{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# I - Coordinates, Grids and Fields\n",
    "\n",
    "HCIPy is a Python library for high-contrast imaging simulations. It uses the concept of a `Field` to simplify syntax and avoid user error. The concept of `Field`s, and their corresponding `Grid`s and `Coords` is an integral part of HCIPy and is used throughout the codebase. This first chapter will focus on ways to create, modify and use `Field`s.\n",
    "\n",
    "First let's import HCIPy, and a few supporting libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hcipy import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `Grid` defines a set of points in space. There are many functions available for creating a `Field` from scratch. One of these is `make_uniform_grid()`. This function creates a regularly-spaced grid of points in $N$-dimensions in Cartesian space. The following code creates a `Grid` and plots the set of points using Matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAEJCAYAAACKWmBmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAFl5JREFUeJztnX+sZVdVgL/F9AdIS5m2xALyGEENU0up8iYotVh+iCVSS4iNrWVKMThoUWggBBMtP0z9gYgpJkQYCDQZTAaL6ACt1kCZoS2CM5PSCBOjiFJCrQydAm0BO1OXf9wz5XLnzXlv3j373f3e/r7k5Z27z7nrW3Pmzqx77tp3n8hMREREjsYjZp2AiIjUjYVCRER6sVCIiEgvFgoREenFQiEiIr1YKEREpBcLhYiI9GKhEBGRXiwUIiLSy3GzTmAITj/99NywYcOs0xARWTXs3bv3G5n5uKUcuyYKxYYNG9izZ8+s0xARWTVExFeWeqwfPYmISC8WChER6cVCISIivVgoRESkFwuFiIj0YqEQEZFeLBQiItKLhUJERHqxUIiISC8WChER6cVCISIivVgoRESkl5kUiohYFxHbIuKWiLghItZP7H9qRHwkIj4REZfMIkcRERkxqyuKC4A7M/M8YDvwysM7IiKAvwR+JzNfkJnbZ5SjiIgwu0KxEdjbbe8Gzhzb92PAE4F3R8SuiLhgoQARsSUi9kTEnv3795fNVkSkYWbZo3joKOPrgdsy80LgIuCPFzooM7dm5nxmzj/ucUu694aIiCyDWRWKfcCmbntT9/gwXwJ+vPsI6gHgeyucm4iIjDGrO9zdBFwaEbsYFYPLIuJa4LrM/HxEfAj4DHAQ+IMZ5SgiIsyoUGTmQ8DmieGrxva/G3j3iiYlIiIL4vcoRESkFwuFiIj0YqEQEZFeLBQiItKLhUJERHqxUIiISC8WChER6cVCISIivVgoRESkl6YLxVcPPMhXDzzYO7aUY4Ye06lTZ7vOaWKVoulCISIiizOrRQFnyuEqvPfO7zw8dte3DvKEU45/eOyubx0E4L+73wsdM/SYTp0623VOEx/gSaeeQCm8ohARkV6avKL4PrmEsaUcM/SYTp0623VOE6sMTReKe+4/8iZ7h8cef8rixww9plOnznadQ8QvRZOF4vBneWc98VEPP54ce9aPPvqI5yzledOM6dSps13nNPFL02ShONzM/sLXvgvAE045/uEG0eGxw/QdM/SYTp0623VOEx/KFowmC8VhTjvpyD/+5NhSjhl6TKdOne06p4lViqYLRR2NK506deocKlYZmi4UrTXLdOrUWa/TZnZl1NC40qlTp86h4pemyUJhM1unTp21OaeJDzazi1FD40qnTp06h4pViqYLxT33Hzrq2OO7Kt13zNBjOnXqbNc5RPxSzGStp4hYFxHbIuKWiLghItYvcMzTI+KuiDhrFjmKiMiIWV1RXADcmZmbI2Iz8Erg7Yd3RsTZwKuAm0smcdpJ6xYdW8oxQ4/p1KmzXec0sUoxq0KxEdjbbe8G3nh4R0Q8nVGReC3wvqMFiIgtwBaAubm5ZSXR2vQ7nTp11ut0euzCHO1P+XzgbOATwNOAn4yI52bm/eMHZeZWYCvA/Pz8MX3zpIapcDp16tQ5VPzSzKpQ7AOeDewANnWPAcjMa4FrASLiOuDPJovEtDg9VqdOnbU5p4kPa3N67E3ApRGxC3gAuCwirgWuy8zPr1QSNUyF06lTp86hYpViJoUiMx8CNk8MX7XAcVcUzmQJY2txLRmdOnXW63Stp6porVmmU6fOep02syujhsaVTp06dQ4VvzRNFgqb2Tp16qzNOU18WJvN7CqooXGlU6dOnUPFKkXThaKOxpVOnTp1DhWrDE0XitaaZTp16qzXaTO7MmpoXOnUqVPnUPFL02ShsJmtU6fO2pzTxAeb2cWooXGlU6dOnUPFKkXThaK1G6Po1KmzXqc3LhIRkVVL01cUNdykRKdOnTqHilWKpgtFa9PvdOrUWa/T6bGVUcNUOJ06deocKn5pmiwUTo/VqVNnbc5p4oPTY4tRw1Q4nTp16hwqVimaLhR1rOuiU6dOnUPFKkPThaK1ZplOnTrrddrMrowaGlc6derUOVT80jRZKGxm69SpszbnNPHBZnYxamhc6dSpU+dQsUrRdKFobS0ZnTp11ut0rScREVm1NH1FUcO6Ljp16tQ5VKxSzKRQRMQ64DpgA/Bt4GWZee/Y/huBk4BHA7+ZmbtL5NHa9DudOnXW63R67JFcANyZmZsjYjPwSuDtY/s3Z+Y9EbEJuBJ4xZDyGqbC6dSpU+dQ8Uszq0KxEdjbbe8G3ji+MzPv6TbPAW5fKEBEbAG2AMzNzR2T3OmxOnXqrM05TXxYu9Nje6+bIuKFwHOAKxban5lbga0A8/Pzy/ouew1T4XTq1KlzqFilmFWh2Ac8G9gBbOoeP0x3tXAWcEVmFvwgroZ1XXTq1KlzqFhlmFWhuAm4NCJ2AQ8Al0XEtYwa3AeAdwKfAz4ZEd/KzItKJNFas0ynTp31Om1mT9BdJWyeGL5qbPtRJf01NK506tSpc6j4pWnyexQ2s3Xq1Fmbc5r4sHab2TOnhsaVTp06dQ4VqxRNF4o6Glc6derUOVSsMjRdKFprlunUqbNep83syqihcaVTp06dQ8UvTZOFwma2Tp06a3NOEx9sZhejhsaVTp06dQ4VqxRNF4rWboyiU6fOep3euEhERFYtTV9R1HCTEp06deocKlYpmi4UrU2/06lTZ71Op8dWRg1T4XTq1KlzqPilabJQOD1Wp06dtTmniQ9Ojy1GDVPhdOrUqXOoWKVoulDUsa6LTp06dQ4VqwxNF4rWmmU6deqs12kzuzJqaFzp1KlT51DxS9NkobCZrVOnztqc08QHm9nFqKFxpVOnTp1DxSpF04WitbVkdOrUWa/TtZ5ERGTV0vQVRQ3ruujUqVPnULFK0XShaG36nU6dOut1Oj22MmqYCqdTp06dQ8UvzaKFIiKuBD6Ymd8eShoR64DrgA3At4GXZea9Y/tfB/xK9/DVmXn7UG5weqxOnTrrc04TH2Y/PfbJwOcjYiewNTM/O4D3AuDOzNwcEZuBVwJvB4iI9cCLgXOBJwHvAi4cwHkENUyF06lTp86hYpVi0VlPmflG4CeAjwFXR8TtEfHbEXHKFN6NwN5uezdw5ti+pwJfyBF3AqcvFCAitkTEnojYs3///mWmkSy8zkoe4zFDj+nUqbNd5zSxyrCkkpSZhyLiXuBe4GxgE3BVRNyamVcs093XiVm0S5OZW4GtAPPz88s6W601y3Tq1Fmvc1U3syPi94ArgC8D7wNekZkHI+I44KXL9O4Dng3sYFR09o3t+xKjYkREzAHfWKbjqNTQuNKpU6fOoeKXZilXFCcCL8jMr4wPZuYh4K+X6b0JuDQidgEPAJdFxLXAdZn5+Yi4MSJuBQJ4zTIdR8Vmtk6dOmtzThMfZtzMzsw3DS3NzIeAzRPDV43tfwfwjqG9k9TQuNKpU6fOoWKVYuVMVbJQa2OhhtFynjfNmE6dOtt1ThOrDE0XitaaZTp16qzXuaqb2WuRGhpXOnXq1DlU/NI0WShsZuvUqbM25zTxYfbfzF6z1NC40qlTp86hYpWi6ULR2o1RdOrUWa/TGxeJiMiqpekrihpuUqJTp06dQ8UqRdOForXpdzp16qzX6fTYyqhhKpxOnTp1DhW/NE0WCqfH6tSpszbnNPHB6bHFqGEqnE6dOnUOFasUTReKOtZ10alTp86hYpWh6ULRWrNMp06d9TptZldGDY0rnTp16hwqfmmaLBQ2s3Xq1Fmbc5r4YDO7GDU0rnTq1KlzqFilaLpQtLaWjE6dOut1utaTiIisWpq+oqhhXRedOnXqHCpWKZouFK1Nv9OpU2e9TqfHVkYNU+F06tSpc6j4pWmyUDg9VqdOnbU5p4kPTo8tRg1T4XTq1KlzqFilWPFCEREnAx8ETgW+BlyemQ+O7X8MsAM4ntGsrJdl5pfLZFPDui46derUOVSsMsziiuJy4OOZ+d6IuBq4CLh+bP93gV/OzPsi4mJgM/DWEom01izTqVNnvU6b2T/IRuD93fZu4FnjOzPzIHCwe3gO8LmFgkTEFmALwNzc3DElUEPjSqdOnTqHil+aYoUiIs4Atk8MHwDuAhYthRHxcuCRmfnRhfZn5lZgK8D8/PwxXYPZzNapU2dtzmniwyptZmfm3cD5k+MRcSWwCbij+71vYn8AbwIOZebrS+UHdTSudOrUqXOoWKWYxRIe24ALI2IXcBajxjURsb27CjkPuAr4hYjYGRHvKZdKsnAjKY/xmKHHdOrU2a5zmlhlWPEeRWbex6iBPTl+Sbd5N7B+JXJprVmmU6fOep02syujhsaVTp06dQ4VvzRNFgqb2Tp16qzNOU18WKXN7NVADY0rnTp16hwqVimaLhSt3RhFp06d9Tq9cZGIiKxamr6iqOEmJTp16tQ5VKxSNF0oWpt+p1OnznqdTo+tjBqmwunUqVPnUPFL02ShcHqsTp06a3NOEx+cHluMGqbC6dSpU+dQsUrRdKFYeJ2UhdZTWc7zphnTqVNnu85pYpWh6ULRWrNMp06d9TptZldGDY0rnTp16hwqfmmaLBQ2s3Xq1Fmbc5r4YDO7GDU0rnTq1KlzqFilaLpQtLaWjE6dOut1utaTiIisWpq+oqhhXRedOnXqHCpWKZouFK1Nv9OpU2e9TqfHVkYNU+F06tSpc6j4pWmyUDg9VqdOnbU5p4kPTo8tRg1T4XTq1KlzqFilaLpQ1LGui06dOnUOFasMTReK1pplOnXqrNdpM3uMiDgZ+CBwKvA14PLMfHCB454H/C3wxMy8f8gcamhc6dSpU+dQ8UsziyuKy4GPZ+Z7I+Jq4CLg+vEDIuL5wHOB20skYDNbp06dtTmniQ9rr5m9EXh/t70beNb4zq5InJ+Zvx8RO48WJCK2AFsA5ubmlpVIDY0rnTp16hwqVimKmSLiDGD7xPAB4C6g78O1C4BNXZE4h9HVxosmD8rMrcBWgPn5+WV2dWpoXOnUqVPnULHKUKxQZObdwPmT4xFxJbAJuKP7vW/ieW8YO3YncHGpHFtrlunUqbNep83sH2Qb8MGI2AzcDbwNICK2A1d1BaYoNTSudOrUqXOo+KVZ8UKRmfcxamBPjl+ywNj5JXKwma1Tp87anNPEh7XXzK6GGhpXOnXq1DlUrFI0XShauzGKTp0663V64yIREVm1NH1FUcNNSnTq1KlzqFilaLpQtDb9TqdOnfU6nR5bGTVMhdOpU6fOoeKXpslC4fRYnTp11uacJj44PbYYNUyF06lTp86hYpWi6UJRx7ouOnXq1DlUrDI4PVZERHpp8opi8rO88QbR5DFfPXB87zFDj+nUqbNd53Ljl8YrChER6SUyV+5zrlLMz8/nnj17Zp2GiMiqISL2Zub8Uo71ikJERHqxUIiISC8WChER6cVCISIivVgoRESkFwuFiIj0YqEQEZFeLBQiItKLhUJERHqxUIiISC8WChER6WXFC0VEnBwROyLilojYHhFHLH0YEc+MiBsi4uaI+PmVzlFERL7PLK4oLgc+npnnAV8ELhrfGRE/BPwp8GuZ+bzM3DWDHEVEpGMWhWIjsLfb3g2cObH/XOBkYHtEfCIiFlzdMCK2RMSeiNizf//+ctmKiDROsRsXRcQZwPaJ4QPAXcBDPU9dD/xdZv5RRMwB24AjPn7KzK3AVhgtMz5I0iIicgTFCkVm3g2cPzkeEVcCm4A7ut/7Jg7ZB7yk274POFgqRxERWZxZfPS0DbgwInYBZwE7ALrG9hmZ+QXgPyLiVuAjwO/OIEcREelY8XtmZ+Z9TDSwu/FLxravXtGkRETkqPg9ChER6cVCISIivVgoRESkFwuFiIj0YqEQEZFeLBQiItKLhUJERHqxUIiISC8WChER6cVCISIivVgoRESkl8hc/St0R8R+4CvH8JTTgW8USmdazO3YqTUvMLflUGtesLZye3JmPm4pB66JQnGsRMSezFzwhkizxtyOnVrzAnNbDrXmBe3m5kdPIiLSi4VCRER6abVQbJ11Aj2Y27FTa15gbsuh1ryg0dya7FGIiMjSafWKQkREloiFQkREelnThSIi1kXEroj4VkScdJRj3hERt0TEpyLiyd3YJRHx2e7nFwvldnJE7Ojc2yPihIn9z4yInWM//9qNXxcRuw+PzyK37ph/H8vt2m6s6Hlbwjl7TPf3eGtEfCYintKNFzln3etrW5fPDRGxfmL/67o8PhMRP9WNnT92jq4YKpdl5HZjRHw6IvZGxKZu7C0R8S9jf69nzCCvnd2+nRGxvRub+TmLiCdO/Hv8Zjde/Jx1ng9HxNcj4qwF9pV/nWXmmv8BdgInLTB+JvBX3fZ5wLuAAD4LnACcBNxWKKdXA7/RbV8NXNxz7LnAO7vt64CzCp+vRXMD9kw8Ln7eFssLOB44udu+GHhzyXMG/BLwh932ZuANY/vWAzd352UO+NjYa/GxwHHd+Tq+0N/hUXPrxk7rfm8CPtBtvwV4ceHX1mJ5HfFvtZZzNnbcU4DrV+qcjXmPeB2v1OtsTV9RLIEzgb3d9u7u8WnA1zPzwcy8