{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# PSF normalization\n",
"\n",
"Let us assume that we have reduced an observation, for which we have determined the PSF by stacking the flux of point-like sources. The PSF we obtain will not be as high S/N as the instrumental PSF that has been determined by the instrument team. Moreover, it is likely to be fattened due to the some small pointing errors. We need to find out what fraction of a point-like flux the PSF we have determined represent. In order to do this, we use the growth curve of the theoretical PSF that has been determine by the instrument team, and compare it to the growth curve we determine from our PSF.\n",
"\n",
"We will first look at a theoretical case, then go practical with an example drawn from the PACS observation of the the XMM-LSS.\n",
"\n",
"## 1) Theoretical example. \n",
"\n",
"Let us suppose we have a perfect telescope, without any central obscuration and spider to support the secondary. Diffraction theory gives us the shape of a PSF in this case, an Airy function. Let's compute it, and assume the resolution is 10\".\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# import what we will need. \n",
"%matplotlib inline\n",
"import numpy as np\n",
"from astropy.io import fits\n",
"from astropy.table import Table\n",
"from astropy.io import ascii as asciiread\n",
"from matplotlib import pyplot as plt\n",
"from scipy import interpolate \n",
"from scipy import special\n",
"from scipy import signal\n",
"from scipy import fftpack"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Let us perform our computation with a 0.1\" resolution on a 5' field of view\n",
"resol = 0.1\n",
"size = 300.\n",
"# wavelength\n",
"wavelength = 250e-6\n",
"# primary aperture = 3.6 m diameter\n",
"aperture = 3.6 / 2."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Ensure we have an odd number of points \n",
"nbpix = np.ceil(size/resol) // 2 * 2 + 1\n",
"xcen = int((nbpix - 1) / 2)\n",
"ycen = int((nbpix - 1) / 2)\n",
"x = y = (np.arange(nbpix) - xcen)*resol\n",
"xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
"r = np.sqrt(xv**2+yv**2)\n",
"# avoid division by 0 problems in the center\n",
"r[xcen,ycen] = 1e-6\n",
"# coordinates in fourier\n",
"q = 2 * np.pi / wavelength * aperture * np.sin(r/3600.*np.pi/180.)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"psf = (2*special.jn(1, q)/q)**2"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# put back the correct value at center\n",
"psf[xcen, ycen] = 1.\n",
"# and normalize the PSF\n",
"psf = psf/(np.sum(psf)*resol**2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.imshow(np.log10(psf))\n",
"print(r'$\\int\\int$ psf dx dy = {}'.format(np.sum(psf)*resol**2))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Without obscuration')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us now suppose that we observe a point source, and our image reconstruction has a ...This will shows a a blurring of the image, with a gaussian of 10\" FWHM. Let's generate this blurring"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"fwhm = 10.\n",
"sigma = fwhm / 2. / np.sqrt(2. * np.log(fwhm))\n",
"sigmasq = sigma**2\n",
"kernel_blur = 1./ 2./ np.pi / sigmasq * np.exp(-(r**2/2./sigmasq))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Check our kernel is properly normalized\n",
"np.sum(kernel_blur*resol**2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# apply the blur\n",
"psfblur = signal.convolve(psf, kernel_blur, mode='same')*resol**2"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Original')\n",
"plt.plot(y[ycen-500:ycen+500], psfblur[ycen-500:ycen+500, xcen], label='With blurring')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see the effect of blurring, the, observed PSF is wider, and we have lost some flux in the central core. Suppose now that we observed this psf with sources of unknown fluxes, so that we re unsure of its scaling, and that a background remain in our observation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"psfobs = psfblur * 2. + 1e-4"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The question is now how to recover the PSF that serve for our observation. For this, we will use the PSFs curve of growth. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"radii = np.arange(0, np.max(r), resol)\n",
