Detector Time Constant Testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.constants as constants\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from MMTModules import *\n",
    "from DetectorTimeConstantModules import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1D Calculation\n",
    "\n",
    "The finite response of a detector in the time domain is exponential decay ($a(t) = e^{-t/\\tau}$), where t=0 is when the detector 'sees' the signal and $\\tau$ is the detector's time constant. This can be represented in the spatial domain by introducing a scan speed as a unit conversion ($e^{-\\theta/(s\\tau)}$). Given this spatial representation of the detector response function, this can be transformed to $\\ell$-space through fourier transforming\n",
    "\n",
    "$$a(k) = \\int _{-\\infty}^\\infty e^{-\\frac{\\theta}{s\\tau}} e^{-ik\\theta}d\\theta$$\n",
    "\n",
    "This can be found to be a Lorentzian\n",
    "\n",
    "$$a(k) = \\frac{1}{\\pi}\\frac{k_0}{k_0^2+k^2}$$\n",
    "\n",
    "and the relation between k and $\\ell$ needs to be established\n",
    "\n",
    "In the limit that a cross linking scan strategy is perfect, the exponential response function radially in 2D space. For a rastering scan strategy, the response function need only be applied along the direction of scan, only affecting the k-modes along the scan. This should mean that the 1D radial model should be equivalent to the 2D model applied to both axes, which can serve as a sanity check on the pipeline without the model. \n",
    "\n",
    "The fourier transform of the response function should look like a lowpass filter (normalized):\n",
    "\n",
    "$$a(\\ell) = \\frac{1}{1 + \\frac{\\ell^2}{\\ell_{cutoff}^2}}$$\n",
    "\n",
    "This analytical form is not exact because it does not take into account the pixel window function, which will cause boundary effects for fast time constants. This presumption is checked below by increasing tau and watching the fit get better:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter values are [0.43292807 3.14159173]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnitude (arb)')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define relevant constants\n",
    "N = 1024  # []: pixels in map\n",
    "pixel_size = 0.25  # [arcmin/pixel]: size in arcmin of pixel\n",
    "ell_max = 5000  # [ell]: maximum ell\n",
    "delta_ell = 50  # [ell]: bin width for power spectra\n",
    "perc_err = 0.05  #[%]: percent the measure is off by\n",
    "scan_sp = 1.  # [deg/s]: scan speed of telescope\n",
    "tau = 10e-3  # [s]: time constant of detector\n",
    "ell = np.arange(ell_max)  # [ell]: array of ell\n",
    "L = N*pixel_size\n",
    "\n",
    "##########################################################################################################\n",
    "\n",
    "#setup exponential decay in position space\n",
    "x = (np.arange(N)/N -0.5)*L\n",
    "exp_decay_1d = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*60.))\n",
    "\n",
    "#take fft\n",
    "exp_decay_1d_fft = np.fft.fftshift(np.fft.fft(exp_decay_1d))\n",
    "\n",
    "exp_decay_1d_fft = np.sqrt(np.real(np.conj(exp_decay_1d_fft)*exp_decay_1d_fft))\n",
    "\n",
    "#calculate the fourier modes\n",
    "freqs_array = np.zeros(N)\n",
    "k_array = np.arange(N)\n",
    "for i in range(N):\n",
    "    k = k_array[i]\n",
    "    freqs_array[i] = 2*np.pi/N*k\n",
    "    \n",
    "\n",
    "\n",
    "####################################################################################################\n",
    "\n",
    "#curve fit with offset lorentzian\n",
    "def offset_lorentzian(x, xp, x0):\n",
    "    return 1 / ( 1 + ((x-x0)/xp)**2. )\n",
    "\n",
    "import scipy.optimize as optimization\n",
    "\n",
    "#ell_set is the range of ell values the binned spectrum goes over\n",
    "ell_set = freqs_array\n",
    "initial_guess = np.array([1,3.2])\n",
    "\n",
    "#right now for one simulation just take the std of the dataset. If it's necessary, multiple simulations can be run\n",
    "#to make the weighting in the optimization more accurate, but for now I don't care as much\n",
    "sigma = np.sqrt(np.var(exp_decay_1d_fft/np.max(exp_decay_1d_fft)))\n",
    "errors = sigma*np.ones(len(exp_decay_1d_fft))\n",
    "curve_fit = optimization.curve_fit(offset_lorentzian, ell_set, exp_decay_1d_fft/np.max(exp_decay_1d_fft), initial_guess, errors)\n",
    "\n",
    "parameters = curve_fit[0]\n",
    "tf_fit_r = offset_lorentzian(freqs_array,parameters[0],parameters[1])\n",
    "print('Parameter values are ' + str(parameters))\n",
    "plt.semilogy(freqs_array,exp_decay_1d_fft/np.max(exp_decay_1d_fft))\n",
    "plt.semilogy(freqs_array, tf_fit_r/np.max(tf_fit_r))\n",
    "plt.title('Curve Fit to Contamination Spectrum')\n",
    "plt.legend(['Spectrum','Fit to Spectrum'])\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Magnitude (arb)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2D Numerical Simulation\n",
    "\n",
    "- Radial Smearing\n",
    "\n",
    "- Preferred Scan Direction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define relevant constants\n",
    "N = 1024  # []: pixels in map\n",
    "pixel_size = 0.25  # [arcmin/pixel]: size in arcmin of pixel\n",
    "ell_max = 5000  # [ell]: maximum ell\n",
    "delta_ell = 50  # [ell]: bin width for power spectra\n",
    "perc_err = 0.05  #[%]: percent the measure is off by\n",
    "scan_sp = 1.  # [deg/s]: scan speed of telescope\n",
    "tau = 10e-3  # [s]: time constant of detector\n",
    "ell = np.arange(ell_max)  # [ell]: array of ell\n",
    "L = N*pixel_size\n",
    "\n",
    "#define 2D model\n",
    "##define 2D coordinate system in map space\n",
    "x_1d = (np.arange(N)/N - 0.5)*L*np.pi/(180.*60.)\n",
    "y_1d = np.copy(x_1d)\n",
    "x,y = np.meshgrid(x_1d,y_1d)\n",
    "\n",
    "r = np.sqrt(x**2. + y**2.)\n",
    "exp_decay_2d = np.exp(-r/(scan_sp*tau*np.pi/180.))\n",
    "exp_decay_2d_meas = np.exp(-r/(scan_sp*tau*np.pi/180.*(1-perc_err)))\n",
    "\n",
    "#take fft's and deconvolve\n",
    "exp_decay_2d_fft = np.fft.fftshift(np.fft.fft2(exp_decay_2d))\n",
    "exp_decay_2d_meas_fft = np.fft.fftshift(np.fft.fft2(exp_decay_2d_meas))\n",
    "exp_decay_2d_res_fft = np.zeros((N,N),dtype=complex)\n",
    "\n",
    "exp_decay_2d_res_fft = exp_decay_2d_fft / exp_decay_2d_meas_fft\n",
    "\n",
    "#for posterity, this works here for radial but not if there's a preferred scan direction\n",
