{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Geometric Optics: Caustics\n", "\n", "A caustic is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. An example of this is the light seen at the bottom of a swimming pool\n", "\n", "\n", "\n", "By performing refraction and ray tracing, an image of a caustic can be visualized for an arbitrary surface (as long as its height and gradients can be expressed as functions of position). This simulation is performed by the [PyCav Optics module](http://pycav.readthedocs.io/en/latest/api/optics/index.html)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#NAME: Caustics\n", "#DESCRIPTION: ...\n", "\n", "import numpy as np\n", "from pycav.display import display_animation\n", "import pycav.optics as opt\n", "from pycav.pde import LW_wave_equation\n", "import matplotlib\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EXnzxRQwZMkS26+2Pffv24fPPP8ejjz6KG2+8EQAwZMgQFBUVQalU4sqVK2ho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\n2LZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def oneD_gaussian(x,mean,std):\n", " return np.exp(-((x-mean)**2)/(2*std**2))\n", "\n", "def sinc(x,y,x_0,y_0,m):\n", " r = np.sqrt((x-x_0)**2+(y-y_0)**2)\n", " return np.sinc(m*r)\n", "\n", "def dsinc(x,y,x_0,y_0,m):\n", " r = np.sqrt((x-x_0)**2+(y-y_0)**2)\n", " return [(np.cos(np.pi*m*r)/r-np.sinc(m*r)/r)*(x-x_0)/r,(np.cos(np.pi*m*r)/r-np.sinc(m*r)/r)*(y-y_0)/r]\n", "\n", "def f(x,y,t):\n", " f_val = 0.01*oneD_gaussian(x,0.4,0.1)*oneD_gaussian(y,0.4,0.1)\n", " #f_val += 0.01*oneD_gaussian(x,0.8,0.1)*oneD_gaussian(y,0.5,0.1)\n", " #f_val += 0.01*oneD_gaussian(x,0.3,0.2)*oneD_gaussian(y,0.7,0.1)\n", " return f_val\n", " \n", "def dfdx(x,y,t):\n", " df = -0.01*(x-0.4)*oneD_gaussian(x,0.4,0.1)*oneD_gaussian(y,0.4,0.1)/0.1**2\n", " #df += -0.01*(x-0.8)*oneD_gaussian(x,0.8,0.1)*oneD_gaussian(y,0.5,0.1)/0.1**2\n", " #df += -0.01*(x-0.3)*oneD_gaussian(x,0.3,0.2)*oneD_gaussian(y,0.7,0.1)/0.2**2\n", " #df = 0.01*dsinc(x,y,0.5,0.5,6)[0]\n", " return df\n", " \n", "def dfdy(x,y,t):\n", " df = -0.01*(y-0.4)*oneD_gaussian(x,0.4,0.1)*oneD_gaussian(y,0.4,0.1)/0.1**2\n", " #df += -0.01*(y-0.5)*oneD_gaussian(x,0.8,0.1)*oneD_gaussian(y,0.5,0.1)/0.1**2\n", " #df += -0.01*(y-0.7)*oneD_gaussian(x,0.3,0.2)*oneD_gaussian(y,0.7,0.1)/0.1**2\n", " #df = 0.01*dsinc(x,y,0.5,0.5,6)[1]\n", " return df\n", "\n", "N_x = 100\n", "N_y = 100\n", "n_arr = [1.,2.]\n", "h = 1.\n", "\n", "x,y,rays = opt.ray_grid(N_x,N_y,n_arr,h,f,dfdx,dfdy)\n", "\n", "boxsize_x = 0.02\n", "boxsize_y = 0.02\n", "rays_x,rays_y,X,Y,I = opt.single_time_image(rays,boxsize_x,boxsize_y)\n", "opt.caustic_image(x,y,[N_x,N_y],X,Y,I,h,f,0.01,0.25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Combining a wave equation solver and the Optics module\n", "\n", "Solving the wave equation for given initial conditions can be used as the surface function on which the geometric optics can be performed. The gradient functions can be calculated using central differencing approximations" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def twoD_gaussian(XX,YY,mean,std):\n", " return 0.1*np.exp(-((XX-mean[0])**2+(YY-mean[1])**2)/(2*std**2))\n", "\n", "def gradient_2d(XX,YY,mean,std):\n", " def D(psi_0):\n", " dfdx = -(XX-mean[0])*twoD_gaussian(XX,YY,mean,std)/std**2\n", " dfdy = -(YY-mean[1])*twoD_gaussian(XX,YY,mean,std)/std**2\n", " return dfdx,dfdy\n", " return D\n", " \n", "def c_2d(x,y):\n", " XX,YY = np.meshgrid(x,y, indexing='ij')\n", " return np.ones_like(XX)\n", "\n", "N_x = 100\n", "N_y = 100\n", "N_t = 50\n", "\n", "dx = 0.01\n", "x_wave = dx*np.arange(-1,N_x+2)\n", "y_wave = dx*np.arange(-1,N_x+2)\n", "\n", "XX,YY = np.meshgrid(x_wave,y_wave,indexing='ij')\n", "\n", "psi_0_2d = twoD_gaussian(XX,YY,[0.5,0.45],0.25)\n", "grad_2d = gradient_2d(XX,YY,[0.5,0.45],0.25)\n", "\n", "psi_2d,t = LW_wave_equation(psi_0_2d,[x_wave,y_wave],dx,N_t,c_2d, a = 0.6,\n", " init_grad = grad_2d,bound_cond = 'periodic')\n", "\n", "def near_point(x_0,y_0,t_0):\n", " return (np.where(abs(x_wave-x_0) < dx/2.)[0][0],\n", " np.where(abs(y_wave-y_0) < dx/2.)[0][0],\n", " np.where(t == t_0)[0][0])\n", "\n", "def wave_f(x_0,y_0,t_0):\n", " x_idx,y_idx,t_idx = near_point(x_0,y_0,t_0)\n", " return psi_2d[x_idx,y_idx,t_idx]\n", "\n", "def wave_dfdx(x_0,y_0,t_0):\n", " x_idx,y_idx,t_idx = near_point(x_0,y_0,t_0)\n", " return (psi_2d[x_idx+1,y_idx,t_idx]-psi_2d[x_idx-1,y_idx,t_idx])/(2*dx)\n", " \n", "def wave_dfdy(x_0,y_0,t_0):\n", " x_idx,y_idx,t_idx = near_point(x_0,y_0,t_0)\n", " return (psi_2d[x_idx,y_idx+1,t_idx]-psi_2d[x_idx,y_idx-1,t_idx])/(2*dx)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_arr = [1.,1.3]\n", "h = 1.\n", "\n", "x,y,rays = opt.ray_grid(N_x,N_y,n_arr,h,wave_f,wave_dfdx,wave_dfdy)\n", "\n", "boxsize_x = 0.02\n", "boxsize_y = 0.02\n", "X_t,Y_t,I_t = opt.evolve(rays,t,boxsize_x,boxsize_y)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "animation = opt.caustic_anim(x,y,t,[N_x,N_y],X_t,Y_t,I_t,h,wave_f,0.1,0.25);\n", "display_animation(animation)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }