HWP_sim-MF.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.]\n",
      "[0.78539816]\n",
      "the transfer matrix\n",
      "[[ 2.22044605e-16+5.39030286e-15j  1.00000000e+00-8.72239442e-14j]\n",
      " [ 1.00000000e+00-8.72239442e-14j -2.22044605e-16+5.39030286e-15j]]\n",
      "checking unitatity\n",
      "[[ 1.00000000e+00+0.00000000e+00j -9.40322199e-28-1.41994963e-29j]\n",
      " [-9.40322199e-28+1.41994963e-29j  1.00000000e+00+0.00000000e+00j]]\n",
      "(2.220446049250313e-16+5.390302858158106e-15j)\n",
      "(1-8.72239441892112e-14j)\n"
     ]
    }
   ],
   "source": [
    "def make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength):\n",
    "    ## this code caculats the transfer matrix assumng x-y input and output\n",
    "    ################\n",
    "    ## thick --- the thickness of each layer, use mm\n",
    "    ## theta --- the angle of the ordinary axis relative to the x axis\n",
    "    ## no    --- the index along the ordinary axis\n",
    "    ## ne    --- the index along the extrodinary axis\n",
    "    ## wavelength  --- the wavelenght, use mm\n",
    "    ################\n",
    "    # set up the input layer, assumed to be vacuume\n",
    "    TF = np.matrix([[1,0],\n",
    "                    [0,1]])\n",
    "    theta_prev = 0.\n",
    "    # now iterate through the layers of HWP\n",
    "    N_layers = np.size(thicks)\n",
    "    i = 0\n",
    "    while (i < N_layers):\n",
    "        d_th = thetas[i] - theta_prev\n",
    "        Mrot = np.matrix([[np.cos(d_th),np.sin(d_th)],\n",
    "                         [-np.sin(d_th),np.cos(d_th)]])\n",
    "        k = 2 * np.pi / wavelength\n",
    "        phi_o = k * no * thicks[i]\n",
    "        phi_e = k * ne * thicks[i]\n",
    "        Mphase = np.matrix([[np.exp(np.complex(0,1)*phi_o),0],\n",
    "                         [0, np.exp(np.complex(0,1)*phi_e)]])\n",
    "        TF_layer = np.matmul(Mphase,Mrot)\n",
    "        TF = np.matmul(TF_layer,TF)\n",
    "        ## now iterate\n",
    "        theta_prev = thetas[i]\n",
    "        i+=1\n",
    "    # now do the last layer\n",
    "    d_th = 0 - theta_prev\n",
    "    Mrot = np.matrix([[np.cos(d_th),np.sin(d_th)],\n",
    "                      [-np.sin(d_th),np.cos(d_th)]])\n",
    "    TF = np.matmul(Mrot,TF)\n",
    "    return(TF)\n",
    "\n",
    "##########\n",
    "wavelength = 2.\n",
    "no = 3\n",
    "ne = 3.1\n",
    "thicks = np.array([1/(ne-no)*wavelength/2.])\n",
    "thetas = np.array([np.pi/4.])\n",
    "\n",
    "\n",
    "print(thicks)\n",
    "print(thetas)\n",
    "\n",
    "tmp = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "\n",
    "print(\"the transfer matrix\")\n",
    "print(tmp)\n",
    "print(\"checking unitatity\")\n",
    "print(np.matmul(np.conj(tmp),tmp))\n",
    "\n",
    "print(tmp[0,0])\n",
    "print(tmp[1,0])   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate_HWP(TF,psi):\n",
    "    Mrot = np.matrix([[np.cos(psi),np.sin(psi)],\n",
    "                      [-np.sin(psi),np.cos(psi)]])\n",
    "    out = np.matmul(TF,Mrot)\n",
    "    out = np.matmul(np.transpose(Mrot),out)\n",
    "    return(out)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sim_rot_HWP(TF,nsamps):\n",
    "    angs = np.arange(nsamps)/nsamps * 2 * np.pi\n",
    "    Ex_out = np.zeros(nsamps) * np.complex(0,1)\n",
    "    Ey_out = np.zeros(nsamps) * np.complex(0,1)\n",
    "    i = 0\n",
    "    while(i<nsamps):\n",
    "        TF_tmp = rotate_HWP(TF,angs[i])\n",
    "        Ex_out[i] = TF_tmp[0,0]\n",
    "        Ey_out[i] = TF_tmp[1,0]\n",
    "        i+=1\n",
    "    return(angs,Ex_out,Ey_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105a6def0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.33333333]\n"