    "#for i in range(N):\n",
    "#    for j in range(N):\n",
    "#        if exp_decay_2d_meas_fft[i,j] == 0. + 0*1j:\n",
    "#            exp_decay_2d_res_fft[i,j] = 0. + 0*1j\n",
    "#        else:\n",
    "#            exp_decay_2d_res_fft[i,j] = exp_decay_2d_fft[i,j] / exp_decay_2d_meas_fft[i,j]\n",
    "\n",
    "\n",
    "#bin to 1d\n",
    "#exp_decay_2d_deproj_fft = np.fft.fftshift(np.fft.fft2((exp_decay_2d_deproj)))\n",
    "maps_dict = {}\n",
    "maps_dict['TT'] = exp_decay_2d_res_fft#/exp_decay_2d_deproj_fft\n",
    "binned_ell, binned_exp_decay_2d_res = bin_maps_to_1d(maps_dict, delta_ell=delta_ell, ell_max=ell_max, pix_size=pixel_size, N=N)\n",
    "\n",
    "#normalize\n",
    "binned_exp_decay_2d_res['TT'] = binned_exp_decay_2d_res['TT'] / np.max(binned_exp_decay_2d_res['TT'])\n",
    "\n",
    "#plot\n",
    "plt.semilogy(binned_ell, binned_exp_decay_2d_res['TT'])\n",
    "plt.title('2D Exponential Binned to 1D $\\ell$')\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define relevant constants\n",
    "N = 1024  # []: pixels in map\n",
    "pixel_size = 0.25  # [arcmin/pixel]: size in arcmin of pixel\n",
    "ell_max = 5000  # [ell]: maximum ell\n",
    "delta_ell = 50  # [ell]: bin width for power spectra\n",
    "perc_err = 0.05  #[%]: percent the measure is off by\n",
    "scan_sp = 1.  # [deg/s]: scan speed of telescope\n",
    "tau = 10e-3  # [s]: time constant of detector\n",
    "ell = np.arange(ell_max)  # [ell]: array of ell\n",
    "L = N*pixel_size\n",
    "\n",
    "#############################################################################\n",
    "\n",
    "#define 2D model\n",
    "##define 2D coordinate system in map space\n",
    "x_1d = (np.arange(N)/N - 0.5)*L*np.pi/(180.*60.)\n",
    "y_1d = np.copy(x_1d)\n",
    "x,y = np.meshgrid(x_1d,y_1d)\n",
    "\n",
    "exp_decay_2d_scanx = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*np.pi/180.))\n",
    "exp_decay_2d_scanx_meas = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*np.pi/180.*(1-perc_err)))\n",
    "\n",
    "#take fft of horizontal rows (scan axis)\n",
    "exp_decay_2d_scanx_res_fft = np.zeros((N,N), dtype=complex)\n",
    "for row in range(N):\n",
    "    real_fft = np.fft.fftshift(np.fft.fft(exp_decay_2d_scanx[row,:]))\n",
    "    meas_fft = np.fft.fftshift(np.fft.fft(exp_decay_2d_scanx_meas[row,:]))\n",
    "    exp_decay_2d_scanx_res_fft[row,:] = real_fft / meas_fft\n",
    "\n",
    "\n",
    "#bin to 1D PS\n",
    "#exp_decay_2d_deproj_fft = np.fft.fftshift(np.fft.fft2((exp_decay_2d_deproj)))\n",
    "maps_dict = {}\n",
    "maps_dict['TT'] = exp_decay_2d_scanx_res_fft\n",
    "binned_ell, binned_exp_decay_2d_scanx_res = bin_maps_to_1d(maps_dict, delta_ell=delta_ell, ell_max=ell_max, pix_size=pixel_size, N=N)\n",
    "\n",
    "#normalize\n",
    "binned_exp_decay_2d_scanx_res = binned_exp_decay_2d_scanx_res['TT'] / np.max(binned_exp_decay_2d_scanx_res['TT'])\n",
    "\n",
    "#plot\n",
    "plt.semilogy(binned_ell, binned_exp_decay_2d_scanx_res)\n",
    "plt.title('Scan Along Horizontal')\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnitude (arb)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define 9th order polynomial\n",
    "def polynomial_9(x, a, b, c, d, e, f, g, h, i, j):\n",
    "    return a*x**9. + b*x**8. + c*x**7. + d*x**6. + e*x**5. + f*x**4. + g*x**3. + h*x**2. + i*x + j\n",
    "\n",
    "#For TE\n",
    "import scipy.optimize as optimization\n",
    "\n",
    "#ell_set is the range of ell values the binned spectrum goes over\n",
    "ell_set = binned_ell\n",
    "initial_guess = np.array([0.,0.,0.,0.,0.,0.,0.,0.,0.,0.])\n",
    "\n",
    "#right now for one simulation just take the std of the dataset. If it's necessary, multiple simulations can be run\n",
    "#to make the weighting in the optimization more accurate, but for now I don't care as much\n",
    "sigma = np.sqrt(np.var(binned_exp_decay_2d_scanx_res))\n",
    "errors = sigma*np.ones(len(binned_exp_decay_2d_scanx_res))\n",
    "curve_fit = optimization.curve_fit(polynomial_9, ell_set, binned_exp_decay_2d_scanx_res, initial_guess, errors)\n",
    "\n",
    "parameters = curve_fit[0]\n",
    "ell = np.arange(ell_max+101)\n",
    "tf_fit = polynomial_9(ell,parameters[0],parameters[1],parameters[2],\n",
    "                      parameters[3],parameters[4],parameters[5],\n",
    "                      parameters[6],parameters[7],parameters[8],parameters[9])\n",
    "plt.semilogy(binned_ell,binned_exp_decay_2d_scanx_res)\n",
    "plt.semilogy(ell,tf_fit)\n",
    "plt.title('Curve Fit of Residual Spectrum')\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "row_fft = np.fft.fftshift(np.fft.fft(exp_decay_2d_scanx[512,:]))\n",
    "plt.plot(np.real(row_fft))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare to Radial Smear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(binned_ell, binned_exp_decay_2d_scanx_res,color='b')\n",
    "plt.semilogy(binned_ell, binned_exp_decay_2d_res['TT'],color='r')\n",
    "plt.legend(['Smear X','Radial Smear'])\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')\n",
    "plt.title('Comparing the Radial Smear to the X Smear for %s s Tau and %s uncertainty'%(tau,perc_err))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There appears to be some noise in the anisotropic smear that seems to increase by making the leakage worse (i.e. increasing the time constant or increasing the measurement uncertainty). This could be mitigated by fitting the noisy spectrum to a polynomial. An illustration is below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau_set = [1e-3,5e-3,10e-3,50e-3,100e-3]\n",
    "perc_err = 0.05\n",
    "\n",
    "#define relevant constants\n",
    "N = 1024  # []: pixels in map\n",
    "pixel_size = 0.25  # [arcmin/pixel]: size in arcmin of pixel\n",
    "ell_max = 5000  # [ell]: maximum ell\n",
    "delta_ell = 50  # [ell]: bin width for power spectra\n",
    "scan_sp = 1.  # [deg/s]: scan speed of telescope\n",
    "ell = np.arange(ell_max)  # [ell]: array of ell\n",
    "L = N*pixel_size\n",
    "\n",
    "#############################################################################\n",
    "\n",
    "#define 2D model\n",
    "##define 2D coordinate system in map space\n",
    "x_1d = (np.arange(N)/N - 0.5)*L*np.pi/(180.*60.)\n",
    "y_1d = np.copy(x_1d)\n",
    "x,y = np.meshgrid(x_1d,y_1d)\n",
    "\n",
    "binned_exp_decay_2d_scanx_tau_set = np.zeros((len(tau_set),int(ell_max/delta_ell)))\n",
    "for tau in tau_set:\n",
