DM_Aberration_Control.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "import matplotlib.colors as colors\n",
    "from matplotlib.patches import Circle, PathPatch\n",
    "import scipy.integrate as integrate\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "import cmath\n",
    "import csv\n",
    "from scipy.special import factorial "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Mathematical Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "g\n",
      "gg\n",
      "ggg\n",
      "gggg\n",
      "ggggg\n",
      "gggggg\n",
      "ggggggg\n",
      "gggggggg\n",
      "ggggggggg"
     ]
    }
   ],
   "source": [
    "for n in range(10):\n",
    "    print('')\n",
    "    for m in range(-n,n,2):\n",
    "        if (n,m) == fromNoll(singleIndex(n,m)):\n",
    "            print('g',end='')\n",
    "        else:\n",
    "            print(\"ERROR!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def singleIndex(n,m):\n",
    "    _x = (n-m)/2\n",
    "    if _x != int(_x):\n",
    "        raise ValueError('Zernike index invalid (difference between n and m should be even)')\n",
    "    if abs(m) > n:\n",
    "        raise ValueError('Zernike index invalid (did you switch n and m?)')\n",
    "    return int((n*(n+2)+m)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def fromNoll(j):\n",
    "    n = 0\n",
    "    m = 0\n",
    "    while (j > n):\n",
    "        n += 1\n",
    "        j -= n\n",
    "    m = -n+2*j\n",
    "    return int(n),int(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def polar(x,y):\n",
    "    r = np.sqrt(x**2+y**2)\n",
    "    phi = np.arctan2(y,x)\n",
    "    return r,phi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def cartesian(r,theta):\n",
    "    x = r*np.cos(theta)\n",
    "    y = r*np.sin(theta)\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def zernikeTheta(m,theta):\n",
    "    if (m >= 0):\n",
    "        return np.cos(m*theta)\n",
    "    else:\n",
    "        return np.sin(-m*theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def zernikeRadial(n,m,r):\n",
    "    m = abs(m)\n",
    "    if (m > n):\n",
    "        print('Error: n must be greater than or equal to n!')\n",
    "        return 0\n",
    "    if (((n-m)%2) > 0):\n",
    "        print('Error: (n - m) must be even!')\n",
    "        return 0\n",
    "    kArray = np.linspace(0,(n-m)/2,int((n-m)/2+1))\n",
    "    rArray = 0\n",
    "    i = 0\n",
    "    for k in kArray:\n",
    "        rArray=rArray+(r**(n-2*k))*((-1)**k)*factorial(n-k)/(factorial(k)*factorial((n+m)/2-k)*factorial((n-m)/2-k))\n",
    "        i = i+1\n",
    "    return rArray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def normalization(n,m):\n",
    "    if (m == 0) :\n",
    "        a = 2*np.pi\n",
    "    else:\n",
    "        a = 1*np.pi\n",
    "    return np.sqrt((2*n+2)/a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def zernike(n,m,x,y):\n",
    "    if (m == 0) :\n",
    "        a = 2*np.pi\n",
    "    else:\n",
    "        a = 1*np.pi\n",
    "    r,theta = polar(x,y)\n",
    "    return zernikeTheta(m,theta)*zernikeRadial(n,m,r)*(np.sqrt((2*n+2)/a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def zernikePolar(n,m,r,theta):\n",
    "    if (m == 0) :\n",
    "        a = 2*np.pi\n",
    "    else:\n",
    "        a = 1*np.pi\n",
    "    return zernikeTheta(m,theta)*zernikeRadial(n,m,r)*(np.sqrt((2*n+2)/a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def zernikeFit(X,*param):\n",
    "    x,y = X\n",
    "    height = param[0]*zernike(fromNoll(0)[0],fromNoll(0)[1],x,y)\n",
