good_to_know.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "<div align=center>\n",
    "\n",
    "# RMS (Root Mean Square)\n",
    "\n",
    "$$\n",
    "RMS = \\sqrt{ \\frac{1}{T}\\cdot \\int_{t_0}^{t_0 + T} x^2(t)\\cdot \\mathrm{d}t}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1000,1000,1000)\n",
    "gaussian = lambda x, mu, sig: 1/(sig*np.sqrt(2*np.pi))*np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))\n",
    "y = gaussian(x, 1, 100)\n",
    "m = np.mean(y)\n",
    "RMS = np.sqrt(np.mean(y**2))\n",
    "\n",
    "plt.plot(x, y, label=\"y\")\n",
    "plt.plot(x, np.ones_like(x)*m, label=\"mean\")\n",
    "plt.plot(x, np.ones_like(x)*RMS, label=\"RMS\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\rightarrow$ RMS is more sensitive to outliers\n",
    "\n",
    "$\\rightarrow$ In the context of perturbations, the usage of RMS instead of the mean is more relevant because a lower RMS also indicates a lower variance in the perturbations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=center>\n",
    "\n",
    "---\n",
    "\n",
    "# Polynôme de Zernike\n",
    "\n",
    "https://fr.wikipedia.org/wiki/Polyn%C3%B4me_de_Zernike\n",
    "\n",
    "</div>\n",
    "\n",
    "\n",
    "Pair:\n",
    "$$\\displaystyle Z_{n}^{m}(\\rho ,\\varphi )=R_{n}^{m}(\\rho )\\,\\cos(m\\,\\varphi )\\!$$\n",
    "Impair:\n",
    "$$\\displaystyle Z_{n}^{-m}(\\rho ,\\varphi )=R_{n}^{m}(\\rho )\\,\\sin(m\\,\\varphi ),\\!$$\n",
    "\n",
    "Avec:\n",
    "$$\n",
    "\\displaystyle R_{n}^{m}(\\rho )=\\sum _{k=0}^{\\tfrac {n-m}{2}}{\\frac {(-1)^{k}\\,(n-k)!}{k!\\left({\\tfrac {n+m}{2}}-k\\right)!\\left({\\tfrac {n-m}{2}}-k\\right)!}}\\;\\rho ^{n-2k}\n",
    "$$\n",
    "\n",
    "- $\\rho$ est la distance au centre du disque unité (0 ≤ $\\rho$ ≤ 1)\n",
    "- $\\varphi$ est l'angle polaire (0 ≤ $\\varphi$ ≤ 2π)\n",
    "- $n$ et $m$ sont des entiers tels que $n \\geq m \\geq 0$ et $n-m$ est pair\n",
    "\n",
    "> A quoi ça sert ? 🤔\n",
    "\n",
    "Une déformation de front d'onde dû à des aberrations optiques peut être décrite par une combinaison linéaire de polynômes de Zernike. Chaque polynôme de Zernike correspond à une aberration optique particulière.\n",
    "\n",
    "$$\n",
    "\\displaystyle W(\\rho ,\\varphi )=\\sum _{n=0}^{\\infty }\\sum _{m=-n}^{n}a_{n}^{m}\\,Z_{n}^{m}(\\rho ,\\varphi )\n",
    "$$\n",
    "\n",
    "> Ok, et du coup, ça sert à quoi ? 🤔\n",
    "\n",
    "Avoir cette forme décomposée (et généralement approximé en prenant un nombre fini de polynômes de Zernike) permet de déterminer formellement comment déformer un front d'onde pour compenser les aberrations optiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e231e32f529a4ada91a19aa42219a975",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, continuous_update=False, description='n:'), IntSlider(value=0, contin…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def zernike(n,m):\n",
    "    X, Y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))\n",
    "    RHO = np.sqrt(X**2 + Y**2)\n",
    "    PHI = np.arctan2(Y,X)\n",
    "\n",
    "    def R(n,m,rho):\n",
    "        R = np.zeros_like(rho)\n",
    "        if (n-m)%2==0:\n",
    "            for k in range((n-np.abs(m))//2+1):\n",
    "                R += (-1)**k \\\n",
    "                    * math.factorial(n-k) \\\n",
    "                    / (math.factorial(k) \\\n",
    "                    * math.factorial((n+m)//2-k) \\\n",
    "                    * math.factorial((n-m)//2-k)) \\\n",
    "                    * rho**(n-2*k)\n",
    "        return R\n",
    "    \n",
    "    mask = RHO <= 1\n",
    "    RHO = RHO * mask\n",
    "    \n",
    "    return R(n,m,RHO) * np.cos(m*PHI)\n",
    "\n",
    "n_slider = widgets.IntSlider(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=100,\n",
    "    step=1,\n",
    "    description='n:',\n",
    "    disabled=False,\n",
    "    continuous_update=False,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='d'\n",
    ")\n",
    "\n",
    "def get_min_max_m(n):\n",
    "    if n%2==0:\n",
    "        start = 0\n",
    "    else:\n",
    "        start=1\n",
    "    return -n, n\n",
    "\n",
    "def get_m_slider():\n",
    "\n",
    "    start, stop = get_min_max_m(n_slider.value)\n",
    "\n",
    "    m_slider = widgets.IntSlider(\n",
    "        value=start,\n",
    "        min=start,\n",
    "        max=stop,\n",
    "        step=2,\n",
    "        description='m:',\n",
    "        disabled=True,\n",
    "        continuous_update=False,\n",
    "        orientation='horizontal',\n",
    "        readout=True,\n",
    "        readout_format='d'\n",
    "    )\n",
    "\n",
    "    return m_slider\n",
    "\n",
    "def update_slider_minmax(slider, min, max):\n",
    "\n",
    "    slider.disabled = False\n",
    "    if min == max:\n",
    "        slider.disabled = True\n",
    "        max += 1\n",
    "\n",
    "    if min < slider.max:\n",
    "        slider.min = min\n",
    "        slider.max = max\n",
    "        return\n",
    "\n",
    "    if max > slider.min:\n",
    "        slider.max = max\n",
    "        slider.min = min\n",
    "        return\n",
    "    \n",
    "    raise ValueError(\"min and max are out of range\")\n",
    "\n",
    "m_slider = get_m_slider()\n",
    "\n",
    "def update_m_slider(change):\n",
    "    start, stop = get_min_max_m(n_slider.value)\n",
    "    update_slider_minmax(m_slider, start, stop)\n",
    "    \n",
    "    m_slider.value = start\n",
    "\n",
    "def plot_zernike(n,m):\n",
    "    plt.title(f\"Zernike({n},{m})\")\n",
    "    plt.imshow(zernike(n,m))\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "\n",
    "n_slider.observe(update_m_slider, 'value')\n",
    "_= widgets.interact(plot_zernike, n=n_slider, m=m_slider)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=center>\n",
    "\n",
    "---\n",
    "\n",
    "# Bruit de photon\n",
    "\n",
    "</div>\n",
    "\n",
    "\n",
    "Noise photon power:\n",
    "$$\n",
    "\\text{NEP}^2 = 2h^2\\nu^2\\Delta\\nu\\left(\\frac{n}{\\eta}+n^2\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}