{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a1b2c3d4",
   "metadata": {},
   "source": [
    "# Stray Light Analysis\n",
    "\n",
    "**Stray light** is any light that reaches the detector via an unintended path.\n",
    "In imaging systems the most common form is **ghost images** — weak secondary\n",
    "images caused by multiple internal reflections from lens surfaces.\n",
    "\n",
    "The NSQ engine is ideal for stray light analysis because rays propagate freely\n",
    "between any surfaces and every Fresnel reflection is tracked probabilistically.\n",
    "\n",
    "This notebook demonstrates:\n",
    "1. Converting a sequential design to an NSQ scene with `sequential_to_nonsequential`\n",
    "2. Using `max_depth` to reveal ghost contributions\n",
    "3. Comparing single-pass vs. multi-bounce irradiance\n",
    "4. Suppressing ghosts with AR coatings, and using importance-biased sampling to\n",
    "   measure the resulting faint ghost without a huge ray budget"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b2c3d4e5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:16.634558Z",
     "iopub.status.busy": "2026-08-18T17:51:16.633558Z",
     "iopub.status.idle": "2026-08-18T17:51:19.706074Z",
     "shell.execute_reply": "2026-08-18T17:51:19.706074Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import warnings\n",
    "\n",
    "from optiland.coatings import SimpleCoating\n",
    "from optiland.coordinate_system import CoordinateSystem\n",
    "from optiland.nonsequential import (\n",
    "    NSQScene, Spectrum,\n",
    "    CollimatedSourceConfig,\n",
    "    IrradianceDetectorConfig,\n",
    "    LensConfig, SurfaceConfig,\n",
    "    sequential_to_nonsequential,\n",
    ")\n",
    "from optiland.nonsequential.ir.scene_ir import SamplingPolicy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3d4e5f6",
   "metadata": {},
   "source": [
    "## 1. Why Sequential-to-NSQ Conversion?\n",
    "\n",
    "The sequential tracer assumes all light is transmitted at every surface —\n",
    "there are no reflected beams. The NSQ tracer applies **Fresnel splitting** at\n",
    "every uncoated interface: each ray is probabilistically refracted *or* reflected\n",
    "based on the Fresnel equations.\n",
    "\n",
    "`sequential_to_nonsequential` converts an `Optic` sequential design into an\n",
    "`NSQScene` automatically:\n",
    "- Singlet surfaces → `Lens` components\n",
    "- Cemented doublets → `Doublet` components  \n",
    "- Mirror surfaces → `Mirror` components\n",
    "- Image surface → `IrradianceDetector`\n",
    "- Each sequential field → one NSQ source"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d4e5f6a7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:19.708080Z",
     "iopub.status.busy": "2026-08-18T17:51:19.708080Z",
     "iopub.status.idle": "2026-08-18T17:51:19.868963Z",
     "shell.execute_reply": "2026-08-18T17:51:19.868963Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compound components: ['L1', 'L3', 'L5']\n",
      "Sources            : ['S0', 'S1', 'S2']\n",
      "Detectors          : ['D1']\n",
      "Total surfaces     : 12\n"
     ]
    }
   ],
   "source": [
    "from optiland.samples.objectives import CookeTriplet\n",
    "\n",
    "triplet = CookeTriplet()\n",
    "\n",
    "# Suppress the expected Fresnel-reflection warning from the converter\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    scene_triplet = sequential_to_nonsequential(\n",
    "        triplet,\n",
    "        detector_pixels=(256, 256),\n",
    "    )\n",
    "\n",
    "print(\"Compound components:\", scene_triplet.component_names)\n",
    "print(\"Sources            :\", scene_triplet.source_names)\n",
    "print(\"Detectors          :\", scene_triplet.detector_names)\n",
    "print(f\"Total surfaces     : {len(scene_triplet.surfaces)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5f6a7b8",
   "metadata": {},
   "source": [
    "## 2. Baseline Trace\n",
    "\n",
    "`max_depth` counts **every** interaction a ray has, including the one with the\n",
    "detector. So the smallest value that lets light through a system is\n",
    "\n",
    "```\n",
    "max_depth >= (number of refracting surfaces on the direct path) + 1\n",
    "```\n",
    "\n",
    "A Cooke Triplet has 6 refracting surfaces, so `max_depth=7` is the minimum for\n",
    "a direct image and anything above that starts adding ghost paths. We use a\n",
    "generous limit here so the baseline includes the full Fresnel behaviour.\n",
    "\n",
    "Note the converter creates one source per sequential field, so `total_flux_in`\n",
    "is the sum over all fields rather than 1 W.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f6a7b8c9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:19.870417Z",
     "iopub.status.busy": "2026-08-18T17:51:19.870417Z",
     "iopub.status.idle": "2026-08-18T17:51:22.037843Z",
     "shell.execute_reply": "2026-08-18T17:51:22.037843Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Baseline flux on detector: 1.70100 W\n",
      "Rays on detector         : 56,750\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_base = scene_triplet.trace(num_rays=100_000, max_depth=200, seed=42)\n",
    "irr_base = result_base.detectors['D1']\n",
    "\n",
    "print(f\"Baseline flux on detector: {irr_base.total_flux:.5f} W\")\n",
    "print(f\"Rays on detector         : {irr_base.num_rays_hit:,}\")\n",
    "\n",
    "fig = irr_base.plot(cmap='hot')\n",
    "plt.title('Cooke Triplet — baseline trace (max_depth=200)')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7b8c9d0",
   "metadata": {},
   "source": [
    "## 3. Limited-Bounce Comparison\n",
    "\n",
    "Lowering `max_depth` restricts how many surface interactions each ray can\n",
    "have. Rays exceeding the limit are killed without reaching the detector.\n",
    "Here we compare a tight limit (few ghost paths possible) against the full trace:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b8c9d0e1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:22.039848Z",
     "iopub.status.busy": "2026-08-18T17:51:22.038849Z",
     "iopub.status.idle": "2026-08-18T17:51:25.537863Z",
     "shell.execute_reply": "2026-08-18T17:51:25.537863Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multi-bounce flux on detector : 1.69661 W\n",
      "Rays on detector              : 113,206\n"
     ]
    },
    {
     "data": {