"growth_psf = np.zeros(radii.shape)\n",
"growth_psfobs = np.zeros(radii.shape)\n",
"nbpix_psfobs = np.zeros(radii.shape)\n",
"for i, radius in enumerate(radii):\n",
" if ((i % 100) == 0):\n",
" print(radius, np.max(radii))\n",
" if i == 0:\n",
" idj, idi = np.where(r <= radius)\n",
" growth_psf[i] = np.sum(psf[idj, idi])*resol**2\n",
" growth_psfobs[i] = np.sum(psfobs[idj, idi])*resol**2\n",
" nbpix_psfobs[i] =len(idi)\n",
" else:\n",
" idj, idi = np.where((r > radii[i-1]) & (r <= radius))\n",
" growth_psf[i] = growth_psf[i-1]+np.sum(psf[idj, idi])*resol**2\n",
" growth_psfobs[i] = growth_psfobs[i-1]+np.sum(psfobs[idj, idi])*resol**2\n",
" nbpix_psfobs[i] = nbpix_psfobs[i-1]+len(idi)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(radii, growth_psf, label='PSF')\n",
"plt.plot(radii, growth_psfobs, label='Observed PSF')\n",
"plt.xlabel('Radius [arcsec]')\n",
"plt.ylabel('Encircled flux')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This strongly rising shape of the observed PSF is a sure sign of an non zero background. Let's determine it. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(nbpix_psfobs, growth_psfobs)\n",
"plt.xlabel('Number of pixels')\n",
"plt.ylabel('Encircled flux')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When plotted as a function of the intergated area, there is a clear linear relation, that we will fit:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"idx, = np.where(radii > 50)\n",
"p = np.polyfit(nbpix_psfobs[idx], growth_psfobs[idx], 1)\n",
"bkg = p[0]/resol**2"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Correct PSF and curve of growth\n",
"psfcor = psfobs-bkg\n",
"growth_psfcor = growth_psfobs - bkg*nbpix_psfobs*resol**2"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(radii, growth_psf, label='PSF')\n",
"plt.plot(radii, growth_psfcor, label='Observed PSF')\n",
"plt.xlabel('Radius [arcsec]')\n",
"plt.ylabel('Encircled flux')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Let's have a look at the ratio of the two:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(radii[1:], growth_psfcor[1:]/growth_psf[1:])\n",
"plt.xlabel('Radius [arcsec]')\n",
"plt.ylabel('Ratio of encircled flux')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Due to the different resolution, the ratio is not constant. Let's note the calibration $C(r)$. Let us assume that our observed PSF encirled energy is of the form:\n",
"\n",
"$E(r) = \\alpha C(r \\times \\beta)$\n",
"\n",
"Where $\\beta$ is the fattening of the PSF. If we differentiate as a function of $r$:\n",
"\n",
"$E'(r) = \\alpha \\beta C'(r \\times \\beta)$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# compute the derivatives\n",
"deriv_growth_psf = (growth_psf[2:]-growth_psf[0:-2])/(radii[2:]-radii[0:-2])\n",
"deriv_growth_psfcor = (growth_psfcor[2:]-growth_psfcor[0:-2])/(radii[2:]-radii[0:-2])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(radii[1:-1], deriv_growth_psf)\n",
"plt.plot(radii[1:-1], deriv_growth_psfcor)\n",
"plt.xlim([0,60])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compared with the growth curve plot, the derivative show clear maxima and minima that are out of phase. Findind the positions of the these will tell us if our assumption of homothetical variation is correct."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Find the local minima and maxima of the two curves.\n",
"# To find a local extremum, we will fit the portion of curve with a degree 3 polynomial, \n",
"# extract the roots of its derivative and only retain the one that are between the bounds.\n",
"# This is what the following function does.\n",
"def local_max(xvalues, yvalues, lower_bound, upper_bound, check_plot=False):\n",
" idx,=np.where((xvalues > lower_bound) & (xvalues < upper_bound))\n",
" p = np.polyfit(xvalues[idx], yvalues[idx], 3)\n",