    "    exp_decay_2d_scanx = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*np.pi/180.))\n",
    "    exp_decay_2d_scanx_meas = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*np.pi/180.*(1-perc_err)))\n",
    "\n",
    "    #take fft's and deconvolve\n",
    "    exp_decay_2d_scanx_fft = np.fft.fftshift(np.fft.fft2(exp_decay_2d_scanx))\n",
    "    exp_decay_2d_scanx_meas_fft = np.fft.fftshift(np.fft.fft2(exp_decay_2d_scanx_meas))\n",
    "    exp_decay_2d_scanx_res_fft = np.zeros((N,N),dtype=complex)\n",
    "\n",
    "    exp_decay_2d_scanx_res_fft[512,:] = exp_decay_2d_scanx_fft[512,:] / exp_decay_2d_scanx_meas_fft[512,:]\n",
    "    for row in range(N):\n",
    "        exp_decay_2d_scanx_res_fft[row,:] = exp_decay_2d_scanx_fft[512,:] / exp_decay_2d_scanx_meas_fft[512,:]\n",
    "\n",
    "    #bin to 1d PS\n",
    "    #exp_decay_2d_deproj_fft = np.fft.fftshift(np.fft.fft2((exp_decay_2d_deproj)))\n",
    "    maps_dict = {}\n",
    "    maps_dict['TT'] = exp_decay_2d_scanx_res_fft\n",
    "    binned_ell, binned_exp_decay_2d_scanx_res = bin_maps_to_1d(maps_dict, delta_ell=delta_ell, ell_max=ell_max, pix_size=pixel_size, N=N)\n",
    "\n",
    "    #normalize\n",
    "    binned_exp_decay_2d_scanx_res['TT'] = binned_exp_decay_2d_scanx_res['TT'] / np.max(binned_exp_decay_2d_scanx_res['TT'])\n",
    "\n",
    "    #plot\n",
    "    plt.semilogy(binned_ell, binned_exp_decay_2d_scanx_res['TT'])\n",
    "    \n",
    "plt.title('Scan Along Horizontal Varying Tau')\n",
    "plt.legend(tau_set)\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2D Rotated Scan Direction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rotate_map(beam_map, ang):\n",
    "    import numpy as np\n",
    "    \n",
    "    #ang in radians\n",
    "    #beam_map in any units\n",
    "    N_x = len(beam_map[0,:])\n",
    "    N_y = len(beam_map[:,0])\n",
    "    ind_x = np.arange(N_x)\n",
    "    ind_y = np.arange(N_y)\n",
    "    pix_x = np.arange(-int(N_x/2.),int(N_x/2.-1))\n",
    "    pix_y = np.arange(-int(N_y/2.),int(N_y/2.-1))\n",
    "    \n",
    "    #define 2D rotation matrix\n",
    "    R = np.array([[np.cos(ang),-np.sin(ang)],[np.sin(ang),np.cos(ang)]])\n",
    "    \n",
    "    \n",
    "    #rotate each pixel individually\n",
    "    rotated_beam_map = np.zeros((int(N_x*np.sqrt(2)),int(N_y*np.sqrt(2))))\n",
    "    pix_x_rot = np.arange(-int(N_x*np.sqrt(2)/2),int(N_x*np.sqrt(2)/2-1.) )\n",
    "    pix_y_rot = np.arange(-int(N_y*np.sqrt(2)/2),int(N_y*np.sqrt(2)/2-1.) )\n",
    "    ind_to_return_x = [ np.where(pix_x_rot==pix_x[0])[0]-1,np.where(pix_x_rot==pix_x[-1])[0]+1 ]\n",
    "    ind_to_return_y = [ np.where(pix_y_rot==pix_y[0])[0]-1,np.where(pix_y_rot==pix_y[-1])[0]+1 ]\n",
    "    \n",
    "    for i in pix_x:\n",
    "        for j in pix_y:\n",
    "            x = np.where(pix_x==i)[0]\n",
    "            y = np.where(pix_y==j)[0]\n",
    "            coords_to_rotate = np.array([i,j])\n",
    "            ip,jp = np.matmul(R,coords_to_rotate)\n",
    "            \n",
    "            xp = np.where(pix_x_rot==int(ip))[0]\n",
    "            yp = np.where(pix_y_rot==int(jp))[0]\n",
    "            \n",
    "            rotated_beam_map[int(xp),int(yp)] = beam_map[int(x),int(y)]\n",
    "                \n",
    "    return rotated_beam_map[ind_to_return_x[0][0]:ind_to_return_x[-1][0],ind_to_return_y[0][0]:ind_to_return_y[-1][0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+K4M7/VO5psDfAt8E7gX+GVg+DesKXM/gPswxBmdz23rWEPjjVu8ccNWpHNuvp0vqMq2XLZKmnOEhqYvhIamL4SGpi+EhqYvhIamL4SGpy/8B4/ToJUzlrs8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#test above function\n",
    "#create map with 1 along center\n",
    "N = 1024\n",
    "beam_map = np.zeros((N,N))\n",
    "beam_map[512,:] = np.ones(N)\n",
    "rot_beam_map = rotate_map(beam_map, np.pi/4.)\n",
    "plt.imshow(beam_map)\n",
    "plt.show()\n",
    "plt.imshow(rot_beam_map)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/ipykernel_launcher.py:34: ComplexWarning: Casting complex values to real discards the imaginary part\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define constants\n",
    "perc_err = 0.05\n",
    "ang = 30.*(np.pi/180.) #angle to rotate by in radians\n",
    "\n",
    "#beam parameters\n",
    "beam_sigma = 1.5*(1./60.)*(np.pi/180.)   #radians\n",
    "\n",
    "#define relevant constants\n",
    "N = 1024  # []: pixels in map\n",
    "pixel_size = 0.25  # [arcmin/pixel]: size in arcmin of pixel\n",
    "ell_max = 5000  # [ell]: maximum ell\n",
    "delta_ell = 50  # [ell]: bin width for power spectra\n",
    "scan_sp = 1.  # [deg/s]: scan speed of telescope\n",
    "ell = np.arange(ell_max)  # [ell]: array of ell\n",
    "tau = 10e-3\n",
    "L = N*pixel_size\n",
    "\n",
    "#make normal coordinate system\n",
    "#define 2D model\n",
    "##define 2D coordinate system in map space\n",
    "x_1d = (np.arange(N)/N - 0.5)*L*np.pi/(180.*60.)\n",
    "y_1d = np.copy(x_1d)\n",
    "x,y = np.meshgrid(x_1d,y_1d)\n",
    "\n",
    "\n",
    "#generate rotated beam and perpendicular\n",
    "beam_gaussian = np.exp(-0.5*(x/beam_sigma)**2. -0.5*(y/beam_sigma)**2.)\n",
    "exp_decay = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*np.pi/180.))\n",
    "exp_decay_meas = np.exp(-np.sqrt(x**2.)/(scan_sp*tau*np.pi/180.*(1-perc_err)))\n",
    "\n",
    "#take fft along horizontal\n",
    "exp_decay_fft = np.zeros((N,N),dtype=complex)\n",
    "exp_decay_meas_fft = np.zeros((N,N),dtype=complex)\n",
    "for row in range(N):\n",
    "    exp_decay_fft[row,:] = np.fft.fftshift(np.fft.fft(exp_decay[row,:]))\n",
    "    exp_decay_meas_fft[row,:] = np.fft.fftshift(np.fft.fft(exp_decay_meas[row,:]))\n",
    "\n",
    "#beam fft\n",
    "beam_gaussian_fft = np.fft.fftshift(np.fft.fft2(beam_gaussian))\n",
    "    \n",
    "#rotate fft's\n",
    "exp_decay_rot_para_fft = rotate_map(exp_decay_fft, ang)\n",
    "exp_decay_rot_perp_fft = rotate_map(exp_decay_fft, ang+np.pi/2.)\n",
    "exp_decay_rot_para_meas_fft = rotate_map(exp_decay_meas_fft, ang)\n",
    "exp_decay_rot_perp_meas_fft = rotate_map(exp_decay_meas_fft, ang+np.pi/2.)\n",
    "\n",
    "\n",
    "exp_decay_rot_para = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_para_fft)))#*beam_gaussian_fft) ))\n",
    "exp_decay_rot_perp = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_perp_fft)))#*beam_gaussian_fft) ))\n",
    "exp_decay_rot_para_meas = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_para_meas_fft)))#*beam_gaussian_fft) ))\n",