H8iIWFfAvXEB99F4M3BNt/2/wPu6d80vKZDXUnM7vntHelNErNR5680rMw9m5n3dw3OA27vtUuesL5+nAl/IEXcy+tYswAmZ+c3MPAT8F/CEAfNZam5k5j3d5vh5OgS8tXtnumUWeQHfBf6he3f+c91YFedsjGsYFQhYmXPWx4q8zo6bLsc66C73tk8MH8jMly7h6Q8tMhbAsqeGHS034K6juCeffwlwS2buB8jMV3XjpwC3RsSO7N5CrGRumfmMLsZPA38C/DoDnbcBztnLgUdm5ke7XAc7ZwvQl89ir63S9Loi4oXAc4ArADLzGuCaiDgR+HRE/M1YQVmRvDLzRV1uPwJ8GPiZvuMLsNg5+1ngO5n5RVjRc9ZH8dfZmigUmXk3cP4ynroPOPwOc1P3+B7gjIg4HjiR0RTi/xs6t4i4snPeMeaePOZE4LXAC8bGTuteiN8DHpzmP7zl5hYRjwTWZeYDwHeAgwx43qbIK4A3AYcy8/Vj44Odswn2Ac8GdiyQz5eAszv/HN9fg+dQRDwWuB/YwKj4laAvN7p3v2cBV2TmQ93Y4fP0IKOrsGW/7qfI69TMPMD3X1dQyTnruAZ4+Vi+K3HO+liZ19lKfLY2qx9GzfrtwNcZvTt5Rje+HTij2/5zYBfwKWBDN3Yp8BlGn+1dUCi3kxm9IHcBH2J0qTiZ2xuA35p43vXArcBtwEtmkRvww9352QV8EnjaSpy3JeT1HOBeRp/P7gTeU/KcAeuAbV0+NzL6vPha4Jxu/+vHvM/sxp7bnaN/Al5R8LV/1NwYfZb93bHztKN7zl90ud4GvGoGeT0C+PTYz7m1nLNu/8XA2yaeU/ycdZ53Af8J/D2jN44r+jrzC3ciItJL681sERFZBAuFiIj0YqEQEZFeLBQiItKLhUJERHqxUIiISC8WChER6cVCITIwEfGrEfHPEXFctyLpbRHxgsWfKVInfuFOpAARsQ34N0bLUKzPzDfOOCWRZWOhEClAtwDhHuB/gOdm5sFFniJSLX70JFKGZLSw3WMYrSEksmrxikKkAN1HTzczuqfBiZn5mhmnJLJs1sQy4yI10d1D5JTM/EC3JPveiHhhZv7jrHMTWQ5eUYiISC/2KEREpBcLhYiI9GKhEBGRXiwUIiLSi4VCRER6sVCIiEgvFgoREenFQiEiIr38P07+6Ov0IRtJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f35eba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = make_uniform_grid([64,64], [2,1])\n",
    "\n",
    "plt.plot(grid.x, grid.y, '+')\n",
    "plt.axis('equal')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the coordinate system of the `Grid`, it exposes the arguments `x`, `y`, `z` for Cartesian coordinates, or `r`,`theta` for polar coordinates. Simply said, the `Grid` facilitates the conversion between an index, and a point in $N$-dimensional space.\n",
    "\n",
    "The coordinate values for each dimension are stored internally in a `Coords` object. There exist some variants of this type of object. Each of these derived classes indicates a structure in the coordinate values. For instance, in the case above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class of grid: <class 'hcipy.field.coordinates.RegularCoords'>\n",
      "Distance between points: [ 0.03125   0.015625]\n",
      "Number of points on each dimension: [64 64]\n",
      "Zero-point of the grid: [-0.984375  -0.4921875]\n"
     ]
    }
   ],
   "source": [
    "print('Class of grid:', grid.coords.__class__)\n",
    "print('Distance between points:', grid.delta)\n",
    "print('Number of points on each dimension:', grid.dims)\n",
