1,1/0.9] # before and after\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 透镜剖面图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.linspace(-3, 3, 500)\n",
    "fig, ax = plt.subplots()\n",
    "plt.axis('equal')\n",
    "ax=draw_surface(r, surface_0, ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 透镜屈光度图\n",
    "\n",
    "𝜅  > 0\t椭圆 （oblate spheroid），中央屈光度更高，周边逐渐降低，这是一个“负球差”透镜"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.linspace(0, 3, 100)\n",
    "fig, ax = plt.subplots()\n",
    "ax=draw_power(r, surface_0, ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ray Tracing（光路追迹，光线追踪）\n",
    "\n",
    "* 光线在均一介质中传播\n",
    "* 光线在界面上的折射"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 光线在均一介质中传播\n",
    "\n",
    "直线的方程, 从点$P_0$沿着方向矢量$\\vec l$ 传播距离d, 到达点$P(d)$\n",
    "\n",
    "$$\n",
    "P(d)=P_0+d  \\vec l  \n",
    "$$\n",
    "考虑r方向和z方向两个分量\n",
    "$$\n",
    "P(d)_r=P_{0r}+d_r  l_r \\\\\n",
    "P(d)_z=P_{0z}+d_z  l_z \\\\\n",
    "其中 \\frac{d_r}{d_z}=\\frac{l_r}{l_z}\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def travel_in_space(p0,vec_l,dz):\n",
    "    vec_lz =vec_l[:,0].reshape(-1,1)\n",
    "    vec_l_in_z=vec_l/vec_lz\n",
    "    dz=dz.reshape(-1,1)\n",
    "    pdz=p0+dz*vec_l_in_z\n",
    "    return pdz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 折射\n",
    "$$\n",
    "n_1 Sin(\\theta_1) = n_2 Sin(\\theta_2)\n",
    "$$\n",
    "参考 https://en.wikipedia.org/wiki/Snell's_law 中的矢量形式\n",
    "\n",
    "\n",
    "* 入射光方向: $\\vec l$\n",
    "* 曲面的法向量: $\\vec n$\n",
    "* 入射面介质折射率: $n_1$\n",
    "* 出射面介质折射率: $n_2$\n",
    "\n",
    "$$\n",
    "r=n_1/n_2\\\\\n",
    "c=-\\vec n \\cdot \\vec l \\\\\n",
    "\\vec V_{refract}=r\\vec l+(rc-\\sqrt{1-r^2(1-c^2)})\\vec n\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def V_refract(vec_l,vec_n,n1,n2):\n",
    "    r=n1/n2\n",
    "    if len(vec_l.shape)>1:\n",
    "        c=np.diag(-np.matmul(vec_n, np.transpose(vec_l))).reshape(-1,1)\n",
    "    else:\n",
    "        c=-np.matmul(vec_n.reshape(1,-1),vec_l.reshape(-1,1))    \n",
    "    V=r*vec_l  + (r*c-np.sqrt(1-r**2*(1-c**2))) * vec_n\n",
    "    return V/np.linalg.norm(V,axis=1,keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.63639614, -0.7713624 ],\n",
       "       [ 0.63639614, -0.7713624 ],\n",
       "       [ 0.63639614, -0.7713624 ]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 测试：\n",
    "vec_l=np.asarray([[0.707107,-0.707107],[0.707107,-0.707107],[0.707107,-0.707107]])\n",
    "vec_n=np.asarray([[0,1],[0,1],[0,1]])\n",
    "n1=1\n",
    "n2=1/0.9\n",
    "V_refract(vec_l,vec_n,n1,n2)\n",
    "# should be:\n",
    "# [ 0.6364, -0.7714]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 曲面的法向量: $\\vec n$\n",
    "\n",
    "* 简化，仅仅考虑二维"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "已知有曲面\n",
    "$$\n",
    "z=z(r)\n",
    "$$\n",
    "则曲面在(z0,r0)位置的法向量: \n",
    "$$\n",
    "\\left[ \n",
    "\\begin{array}{c} \n",
    "-1\\\\ \n",
    "\\frac{\\partial }{\\partial r}z\\left(r \\right) |_{r=r0} \n",
    "\\end{array} \n",
    "\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def norm_vec(r,surface_parameter):\n",
    "    R=surface_parameter[\"R\"]\n",
    "    kappa=surface_parameter[\"kappa\"]\n",
    "    a=surface_parameter['a']\n",
    "    \n",
    "    V=-1*np.ones([r.shape[0],2])\n",
    "    V[:,1]=dz(r,surface_parameter)\n",
    "    return V/np.linalg.norm(V,axis=1,keepdims=True )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 绘制曲面上的法向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "plt.axis('equal')\n",
    "# 绘制曲面\n",
    "r = np.linspace(-4, 4, 500)\n",
    "ax=draw_surface(r, surface_0, ax)\n",
    "\n",
    "# 计算法向量\n",
    "N=5\n",
    "rn = np.linspace(-3, 3, N)\n",