      "image/png": 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HSZMmaR0/ZcoUnc6zd+9eVKtWDX369NGU2dnZFTlt38nJCUOHDtU8trW1RatWrbSu87///S+8vb0xaNAgTZmNjY1m9tXRo0cB5L12mZmZWt3xpjJu3Ditx9u2bYOLiwteffVVrdczKCgITk5OBo1n2rZtGzp06AA3NzetOkNCQqBSqTRdr99//z1kMhkiIyML1GHIOJGDBw8iJycHU6ZM0WrFHDNmDBQKBX766Set/XV5z1xdXXHv3j2cPXtW73jMXal23wB5X6ohISHYtGkTnj59CpVKhX/+85+lfdpipaena/2itbW11ep7r1OnToFj6tati6dPn+LBgwcA8poC69WrV2C/Bg0aQK1WIzk5WdPdoo8aNWoUKHNzc9PqR7116xb69+9fbD03btzAlStXtLoKXpSWllZiLKKY2RUvx5n/Bf9id0h++YuxA8Du3bvx4YcfIiEhQau/vbAf+DfffBPffPMNfvrpJ7z99tvo2rVriXG/6O7duwAKvqc2NjZaCSWg/2tW0udElwRBl/fbzc2twNgeU8pPEgsba/Ts2TOtJDJf/mejuF/SGRkZBaYU68rJyUnTNWKM/PEAL3JxcUH16tULxF7YZ1VXun527t69CysrqwJN/YX9LinM3bt3UatWrQKxFzVDrrDrdHNzw6+//qpVZ506dQp0++V3u+T/DI0fPx7fffcdwsLCUK1aNYSGhuKNN95A9+7ddYq9KJUqVUL16tW1ym7cuIH09HR4enoWeowuv79eduPGDfz6668lvke3bt2Cj4+PTuOxdJH/+r38Htva2iIgIEDzfD5d3rNZs2bh4MGDaNWqFWrXro3Q0FAMHjwY7dq1M0nMUir1pAQABg8ejDFjxiA1NRVhYWFwdXUtdL+ifsHp+lenriZPnqw1iKtTp06ltkCSvtdU1OyB4hKEwqjVagQGBmLJkiWFPv9y8vCyypUrF/sLuqg4Cyt/Mfbjx4+jT58+6NixI7744gtUrVoVNjY2iI2NLXSQ1sOHDzWDy37//Xeo1epSmw1h7GtmCF3e75ycHDx69Ein+jw8PPSegVK1alUAeeuavCwlJQU+Pj4Fyv/++284ODgUmrDk++STTxAdHa1XLPkiIyNNspCYPp9TQP+fs3xSfHZ0Ycrr9PT0REJCAvbt24c9e/Zgz549iI2NxfDhwwsdFKsruVxe4GdarVbD09MT3377baHHFJVYFEetVuPVV1/FzJkzC32+bt26etdZGnR5zxo0aIBr165h9+7d2Lt3L77//nt88cUXmDdvnsE/c+aiTJKS119/HRERETh9+jS2bt1a5H753QUvj0h+OZMsiq5NazNnztRqHnu5m+LGjRsFjrl+/TocHBw0PwwODg64du1agf2uXr0KKysrzS+hF6/pxWRM12sqTK1atXD58uUS97l48SK6du1qUJNj/fr18f333xsaYpG+//572NnZYd++fVrdBbGxsYXuP2HCBDx58gQxMTGYM2cOli5dWuL01hflD9S9ceOGpikdyBs8mpiYiKZNm2rK9H3NdPmcmGJaYHx8PIKDg3XaNzExUWtGiC4aN26MSpUq4dy5c1pdGjk5OUhISCh0WnhiYmKJAxiHDx+O9u3b6xVLvpdbscxFUe+nrp8dPz8/qNVq3Lp1S+sv58J+lxR1/O+//w4hhNZ5bt68qeMVFF7nr7/+WiDhv3r1qub5fLa2tujduzd69+4NtVqN8ePHY82aNZg7dy5q165tsmmwtWrVwsGDB9GuXbtiE19968zIyCix1bFWrVrYt28fHj16VGxria7Xmv/6Xbt2TetznZOTg8TERINbQR0dHTFw4EAMHDgQOTk56NevHxYsWIA5c+bAzs7OoDrNQZlMwHdycsKqVasQFRWF3r17F7mfn58frK2tC0y//eKLL3Q6j6Ojo06LVDVs2BAhISGa7cVxAQBw6tQprfENycnJ+PHHHxEaGgpra2tYW1sjNDQUP/74o9a0r/v372PTpk1o3769ZtxDfjPti9eUP5XMUP3798fFixfxww8/FHguP5t+44038Mcff+DLL78ssE9WVlaJawG0adMGf//9t8F97EWxtraGTCbTaim6c+dOobOBtm/fjq1bt+Kjjz7C7Nmz8eabb+L999/H9evXdT5fy5Yt4eHhgdWrVyMnJ0dTvmHDhgKfFX1fs5I+J0DeZxIomGjro7THlLi4uCAkJATffPMNnjx5oin/+uuvkZGRUWABNQC4cOFCkbMc8gUEBGj9nOmzmWtS4ujoWOhMKF0/O/mzJ16eeajrgmzdunXDH3/8gV27dmnKnj17Vuh5ddWjRw+kpqZq/cGYm5uL5cuXw8nJCZ06dQKQ12r5IisrKzRp0gTA/3f9meLzDuS9niqVCvPnzy/wXG5urkH1v/HGGzh16hT27dtX4LnHjx9r1tPq378/hBCFtji82Fqh6/dNSEgIbG1tsWzZMq3j161bh/T0dJ1nXr3o5ffC1tYWDRs2hBACz58/17s+c1ImLSUAEB4eXuI+Li4uGDBgAJYvXw6ZTIZatWph9+7dOvcfBgUF4eDBg1iyZAl8fHzg7+9v0NTcxo0bo1u3blpTPQFofUg//PBDHDhwAO3bt8f48eNRqVIlrFmzBtnZ2VpzykNDQ1GjRg2MHj0aM2bMgLW1NdavXw8PDw8kJSXpHRsAzJgxA9u3b8eAAQMwatQoBAUF4dGjR9i1axdWr16Npk2bYtiwYfjuu+8wduxYxMXFoV27dlCpVLh69Sq+++477Nu3r8AU0Bf17NkTlSpVwsGDBzVT3kyhZ8+eWLJkCbp3747BgwcjLS0NK1euRO3atbX6TNPS0jBu3DgEBwdr7g+zYsUKxMXFYcSIEThx4oRO3Tg2Njb48MMPERERgS5dumDgwIFITExEbGxsgS8+fV8zXT4n+Qnvv/71L7z55puwsbFB7969Nb+8dWHMmJIPP/wQQN4UdiAv0ci/9cP777+v2W/BggVo27YtOnXqhLfffhv37t3Dp59+itDQ0AJjBs6fP49Hjx6hb9++BsVkyYKCgrB161ZMmzYNr7zyCpycnNC7d2+dPzvNmjXDoEGD8MUXXyA9PR1t27bFoUOHdG7piIiIwIoVKzBo0CBMnjwZVatWxbfffqv5y9iQloq3334ba9aswYgRI3D+/HnUrFkT27dvx8mTJ7F06VI4OzsDyBsw/OjRI3Tp0gXVq1fH3bt3sXz5cjRr1kzTatasWTNYW1tj0aJFSE9Ph1wuR5cuXYocG1KUTp06ISIiAjExMUhISEBoaChsbGxw48YNbNu2DZ9//rneYxNnzJiBXbt2oVevXpplFjIzM3Hp0iVs374dd+7cQZUqVRAcHIxhw4Zh2bJluHHjBrp37w61Wo3jx49r/T7S9fvGw8MDc+bMQXR0NLp3744+ffrg2rVr+OKLL/DKK69otdrrKjQ0FN7e3mjXrh28vLxw5coVrFixAj179tS8XxarNKb0vDgluDgvTwkWQogHDx6I/v37CwcHB+Hm5iYiIiLE5cuXdZoSfPXqVdGxY0dhb28vAGima+k7JXjChAnim2++EXXq1BFyuVw0b9680CluFy5cEN26dRNOTk7CwcFBBAcHi/j4+AL7nT9/XrRu3VrY2tqKGjVqiCVLlhQ5Jfjl10OIgtMfhRDi4cOHYuLEiaJatWrC1tZWVK9eXYSHh4u//vpLs09OTo5YtGiRaNSokZDL5cLNzU0EBQWJ6OhonabV9unTR3Tt2lWrrKj3Nv/9ePDggVZ5YdP11q1bp3lt69evL2JjYwu8n/369RPOzs7izp07Wsf++OOPAoBYtGhRifG/6IsvvhD+/v5CLpeLli1bimPHjhX6uur6munzOZk/f76oVq2asLKy0nrP8+t42ctTGY2BYqYPv+z48eOibdu2ws7OTnh4eIgJEyZopoO+aNasWaJGjRpa0yPLmq5TggubKtqpU6dCp1PqskRBRkaGGDx4sHB1dRUAtKYH6/rZycrKEpMmTRKVK1cWjo6Oonfv3iI5OVmnKcFCCHH79m3Rs2dPYW9vLzw8PMT06dPF999/LwCI06dPl3id4eHhBaY1379/X4wcOVJUqVJF2NraisDAQK3XUgghtm/fLkJDQ4Wnp6fmd1lERIRISUnR2u/LL78UAQEBwtrausTpwUW9R/nWrl0rgoKChL29vXB2dhaBgYFi5syZ4s8//yyxjsJ+jp48eSLmzJkjateuLWxtbUWVKlVE27ZtxSeffCJycnI0++Xm5orFixeL+vXrC1tbW+Hh4SHCwsLE+fPnNfvo+32zYsUKUb9+fWFjYyO8vLzEuHHjxN9//621j67v2Zo1a0THjh1F5cqVhVwuF7Vq1RIzZszQa7kEcyUTwoxuYEFm5fjx4+jcuTOuXr1a6EyTikwmk2HChAlYsWKF1KGUqezsbNSsWROzZ8/WLKpF0lu6dCmmTp2Ke/fuoVq1alKHQ2Qw3tSBitShQweEhoYWusQxVUyxsbGwsbHB2LFjpQ6lwnp53Zhnz55hzZo1qFOnDhMSsnhlNqaELNOePXukDqFIjx490hq8+jJra2uDpg5S0caOHcuERGL9+vVDjRo10KxZM6Snp+Obb77B1atXi5w+S2RJmJSQxerXr59mtcnC+Pn5lekt1InKQrdu3fDVV1/h22+/hUqlQsOGDbFlyxYMHDhQ6tCIjMYxJWSxzp8/X+wCb/b29uVihUMiooqCSQkRERGZBQ50JSIiIrPAMSUvUavV+PPPP+Hs7GyyJZOJiMj8CSHw5MkT+Pj4lNo9tgrz7NmzYgft68PW1tail5lnUvKSP//8U7KbZxERkfSSk5ML3Lm4tDx79gz+/v5ITU01SX3e3t5ITEy02MSESclL8pfotQPAdhKqSGwAtANgCyAHwHEApr0/N5F5EwCeAWW6VHtOTg5SU1ORnJysuWeaoZRKJXx9fZGTk8OkpLzI77KRgUkJVSy5AE688FgN/gxQxSRF171C4QCFwsHIWnJNEouUmJQQkQZbRoikkgvjkwrLT0o4+4aIiIjMAltKiIiIJMeWEoBJCRERkRlgUgKw+4aIiIjMBFtKiIiIJKeC8S0dlj9UnUkJERGR5Nh9A7D7hoiIqEJSqVSYO3cu/P39YW9vj1q1amH+/PmQ8j69bCkhIiKSXNm3lCxatAirVq3Cxo0b0ahRI5w7dw4jR46Ei4sLJk2aZGQshmFSQkREJLmyT0ri4+PRt29f9OzZEwBQs2ZNbN68GT///LORcRiO3TdEREQVUNu2bXHo0CFcv34dAHDx4kWcOHECYWFhksXElhIiIiLJqWD87Jm845VKpVapXC6HXC4vsPfs2bOhVCpRv359WFtbQ6VSYcGCBRgyZIiRcRiOLSVERESSy58SbMyWl5T4+vrCxcVFs8XExBR6xu+++w7ffvstNm3ahAsXLmDjxo345JNPsHHjxlK8zuKxpYSIiKgcSU5OhkKh0DwurJUEAGbMmIHZs2fjzTffBAAEBgbi7t27iImJQXh4eJnE+jImJURERJIz3UBXhUKhlZQU5enTp7Cy0u4wsba2hlqtNjIOwzEpISIiklzZz77p3bs3FixYgBo1aqBRo0b45ZdfsGTJEowaNcrIOAzHpISIiKgCWr58OebOnYvx48cjLS0NPj4+iIiIwLx58ySLSSakXLrNDCmVSri4uMAegEzqYIiIqMwIAFkA0tPTder+MIX875z09CNQKJyMrCsDLi6dyzR+U2NLCRERkeR4Qz6AU4KJiIjITLClhIiISHK8SzDApISIiMgMMCkB2H1DREREZoItJURERJJjSwnApISIiMgMMCkBLKz75tixY+jduzd8fHwgk8mwc+dOredHjBgBmUymtXXv3l2aYImIiEgvFtVSkpmZiaZNm2LUqFHo169foft0794dsbGxmsdF3YiIiIjIfHCdEsDCkpKwsDCEhYUVu49cLoe3t3cZRURERGQK7L4BLKz7RhdHjhyBp6cn6tWrh3HjxuHhw4dSh0REREQ6sKiWkpJ0794d/fr1g7+/P27duoX33nsPYWFhOHXqFKytrQs9Jjs7G9nZ2ZrHSqWyrMIlIiL6H7aUAOUsKXnzzTc1/w8MDESTJk1Qq1YtHDlyBF27di30mJiYGERHR5dViERERIVgUgKUw+6bFwUEBKBKlSq4efNmkfvMmTMH6enpmi05ObkMIyQiIqJ85aql5GX37t3Dw4cPUbVq1SL3kcvlnKFDREQSY0sJYGFJSUZGhlarR2JiIhISEuDu7g53d3dER0ejf//+8Pb2xq1btzBz5kzUrl0b3bp1kzBqIiKiknBKMGBhScm5c+cQHByseTxt2jQAQHh4OFatWoVff/0VGzduxOPHj+Hj44PQ0FDMnz+fLSFEREQWwKKSks6dO0MIUeTz+/btK8NoiIiITEUF41s62