{
 "cells": [
  {
   "attachments": {
    "Ellipticity.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weak gravitational lensing\n",
    "\n",
    "Gravitational lensing can lead to the formation of multiple images of the same background source, especially if it is in near perfect alignment towards the line-of-sight of a massive lens. Owing to this condition of alignment, such phenomenon are rare (about 1 in 1000 massive elliptical galaxies act as lenses). This is the strong lensing regime. In most cases however, the background galaxy will not be perfectly aligned to produce multiple images, but nevertheless its shape will get distorted due to the shear due to object at its location.\n",
    "\n",
    "This distortion can be characterized using the Jacobian of the mapping from the source plane to the lens plane at the observed location of the image.\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\mathcal{M}^{-1}(\\boldsymbol{\\theta}) &=&\n",
    "\\begin{pmatrix}\n",
    "1 - \\kappa - \\gamma_1 & -\\gamma_{2}\\\\\n",
    "-\\gamma_2 & 1-\\kappa + \\gamma_1\n",
    "\\end{pmatrix} \\\\ \n",
    "&=& \n",
    "(1-\\kappa)\\begin{pmatrix}\n",
    "1-\\frac{\\gamma_1}{(1-\\kappa)} & -\\frac{\\gamma_2}{(1-\\kappa)} \\\\\n",
    "-\\frac{\\gamma_2}{(1-\\kappa)}  & 1+\\frac{\\gamma_1}{(1-\\kappa)} \n",
    "\\end{pmatrix}\n",
    "\\end{eqnarray}\n",
    "\n",
    "where the two components of the shear are given by\n",
    "\\begin{eqnarray}\n",
    "\\gamma_1 &=& \\frac{1}{2} \\left[ \\psi_{,11} - \\psi_{,22} \\right] \\\\\n",
    "\\gamma_2 &=& \\psi_{,12}\n",
    "\\end{eqnarray}\n",
    "and that the larger eigenvector of the distortion is inclined at an angle $\\phi$, with\n",
    "\\begin{eqnarray}\n",
    "\\tan 2\\phi = \\frac{\\gamma_2}{\\gamma_1}\\,.\n",
    "\\end{eqnarray}\n",
    "\n",
    "A circular source thus gets distorted in to an ellipse, where the angle of orientation is related the relative ratio of the two shear components, and the ellipticity is related to the reduced shear at the location of the source.\n",
    "\\begin{eqnarray}\n",
    "e=\\frac{a-b}{a+b} &=& \\frac{\\frac{1}{1-\\kappa-|\\gamma|} - \\frac{1}{1-\\kappa+|\\gamma|}}{\\frac{1}{1-\\kappa-|\\gamma|} + \\frac{1}{1-\\kappa+|\\gamma|}} \\\\\n",
    "&=& \\frac{|\\gamma|}{1-\\kappa}\n",
    "\\end{eqnarray}\n",
    "One can also consider another way to quantify the ellipticity\n",
    "\\begin{eqnarray}\n",
    "\\chi=\\frac{a^2-b^2}{a^2+b^2} &=& \\frac{\\frac{1}{(1-\\kappa-|\\gamma|)^2} - \\frac{1}{(1-\\kappa+|\\gamma|)^2}}{\\frac{1}{(1-\\kappa-|\\gamma|)^2} + \\frac{1}{(1-\\kappa+|\\gamma|)^2}} \\\\\n",
    "\\end{eqnarray}\n",
    "This shows\n",
    "\\begin{eqnarray}\n",
    "\\chi =\\frac{2|\\gamma|}{(1-\\kappa)}\n",
    "\\end{eqnarray}\n",
    "\n",
    "![Ellipticity.png](attachment:Ellipticity.png)\n",
    "\n",
    "The above figure shows how the ellipses are oriented given the values of these components. Pay special attention to cases along the two different axes."
   ]
  },
  {
   "attachments": {
    "Tangential.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Weak lensing as mass probe\n",
    "\n",
    "Let us now consider the case where we have determined the estimate of shear around a galaxy cluster. How do we infer the surface mass density of the cluster from the shear? \n",
    "\n",
    "Consider the following figure which shows how the presence of shear distorts the shapes of galaxies. The left hand panel shows a distribution of background galaxies which are intrinsically circular in shape. The right hand panel shows the impact of including an azimuthally symmetric mass distribution. We see that the background shapes are now distorted in a coherent manner, all tangentially oriented with respect to the center of the mass distribution. The galaxies nearer to the center have larger distortions while those further away have weaker distortions.\n",
    "\n",
    "![Tangential.png](attachment:Tangential.png)\n",
    "\n",
    "We can define the tangential shear by defining a coordinate system with one axis which is the line joining the center of the mass distribution to the position of the source galaxy. Let $\\theta$ be the angle made by this line with respect to the x-axis.\n",
    "\\begin{eqnarray} \n",
    "\\gamma_{\\rm t} = - {\\rm Re}({\\boldsymbol \\gamma }e^{-2i\\theta})\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "attachments": {
    "TangentialShear.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![TangentialShear.png](attachment:TangentialShear.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tangential shear average over circles\n",
    "\n",
    "Consider first Gauss's law and integrate the Laplacian of the lensing potential within a disk inside radius R.\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\int_{0}^{\\theta} d\\vec\\theta' \\nabla. \\nabla \\psi &=&  \\theta \\oint d\\varphi \\nabla \\psi.\\hat n \\\\\n",
    "2 \\int_0^{\\theta} d\\vec\\theta' \\kappa(\\vec\\theta') &=& \\theta \\oint d\\varphi \\partial_{\\theta} \\psi \\\\\n",