    "exp_decay_rot_perp_meas = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_perp_meas_fft)))#*beam_gaussian_fft) ))\n",
    "\n",
    "#########################################archive####################################################\n",
    "\n",
    "#exp_decay_rot_para = rotate_map(exp_decay, ang)\n",
    "#exp_decay_rot_perp = rotate_map(exp_decay, ang+np.pi/2.)\n",
    "#exp_decay_rot_meas_para = rotate_map(exp_decay_meas, ang)\n",
    "#exp_decay_rot_meas_perp = rotate_map(exp_decay_meas, ang+np.pi/2.)\n",
    "\n",
    "#convolve with beam\n",
    "#beam_gaussian_fft = np.fft.fftshift(np.fft.fft2(beam_gaussian))\n",
    "#exp_decay_rot_para_fft = np.fft.fftshift(np.fft.fft2(exp_decay_rot_para))\n",
    "#exp_decay_rot_perp_fft = np.fft.fftshift(np.fft.fft2(exp_decay_rot_perp))\n",
    "#exp_decay_rot_meas_para_fft = np.fft.fftshift(np.fft.fft2(exp_decay_rot_meas_para))\n",
    "#exp_decay_rot_meas_perp_fft = np.fft.fftshift(np.fft.fft2(exp_decay_rot_meas_perp))\n",
    "\n",
    "#exp_decay_rot_para = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_para_fft*beam_gaussian_fft)))\n",
    "#exp_decay_rot_perp = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_perp_fft*beam_gaussian_fft)))\n",
    "#exp_decay_rot_meas_para = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_meas_para_fft*beam_gaussian_fft)))\n",
    "#exp_decay_rot_meas_perp = np.fft.fftshift(np.real(np.fft.ifft2(exp_decay_rot_meas_perp_fft*beam_gaussian_fft)))                      \n",
    "\n",
    "#plt.imshow(np.real(np.log(exp_decay_rot_para_fft + 0.00000001)))\n",
    "#plt.show()\n",
    "\n",
    "##################################################################################################\n",
    "\n",
    "\n",
    "#average the two contributions in map space\n",
    "exp_decay_rot = (exp_decay_rot_para + exp_decay_rot_perp)/2.\n",
    "exp_decay_rot_meas = (exp_decay_rot_para_meas + exp_decay_rot_perp_meas)/2.\n",
    "\n",
    "\n",
    "#take fft and deconvolve gaussian beam\n",
    "exp_decay_rot_fft = np.fft.fftshift(np.fft.fft2(exp_decay_rot))\n",
    "exp_decay_rot_meas_fft = np.fft.fftshift(np.fft.fft2(exp_decay_rot_meas))\n",
    "exp_decay_rot_res_fft = np.zeros((N,N),dtype=complex)\n",
    "\n",
    "exp_decay_rot_res_fft = exp_decay_rot_fft / exp_decay_rot_meas_fft\n",
    "\n",
    "#exp_decay_rot_res_fft[512,:] = exp_decay_rot_fft[512,:] / exp_decay_rot_meas_fft[512,:]\n",
    "#for row in range(N):\n",
    "#    exp_decay_rot_res_fft[row,:] = exp_decay_rot_fft[512,:] / exp_decay_rot_meas_fft[512,:]\n",
    "\n",
    "#bin to 1D\n",
    "maps_dict = {}\n",
    "maps_dict['TT'] = exp_decay_rot_res_fft\n",
    "binned_ell, binned_exp_decay_rot_res = bin_maps_to_1d(maps_dict, delta_ell=delta_ell, ell_max=ell_max, pix_size=pixel_size, N=N)\n",
    "\n",
    "#normalize\n",
    "binned_exp_decay_rot_res['TT'] = binned_exp_decay_rot_res['TT'] / np.max(binned_exp_decay_rot_res['TT'])\n",
    "\n",
    "#plot\n",
    "plt.semilogy(binned_ell, binned_exp_decay_rot_res['TT'])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Archive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Smear Beam along x as scan direction by extending beam sigma by the characteristic lag in degrees (scan_speed*$\\tau$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ffd8f650c50>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define detector properties\n",
    "det_tau = 15.e-3    #detector time constant in seconds\n",
    "scan_sp = 1.    #scan speed of telescope in deg/s\n",
    "\n",
    "#generate beam\n",
    "N = 100    #number of pixels in beam map\n",
    "pixel_size = 0.25    #pixel size in arcmin\n",
    "L = N*pixel_size\n",
    "\n",
    "x_1d = (np.arange(N)/N - 0.5)*L\n",
    "y_1d = np.copy(x_1d)\n",
    "x,y = np.meshgrid(x_1d,y_1d)\n",
    "\n",
    "#lag in arcminutes due to detector tau\n",
    "lag_scale = det_tau*scan_sp*(60.)\n",
    "\n",
    "#smear beam sigma along scan direction (x)\n",
    "nominal_sigma = 1.5    #normal beam sigma in ideal conditions in arcmin\n",
    "sigma_x = nominal_sigma + lag_scale    #\n",
    "sigma_y = nominal_sigma    #beam sigma along perpendicular\n",
    "beam = np.exp(-0.5*((x/sigma_x)**2 + (y/sigma_y)**2   ))\n",
    "plt.imshow(beam)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This lag is deprojected by some measurement uncertainty, which should be equivalent to subtracting the lag in the exponential sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ffd8f4c2588>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#percent level of uncertainty in measurement of detector tau\n",
    "det_tau_unc = 0.3\n",
    "\n",
    "#lag scale of measured detector tau in arcmin\n",
    "lag_scale_measured = scan_sp*det_tau*(1-det_tau_unc)*(60.)\n",
    "\n",
    "sigma_x_deproj = sigma_x - lag_scale_measured\n",
    "\n",
    "#plot beam\n",
    "beam_deproj = np.exp(-0.5*((x/sigma_x_deproj)**2 + (y/sigma_y)**2   ))\n",
    "plt.imshow(beam_deproj)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare 1D and 2D (Not the Residual Contamination Spectrum):\n",
    "\n",
    "The finite response of a detector in the time domain is exponential decay ($a(t) = e^{-t/\\tau}$), where t=0 is when the detector 'sees' the signal and $\\tau$ is the detector's time constant. This can be represented in the spatial domain by introducing a scan speed as a unit conversion ($e^{-\\theta/(s\\tau)}$). Given this spatial representation of the detector response function, this can be transformed to $\\ell$-space through fourier transforming\n",
    "\n",
    "$$a(k) = \\int _0^\\infty e^{-\\frac{\\theta}{s\\tau}} e^{-ik\\theta}d\\theta$$\n",
    "\n",
    "This can be found to be a Lorentzian\n",
    "\n",
    "$$a(k) = \\frac{1}{\\pi}\\frac{k_0}{k_0^2+k^2}$$\n",
    "\n",
    "and the relation between k and $\\ell$ needs to be established\n",
    "\n",
    "In the limit that a cross linking scan strategy is perfect, the exponential response function radially in 2D space. For a rastering scan strategy, the response function need only be applied along the direction of scan, only affecting the k-modes along the scan. This should mean that the 1D radial model should be equivalent to the 2D model applied to both axes, which can serve as a sanity check on the pipeline without the model. \n",
    "\n",
    "The fourier transform of the response function should look like a lowpass filter (normalized):\n",
    "\n",