" delta = (2.*p[1])**2 - 4.*3.*p[0]*p[2]\n",
" r1 = (-2*p[1]+np.sqrt(delta))/(2*3*p[0])\n",
" r2 = (-2*p[1]-np.sqrt(delta))/(2*3*p[0])\n",
" result = r1 if ((r1 > lower_bound) and (r1 < upper_bound)) else r2\n",
" if check_plot:\n",
" plt.plot(xvalues[idx], yvalues[idx])\n",
" plt.plot(xvalues[idx], p[0]*xvalues[idx]**3+p[1]*xvalues[idx]**2+\n",
" p[2]*xvalues[idx]+p[3], '--')\n",
" plt.plot(np.array([result, result]), np.array([np.min(yvalues), np.max(yvalues)]), '-')\n",
" return result\n",
" \n",
" \n",
"max_dpsf_1 = local_max(radii[1:-1], deriv_growth_psf, 3, 10, check_plot=True)\n",
"max_dpsfcor_1 = local_max(radii[1:-1], deriv_growth_psfcor, 3, 10, check_plot=True)\n",
"\n",
"max_dpsf_2 = local_max(radii[1:-1], deriv_growth_psf, 14, 21, check_plot=True)\n",
"max_dpsfcor_2 = local_max(radii[1:-1], deriv_growth_psfcor, 14, 21, check_plot=True)\n",
"\n",
"max_dpsf_3 = local_max(radii[1:-1], deriv_growth_psf, 21, 28, check_plot=True)\n",
"max_dpsfcor_3 = local_max(radii[1:-1], deriv_growth_psfcor, 21, 28, check_plot=True)\n",
"\n",
"max_dpsf_4 = local_max(radii[1:-1], deriv_growth_psf, 28, 35, check_plot=True)\n",
"max_dpsfcor_4 = local_max(radii[1:-1], deriv_growth_psfcor, 28, 35, check_plot=True)\n",
"\n",
"max_dpsf_5 = local_max(radii[1:-1], deriv_growth_psf, 35, 45, check_plot=True)\n",
"max_dpsfcor_5 = local_max(radii[1:-1], deriv_growth_psfcor, 35, 45, check_plot=True)\n",
"\n",
"max_dpsf_6 = local_max(radii[1:-1], deriv_growth_psf, 40, 50, check_plot=True)\n",
"max_dpsfcor_6 = local_max(radii[1:-1], deriv_growth_psfcor, 40, 50, check_plot=True)\n",
"\n",
"plt.xlabel('Radius [arcsec]')\n",
"\n",
"# Lets pack all of them, adding the r=0 point. \n",
"max_dpsf = np.array([0, max_dpsf_1, max_dpsf_2, max_dpsf_3, max_dpsf_4, max_dpsf_5, max_dpsf_6])\n",
"max_dpsfcor = np.array([0, max_dpsfcor_1, max_dpsfcor_2, max_dpsfcor_3, max_dpsfcor_4, \n",
" max_dpsfcor_5, max_dpsfcor_6])\n",
"\n",
"print(max_dpsf,max_dpsfcor)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the plot, we can deduce that our homothetical assumption is not perfect: the spacing increases for the first three (don't forget the point at 0, 0, not shown), is very small for the 4th and 6th, and gets narrower for the 5th and 7th...\n",
"Let's plot the situation"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"plt.plot(max_dpsf, max_dpsfcor, 'o-')\n",
"p = np.polyfit(max_dpsf[0:3], max_dpsfcor[0:3], 1)\n",
"plt.plot(max_dpsf, p[0]*max_dpsf+p[1])\n",
"plt.xlabel('extremum position of theoretical psf [arcsec]')\n",
"plt.ylabel('extremum position of observed blurred psf [arcsec]')\n",
"\n",
"\n",
"print(p)\n",
"print((max_dpsfcor[1]-max_dpsfcor[0])/(max_dpsf[1]-max_dpsf[0]))\n",
"print((max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0]))\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Lets use the data before 20\", corresponding to the central core\n",
"beta = (max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0])\n",
"\n",
"# lets interpolate at the scaled radius\n",
"tckpsfcor = interpolate.splrep(radii, growth_psfcor, s=0)\n",
"interp_growth_psfcor = interpolate.splev(radii*beta, tckpsfcor, der=0)\n",
"\n",
"# check interpolation\n",
"plt.plot(radii*beta, growth_psf)\n",
"plt.plot(radii, growth_psfcor)\n",
"plt.plot(radii*beta, interp_growth_psfcor)\n",
"plt.xlim([0,60])\n",
"plt.xlabel('radius [arcsec]')\n",
"plt.ylabel('Encircled flux')\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us check the ratio, using the psf with a corrected radius"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"plt.plot(radii[1:]*beta, interp_growth_psfcor[1:]/growth_psf[1:])\n",
"plt.xlabel('radius [arcsec]')\n",
"plt.ylabel('Ratio of encircled flux')\n",
"plt.xlim([0,60])\n",
"idx, = np.where(((radii*p[0]) > 0) & ((radii*p[0]) < 60))\n",
"scale_factor = np.median(interp_growth_psfcor[idx]/growth_psf[idx])\n",