FJCRERERuOYEqCcz74hIiIiy8GWEiIiIsmxpQRgUkJERGQGOPsGYPcNERERmQm2lBAREUmO3TcAkxIiIiIzwKQEYPcNERERmQm2lBAREUmOLSUAkxIiIiIzwKQEYPcNERERmQm2lBAREUmO65QATEqIiIjMQC4AaxPUYdnYfUNERERmgS0lREREkmNLCcCkhIiIyAwwKQHYfUNERERmgi0lREREkuPsG4AtJURERGYg10Sb7mrWrAmZTFZgmzBhgmkuyQBsKSEijRd7tC3/by4iKs7Zs2ehUv3/T/rly5fx6quvYsCAAZLFxKSEiDQckJeYqAA8kTgWooolF8Z3XujXUuLh4aH1+KOPPkKtWrXQqVMnI+MwHJMSIoI1AB8AV0cD8AbwAKi/FkiWNiyiCsR0SYlSqdQqlcvlkMvlxR6Zk5ODb775BtOmTYNMJjMyDsNxTAkRQQXgOQCc+f/tuaQREZGhfH194eLiotliYmJKPGbnzp14/PgxRowYUfoBFoMtJUQEAHgA4JXLgPXlvCTlgdQBEVUoKhg/kivv+OTkZCgUCk1pSa0kALBu3TqEhYXBx8fHyBiMw6SEiADk/Tq7/dJjIiorppsSrFAotJKSkty9excHDx7Ejh07jDy/8ZiUEJHGM6kDIKIyFxsbC09PT/Ts2VPqUJiUEBERSS8XgLEDTPVvaVGr1YiNjUV4eDgqVZI+JZA+AiIiogpPmqTk4MGDSEpKwqhRo4w8t2kwKSEiIqqgQkNDIYSQOgwNJiVERESSk6alxNwwKSEiIpIckxKAi6cRERGRmWBLCRERkeRUML6lxPJXF2JSQkREJDlTdL2w+4aIiIjIJNhSQkREJDm2lABMSoiIiMwAkxKA3TdERERkJthSQkREJDlTzJzh7BsiIiIyWi4AY5d7t/ykhN03REREZBbYUkJERCQ5tpQATEqIiIjMAJMSwMK6b44dO4bevXvDx8cHMpkMO3fu1HpeCIF58+ahatWqsLe3R0hICG7cuCFNsERERKQXi0pKMjMz0bRpU6xcubLQ5z/++GMsW7YMq1evxpkzZ+Do6Ihu3brh2bNnZRwpERGRPnJNtFk2i+q+CQsLQ1hYWKHPCSGwdOlSvP/+++jbty8A4N///je8vLywc+dOvPnmm2UZKhERkR5UML77Rm2KQCRlUS0lxUlMTERqaipCQkI0ZS4uLmjdujVOnTpV5HHZ2dlQKpVaGxEREZW9cpOUpKamAgC8vLy0yr28vDTPFSYmJgYuLi6azdfXt1TjJCIiKkhlos2ylZukxFBz5sxBenq6ZktOTpY6JCIiqnA4pgQoR0mJt7c3AOD+/fta5ffv39c8Vxi5XA6FQqG1ERERUdkrN0mJv78/vL29cejQIU2ZUqnEmTNn0KZNGwkjIyIiKglbSgALm32TkZGBmzdvah4nJiYiISEB7u7uqFGjBqZMmYIPP/wQderUgb+/P+bOnQsfHx+89tpr0gVNRERUolwY305g+bNvLCopOXfuHIKDgzWPp02bBgAIDw/Hhg0bMHPmTGRmZuLtt9/G48eP0b59e+zduxd2dnZShUxEREQ6kgkhjJ0YXa4olUq4uLjAHoBM6mCIiKjMCABZANLT08tsfGH+d056ugIKhXHfOkqlgIuLskzjNzWLaikhIiIqn3Jh/J/Clt/GUG4GuhIREZFlY0sJERGR5NhSAjApISIiMgNMSgB23xAREZGZYEsJERGR1ITa+IYOy28oYVJCREQkOTWMX/vM8tdOY/cNERERmQe2lBAREUlN9b/N2DosHJMSIiIiqTEpAcDuGyIiogrrjz/+wNChQ1G5cmXY29sjMDAQ586dkywetpQQERFJTYKBrn///TfatWuH4OBg7NmzBx4eHrhx4wbc3NyMDMRwTEqIiIikJkH3zaJFi+Dr64vY2FhNmb+/v5FBGIfdN0REROWIUqnU2rKzswvdb9euXWjZsiUGDBgAT09PNG/eHF9++WUZR6uNSQkREZHU1CbaAPj6+sLFxUWzxcTEFHrK27dvY9WqVahTpw727duHcePGYdKkSdi4cWPpXWcJ2H1DREQkNTWM7775X1KSnJwMhUKhKZbL5YXvrlajZcuWWLhwIQCgefPmuHz5MlavXo3w8HAjgzEMW0qIiIjKEYVCobUVlZRUrVoVDRs21Cpr0KABkpKSyiLMQrGlhIiISGoSDHRt164drl27plV2/fp1+Pn5GRmI4dhSQkREJDUTjinR1dSpU3H69GksXLgQN2/exKZNm7B27VpMmDDBJJdkCCYlREREFdArr7yCH374AZs3b0bjxo0xf/58LF26FEOGDJEsJnbfEBERSU2iZeZ79eqFXr16GXli02FSQkREJDXe+wYAu2+IiIjITLClhIiISGoS3PvGHDEpISIikhq7bwAwKSEiIiIdKJVKvY95cWVZXTApISIikpqA8d0vwhSBFM3V1RUymUzn/WUyGa5fv46AgACdj2FSQkREJDUL6b7Zvn073N3dS9xPCIEePXroXT+TEiIiIiqRn58fOnbsiMqVK+u0f0BAAGxsbPQ6B5MSIiIiqVlAS0liYqJe+1++fFnvczApISIikhqnBAPg4mlERESkh6ysLJw4cQK///57geeePXuGf//73wbXzaSEiIhIaioTbaXs+vXraNCgATp27IjAwEB06tQJKSkpmufT09MxcuRIg+tnUkJERCQ1C0lKZs2ahcaNGyMtLQ3Xrl2Ds7Mz2rVrh6SkJJPUz6SEiIiIdBIfH4+YmBhUqVIFtWvXxn/+8x9069YNHTp0wO3bt42un0kJERGR1NQm2kpZVlYWKlX6/zkyMpkMq1atQu/evdGpUydcv37dqPo5+4aIiEhqahjf/VIGSUn9+vVx7tw5NGjQQKt8xYoVAIA+ffoYVT9bSoiIiEgnr7/+OjZv3lzocytWrMCgQYMghOHr3cuEMUeXQ0qlEi4uLrAHoPsK/0REZOkEgCzkzSDR90Zyhsr/zknfDygcjawrE3AJLdv4TY3dN0RERFKzgBVdywK7b4iIiEgvN27cKJV6mZQQERFJzULWKQGA8+fPo3PnzqVSd7lKSqKioiCTybS2+vXrSx0WERFR8SxkSvDhw4cREhKCjz76qFTqL3djSho1aoSDBw9qHr84n5qIiIgMs2PHDgwdOhRLlizBsGHDSuUc5e4bu1KlSvD29pY6DCIiIt1ZwEDXgQMHIioqCmPHji21c5Sr7hsgb/CNj48PAgICMGTIkBLX48/OzoZSqdTaiIiIypQFjCmpVasW9u/fj6ysrFI7R7lKSlq3bo0NGzZg7969WLVqFRITE9GhQwc8efKkyGNiYmLg4uKi2Xx9fcswYiIiIstw4sQJPH36FK+//jqeP39eKuco14unPX78GH5+fliyZAlGjx5d6D7Z2dnIzs7WPFYqlfD19eXiaUREFYyki6dtAxQORtb1FHAZULrxZ2RkoE+fPnBxccEPP/xg8vrLVUvJy1xdXVG3bl3cvHmzyH3kcjkUCoXWRkREVKYsoPsGAJycnLBnzx5YWZVO+lCuk5KMjAzcunULVatWlToUIiKickEul2Pbtm2lUne5SkreffddHD16FHfu3EF8fDxef/11WFtbY9CgQVKHRkREVDQLWackX2m1lJSrKcH37t3DoEGD8PDhQ3h4eKB9+/Y4ffo0PDw8pA6NiIioaBYwJbgwaWlpSEtLg1qtnRE1adLEoPrKVVKyZcsWqUMgIiIq986fP4/w8HBcuXIF+fNlZDIZhBCQyWRQqQzLkMpVUkJERGSRLKylZNSoUahbty7WrVsHLy8vyGSmma/KpISIiEhqphgTUoZjSm7fvo3vv/8etWvXNmm95WqgKxEREZW+rl274uLFiyavly0lREREUpOg+yYqKgrR0dFaZfXq1cPVq1dLPParr75CeHg4Ll++jMaNG8PGxkbr+T59+ugXzP8wKSEiIpKaGsYnJQZ03zRq1AgHDx7UPK5USbe04NSpUzh58iT27NlT4DljBrqy+4aIiKiCqlSpEry9vTVblSpVdDrunXfewdChQ5GSkgK1Wq21GZqQAExKiIiIpCfR4mk3btyAj48PAgICMGTIECQlJel03MOHDzF16lR4eXnpf9JiMCkhIiKSmgnvfaNUKrW2F286+6LWrVtjw4YN2Lt3L1atWoXExER06NABT548KTHcfv36IS4uzogLLhzHlBAREZUjvr6+Wo8jIyMRFRVVYL+wsDDN/5s0aYLWrVvDz88P3333HUaPHl3sOerWrYs5c+bgxIkTCAwMLDDQddKkSQbFzqSEiIhIaiZcpyQ5OVnrjvdyuVynw11dXVG3bl3cvHmzxH2/+uorODk54ejRozh69KjWczKZjEkJERGRxTLhlGCFQqGVlOgqIyMDt27dwrBhw0rcNzExUe/6dcExJURERBXQu+++i6NHj+LOnTuIj4/H66+/DmtrawwaNEiymNhSQkREJDUJFk+7d+8eBg0ahIcPH8LDwwPt27fH6dOn4eHhUeKxQghs374dcXFxhd4leMeOHfoF8z9MSoiIiKQmwb1vtmzZYvCppkyZgjVr1iA4OJg35CMiIiLpfP3119ixYwd69Ohh0nqZlBAREUlNomXmDeXi4oKAgACT18uBrkRERFKTaEVXQ+XfzC8rK8uk9bKlhIiIiPTyxhtvYPPmzfD09ETNmjULLJ524cIFg+plUkJERCQ1CWbfGCM8PBznz5/H0KFDOdCViIiIpPPTTz9h3759aN++vUnrZVJCREQkNQtrKfH19TVo1diScKArERGR1CxsoOunn36KmTNn4s6dOyatly0lREREpJehQ4fi6dOnqFWrFhwcHAoMdH306JFB9eqUlCxbtkzvikeOHAlnZ2e9jyMiIqpwLKz75rPPPjPZ4NYX6ZSUTJkyBdWrV4e1tbVOlSYnJ6NXr15MSoiIiHRhIUnJ4cOH0alTJ4wYMaJU6te5++bcuXPw9PTUaV8mI0REROXPW2+9hcePH6N79+7o27cvwsLCTDrgVaeBrpGRkXByctK50vfeew/u7u4GB0VERFShCBg/yFWUfpi3b9/GkSNH0LBhQ3z66afw8vLCq6++iuXLlyMpKcno+mVCiDK4DMuhVCrh4uICewCm7y0jIiJzJQBkAUhPTy+V6a6Fyf/OSX8XUMiNrCsbcPmkbOP/888/sWvXLuzatQtxcXGoV68e+vTpgz59+qBly5Z618cpwURERGQQHx8fjB07Fv/973/x119/Ye7cubhz5w66d++OhQsX6l2f3lOCHz58iHnz5iEuLg5paWlQq7UnRhs6DYiIiKjCMsU6I2WwTkliYiL8/f0Lfc7R0RH9+/dH//79oVKpDMoH9E5Khg0bhps3b2L06NEmXe+eiIiowrKQ2Te1atWCn58fgoODNVv16tUL7GdtbQ0PDw+969c7KTl+/DhOnDiBpk2b6n0yIiIislyHDx/GkSNHcOTIEWzevBk5OTkICAhAly5dNEmKl5eXwfXrnZTUr18fWVlZBp+QiIiIXmIhLSWdO3dG586dAQDPnj1DfHy8JknZuHEjnj9/jvr16+O3334zqH69k5IvvvgCs2fPxrx589C4ceMCS8uW1YhfIiKicsNCxpS8yM7ODl26dEH79u0RHByMPXv2YM2aNbh69arBdeqdlLi6ukKpVKJLly5a5UIIyGQyqFRluM4tERERlamcnBycPn0acXFxOHLkCM6cOQNfX1907NgRK1asQKdOnQyuW++kZMiQIbCxscGmTZs40JWIiMgULKT7pkuXLjhz5gz8/f3RqVMnREREYNOmTahatapJ6tc7Kbl8+TJ++eUX1KtXzyQBEBERVXhqGJ9UlEH3zfHjx1G1alV06dIFnTt3RqdOnVC5cmWT1a/34mktW7ZEcnKyyQIgIiIiy/D48WOsXbsWDg4OWLRoEXx8fBAYGIiJEydi+/btePDggVH1673M/LZt2xAVFYUZM2YgMDCwwEDXJk2aGBWQ1LjMPBFRxSTpMvOjAYWtkXXlAC7ryjb+J0+e4MSJE5rxJRcvXkSdOnVw+fJlg+rTu/tm4MCBAIBRo0ZpymQyGQe6EhERGcpCxpS8zNHREe7u7nB3d4ebmxsqVaqEK1euGFyf3klJYmKiwScjIiIiy6VWq3Hu3DkcOXIEcXFxOHnyJDIzM1GtWjUEBwdj5cqVCA4ONrh+vZMSPz8/g09GREREhbCQdUpcXV2RmZkJb29vBAcH47PPPkPnzp1Rq1Ytk9Svd1IC5N2q+MSJE4XekG/SpEkmCcwYK1euxOLFi5GamoqmTZti+fLlaNWqldRhERERFc5Cum8WL16M4OBg1K1bt1Tq1zsp2bBhAyIiImBra4vKlStrrVMik8kkT0q2bt2KadOmYfXq1WjdujWWLl2Kbt264dq1a/D09JQ0NiJz9+Kw9eeSRUFE5ioiIqJU69d7SvDcuXMxb948pKen486