    "2 \\int_0^{\\theta} d\\varphi \\vartheta d\\vartheta \\kappa(\\vartheta, \\varphi) &=& \\theta \\oint d\\varphi \\partial_{\\theta} \\psi \\\\\n",
    "2 \\int_0^{\\theta} 2 \\pi \\vartheta d\\vartheta \\langle\\kappa(\\vartheta)\\rangle &=& \\theta \\oint d\\varphi \\partial_{\\theta} \\psi\\,, \n",
    "\\end{eqnarray}\n",
    "where we define\n",
    "\\begin{eqnarray}\n",
    "\\langle\\kappa(\\vartheta)\\rangle &=& \\frac{1}{2\\pi} \\int d\\varphi \\kappa(\\vartheta, \\varphi)\n",
    "\\end{eqnarray}\n",
    "which denotes the scaled surface density $\\kappa$ averaged over all angles for a given $\\theta$.\n",
    "\n",
    "Differentiating both sides with respect to $\\theta$, we obtain\n",
    "\\begin{eqnarray}\n",
    "4\\pi \\theta \\langle\\kappa(\\theta)\\rangle &=& \\frac{\\partial}{\\partial \\theta} \\left[\\theta \\oint d\\varphi \\partial_\\theta\\psi\\right] \\\\\n",
    "&=& \\frac{2}{\\theta} \\int_0^{\\theta} d\\vec\\theta' \\kappa(\\vec\\theta') + \\theta \\oint d\\varphi \\partial^2_{\\theta} \\psi\\\\\n",
    "&=& \\frac{2}{\\theta} \\int_0^{\\theta} d\\vec\\theta' \\kappa(\\vec\\theta') + \\theta \\oint d\\varphi \\left[\\kappa(\\theta) - \\gamma_{\\rm t}(\\theta)\\right] \\\\\n",
    "&=& \\frac{2 \\pi \\theta}{\\pi \\theta^2} \\int_0^{\\theta} d\\vec\\theta' \\kappa(\\vec\\theta') + 2\\pi \\theta \\left[\\langle\\kappa(\\theta)\\rangle - \\langle\\gamma_{\\rm t}(\\theta)\\rangle\\right]  \\\\\n",
    "&=& 2 \\pi \\theta \\bar\\kappa(<\\theta)+ 2\\pi \\theta \\left[\\langle\\kappa(\\theta)\\rangle - \\langle\\gamma_{\\rm t}(\\theta)\\rangle\\right]\\\\\n",
    "\\langle\\gamma_{\\rm t}\\rangle &=& \\bar\\kappa(<\\theta) - \\langle\\kappa(\\theta)\\rangle\n",
    "\\end{eqnarray}\n",
    "\n",
    "The third equality can be understood in the following way: consider a point on the x-axis $\\partial^2\\psi/\\partial\\theta^2=\\psi_{11}=\\kappa+\\gamma_{\\rm 1}$. However in this case, $\\gamma_1=-\\gamma_{\\rm t}$. Thus for the point on the x-axis $\\partial^2\\psi/\\partial\\theta^2=\\kappa-\\gamma_{\\rm t}$. The double derivative can be evaluated at every point by performing a rotation, and it will always yield the value $\\kappa-\\gamma_{\\rm t}$.\n",
    "\n",
    "The last equality is a very important result. It says that regardless of the absence of symmetry, when the tangential shear is averaged over an annulus surrounding any mass distribution it's value is the difference between the average surface density inside that annulus and the surface density averaged over the annulus. Thus measurements of the averaged shear on annuli can be used to derive the surface density profile of any object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mass maps from shear estimates\n",
    "\n",
    "Let us consider the definition for the lensing potential once again:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\psi(\\vec\\theta)&=& \\left[  \\frac{1}{\\pi}\\int d^2\\vec \\theta' \\kappa(\\vec \\theta') \\ln (|\\vec\\theta-\\vec\\theta'|)\\right]\\\\\n",
    "\\end{eqnarray}\n",
    "and the definition of the shear components:\n",
    "\\begin{eqnarray}\n",
    "\\gamma_1 &=& \\frac{1}{2} \\left[ \\psi_{,11} - \\psi_{,22} \\right] \\\\\n",
    "\\gamma_2 &=& \\psi_{,12}\n",
    "\\end{eqnarray}\n",
    "\n",
    "One can consider the Fourier transform of the potential\n",
    "\\begin{eqnarray}\n",
    "\\tilde \\psi({\\vec\\ell}) = \\int d\\vec\\theta e^{-i\\vec\\ell.\\vec\\theta}\\,\\psi\n",
    "\\end{eqnarray}\n",
    "The derivatives are simpler in Fourier space. Given that the lensing potential and the surface density obey Poisson equation $\\nabla^2\\psi = 2 \\kappa$, we have\n",
    "\\begin{eqnarray}\n",
    "|\\vec\\ell|^2\\tilde \\psi({\\vec\\ell}) = -2\\kappa(\\vec\\ell)\n",
    "\\end{eqnarray}\n",
    "From the definition of double derivative we also obtain\n",
    "\\begin{eqnarray}\n",
    "{\\boldsymbol\\gamma} &=& -\\left(\\frac{1}{2} \\left[ \\ell_{1}^2 - \\ell_{2}^2 \\right] + i \\ell_1 \\ell_2\\right) \\psi (\\vec\\ell) \\\\\n",
    "&=& \\frac{1}{|\\vec\\ell|^2}\\left( \\left[ \\ell_{1}^2 - \\ell_{2}^2 \\right] + i 2 \\ell_1 \\ell_2\\right) \\kappa(\\vec\\ell)\\\\\n",
    "\\kappa(\\vec\\ell) &=& \\frac{1}{|\\vec\\ell|^2} \\left( \\left[ \\ell_{1}^2 - \\ell_{2}^2 \\right] - i 2 \\ell_1 \\ell_2\\right) {\\boldsymbol\\gamma}(\\vec\\ell)\n",
    "\\end{eqnarray}\n",
    "where in the last equality we have used ${\\bf a}^{-1} = |a|^{-2}{\\bf a}^{*}$.\n",
    "\n",
    "This is another interesting and useful result. If we can measure the shear field in a region on a grid, take its Fourier transform using FFT and use the above equation, one can get the convergence field (surface density field). The corresponding result in real space is (Kaiser & Squires, 1993)\n",
    "\\begin{eqnarray}\n",
    "\\kappa = \\frac{1}{\\pi}\\int d\\vec\\theta' {\\cal D}_{\\gamma\\rightarrow\\kappa}(\\vec\\theta-\\vec\\theta').{\\boldsymbol\\gamma}(\\vec\\theta')\n",
    "\\end{eqnarray}\n",
    "where \n",
    "\\begin{eqnarray}\n",
    "{\\cal D}_{\\gamma\\rightarrow\\kappa}(\\vec\\theta) = \\frac{1}{|\\vec\\theta|^4}[\\theta_2^2-\\theta_1^2, 2\\theta_1\\theta_2]\n",