    "norm_v=norm_vec(rn,surface_0)\n",
    "zn  = surface(rn, surface_0)\n",
    "zn1 = zn+norm_v[:,0]\n",
    "rn1 = rn+norm_v[:,1]\n",
    "for i in range(N):\n",
    "    ax.plot([zn[i],zn1[i]],[rn[i],rn1[i]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 在曲面上折射"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def refract_from_surface(p, vec_l,surface_parameter):\n",
    "    (z0,r0)=surface_parameter[\"apex\"]\n",
    "    (n1,n2)=surface_parameter['refractive_index']\n",
    "    r = p[:,1]\n",
    "    r = r-r0\n",
    "    vec_n = norm_vec(r,surface_parameter)\n",
    "    return V_refract(vec_l,vec_n,n1,n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 薄透镜近似\n",
    "\n",
    "* 薄透镜\n",
    "    * 直线与曲线的交点，化简成为直线与直线的交点. **这个简化大大降低了运算难度，但也引入很大误差**\n",
    "* 暂不考虑瞳孔大小"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 已知模型，模拟成像过程\n",
    "\n",
    "一组平行光，经过两个非球面镜，聚焦到屏幕上。\n",
    "\n",
    "* 非球面镜0: 镜头垂直于光轴，镜头中心位于光轴上，是一个简单的椭球面\n",
    "* 非球面镜1: 镜头垂直于光轴，但镜头中心有一定的偏位\n",
    "* 屏幕：垂直于光轴\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "surface_0={\n",
    "    \"R\":8,\n",
    "    \"kappa\": -0.8,\n",
    "    \"a\":[0],\n",
    "    'apex':[0,0],\n",
    "    'refractive_index':[1,1.3] # before and after\n",
    "}\n",
    "\n",
    "surface_1={\n",
    "    \"R\":7,\n",
    "    \"kappa\": 0.5,\n",
    "    \"a\":[0,0],\n",
    "    'apex':[4,1],\n",
    "    'refractive_index':[1.3, 1.5] # before and after\n",
    "}\n",
    "\n",
    "surface_2={\n",
    "    \"R\":1e+10,\n",
    "    \"kappa\": 0,\n",
    "    \"a\":[0,0],\n",
    "    'apex':[30,0],\n",
    "    'refractive_index':[1.5, 1.5] # before and after\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ray Tracing（光路追迹，光线追踪）\n",
    "\n",
    "追踪每一条光线所走的路径：\n",
    "* 在均一介质内直线行进：位置改变，方向不变\n",
    "* 在镜头界面上折射：位置不变，方向改变\n",
    "\n",
    "依次穿过每一个透镜界面，计算出最终在屏幕上光线的位置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ray_tracing(light_position_start, light_direction_start, surfaces):\n",
    "\n",
    "    # 记录光线的位置\n",
    "    light_postion_list=[light_position_start]\n",
    "    \n",
    "    # 从被追踪光线的起始位置和起始方向开始：\n",
    "    light_position=light_position_start\n",
    "    light_direction=light_direction_start\n",
    "    \n",
    "    for s in surfaces: # 遍历每一个曲面\n",
    "        #光线在均匀介质内传播，到达该曲面\n",
    "        dz=s['apex'][0]-light_position[:,0]\n",
    "        light_position=travel_in_space(light_position,light_direction,dz)\n",
    "        #光线经过该曲面发生折射\n",
    "        light_direction=refract_from_surface(light_position, light_direction,s)\n",
    "        #记录下光线的位置\n",
    "        light_postion_list.append(light_position)\n",
    "        \n",
    "    return light_postion_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_light(N):\n",
    "    #初始化光线\n",
    "    light_position_start=-5*np.ones([N,2]) #从z=-5平面开始发出光线\n",
    "    light_position_start[:,1]= np.linspace(-3, 3, N)\n",
    "    light_direction_start=np.zeros([N,2])\n",
    "    light_direction_start[:,0]=1 #方向矢量(1,0)，指向Z轴方向\n",
    "    return light_position_start,light_direction_start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_ray_tracing(N,surfaces):\n",
    "    # 绘制出各个曲面的位置：\n",
    "    fig, ax = plt.subplots()\n",
    "    plt.axis('equal')\n",
    "    r = np.linspace(-5, 5, 500)\n",
    "    for s in surfaces:\n",
    "        ax=draw_surface(r, s, ax)\n",
    "    # 光线的起点和方向\n",
    "#     N=3 # 光线数量\n",
    "    light_position_start,light_direction_start = init_light(N)\n",
    "\n",
    "    # 追踪光线，获得光线在各个曲面上经过时的坐标\n",
    "    light_postion_list=ray_tracing(light_position_start, light_direction_start, surfaces)\n",
    "\n",
    "    # 绘制出每一根光线\n",
    "    for i in range(N):\n",
    "        x=[light_postion[i,0] for light_postion in light_postion_list]\n",