    "    for k in range(1,41):\n",
    "        height += param[k]*zernike(fromNoll(k)[0],fromNoll(k)[1],x,y)\n",
    "    return height"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Verifying Orthogonality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-7.243814608430614e-17, 9.871058785287423e-09)\n",
      "0.5235987755982988\n"
     ]
    }
   ],
   "source": [
    "n = 5\n",
    "m = 1\n",
    "#def integrand(r,theta):\n",
    " #   return r*zernikePolar(n,m,r,theta)**2\n",
    "f = lambda theta, r: r*zernikePolar(4,0,r,theta)*zernikePolar(4,2,r,theta)\n",
    "print(integrate.dblquad(f, 0, 1, lambda r: 0, lambda r: 2*np.pi))\n",
    "print(np.pi/(2*2+2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## DM Lookup Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def DM_Array_Index(x1,y1,ratio,xcenter,ycenter):\n",
    "    y1 = -y1\n",
    "    rNew = polar(x1,y1)[0]*ratio\n",
    "    theta = polar(x1,y1)[1]\n",
    "    x2,y2 = cartesian(rNew,theta)\n",
    "    x3 = x2+xcenter\n",
    "    y3 = y2+ycenter\n",
    "    return int(x3),int(y3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def DM_Index_Array(index_X,index_Y,ratio,xcenter,ycenter):\n",
    "    x2 = index_X-xcenter\n",
    "    y2 = index_Y-ycenter\n",
    "    theta = polar(x2,y2)[1]\n",
    "    r = polar(x2,y2)[0]\n",
    "    rNew = r/ratio\n",
    "    x1,y1 = cartesian(rNew,theta)\n",
    "    return x1,-y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "inc = 1.0/(3)\n",
    "\n",
    "def DM_Lookup(argument):\n",
    "    switcher = {\n",
    "        0: [-2*inc,6*inc],\n",
    "        1: [-1*inc,6*inc],\n",
    "        2: [0,6*inc],\n",
    "        3: [1*inc,6*inc],\n",
    "        4: [2*inc,6*inc],\n",
    "        5: [-4*inc,5*inc],\n",
    "        6: [-3*inc,5*inc],\n",
    "        7: [-2*inc,5*inc],\n",
    "        8: [-1*inc,5*inc],\n",
    "        9: [-0*inc,5*inc],\n",
    "        10: [1*inc,5*inc],\n",
    "        11: [2*inc,5*inc],\n",
    "        12: [3*inc,5*inc],\n",
    "        13: [4*inc,5*inc],\n",
    "        14: [-5*inc,4*inc],\n",
    "        15: [-4*inc,4*inc],\n",
    "        16: [-3*inc,4*inc],\n",
    "        17: [-2*inc,4*inc],\n",
    "        18: [-1*inc,4*inc],\n",
    "        19: [0,4*inc],\n",
    "        20: [1*inc,4*inc],\n",
    "        21: [2*inc,4*inc],\n",
    "        22: [3*inc,4*inc],\n",
    "        23: [4*inc,4*inc],\n",
    "        24: [5*inc,4*inc],\n",
    "        25: [-5*inc,3*inc],\n",
    "        26: [-4*inc,3*inc],\n",
    "        27: [-3*inc,3*inc],\n",
    "        28: [-2*inc,3*inc],\n",
    "        29: [-1*inc,3*inc],\n",
    "        30: [0,3*inc],\n",
    "        31: [1*inc,3*inc],\n",
    "        32: [2*inc,3*inc],\n",
    "        33: [3*inc,3*inc],\n",
    "        34: [4*inc,3*inc],\n",
    "        35: [5*inc,3*inc],\n",
    "        36: [-6*inc,2*inc],\n",
    "        37: [-5*inc,2*inc],\n",
    "        38: [-4*inc,2*inc],\n",
    "        39: [-3*inc,2*inc],\n",
    "        40: [-2*inc,2*inc],\n",
    "        41: [-1*inc,2*inc],\n",
    "        42: [0,2*inc],\n",
    "        43: [1*inc,2*inc],\n",
    "        44: [2*inc,2*inc],\n",
    "        45: [3*inc,2*inc],\n",
    "        46: [4*inc,2*inc],\n",
    "        47: [5*inc,2*inc],\n",
    "        48: [6*inc,2*inc],\n",
    "        49: [-6*inc,inc],\n",
    "        50: [-5*inc,inc],\n",
    "        51: [-4*inc,inc],\n",
    "        52: [-3*inc,inc],\n",
    "        53: [-2*inc,inc],\n",
    "        54: [-1*inc,inc],\n",
    "        55: [0,inc],\n",
    "        56: [1*inc,inc],\n",
    "        57: [2*inc,inc],\n",