    "\\end{eqnarray}\n",
    "Because $[\\theta_1^2-\\theta_2^2)^2 + (2\\theta_1\\theta_2)^2]=|\\vec\\theta|^2$, we can write this as\n",
    "\\begin{eqnarray}\n",
    "{\\cal D}_{\\gamma\\rightarrow\\kappa}(\\vec\\theta) = \\frac{1}{|\\vec\\theta|^2}[\\cos 2 \\varphi, \\sin 2\\varphi]\n",
    "\\end{eqnarray}\n",
    "This kernel is similar to the ellipticity pattern induced by a point mass around its position. Thus there is an intuitive way to understand this equation in real space. It is a sort of a match filter, the value of $\\kappa$ will be large when the pattern matches the pattern induced by a point mass."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to see some of the similarity between the expressions is as follows. Let us start from the equation for the deflection angle in terms of components\n",
    "\\begin{eqnarray}\n",
    "\\psi_{,i} = \\alpha_i = \\frac{1}{\\pi}\\int d\\vec{\\theta'} \\kappa(\\vec\\theta') \\frac{\\theta_i-\\theta_i'}{|\\vec\\theta-\\vec\\theta'|^2}\n",
    "\\end{eqnarray}\n",
    "Differentiating once again with respect to $\\theta_j$,\n",
    "\\begin{eqnarray}\n",
    "\\psi_{,ij} = \\frac{1}{\\pi}\\int d\\vec{\\theta'} \\kappa(\\vec\\theta') \\left[\\frac{\\delta^{\\rm D}_{ij}}{|\\vec\\theta-\\vec\\theta'|^2} - 2\\frac{(\\theta_i-\\theta'_i)(\\theta_j-\\theta'_j)}{|\\vec\\theta-\\vec\\theta'|^4}\\right]\n",
    "\\end{eqnarray}\n",
    "Using the definitions of the shear components we get\n",
    "\\begin{eqnarray}\n",
    "{\\boldsymbol \\gamma} = \\frac{1}{\\pi}\\int d\\vec\\theta' {\\cal D}_{\\kappa\\rightarrow\\gamma}(\\vec\\theta-\\vec\\theta') \\kappa(\\vec\\theta')\n",
    "\\end{eqnarray}\n",
    "where \n",
    "\\begin{eqnarray}\n",
    "{\\cal D}_{\\kappa\\rightarrow\\gamma}(\\vec\\theta) = \\frac{\\theta_2^2 - \\theta_1^2-2i\\theta_1\\theta_2}{|\\vec \\theta|^4}\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shape measurements\n",
    "\n",
    "Clearly once the shear of galaxies is measured, it allows us to create mass maps in the Universe and to study the matter distribution around galaxies. Let us next discuss how one can measure the shapes of galaxies and how one can obtain the value of the shear from them.\n",
    "\n",
    "Let $I(\\vec\\theta)$ be the surface brightness of an object. One can define the centroid of the object by computing the first moment of the object\n",
    "\\begin{eqnarray}\n",
    "{\\vec\\theta}_{\\rm cen} = \\frac{\\int d\\vec\\theta\\,I(\\vec \\theta)\\,q(I)\\,\\vec\\theta}{\\int d\\vec\\theta\\,I(\\vec\\theta)\\,q(I) }\n",
    "\\end{eqnarray}\n",
    "where we have included a weight $q(I)$. The second moments of the brightness distribution are given by\n",
    "\\begin{eqnarray}\n",
    "Q_{ij} = \\frac{\\int d\\vec\\theta\\,I(\\vec \\theta)\\,q(I)\\,(\\theta_i-\\theta_{\\rm cen, i})(\\theta_j-\\theta_{\\rm cen, j})}{\\int d\\vec\\theta\\,I(\\vec\\theta)\\,q(I) }\n",
    "\\end{eqnarray}\n",
    "\n",
    "One can define two different types of ellipticities with this definition\n",
    "\\begin{eqnarray}\n",
    "\\chi = \\frac{Q_{11}-Q_{22}+2iQ_{12}}{Q_{11}+Q_{22}}\\,;\n",
    "\\epsilon = \\frac{Q_{11}-Q_{22}+2iQ_{12}}{Q_{11}+Q_{22}+[Q_{11}Q_{22}-Q_{12}^2]^{1/2}}\\,\n",
    "\\end{eqnarray}\n",
    "Consider an elliptical galaxy with a gaussian shape oriented in the positive x-axis, the two axes have sigmas equal to $a$ and $b$. In this case $Q_{11}=a^2; Q_{22}=b^2; Q_{12}=0$. The first definition will result in \n",
    "\\begin{eqnarray}\n",
    "\\chi &=& \\frac{a^2-b^2}{a^2+b^2}\\,;\\\\\n",
    "&=& \\frac{1-|r|^2}{1+|r|^2}\\\\\n",
    "\\epsilon &=& \\frac{a^2-b^2}{a^2+b^2+2ab}\\,\\\\\n",
    "&=& \\frac{1-|r|}{1+|r|}\n",
    "\\end{eqnarray}\n",
    "where r is the minor to major axis ratio.\n",
    "\n",
    "Similar to the image ellipticities one can also infer the source ellipticities and figure out how the lensing transformation changes the ellipticities of galaxies. Locally the transformation is given by the inverse of magnification matrix. The moments of the source will be given by\n",
    "\\begin{eqnarray}\n",
    "Q_{ij}^{\\rm s} = \\frac{\\int d\\vec\\beta I^{\\rm s}(\\vec\\beta) q[I^s] (\\beta_{\\rm cen,i}-\\beta_i)(\\beta_{\\rm cen, j}-\\beta_j)}{\\int d\\vec\\beta I^{\\rm s}(\\vec\\beta) q[I^s]}\\,,\n",
    "\\end{eqnarray}\n",
    "Using $\\beta_{\\rm cen, i}-\\beta_i=A_{ik} (\\theta_{\\rm cen, i} - \\theta)$, and that the surface brightness is conserved, we obtain\n",
    "\\begin{eqnarray}\n",
    "Q_{ij}^{\\rm s} &=& \\frac{\\int d\\vec\\theta I(\\vec\\theta) q[I] A_{ik}(\\theta_{\\rm cen,i}-\\beta_i)A_{jl}(\\theta_{\\rm cen, j}-\\theta_j)}{\\int d\\vec\\theta I(\\vec\\theta) q[I]}\\,,\\\\\n",
    "&=& A_{ik}A_{jl} Q_{kl}\n",
    "\\end{eqnarray}\n",
    "Thus the lens local transformation can be used to relate the image ellipticities to the source ellipticities. The rule of transformation is given by\n",
    "\\begin{eqnarray}\n",
    "\\chi^{\\rm s} &=& \\frac{\\chi-2g+g^2\\chi^*}{1+|g|^2-2{\\rm Re}(g\\chi^*)}\\\\\n",
    "\\epsilon^{\\rm s} &=& \\frac{\\epsilon-g}{1-g^*\\epsilon} {\\,\\,\\,\\rm if\\,\\,|g|\\le 1}\\\\\n",