dO0hMTNRst2/fLo0Y9bJkyRKMGTMGI0eORMOGDbF69Wo4ODhg/fr1UodGZNasATQD0OJ//1pLGQxRRaMy0VaK+vXrB6VSqfP+Q4YMQVpaml7n0Dspefr0Kd58801YWel9aKnLycnB+fPnERISoimzsrJCSEgITp06JWFkRObNBkBLAEdEFA6LvTgi5qAFtFtOiKgUqU20laIff/wRDx48gFKpLHFLT0/Hf/7zH2RkZOh1Dr27b0aPHo1t27Zh9uzZ+h5a6v766y+oVKoCt0328vIq8gZB2dnZyM7O1jzWJwskKk/yWkY6AWgPALBCjITREJG5EUKU2liSfHonJTExMejVqxf27t1b6OJpS5YsMVlwZSEmJgbR0dFSh0EkubyW3zP/e3S6rG84SlSxWcAy83FxcXofU61aNb32Nygp2bdvn+beNy8PdJVSlSpVYG1tjfv372uV379/H97e3oUeM2fOHEybNk3zWKlUwtfXt1TjJDI3zwFcAPCqbDas/vc4ARzsSlRmVDBgQEUhdZQiY+7+qyu9X4JPP/0U69evx5UrVzSLp+Rvhw8fLo0YdWZra4ugoCAcOnRIU6ZWq3Ho0CG0adOm0GPkcjkUCoXWRlQRPQdwFnltJRfAhISoIvnoo48gk8kwZcoUSePQu6VELpejXbt2pRGLSUybNg3h4eFo2bIlWrVqhaVLlyIzMxMjR46UOjQis8dEhEgiEi6edvbsWaxZs8Ys7l2nd0vJ5MmTsXz58tKIxSQGDhyITz75BPPmzUOzZs2QkJCAvXv3Fhj8SkREZDYkmhKckZGBIUOG4Msvv4Sbm5vRl2EsvVtKfv75Zxw+fBi7d+9Go0aNCgx03bFjh8mCM9TEiRMxceJEqcMgIiIyaxMmTEDPnj0REhKCDz/8UOpw9E9KXF1d0a9fv9KIhYiIqGIyYffNy0tbyOVyyOXyArtv2bIFFy5cwNmzZw06XW5uLo4cOYJbt25h8ODBcHZ2xp9//gmFQgEnJyeD6tQ7KYmNjTXoRERERFQEE86+eXkGaWRkJKKiorTKkpOTMXnyZBw4cAB2dnZ6n+ru3bvo3r07kpKSkJ2djVdffRXOzs5YtGgRsrOzsXr1aoMuwaAb8hEREZF5Sk5O1ppJWlgryfnz55GWloYWLVpoylQqFY4dO4YVK1YgOzsb1tZF32xi8uTJaNmyJS5evIjKlStryl9//XWMGTPG4Nh1SkpatGiBQ4cO6TwIpn379ti6davei6YQERFVSCZsKdFleYuuXbvi0qVLWmUjR45E/fr1MWvWrGITEgA4fvw44uPjYWtrq1Ves2ZN/PHHH/rH/j86JSUJCQm4ePEi3N3ddao0ISFBa+l2IiIiKoaA8WNKhO67Ojs7o3Hjxlpljo6OqFy5coHywqjVaqhUBaf73Lt3D87OzroH8hKdu2+6du0KIXS7YqlXdiUiIqLSExoaiqVLl2Lt2rUA8r73MzIyEBkZiR49ehhcr0zokGncvXtX74qrV69eYvOPOVIqlXBxcYE9AKZWREQVhwCQBSA9Pb3MVvfO/85J7wwojBzlqcwFXI6UTfz37t1Dt27dIITAjRs30LJlS9y4cQNVqlTBsWPH4OnpaVC9Or0Efn5+BlVOREREOlDB+L+ES/neNy+qXr06Ll68iK1bt+LixYvIyMjA6NGjMWTIENjb2xtcL2ffEBERkd4qVaqEIUOGYMiQISar09ixvkRERGQstYm2MhITE4P169cXKF+/fj0WLVpkcL1MSoiIiKQm0b1vDLVmzRrUr1+/QHmjRo0MXjgNYFJCREREekpNTUXVqlULlHt4eCAlJcXgevVOSsLDw3Hs2DGDT0hEREQvsbDuG19fX5w8ebJA+cmTJ+Hj42NwvXoPdE1PT0dISAj8/PwwcuRIhIeHc+VWIiIiY1jY7JsxY8ZgypQpeP78Obp06QIAOHToEGbOnInp06cbXK/eScnOnTvx4MEDfP3119i4cSMiIyMREhKC0aNHo2/fvrCxsTE4GCIiIjJ/M2bMwMOHDzF+/Hjk5OQAAOzs7DBr1izMmTPH4Hp1WjytOBcuXEBsbCy++uorODk5YejQoRg/fjzq1KljTLWS4eJpREQVk6SLpzUHFEauN6pUAS6/lG38GRkZuHLlCuzt7VGnTp1Cb/6nD6MGuqakpODAgQM4cOAArK2t0aNHD1y6dAkNGzbEZ599ZlRgREREFYaFjSnJ5+TkhFdeeQWNGzc2OiEBDOi+ef78OXbt2oXY2Fjs378fTZo0wZQpUzB48GBNZvbDDz9g1KhRmDp1qtEBEhERkXnJzMzERx99hEOHDiEtLQ1qtXZGdPv2bYPq1TspqVq1KtRqNQYNGoSff/4ZzZo1K7BPcHAwXF1dDQqIiIiowjHFINUyHOj61ltv4ejRoxg2bBiqVq1qshvx6p2UfPbZZxgwYADs7OyK3MfV1RWJiYlGBUZERFRhWFhSsmfPHvz0009o166dSevVOykZNmyYSQMgIiIiy+Lm5gZ3d3eT18sVXYmIiKRmYQNd58+fj3nz5uHp06cmrZd3CSYiIpKahXXffPrpp7h16xa8vLxQs2bNAmuUXbhwwaB6mZQQERGRXl577bVSqZdJCRERkdTUMH7FzjLsvomMjCyVepmUEBERSc0UCYUEi6eZGpMSIiIi0otKpcJnn32G7777DklJSZr73+R79OiRQfVy9g0REZHUVCbaykh0dDSWLFmCgQMHIj09HdOmTUO/fv1gZWWFqKgog+tlUkJERCQ1C5sS/O233+LLL7/E9OnTUalSJQwaNAhfffUV5s2bh9OnTxtcL5MSIiIi0ktqaioCAwMB5N2ULz09HQDQq1cv/PTTTwbXy6SEiIhIahbWfVO9enWkpKQAAGrVqoX9+/cDAM6ePWvU3YKZlBAREUnNwpKS119/HYcOHQIAvPPOO5g7dy7q1KmD4cOHY9SoUQbXKxNCCFMFWR4olUq4uLjAHsZPGSciIsshAGQBSE9Ph0KhKJNz5n/npHsACiObCZRqwOVB2caf79SpUzh16hTq1KmD3r17G1wPpwQTERFJzcLXKWnTpg3atGljdD1MSoiIiKSmRl5TjTFKud9j165dCAsLg42NDXbt2lXsvn369DHoHOy+eQm7b4iIKiZJu2/cAIWRXzpKAbj8XXrxW1lZITU1FZ6enrCyKrqvSSaTQaUybIALW0qIiIikZop735RyE4NarS70/6bEpISIiEhqKph9UlIWmJQQERFRiZYtW6bzvpMmTTLoHBxT8hKOKSEiqpgkHVNib6IxJVmlF7+/v7/W4wcPHuDp06dwdXUFADx+/BgODg7w9PTE7du3DToHF08jIiKSmgXc+yYxMVGzLViwAM2aNcOVK1fw6NEjPHr0CFeuXEGLFi0wf/58g8/BlpKXsKWEiKhikrSlRG6ilpLssom/Vq1a2L59O5o3b65Vfv78efzzn/9EYmKiQfWWq5aSmjVrQiaTaW0fffSR1GEREREVz8KWmU9JSUFubm6BcpVKhfv37xtcb7lKSgDggw8+QEpKimZ75513pA6JiIioeBIkJatWrUKTJk2gUCigUCjQpk0b7NmzR6dju3btioiICFy4cEFTdv78eYwbNw4hISH6BfKCcpeUODs7w9vbW7M5OjpKHRIREZHZqV69Oj766COcP38e586dQ5cuXdC3b1/89ttvJR67fv16eHt7o2XLlpDL5ZDL5WjVqhW8vLzw1VdfGRxTuRpTUrNmTTx79gzPnz9HjRo1MHjwYEydOhWVKuk+85ljSoiIKiZJx5QAMPaMSgAuMC5+d3d3LF68GKNHj9Zp/+vXr+Pq1asAgPr166Nu3boGnTdfuVqnZNKkSWjRogXc3d0RHx+POXPmICUlBUuWLCnymOzsbGRnZ2seK5XKsgiViIhIwxRDQvKPf/l7LL8lo9hjVSps27YNmZmZet1Yr27dukYnIi8y+5aS2bNnY9GiRcXuc+XKFdSvX79A+fr16xEREYGMjIwi35CoqChER0cXKGdLCRFRxSJlS8kjmKalxL2Q8sjISERFRRV6zKVLl9CmTRs8e/YMTk5O2LRpE3r06KHT+e7du4ddu3YhKSkJOTk5Ws8V1xhQHLNPSh48eICHDx8Wu09AQABsbW0LlP/2229o3Lgxrl69inr16hV6bGEtJb6+vkxKiIgqGCmTkgcwTVLiASA5OVkr/uJaSnJycpCUlIT09HRs374dX331FY4ePYqGDRsWe65Dhw6hT58+CAgIwNWrV9G4cWPcuXMHQgi0aNEChw8fNugazL77xsPDAx4eHgYdm5CQACsrK3h6eha5jy7NWkRERKXJFGuf5R+fP5tGF7a2tqhduzYAICgoCGfPnsXnn3+ONWvWFHvcnDlz8O677yI6OhrOzs74/vvv4enpiSFDhqB79+4GX4PZJyW6OnXqFM6cOYPg4GA4Ozvj1KlTmDp1KoYOHQo3NzepwyMiIjJ7arVaq/egKFeuXMHmzZsBAJUqVUJWVhacnJzwwQcfoG/fvhg3bpxB5y83SYlcLseWLVsQFRWF7Oxs+Pv7Y+rUqZg2bZrUoRERERXLlANddTVnzhyEhYWhRo0aePLkCTZt2oQjR45g3759JR7r6OioGUdStWpV3Lp1C40aNQIA/PXXX/qGrlFukpIWLVrg9OnTUodBRESkN1N23+gqLS0Nw4cPR0pKClxcXNCkSRPs27cPr776aonH/uMf/8CJEyfQoEED9OjRA9OnT8elS5ewY8cO/OMf/zDsAlCOkhIiIiLS3bp16ww+dsmSJcjIyAAAREdHIyMjA1u3bkWdOnUMnnkDMCkhIiKSnBTdNwafR6XCvXv30KRJEwB5XTmrV682Sd3lbpl5IiIiS6OG8be9Mbb7R1fW1tYIDQ3F33//bfK6mZQQERGRXho3bozbt2+bvF4mJURERBJTm2grKx9++CHeffdd7N69GykpKVAqlVqboTimhIiISGKWNKYEgGYp+j59+kAm+//1z4UQkMlkUKkMi4ZJCREREeklLi6uVOplUkJERCQxS2opef78OT744AOsXr0aderUMWndTEqIiIgkJsXiaYaysbHBr7/+Wip1c6ArERER6WXo0KFGLb5WFLaUEBERScySum8AIDc3F+vXr8fBgwcRFBQER0dHrecNXdWVSQkREZHELKn7BgAuX76MFi1aAACuX7+u9dyLs3H0xaSEiIiI9MLZN0REROVU/jLzxtZh6ZiUEBERScxSxpT069dPp/127NhhUP1MSoiIiEgnLi4upVo/kxIiIiKJWcpA19jY2FKtn0kJERGRxCyl+6a0cfE0IiIiMgtsKSEiIpIYW0ryMCkhIiKSmKWMKSlt7L4hIiIis8CWEiIiIomx+yYPkxIiIiKJCRjf/SJMEYjE2H1DREREZoEtJURERBJj900eJiVEREQSY1KSh903REREZBbYUkJERCQxrlOSh0kJERGRxNh9k4fdN0RERGQW2FJCREQkMbaU5GFSQkREJDGOKcnD7hsiIiIyC2wpISIikpgaxne/lIeWEiYlREREEmP3TR523xAREVVAMTExeOWVV+Ds7AxPT0+89tpruHbtmqQxMSkhIiKSmMpEmz6OHj2KCRMm4PTp0zhw4ACeP3+O0NBQZGZmmuKSDMLuGyIiIolJMSV47969Wo83bNgAT09PnD9/Hh07djQyGsMwKSEiIipHlEql1mO5XA65XF7icenp6QAAd3f3UolLF+y+ISIikpjaRBsA+Pr6wsXFRbPFxMSUfH61GlOmTEG7du3QuHFjk16bPthSQkREJDFTdt8kJydDoVBoynVpJZkwYQIuX76MEydOGBmFcSympWTBggVo27YtHBwc4OrqWug+SUlJ6NmzJxwcHODp6YkZM2YgNze3bAMlIiKSkEKh0NpKSkomTpyI3bt3Iy4uDtWrVy+jKAtnMS0lOTk5GDBgANq0aYN169YVeF6lUqFnz57w9vZGfHw8UlJSMHz4cNjY2GDhwoUSRExERKQbKQa6CiHwzjvv4IcffsCRI0fg7+9vZATGs5ikJDo6GkDe6ODC7N+/H7///jsOHjwILy8vNGvWDPPnz8esWbMQFRUFW1vbMoyWiIhIdwLGL34m9Nx/woQJ2LRpE3788Uc4OzsjNTUVAODi4gJ7e3sjozGMxXTflOTUqVMIDAyEl5eXpqxbt25QKpX47bffJIyMiIjI/KxatQrp6eno3Lkzqlatqtm2bt0qWUwW01JSktTUVK2EBIDmcX72V5js7GxkZ2drHr88lYqIiKi0SdV9Y24kbSmZPXs2ZDJZsdvVq1dLNYaYmBitqVO+vr6lej4iIqKXmXJKsCWTtKVk+vTpGDFiRLH7BAQE6FSXt7c3fv75Z62y+/fva54rypw5czBt2jTNY6VSycSEiIhIApImJR4eHvDw8DBJXW3atMGCBQuQlpYGT09PAMCBAwegUCjQsGHDIo/