    "$$a(\\ell) = \\frac{1}{1 + \\frac{\\ell^2}{\\ell_{cutoff}^2}}$$\n",
    "\n",
    "where doing the above integral should pull out what $\\ell_{cutoff}$ is in terms of s, $\\tau$, and constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define relevant constants\n",
    "N = 1024  # []: pixels in map\n",
    "pixel_size = 0.25  # [arcmin/pixel]: size in arcmin of pixel\n",
    "ell_max = 5000  # [ell]: maximum ell\n",
    "delta_ell = 50  # [ell]: bin width for power spectra\n",
    "perc_err = 0.05  #[%]: percent the measure is off by\n",
    "scan_sp = 1.  # [deg/s]: scan speed of telescope\n",
    "tau = 200e-3  # [s]: time constant of detector\n",
    "ell = np.arange(ell_max)  # [ell]: array of ell\n",
    "L = N*pixel_size\n",
    "\n",
    "#define 1D model\n",
    "def lpf_tf_1d(ell, scan_sp, tau, N, pixel_size):\n",
    "    import numpy as np\n",
    "    \n",
    "    ell_cutoff = 0.55/(scan_sp*tau*np.pi/180.)\n",
    "    \n",
    "    #theta_w = 0.5*N*pixel_size/60.*np.pi/180.\n",
    "    #k_cutoff = scan_sp*tau*np.pi/180.\n",
    "    lpf_tf = 1 / (1 + ell**2./ell_cutoff**2.)\n",
    "    #lpf_tf = 0.5*( np.exp(-0.00001*theta_w/(k_cutoff)) + 2*np.cos(2*ell*theta_w) + np.exp(0.00001*theta_w/(k_cutoff)) )\n",
    "    \n",
    "    return lpf_tf\n",
    "\n",
    "exp_decay_1d = lpf_tf_1d(ell, scan_sp, tau, N, L)\n",
    "exp_decay_1d_deproj = lpf_tf_1d(ell, scan_sp*(1-perc_err), tau, N, L)\n",
    "exp_decay_1d_res = exp_decay_1d#/exp_decay_1d_deproj\n",
    "\n",
    "#define 2D model\n",
    "##define 2D coordinate system in map space\n",
    "x_1d = (np.arange(N)/N - 0.5)*L*np.pi/(180.*60.)\n",
    "y_1d = np.copy(x_1d)\n",
    "x,y = np.meshgrid(x_1d,y_1d)\n",
    "\n",
    "r = np.sqrt(x**2. + y**2.)\n",
    "exp_decay_2d = np.exp(-r/(scan_sp*tau*np.pi/180.))\n",
    "exp_decay_2d_deproj = np.exp(-r/(scan_sp*tau*np.pi/180.*(1-perc_err)))\n",
    "\n",
    "\n",
    "##fourier transform and bin to ell space\n",
    "exp_decay_2d_fft = np.fft.fftshift(np.fft.fft2((exp_decay_2d)))\n",
    "#exp_decay_2d_deproj_fft = np.fft.fftshift(np.fft.fft2((exp_decay_2d_deproj)))\n",
    "maps_dict = {}\n",
    "maps_dict['TT'] = exp_decay_2d_fft#/exp_decay_2d_deproj_fft\n",
    "binned_ell, binned_exp_decay_2d = bin_maps_to_1d(maps_dict, delta_ell=delta_ell, ell_max=ell_max, pix_size=pixel_size, N=N)\n",
    "\n",
    "#generate 1D radial $\\ell$-space response function\n",
    "\n",
    "#generate 2D x-scan $\\ell$-space response function\n",
    "\n",
    "#generate 2D y-scan $\\ell$-space response function\n",
    "\n",
    "#compare\n",
    "plt.semilogy(binned_ell, binned_exp_decay_2d['TT']/np.max(binned_exp_decay_2d['TT']), color='m')\n",
    "plt.semilogy(ell, exp_decay_1d_res, color='g')\n",
    "plt.title('Comparing the 1D Model to the 2D Numerical Model')\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.legend(['2D Model','1D Model'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try Curve Fitting to get functional form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter values are [5746.03526511]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnitude (arb)')"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def lorenzian(x,xp):\n",
    "    return ( 1  / ( 1. + (x/(xp))**2. )**3.)\n",
    "\n",
    "import scipy.optimize as optimization\n",
    "\n",
    "#ell_set is the range of ell values the binned spectrum goes over\n",
    "ell_set = binned_ell\n",
    "initial_guess = np.array([50])\n",
    "\n",
    "#right now for one simulation just take the std of the dataset. If it's necessary, multiple simulations can be run\n",
    "#to make the weighting in the optimization more accurate, but for now I don't care as much\n",
    "sigma = np.sqrt(np.var(binned_exp_decay_2d['TT']/np.max(binned_exp_decay_2d['TT'])))\n",
    "errors = sigma*np.ones(len(binned_exp_decay_2d['TT']))\n",
    "curve_fit = optimization.curve_fit(lorenzian, ell_set, binned_exp_decay_2d['TT']/np.max(binned_exp_decay_2d['TT']), initial_guess, errors)\n",
    "\n",
    "parameters = curve_fit[0]\n",
    "tf_fit_r = lorenzian(ell,parameters[0])\n",
    "print('Parameter values are ' + str(parameters))\n",
    "plt.semilogy(binned_ell,binned_exp_decay_2d['TT']/np.max(binned_exp_decay_2d['TT']))\n",
    "plt.semilogy(ell, tf_fit_r)\n",
    "plt.title('Curve Fit to Contamination Spectrum')\n",
    "plt.legend(['Spectrum','Fit to Spectrum'])\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f250de2a710>]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7xpgU4HfAjV0rPXAYY/ify0ZjMDz50U7OGDaIWVO+Cjkz4dU7Yf63YeOrcNn9EJ/pcrUi0l91agvfWvs+cOTlm6YB26y1O6y1LcBzwBXW2k+ttZcdcSu31h4ckK4CwrutBwHCGMM9c0YyOi2W/35lA9UNLTAwC748H2b/Ggo/hoenwyd/Al+72+WKSD/UlTH8dKDjAHOJv+2ojDFXGWMeBf6G82vhWMvdZoxZaYxZWVFR0YXy+p9Qr4df/9t4qhta+NmCTU6jxwPTb4NvfQJZZ8Ibd8PjF8LuNe4WKyL9Tq/ttLXWvmytvd1ae5219t3jLPeYtXaqtXZqUlJSb5XXZ4wZHMcd5w7jpdUlvLul/PAL8UPghhfgmiehpgQeOw8WfA8adN1cEemcrgR+KdBxQDnD3yZd9O0LhjM8OZq7X/qULXtrD79gDIy9Gr69EqbfAav+An+YCiuf1DCPiJxQVwJ/BZBrjMk2xoQB1wPzu6es4BYe4uX+6ybS5rNc8fCHvLjyiKmZEXEw+5dw+/uQmAcL/h0eORt2vOdOwSLSL3R2WuY84GMgzxhTYoy5xVrbBtwJvAlsAl6w1m7ouVKDy9j0OF7/zllMyhzIf/xjPT94cR2NLUdsxaeOg5tfh397Clpq4enL4dlrnZOyiYgcwdg+PL976tSpduXKlW6X4ap2n+WBt7fy0JJtjEqN5dGbppCZEPn5BVubYNmf4IPfO+E/8QaYeQ/EZfR+0SLiKmPMKmvt1M+1K/D7hyWby7nruTV4PYaH5k7i7Nxj7NBu2A8f/BaWPwYYmPo1OPt7EJ3cq/WKiHuOFfg6l04/cd7IZF678yxSYiL4ypPLeWHFMU65EJkAl9wH314F4//NCf4HJsCie6F+X+8WLSJ9igK/H8lKjOLlb87grNwk/vOl9Tzx4c5jLxw/BK54GL61HPLmwEcPwP3j4a0fQV1wHd8gIg4Ffj8TFR7Cn788hdljU/nZgo08uLiA4w7LJQ6Ha56Aby2DkXPg4z/A/WPh9f/UidlEgowCvx8KD/Hy0NxJXD05g98t2soDiwtO/KakPLj6cfjWChh3Dax8Ah6c6FxMvXxTj9csIu7TRcz7qRCvh19fMx5j4P63C4gOD+HWs3NO/MbE4c5Qz7l3w9KHYM3fYO2zkHsxzPg2ZJ3tHOAlIgFHW/j9mMdj+L+rx3PpuDR+vnATf19W1Pk3x2fCnF/Bv2+A834IpavhqS84B3CteRbamnuucBFxhaZlBoCWNh93PLOKJVvK+frZOXz7/OHERISe3Ie0NsKnL8LHf4SKTRCVBFO+6kzrjB3cI3WLSM/QPPwA19Tazr2vbuD5lcUkxYRz96yRfHFSOh7PSQ7PWAs7lsCyx2DrG2A8MOoymHoLZJ+j4R6RfkCBHyTWFldz7/wNrCuu5oKRyfzu2onERZ7k1v5BVbtgxeOw5hlorIJBw2HKzTBhLkQN6ta6RaT7KPCDiM9neerjXfzv65tIjYvgTzdOYWx63Kl/YGujc8WtFU9AyXLwhsGoL8Dkrzg7eT3aFSTSlyjwg9Dqoiq+9exqKutbePD6Scwam9r1Dy3bAKuegvXPQVONc4DXxC/BxLnOYxFxnQI/SFXWNfP1p1eSv/sAf791OlOzErrng1sbYdMCWPsM7HgXMJB1lnPStlFfgPCY7vkeETlpCvwgVlXfwlV/WkpVQwsvf2MGOUnR3fwFhbDuOVg3D6p2QmgkjLwUxl8HOeeBV4d7iPQmBX6QK6ys56o/LiUqPIS/f306GQOPcorlrrIWipc7wb/hn9BUDZGJMOaLztG9GdM03i/SCxT4wpqiKub++ROaWn2MTovl3Lwkrp6czvDkHhh+aWuBbYtg/QvO9M62JojLhDFXOiuAwZM1xVOkhyjwBYAdFXX8K38v722tYHVhFQBfnZHFdy7MPfmDtTqruRY2vw75L8H2d8DX6uzgHX0ljL4C0qco/EW6kQJfPqeyrpnfvLWF51YUkxQdzk+vGMOssWk9+6WNVbB5oTPks+M9J/xjM5yDu0Z9AYacAR5vz9YgEuAU+HJM64qr+e9X8vm0tIZvzhzG9y/Ow3uyR+ieisYq2PIGbJoP2xZDezNEDoK82ZB3KeTMhLAe2NcgEuAU+HJcLW0+7p2fz7zlxZw/Mpn7r59IbE8N8RxNcx1sexs2vQYFi6C5BkIGwLDznBVA7iUQk9J79Yj0Ywp8OSFrLc98UshPXtvIkIRIHr5xMqPSYnu/kLYWKPzIGfrZ+gbU+C/UMngyjLjEOZVz2kTN+BE5BgW+dNqyHZXcOW8NBxpb+dmVY7l2aqZ7xVjrHN275V9Q8CaUrAQsRCXD8Ash90IYdj4MGOhejSJ9jAJfTkpFbTPfeW4NS7dXcum4NG49O5uJmfEYt2fT1O9zhn4K3nLG/ZuqnTN6pk+F4Rc4K4HBk7TjV4KaAl9OWrvP8uDiAv78wQ4aWtoZnRbLzWdmcfXkjJM/7XKPFNgGpaucFcD2xc5FXLAQEQfZ5zpb/jkzISHb7UpFepUCX05ZbVMrr67dzTOfFLJ5by1nDU/kV9eMZ3D8ALdL+6z6Stj5rjPXf/sSOFDqtMcPdYI/51zIOgeik9ysUqTHKfCly6y1/H15Efct3ITXY/jJ5WP44qR094d5jsZa2LfVmeu/413Y9QE0H3BeSx4D2Wc7F3QZOkPj/xJwFPjSbQor6/n+C+tYWVjFZePTuO/Kcad+kZXe0t4Ge9bCzveclUDxMud0DxhIHeec6XPomc4KILKbzigq4hIFvnSrdp/lkfe28/tFW0mOCee3107kjGH96CpYbc3OjJ9dH8CuD6FkhX8FgPMLYOiMw7eYbriOgEgvUuBLj1hbXM13n1vDrsoGhidHM2tMKrPGpjJmcGzfHOo5lrZmZwdw4UdQuBSKlkFrvfPawGwn+DOnO6d+SMzVuX+kT1PgS4+pb27jpdUlvJG/l2U799Pus4xNj+Wm04dy+YR0BoT1wymS7a2wdz0UfgxF/ltDpfPagATInOasADKnO9NAdQoI6UMU+NIr9te3sHD9bp75pIgtZbXEDQjlgesnMjMv2e3SusZaqNzmD/9lzj6AygLnNU+Isx8gY5qzIsiY6swM0q8AcYnrgW+MORu4EQgBRltrZ5zoPQr8/stay4pdVfx4/ga2ltXy22sncMXEdLfL6l71lc5F3Yv9t92robXBeS0qyTkYLMN/GzzJOT5ApBd0KfCNMU8ClwHl1tqxHdpnAQ8AXuBxa+0vO/FZVwIp1tpHT7SsAr//O9DUyq1PrWTFrv389PIx3HRGltsl9Zz2Nijf6KwESlY5O4IP/grAQOII59z/6ZOdW8pYCAl3tWQJTF0N/HOAOuDpg4FvjPECW4GLgBJgBTAXJ/x/ccRHfM1aW+5/3wvALdba2hN9rwI/MDS1tnPn31fz9qZyRqbGcOm4NGaPS2N4cjdfW7cvaqxyjgAuXQ2lK50dw/UVzmueUEgZ42z9D54EgydC8mjw9vEprtLndXlIxxiTBSzoEPhnAD+21l7if34PgLX2yLDv+BlDgB9Za79+nGVuA24DGDJkyJTCwsJO1Sd9W1u7j2c+KeS19XtY5b/S1oiUg7N60hiVFtO/ZvWcKmuhpsQJ/t2rYfca2L3OOR00gDfcvxKY6JwRdPBESBoFIWEuFi39TU8E/jXALGvtrf7nNwHTrbV3HuczfgK8aa1d2pnv1BZ+YNpb08Qb+Xv4V/5eVuzaj8/CGTmD+NFloxk92IXTMbvN54Oqnf7wXwN71jm3g0cGe0IheRSkjYfUCc59ylgID4JfSHJK+kTgnywFfuDbV9fMq2t389A7BRxobOW604bwg4tHMCg6yMe2fT6o3gW71zrTQw+uBA5ODcVAQo4zOyh1HKSOh9SxEJOm2UFyzMAP6cJnlgIdT5Se4W8T6bTE6HBuOSubqyenc//bBfztk0IWrt/NDy7J48bpQ3vnUot9kcfjBHpCDoy9ymmzFg7s9q8A1jv3u9fAxlcOvy9ykDMklDLOfz8GkkZCaIQr3ZC+pStb+CE4O20vwAn6FcAN1toN3VWctvCDT0FZLffO38DS7ZWMTovl9nNzmJ49iNQ4BdYxNVY7F4kpy4e9nzqPyzdBW6PzuvHCoOH+FcBo59QRKaMhboiuGhagujpLZx4wE0gEyoB7rbVPGGPmAPfjzMx50lp7X3cWrcAPTtZaFn66h/sWbmJPjXN+myEJkVw2Po07Zg7r3Wvt9le+dqjcDuUb/CsD/626wySIsGhn6z95lDM7KHmUc4tO0bBQP+f6gVenQoEf3NrafWzeW8uynftZum0fizeXkxAVxncvzGXutCGEerV1etKaa52t//KNULbRuS/f2GHfABAR7wT/wZVBUp4zUyg6WSuCfkKBL/1efmkNP1+4kU927GdYUhT3fmEM54zQxUy6RV2FE/wVm50VQsVm53lTzeFlIuL94Z8HiXmHH8dmaGioj1HgS0Cw1rJoYxn3vb6JwsoGLhyVwn/NyiM3Jcbt0gKPtVBX5g//zbBvC1RscZ53/EUQGunsI0jKc44mPnhLyNHOYpco8CWgNLe18+SHu3jonQIaWtoZOiiSc0ckcUbOIPJSYxg6KCp4Z/j0hvrKwyuAfVsP39cUH17GeCB+iBP+g3Ihcbj/Plf7CXqYAl8CUnltE2/k7+W9LRUs3V5JY2s7AGEhHqYMGcj/XjWO7MQol6sMIi31zllF9xX4b1ud+8pth2cNAYTFwKBhzi+DQ7dhzk0nmesyBb4EvOa2djbvqWVrmXN7cVUJrW0+/veqcYF3ps7+xudzLipfWeDMHtpX4H+8DaqLgQ45FJXsBH/CMBiU478f5gwRhWnl3RkKfAk6pdWN3DVvDasKq7hqUjpXTErntKyBRIZ15XhD6XatTbB/B+zf7qwMKgug0v+8ruyzy0an+sM/21kBDMw+fIBaRBCeluMYFPgSlFrbffx+0Vb+/MEOWtstIR7DhMx4pmUncFrWQKYMTSBugOb191nNtf6VwQ5nZbB/5+HndXs/u2zkIP8KIPvz90G2z0CBL0GtoaWNVYVVLN1eycfbK8kvraHN56wArp+WyV0X5JIcoxkl/UpzHVTtOrwCqDq4MtgFB0rA+g4vGzIABmYd5TbUuTpZgF2iUoEv0kFjSztri6tZsH43z68oJizEw61n53Dr2dk6kjcQtLU4M4b273RWBFW7nMfVhc79wQvUHxSV/NkVQMf72Azw9q9hQAW+yDHs3FfPb97awsL1e4gbEMpt5+Tw1RlZRIX3r//k0knWQv0+J/yrdvlXCP7H1YVQUwq2/fDyxgux6f6VwJDP32IG97kVggJf5ATyS2v4/aKtLN5cTnxkKMOSookODyEmIoSzhidy6fg0YrT1H/jaW50ZRVWFzgqgusj/uMi51e7hM7OKDq4Q4odAfCbEZXa4H+K81ssHoCnwRTppbXE1Ty3dRXltE3XN7eyrbaa0upEBoV5mj0vl9nOGkZeqI3uDVluzc9Wy6iL/CqHYGT6qLnIe1+7+7P4DcIaM4jMhLsNZERxaKfifDxjYrTuVFfgip8hay9rial5YWcJr63bT2NrOV2dk8d0Lc7XFL5938BfCoRVBMdQUOSuJmhLneXvzZ98TGumEf2y6fyWQARNvcH4hnAIFvkg3qKpv4ddvbWHe8iISo8O5enIGI1NjyEuNIScpivAQr9slSl93cB9CjX+FUFPqXxkUOY8PlDrHH3x9CaRPPqWvUOCLdKN1xdXc9/omVhdW0eZz/g95DAwdFMWwpGjOzk3kutMyiQjVCkBOQVuzs2/gFHcGK/BFekBLm4+d++rZvPcA28rr2FZex5ayWnZU1JMSG863zhvOdadlastfepUCX6QXLd2+j98v2sqKXVUkx4Rz85nZ3DB9iI7qlV6hwBfpZdZaPtpWySPvbefDbfuICvNybl7SoSt1pcRGcNPpQ8lMCKyjPMV9CnwRF+WX1vD4BztYW1x9qK20uhFr4YqJ6Xxj5jCGJ0e7V6AEFAW+SB+zp6aRx97fwbzlRTS3+bhwVAq3nZPD1KEDMUF0oi/pfgp8kT5qX10zTy/dxdOfFFLd0MqYwbGMz4hjWFI02YlRZAyMJH3gAKJ1qgfpJAW+SB/X0NLGP1Y5B3dtr6hnf33LZ15PjA7jrgty+dL0oXh0+UY5DgW+SD9TVd/Czsp6SqsaKa1u5P2tzmUcp2Ul8Murx5GTpDF/OToFvkg/Z63lxVUl/HzBRhpb2xkcP4DYiFBiB4SQGB1Ockw4KbERnD8yWSuDIKfAFwkQ5QeaePzDnZQdaOJAYyvVja3sq2um/EAzzW0+jIELR6Vw+zk5TM1KcLtcccGxAl97gUT6meTYCP7fnFGfa7fWUl7bzLOfFPL0J4Us2ljGuPQ4bpw+hMsnDta1fEVb+CKBqKGljZdWlfDMJ0VsKaslJjyErMQomtvaaW7zkZscw1dnZHHm8EGaAhqANKQjEoSstawqrOL5FcXsq2smItRLiNfD0m37qKxvYURKNF+ZkcWVE9N1ha8AosAXkUOaWtt5bd1unvxoF5v2HCA6PIQrJg5m1thUUmIjSIwOJ35AqKZ/9lMKfBH5HGstq4uqeHZZEQvX76G57fCVmjwG4gaEEh8ZRk5iFN+7eARjBse5WK10luuBb4wZDfwYqAQWW2v/caL3KPBFek9NQysb9tRQWddCZV0z++tbqGpopaqhhaXbK6luaOHG6UP5/sUjiI8Mc7tcOY4uzdIxxjwJXAaUW2vHdmifBTwAeIHHrbW/PM7HzAYestZ+YIyZD5ww8EWk98RFhjJjWOJRX6tpaOV3i7bwt08KeX5FMQlRYcRHhhIfGUpMRCgx4SEMig5jzrg0JmbGa0dwH9WpLXxjzDlAHfD0wcA3xniBrcBFQAmwApiLE/6/OOIjvua/vxdoAGZYa8880fdqC1+kb9m4+wCvritlf10L1Y2t1DS0cqCpldqmNirqmmlp8zEqLZYbpg/h8vGDiYvU+f/d0OUhHWNMFrCgQ+CfAfzYWnuJ//k9ANbaI8P+yM/xAi9ba6840Xcq8EX6j9qmVl5du5u/Lyti454DhHoNM/OSuXzCYMYMjmVw/ABd8rGX9MSBV+lAcYfnJcD04xSQBfw/IAr49XGWuw24DWDIkFO7YruI9L6YiFC+dPpQbpw+hPzSA7y6tpT563azaGPZoWUSo8MZEObBawxej+HC0Snced5wYiL0S6A3dGUL/xpglrX2Vv/zm4Dp1to7u6s4beGL9G/tPsva4moKK+spqWpkd3UjzW0+2n2WmsZW3ttaQWJ0GN+/OI+rJqfr2r/dpCe28EuBzA7PM/xtIiIAeD2GKUMHMmXowKO+vr6kmp++tpF7Xv6Ue17+lIGRoSTHRBAW4qGlzUdLu49hSVF8+Ywszs5N1M7gLupK4K8Aco0x2ThBfz1wQ7dUJSJBYXxGPC/ecQbvbC5n4+4DlNU2UX6gmdZ2H2EhHkK8Hpbt2M/bm5YzLCmKL50+lEvHpZEcG+F26f1SZ2fpzANmAolAGXCvtfYJY8wc4H6cmTlPWmvv687iNKQjIs1t7Sxcv4e/Lt3F+pIajIHp2QmMz4inoraZvTVNhIZ4uGZKBrPGpBIW4nG7ZNe5fuDVqVDgi0hHBWW1LFi/hwXrd1O8v5GkmHBS4yIor22ieH8jidFhXDMlk8snDGZUWkzQDgEp8EUkoFhrDwW6z2d5v6CCZz4pYsmWctp9luzEKM4fmUxSTDgxESFEh4cQ6vXg9RiiwkI4PSeBEG9g/hrQ+fBFJKB03Hr3eJw5/zPzkqmsa+atjWUsXL+Hpz/eRWv70TdqsxOj+P7FI5gzNi1oThKnLXwRCVjWWhpa2qlrbqO2qY12n6XN56OwsoEH3i5gS1kto9JiGTs4lqjwjr8CIMTrYVp2ApP64akitIUvIkHHGENUeAhR4SGkxB5uHzM4jkvGpDJ/XSlPfriLD7fto665jbrmNo7cBs5Njua605z9Av19dpC28EVE/Ky1+KxzwFhDSxv/yt/L8yuKWVtcDcDEzHguGp1CRKiXgrJatpbVkhwTwXXTMjknNwlvHxka0k5bEZFTVFBWy5sb9rJoYxnrSmoASIgKIzc5mu0VdeyrayE9fgBXT07nkrGpjE6LdXUYSIEvItINKmqbAUiKCQegpc3Hoo1lzFtexEfb92EtZCYM4LSsBGIjQokK9xLm9dLS3k5zq4+BUWHMnTaEhKieu6aAAl9EpIftq2tm8aYy3txQxuY9Bw7tF/BZ5zQT4SEeGlvbiQz1cvOZ2dx6dvZRLybj8zm5fKqzhxT4IiIusNbS7rOH5vwXlNVy/+ICFq7fgzEQHRZCdEQIEaFeGlraqGtqo6G1nZe/MYNJQ45+DqIT0SwdEREXGGMI8R7eUs9NieHhGyZz53kHeCN/L7VNbdQ1t9LY6iMy1Et0hDOr6OCQUXdS4IuIuGBUWiyj