    "\\epsilon^{\\rm s} &=& \\frac{1-g\\epsilon^*}{\\epsilon^*-g^*} {\\,\\,\\,\\rm if\\,\\,|g|\\gt 1}\\\\\n",
    "\\end{eqnarray}\n",
    "If the source galaxies are randomly oriented with respect to each other the ensemble average $\\langle\\chi^{\\rm s}\\rangle=\\langle\\epsilon^{\\rm s}\\rangle = 0$, which allows us to determine the value of g by performing an ensemble average of the measured ellipticities.\n",
    "\\begin{eqnarray}\n",
    "\\langle \\epsilon \\rangle &=& g {\\,\\,\\,\\rm if\\,\\,|g|\\le 1}\\\\\n",
    "&=& 1/g^* {\\,\\,\\,\\rm if\\,\\,|g|\\gt 1}\n",
    "\\end{eqnarray}\n",
    "The case related to the choice $|g|\\gt 1$ is related to negative parity images (elliptical sources do not care about parity), which can occur in the case of strong lensing. These form in a very small region near the center of the mass distribution where such effects may be more important. But however local measurements of shapes cannot inform us about which regime we are at. One can define distortion which is invariant under change between $g$ and $1/g^{*}$,\n",
    "\\begin{eqnarray}\n",
    "\\delta = \\frac{2g}{1+|g|^2}\n",
    "\\end{eqnarray}\n",
    "The averaging of $\\chi^{\\rm s}$ is a little more involved, and Schneider and Seitz (1995) show that the average of $\\chi^{\\rm s}$ equal to $0$ implies\n",
    "\\begin{eqnarray}\n",
    "\\sum_{i} u_i\\frac{\\chi_i-\\delta}{1+{\\rm Re}(\\delta \\chi^{*}_i)} = 0\n",
    "\\end{eqnarray}\n",
    "where $u_i$'s represent the different weight functions for galaxies depending upon how far they are from the point that we want to estimate the shear. These weights could also be adjusted to give weights to the source galaxies depending upon their SNR, for example. This equation can be solved iteratively to obtain the value of $\\delta$ given the measurements of $\\chi_i$.\n",
    "\n",
    "In the weak lensing regime, it can be shown that\n",
    "\\begin{eqnarray}\n",
    "\\gamma \\approx g \\approx \\langle \\epsilon \\rangle \\approx \\frac{1}{2}  \\langle \\chi \\rangle \\approx \\frac{1}{2}  \\langle \\delta \\rangle\n",
    "\\end{eqnarray}\n",
    "\n",
    "These relations imply that even if we cannot use a single galaxy to perform the weak lensing measurement, when we average over an ensemble of objects with similar shear (say in a small region of space) we will be able to obtain an estimate of the shear. Once the shear estimate can be obtained we can use either the averaging on circles or the mass inversion technique mentioned above in order to obtain mass distributions in the Universe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practical issues\n",
    "\n",
    "We will look at the practical steps taken in order to reduce images from real telescopes in the next chapter. Here we discuss some of the issues relevant for the shape measurements following techniques in Kaiser, Squires and Broadhurst 1995.\n",
    "\n",
    "### Weights in moment measurements\n",
    "\n",
    "The weight function used to define the moments above that we chose were a function of the surface brightness. However, in real life this is much more complicated. Measurements of local surface brightness are difficult specially close to the noise  background. The noise can enter the measured ellipticities in a non-linear fashion in this case. To avoid these issues typically the weight is chosen as a function of $\\vec\\theta$ instead (say a circular gaussian), which avoids the noise in the image from entering the ellipticity measurement. However in this case the expression for how to go from the ellipticity measurements to shear no longer remain perfectly correct for such a weighting scheme.\n",
    "\n",
    "### Point spread function\n",
    "\n",
    "The second important issue is that of the point spread function, primarily due to atmosphere for ground based data and that of the telescope optics for space based data. The image observed on the detector is convolution of the true image with the PSF.\n",
    "\\begin{eqnarray}\n",
    "I^{\\rm obs}(\\vec\\theta) = \\int d\\vec\\vartheta I(\\vec\\vartheta) P(\\vec\\theta-\\vec\\vartheta)\n",
    "\\end{eqnarray}\n",
    "where $P$ represents the PSF and is normalized to unity and is centered at zero. A delta-function image gets converted into the same shape as PSF. In general the PSF smears the image of an object. An isotropic PSF will reduce the ellipticity by smoothing out the image, especially for small objects whose size is comparable to the PSF. In addition, any anisotropy of the PSF will leak into the measured ellipticity.\n",
    "\n",
    "#### Ideal weighting\n",
    "\n",
    "If the weights used for the determination of ellipticity of galaxies are $q(I)=I$, in that case there is a straightforward relation between the PSF ellipticity, the image ellipticity and the observed ellipticity on the detector after the PSF convolution,\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\chi^{\\rm obs} = \\frac{\\chi+T\\chi^{\\rm PSF}}{1+T}\n",
    "\\end{eqnarray}\n",
    "where\n",
    "\\begin{eqnarray}\n",
