Calculations/Siemens star Analyzer/Siemens star analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dd7a79da",
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as mtick\n",
    "\n",
    "import scipy\n",
    "from scipy.signal import savgol_filter\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "from Analyzer import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0da7ff81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = cv2.imread(\"ss.png\",cv2.IMREAD_GRAYSCALE)\n",
    "\n",
    "fig = plt.figure(figsize=(18,12))\n",
    "\n",
    "plt.imshow(data,origin='lower',cmap='gray')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d550c6fd",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x216d1fcd7c0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1800x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1800x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shape   = data.shape[0]\n",
    "R_max   = 300\n",
    "N_theta = 300\n",
    "theta   = np.linspace(0, 2*np.pi, N_theta) \n",
    "N_radii = 120\n",
    "radii   = R_max*1/1.05**np.arange(1, N_radii) ## we take a logarithmic range of radii\n",
    "\n",
    "N_p     = 36      # angular frequency (number of dark (bright) lines)\n",
    "\n",
    "# center of the target (determined manually)\n",
    "x_c     = 345\n",
    "y_c     = 335\n",
    "\n",
    "plt.figure(figsize=(18,12))\n",
    "plt.imshow(data, origin='lower')\n",
    "for r in radii:\n",
    "\n",
    "    freq = get_freq(r, N_p)\n",
    "    I,x,y = get_line(data,theta,r,x_c,y_c)\n",
    "    plt.plot(x,y)\n",
    "\n",
    "r      = radii[10]\n",
    "I,x,y  = get_line(data,theta,r,x_c,y_c)\n",
    "\n",
    "p0     = [(I.max()-I.min())/2, (I.max() -(I.max()-I.min())/2)/5, -(I.max()-I.min())/2 ]\n",
    "m,popt = fit_sinusoid(I,theta,p0)\n",
    "\n",
    "plt.figure(figsize=(18,10)) \n",
    "plt.imshow(data)\n",
    "ax = plt.gca() \n",
    "ax.set_aspect(1) \n",
    "plt.plot(x,y)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(18,10))\n",
    "plt.plot(theta,I)\n",
    "xnew = np.linspace(0,theta.max(),1000)\n",
    "ynew = sinusoidal(xnew,*popt)\n",
    "plt.plot(xnew,ynew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c457fdba",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Karthik\\AppData\\Local\\Temp\\ipykernel_13568\\853626961.py:77: RuntimeWarning: invalid value encountered in arccos\n",
      "  phi = np.arccos(freq_all/freq_c)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x216e5ec6760>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 6000x4200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lines = np.zeros((N_radii,2))\n",
    "n=0\n",
    "for r in radii:\n",
    "\n",
    "    freq = N_p/(2*np.pi*r)\n",
    "    I,x,y = get_line(data,theta,r,x_c,y_c)\n",
    "\n",
    "    if freq<0.45:\n",
    "        yhat = savgol_filter(I, 11, 2)\n",
    "    elif freq>=0.45:\n",
    "        yhat = savgol_filter(I, 15, 2) \n",
    "\n",
    "    maximums = scipy.signal.argrelextrema(yhat, np.greater,order=2)\n",
    "    minimums = scipy.signal.argrelextrema(yhat, np.less,order=2)\n",
    "\n",
    "\n",
    "    m = (I[maximums].mean() - I[minimums].mean())/(I[maximums].mean() + I[minimums].mean())\n",
    "\n",
    "    lines[n][0] = freq; lines[n][1] = m\n",
    "\n",
    "    n=n+1\n",
    "\n",
    "plt.clf()\n",
    "figure=plt.figure(figsize=(20,14),dpi=300)\n",
    "ax = figure.add_subplot(111)\n",
    "ax.set_xlabel('Cycles/pixel',fontsize=24)\n",
    "ax.set_ylabel('MTF',fontsize=24)\n",
    "# major_ticks = np.arange(0, 2,0.5)\n",
    "# minor_ticks = np.arange(0, 2, 0.1)\n",
    "# major_ticks_y = np.arange(0, 1.8,0.2)\n",
    "# minor_ticks_y = np.arange(0, 1.8, 0.05)\n",
    "# ax.set_xticks(major_ticks)\n",
    "# ax.set_xticks(minor_ticks, minor = True)\n",
    "# ax.set_yticks(major_ticks_y)\n",
    "# ax.set_yticks(minor_ticks_y, minor = True)\n",
    "ax.tick_params(axis = 'both', which = 'major', length=6, width=1,labelsize = 22)\n",
    "ax.tick_params(axis = 'both', which = 'minor', length=3, width=1,labelsize=22)\n",
    "\n",
    "\n",
    "freq_all = lines[:,0]\n",
    "M_all = lines[:,1]\n",
    "\n",
    "# remove last outlier point\n",
    "freq_all =freq_all[:-1]#/ 0.5\n",
    "M_all = M_all[:-1]\n",
    "#M_all =M_all/M_all.max()\n",
    "\n",
    "## fit MTF with a gaussian\n",
    "p0_g = [1,0,0.5]\n",
    "popt, pcov = curve_fit(Gaussian,freq_all[:100],M_all[:100],p0_g,maxfev=8000)\n",
    "xnew = np.linspace(0,2,1000)\n",
    "ynew = Gaussian(xnew,*popt)\n",
    "\n",
    "## perfect MTF (circular aperture, no aberrations):\n",
    "\n",
    "# D = \n",
    "# f = \n",
    "# f_stop = f/D\n",
    "\n",
    "NA = 0.6\n",
    "lam = 532*10**(-6)\n",
    "\n",
    "#in pixels\n",
    "# freq_c = 1/(lam * f_stop * 100)\n",
    "\n",
    "freq_c = (2*NA)/(lam * 100)\n",
    "\n",
    "#in arcsec\n",
    "#freq_c = D/(1.22*lam*206265)\n",
    "\n",
    "## plot results\n",
    "plt.plot(freq_all,M_all,label='Dark subtracted star modulation')\n",
    "plt.plot(xnew,ynew,'r',label='Gaussian fit')\n",
    "plt.axhline(y=0,linestyle='dashed',color='red')\n",
    "\n",
    "freq_all = np.arange(0.02, 2*freq_c, 0.01)\n",
    "phi = np.arccos(freq_all/freq_c)\n",
    "MTF_p = (2/np.pi)*(phi - (np.cos(phi))*np.sin(phi))\n",
    "plt.plot(freq_all,MTF_p,label='Theoretical MTF for circular aperture',color='darkcyan',linestyle='-.',linewidth=3)\n",
    "\n",
    "ax.legend(loc='best',fancybox=True, handlelength=4,fontsize=22)\n",
    "# ax.set_xlim(0,0.7)"
   ]
  }
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