    "print('Zero-point of the grid:', grid.zero)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `RegularCoords` object doesn't store the values of each point explicitly, but rather calculates those on the fly from three parameters: 1) the distance between points, 2) the number of points on each dimension, 3) the zero point.\n",
    "\n",
    "Let's use another coordinate system, and differently structured coordinates. We explicitly show how a `Grid` is constructed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f329d860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = np.logspace(-1, 1, 11)\n",
    "theta = np.linspace(0,2*np.pi, 11, endpoint=False)\n",
    "coords = SeparatedCoords((r, theta))\n",
    "\n",
    "polar_grid = PolarGrid(coords)\n",
    "cart_grid = polar_grid.as_('cartesian')\n",
    "\n",
    "plt.plot(cart_grid.x, cart_grid.y, '+')\n",
    "plt.axis('equal')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that to plot the points of this polar grid, we have converted the polar grid to a Cartesian grid. Accessing the Cartesian coordinates on a polar grid is not allowed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'PolarGrid' object has no attribute 'x'\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    print(polar_grid.x) # Doesn't work\n",
    "except AttributeError as err:\n",
    "    print(err)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each `Grid` also stores the weight of each point, that is, the interval, area, volume or hyper-volume that a point subtends in its space. They can be used to simplify doing integrations or taking derivatives on a `Grid`. In some cases, the weights can be calculated automatically, for example when the grid has regular or separated coordinates. For other coordinate structures, the weights must be supplied by the user, for example for an `UnstructuredCoords`.\n",
    "\n",
    "A `Field` is a sampled function on a `Grid`. They can be though of as a physical field, sampled on each point of a `Grid`. We can simply construct a field by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f3550630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values = np.exp(-(grid.x**2 * 10)) * np.sin(20 * grid.y)\n",
    "field = Field(values, grid)\n",
    "\n",