    "        y=[light_postion[i,1] for light_postion in light_postion_list]\n",
    "        ax.plot(x,y)\n",
    "#     ax.set_xlim(28, 32)\n",
    "#     ax.set_ylim(-2,2)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/goldengrape/anaconda3/envs/blog/lib/python3.6/site-packages/ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制ray tracing过程：\n",
    "draw_ray_tracing(10,[surface_0,surface_1,surface_2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 未知模型，求解最佳参数\n",
    "\n",
    "一组平行光，经过两个非球面镜，聚焦到屏幕上。\n",
    "\n",
    "* 非球面镜0: 镜头垂直于光轴，镜头中心位于光轴上，是一个简单的椭球面\n",
    "* 非球面镜1: 镜头垂直于光轴，但镜头中心在一定范围内偏位\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 优化模型\n",
    "\n",
    "当非球面镜1偏位时，每一条光线最好都能够落在焦点附近，\n",
    "\n",
    "* 注意：由于镜头偏位，所以焦点并不一定在光轴上，\n",
    "    * “焦点”，各个光线汇聚的点，或者说，光线的平均位置。\n",
    "* 简化：每一条光线在屏上的位置 **尽量靠近** 非球面镜1的偏位距离\n",
    "    * 尽量靠近：到达给定位置的平方和最小\n",
    "    \n",
    "优化问题： 求loss_function的最小值：\n",
    "$$\n",
    "loss =\\sum_{偏位距离=-\\Delta}^{+\\Delta} \\sum_{光线_i =0 }^{N} |光线_i 在屏上位置- 非球面镜_1 的偏位距离|^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_function(params, light_position_start,light_direction_start  ,data=None):\n",
    "\n",
    "    spots_on_screen_list=[]\n",
    "    Delta=0.9\n",
    "    for apex_r in np.linspace(-Delta,Delta,10): # 将曲面在一定范围内移动\n",
    "    \n",
    "        surface_t={\n",
    "            \"R\":params[\"R\"],\n",
    "            \"kappa\": params[\"kappa\"],\n",
    "            \"a\":[params[\"a4\"],params[\"a6\"],params['a8'],params['a10']],\n",
    "            'apex':[4,apex_r],\n",
    "            'refractive_index':[1.3, 1.5] # before and after\n",
    "        }\n",
    "\n",
    "        surfaces=[surface_0,surface_t,surface_2] \n",
    "\n",
    "        # 追踪光线，获得光线在各个曲面上经过时的坐标\n",
    "        light_postion_list=ray_tracing(light_position_start, light_direction_start, surfaces)\n",
    "        \n",
    "        # 希望屏上的光线落在偏位点的附近\n",
    "        spots_on_screen=(light_postion_list[-1][:,-1]-apex_r)\n",
    "        spots_on_screen_list.append(np.abs(spots_on_screen))\n",
    "        \n",
    "    return spots_on_screen_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 优化器\n",
    "\n",
    "lmfit，scipy优化器的封装，\n",
    "\n",
    "* 设定好需要优化的参数: $ R, \\kappa, a_4,a_6,a_8,a_{10} $ \n",
    "* 设定目标loss_function\n",
    "\n",
    "求解使得loss_function取得最小值的参数表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from lmfit import Minimizer, Parameters, report_fit\n",
    "\n",
    "# 定义待求解的参数，以及初值，参数的数值范围\n",
    "params = Parameters()\n",
    "# add with tuples:(NAME,    初始值,  求解， Min    MAX   EXPR  BRUTE_STEP)\n",
    "params.add_many(  ('R',     7,      True, 6,     12,   None, None),\n",
    "                  ('kappa', 0,      True, None,  None, None, None),\n",
    "                  ('a4',    0,      True, None,  None, None, None),\n",
    "                  ('a6',    0,      True, None,  None, None, None),\n",
    "                  ('a8',    0,      True, None,  None, None, None),\n",
    "                  ('a10',   0,      True, None,  None, None, None),\n",
    "               )\n",
    "\n",
    "\n",
    "# 输入N条光线\n",
    "N=100\n",
    "light_position_start,light_direction_start = init_light(N)\n",
    "\n",
    "# 求解参数\n",
    "minner = Minimizer(loss_function, params, \n",
    "                   fcn_args=(light_position_start,light_direction_start,_),\n",
    "                   nan_policy=\"propagate\")\n",
    "result = minner.minimize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R=6.02\n",
      "kappa=1.34\n",
      "a4=-4.52e-02\n",
      "a6=-2.28e-03\n",
      "a8=4.15e-04\n",
      "a10=-2.71e-05\n"
     ]
    }
   ],
   "source": [
    "print(\"R={:.2f}\".format(result.params[\"R\"].value))\n",