    "T&=&\\frac{P_{11}+P_{22}}{Q_{11}+Q_{22}}\\\\\n",
    "\\chi^{\\rm PSF} &=& \\frac{P_{11}-P_{22}+2iP_{12}}{P_{11}+P_{22}}\n",
    "\\end{eqnarray}\n",
    "T represents the ratio of the PSF size to the galaxy size before convolution. If T is small the galaxy is well resolved (the PSF is much smaller than the galaxy), then the correction factor is small. However for getting more and more galaxies to perform the average, we need to use smaller galaxies and so we run into galaxies with sizes comparable to the PSF size.\n",
    "\n",
    "In reality however we use weight functions which are not the same as the ideal one above, and so the relation between how the PSF changes the ellipticity needs to be calibrated using realistic image simulations.\n",
    "\n",
    "#### Dealing with anisotropic PSF \n",
    "\n",
    "The total PSF can be decomposed into an isotropic and an anisotropic part:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "P(\\vartheta) = \\int d\\vec\\varphi q(\\vec\\varphi) P^{\\rm iso}(\\vec\\vartheta-\\vec\\varphi)\n",
    "\\end{eqnarray}\n",
    "\n",
    "One defines\n",
    "\\begin{eqnarray}\n",
    "I^{\\rm iso}(\\vec\\theta) &=& \\int d\\vec\\varphi I(\\vec\\varphi) P^{\\rm iso}(\\vec\\theta-\\vec\\varphi)\\\\\n",
    "I^{\\rm iso, s}(\\vec\\theta) &=& \\int d\\vec\\varphi I^{\\rm s}(\\vec\\varphi) P^{\\rm iso}(\\vec\\theta-\\vec\\varphi)\\,\\\\\n",
    "\\end{eqnarray}\n",
    "and can use these definitions to compute moments (using the position dependent weights) and ellipticities $\\chi^{\\rm iso}$ and $\\chi^{\\rm iso, s}$. The isotropically smeared ellipticities of the unlensed source still average out to zero, and thus such an average can be used to figure out the shear at a particular location. Both these quantities cannot be observed but we can connect them to the observed ellipticity $\\chi^{\\rm obs}$ via a two step process: $\\chi^{\\rm obs}\\rightarrow \\chi^{\\rm iso}$ and $\\chi^{\\rm iso}\\rightarrow \\chi^{\\rm iso, s}$.\n",
    "\n",
    "Since the anisotropies and shears tend to be small one can compute the effect up to linear order as\n",
    "\\begin{eqnarray}\n",
    "\\chi^{\\rm obs}_{i} = \\chi^{\\rm iso, s}_{i} + P^{\\rm sm}_{ij}q_{j} + P^{\\rm g}_{ij} g_{j}\n",
    "\\end{eqnarray}\n",
    "The quantity $P^{\\rm sm}$ is called the smear polarizability and is the linear response of the observed ellipticity to the anisotropy of the PSF. The quantity P^{\\rm g} is called the shear polarizability and is the linear response of the observed ellipticity to the shear. The reduced shear can then be obtained as\n",
    "\\begin{eqnarray}\n",
    "g = (P^{\\rm g})^{-1}(\\chi^{\\rm obs} - P^{\\rm sm}q)\n",
    "\\end{eqnarray}\n",
    "Although these quantities can be computed for each image given the PSF size and the brightness distribution of the observed image.\n",
    "\n",
    "## Adaptive moments for shapes\n",
    "\n",
    "There are new advances in shape measurements which reduce issues with the KSB techniques. In particular using weight functions which are adaptive to the size of the galaxy. The ellipticity of a galaxy can be measured by asking for the transform that when applied in inverse results in a round galaxy. In this case the optimal weights turn out to be (see Bernstein and Jarvis 2002)\n",
    "\\begin{eqnarray}\n",
    "w(\\theta) =  \\frac{1}{\\theta}\\frac{d\\ln I}{d\\theta}\n",
    "\\end{eqnarray}\n",
    "with the shape of the weight adapted to the shape of the galaxy under consideration. In principle one can change the weight to reflect the profile of each galaxy, but it turns out to be easier and more practical to use a Gaussian weight as it downweights the regions away from the center of the object (which can be a problem in crowded fields). Such shapes can be found by minimizing\n",
    "\\begin{eqnarray}\n",
    "\\chi^2 = \\int d\\vec\\theta \\left[ I(\\vec\\theta) - A \\exp\\left(-\\frac{1}{2}(\\vec\\theta-\\vec\\theta_0)^{\\rm T}M^{-1}(\\vec\\theta-\\vec\\theta_0)\\right) \\right]^2\n",
    "\\end{eqnarray}\n",
    "This allows one to fit for the shape moments of a galaxy $M$ (3 independent numbers), in addition to the amplitude A and the position coordinates $\\vec\\theta_0$ (2 more numbers). One can show that the shapes which minimize the above $\\chi^2$ are weighted moments with\n",
    "\\begin{eqnarray}\n",
    "\\theta_0 &=& \\frac{\\int d\\vec\\theta I(\\vec\\theta) w(\\vec\\theta) \\theta}{\\int d\\vec\\theta I(\\vec\\theta) w(\\vec\\theta)} \\\\\n",
    "M_{ij} &=& 2\\frac{\\int d\\vec\\theta I(\\vec\\theta) w(\\vec\\theta) (\\theta_i-\\theta_{0, i})(\\theta_j-\\theta_{0, j})}{\\int d\\vec\\theta I(\\vec\\theta) w(\\vec\\theta)}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Bernstein and Jarvis 2002 also present an estimator for the distortion $\\delta$ for shapes measured using such adaptive moments when considering an ensemble of sources. They consider how the distribution of the ellipticities transform under the application of a distortion to a random distribution and how to use this change to estimate the distortion. They compute the optimal weights in the case of general distribution $P(e)$, but for a Gaussian distribution for $P(e)$ and in the case of small measurement noise, these weights are approximately given by\n",