0mJPvGA3CszjikVE5HMU+CIiQUKBLyISJBT4IiJBQoEvIhIkFPgiIkFCgS8iEiQU+CIiQaJPn1rBGFMBFJ7CWxOBfd1cTl8XjH2G4Ox3MPYZgrPfp9rnodbapCMb+3TgnypjzMqjnUcikAVjnyE4+x2MfYbg7Hd391lDOiIiQUKBLyISJAI18B9zuwAXBGOfITj7HYx9huDsd7f2OSDH8EVE5PMCdQtfRESOoMAXEQkSARX4xphZxpgtxphtxpi73a6nq4wxTxpjyo0x+R3aEowxi4wxBf77gf52Y4x50N/39caYyR3e8xX/8gXGmK+40ZfOMsZkGmOWGGM2GmM2GGO+428P2H4bYyKMMcuNMev8ff6Jvz3bGLPM37fnjTFh/vZw//Nt/tezOnzWPf72LcaYS1zqUqcZY7zGmDXGmAX+58HQ513GmE+NMWuNMSv9bb3z922tDYgb4AW2AzlAGLAOGO12XV3s0znAZCC/Q9uvgLv9j+8G/s//eA7wL8AApwPL/O0JwA7//UD/44Fu9+04fU4DJvsfxwBbgdGB3G9/7dH+x6HAMn9fXgCu97c/AnzD//ibwCP+x9cDz/sfj/b/3YcD2f7/D163+3eCvn8P+DuwwP88GPq8C0g8oq1X/r5d73w3/iOeAbzZ4fk9wD1u19UN/co6IvC3AGn+x2nAFv/jR4G5Ry4HzAUe7dD+meX6+g14FbgoWPoNRAKrgek4R1iG+NsP/X0DbwJn+B+H+JczR/7Nd1yuL96ADGAxcD6wwN+HgO6zv8ajBX6v/H0H0pBOOlDc4XmJvy3QpFhr9/gf7wVS/I+P1f9+++/i/9k+CWeLN6D77R/aWAuUA4twtlSrrbVt/kU61n+ob/7Xa4BB9LM+A/cD/wn4/M8HEfh9BrDAW8aYVcaY2/xtvfL3rYuY92PWWmuMCch5tcaYaOAl4LvW2gPGmEOvBWK/rbXtwERjTDzwT2CkuxX1LGPMZUC5tXaVMWamy+X0trOstaXGmGRgkTFmc8cXe/LvO5C28EuBzA7PM/xtgabMGJMG4L8v97cfq//97t/FGBOKE/bPWmtf9jcHfL8BrLXVwBKc4Yx4Y8zBjbKO9R/qm//1OKCS/tXnM4HLjTG7gOdwhnUeILD7DIC1ttR/X46zcp9GL/19B1LgrwBy/Xv5w3B27Mx3uaaeMB84uEf+Kzhj3Afbv+zfq386UOP/ifgmcLExZqB/z//F/rY+yTib8k8Am6y1v+vwUsD22xiT5N+yxxgzAGefxSac4L/Gv9iRfT74b3EN8I51BnLnA9f7Z7RkA7nA8l7pxEmy1t5jrc2w1mbh/F99x1p7IwHcZwBjTJQxJubgY5y/y3x66+/b7R0Y3bwzZA7OrI7twA/drqcb+jMP2AO04ozR3YIzbrkYKADeBhL8yxrgYX/fPwWmdvicrwHb/Leb3e7XCfp8Fs4Y53pgrf82J5D7DYwH1vj7nA/8j789Bye8tgEvAuH+9gj/823+13M6fNYP/f8WW4DZbvetk/2fyeFZOgHdZ3//1vlvGw7mVG/9fevUCiIiQSKQhnREROQ4FPgiIkFCgS8iEiQU+CIiQUKBLyISJBT4IiJBQoEvIhIk/j+UwV01R/oNgAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(binned_ell,binned_exp_decay_2d['TT']/np.max(binned_exp_decay_2d['TT']))\n",
    "\n",
    "x = binned_ell\n",
    "plt.plot(x,(1/(1+(x/50.)**2))**2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(exp_decay_2d[512,500:532],'.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter values are [-0.00150062]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Magnitude (arb)')"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "exp_1d_fft = np.fft.fftshift(np.fft.fft(exp_decay_2d[512,:]))\n",
    "freqs_array = np.zeros(len(exp_1d_fft))\n",
    "\n",
    "exp_1d_fft = np.sqrt(np.real(np.conj(exp_1d_fft)*exp_1d_fft))\n",
    "k_array = np.arange(0,1024,1)\n",
    "for i in range(len(freqs_array)):\n",
    "    k = k_array[i]\n",
    "    freqs_array[i] = 2*np.pi/N*k\n",
    "\n",
    "import scipy.optimize as optimization\n",
    "\n",
    "#ell_set is the range of ell values the binned spectrum goes over\n",
    "ell_set = freqs_array\n",
    "initial_guess = np.array([50])\n",
    "\n",
    "#right now for one simulation just take the std of the dataset. If it's necessary, multiple simulations can be run\n",
    "#to make the weighting in the optimization more accurate, but for now I don't care as much\n",
    "sigma = np.sqrt(np.var(exp_1d_fft/np.max(exp_1d_fft)))\n",
    "errors = sigma*np.ones(len(exp_1d_fft))\n",
    "curve_fit = optimization.curve_fit(lorenzian, ell_set, exp_1d_fft/np.max(exp_1d_fft), initial_guess, errors)\n",
    "\n",
    "parameters = curve_fit[0]\n",
    "#tf_fit_r = lorenzian(freqs_array,parameters[0])\n",
    "xp = .0225\n",
    "x = freqs_array\n",
    "tf_fit_r = (1 / (1 + ((x-3.15)/xp-0)**2.))\n",
    "print('Parameter values are ' + str(parameters))\n",
    "plt.semilogy(freqs_array,exp_1d_fft/np.max(exp_1d_fft))\n",
    "plt.semilogy(freqs_array, tf_fit_r/np.max(tf_fit_r))\n",
    "plt.title('Curve Fit to Contamination Spectrum')\n",
    "plt.legend(['Spectrum','Fit to Spectrum'])\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Magnitude (arb)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f250c3565f8>]"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(np.real(exp_1d_fft))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basically, this assumes that taking an fft and binning the 2D exponential decay is correct and then backing out the conversion factor from k to $\\ell$ in the flat space limit. The conversion factor between k modes and $\\ell$ in this space seems to be k dependent. i.e. the conversion factor is different for k mode $\\frac{1}{\\omega*\\tau*\\pi/180}$ as opposed to the measured counterpart $\\frac{1}{\\omega*(1-\\%_{err})*\\tau*\\pi/180}$. This means the analytical expression should find the functional form of this in order to correctly calculate the spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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08QH+qdX+DWB2AjW/lp9/2vIK4L8Z3Gfl88DK1n9aW55r618x5hp/BzjY5vXfGFzpn8o5Bf4O+CZwN/AvwMppmFfgOgbXYZ5mcDS3vWcOgT9p9c4BV57Kvv16uqQu03raImnKGR6SuhgekroYHpK6GB6SuhgekroYHpK6/D/sDfUrKzyYmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "det_tau = 5.e-3   #detector tau in milliseconds\n",
    "obs_freq = 90.    #observation frequency in GHz\n",
    "scan_sp = 1.    #scan speed of telescope in deg/s\n",
    "N = 1024    #number of pixels in map\n",
    "pixel_size = 0.25/60.    #pixel size in deg\n",
    "D_aper = 5.    #aperture diameter of telescope\n",
    "\n",
    "#map_scan_fft = gen_scanx_dir_map(det_tau, obs_freq, scan_sp=scan_sp, N=N, pixel_size=pixel_size, D_aper=D_aper)\n",
    "\n",
    "#relavant params: observing freq, scan speed in deg/s, N resolution of map, pixel size in deg, diameter of main aperture, det tau\n",
    "ell_fac = 100. / 1. #conversion factor from deg to ell\n",
    "obs_lam = constants.c / (obs_freq*10**9)\n",
    "diff_lim = ell_fac / (1.22*(obs_lam / D_aper) * (180. / constants.pi))\n",
    "ell_cutoff = ell_fac / (scan_sp * det_tau)\n",
    "\n",
    "ell_max = ell_fac / (pixel_size)\n",
    "ell = np.linspace(-2500, 2500, N)\n",
    "\n",
    "#create empty map\n",
    "map_scan_fft = np.zeros((N,N))\n",
    "\n",
    "## make a 1/f map, along a single direction to illustrate striping \n",
    "one_over_f_noise_level = 1.\n",
    "one_overf_noise = 0\n",
    "if (one_over_f_noise_level != 0): \n",
    "    ones = np.ones(N)\n",
    "    inds  = (np.arange(N)+.5 - N/2.) \n",
    "    X = np.outer(ones,inds) * pixel_size /60. ## angles relative to 1 degrees \n",
    "    kx = 2 * np.pi/(X+.01) ## 0.01 is a regularization factor\n",
    "    oneoverf_noise = np.fft.fft2(np.random.normal(0,1,(N,N)))\n",
    "    oneoverf_noise = np.fft.ifft2(oneoverf_noise * np.fft.fftshift(kx))* one_over_f_noise_level/pixel_size\n",
    "\n",
    "#fill each row with lpf TF\n",
    "for i in np.arange(N):\n",