    "print(\"kappa={:.2f}\".format(result.params[\"kappa\"].value))\n",
    "print(\"a4={:.2e}\".format(result.params[\"a4\"].value))\n",
    "print(\"a6={:.2e}\".format(result.params[\"a6\"].value))\n",
    "print(\"a8={:.2e}\".format(result.params[\"a8\"].value))\n",
    "print(\"a10={:.2e}\".format(result.params[\"a10\"].value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_surface_target(result,apex_r):\n",
    "    return {\n",
    "            \"R\":result.params[\"R\"].value,\n",
    "            \"kappa\": result.params[\"kappa\"].value,\n",
    "            \"a\":[result.params[\"a4\"].value,\n",
    "                 result.params[\"a6\"].value,\n",
    "                 result.params['a8'].value,\n",
    "                 result.params['a10'].value],\n",
    "            'apex':[4,apex_r],\n",
    "            'refractive_index':[1.3, 1.5] # before and after\n",
    "        }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# surface 0 的光焦度曲线\n",
    "fig, ax = plt.subplots()\n",
    "r = np.linspace(0, 2.5, 500)\n",
    "ax=draw_power(r, surface_0, ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# surface 1 的光焦度曲线\n",
    "fig, ax = plt.subplots()\n",
    "# plt.axis('equal')\n",
    "r = np.linspace(0, 3, 500)\n",
    "# ax=draw_surface(r, surface_0, ax)\n",
    "ax=draw_power(r, get_surface_target(result,1), ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/goldengrape/anaconda3/envs/blog/lib/python3.6/site-packages/ipykernel_launcher.py:5: RuntimeWarning: invalid value encountered in sqrt\n",
      "  \"\"\"\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3XmYLFd93//3qbW3WXqWuy9ztUtIINBFgDHCIJBYbAtk4x84C3nix+L32MTEyxPs2HEUEgdI4oX84uBgA8axQcY4GAwYgWQpIECIK0Ab2u7VnSvd/U7P3lt1VZ3fH1XT0z3Ts92ZXqb7+9LTT1edrq460+r7OVXnVFcprTVCCCG6n9HuCgghhGgNCXwhhOgREvhCCNEjJPCFEKJHSOALIUSPkMAXQogeIYEvhBA9QgJfCCF6hAS+EEL0CKvdFag1MjKix8bG2l0NIYTYVh5++OEJrfXoWst1VOCPjY1x5MiRdldDCCG2FaXUifUsJ106QgjRIyTwhRCiR0jgCyFEj5DAF0KIHiGBL4QQPUICXwgheoQEvhBC9AgJfCGE6BES+EII0SMk8IUQokdI4AshRI+QwBdCiB4hgS+EED1CAl8IIXqEBL4QQvQICXwhhOgREvhCCNEjtiTwlVKfUEqdV0o9XlM2pJT6ulLq2fg5uxXbEkIIcXG2ag//z4E3LSn7TeBerfXlwL3xvBBCiDbZksDXWn8DmFxSfBvwqXj6U8DbtmJbQgghLk4z+/B3aq3PAMTPO5q4LSGEEGto+6CtUuoOpdQRpdSRCxcutLs6QgjRtZoZ+OeUUrsB4ufzjRbSWn9Ma31Ya314dHS0idURQoje1szA/yLw7nj63cAXmrgtIYQQa9iq0zI/A3wHuFIpdVIp9QvAh4A3KqWeBd4YzwshhGgTaytWorV+1wov3bwV6xdCCLF5bR+0FUII0RoS+EII0SMk8IUQokdI4AshRI+QwBdCiB4hgS+EED1CAl8IIXqEBL4QQvQICXwhhOgREvhCCNEjJPCFEKJHSOALIUSPkMAXQogeIYEvhBA9QgJfCCF6hAS+EEL0CAl8IYToERL4QgjRIyTwhRCiR0jgCyFEj5DAF0KIHiGBL4QQPUICXwgheoQEvhBC9AgJfCGE6BES+EII0SMk8IUQokdI4AshRI+QwBdCiB4hgS+EED1CAl8IIXqEBL4QQvQICXwhhOgREvhCCNEjrGZvQCk1DswBAeBrrQ83e5tCCCGWa3rgx16ntZ5o0baEEEI0IF0620gY6nZXQQixjbUi8DXwNaXUw0qpO1qwva701cfPcvtHv8352VJrN6w15I61dptC9IAPP/RhPvzQh1u6zVZ06bxaa31aKbUD+LpS6imt9TcWXowbgTsADhw40ILqbD9zpQp3fvEJBlM22bTTmo1qDUc+Dt/5Y5h8Dt73CGTHWrNtIXrAU5NPtXybTd/D11qfjp/PA58Hblzy+se01oe11odHR0ebXZ1t6fe/9gzn5kp86GdejG22qBfu7n8LX/51yOyEt/4BJAZbs10hRNM0dQ9fKZUGDK31XDx9C/CBZm6z2zx2coZPfWecf/7Kg1y/v0Wh++w98OD/hBvfA2/+MCjVmu0KIZqq2V06O4HPqygwLODTWuuvNnmbXUNrzX/4+ycYSjn8+q1XtmajYQj33hl139zynyTshegiTQ18rfVzwEuauY1u9qVHz3DkxBQfvP06+hN2azb67Nfg7GPwtj8Bq0XjBUKIlpDTMjtUqRLwoX94iqt39/Nzh/e3bsMPfQz6dsN1P9u6bQohWkICv0N9/IHjnJou8u9/6hpMo0XdKhNH4di9cPhfgtmiIwohRMtI4HegmWKF//V/j3HzVTt45SXDrdvw9/4MDBte9u7WbVMI0TIS+B3o4w8cZ7bk86tvvKJ1Gw0q8Ohfw9U/CX07W7ddIUTLSOB3mOmCxyceOM6bXrSLa/cOtG7DR++F4iS8+J2t26YQoqUk8DvMxx84Tt5r8d49RHv3ySG47ObWblcI0TIS+B2k4Pn87wdP8Mard3Llrr7Wbdj34Jm74ZqflsFaIbqYBH4H+duHTzJdqHDHTZe0dsPPfwcqebj81tZuVwjRUhL4HSIINX/2wHGu3z/IDQezrd340Xuis3MOvaa12xVCtJQEfoe476nznMgV+MXXXIJq9eUMxr8J+28Et4XdSEKIlpPA7xB3fe95dvS53PqiFp8S6Zfh7OOwT+48KUS3a9UtDpvq6cmn+fJzX253NdZPwaA7yFBiiOHEMAQZ7jv6DL/wY9dhteryxwvOPg5hBfa8rLXbFUK0XFcE/gtzL/CZpz7T7mqsW6