Ray Tracing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/seyongpark/Projects/gravitational-lensing\n",
      "Working Directory has been set to `/Users/seyongpark/Projects/gravitational-lensing`\n"
     ]
    }
   ],
   "source": [
    "from os import path\n",
    "%matplotlib inline\n",
    "from pyprojroot import here\n",
    "workspace_path = '/Users/seyongpark/Projects/gravitational-lensing'\n",
    "%cd $workspace_path\n",
    "print(f\"Working Directory has been set to `{workspace_path}`\")\n",
    "\n",
    "import autolens as al\n",
    "import autolens.plot as aplt\n",
    "import matplotlib.pylab as plt\n",
    "import numpy as np\n",
    "from scipy.interpolate import griddata\n",
    "from astropy.cosmology import FlatLambdaCDM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scale Deflection Angles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "D_ds: 865.12 Mpc D_s: 1156.85 Mpc  Scale Factor: 0.7478\n"
     ]
    }
   ],
   "source": [
    "# compute scaling ratio for deflection angles\n",
    "cosmo = FlatLambdaCDM(H0=70, Om0=0.3)\n",
    "\n",
    "D_ds = cosmo.angular_diameter_distance_z1z2(0.566,6.2) # distance from source to lens\n",
    "D_s = cosmo.angular_diameter_distance_z1z2(0,6.2) # distance to source\n",
    "ratio = D_ds/D_s\n",
    "\n",
    "print(\"D_ds: {:.2f} D_s: {:.2f}  Scale Factor: {:.4f}\".format(D_ds,D_s,ratio))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# paths for deflection data\n",
    "x_path = path.join(\"glafic-model\",\"hlsp_relics_model_model_whl0137-08_glafic_v1_x-arcsec-deflect.fits\")\n",
    "y_path = path.join(\"glafic-model\",\"hlsp_relics_model_model_whl0137-08_glafic_v1_y-arcsec-deflect.fits\")\n",
    "\n",
    "scale = 0.1 # computed from comparing pixel and arcsec files\n",
    "\n",
    "# read in deflection data\n",
    "deflections_y = al.Array2D.from_fits(\n",
    "    file_path=y_path,\n",
    "    pixel_scales=scale,\n",
    ")\n",
    "deflections_x = al.Array2D.from_fits(\n",
    "    file_path=x_path,\n",
    "    pixel_scales=scale,\n",
    ")\n",
    "\n",
    "# scale deflection angles to account for redshift\n",
    "deflections_y = al.Array2D.no_mask(ratio*deflections_y.native, \n",
    "                                   pixel_scales = scale)\n",
    "deflections_x = al.Array2D.no_mask(ratio*deflections_x.native, \n",
    "                                   pixel_scales = scale)\n",
    "\n",
    "# construct mass profile using deflections\n",
    "deflections_plane_grid_2d = al.Grid2D.uniform(\n",
    "    shape_native=deflections_y.shape_native,\n",
    "    pixel_scales=scale,  # The pixel-scale describes the conversion from pixel units to arc-seconds\n",
    ")\n",
    "input_deflections = al.mp.InputDeflections(\n",
    "    deflections_y=deflections_y,\n",
    "    deflections_x=deflections_x,\n",
    "    image_plane_grid=deflections_plane_grid_2d\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform Ray Tracing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "detector_arcsec_per_pxl = 0.005\n",
    "reco_image_fov = 20  # arcsec on one side\n",
    "num_pix = int(reco_image_fov / detector_arcsec_per_pxl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define image plane\n",
    "image_plane_grid_2d = al.Grid2D.uniform(\n",
    "    shape_native=(num_pix, num_pix),\n",
    "    pixel_scales=detector_arcsec_per_pxl,\n",
    "#    origin=(-29.2,25)\n",
    "    origin=(-30,20)\n",
    ")\n",
    "# define lens, source and tracer\n",
    "lens_galaxy = al.Galaxy(redshift=0.566, mass=input_deflections)\n",
    "source_galaxy = al.Galaxy(redshift=6.2)\n",
    "tracer = al.Tracer.from_galaxies(galaxies=[lens_galaxy, source_galaxy],cosmology=al.cosmo.Planck15())\n",
    "\n",
    "# trace image plane to source plane\n",
    "traced_image_plane_grid_2d = tracer.traced_grid_2d_list_from(grid=image_plane_grid_2d)\n",
    "\n",
    "# save traced plane to file\n",
    "np.save(\"image_plane.npy\",traced_image_plane_grid_2d[0].native)\n",
    "np.save(\"source_plane.npy\",traced_image_plane_grid_2d[1].native)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y (arcsec)')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# perform ray tracing from image plane\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.title(\"Image Plane\")\n",
    "plt.scatter(traced_image_plane_grid_2d[0][:,1],traced_image_plane_grid_2d[0][:,0],color=\"black\",alpha=0.01)\n",
    "plt.xlim([-60,60])\n",
    "plt.ylim([-60,60])\n",
    "plt.xlabel(\"x (arcsec)\")\n",
    "plt.ylabel(\"y (arcsec)\")\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.scatter(traced_image_plane_grid_2d[-1][:,1],traced_image_plane_grid_2d[-1][:,0],color=\"black\",alpha=0.01)\n",
    "plt.title(\"Source Plane\")\n",
    "plt.xlim([-60,60])\n",
    "plt.ylim([-60,60])\n",
    "plt.xlabel(\"x (arcsec)\")\n",
    "plt.ylabel(\"y (arcsec)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y (arcsec)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# perform ray tracing from image plane\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.title(\"Image Plane\")\n",
    "plt.scatter(traced_image_plane_grid_2d[0][:,1],traced_image_plane_grid_2d[0][:,0],color=\"black\",alpha=0.01)\n",
    "plt.xlabel(\"x (arcsec)\")\n",
    "plt.ylabel(\"y (arcsec)\")\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.scatter(traced_image_plane_grid_2d[-1][:,1],traced_image_plane_grid_2d[-1][:,0],color=\"black\",alpha=0.01)\n",
    "plt.title(\"Source Plane\")\n",
    "plt.xlabel(\"x (arcsec)\")\n",
    "plt.ylabel(\"y (arcsec)\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "autolens",
   "language": "python",
   "name": "autolens"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}