TdaU7IiKi0iJF9405spgxJUlJSXj06BGSkpKgUqmQkJAAAKhduzacnJwQGhqKhg0bYtiwYfj444+RmpqK999/HxMmTGDSQUREZo1JSR6LSUrmzZuHjRs3ah43b94cABAXF4fOnTvD2toau3fvxrhx49CmTRs4OjoiPDwcH3zwgVQhExERkR5kwhyH30pIqVTmzdEGIJM6GCIiKjMCQBbybkz34jLtpSn/O+dTAMauDJIFYDrKNn5Ts5iWEiIiovKK3Td5ys3iaURERGTZ2FJCREQkMTWMb+ngOiVERERkNFMsflYekhJ23xAREZFZYEsJERGRxDjQNQ+TEiIiIomx+yYPu2+IiIjILLClhIiISGLsvsnDpISIiEhiTErysPuGiIiIzAJbSoiIiCTGga55mJQQERFJjCu65mH3DREREZkFtpQQERFJjANd8zApISIikhjHlORh9w0RERGZBbaUEBERSYzdN3mYlBAREUmM3Td52H1DREREZoEtJURERBJj900eJiVEREQSY1KSh903REREZBbYUkJERCQxAeMHqgpTBCIxJiVEREQSY/dNHnbfEBERkVlgSwkREZHE2FKSh0kJERGRxLh4Wh523xAREZFZYFJCREQkMZWJNn0cO3YMvXv3ho+PD2QyGXbu3GmCKzEOkxIiIiKJqU206SMzMxNNmzbFypUrTXEJJsExJURERBVQWFgYwsLCpA5DC5MSIiIiiZly9o1SqdQql8vlkMvlRtZeNth9Q0REJDE1jB9Pkt994+vrCxcXF80WExNTlpdiFLaUEBERlSPJyclQKBSax5bSSgIwKSEiIpKcKdcpUSgUWkmJJWFSQkREJDEVjB9PwRVdiYiIyCJlZGTg5s2bmseJiYlISEiAu7s7atSoIUlMTEqIiIgkJkVLyblz5xAcHKx5PG3aNABAeHg4NmzYYGQ0hmFSQkREJDEp7n3TuXNnCCGMPKtpcUowERERmQW2lBAREUmMA13zMCkhIiKSmBTdN+bIYrpvFixYgLZt28LBwQGurq6F7iOTyQpsW7ZsKdtAiYiIyCAW01KSk5ODAQMGoE2bNli3bl2R+8XGxqJ79+6ax0UlMEREROYif5l5Y+uwdBaTlERHRwNAidOUXF1d4e3tXQYRERERmYYKgMwEdVg6i+m+0dWECRNQpUoVtGrVCuvXry9xulN2djaUSqXWRkRERGXPYlpKdPHBBx+gS5cucHBwwP79+zF+/HhkZGRg0qRJRR4TExOjaYUhIiKSAge65pG0pWT27NmFDk59cbt69arO9c2dOxft2rVD8+bNMWvWLMycOROLFy8u9pg5c+YgPT1dsyUnJxt7WURERHpRmWizdJK2lEyfPh0jRowodp+AgACD62/dujXmz5+P7OzsIm/dLJfLLeq2zkREROWVpEmJh4cHPDw8Sq3+hIQEuLm5MekgIiKzxoGueSxmTElSUhIePXqEpKQkqFQqJCQkAABq164NJycn/Oc//8H9+/fxj3/8A3Z2djhw4AAWLlyId999V9rAiYiISsAxJXksJimZN28eNm7cqHncvHlzAEBcXBw6d+4MGxsbrFy5ElOnToUQArVr18aSJUswZswYqUImIiIiPciEud0iUGJKpRIuLi6wh/FNaUREZDkEgCwA6enpUCgUZXLO/O+cIBjfSpAL4DzKNn5Ts5iWEiIiovJKwPjul/LQwlDuFk8jIiIiy8SWEiIiIomZYuYMZ98QERGR0ZiU5GH3DREREZkFtpQQERFJTA3jZ3xynRIiIiIyGrtv8rD7hoiIiMwCW0qIiIgkxpaSPExKiIiIJMYxJXnYfUNERERmgS0lREREEjNFK0d5aClhUkJERCQxJiV52H1DREREZoEtJURERBJTwfi7/JaHlhImJURERBJjUpKH3TdERERkFthSQkREJDEOdM3DpISIiEhi7L7Jw+4bIiIiMgtsKSEiIpKYGsa3lBh7vDlgSwkREZHE1CbaDLFy5UrUrFkTdnZ2aN26NX7++WdjLsUoTEqIiIgqqK1bt2LatGmIjIzEhQsX0LRpU3Tr1g1paWmSxMOkhIiISGIqE236WrJkCcaMGYORI0eiYcOGWL16NRwcHLB+/XpjL8kgTEqIiIgkJkX3TU5ODs6fP4+QkBBNmZWVFUJCQnDq1CmjrsdQHOj6EiHyhgqVhwFDRESku/zf+/nfA1Kc2xR1KJVKrXK5XA65XF5g/7/++gsqlQpeXl5a5V5eXrh69aoJItIfk5KXPHnyBADwTOI4iIhIGk+ePIGLi0uZnMvW1hbe3t5ITU01SX1OTk7w9fXVKouMjERUVJRJ6i9tTEpe4uPjg+TkZDg7O0Mmk5X5+ZVKJXx9fZGcnAyFQlHm5y8NvCbLUR6vi9dkGczhmoQQePLkCXx8fMrsnHZ2dkhMTEROTo5J6hNCFPjuKqyVBACqVKkCa2tr3L9/X6v8/v378Pb2Nkk8+mJS8hIrKytUr15d6jCgUCjKzS+bfLwmy1Eer4vXZBmkvqayaiF5kZ2dHezs7Mr8vLa2tggKCsKhQ4fw2muvAQDUajUOHTqEiRMnlnk8AJMSIiKiCmvatGkIDw9Hy5Yt0apVKyxduhSZmZkYOXKkJPEwKSEiIqqgBg4ciAcPHmDevHlITU1Fs2bNsHfv3gKDX8sKkxIzI5fLERkZWWQfoCXiNVmO8nhdvCbLUB6vyVJMnDhRsu6al8mEFHOfiIiIiF7CxdOIiIjILDApISIiIrPApISIiIjMApMSM7JgwQK0bdsWDg4OcHV1LXQfmUxWYNuyZUvZBqoHXa4pKSkJPXv2hIODAzw9PTFjxgzk5uaWbaBGqlmzZoH35aOPPpI6LL2Y0+3LTSEqKqrAe1K/fn2pw9LLsWPH0Lt3b/j4+EAmk2Hnzp1azwshMG/ePFStWhX29vYICQnBjRs3pAlWRyVd04gRIwq8b927d5cmWCpzTErMSE5ODgYMGIBx48YVu19sbCxSUlI0W/6iN+aopGtSqVTo2bMncnJyEB8fj40bN2LDhg2YN29eGUdqvA8++EDrfXnnnXekDkln5nb7clNp1KiR1nty4sQJqUPSS2ZmJpo2bYqVK1cW+vzHH3+MZcuWYfXq1Thz5gwcHR3RrVs3PHtmvjfKKOmaAKB79+5a79vmzZvLMEKSlCCzExsbK1xcXAp9DoD44YcfyjQeUyjqmv773/8KKysrkZqaqilbtWqVUCgUIjs7uwwjNI6fn5/47LPPpA7DYK1atRITJkzQPFapVMLHx0fExMRIGJVxIiMjRdOmTaUOw2Re/tlXq9XC29tbLF68WFP2+PFjIZfLxebNmyWIUH+F/T4LDw8Xffv2lSQekh5bSizQhAkTUKVKFbRq1Qrr16+X5I6WpnLq1CkEBgZqLdTTrVs3KJVK/PbbbxJGpr+PPvoIlStXRvPmzbF48WKL6YIyx9uXm8qNGzfg4+ODgIAADBkyBElJSVKHZDKJiYlITU3Vet9cXFzQunVri3/fjhw5Ak9PT9SrVw/jxo3Dw4cPpQ6JyggXT7MwH3zwAbp06QIHBwfs378f48ePR0ZGBiZNmiR1aAZJTU0t9LbZ+c9ZikmTJqFFixZwd3dHfHw85syZg5SUFCxZskTq0EpkjrcvN4XWrVtjw4YNqFevHlJSUhAdHY0OHTrg8uXLcHZ2ljo8o+X/fBT2vlnSz87Lunfvjn79+sHf3x+3bt3Ce++9h7CwMJw6dQrW1tZSh0eljElJKZs9ezYWLVpU7D5XrlzReQDe3LlzNf9v3rw5MjMzsXjx4jJNSkx9TeZKn+ucNm2apqxJkyawtbVFREQEYmJiuEKlRMLCwjT/b9KkCVq3bg0/Pz989913GD16tISRUXHefPNNzf8DAwPRpEkT1KpVC0eOHEHXrl0ljIzKApOSUjZ9+nSMGDGi2H0CAgIMrr9169aYP38+srOzy+zLz5TX5O3tXWCWR/5ttKW6dXY+Y66zdevWyM3NxZ07d1CvXr1SiM50zPH25aXB1dUVdevWxc2bN6UOxSTy35v79++jatWqmvL79++jWbNmEkVlegEBAahSpQpu3rzJpKQCYFJSyjw8PODh4VFq9SckJMDNza1M/xo35TW1adMGCxYsQFpaGjw9PQEABw4cgEKhQMOGDU1yDkMZc50JCQmwsrLSXJM5M8fbl5eGjIwM3Lp1C8OGDZM6FJPw9/eHt7c3Dh06pElClEolzpw5U+IMPkty7949PHz4UCvxovKLSYkZSUpKwqNHj5CUlASVSoWEhAQAQO3ateHk5IT//Oc/uH//Pv7xj3/Azs4OBw4cwMKFC/Huu+9KG3gxSrqm0NBQNGzYEMOGDcPHH3+M1NRUvP/++5gwYYLFdHucOnUKZ86cQXBwMJydnXHq1ClMnToVQ4cOhZubm9Th6cTcbl9uCu+++y569+4NPz8//Pnnn4iMjIS1tTUGDRokdWg6y8jI0GrZSUxMREJCAtzd3VGjRg1MmTIFH374IerUqQN/f3/MnTsXPj4+Zr1MQHHX5O7ujujoaPTv3x/e3t64desWZs6cidq1a6Nbt24SRk1lRurpP/T/wsPDBYACW1xcnBBCiD179ohmzZoJJycn4ejoKJo2bSpWr14tVCqVtIEXo6RrEkKIO3fuiLCwMGFvby+qVKkipk+fLp4/fy5d0Ho6f/68aN26tXBxcRF2dnaiQYMGYuHCheLZs2dSh6aX5cuXixo1aghbW1vRqlUrcfr0aalDMsrAgQNF1apVha2trahWrZoYOHCguHnzptRh6SUuLq7Qn5/w8HAhRN604Llz5wovLy8hl8tF165dxbVr16QNugTFXdPTp09FaGio8PDwEDY2NsLPz0+MGTNGa8kAKt94l2AiIiIyC1ynhIiIiMwCkxIiIiIyC0xKiIiIyCwwKSEiIiKzwKSEiIiIzAKTEiIiIjILTEqIiIjILDApISIiIrPApISoHLtz5w5kMhlkMplkN2mLiorSxLB06VJJYiAiy8CkhKgCOHjwIA4dOiTJud99912kpKSgevXqkpyfiCwHb8hHVAFUrlwZlStXluTcTk5OcHJygrW1tSTnJyLLwZYSIgvx4MEDeHt7Y+HChZqy+Ph42Nra6t0KMmLECLz22mtYuHAhvLy84Orqig8++AC5ubmYMWMG3N3dUb16dcTGxmqOye8K+u6779ChQwfY29vjlVdewfXr13H27Fm0bNkSTk5OCAsLw4MHD0x23URUcTApIbIQHh4eWL9+PaKionDu3Dk8efIEw4YNw8SJE9G1a1e96zt8+DD+/PNPHDt2DEuWLEFkZCR69eoFNzc3nDlzBmPHjkVERATu3bundVxkZCTef/99XLhwAZUqVcLgwYMxc+ZMfP755zh+/Dhu3ryJefPmmeqyiagCYVJCZEF69OiBMWPGYMiQIRg7diwcHR0RExNjUF3u7u5YtmwZ6tWrh1GjRqFevXp4+vQp3nvvPdSpUwdz5syBra0tTpw4oXXcu+++i27duqFBgwaYPHkyzp8/j7lz56Jdu3Zo3rw5Ro8ejbi4OFNcLhFVMBxTQmRhPvnkEzRu3Bjbtm3D+fPnIZfLDaqnUaNGsLL6/79LvLy80LhxY81ja2trVK5cGWlpaVrHNWnSROsYAAgMDNQqe/kYIiJdsKWEyMLcunULf/75J9RqNe7cuWNwPTY2NlqPZTJZoWVqtbrI42QyWaFlLx9DRKQLtpQQWZCcnBwMHToUAwcORL169fDWW2/h0qVL8PT0lDo0IiKjsaWEyIL861//Qnp6OpYtW4ZZs2ahbt26GDVqlNRhERGZBJMSIgtx5MgRLF26FF9//TUUCgWsrKzw9ddf4/jx41i1apXU4RERGU0mhBBSB0FEpePOnTvw9/fHL7/8Itky8/lq1qyJKVOmYMqUKZLGQUTmiy0lRBVA27Zt0bZtW0nOvXDhQjg5OSEpKUmS8xOR5WBLCVE5lpubq5mhI5fL4evrW+YxPHr0CI8ePQKQtwCci4tLmcdARJaBSQkRERGZBXbfEBERkVlgUkJERERmgUkJERERmQUmJURERGQWmJQQERGRWWBSQkRERGaBSQkRERGZBSYlREREZBaYlBAREZFZ+D9y+emA13nSXAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Rebuild scene each trace (detectors accumulate across calls)\n",
    "with warnings.catch_warnings():\n",
    "    warnings.simplefilter('ignore')\n",
    "    scene_ghosts = sequential_to_nonsequential(\n",
    "        CookeTriplet(),\n",
    "        detector_pixels=(256, 256),\n",
    "    )\n",