    "\\begin{eqnarray}\n",
    "w \\approx \\frac{1}{{e_{\\rm rms}^2+\\sigma_{\\rm meas}^2}}\n",
    "\\end{eqnarray}\n",
    "where $e_{\\rm rms}$ is the rms intrinsic distortion per component. Thus one can use the estimator $\\hat\\delta$\n",
    "\\begin{eqnarray}\n",
    "\\hat\\delta = \\frac{\\sum w_i e_i}{\\sum w_i}\n",
    "\\end{eqnarray}\n",
    "The estimator needs to be corrected for the responsivity\n",
    "\\begin{eqnarray}\n",
    "{\\cal R} &=& \\frac{\\partial \\hat\\delta}{\\partial \\delta}\\\\\n",
    "&\\approx& 1 - e_{\\rm rms}^2\n",
    "\\end{eqnarray}\n",
    "Thus the shear estimate is given by\n",
    "\\begin{eqnarray}\n",
    "2\\gamma &=& \\delta &=& \\frac{1}{{\\cal R}}\\frac{\\sum w_i e_i}{\\sum w_i}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "## PSF corrections\n",
    "\n",
    "PSF convolution is straightforward when the weighting used to determine the moments are ideal, however as mentioned before such methods have to deal with problems of noise which enter the ellipticity in a non-linear manner. There are several ways proposed to deal with PSF corrections when weighted moments are used for ellipticity determination.\n",
    "\n",
    "One can potentially measure the dilution of PSF using detailed image simulation, however the correction factors can be dependent upon how realistic the simulations are in terms of their unlensed galaxy properties. Perturbative methods like KSB described above have their own limitations when applied to realistic PSFs (Bernstein & Jarvis 2002). Another approach is to deconvolve the PSF by using stacks of galaxies in similar locations (Kuijken 1999). However this requires the galaxies to be similarly sheared and a large number of background galaxies in a region where the PSF does not vary substantially. Bernstein & Jarvis (2002) suggest the use Laguerre exponential functions as basis functions to decompose the image and PSFs into. Such expansions have convenient properties in order apply shears or for convolutions and thus can be used to correct for the effects of the PSF. However, these do require some truncation in the basis fucntion expansion. For this Bernstein & Jarvis (2002) suggest applying a rounding kernel to the PSF first and give an expression to correct for the PSF designed to be accurate in the case of Gaussian PSF and Gaussian objects and which works for well resolved galaxies.\n",
    "\n",
    "Hirata and Seljak (2003) expand on this and suggest that non-Gaussian PSFs can be dealt with in the following manner:\n",
    "\n",
    "Consider a PSF $g(\\vec{x})$ and approximate it with a Gaussian $G(\\vec x)$, and consider the residual function $\\epsilon(\\vec x) = g-G$. Let $I^{\\rm pre}(x)$ be the original pre-seeing image, then the image $I^{\\rm post}(x) = g\\otimes I^{\\rm pre}(x) = G \\otimes I^{\\rm pre}(x) + \\epsilon\\otimes I^{\\rm pre}(x)$. Thus one can determine $G \\otimes I^{\\rm pre}(x) = I^{\\rm post}(x) - \\epsilon\\otimes I^{\\rm pre}(x)$. We do not really know what is $I^{\\rm pre}(x)$ but since this is convolved with a smaller function $\\epsilon$ we can use an approximate function $\\tilde I^{\\rm pre}$ which is a deconvolved image assuming the PSF and the original image to be Gaussians. The Bernstein and Jarvis 2002 can now be made even more accurate. This technique called re-Gaussianization is used to then perform the PSF correction."
   ]
  },
  {
   "attachments": {
    "TangentialShearGeometry.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tangential shear computation\n",
    "\n",
    "The shape measurements for galaxies are carried out typically in sky coordinates. Suppose we want to use method one of averaging the tangential shear around an object (say galaxy G1) at coordinate with right ascension and declination $(\\alpha_1, \\delta_1)$. Let us suppose we have measured the shape of another galaxy (G2) at $(\\alpha_2, \\delta_2)$. We want to define the tangential shear with respect to the line joining G1 and the galaxy G2 whose shape we have measured.\n",
    "\n",
    "Consider this Figure from Kiblinger et al. 2013.\n",
    "\n",
    "![TangentialShearGeometry.png](attachment:TangentialShearGeometry.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Angles should always be measured with respect to great circles. We need to consider the angle between the great circle joining G1G2 and the great circle passing through G2, in order to define the tangential shear. The great circle passing through G1G2 has a normal given by $\\hat n_{G_1} \\times \\hat n_{G_2}/\\sin(\\vartheta)$, where $\\hat n$ are the unit vectors which point towards the corresponding galaxies. The unit vectors are given by $\\cos\\delta \\cos\\alpha \\hat i + \\cos\\delta \\sin\\alpha \\hat j +  \\sin\\delta \\hat k$. The cosine of the angle between the two positions is given by\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\cos\\vartheta &=& \\cos\\delta_1\\cos\\alpha_1\\cos\\delta_2\\cos\\alpha_2 +  \\cos\\delta_1 \\sin\\alpha_1 \\cos\\delta_2 \\sin\\alpha_2 + \\sin\\delta_1\\sin\\delta_2\\\\\n",
    "&=& \\cos\\delta_1\\cos\\delta_2 \\cos(\\alpha_1-\\alpha_2) + \\sin\\delta_1\\sin\\delta_2\n",
    "\\end{eqnarray}\n",
    "\n",
    "The great circle passing through G2 and the north pole can be calculated using a similar dot product between the unit vector denoting the galaxy and the unit vector passing through the north pole. This product will give a vector of magnitude $\\sin(90-\\delta_2)=\\cos\\delta_2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{- \\sin{\\left(\\delta_{1} \\right)} \\cos{\\left(\\delta_{2} \\right)} + \\sin{\\left(\\delta_{2} \\right)} \\cos{\\left(\\delta_{1} \\right)} \\cos{\\left(\\alpha_{1} - \\alpha_{2} \\right)}}{\\left|{\\sin{\\left(\\theta \\right)}}\\right|}$"
      ],
      "text/plain": [
       "(-sin(delta1)*cos(delta2) + sin(delta2)*cos(delta1)*cos(alpha1 - alpha2))/Abs(sin(theta))"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as s\n",
    "alpha1, delta1, alpha2, delta2,theta = s.symbols(\"alpha1,delta1,alpha2,delta2 theta\")\n",
    "\n",
    "# Define unit vectors\n",
    "nG1 = s.Matrix([s.cos(delta1)*s.cos(alpha1), s.sin(alpha1)*s.cos(delta1), s.sin(delta1)])\n",
    "nG2 = s.Matrix([s.cos(delta2)*s.cos(alpha2), s.sin(alpha2)*s.cos(delta2), s.sin(delta2)])\n",
    "\n",
    "# Define north pole\n",
    "nNP = s.Matrix([0, 0, 1])\n",
    "\n",
    "# G1 \\cross G2/sin(theta)\n",
    "L_G1G2=nG1.cross(nG2)/s.Abs(s.sin(theta))\n",
    "\n",
    "# G2 \\cross NP/cos(delta2)\n",
    "L_GC = nG2.cross(nNP)/s.cos(delta2)\n",
    "\n",
    "# Compute dot product for cos(beta2) = sin(phi2)\n",
    "s.simplify(((L_GC.dot(L_G1G2))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(\\delta_{1} \\right)} \\sin{\\left(\\delta_{2} \\right)} + \\cos{\\left(\\delta_{1} \\right)} \\cos{\\left(\\delta_{2} \\right)} \\cos{\\left(\\alpha_{1} - \\alpha_{2} \\right)}$"
      ],
      "text/plain": [
       "sin(delta1)*sin(delta2) + cos(delta1)*cos(delta2)*cos(alpha1 - alpha2)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute dot product G1 G2 to get \\cos\\theta\n",
    "s.simplify(nG1.dot(nG2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{\\sin{\\left(\\alpha_{1} - \\alpha_{2} \\right)} \\cos{\\left(\\alpha_{2} \\right)} \\cos{\\left(\\delta_{1} \\right)} \\cos{\\left(\\delta_{2} \\right)}}{\\sin{\\left(\\theta \\right)}}\\\\- \\frac{\\sin{\\left(\\alpha_{2} \\right)} \\sin{\\left(\\alpha_{1} - \\alpha_{2} \\right)} \\cos{\\left(\\delta_{1} \\right)} \\cos{\\left(\\delta_{2} \\right)}}{\\sin{\\left(\\theta \\right)}}\\\\- \\frac{\\sin{\\left(\\delta_{2} \\right)} \\sin{\\left(\\alpha_{1} - \\alpha_{2} \\right)} \\cos{\\left(\\delta_{1} \\right)}}{\\sin{\\left(\\theta \\right)}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-sin(alpha1 - alpha2)*cos(alpha2)*cos(delta1)*cos(delta2)/sin(theta)],\n",
       "[-sin(alpha2)*sin(alpha1 - alpha2)*cos(delta1)*cos(delta2)/sin(theta)],\n",
       "[            -sin(delta2)*sin(alpha1 - alpha2)*cos(delta1)/sin(theta)]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Obtain sin(beta2) = cos(phi2)\n",
    "x = L_G1G2.cross(L_GC)\n",
    "s.simplify(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above calculations show that\n",
    "\\begin{eqnarray}\n",
    "\\cos\\beta_2 &=& \\sin\\phi_2 = \\frac{-\\sin\\delta_1\\cos\\delta_2+\\sin\\delta_2\\cos\\delta_1\\cos(\\alpha_2-\\alpha_1)}{|\\sin\\theta|}\\\\\n",
    "\\sin\\beta_2 &=& \\cos\\phi_2 = \\frac{ \\sin(\\alpha_2-\\alpha_1)\\cos\\delta_1}{|\\sin\\theta|}\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One has to thus compute the tangential shear with respect to the line at an angle $\\phi_2$ given the shape of the galaxy. Therefore,\n",
    "\n",
    "\\begin{eqnarray}\n",
    "e_{\\rm tan} &=& - {\\rm Re}\\left[(e_1 + i e_2)e^{-i2\\phi_2}\\right]\\\\\n",
    "&=& -e_1\\cos 2\\phi_2 - e_2 \\sin2\\phi_2\n",
    "\\end{eqnarray}\n",
    "\n",
    "These values of the tangential ellipticity can be averaged (in a weighted manner) over a large number of sources to yield measurements of the tangential shear profile.\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\langle e_{\\rm tan}\\rangle = \\frac{\\sum w_i e_{\\rm tan, i}}{w_i}\n",
    "\\end{eqnarray}\n",
    "which can then be related to the tangential shear depending upon the definition of ellipticity used.\n",
    "\n",
    "## Measurement of the weak lensing signal\n",
    "\n",
    "The weak lensing signal can be measured from an ensemble average of ellipticities.\n",
    "\\begin{eqnarray}\n",
    "\\langle \\gamma_{\\rm t} (\\theta) \\rangle &=& \\bar\\kappa(<\\theta) - \\langle\\kappa\\rangle(\\theta)\\\\\n",
    "&=& \\frac{\\bar\\Sigma(<\\theta)-\\langle\\Sigma\\rangle(\\theta)}{\\Sigma_{\\rm crit}} \\\\\n",
    "&=& \\frac{\\Delta \\Sigma}{\\Sigma_{\\rm crit}}\\\\\n",
    "&=& \\frac{1}{2{\\cal R}}\\frac{\\sum w_i e_{\\rm tan}}{\\sum w_i}\n",
    "\\end{eqnarray}\n",
