"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# need to be careful around edges that cubic spline interpolation doesn't give negative values,\n",
"# because they will cause the Poisson routine to fail (why?). Set negatives to 0.\n",
"rvsim_logwave = rvinterp(np.exp(logwave))\n",
"\n",
"rvsim_logwave[rvsim_logwave<0]= 0.\n",
"\n",
"# now add noise using the addnoise routine from above\n",
"out=addnoise(rvsim_logwave,sn=100,rn=10)\n",
"plt.clf()\n",
"plt.plot(np.exp(logwave),sim_logwave,label='noiseless rest')\n",
"plt.plot(np.exp(logwave),out,label='RV shifted with noise')\n",
"plt.plot(np.exp(logwave),rvsim_logwave,label='RV shifted, no noise')\n",
"plt.legend()\n",
"plt.xlim(5000,5050)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"OK, now we will see if we can recover the radial velocity using cross correlation.\n",
"\n",
"Apart from sampling on a $\\log\\lambda$ grid, another thing we need to be careful of in cross correlation is the continuum level. If the signal has a mean value greater than 0, the cross correlation will be \"diluted\" by the continuum contribution, and edge effects will be very significant; imagine that the signal drops to zero off the edges, which will lead to a big change in cross-correlation as the edges slide relative to each other. As a result, the mean level is typically removed before cross-correlation. Here, the continuum level is clearly a function of wavelength. We'll remove an approximate continuum by subtracting a \"median-filtered\" version of the spectrum: imagine running a window across the spectrum and taking the median value in the window around each pixel. We will use scipy.signal.medfilt() to do this, although the principle is simple.\n",
"\n",
"We will build this continuum subtraction into a short cross-correlation function, using numpy.correlate to do the actual cross-correlation of the continuum-removed spectra. numpy.correlate() will cross-correlate two spectra across a large range of shifts, depending on the mode keyword, but even the smallest of these is likely overkill for the RV problem, if we expect that the shift is small (pixels or tens of pixels). Here, we use it with the mode='same' option, which will produce a cross-correlation function of the same size as the first array, which means it is computing shifts from the second array being shifted one half of its length to the left up through one half of its length to the right: zero lag will be in the middle of cross-correlation array.\n",
"\n",
"It would be very straightforward, and possibly simpler to understand, to write your own (perhaps one-line!) cross correlation routine that returned the cross-correlation function as a function of shift (lag)."
]
},
{
"cell_type": "code",
"execution_count": 186,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-20, 20)"
]
},
"execution_count": 186,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import scipy.signal\n",
"def xcorr(a,b,filter=401) :\n",
" \"\"\" Cross correlate two spectra, but remove the median levels first\n",
" \n",
" filter gives the width for the median filtering\n",
" \n",
" returns the lag array and the cross correlation function\n",
" \"\"\"\n",
" xc=np.correlate(a-scipy.signal.medfilt(a,filter),b-scipy.signal.medfilt(b,filter),mode='same')\n",
" # with mode='same', the zero shift cross-correlation is in the middle of the output array\n",
" if len(xc)%2 == 0 :\n",
" lag=np.arange(len(xc))-len(xc)/2\n",
" else :\n",
" lag=np.arange(len(xc))-(len(xc)-1)/2\n",
"\n",
" return lag, xc \n",
"\n",
"# cross correlate template with itself as a check\n",
"lag,xc=xcorr(sim_logwave,sim_logwave)\n",
"\n",
"# cross correlate template with object\n",
"lag,xc2=xcorr(out,sim_logwave)\n",
"\n",
"# plot cross correlation as a function of lag\n",
"plt.plot(lag,xc/xc.max())\n",
"plt.plot(lag,xc/xc.max(),'bo', label='autocorrelation')\n",
"plt.plot(lag,xc2/xc2.max(),'ro',label='cross correlation of shifted and rest')\n",
"plt.legend()\n",
"plt.xlim(-20,20)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can look for the peak of the cross correlation, which will give us the pixel shift in the $\\log\\lambda$ data arrays. To turn that into a velocity, we need to determine the velocity shift per pixel, which is just $d\\log\\lambda \\times c$"
]
},
{
"cell_type": "code",
"execution_count": 195,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dloglambda: 0.000064 velocity per pixel: 19.068622\n",
"peak pixel: 6671 corresponding lag: 10.000000\n",
"corresponding RV: 190.686222\n"
]
}
],
"source": [
"print('dloglambda: {:f} velocity per pixel: {:f}'.format(dlog_lambda,dlog_lambda*3.e5))\n",
"# get the peak pixel, the lag corresponding to this pixel, and the corresping RV\n",
"imax=xc2.argmax()\n",
"print('peak pixel: {:d} corresponding lag: {:f}'.format(imax,lag[imax]))\n",
"print('corresponding RV: {:f}'.format(lag[imax]*dlog_lambda*3.e5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How well does this match the input radial velocity? Note that we can do (much) better by fitting for the peak: if you look carefully you can see that the cross-correlation is not symmetric around the peak pixel. Write this as a function so we can use it later (always good to write things as function!)"