     ]
    }
   ],
   "source": [
    "## setup a HWP for 2 mm\n",
    "wavelength = 2.\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thicks = np.array([1/(ne-no)*wavelength/2.])\n",
    "thetas = np.array([np.pi/4.])\n",
    "\n",
    "\n",
    "\n",
    "## make the transfer funciton\n",
    "wavelength = 2.\n",
    "TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "\n",
    "# simulate its output vs angle for x poliazed input\n",
    "n_angles = 128\n",
    "angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "\n",
    "## plot the results\n",
    "plt.plot(angs,(np.abs(Exo))**2,\"b.\")\n",
    "plt.plot(angs,(np.abs(Eyo))**2,\"r.\")\n",
    "plt.show()\n",
    "\n",
    "print(thicks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105a62128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.75000000e-01+0.00000000e+00j -2.58158612e-17+1.60768989e-17j\n",
      " -4.03767227e-17-1.31022784e-17j -3.35645003e-17-6.25840893e-18j\n",
      "  1.87500000e-01+2.85362012e-16j  2.90777807e-17+9.98593750e-18j\n",
      "  7.02341155e-18-9.14254992e-19j  1.06868768e-17+1.02286366e-17j]\n",
      "[ 1.23569707e-17-1.30203285e-18j  1.06868768e-17-1.02286366e-17j\n",
      "  7.02341155e-18+9.14254992e-19j  2.90777807e-17-9.98593750e-18j\n",
      "  1.87500000e-01+1.61329283e-16j -3.35645003e-17+6.25840893e-18j\n",
      " -4.03767227e-17+1.31022784e-17j -2.58158612e-17-1.60768989e-17j]\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "## make the transfer funciton\n",
    "wavelength = 3.0\n",
    "TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "\n",
    "# simulate its output vs angle for x poliazed input\n",
    "n_angles = 128\n",
    "angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "\n",
    "## plot the results\n",
    "plt.plot(angs*180/np.pi,(np.abs(Exo))**2,\"b.\")\n",
    "plt.plot(angs*180/np.pi,(np.abs(Eyo))**2,\"r.\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "## fit fourier modes to the output\n",
    "\n",
    "tmp = ( np.fft.ifft((np.abs(Eyo))**2))\n",
    "\n",
    "print(tmp[0:8])\n",
    "print(tmp[-8:])\n",
    "\n",
    "print(2*np.abs(tmp[4])/np.abs(tmp[0]))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.7500000000000007, 2.842170943040401e-14)\n"
     ]
    }
   ],
   "source": [
    "def mod_eff_and_phase(E):\n",
    "    tmp = np.fft.ifft((np.abs(E))**2)\n",
    "    mod_eff = 2. * np.abs(tmp[4]) /.5 #/ np.abs(tmp[0])\n",
    "    ##\n",
    "    tmp = np.arctan2(np.imag(tmp[4]),np.real(tmp[4]))\n",
    "    phase =  45 + 180/np.pi * tmp/4.\n",
    "    return(mod_eff,phase)\n",
    "\n",
    "print(mod_eff_and_phase(Exo))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105d4c080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## wavelenght range\n",
    "wavelengths = ((np.arange(0,500)+1)/500.)*10. + 1\n",
    "freq_GHZ = 1./wavelengths * 300./1.  ## \n",
    "mod_effs = np.zeros(np.shape(wavelengths))\n",
    "phases =   np.zeros(np.shape(wavelengths))\n",
    "\n",
    "## numer of angles to use in the simulations of the HWP\n",
    "n_angles = 32\n",
    "\n",
    "## setup a HWP for 2 mm\n",
    "wavelength = 2.\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thicks = np.array([1/(ne-no)*wavelength/2.])\n",
    "thetas = np.array([np.pi/4.])\n",
    "\n",
    "\n",
    "\n",
    "## make the transfer funciton\n",
    "i = 0\n",
    "while (i < np.size(wavelengths)):\n",
    "    wavelength = wavelengths[i]\n",
    "    TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "    angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "    mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "    mod_effs[i] = mod_eff\n",