"print(\"alpha = {:.3f}\".format(scale_factor))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now have a much better looking ratio [compared with the cell where we computed the direct ratio](#the_ratio), and we have a decent determination of the psf scaling. The normalized PSF to use for our observations is then:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"psf_obs_norm = psfcor / scale_factor"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"print('\\int \\int psf_obs_norm dx dy = {}'.format(np.sum(psf_obs_norm)*resol**2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed, let's look at the encircled energy in the core of our psf:\n",
"In this example, we have used the derivative of the scale factor"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"idj, idi = np.where(r"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"stackhd_im = fits.open('./data/input_data/XMM-LSS_PACS100_v0.9.fits')\n",
"im=stackhd_im[1].data\n",
"stackhd = fits.open('./data/output_data/100um/psf_native.fits')\n",
"psf = stackhd[1].data\n",
"hd = stackhd[1].header\n",
"plt.imshow(psf)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Convert units MJy/sr to mJy/pixel: http://coolwiki.ipac.caltech.edu/index.php/Units\n",
"#psf=psf*2.35045e-2*(np.abs(stackhd[1].header['CDELT1'])*3600)**2\n",
"#print(psf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set the resolution of the psf. Because the map is in units of Jy/pixel, this turns out to be:\n",
"* =1 if psf at same resolution of map\n",
"* otherwise, should be in factor of map pixel size\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.33333333333393333"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"resol"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's build the growthcurve for our PSF."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# find the brightest pixel, it will be our center.\n",
"jmax, imax = np.unravel_index(np.argmax(psf), psf.shape)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"# build the array of coordinates\n",
"x = np.arange(hd['NAXIS1'])\n",
"y = np.arange(hd['NAXIS2'])\n",
"xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
"xp = (xv-imax)*np.abs(hd['CDELT1'])*3600.\n",
"yp = (yv-jmax)*np.abs(hd['CDELT2'])*3600.\n",
"r = np.sqrt(xp**2 + yp**2)\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# build the growth curve\n",
"radii = np.unique(r)\n",
"encircled_flux = np.zeros(radii.shape)\n",
"nbpix = np.zeros(radii.shape)\n",
"for i, radius in enumerate(radii):\n",
" idj, idi = np.where(r <= radius)\n",
" nbpix[i] =len(idi)\n",
" #encircled_flux[i] = np.sum(psf[idj, idi])*resol**2\n",
" #multiply by ((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10 as map is in units of MJy/sr\n",
" encircled_flux[i] = np.sum(psf[idj, idi])*((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.6666666828012"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"hd['CDELT1']*3600."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Encircled flux')"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(radiuseff*rfactor[rmin], valeff, label='Calibration')\n",
"plt.plot(radii, encircled_flux/np.max(encircled_flux)/ffactor[fmin], label='Our PSF')\n",
"plt.xlim([0, 200])\n",
"plt.xlabel('Radius [arcsec]')\n",
"plt.ylabel('Encircled flux')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"37819220000.0"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# The two curve overlap\n",
"psfok = psf/np.max(encircled_flux)/ffactor[fmin]\n",
"np.sum(psfok)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"### As units of map in MJy/sr, divide by 1E6\n",
"psfok=psfok/1.0E6"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Validation\n",
"To check PSF is reasonable, lets look at a 100 micron source, e.g. `XMM-PACSxID24-1-69605`. We can see from `XMM-LSS_PACS100_v0.9.fits` that it has a flux of 27 mJy. Maximum value in our normalised PSF gives a peak below. Since PSF is three times resolution of map, it could also be off centre. \n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from astropy.table import Table"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"PACScat=Table.read('./data/XMM-LSS_PACSxID24_v1.fits')"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<Column name='HELP_ID' dtype='bytes21' length=69614>\n",
"