    "        58: [3*inc,inc],\n",
    "        59: [4*inc,inc],\n",
    "        60: [5*inc,inc],\n",
    "        61: [6*inc,inc],\n",
    "        62: [-6*inc,0],\n",
    "        63: [-5*inc,0],\n",
    "        64: [-4*inc,0],\n",
    "        65: [-3*inc,0],\n",
    "        66: [-2*inc,0],\n",
    "        67: [-inc,0],\n",
    "        68: [0,0],\n",
    "        69: [inc,0],\n",
    "        70: [2*inc,0],\n",
    "        71: [3*inc,0],\n",
    "        72: [4*inc,0],\n",
    "        73: [5*inc,0],\n",
    "        74: [6*inc,0],\n",
    "        75: [-6*inc,-inc],\n",
    "        76: [-5*inc,-inc],\n",
    "        77: [-4*inc,-inc],\n",
    "        78: [-3*inc,-inc],\n",
    "        79: [-2*inc,-inc],\n",
    "        80: [-1*inc,-inc],\n",
    "        81: [0,-inc],\n",
    "        82: [inc,-inc],\n",
    "        83: [2*inc,-inc],\n",
    "        84: [3*inc,-inc],\n",
    "        85: [4*inc,-inc],\n",
    "        86: [5*inc,-inc],\n",
    "        87: [6*inc,-inc],\n",
    "        88: [-6*inc,-2*inc],\n",
    "        89: [-5*inc,-2*inc],\n",
    "        90: [-4*inc,-2*inc],\n",
    "        91: [-3*inc,-2*inc],\n",
    "        92: [-2*inc,-2*inc],\n",
    "        93: [-1*inc,-2*inc],\n",
    "        94: [0*inc,-2*inc],\n",
    "        95: [1*inc,-2*inc],\n",
    "        96: [2*inc,-2*inc],\n",
    "        97: [3*inc,-2*inc],\n",
    "        98: [4*inc,-2*inc],\n",
    "        99: [5*inc,-2*inc],\n",
    "        100: [6*inc,-2*inc],\n",
    "        101: [-5*inc,-3*inc],\n",
    "        102: [-4*inc,-3*inc],\n",
    "        103: [-3*inc,-3*inc],\n",
    "        104: [-2*inc,-3*inc],\n",
    "        105: [-1*inc,-3*inc],\n",
    "        106: [0,-3*inc],\n",
    "        107: [1*inc,-3*inc],\n",
    "        108: [2*inc,-3*inc],\n",
    "        109: [3*inc,-3*inc],\n",
    "        110: [4*inc,-3*inc],\n",
    "        111: [5*inc,-3*inc],\n",
    "        112: [-5*inc,-4*inc],\n",
    "        113: [-4*inc,-4*inc],\n",
    "        114: [-3*inc,-4*inc],\n",
    "        115: [-2*inc,-4*inc],\n",
    "        116: [-1*inc,-4*inc],\n",
    "        117: [0,-4*inc],\n",
    "        118: [1*inc,-4*inc],\n",
    "        119: [2*inc,-4*inc],\n",
    "        120: [3*inc,-4*inc],\n",
    "        121: [4*inc,-4*inc],\n",
    "        122: [5*inc,-4*inc],\n",
    "        123: [-4*inc,-5*inc],\n",
    "        124: [-3*inc,-5*inc],\n",
    "        125: [-2*inc,-5*inc],\n",
    "        126: [-1*inc,-5*inc],\n",
    "        127: [0,-5*inc],\n",
    "        128: [1*inc,-5*inc],\n",
    "        129: [2*inc,-5*inc],\n",
    "        130: [3*inc,-5*inc],\n",
    "        131: [4*inc,-5*inc],\n",
    "        132: [-2*inc,-6*inc],\n",
    "        133: [-1*inc,-6*inc],\n",
    "        134: [0,-6*inc],\n",
    "        135: [1*inc,-6*inc],\n",
    "        136: [2*inc,-6*inc]\n",
    "    }\n",
    "    return np.array(switcher.get(argument, \"Invalid Entry\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Program Pure Zernike Polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "    inc = 1/3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def programPureZernike(amplitudes,file1,file2):\n",
    "    inc = 1/3\n",
    "    vals = []\n",
    "    flatVoltage = np.linspace(0, 136, 137)\n",
    "    newVoltage = np.linspace(0, 136, 137)\n",
    "    sign=0\n",
    "    with open(file1, newline='') as csvfile:\n",
    "        DM_Reader = csv.reader(csvfile, delimiter=' ', quotechar='|', quoting=csv.QUOTE_NONNUMERIC)\n",
    "        i = 0\n",
    "        for row in DM_Reader:\n",
    "            flatVoltage[i]=row[0]\n",
    "            i=i+1\n",