    "    phases[i] = phase\n",
    "    i +=1\n",
    "\n",
    "\n",
    "mod_effs_single = np.copy(mod_effs)\n",
    "mod_phsses_single = np.copy(phases)\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs_single) \n",
    "plt.show()\n",
    "\n",
    "\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c47668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.89873243e-01+0.00000000e+00j -1.87136807e-17+1.68724832e-17j\n",
      " -6.95216274e-17-4.55285637e-19j -3.13424964e-17-2.96640732e-18j\n",
      "  2.44936622e-01+3.54750951e-16j  4.57087354e-17-1.87979620e-18j\n",
      "  5.66845454e-18+2.84595803e-17j  1.46170949e-17+1.92287114e-17j]\n"
     ]
    }
   ],
   "source": [
    "wavelength = 2.2\n",
    "n_angles = 128\n",
    "\n",
    "TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelength)\n",
    "angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "\n",
    "\n",
    "## plot the results\n",
    "plt.plot(angs*180./np.pi,(np.abs(Exo))**2,\"b.\")\n",
    "plt.plot(angs*180./np.pi,(np.abs(Eyo))**2,\"r.\")\n",
    "plt.xlim(0,45)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "## fit fourier modes to the output\n",
    "\n",
    "tmp = ( np.fft.ifft((np.abs(Eyo))**2)[0:8])\n",
    "\n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3566889860503669\n",
      "0.3566889860503669\n"
     ]
    }
   ],
   "source": [
    "## compute the fraction of the simualted band that is usable, defined as above a threshold\n",
    "#def fractional_BW_usable(mod_eff,thresshold):\n",
    "#    ok = np.where(mod_eff > thresshold )\n",
    "#    return(np.size(ok)/np.size(mod_eff))\n",
    "\n",
    "def fractional_BW_usable(mod_eff):\n",
    "    tmp = np.sum(mod_eff)\n",
    "    tmp = tmp / np.size(mod_eff)\n",
    "    return(tmp)\n",
    "\n",
    "print(fractional_BW_usable(mod_effs_single))\n",
    "print(fractional_BW_usable(mod_effs))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## calcuatle the dispersion in the phase angle\n",
    "def phase_angle_dispersion(phase_angle,frequency):\n",
    "    phase_angle  = np.unwrap(phase_angle*4.*np.pi/180)/4. * 180/np.pi\n",
    "    low_band = np.where(frequency  < 112.)\n",
    "    high_band =np.where(frequency > 122.)\n",
    "    out = np.std(phase_angle[low_band])\n",
    "    out += np.std(phase_angle[high_band])\n",
    "    return(out)\n",
    "\n",
    "#print(phase_angle_dispersion(mod_phsses_single))\n",
    "#print(phase_angle_dispersion(phases))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optomization_function(mod_effs,phase_angles,frequency):\n",
    "    ## the bandwidth part, this is multiplitative, with small values being bad\n",
    "    fBW = fractional_BW_usable(mod_effs)\n",
    "    alpha = 0.05 ## smaller aphpah penalizes more for loss of BW\n",
    "                ## 0.1 means 10% bw loss results in a 70% penalty\n",
    "    BW_penalty = ( ((1-fBW)/alpha))\n",
    "    ## the phase constancy part, small is good\n",
    "    rms_phi = np.sqrt(phase_angle_dispersion(phase_angles,frequency)**2)\n",
    "    ## optomization funciton should get small as things improe\n",
    "    opt = rms_phi + 2*BW_penalty ## consider addign a thickness penalty\n",
    "    return(opt)\n",
    "\n",
    "#print(optomization_function(mod_effs,phases))\n",
    "#print(optomization_function(mod_effs_single,mod_phsses_single))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "81.96535032744539\n"
     ]
    }
   ],
   "source": [
    "def evaluate_HWP(params):\n",
    "    ##unpack the params\n",
    "    thicks = np.abs(params[:int(np.size(params)/2)])\n",
    "    thetas = params[int(np.size(params)/2):]*np.pi/180.\n",
    "    ne = 3.2 + 0.31/2.\n",