    "\n",
    "result_ghosts = scene_ghosts.trace(\n",
    "    num_rays=200_000,\n",
    "    max_depth=10,\n",
    "    min_flux_fraction=1e-8,  # track very faint rays\n",
    "    seed=42,\n",
    ")\n",
    "irr_ghosts = result_ghosts.detectors['D1']\n",
    "\n",
    "print(f\"Multi-bounce flux on detector : {irr_ghosts.total_flux:.5f} W\")\n",
    "print(f\"Rays on detector              : {irr_ghosts.num_rays_hit:,}\")\n",
    "\n",
    "fig = irr_ghosts.plot(cmap='hot')\n",
    "plt.title('Multi-bounce (max_depth=10) — limited ghost reflections')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9d0e1f2",
   "metadata": {},
   "source": [
    "## 4. Ghost Contribution as a Function of Bounces\n",
    "\n",
    "Track how the detected flux changes as we allow more reflections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d0e1f2a3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:25.539865Z",
     "iopub.status.busy": "2026-08-18T17:51:25.539865Z",
     "iopub.status.idle": "2026-08-18T17:51:31.707684Z",
     "shell.execute_reply": "2026-08-18T17:51:31.707684Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max_depth= 10: flux=1.69010 W  delta=+0.000%\n",
      "max_depth= 20: flux=1.69860 W  delta=+0.503%\n",
      "max_depth= 50: flux=1.69872 W  delta=+0.510%\n",
      "max_depth=100: flux=1.69872 W  delta=+0.510%\n",
      "max_depth=200: flux=1.69872 W  delta=+0.510%\n"
     ]
    }
   ],
   "source": [
    "bounce_levels = [10, 20, 50, 100, 200]\n",
    "detected_fluxes = []\n",
    "\n",
    "for max_b in bounce_levels:\n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter('ignore')\n",
    "        sc = sequential_to_nonsequential(CookeTriplet(), detector_pixels=(128, 128))\n",
    "    r = sc.trace(num_rays=50_000, max_depth=max_b, min_flux_fraction=1e-8, seed=42)\n",
    "    detected_fluxes.append(r.detectors['D1'].total_flux)\n",
    "\n",
    "# Compute ghost fraction relative to lowest-bounce baseline (guard against zero)\n",
    "base = detected_fluxes[0] if detected_fluxes[0] > 1e-12 else max(detected_fluxes)\n",
    "ghost_fractions = [\n",
    "    (f - base) / base * 100\n",
    "    for f in detected_fluxes\n",
    "]\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(11, 4))\n",
    "axes[0].plot(bounce_levels, detected_fluxes, 'o-')\n",
    "axes[0].set_xlabel('max_depth')\n",
    "axes[0].set_ylabel('Flux on detector [W]')\n",
    "axes[0].set_title('Detected flux vs. bounce limit')\n",
    "axes[0].grid(True, alpha=0.4)\n",
    "\n",
    "axes[1].plot(bounce_levels, ghost_fractions, 's-', color='orange')\n",
    "axes[1].set_xlabel('max_depth')\n",
    "axes[1].set_ylabel('Flux change vs. baseline [%]')\n",
    "axes[1].set_title('Ghost/stray contribution vs. bounce limit')\n",
    "axes[1].grid(True, alpha=0.4)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)\n",
    "\n",
    "for b, f, g in zip(bounce_levels, detected_fluxes, ghost_fractions):\n",
    "    print(f\"max_depth={b:>3}: flux={f:.5f} W  delta={g:+.3f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1f2a3b4",
   "metadata": {},
   "source": [
    "## 5. Isolating the Ghost Contribution\n",
    "\n",
    "Building a scene by hand gives full control over the bounce budget, and\n",
    "comparing two bounce limits separates the direct image from the stray light:\n",
    "\n",
    "- `max_depth = surfaces + 1` allows **only** the direct path.\n",
    "- A larger limit additionally admits rays that reflected an even number of\n",
    "  times inside the system, which is exactly what forms a ghost.\n",
    "\n",
    "Subtracting the two irradiance maps leaves the ghost pattern on its own.\n",
    "\n",
    "Every surface below is left **uncoated** on purpose, so this is bare-Fresnel\n",
    "physics: ~4% reflectance at each glass-air interface. That is close to a\n",
    "worst case — most real imaging lenses carry an AR coating specifically to\n",
    "suppress this — and section 6 quantifies just how much difference that\n",
    "coating makes on this exact system.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f2a3b4c5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:31.709699Z",
     "iopub.status.busy": "2026-08-18T17:51:31.709699Z",
     "iopub.status.idle": "2026-08-18T17:51:36.740334Z",
     "shell.execute_reply": "2026-08-18T17:51:36.740334Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Direct path only (max_depth=5) : 0.80252 W (160,914 rays)\n",
      "All paths (max_depth=16)       : 0.80974 W (162,368 rays)\n",
      "Ghost contribution             : 0.00722 W (0.89% of the detected light)\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1400x400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "spec = Spectrum.monochromatic(0.55)\n",
    "\n",
    "\n",
    "def build_stray_scene():\n",
    "    \"\"\"Two-element system: 4 refracting surfaces on the direct path.\"\"\"\n",
    "    sc = NSQScene()\n",
    "    sc.add_source(\n",
    "        'S', CoordinateSystem(z=-80),\n",
    "        CollimatedSourceConfig(spectrum=spec, total_flux=1.0, aperture_radius=10.0),\n",
    "    )\n",
    "    sc.add_lens(\n",
    "        'L1', CoordinateSystem(z=0),\n",
    "        LensConfig(r1=50, r2=-50, thickness=5, material='N-BK7',\n",
    "                   front_aperture_radius=12.5),\n",
    "    )\n",
    "    sc.add_lens(\n",
    "        'L2', CoordinateSystem(z=40),\n",
    "        LensConfig(r1=-80, r2=80, thickness=4, material='N-SF5',\n",
    "                   front_aperture_radius=12.5),\n",
    "    )\n",
    "    # The biconvex/biconcave pair focuses at z = 60 mm. Stray light is judged\n",
    "    # against the signal, so the detector belongs where the signal is: at the\n",
    "    # image, where the wanted light is concentrated and any ghost is not.\n",
    "    sc.add_detector(\n",
    "        'D', CoordinateSystem(z=60),\n",
    "        IrradianceDetectorConfig(width=20, height=20,\n",
    "                                 num_pixels_x=128, num_pixels_y=128),\n",
    "    )\n",
    "    return sc\n",
    "\n",
    "\n",
    "# 4 refracting surfaces + 1 detector hit = 5 interactions for the direct path.\n",
    "r_direct = build_stray_scene().trace(\n",
    "    num_rays=200_000, max_depth=5, min_flux_fraction=1e-8, seed=42)\n",
    "r_full = build_stray_scene().trace(\n",
    "    num_rays=200_000, max_depth=16, min_flux_fraction=1e-8, seed=42)\n",
    "\n",
    "i_direct = r_direct.detectors['D']\n",