    "imshow_field(field)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A field can be shown by using `imshow_field()`, which acts very similar to the standard Matplotlib `pyplot.imshow()` function. It however does some things in the background. The axes are set to the correct values, according to the `Grid` of the `Field`. Additionally, it supports many other features. For instance, a complex valued field is automatically converted to a two-dimensional colorscale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f365e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "values2 = np.exp(1j * grid.x * 20) * np.sqrt(np.abs(np.sinc(5*grid.y)))\n",
    "field2 = Field(values2, grid)\n",
    "\n",
    "imshow_field(field2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These images can be extremely useful for viewing both phase and amplitude of a complex speckle field at the same time. Additionally, it supports masking out parts of the array during plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f36b22b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mask = circular_aperture(0.7)(grid)\n",
    "\n",
    "imshow_field(field2, mask=mask)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `circular_aperture(0.7)` here constructs a so-called Field generator. These are functions that take a grid as their sole parameter, and spit out a `Field` on that grid. Essentially, this can be used to calculate any analytical function at a set of points. Some classes and functions in HCIPy take Field generators as arguments, and they are used as output in some cases as well. An important class of Field generators are those generated by aperture functions. These include the above mentioned `circular_aperture`, but also `rectangular_aperture`, `hexagon_aperture`, or even complete telescopes, such as `make_magellan_aperture`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qGl+SdFSHO+ypavk3JL0i6eeSHshg+y+tV9J9Opy3ma3Py7nWWrvdc5JO9FUXJzgBSJQ6+QigARoDgASNAUCCxgAgQWMAkKAxAEjQGAAkaAwAEn8HRwoAYYDSD/8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f3813a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pupil_grid = make_pupil_grid(128)\n",
    "aperture = make_magellan_aperture(True)\n",
    "\n",
    "imshow_field(aperture(pupil_grid), cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the spiders for the Magellan aperture are very small, we have some aliasing effects. This can be avoided using supersampling during the evaluation. HCIPy implements standard functions for these:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x237f389c668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pupil = evaluate_supersampled(aperture, pupil_grid, 8)\n",
    "imshow_field(pupil, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}