    "In the last line we have assumed that the ellipticity measure used gives an estimate of distortion. The fact that the background source galaxies are not circular results in a statistical noise in the measurement of the average tangential shear from the shape of galaxies. This noise can be beaten down by averaging over a large number of source galaxies. A single object may not have enough number of source galaxies to beat down the shape noise. In that case, we can  average over a large number of lensing objects. The source galaxies that we consider may also not lie at the same redshift, and so each source galaxy will have a different critical surface density. In this case, it is better to devise an estimator for $\\Delta\\Sigma$ instead of $\\gamma_{\\rm t}$. An individual galaxy gives an estimate of $\\gamma_{\\rm t}\\Sigma_{\\rm crit}/(2{\\cal R})$. The error on this individual estimate is $[e_{\\rm rms}^2+e_{\\rm meas}^2]^{1/2}\\Sigma_{\\rm crit}$. The estimator \n",
    "\\begin{eqnarray}\n",
    "\\tilde{\\Delta\\Sigma}\\left[R_{\\rm p}=D_{\\rm d}\\theta\\right] = \\frac{\\sum w_{ls} \\left(e_{\\rm tan} \\Sigma_{\\rm crit}\\right)}{(2{\\cal R})\\sum w_{\\rm ls}}\n",
    "\\end{eqnarray}\n",
    "would then result in a minimum variance estimate if\n",
    "\\begin{eqnarray}\n",
    "w_{\\rm ls} = \\frac{1}{\\Sigma_{\\rm crit}^2(e_{\\rm rms}^2+e_{\\rm meas}^2)}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Also it is common to measure the signal as a function of projected radius from the center of the lensing object. In this case one has to use the critical surface density also in comoving units.\n",
    "\\begin{eqnarray}\n",
    "\\Sigma_{\\rm crit}^{\\rm com} = \\frac{1}{(1+z_{\\rm d})^2}\\frac{c^2}{4\\pi G}\\frac{D_{\\rm s}}{D_{\\rm d} D_{\\rm ds}}\n",
    "\\end{eqnarray}\n",
    "The distances here are angular diameter distances, because they were used in order to convert physical distances into angles ($D_{\\rm s}, D_{\\rm ds}$ to convert deflection angle to scaled deflection angle, and $D_{\\rm d}$ to convert $\\theta$ to the physical impact parameter). Thus we will use\n",
    "\\begin{eqnarray}\n",
    "\\tilde{\\Delta\\Sigma}^{\\rm com}\\left[R_{\\rm p}=(1+z_{\\rm d})D_{\\rm d}\\theta\\right] &=& \\frac{\\sum w_{ls} \\left(e_{\\rm tan} \\Sigma^{\\rm com}_{\\rm crit}\\right)}{(2{\\cal R})\\sum w_{\\rm ls}}\\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "##  Weak lensing magnification\n",
    "\n",
    "Until now we have talked about the effects of weak lensing on the shapes of galaxies. However weak lensing also magnifies the flux coming from an object. At the same time, weak lensing conserves surface brightness, which means the solid angle corresponding to the images seen in the sky is in reality smaller. The surface density of sources in a given region with magnification $\\mu$ will thus \n",
    "\\begin{eqnarray}\n",
    "n(>S, \\vec\\theta, z) = \\frac{n(>S/\\mu(\\vec\\theta, z))}{\\mu(\\vec\\theta, z))}\n",
    "\\end{eqnarray}\n",
    "The numerator implies in area of magnification greater than unity, we expect to see galaxies with lower fluxes, while the denominator represents the fact that the increase in observed effective area, implies the observed number of galaxies from a smaller area will get spread out over a larger area and therefore the observed surface density should be lower.\n",
    "\n",
    "For power law source surface densities, $n_0(>S) \\propto S^{-\\alpha}$. Thus we obtain\n",
    "\n",
    "\\begin{eqnarray}\n",
    "n(>S) &=& \\frac{n_0(>S)}{\\mu^{-\\alpha}\\mu} \\\\\n",
    "\\frac{n(>S)}{n(>S_0)}&=& \\mu^{\\alpha-1}\\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "Given the two competing effects the magnification depends upon the value of the local slope of the number counts at the limiting magnitude of the survey. For values of $\\alpha>1$, the source counts are enhanced in regions of $\\mu>1$. Such magnification effects have also been seen in real observations, especially the dependence of this ratio on the flux limit has been used to verify that the behaviour seen is indeed due to magnification.\n",
    "\n",
    "In the weak lensing regime, the magnification is given by\n",
    "\\begin{eqnarray}\n",
    "\\mu = \\frac{1}{(1-\\kappa)^2+\\gamma^2} \\approx 1 + 2\\kappa\n",
    "\\end{eqnarray}\n",
    "and therefore the enhancement/depletion is given by\n",
    "\\begin{eqnarray}\n",
    "\\frac{n(>S)}{n(>S_0)}&\\approx& 1 + 2(\\alpha-1)\\kappa\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{eqnarray}\n",
    "\\gamma' &=& \\gamma e^{-2i\\theta}\\\\\n",
    "\\gamma'_1 + i \\gamma'_2 &=& (\\gamma_1 + i \\gamma_2) (\\cos2\\theta - i\\sin2\\theta)\\\\\n",
    "\\gamma'_1 &=& \\gamma_1 \\cos2\\theta + \\gamma_2 \\sin 2\\theta \\\\\n",
    "&=& |\\gamma|(\\cos2\\phi \\cos2\\theta + \\sin2 \\phi \\sin 2\\theta )\\\\\n",
    "&=& |\\gamma| \\cos(2(\\phi-\\theta)) \\\\\n",
    "\\gamma'_2 &=& -\\gamma_1 \\sin2\\theta + \\gamma_2 \\cos 2\\theta \\\\\n",
    "&=& |\\gamma|(-\\cos2\\phi \\sin2\\theta + \\sin2 \\phi \\cos 2\\theta )\\\\\n",
    "&=& |\\gamma| \\sin(2(\\phi-\\theta))\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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