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@beckermr
Last active September 9, 2021 18:22
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{
"cells": [
{
"cell_type": "markdown",
"id": "essential-patio",
"metadata": {},
"source": [
"## Some Math\n",
"\n",
"Let's assume all objects are always centered at $x=0$ to simplify the FFT handling. \n",
"\n",
"We need a few relations to understand the math. \n",
"\n",
"1. The Fourier transform of a function like $x^2W(x)$ is $F[x^2W(x)] \\propto \\frac{d^2\\hat{W}(k)}{dk^2}$.\n",
"2. The Fourier transform of a Gaussian is a Gaussian, which we can write generically as $\\exp(-\\alpha^2 k^2)$. Here $\\alpha$ is related to the real-space FWHM of the profile via some constants we won't bother with.\n",
"3. A convolution in real-space is a product in Fourier space.\n",
"4. A weighted sum over a profile in real-space can be written as an integral in Fourier space.\n",
"\n",
"This last relation is worth discussin in detail. Suppose we have an image $I(x)$, a weight function $W(x)$, and we want to compute the integral $f = \\int dx I(x) W(x)$. This integral is actuall the value of the convolution of $I(x)$ with $W(x)$ at $x=0$,\n",
"\n",
"$$\n",
"f = \\int dx I(x) W(x) = \\left. \\int dx I(x) W(x - y)\\right|_{y = 0}\n",
"$$\n",
"\n",
"In Fourier space we can write this relation as \n",
"\n",
"$$\n",
"f \\propto \\left.\\int dk \\hat{I}(k)\\hat{W}(k) \\exp(-iky)\\right|_{y=0} = \\int dk \\hat{I}(k)\\hat{W}(k)\n",
"$$\n",
"\n",
"So this property combined item 1 above means we can write the weighted moments of an object in real-space as integrals in Fourier space over the weight function and its derivatives\n",
"\n",
"$$\n",
"f \\propto \\int dk \\hat{I}(k)\\hat{W}(k)\n",
"$$\n",
"\n",
"$$\n",
"<x^2> \\propto \\int dk \\hat{I}(k)\\frac{d^{2}\\hat{W}(k)}{dk_x^2}\n",
"$$\n",
"\n",
"$$\n",
"<xy> \\propto \\int dk \\hat{I}(k)\\frac{d^2\\hat{W}(k)}{dk_x dk_y}\n",
"$$\n",
"\n",
"$$\n",
"<y^2> \\propto \\int dk \\hat{I}(k)\\frac{d^2\\hat{W}(k)}{dk_y^2}\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"id": "competitive-wrapping",
"metadata": {},
"source": [
"## What about the PSF?\n",
"\n",
"So now let's assume we have an object, a PSF, and a weight function. Further, let's assume that the weight function is always bigger than the PSF and that the weight function is Gaussian.\n",
"\n",
"In this case, we can immediately see that all of the derivatives of the weight function in Fourier space can be written as a product of some polynomial and the weight function iself. The constraint that the weight function be larger than the PSF means that $\\alpha_{psf} < \\alpha_{w}$. Finally, we have some object with $\\alpha_g$. \n",
"\n",
"In terms of the profile of $k$ we have the following situation illustrated in the plot below."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "realistic-indonesia",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/beckermr/miniconda3/envs/ngmix-dev/lib/python3.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in log10\n",
" \"\"\"\n",
"/Users/beckermr/miniconda3/envs/ngmix-dev/lib/python3.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in log10\n",
" \"\"\"\n",
"/Users/beckermr/miniconda3/envs/ngmix-dev/lib/python3.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in log10\n",
" \"\"\"\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x14276fdd0>"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 400,
"width": 400
}
},
"output_type": "display_data"
}
],
"source": [
"import proplot as plot\n",
"import numpy as np\n",
"\n",
"def prof(k, a):\n",
" return np.log10(np.exp(-(a*k)**2))\n",
"\n",
"k = np.logspace(-1, 1.5, 100)\n",
"apsf = 1\n",
"aw = 1.5\n",
"ag = 0.25\n",
"\n",
"fig, axs = plot.subplots(figsize=(4, 4))\n",
"axs.semilogx(k, prof(k, np.sqrt(ag**2+apsf**2)), label='gal+psf')\n",
"axs.semilogx(k, prof(k, apsf), label='psf')\n",
"axs.semilogx(k, prof(k, ag), label='gal')\n",
"axs.semilogx(k, prof(k, aw), label='wgt')\n",
"axs.format(xlabel='log10[k]', ylabel='log10[f(k)]')\n",
"axs.legend()"
]
},
{
"cell_type": "markdown",
"id": "emerging-contrast",
"metadata": {},
"source": [
"From this plot you can see that even for real-space moments, as long as the Fourier transforms of the moment kernels are broader than PSF, we remove modes suppressed by the PSF. Thus we can set these suppressed modes (where the PSF amplitude cannot be deconvolved) in Fourier space to zero without harm."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "married-garlic",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:ngmix-dev] *",
"language": "python",
"name": "conda-env-ngmix-dev-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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