    "\n",
    "    with open(file2, 'w', newline='') as csvfile:\n",
    "        DM_Writer = csv.writer(csvfile, delimiter=' ',\n",
    "                            quotechar ='|', quoting=csv.QUOTE_MINIMAL)\n",
    "        for i in range(0,137):\n",
    "            sign=0\n",
    "            weightFactor = 1#np.exp(2*(DM_Lookup(i)[0]**2+DM_Lookup(i)[1]**2))\n",
    "            if (DM_Lookup(i)[0]**2+DM_Lookup(i)[1]**2)>1:\n",
    "                weightFactor =0# 0.000001\n",
    "            for j in range(45):\n",
    "                sign  += amplitudes[j]*zernike(fromNoll(j)[0],fromNoll(j)[1],DM_Lookup(i)[0],DM_Lookup(i)[1])\n",
    "                #print(j,amplitudes[j],fromNoll(j)[0],fromNoll(j)[1])\n",
    "            value = (-1 if sign < 0 else 1)*sign**2*weightFactor+flatVoltage[i]\n",
    "            if value < 0 or value > 1:\n",
    "                raise ValueError(\"Value out of range for DM!\")\n",
    "            DM_Writer.writerow([value])\n",
    "            vals.append(value)\n",
    "    return vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, -1)"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fromNoll(7) # I use the Noll index notation, to see the (n,m) coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "inc = 1/3 # Defines Zernike Polynomial Radius, I found experimentally a radius of 3 as set here, gives the best result\n",
    "currentAmps = np.linspace(0,0,45) \n",
    "currentAmps[7] = 0.12   #Sets coma to have an amplitude of 0.17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### Astigmatism Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('C:/Users/Regal-Lab/Code/Data-Analysis-Code/DM_Profiles/25CW012#060_CLOSED_LOOP_COMMANDS.txt') as f:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "singleIndex(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.pyplot import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "currentAmps = np.zeros(45)\n",
    "currentAmps[singleIndex(2,2)] = 0.1\n",
    "currentAmps[singleIndex(2,-2)] = 0.1\n",
    "res = programPureZernike(currentAmps,'C:/Users/Regal-Lab/Code/Data-Analysis-Code/DM_Profiles/25CW012#060_CLOSED_LOOP_COMMANDS.txt','DM_Profiles/Astigmatism_' + str(int(100*val)) + '.txt')\n",
    "currentAmps = np.zeros(45)\n",
    "res0 = programPureZernike(currentAmps,'C:/Users/Regal-Lab/Code/Data-Analysis-Code/DM_Profiles/25CW012#060_CLOSED_LOOP_COMMANDS.txt','DM_Profiles/Astigmatism_' + str(int(100*val)) + '.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [],
   "source": [
    "def makeIm(actuatorValueList):\n",
    "    pic = np.zeros((13,13))\n",
    "    rowOff = [4,2,1,1,0,0,0,0,0,1,1,2,4]\n",
    "    tc = 0\n",
    "    for i, rowO in enumerate(rowOff):\n",
    "        numInRow = (7-(rowO+1))*2+1\n",
    "        for j in range(numInRow):\n",
    "            pic[i][rowO+j] = actuatorValueList[tc]\n",
    "            tc += 1\n",
    "    return pic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x21336a0cd30>"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imshow(makeIm(res)-makeIm(res0))\n",
    "colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "for val in np.arange(-0.41, 0.42, 0.01):\n",
    "    currentAmps = np.linspace(0,0,45) \n",
    "    currentAmps[singleIndex(2,2)] = val\n",
    "    programPureZernike(currentAmps,'C:/Users/Regal-Lab/Code/Data-Analysis-Code/DM_Profiles/25CW012#060_CLOSED_LOOP_COMMANDS.txt','DM_Profiles/Astigmatism_' + str(int(100*val)) + '.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "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": "3.6.6"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}