    "    no = 3.2 - 0.31/2.\n",
    "    ## set up the wavelenght range\n",
    "    freq_GHZ = np.arange(100) + 70.  ## from 70 to 170 GHz \n",
    "    ok = np.where(np.logical_or(freq_GHZ < 112, freq_GHZ > 122))\n",
    "    freq_GHZ = freq_GHZ[ok]\n",
    "    wavelengths = 1./freq_GHZ *300.  ## convert to mm\n",
    "    ## set up the outputs for the calcaulation\n",
    "    mod_effs = np.zeros(np.shape(wavelengths))\n",
    "    phases =   np.zeros(np.shape(wavelengths))\n",
    "\n",
    "    ## numer of angles to use in the simulations of the HWP\n",
    "    n_angles = 32\n",
    "    \n",
    "    ## make the transfer funciton\n",
    "    i = 0\n",
    "    while (i < np.size(wavelengths)):\n",
    "        wavelength = wavelengths[i]\n",
    "        TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "        angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "        mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "        mod_effs[i] = mod_eff\n",
    "        phases[i] = phase\n",
    "        i +=1 \n",
    "    \n",
    "    phases  = np.unwrap(phases*4.*np.pi/180)/4. * 180/np.pi\n",
    "    ## plots for debugging\n",
    "    if (np.random.random_sample() < .01):  ## very important for speeding it up\n",
    "        print(\"thicks: \", thicks)\n",
    "        print(\"agnles: \", thetas*180./np.pi)\n",
    "        plt.plot(freq_GHZ,mod_effs,\"b.\")\n",
    "        plt.ylim(0,1)\n",
    "        plt.show()\n",
    "        plt.plot(freq_GHZ,phases-np.mean(phases),\"r.\")\n",
    "        plt.show()\n",
    "\n",
    "    return(optomization_function(mod_effs,phases,freq_GHZ))\n",
    "\n",
    "\n",
    "freq_GHZ = np.arange(100) + 70.  ## from 70 to 170 GHz \n",
    "\n",
    "thicks = np.ones(5)* 1/(.3)*2./2.*1.4\n",
    "angles = np.array([0,25,85,25,0])*np.pi/180.\n",
    "params = np.concatenate((thicks,angles))\n",
    "print(evaluate_HWP(params))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## these are several optomizaitons I tried... be ware of running them all, I would be selective and perhaps skip to the checks on specific deisngs below the hedings below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#tmp = opt.minimize(evaluate_HWP, params,method='Newton-CG')\n",
    "params = np.array([ 5,  7.9 ,  4.3,  4.7 ,7.9,\n",
    "                   20,-31, 41,  -20,-72])\n",
    "\n",
    "params = np.array([ 4,  4 ,  4,  4 ,4,\n",
    "                   25,-25, 40,  -25,-75])\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#tmp = opt.minimize(evaluate_HWP, params,method='Newton-CG')\n",
    "\n",
    "params = np.array([ 8,  4 ,  8, \n",
    "                   0, 30,  -45])\n",
    "\n",
    "params = np.array([ 8,  4 ,  8, \n",
    "                   0, 60,  0])\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "#tmp = opt.minimize(evaluate_HWP, params,method='Newton-CG')\n",
    "params = np.array([ 4,  7.9 ,  4.3,  4.7 ,7.9,\n",
    "                   20,-31, 41,  -20,-72])\n",
    "\n",
    "params = np.array([ 4,  4 ,  4,  4 ,4,\n",
    "                   0,29, 94,  29,0])\n",
    "\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#tmp = opt.minimize(evaluate_HWP, params,method='Newton-CG')\n",
    "params = np.array([ 4,  8 ,  4,  4 ,\n",
    "                   -26, 1,  78,  26])\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = np.array([ 4,  8 ,  4,  4 ,\n",
    "                   -26, 1,  30,  -30])\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "scale = 1.0\n",
    "params = np.array([ 2.861*scale,  5.716*scale ,  5.716*scale,  2.861*scale ,\n",
    "                   22.5, -33.2,  33.2,  -22.5])\n",
    "\n",
    "params = np.array([ 4,  2 ,  2,  4 ,\n",