    "\n",
    "    #map_scan_fft[i][int(N/2):] = lpf_tf(ell[:int(N/2)], scan_sp, det_tau)\n",
    "    #map_scan_fft[i][:int(N/2)] = lpf_tf(np.flip(ell[:int(N/2)],0), scan_sp, det_tau)\n",
    "    if i == int(N/2):\n",
    "        map_scan_fft[i][int(N/2):] = np.exp(-ell[:int(N/2)]*scan_sp*det_tau/100)\n",
    "        #map_scan_fft[i][:] = np.exp(-ell*scan_sp*det_tau/100)\n",
    "        map_scan_fft[i][:int(N/2)] = np.exp(-np.flip(ell[:int(N/2)])*scan_sp*det_tau/100)\n",
    "    else:\n",
    "        map_scan_fft[i][:] = np.zeros(N)\n",
    "\n",
    "\n",
    "plt.imshow(map_scan_fft)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ahryciuk/.local/lib/python3.6/site-packages/numpy/core/_asarray.py:85: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta_t = 1e-4\n",
    "time_array = np.array([i*delta_t for i in range(N)])\n",
    "freq_array = np.array([i/delta_t for i in range(N)])\n",
    "exp_time = np.exp(-time_array/det_tau)\n",
    "exp_freq = np.fft.fftshift(np.fft.fft(exp_time))\n",
    "exp_freq = exp_freq / np.sum(exp_freq)\n",
    "\n",
    "plt.semilogy(freq_array,exp_freq)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beam_map = make_2d_gaussian_beam(N, pixel_size, 1.4)\n",
    "\n",
    "#map_scan_fft_fft = np.fft.fft2(np.fft.fftshift(map_scan_fft)) / np.sum(np.fft.fft2(np.fft.fftshift(map_scan_fft)))\n",
    "beam_map_fft = np.fft.fft2(np.fft.fftshift(beam_map))\n",
    "convolved_map_fft = beam_map_fft*map_scan_fft\n",
    "convolved_map = np.fft.fftshift(np.real(np.fft.ifft2(convolved_map_fft)))\n",
    "plt.imshow(beam_map[int(N/2)-10:int(N/2)+10,int(N/2)-10:int(N/2)+10])\n",
    "plt.show()\n",
    "\n",
    "plt.imshow(convolved_map[int(N/2)-100:int(N/2)+100,int(N/2)-100:int(N/2)+100])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using concrete pixel lag to smear beam along scan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "code_folding": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "det_tau = 5.e-3   #detector tau in milliseconds\n",
    "obs_freq = 90.    #observation frequency in GHz\n",
    "scan_sp = 10.    #scan speed of telescope in deg/s\n",
    "N = 1024    #number of pixels in map\n",
    "pixel_size = 0.25/60.    #pixel size in deg\n",
    "D_aper = 5.    #aperture diameter of telescope\n",
    "\n",
    "#when generate detector sky maps, add a feature that lags the two pixel values along the scan direction by some amount\n",
    "#lag even rows by +x and odd rows by -x\n",
    "def lag_map_along_scan(det_map, tau_det, scan_sp=3., pix_size=0.25/60., leftright = 'right'):\n",
    "    import numpy as np\n",
    "    \n",
    "    #scan speed is deg/sec, tau_det in milliseconds, pixel size is in deg\n",
    "    num_pix_lag = int(scan_sp * tau_det / pix_size)\n",
    "    #print(num_pix_lag)\n",
    "    \n",
    "    #lag all the 1's in the detector map by pixel amt\n",
    "    #indices_to_lag = np.where(det_map == 1.)\n",
    "    indices_to_lag = det_map.nonzero()\n",
    "    col_inds = indices_to_lag[0]\n",
    "    row_inds = indices_to_lag[1]\n",
    "    \n",
    "    lagged_beam_map = det_map.copy()\n",
    "    \n",
    "    if col_inds.any():\n",
    "        for i in range(len(col_inds)):\n",
    "            \n",
    "            #store pixel value\n",
    "            pixel_value = det_map[col_inds[i], row_inds[i]]\n",
    "            \n",
    "            #set map at unlagged position to zero\n",
    "            lagged_beam_map[col_inds[i], row_inds[i]] = 0.\n",
    "            \n",
    "            if leftright == 'right':\n",
    "                if row_inds[i]+num_pix_lag >= len(det_map[0,:]):\n",
    "                    pass\n",
    "                else:\n",
    "                    lagged_beam_map[col_inds[i], row_inds[i] + num_pix_lag] = pixel_value\n",
    "            elif leftright == 'left':\n",
    "                lagged_beam_map[col_inds[i], row_inds[i] - num_pix_lag] = pixel_value\n",
    "            else:\n",
    "                print('define scan direction as left or right')\n",
    "    else:\n",
    "        pass\n",
    "    \n",
    "    return lagged_beam_map\n",
    "\n",
    "\n",
    "lagged_beam_map = lag_map_along_scan(beam_map, det_tau,scan_sp=scan_sp, pix_size = pixel_size, leftright='right')\n",
    "\n",
    "plt.imshow(beam_map[int(N/2)-10:int(N/2)+10,int(N/2)-10:int(N/2)+10])\n",
    "plt.show()\n",
    "plt.imshow(lagged_beam_map[int(N/2)-10:int(N/2)+10,int(N/2)-10:int(N/2)+10])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0]), array([1]))"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[0,1],[0,0]])\n",
    "a.nonzero()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#check the numbering scheme by plotting parts of rhombuses\n",
    "#start with rows and make sure the bonpad pairs are attached to the detectors such that the detectors closest to the module\n",
    "#are attached to the leftmost bondpad pairs and towards the right as the pixels get farther away\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#map parameters\n",
    "pixel_size = 0.25/60.    #deg\n",
    "N = 200    #number of pixels to a side\n",
    "det_map = np.zeros((N,N))\n",
    "\n",
    "#use the rhom_layout_dict to index the det_dict to pull out columns\n",
    "#det_list_to_plot = rhom_layout_dict[2][150][11]\n",
    "\n",
    "x_list = []\n",
    "y_list = []\n",
    "\n",
    "#for readout_col in range(12):\n",
    "#    det_list_to_plot = rhom_layout_dict[2][90][readout_col]\n",
    "det_list_to_plot = rhom_layout_dict[0][150][5]\n",
    "for det in det_list_to_plot:\n",
    "    i = np.where(det_list_to_plot == det)\n",
    "    x = det_dict[90][det]['x']    #in degrees\n",
    "    y = det_dict[90][det]['y']    #in degrees\n",
    "\n",
    "    pix_x = int(N/2. + x/pixel_size)\n",
    "    pix_y = int(N/2. + y/pixel_size)\n",
    "\n",
    "\n",
    "    x_list.append(pix_x)\n",
    "    y_list.append(pix_y)\n",
    "\n",
    "    det_map[pix_x,pix_y] = 100.\n",
    "    #plt.text(x_list[-1],y_list[-1],det,size=16)\n",
    "    #plt.text(pix_x, pix_y, det, size=8, color='white')\n",
    "\n",
    "#plt.imshow(det_map[int(N/2)-70:int(N/2)+70,int(N/2)-70:int(N/2)+70])\n",
    "plt.imshow(det_map)\n",
    "#plt.scatter(x_list, y_list)\n",
    "#plt.savefig(\"Rhombus1.png\",bbox_inches = 'tight')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.9"
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 },
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