]
},
{
"cell_type": "code",
"execution_count": 200,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"10.0\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# plot around peak\n",
"plt.plot(lag,xc2/xc2.max(),'ro',label='cross correlation of shifted and rest')\n",
"plt.xlim(lag[imax-5],lag[imax+5])\n",
"plt.ylim(0.8,1.05)\n",
"print(lag[imax])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see by eye that the maximum is probably closer to a lag of 10.5. Getting a little ahead of ourselves, let's do a quick quadratic fit to the peak."
]
},
{
"cell_type": "code",
"execution_count": 227,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"peak lag: 10.470327 corresponding RV: 199.654714\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def fitpeak(lag,xcorr,plot=True) :\n",
" imax=xcorr.argmax()\n",
" x=lag[imax-5:imax+6]\n",
" y=xcorr[imax-5:imax+6]/xcorr.max()\n",
" fit=np.polyfit(x,y,2)\n",
" if plot :\n",
" plt.plot(x,y,'ro',label='cross correlation of shifted and rest')\n",
" plt.xlim(lag[imax-5],lag[imax+5])\n",
" xx=np.linspace(x[0],x[-1],100)\n",
" plt.plot(xx,fit[0]*xx**2+fit[1]*xx+fit[2])\n",
"\n",
" #for a quadratic fit y = ax**2 + bx + c, the peak is where the derivative, 2ax +b, equals 0, so xpeak=-b/2a\n",
" return -fit[1]/2/fit[0]\n",
"\n",
"peak=fitpeak(lag,xc2)\n",
"\n",
"#convert this to a velocity as above\n",
"print('peak lag: {:f} corresponding RV: {:f}'.format(peak,peak*dlog_lambda*3.e5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Better? Try doing this at different S/N for the input spectrum, and report your results. See how compact it is if we use functions for the different steps!"
]
},
{
"cell_type": "code",
"execution_count": 231,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"S/N: 5.000000 peak lag: 10.004497 corresponding RV: 190.771965\n",
"S/N: 10.000000 peak lag: 10.428714 corresponding RV: 198.861203\n",
"S/N: 50.000000 peak lag: 10.449020 corresponding RV: 199.248410\n",
"S/N: 100.000000 peak lag: 10.469787 corresponding RV: 199.644413\n",
"S/N: 1000.000000 peak lag: 10.466854 corresponding RV: 199.588477\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for sn in [5,10,50,100,1000] :\n",
" # get the simulated spectrum for this S/N\n",
" out=addnoise(rvsim_logwave,sn=sn,rn=10)\n",
" plt.figure()\n",
" plt.plot(out)\n",
" \n",
" # do the cross correlation including continuum removal\n",
" lag,xc2=xcorr(out,sim_logwave)\n",
" \n",
" # fit the cross correlation peak and report results\n",
" peak=fitpeak(lag,xc2,plot=False)\n",
"\n",
" #convert this to a velocity as above\n",
" print('S/N: {:f} peak lag: {:f} corresponding RV: {:f}'.format(sn,peak,peak*dlog_lambda*3.e5))\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 2
}