ADKmGlrix1GXzmPPz9pzNRQ5AcZigxVPdYKBtORM/9bj+G2mQDcfr70fNeCXwhul1XBP4bDr6BNxx8Q7ursW5aa4p+kVwpR66Y45fu+iaZVJGfvXGQydIkk8VJJkuTnJg9wQ/O/4Cp0hSa5fezNZVJNpGtNgBDyZrGITG8rNFIWInllckdBScDAy28QJsQoi26IvC3G6UUKTtFyk4xNzfA6dOn+ODt1/GuFze+xWMQBkyXp5ksTZIr5aoNwsIjV8wxWZrk+bnnmSxNUvSLDdeTttPLjxoufJeR0T2MPH8PI8kRhhPDjCRHSNmpZn4EQog2kMBvs688dgZDwS3XrDxYaxomw8loj/1yLl9znYVKoa5BqG0YcqWocTg5f5JHLjzCdDhJ6AD3/1rdOpJWkpHkSPUxlBiqm68td0y5br4Q24EEfhtprfnKY2d45SXDDGfcLVvvwtHDvr59qy8YBgT/aQdTr7iD3Mv/BRPFieojV8pFz8Ucx6aP8d3id5n1Zhuupt/przYAw8nhxenEcF151s1iGuaW/Z1CiI3pjsA/dh/cu41ulasUuH3Mqz5+YbrAS0bH4IEHIZmF5GB0w/DqczY6P74Z5+bnJzBDn5HsJYwMXcmVrH4bRS/wmCxN1jUMC4+F8scnHmeiONGwW8lQRnV8YWnjUNtADCeH6Xf6W/97BCG6XHcEvuVCqoXXjd8sHUJ5lmBynFvMSUZO/F847q+8vDIhMRA1Asns8gahtpFY+rqTXrmxyJ+PnjM71lVtx3TYld7FrvSuNZctVAp1RwrVI4dizZHDzDEmihP44fK/3TbsuoZgaeNQWy7jDUKsT3cE/sEfix7bzK9+8iHGjQL3/fprwctDaRqK01CcWpwuxfPV6fh56vjitA5X3ohhNz5qSA5G6wU4/QiYTk1jEb9uXXw3U8pOccA+wIH+xgPRC7TWzHqzyxqEidLi9On8aR6beIzJ0mTDs5VSVqqu66i2K2lpuS0XhxM9rDsCfxvy/JDvHp/kZ162L+7iyUSPgTX63ZfSGspzazcSC6/nL0Du2fi1mWgdD/x+43XbqTj8s/VHENXn2gaiptztX3cXlFKKAXeAAXeASwcvXXVZP/SZLk+veMQwUZrg6PRRHiw+yJw313AdA+4AI4n68Ybq0UNicXrQHZTxBtF1JPDb5JGT0xS8gB+/fGRzK1IKEv3Rg4Mbe++3PgJf/114zzcgDOJGYqq+wahtLCafWyxf4dTPqE4LXVDraBw2cFRhGVZ1j30t5aDMZLFmvKG02EAsNBKPXniUieIEpaC07P0Lv3GoNgiJBkcMcePQZ/fJeIPYFroi8P0gxAtW6dboMArFD05E3SktvzJmLa8QPe+8DowN/mK3UlxyNDG12DjUNRpTUJiE3LG4fAYadMtUbeiooqZsyVGFa7rszuxmd2b3qn+G1pqCX1jsSlpyptJC+dGpo+SKOXy9fLzBMZzF01STNaevJpY3DkkrubHPWYgt1BWBf/cT5/jlT3+/3dXYMAW8+SPfJO2YpByLjGuRck3SjkXajcrSrknatUg7Fiknnnathu9J2MbG9jS9+ShgNxr2AHYyevSvHqjLhCGUZ1ZpIC72qMJo3BCscVShkoOk7TRpO73meEOoQ2bLs8sGo2sbi9Pzp3n0wqMr/jo6baeXnZG09MhhJBE1HLYh4w1ia3VF4F+1u4/fevNV7a7GuoUa/uf9RxnJuLzykmHyZZ+C55MvB0zmPV6YLFDwAubLPvmyT7jKDnEtQxE1DEsaiahRqG0kzGj++SHS+rWkHj8bNyZxI+NsohFZs5LGYuhuVLuOKuLGwUhmGUwOMpjMcln2Kti18liFH/pMlaYa/q5hoeyZqWfIncmtON4w6A6uOMZQ21AMuoObv6aS6AldEfiXjma49LWZdldj3abyHh/+6lP8q9dfxh03rT5QqbWm7IdxoxCQ96JGIF8OKHg+8/FzvhxE5Z5PoRww7/kUyj55L+DsbCl6b9yA5L0gXvtV0eMvH15x+ypuRJKOWW0wao8+ogYiakBStrnYsNQ0MAvLpRyz2pjYF3NV0E0fVazQODThqMJKZhlNZhmtlu+C/qsajlWUg/KyLqXa7qSJ4gQ/PP9DcsXciuMNC7+EbvTbhtqyjJ2R8YYe1hWBv90cuzAPwOU7177hiFKKhG2SsE226pcGYagp/fBvmP/S71DwoZA5SOGG95Df/9pqI7HQiCw8Fyv189MFj1PTQXX5ohdsaBzFMY3qUUSqroFo3JgsNB6pFRqTtGuStM3GYVZ3VHFoYx/WxRxVLJwZtZ6jisQgbjLLnuQge5Z2OWWugdHFxkQnBimYFhMNfttQ28X0zNQzTBYnG443uKa74umr1aOHuLzhxfbEpmmtCaam2PvcHJkZD97Uum1L4LfBQuBfOtKeoxLj8b8h9Q+/QiosRrfAKZyDBx+D0f8OL/65i16v54cU46OQ6lFHfMSR9/z4taBxo+IFFD2f09OV6nyh7mhkbUpByjZJrtJgpF0zPlpZHBOpPfJIV5dZeI+L07+7I44qFJBWBunEIAcbjknsgeFrIJklTAwwY9rkDMUEPhNhmZw3U9dILFxPaaXxhoydadgQLD2SyCayMt7QQFgo4D3/PN7x43jj43jj45SPR8/h7Cz/BAgN0L9RQdmt+fy6IvDPlSs8OldodzXW7d7cLMaOBCdVwMRsHtcwcA2FoxQJw8AxFE5cZjbj8PveD0R7rrUqxah8E4HvWAaOZTCQ2rovbxhqSn5QbRgKDY4+ljYQS5eZKVY4M12sdokVvADPX//RiG2qZY1HtdFY4WijejTipEm7A6RSl5IeXGxUkraJYazw/3a1o4qlZSscVRhANn5cVv1DUtQPZA9C8loqgwNMOUkmTIucaTChQnK6wkRQYsLPM1Ge4enJp8kVc8xVGo83ZN3smt1JI8kRBtyBrhpv0L5P5fTpaqiXx8fx4lD3z56tW9basxt3bIyBn3wrztgY/yP3eSZHE/yh2brfe3RF4H93Js8dT4y3uxrr5wIvHeb2R46tuailqGkQ4mejtmGomY5fjx5RWV1jYho4SuEkriXhXI4TVnC0hxP62LqCG/rYcwXseF12/L6lz63sAzYMFYenRfTBbY1KEK7aeBRXbEziLq4lYyMLjYle5wA7EDcINeMbDY42Uk6WlDO62JgMLRk3idcRLatwKvOo0saOKuziNDv8IiteYKNmrKKUHCGX6GPCSTJhO+Qsi5wBEwRMhB4T+fP8YPoYE+UZyqG3bFWWsqo382n4u4aa3zuk7XRHjDdorQlyObzjx6NAHx/HGz8RhfwLL0Bl8WZGxsAA7tgY6Ve8AufQGM7Yoej5wAGMZP0puce/eh8A6mLOkrtIXRH4r8lm+Icbrmh3NdbtN/7mEZKuyfvfcjWlMMTTmnKoKYchXvwczWu8MKSsa6brloumpysBno7KSnXLRa8v25e96jdXrtyRZ9asv92gEbANha2iBsiOG57qctXXjJplotfc6jqMumWXrt8xjOXba9AwuTV1WS0sbNNgIGkwkNy6oxGtNaVKWNN9tfqRSLFBYzJX8jk3W6o7oilv4GjEMlR94+HuJGnvqW9MMibpoZqjDcekzwzoV/P0h/Okw1nSep6kP4vrz2J7Mxhxw5EoTrO3OMXeyedXHavQQF4pJhJpJpIDTLhpck6SnG0zESgm8pNMzJ/n6bBEzi8SLP+WkjATDRuCpWcqDSeGt2S8IcznawK9JtTHxwnn56vLKcfBOXgQ99JL6bv5ZpxDh3DGxnAOjWFlVz/7zK8E5KfLzE+VGXrhEJbX2kuLd0XgZ22LrL19/pTShSIvuWSI1wytPWi7FfxQU9Y1jcSP/p7yfR/EC0I8w8YzbCp2Gu+V76Vy8DV4WlOJG6JKqPG0xgsXpsNqWSXUVBZei58XGp6F1/KVsGaZcMmyi8s1w0oNk6OMmkZo5YbJbdj4GEuWXXhteYPkJE2ctEXaSLBvhSOmtRomiH5YWKgE1bGQ6vNCF1d5sauqerRRc9RR8ALOz5WWvX/1031dYDR+QMI2lhx5mKQzFmlbMWyVGTLzZFWBQTXPAHn69ByZcI5UOM/+YJbLKrM43gzW/AxWeQZVmkbFYxUhMGMYTJgmE2b0nLMsJtwUuWKZCes8zxuKHxAyReOLDPZZqWiMITXKcGp05Ut0m33oM+coHz8eBfr4eDXU/fPnF1eoFPaePThjYwzcdttiqI+NYe/ehWrQDVMpB0ydzTM/XSY/FYV6NF1iPg750vzi0cAl/DiakDAIMVp0L+vtk5JdQmvNhbkyO/padwaEZSgsTNIL39GX3g6mD1/8lWiAcGA/3PSv4MU/2bI61dI6Cv3ahmThuRw3MI1eq22YahuS1RqmaNmwbtmVGqal22tFw1TfEDVumNza12yF4ypsZWMbDo5SpA1FduH1ZY1M1DBZClSgCYKQ0A/xKyG+r/ErAV4lpFIJKFdCvEpAyQsoVxbGRhYbk/myz/nZgMc9n6JnkveSlCourPN8sqRRYZdTYpdVZIddYMQqMmTkGTLy7FQFrvDn6KvMkwnnSYVzJP1ZTH+W+XA+GmswTXKmGTcUc+TMC0yYz/KUZZEzTeYbjJEorekva7JFTbagGVQ2w5cNMHTdDkYGX8bOXZeyc/9V7D50Ldn+nSil0FrjlQLmp0pMTpWZP3GO+an6IM9PlykXljdGiYxNJuuSGXQZPZDCTVSw3QqGVeaup/4crUoYZutuzyqB32KzJR8vCBnJtPkuUS/+OTj2jzD+LfjVx9paFaUWwg7Sba3J6lZqmLyaBma1hqm89KhohYapXF1m9YZp6Xub1jDZ0cNJLzQY7rIuvKyh2KEUDmBqjeFrjFCjfFChBj9EBRrta3QQon1N4EeNzXwlZMYPedKPGppKJcSLG5tyJaDsBXVHI4qQPgoMqDyD5KtHFYNqnmvIM8wsQ3qWtJoDa57AKlK2K+QtnxmL6CjCMcklTZ4x4YI5hWdMA8/A5D0wCTwCloaBwKS/YtNXSZCppEhXMiQrA7jlftIqS8bK0mdlGd7jYFoehiqjwyKBn8cv5ynl55g9M8u5p2eplOt/Q7Eb0Ap0GLasH7/pga+UehPwEcAE/kxr/aGt3sbc3JOcPfd3W73apsiXA95xxQl28G2OHhtEYYAyUBgotTAdn0+uzGXlKIWqLa973UCpeBnM5eWo+HUDhUK5JXDyMPsIRK+uUOua8pruh/rlV5hecfmNrL/xulfuClnP8mtPN16/wgSSQFKpaHFzo5+Fqlne3JL61i4bNUzEDQM1DQLVBqH29YVGLGqQqDnSYbEhWdq912iZajlUbKJtW9E6Pa3idYMXGnEd4g9vLVpH/T5BCIFGBZqSr5mI5/GjMoIQfI3phxhBiBGCEWgIAD+Eksb2S/QH8wyEcwyE8+xTeV6k5kgZM9jWDKYVNRK+WaJslSiaHnNWkRl3lqMpg5xpEjT4XiTCkGyg6fcV/YFBxrTIWAnSqSR9wxn61CCDxgFGzR30OztIOUM8knsWzFXuV9EESjfpMBVARSnzDPBG4CTwPeBdWusfNVr+8OHD+siRIxvezvnzd/PEj359M1VtGT/UVIIABRgqxDRAsf5zzYXoFhoIsKhg4S88tE1Qna4px8LHjp5V7XxUFsTzFWXG77PxMZe831pcNxYVbVEJbCqBhR9Y+IFJEJgEgUHgmwSBIgwMwkBh+AF9lXkG/FkGggukuICrc1hqGsOYQ5t5KkaRkulRsHzmzJA5s3GQ9wUhI0HASBCQDUIeHT7Ev77xV3nrJW+96M9SKfWw1vrwWss1ew//RuCo1vq5uFJ3AbcBDQP/Yu3YcSs7dty6latsir/7wSne/7eP1p11kbRNPnj7ddx2/R4gROuAqBEO0DpE63CxHA16afnis9YBoONlQ4iX0wSgl5fzyGfQj30Wfv6zS/YydM1UzQ5B3c5B4+n65Vl7mTXWv/L217HuLarv2nVZ6W+rXWQ9y1/k+rds3TWlYUiow+g5DNFarzBfU6714vtqp0ON1iGB5xEWiwSlIkGpRFAqEZY9woqH1hpDReMZlmHiOA6h5aBNk1ApQoi/uyW0XvjbdM3BjkY3PiBb9reuuD+tGny2BmBoAtvET5kEyiTEIjAsQmUSqhSB6ic0LEJlUVFRY1PWDsXQIh8GlIISoT9PGMwThAV8PY+ni7xgljhuBUyUz3Hnt+8E2FTor0ezA38v8ELN/EngFU3eZsf6r3c/vewUu2Il4L/e/TRve+lewIy7Xlok+RhM/RWkr4fUUOu22yPCOByDIKg+NjK/mfdudv7irdZNkyb6KViUrYaOuraM2odWGBiY8cPAwMKMXzeqzyYKQ0fzZt1r0VlPhmlgmiamZWLZNpZjY7k2lm1h2hamY2E50bPp2FiuhenaWInFh+na2Mno2TRNTNPE2IK+9ls+dwtn8rm6slJQ4iPf/8i2D/xGjWldM6qUugO4A+DAgdUvT7vdnZ5u/JP5lcqbLh2dckd+omMDX2vd0qDbynU1s7sUwDAMDMOohtFCIK00b9t23byhFoIyClClFaZWqDAO3lBhhETzocIIiAZhA40qVtBFD+WFqACM0MTExlJWfThXQ7kmkOP//LCCryv4oYevfQICQqXRJmAbGK6FlXZwMi5OfxKnL4nTl8Lpz+D0JTFcC+UYKNfEcEyUY6Kszv8V79n82Q2Vb6VmB/5JYH/N/D7gdO0CWuuPAR+DqA+/yfVpqz2DSU41CPc9g5u/KYbWuvpYOOReez5DyADBqeOEQX/b9ibXeq3ZagNyPaHpuu66l186v5Flq/OGiQo1hq9QPhg+KF+jKyG6HKC9AF0OCL2wZjqony6Ei9Pxe1a7tttSvvaigA49KqG3OK89Kgvl1TJNgMLXEBomyrZRiQROJok7kCY1PEDfzkGyu/ewc+8wmaH+lv7atN12pXdxJn+mYXmzNXvQ1iIatL0ZOEU0aPvzWusnGi1/sYO2x44d45577tlMVVtiulDh5HQRrTUKUGhMBTv6XDKuucGwri9rty0JtibNr/XaVtKBRnv1wRouhLIXoMth/Wt103GALwlsXdnA/18DsA2wFNrUhCokVD6+rkRBHZQp+0U8r0CpnKdYnKNcKcR72Qt724shHp3kYoORQhlJlEqCSqCMJLaTItnfT2ZoiP7hLP07sgzuzNI3lCSTTZAedLFduS/wUl9+7svc+e076y51nTAT3Pljd150l05HDNpqrX2l1HuBu4k69j6xUthvhmVZZDKdfz38TAa05fLs+Xk00WWPD+3sZ282GfU7GtHNRhYeG53f8HvKcxh3vx/z+ndhXnnLRYfqwjq3E601BJqgWKnfE14avssCu8GedE14429gB8pSi10RC90SromRtrEdA2yDUAXVIPaCEl6lSNkrUCrPUyzOUSzOki/Mkp+fYn52klKx8cXNAEzLwTRcDO2AdtEkCYwMGANgJKNAN6NAdy2ToVSCTDZJ385++vcNkRlORT8iyiZIDzpYtoT5xVgI9d/91u/ihR6707t538ve1/T+e2jBefha668AX2nmNg4ePMjBgxu8