    "i_full = r_full.detectors['D']\n",
    "ghost_flux = i_full.total_flux - i_direct.total_flux\n",
    "\n",
    "print(f\"Direct path only (max_depth=5) : {i_direct.total_flux:.5f} W \"\n",
    "      f\"({i_direct.num_rays_hit:,} rays)\")\n",
    "print(f\"All paths (max_depth=16)       : {i_full.total_flux:.5f} W \"\n",
    "      f\"({i_full.num_rays_hit:,} rays)\")\n",
    "print(f\"Ghost contribution             : {ghost_flux:.5f} W \"\n",
    "      f\"({ghost_flux / i_full.total_flux * 100:.2f}% of the detected light)\")\n",
    "\n",
    "ghost_map = i_full.irradiance - i_direct.irradiance\n",
    "extent = [i_full.x_coords[0], i_full.x_coords[-1],\n",
    "          i_full.y_coords[0], i_full.y_coords[-1]]\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(14, 4))\n",
    "for ax, data, title in zip(\n",
    "    axes,\n",
    "    [i_direct.irradiance, i_full.irradiance, ghost_map],\n",
    "    ['Direct path only', 'All paths (direct + ghosts)', 'Ghosts alone (difference)'],\n",
    "):\n",
    "    im = ax.imshow(data, origin='lower', extent=extent, cmap='hot')\n",
    "    plt.colorbar(im, ax=ax, label='W/mm$^2$')\n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel('x [mm]')\n",
    "    ax.set_ylabel('y [mm]')\n",
    "\n",
    "plt.suptitle('Separating stray light from the direct image', fontsize=12)\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "414c0eba",
   "metadata": {},
   "source": [
    "## 6. AR Coatings Suppress Ghosts\n",
    "\n",
    "`SurfaceConfig(coating=...)`, passed as `front=`/`back=` on a `LensConfig`,\n",
    "attaches a real coating model from `optiland.coatings` to a refractive face —\n",
    "the same model class the sequential engine uses, so NSQ and the sequential\n",
    "tracer agree on R/T for that coating. A bare glass-air interface reflects\n",
    "about 4% (the Fresnel value used implicitly in section 5); a single-layer\n",
    "AR coating (e.g. MgF2, quarter-wave at the design wavelength) brings that\n",
    "down to roughly 0.25% — about a 16x drop in the reflectance feeding every\n",
    "ghost path, and since a ghost involves *two* such reflections, the drop in\n",
    "ghost **flux** compounds well beyond that.\n",
    "\n",
    "There is a sampling wrinkle that comes with the coating being this\n",
    "effective. At 0.25% reflectance, the reflect branch is a genuinely rare\n",
    "event, so `scene.sampling_policy = SamplingPolicy(reflect_prob=0.25)`\n",
    "fixes the reflect/refract branch probability at 25% regardless of the\n",
    "physical reflectance — the throughput weight compensates so the *expected*\n",
    "result is unchanged (the same detached-sample / attached-weight estimator\n",
    "described in the developer guide), and only the variance improves. The\n",
    "**same policy must be applied to both the direct-only and full-depth\n",
    "traces being compared** — used consistently, the two traces share the same\n",
    "biased branch decisions at the surfaces the direct path also crosses, so\n",
    "that shared randomness cancels in the subtraction instead of adding two\n",
    "independently noisy estimates together.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9acef508",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:36.742339Z",
     "iopub.status.busy": "2026-08-18T17:51:36.741339Z",
     "iopub.status.idle": "2026-08-18T17:51:45.431766Z",
     "shell.execute_reply": "2026-08-18T17:51:45.431766Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uncoated (bare Fresnel):\n",
      "  direct=0.80252 W  full=0.80974 W  ghost=0.007224 W (0.892% of detected)\n",
      "\n",
      "AR-coated (importance-biased sampling, reflect_prob=0.25):\n",
      "  direct=0.98220 W  full=0.98222 W  ghost=0.0000194 W (0.00198% of detected)\n",
      "\n",
      "Ghost flux, uncoated -> AR-coated: 372x reduction\n",
      "Direct-path flux is also higher with coating: 0.98220 W vs 0.80252 W uncoated (less flux lost to reflection, more transmitted)\n"
     ]
    }
   ],
   "source": [
    "# A representative single-layer AR coat: ~0.25% reflectance, no absorption.\n",
    "AR_COATING = SimpleCoating(reflectance=0.0025, transmittance=0.9975)\n",
    "\n",
    "\n",
    "def build_stray_scene(coated=False):\n",
    "    \"\"\"Same two-element system as section 5, optionally with an AR coating\n",
    "    on every refractive face.\"\"\"\n",
    "    sc = NSQScene()\n",
    "    sc.add_source(\n",
    "        'S', CoordinateSystem(z=-80),\n",
    "        CollimatedSourceConfig(spectrum=spec, total_flux=1.0, aperture_radius=10.0),\n",
    "    )\n",
    "    face = SurfaceConfig(coating=AR_COATING) if coated else None\n",
    "    sc.add_lens(\n",
    "        'L1', CoordinateSystem(z=0),\n",
    "        LensConfig(r1=50, r2=-50, thickness=5, material='N-BK7',\n",
    "                   front_aperture_radius=12.5, front=face, back=face),\n",
    "    )\n",
    "    sc.add_lens(\n",
    "        'L2', CoordinateSystem(z=40),\n",
    "        LensConfig(r1=-80, r2=80, thickness=4, material='N-SF5',\n",
    "                   front_aperture_radius=12.5, front=face, back=face),\n",
    "    )\n",
    "    sc.add_detector(\n",
    "        'D', CoordinateSystem(z=60),\n",
    "        IrradianceDetectorConfig(width=20, height=20,\n",
    "                                 num_pixels_x=128, num_pixels_y=128),\n",
    "    )\n",
    "    return sc\n",
    "\n",
    "\n",
    "def ghost_flux(coated, reflect_prob='fresnel', num_rays=200_000, seed=42):\n",
    "    \"\"\"Direct-only vs. full-depth flux under one sampling policy, applied to\n",
    "    *both* traces so their shared randomness at the surfaces they have in\n",
    "    common cancels in the subtraction rather than adding independent noise.\"\"\"\n",
    "    sc_direct = build_stray_scene(coated)\n",
    "    sc_full = build_stray_scene(coated)\n",
    "    policy = SamplingPolicy(reflect_prob=reflect_prob)\n",
    "    sc_direct.sampling_policy = policy\n",
    "    sc_full.sampling_policy = policy\n",
    "\n",
    "    r_d = sc_direct.trace(num_rays=num_rays, max_depth=5,\n",
    "                          min_flux_fraction=1e-9, seed=seed)\n",
    "    r_f = sc_full.trace(num_rays=num_rays, max_depth=16,\n",
    "                        min_flux_fraction=1e-9, seed=seed)\n",
    "    direct = r_d.detectors['D'].total_flux\n",
    "    full = r_f.detectors['D'].total_flux\n",