    "                  28, -28,  28,  -28])\n",
    "\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = np.array([ 4,  2 ,  4,  2 ,4,4,\n",
    "                   -26,-83, 0,  26,83,0])\n",
    "\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#tmp = opt.minimize(evaluate_HWP, params,method='Newton-CG')\n",
    "params = np.array([ 2.861,  5.716 ,  5.716,  2.861 ,\n",
    "                   41.699, -14.033,  52.428,  -3.301])\n",
    "\n",
    "tmp = opt.basinhopping(evaluate_HWP, params, niter=100, T=5.0, stepsize=1.0)\n",
    "             \n",
    "             \n",
    "print(tmp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## things to try\n",
    "\n",
    "* tolerancing, assume $0.1^\\circ$ uncertaanty in angle and 20$\\mu$ (e.g., 0.020 mm) uncertanty in thickness.  Write a code to draw errors with these magnitudes from guassian distributions (indepandt draws for each paramter) and then plot ~100 of these variations on top of the same plot, once that is done see how far you can push the uncertaintyes and still get accptable performance\n",
    "\n",
    "* see if you can come up with a thinner design of a 4 layer\n",
    "\n",
    "* see if you can interpret this soltuion in terms of the poincerre sphere\n",
    "\n",
    "* once these are done, lets talk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# this is the four layer design, I favor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.04 4.08 4.08 2.04]\n",
      "[-28.5  28.5 -28.5  28.5]\n",
      "3.9999999999999964\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jeffmcm/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:68: RuntimeWarning: divide by zero encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105d2bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9986561318486675\n",
      "0.9992541580067937\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102faedd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105e2aba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105ea25c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## setup a HWP for 2 mm\n",
    "wavelength = 2.4\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "HWP_thick = 1/(ne-no)*wavelength/2.\n",
    "\n",
    "## one stack, standard\n",
    "thicks = np.array([HWP_thick])\n",
    "thetas = np.array([22])*np.pi/180.\n",
    "\n",
    "\n",
    "## three stack, standard\n",
    "#thicks = np.array([HWP_thick,HWP_thick,HWP_thick])\n",
    "#thetas = np.array([0,58*np.pi/180.,0])\n",
    "\n",
    "\n",
    "## five stack, standard\n",
    "thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "thetas = np.array([0,28.6,94.1,28.6,1.6])*np.pi/180.\n",
    "\n",
    "\n",
    "## five stack, standard\n",
    "thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "thetas = np.array([0,28.6,94.1,28.6,1.6])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## nine stack, standard\n",
    "#thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "#thetas = np.array([0.,18.5,37.5,73.9,141.5,73.9,37.5,18.5,22.7])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## fiducial SO design\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thick_HWP = 4.08\n",
    "epsi = 0\n",
    "angle = 28.5\n",
    "delta = 0\n",
    "eta = 0.\n",
    "thicks = np.array([ 1/2,  1 +epsi,  1+epsi,  1/2])* thick_HWP\n",
    "thetas = np.array([angle+delta, -angle+eta,  angle+delta,  -angle+eta])*np.pi/180. *-1.\n",
    "\n",
    "\n",
    "\n",
    "print(thicks)\n",
    "print(thetas*180./np.pi)\n",
    "\n",
    "## three stack, standard\n",
    "thicks = np.array([thick_HWP,thick_HWP,thick_HWP])\n",
    "thetas = np.array([0,58*np.pi/180.,0])\n",
    "print(HWP_thick)\n",
    "\n",
    "## five stack, non standard\n",