gXebzJUqXHfn1/jtt1zNL950SXsrE4Zw73FInoerr25vXVahdX33xWIAh3VhHNZ0b2hvlT3pchTY676VGKDsqK9YOYvBrBImdr9TLa/rS3aNujDHhopfplwpUirNUyrNUczPUZybjR6zsxTnZiiema2WlfP5FetjuwkSmT7sRAbLSWP372QwvY+wbOCXTSqeixem0UY63itPRicE6BC3MktSlUglNOlBJwr0/SMMXLaX/j0DpAdczG3QF76dvfWSt/K5Zz4HwCff9MmWbVd+adtiGdfCNhWTheVXEmw5w4DBgzA1vmWr1KFeEsBh4z7lhe6Nsh8tsyywF0I6RFc20N+siELWMTFcszqoZ6Zt1FCiPrAdE8MxVgjsheUMlG2ian6mr8OQcqEQBfTcbM3zLMWphfCuf5Tm51Y8rdS0bZL9AyT7+kn29dM/shPLTWNYURdKGCYIfIdK2aaUNylOa4p5RSVUVApAfGVwFfq45Wnc8jSZyiwpt0BmYIbMaIb+AyMMXraHgasOYe8c3XZHZGJrSOC3mFKKwZTDVL69ga919AtF3Xcl4YVJ9Ln8qnvMKw0ILu3+2Fh/s6oP1jiMjUG3JrCj0F6crilvFNobvAev1hqvWIyDeZLidBTYpfm5mj3v5Q+9wriJYVok+/ur4T16YCyajsvcdB+GEYW4X7HxPYfCnK5eQTE/XebC6TJ6yeoNHeBWZnALE2TK0wyXp0mUp0klITOapn/fEP2X7sM9NIYz9grsvXtRlvzzFvW64huhA43ewCVk221P0iE/VSKYKaP9MH7o6jRL5nUQQiWM/s5KWL0WCdX31q+jWh4sXWfNMsHC3uYd0dMffn/1SlsGRhzKtaFrZBzsmj3puj3kZSHd3FPotNb45XJNN8nMkqCeWx7es7OEQeMrMCrDqAZ3sq+foT376sK77tHfj5PIUC4ZFGbiKyVWr5ZYZupYdKGtwqwHuma3HDANTcos4/qz9M9fYGTyFG4xV91bT1oV0gd24o4dxBkbwz30kujKjQcOYKQ7+epDotN0ReAXn5hg8tNPtbsa6/bHKDhf5swHH7q4FSjANFCWgbJU/BxNszDtmBiWgTIV2AbKNKK9XzNavrrcuYcxHv9L1JvvRA3vifaWlwwiKtuM1tNiFa9MaW6uvo97SVgX5xdDvDQ7i19Z4chJKZKZPpJ9/ST6+hkYka5QAAAR4klEQVTYsYtdl16xYngn+/pxk6nq6YIVL4gvebt4hcQLJ8vx9DT56XMU5yrLNuskTFJpRcr02GnO4tgTOFOnMM88hzN1Crc8jeUXMWwb++CBKNBfMoZz6OXVy/GaQ0PSBSO2RFcEvr07zcBbNnhz6ja650fn+O7zU/zObS+qCeslgb0kzKmZx9jCu06dmYSnvg4DPw9XXbs162wg8CuLe9h13SQzDbtOSnNzy64uWCuRzpDsj8K7b3iEHQcvWT2802kMo/FZJV7Jjy93W2ZmosSpZ8vMT59cDPipxpe+ddMWmcHojJWRYYNE4OMWcliTJ7HOHsc88RScfr7uPQu3uXNuuhxn7Jb4rkhj2Hv2NLzGuhBbqTsCfzSFPZpqdzXWbc72uWv8LL92dZYd/a27Ln5Do1eDYcOZH8K1t6/rLWEQ1AVzfTfJTMN+b6+48q+JnWSqGszpwSwj+w8uD+6a8E5k+jDWEY5aa8oFn/x0mfMnpqt75/mp8uJ1zKdKeKXllxJI9tlksgn6hpPsvmyQ9KBLyvKiQJ8+jXX2OOGJ43hPjq94mzvn5S/FOXR79W5IjW5zJ0QrdUXgbzcHh6N+12MX8m0P/NAwKY2+jOIT36a4/4nlId6gK2Wt0wVr97Szu/fWBXYi07+kH7wP09r4bQa11pTmK/V3FaoN8ulo79z3loztKEj1O2QGXbI7U+y7KhufW+6SGUyQcgOs6TMEL5zAG38U77nFW96F8/N4gMfmbnMnRLtI4LfBNbv7AfjRmVleden67g60IPB9vFKRSqlIpVTCKxbj+VK13IvLKzXlXs3ylVIRr1yiUixSLhZAxzdj+c7767a17HTB0Z3L9rZrH4m+Pmxn8zca16GmMOdVz1yJAry0bCA0WDJQrwxFesAhk3UZ3pvh4LXDZLIu6cHox0KZrEtqwMEIA7yTJxfvW/pEdIu7/Pg4M5u8zZ0QnawrAn9+Mse548faXY1101pz2D/O8QdO8/DM6IqhXVkoLy8GdeA3PqOkEdtNYCcSOIkkdjKJk4j2vgd27KyWu6kUST9H8sj/IPn6XyP5oluqAW657pYPFoZBSGHWqwnycn1XS1wWLvlRlGGqanjvHOsnc71LumbPPJN1SfY7GPH58lpr/PMXolA/Ft23dHp8nPPj43gnT0LN52hmszhjY6Rf/eo41A8ungWTaHOXmxBbqCsC/9TTT/KlP9ryG2k11asAXoD7fxDNW7ZTDWU7kcRJJHFSKTJDw1E4J5NRubs4vVDuuMn6ZRIJbDex/gtS+R688AdQeQQu+aWL/psCP4wCvO4mzqW6PvPCTHnZ749M2yAzGIX37ssHqgGeHnTpG4quyZLM2HU/fqpuc34e7/g43uPj5GpuSO2NjxMWFk99VIlE1AVz5ZX03XorzqGxqJ99bAxzcPCi/2YhtpOuCPwD172Ef/Kf/7Dd1Vg3pRR/+fAZ/vyh09z/W7eSHVjfIGTTWA5c/VPwxBegUgR7+cCiXwmWdLEsTJeq04U5b9kvYi3XpC8O7/1XZ6sX1artN3fT1qpHEtrz8MbjID8+Hk0fH6d8YpzgwsTigoaBvXdv1AVzww11oW7t2tVTV2QUopGuCPxkpo9kpq/d1diQV4aD/H8Pz/LoeY/XDbW3L7hSDpjf8zPMP/gI+S/ex3zymsWB0DjMS/MNzjFPWtXgHtmXIR33k2cGF7pbEjgJc13dQlpr/HPnqnvn3vHjlOPpyslTUHNTDnN4GGdsjMxNN+HW9qsfOIDhtPnm8EJ0sK4I/O3oZQeyOKbBd57L8bqrdmzJOn0voFzwKeUrlAs+5UJlyfzysuKcV3OO+Qfg6wDPkUjb1T7ynWP9cRdLohrw6UEXJ7Hxr08wO1sN9XK1++UE3vg4uubUTZVM4oyNkbjmGvrf8pbFYD94EHNgYEs+LyF6jQR+myQdk+v3D/Lgc/W3OgsqIaXCkoDOVyjVzdcEd8GnHIf30rNW6ihwkxZuysJN2bgpi0w2EZ9vHp/F8txfk37io2Te91Ws0bGL/ttCz6Py/PNLgj0K9SBX8/eaJva+qAsmfePL686CsXbulF+XCrHFuiLwJ07O8dSDzb892FbRocYr+rzmnObUhSJ/eeeD+KWAcqGy/LzxJZyEGQV2Ogrv7K4UiYUQTy+GeaJmGTdl4ySt6hksK7rydnjmTnj0L+Dm313jbwjxz56NAr3atx53wZw6FV16OWaOjuAeHKPv9a/DGTtU/XWps28fSrpghGiZrgj82QslfvTN02sv2Cnive0+20BrKLqKSy4ZWgzqlFUN77r5pIVhNnHgcXA/XPEm+P5fwE3/BuwEwfR0w1D3TpxAlxYvfWCkUjhjYySvu46Bn/7p6p66M3YQs297ja8I0a26IvAveekod7z0te2uxoZprXn1h/6Ryb0mv/jP23cDkrBcxjsRdbl4zx/Cu//beN94K95EkWBqanFBy8LZty/qgnnVq+q7YHbINdaF6HRdEfjblVKKN16zk78+8gJFLyDpbN3ZOlprwnyeYGICf3ISP5cjyE3iT+YIJnL4k5MEuRyV06epnD5dd3MOK9OH03eavte/HeeyKxZ/iLRvH8re+GUQhBCdQQK/zW590S4+9Z0T3PPkOX7qJXtWXVZXKviTUwS5CfzcJMFkbvF5IheFeW6yGubaa3ypYGNgAGt4GGtoiOT11zPw9rcv9qsfHMOcfAw+8Sa47jy87QNgytdEiG4g/5LbSGvN4RGb65nhoS/cy2vP7qwP8dwkfm6iGuLhzEzD9SjHwYwD3BwZxr3iCqzhIcyh4eh5eGRxPju49kBp5pXw+t+Bf/yPcPoHcPktsPNFcOnroX/1RkkI0bm6IvDnv/UtLvz+H7S7Guumw5Bgagp/chIqFT4Yl5/69OIy5uBgNcTdK68kPTyMOTyENRQ/Dw9jDQ9jDg9jpNNb339+02/AjqvhW/8djnwS/CL8P38lgS/ENtYVgW8kElg7tubHSy1hGCSuuSbe+x4mZ6d5/70necfN1/GON74YK5vtjL7yq94aPcIgutF5Zht9xkKIZboi8FM33EDqhhvaXY2LNgww8y3+7GyFd46MNrxIWFsZJgxf2u5aCCE2Sa4m1SHe/aoxnruQ55tHJ9ZeWAghLoIEfod4y3W7Ge1z+eS3jre7KkKILiWB3yEcy+CfvuIg9z99gWMX5ttdHSFEF5LA7yA//4oDOJbBn37juXZXRQjRhSTwO8hon8u7Xr6fzz18kpNThbXfIIQQGyCB32H+35+4FEMpPnr/9rlHrxBie5DA7zC7B5K84/A+PnvkBU5PF9d+gxBCrJMEfgf6pdddhkLxR/c80+6qCCG6iAR+B9o7mOTdP3aQv3n4JE+emW13dYQQXUICv0O993WX05+w+c9febLdVRFCdAkJ/A41kLL5lZsv55vPTnD/0+fbXR0hRBeQwO9g/+yVBxkbTvGBv/8RZT9od3WEENtc0wJfKXWnUuqUUuqH8eMtzdpWt3Isgw/cdi3PTeT5k/vlx1hCiM1p9h7+H2qtr48fX2nytrrSTVeM8lMv2cMf33+U4xP5dldHCLGNSZfONvDvfvJqXMvg3/3d4+iae88KIcRGNDvw36uUelQp9QmlVLbRAkqpO5RSR5RSRy5cuNDk6mxPO/oS/Jtbr+To+XnOzpbaXR0hxBa4augqrhq6qqXbVJvZY1RK3QPsavDSbwMPAhOABv4jsFtr/S9XW9/hw4f1kSNHLro+3SwINcVKQMbtinvWCCG2kFLqYa314bWW21R6aK3fsM7K/Cnwpc1sq9eZhpKwF0JsSjPP0tldM/t24PFmbUsIIcTamrnL+F+UUtcTdemMA+9p4raEEEKsoWmBr7X+Z81atxBCiI2T0zKFEKJHSOALIUSPkMAXQogeIYEvhBA9QgJfCCF6hAS+EEL0CAl8IYToERL4QgjRIyTwhRCiR0jgCyFEj5DAF0KIHiGBL4QQPUICXwgheoQEvhBC9AgJfCGE6BES+EII0SMk8IUQokdI4AshRI+QwBdCiB4hgS+EED1CAl8IIXqEBL4QQvQICXwhhOgREvhCCNEjJPCFEKJHSOALIUSPkMAXQogeIYEvhBA9QgJfCCF6hAS+EEL0CAl8IYToERL4QgjRIyTwhRCiR0jgCyFEj9hU4Cul3qGUekIpFSqlDi957beUUkeVUk8rpW7dXDWFEEJslrXJ9z8O3A78r9pCpdQ1wDuBFwF7gHuUUldorYNNbk8IIcRF2tQevtb6Sa310w1eug24S2td1lofB44CN25mW0IIITanWX34e4EXauZPxmXLKKXuUEodUUoduXDhQpOqI4QQYs0uHaXUPcCuBi/9ttb6Cyu9rUGZbrSg1vpjwMcADh8+3HAZIYQQm7dm4Gut33AR6z0J7K+Z3wecvoj1CCGE2CLN6tL5IvBOpZSrlDoEXA481KRtCSGEWIfNnpb5dqXUSeBVwJeVUncDaK2fAD4L/Aj4KvDLcoaOEEK016ZOy9Rafx74/Aqv/R7we5tZvxBCiK0jv7QVQogeIYEvhBA9QgJfCCF6hAS+EEL0CAl8IYToERL4QgjRIyTwhRCiR0jgCyFEj5DAF0KIHiGBL4QQPUICXwgheoQEvhBC9AgJfCGE6BES+EII0SMk8IUQokdI4AshRI+QwBdCiB6htNbtrkOVUuoCcOIi3z4CTGxhdZptO9VX6tocUtfm6MW6HtRaj661UEcF/mYopY5orQ+3ux7rtZ3qK3VtDqlrc0hdVyZdOkII0SMk8IUQokd0U+B/rN0V2KDtVF+pa3NIXZtD6rqCrunDF0IIsbpu2sMXQgixiq4KfKXUnUqpU0qpH8aPt7S7Tksppd6klHpaKXVUKfWb7a7PapRS40qpx+LP8ki767OUUuoTSqnzSqnHa8qGlFJfV0o9Gz9n21nHBSvUteO+r0qp/Uqp+5RSTyqlnlBKvS8u77jPdZW6dtznCqCUSiilHlJKPRLX9z/E5YeUUt+NP9u/Vko5TatDN3XpKKXuBOa11v+t3XVpRCllAs8AbwROAt8D3qW1/lFbK7YCpdQ4cFhr3ZHnNCulbgLmgb/QWl8bl/0XYFJr/aG4Qc1qrd/fznrG9WpU1zvpsO+rUmo3sFtr/X2lVB/wMPA24F/QYZ/rKnX9OTrscwVQSikgrbWeV0rZwAPA+4BfA/6P1voupdSfAI9orT/ajDp01R7+NnAjcFRr/ZzW2gPuAm5rc522La31N4DJJcW3AZ+Kpz9FFABtt0JdO47W+ozW+vvx9BzwJLCXDvxcV6lrR9KR+XjWjh8aeD3wubi8qZ9tNwb+e5VSj8aH0G0/7FxiL/BCzfxJOvgLSvRl/JpS6mGl1B3trsw67dRan4EoEIAdba7PWjr2+6qUGgNeCnyXDv9cl9QVOvRzVUqZSqkfAueBrwPHgGmttR8v0tRM2HaBr5S6Ryn1eIPHbcBHgUuB64EzwO+3tbLLqQZlndyn9mqt9cuANwO/HHdLiK3Tsd9XpVQG+FvgX2utZ9tdn9U0qGvHfq5a60BrfT2wj+iI/+pGizVr+1azVtwsWus3rGc5pdSfAl9qcnU26iSwv2Z+H3C6TXVZk9b6dPx8Xin1eaIv6DfaW6s1nVNK7dZan4n7eM+3u0Ir0VqfW5jupO9r3L/8t8Bfaa3/T1zckZ9ro7p26udaS2s9rZS6H3glMKiUsuK9/KZmwrbbw19N/EVc8Hbg8ZWWbZPvAZfHo/IO8E7gi22uU0NKqXQ8EIZSKg3cQud9no18EXh3PP1u4AttrMuqOvH7Gg8sfhx4Umv9BzUvddznulJdO/FzBVBKjSqlBuPpJPAGonGH+4CfjRdr6mfbbWfp/G+iwzgNjAPvWeh37BTxKWJ/BJjAJ7TWv9fmKjWklLoE+Hw8awGf7rS6KqU+A/wE0RUHzwH/Hvg74LPAAeB54B1a67YPlq5Q15+gw76vSqkfB74JPAaEcfG/Jeob76jPdZW6vosO+1wBlFIvJhqUNYl2tj+rtf5A/G/tLmAI+AHwT7XW5abUoZsCXwghxMq6qktHCCHEyiTwhRCiR0jgCyFEj5DAF0KIHiGBL4QQPUICXwgheoQEvhBC9AgJfCGE6BH/P0f0/+NwlK/2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 不同偏位状态时的聚焦情况\n",
    "for apex_r in np.linspace(0,1,3):\n",
    "    draw_ray_tracing(10,[surface_0,get_surface_target(result,apex_r),surface_2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}