    "    return direct, full, full - direct\n",
    "\n",
    "\n",
    "# Same 200k-ray budget as section 5.\n",
    "d_bare, f_bare, ghost_bare = ghost_flux(coated=False)\n",
    "d_ar, f_ar, ghost_ar = ghost_flux(coated=True, reflect_prob=0.25)\n",
    "\n",
    "print(\"Uncoated (bare Fresnel):\")\n",
    "print(f\"  direct={d_bare:.5f} W  full={f_bare:.5f} W  \"\n",
    "      f\"ghost={ghost_bare:.6f} W ({ghost_bare / f_bare * 100:.3f}% of detected)\")\n",
    "print(\"\\nAR-coated (importance-biased sampling, reflect_prob=0.25):\")\n",
    "print(f\"  direct={d_ar:.5f} W  full={f_ar:.5f} W  \"\n",
    "      f\"ghost={ghost_ar:.7f} W ({ghost_ar / f_ar * 100:.5f}% of detected)\")\n",
    "print(f\"\\nGhost flux, uncoated -> AR-coated: {ghost_bare / ghost_ar:.0f}x reduction\")\n",
    "print(f\"Direct-path flux is also higher with coating: {d_ar:.5f} W vs \"\n",
    "      f\"{d_bare:.5f} W uncoated (less flux lost to reflection, more transmitted)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8eda6ff",
   "metadata": {},
   "source": [
    "### How much does importance biasing actually help?\n",
    "\n",
    "To see the variance reduction directly, repeat the AR-coated ghost\n",
    "measurement at a *much* smaller ray budget (50,000 rays — a quarter of what\n",
    "was used above), several times with different seeds, once under the default\n",
    "Fresnel-probability sampling and once under `reflect_prob=0.25`. If biasing\n",
    "is doing its job, the biased estimates should cluster tightly around the\n",
    "true value while the default ones scatter widely — same expectation, very\n",
    "different spread.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6d27a73f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-18T17:51:45.433771Z",
     "iopub.status.busy": "2026-08-18T17:51:45.433771Z",
     "iopub.status.idle": "2026-08-18T17:52:07.456413Z",
     "shell.execute_reply": "2026-08-18T17:52:07.455405Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50,000 rays x 8 repeats, AR-coated ghost flux estimate:\n",
      "  default sampling   : mean=0.000030 W, rel. std=100%\n",
      "  reflect_prob=0.25  : mean=0.000019 W, rel. std=3.8%\n",
      "  variance reduction : 1620x, at zero extra ray cost\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_repeats = 8\n",
    "budget = 50_000\n",
    "\n",
    "\n",
    "def repeated_ghosts(reflect_prob):\n",
    "    return np.array([\n",
    "        ghost_flux(coated=True, reflect_prob=reflect_prob,\n",
    "                  num_rays=budget, seed=s)[2]\n",
    "        for s in range(n_repeats)\n",
    "    ])\n",
    "\n",
    "\n",
    "ghosts_default = repeated_ghosts('fresnel')\n",
    "ghosts_biased = repeated_ghosts(0.25)\n",
    "\n",
    "rel_std_default = 100 * ghosts_default.std() / ghosts_default.mean()\n",
    "rel_std_biased = 100 * ghosts_biased.std() / ghosts_biased.mean()\n",
    "variance_reduction = (ghosts_default.std() / ghosts_biased.std()) ** 2\n",
    "\n",
    "print(f\"{budget:,} rays x {n_repeats} repeats, AR-coated ghost flux estimate:\")\n",
    "print(f\"  default sampling   : mean={ghosts_default.mean():.6f} W, \"\n",
    "      f\"rel. std={rel_std_default:.0f}%\")\n",
    "print(f\"  reflect_prob=0.25  : mean={ghosts_biased.mean():.6f} W, \"\n",
    "      f\"rel. std={rel_std_biased:.1f}%\")\n",
    "print(f\"  variance reduction : {variance_reduction:.0f}x, at zero extra ray cost\")\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 4))\n",
    "ax.axhline(ghosts_biased.mean(), color='gray', lw=1, ls='--',\n",
    "           label='Biased-sampling mean (best estimate)')\n",
    "ax.scatter(np.zeros(n_repeats), ghosts_default * 1e6, label='Default sampling')\n",
    "ax.scatter(np.ones(n_repeats), ghosts_biased * 1e6, label='reflect_prob=0.25')\n",
    "ax.set_xticks([0, 1])\n",
    "ax.set_xticklabels(['default\\n(Fresnel prob.)', 'importance-biased\\n(reflect_prob=0.25)'])\n",
    "ax.set_ylabel('Estimated ghost flux [µW]')\n",
    "ax.set_title(f'Repeated ghost-flux estimates, {budget:,} rays, {n_repeats} seeds')\n",
    "ax.legend()\n",
    "ax.grid(True, alpha=0.4)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "plt.close(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3b4c5d6",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "- `sequential_to_nonsequential(optic)` converts an `Optic` into an `NSQScene`\n",
    "- The NSQ tracer applies **Fresnel splitting** at every uncoated interface, which\n",
    "  is what produces ghosts; the sequential tracer transmits everything\n",
    "- `max_depth` counts every interaction including the detector hit, so the direct\n",
    "  path needs `surfaces + 1`. Anything beyond that admits ghost paths\n",
    "- Tracing the same scene at two bounce limits and subtracting the irradiance maps\n",
    "  isolates the stray-light pattern\n",
    "- `min_flux_fraction` sets the Russian-roulette threshold that decides how far\n",
    "  faint ghost rays are followed before being unbiasedly killed; lower it when\n",
    "  chasing weak stray light\n",
    "- `SurfaceConfig(coating=SimpleCoating(...))`, attached via `front=`/`back=` on a\n",
    "  `LensConfig`, models a real AR coating instead of bare Fresnel — going from\n",
    "  ~4% uncoated reflectance to a ~0.25% single-layer AR coat suppresses ghost\n",
    "  flux by roughly an order of magnitude on the two-lens example above.\n",
    "  **Ghost/stray-light numbers computed without coatings overstate what a real,\n",
    "  coated lens would actually produce** — treat an uncoated analysis as a\n",
    "  worst-case bound, not a prediction\n",
    "- `scene.sampling_policy = SamplingPolicy(reflect_prob=...)` biases how often\n",
    "  the tracer samples the reflect branch (with a compensating weight, so the\n",
    "  expected result is unchanged) — essential for getting usable statistics on\n",
    "  a faint, AR-coated ghost without a much larger ray budget\n",
    "- Mirrors also carry a required, physically real `reflectance` now (see\n",
    "  notebook 09), so a stray-light budget that includes mirrors is likewise more\n",
    "  meaningful than a model that silently assumed 100% reflection\n",
    "- `result.report()` flags undersampled detectors and Russian-roulette losses —\n",
    "  worth checking whenever a faint stray-light signal is the thing you actually\n",
    "  care about\n"
   ]
  }
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