    "HWP_thick = 3.95\n",
    "thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "thetas = np.array([22.9,-50,0,50,-22.9])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## setup the sim\n",
    "freq_GHZ = np.arange(600)  ## from 70 to 170 GHz \n",
    "wavelengths = 1./freq_GHZ *300.  ## convert to mm\n",
    "\n",
    "mod_effs = np.zeros(np.shape(wavelengths))\n",
    "phases = np.zeros(np.shape(wavelengths))\n",
    "\n",
    "## make the transfer funciton\n",
    "i = 0\n",
    "while (i < np.size(wavelengths)):\n",
    "    wavelength = wavelengths[i]\n",
    "    TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "    angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "    mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "    mod_effs[i] = mod_eff\n",
    "    phases[i] = phase\n",
    "    i +=1\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.9,1.0)\n",
    "plt.xlim(65,180)\n",
    "plt.plot(np.array([1,1])*75,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>75,freq_GHZ<112))]))\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>122,freq_GHZ<170))]))\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.0,1.0)\n",
    "plt.xlim(65,180)\n",
    "plt.plot(np.array([1,1])*75,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,phases) \n",
    "delta = 45\n",
    "plt.ylim(0,30)\n",
    "plt.xlim(65,180)\n",
    "plt.plot(np.array([1,1])*75,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([-1,1])*200,\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([-1,1])*200,\"g\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(freq_GHZ,phases - np.mean(phases[50:150])) \n",
    "plt.xlim(65,180)\n",
    "plt.ylim(np.array([-1,1])*0.1 )\n",
    "plt.plot(np.array([1,1])*75,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([-1,1])*200,\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([-1,1])*200,\"g\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#plt.plot(freq_GHZ,phases-np.mean(phases))\n",
    "\n",
    "#phase_angle_s  = np.unwrap(mod_phsses_single*4.*np.pi/180)/4. * 180/np.pi\n",
    "\n",
    "#plt.plot(freq_GHZ,phase_angle_s)\n",
    "#plt.show() \n",
    "\n",
    "#plt.plot(freq_GHZ,phases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# this is the five layer I favor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.95 3.95 3.95 3.95 3.95]\n",
      "[ 22.9 -50.    0.   50.  -22.9]\n",
      "3.9999999999999964\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jeffmcm/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:68: RuntimeWarning: divide by zero encountered in true_divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104fa4780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9986561318486675\n",
      "0.9992541580067937\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105fcce48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105fad898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c88a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## setup a HWP for 2 mm\n",
    "wavelength = 2.4\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "HWP_thick = 1/(ne-no)*wavelength/2.\n",
    "\n",
    "## one stack, standard\n",
    "thicks = np.array([HWP_thick])\n",
    "thetas = np.array([22])*np.pi/180.\n",
    "\n",
    "\n",
    "## three stack, standard\n",
    "#thicks = np.array([HWP_thick,HWP_thick,HWP_thick])\n",
    "#thetas = np.array([0,58*np.pi/180.,0])\n",
    "\n",
    "\n",
    "## five stack, standard\n",
    "thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "thetas = np.array([0,28.6,94.1,28.6,1.6])*np.pi/180.\n",
    "\n",
    "\n",
    "## five stack, standard\n",
    "thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "thetas = np.array([0,28.6,94.1,28.6,1.6])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## nine stack, standard\n",
    "#thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "#thetas = np.array([0.,18.5,37.5,73.9,141.5,73.9,37.5,18.5,22.7])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## fiducial SO design\n",
    "no = 3.05\n",
    "ne = 3.35\n",
    "thick_HWP = 3.95\n",
    "epsi = 0\n",
    "angle = 28.5\n",
    "delta = 0\n",
    "eta = 0.\n",
    "thicks = np.array([ 1,  1 ,  1,  1,1])* thick_HWP\n",
    "thetas = np.array([22.9, -50,0,  50,  -22.9])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "print(thicks)\n",
    "print(thetas*180./np.pi)\n",
    "\n",
    "## three stack, standard\n",
    "thicks = np.array([thick_HWP,thick_HWP,thick_HWP])\n",
    "thetas = np.array([0,58*np.pi/180.,0])\n",
    "print(HWP_thick)\n",
    "\n",
    "## five stack, non standard\n",
    "HWP_thick = 3.95\n",
    "thicks = np.array([HWP_thick,HWP_thick,HWP_thick,HWP_thick,HWP_thick])\n",
    "thetas = np.array([22.9,-50,0,50,-22.9])*np.pi/180.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## setup the sim\n",
    "freq_GHZ = np.arange(600)  ## from 70 to 170 GHz \n",
    "wavelengths = 1./freq_GHZ *300.  ## convert to mm\n",
    "\n",
    "mod_effs = np.zeros(np.shape(wavelengths))\n",
    "phases = np.zeros(np.shape(wavelengths))\n",
    "\n",
    "## make the transfer funciton\n",
    "i = 0\n",
    "while (i < np.size(wavelengths)):\n",
    "    wavelength = wavelengths[i]\n",
    "    TF = make_HWP_transfer_matrix(thicks,thetas,no,ne,wavelengths[i])\n",
    "    angs,Exo,Eyo = sim_rot_HWP(TF,n_angles)\n",
    "    mod_eff,phase = mod_eff_and_phase(Exo)\n",
    "    mod_effs[i] = mod_eff\n",
    "    phases[i] = phase\n",
    "    i +=1\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.9,1.0)\n",
    "plt.xlim(65,180)\n",
    "plt.plot(np.array([1,1])*75,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>75,freq_GHZ<112))]))\n",
    "print(np.mean(mod_effs[np.where(np.logical_and(freq_GHZ>122,freq_GHZ<170))]))\n",
    "\n",
    "plt.plot(freq_GHZ,mod_effs) \n",
    "#plt.plot(freq_GHZ,mod_effs_single)\n",
    "plt.ylim(0.0,1.0)\n",
    "plt.xlim(65,180)\n",
    "plt.plot(np.array([1,1])*75,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([0,1]),\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([0,1]),\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([0,1]),\"g\")\n",
    "#plt.plot(np.array([1,1])*195,np.array([0,1]),\"b\")\n",
    "#plt.plot(np.array([1,1])*250,np.array([0,1]),\"b\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "plt.plot(freq_GHZ,phases) \n",
    "delta = 45\n",
    "plt.ylim(0,30)\n",
    "plt.xlim(65,180)\n",
    "plt.plot(np.array([1,1])*75,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([-1,1])*200,\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([-1,1])*200,\"g\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(freq_GHZ,phases - np.mean(phases[50:150])) \n",
    "plt.xlim(65,180)\n",
    "plt.ylim(np.array([-1,1])*0.1 )\n",
    "plt.plot(np.array([1,1])*75,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*112,np.array([-1,1])*200,\"r\")\n",
    "plt.plot(np.array([1,1])*125,np.array([-1,1])*200,\"g\")\n",
    "plt.plot(np.array([1,1])*170,np.array([-1,1])*200,\"g\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#plt.plot(freq_GHZ,phases-np.mean(phases))\n",
    "\n",
    "#phase_angle_s  = np.unwrap(mod_phsses_single*4.*np.pi/180)/4. * 180/np.pi\n",
    "\n",
    "#plt.plot(freq_GHZ,phase_angle_s)\n",
    "#plt.show() \n",
    "\n",
    "#plt.plot(freq_GHZ,phases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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