13 Conventions.ipynb

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   "source": [
    "# Conventions and interoperability"
   ]
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    "## Conventions for template matching\n",
    "Template matching in pyxem is typically used to determine the orientation of the crystal that formed the diffraction pattern. To describe the orientation of a crystal, two coordinate systems are needed: the lab reference frame (sometimes called the sample reference frame) and the crystal reference frame. The crystal reference frame ($X_c, Y_c, Z_c$) is fixed to the unit cell of the crystal, while the lab reference frame ($X_L, Y_L, Z_L$) is in pyxem fixed to the detector. The orientation of the crystal is the rotation needed to bring the lab reference frame into coincidence with the crystal reference frame [[Rowenhorst *et al.*, 2015](http://dx.doi.org/10.1088/0965-0393/23/8/083501)].\n",
    "\n",
    "In addition, there are grid coordinate systems associated with the acquisition of scanning electron diffraction data ($X_\\text{scan}, Y_\\text{scan}$), and the layout of the diffraction pattern array in computer memory ($X_\\text{Signal2D}, Y_\\text{Signal2D}$). These reference frames are illustrated in the figure below."
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    "<img src=\"data/13/ref_frames.png\" alt=\"Reference frames\"/>\n",
    "\n",
    "**Figure 1** The different reference frames used by pyxem. Note the TEM convention of viewing the diffraction pattern from above (i.e., looking from the electron source to the detector). (a) Perspective view (b) The diffraction pattern on the detector"
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    "### Rotation conventions\n",
    "Rotations and orientations in three dimensions can be described using Euler angles. Pyxem uses the following conventions for Euler angles:\n",
    "1. Rotations and coordinate systems are right-handed.\n",
    "2. Rotations are passive (also known as intrinsic), meaning that it is the coordinate axes that rotate.\n",
    "3. Euler angles ($\\phi_1$, $\\Phi$, $\\phi_2$) are given in the form ZX'Z''.\n",
    "4. Euler angles rotate the sample reference frame to the crystal reference frame (\"lab2crystal\")."
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    "The sample reference frame is first rotated $\\phi_1$ around $Z_L$ (the lab z-axis), followed by $\\Phi$ around the new $X_L$, followed by $\\phi_2$ around the updated $Z_L$. If $\\phi_1=\\Phi=\\phi_2=0$, then $X_L || X_c, Y_L || Y_c$ and $Z_L || Z_c$."
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    "### Cartesian crystal reference frame\n",
    "For convenience, it is standard to always use a Cartesian crystal reference frame even when the crystal lattice is not cubic. The choice of Cartesian reference frame is relatively straightforward for crystal systems with orthogonal lattice vectors, but for the other crystal systems (triclinic, monoclinic, trigonal, hexagonal) there is no obvious choice. Since the diffraction pattern templates are created by diffsims (which uses the `diffpy.structure.Structure` class) the convention used by diffsims determines the convention of pyxem:\n",
    "\n",
    "$\\mathbf{X_c} || \\mathbf{a^*}$, $\\mathbf{Y_c} || (\\mathbf{Z_c} \\times \\mathbf{X_c})$, $\\mathbf{Z_c} || \\mathbf{c}$."
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    "### Experimental diffraction patterns\n",
    "We see in Figure 1 that in the reference frame of the detector, the lab reference frame is oriented with $X_L$ pointing to the right, $Y_L$ pointing up, and $Z_L$ pointing outwards. This is also the reference frame used when simulating diffraction patterns with diffsims (see below). However, in Matplotlib, Hyperspy and pyxem, images (including diffraction patterns) are typically plotted with the origin in the top-left corner and the y-axis pointing *down*. We therefore have to be careful when comparing a diffraction pattern stored as a numpy/dask array with simulated diffraction patterns during template matching. In pyxem, we assume that the pyxem/hyperspy [`Signal2D`](https://hyperspy.org/hyperspy-doc/current/api/hyperspy._signals.signal2d.html) or numpy array to be template matched is oriented correctly when plotted with the x-axis ($X_\\text{Signal2D}$) pointing to the right and the y-axis ($Y_\\text{Signal2D}$) pointing *down*. In other words, $Y_L || -Y_\\text{Signal2D}$."
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    "### Scanning electron diffraction\n",
    "The lab reference frame is fixed to the detector that records the diffraction patterns. However, the sides of the detector are often *not* parallel to the scan directions in a scanning electron diffraction (i.e., 4D) dataset. If the in-plane orientation of the diffraction patterns is of interest, care must be taken to modify the in-plane rotation ($\\phi_1$) to compensate for this. Pyxem uses the same convention as hyperspy for the navigation axes: x-axis ($X_\\text{scan}$) to the right and the y-axis ($Y_\\text{scan}$) down."
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   "source": [
    "### Examples"
   ]
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   "source": [
    "We can illustrate these convention using diffsims (the package used to simulate diffraction patterns used for template matching) for some simple orientations. First we create the structure (using cubic aluminium as an example):"
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import diffpy\n",
    "from diffsims.generators.diffraction_generator import DiffractionGenerator\n",
    "\n",
    "latt = diffpy.structure.lattice.Lattice(4,4,4,90,90,90)\n",
    "atoms = [diffpy.structure.atom.Atom(atype='Al',xyz=[0.0,0.0,0.0],lattice=latt),\n",
    "         diffpy.structure.atom.Atom(atype='Al',xyz=[0.5,0.5,0.0],lattice=latt),\n",
    "         diffpy.structure.atom.Atom(atype='Al',xyz=[0.5,0.0,0.5],lattice=latt),\n",
    "         diffpy.structure.atom.Atom(atype='Al',xyz=[0.0,0.5,0.5],lattice=latt)]\n",
    "structure_matrix = diffpy.structure.Structure(atoms=atoms,lattice=latt)"
   ]
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   "source": [
    "We can then simulate a diffraction pattern for the orientation (10&deg;, 0&deg;, 0&deg;) in Euler angles:"
   ]
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   "source": [
    "scale = 0.027; half_shape = 64; rec_rad = scale * half_shape; phi1 = 10\n",
    "diff_gen = DiffractionGenerator(accelerating_voltage=200,\n",
    "                                precession_angle=0,\n",
    "                                scattering_params='xtables',\n",
    "                                shape_factor_model=\"linear\",\n",
    "                                minimum_intensity=0.01,\n",
    "                                )\n",
    "sim = diff_gen.calculate_ed_data(structure_matrix, reciprocal_radius=rec_rad,\n",
    "                                rotation=(phi1, 0, 0), with_direct_beam=True,\n",
    "                                max_excitation_error=0.04)"
   ]
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   "source": [
    "and plot the diffsims simulation with labeled diffraction spots:"
   ]
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots()\n",
    "axs.set_aspect(\"equal\")\n",
    "sim.plot(size_factor=30, show_labels=True, ax=axs)\n",
    "axs.set_title(\"$(10\\degree, 0\\degree, 0\\degree)$\")\n",
    "# Draw coordinate systems\n",
    "length = 0.15\n",
    "width = 0.02\n",
    "axs.arrow(-0.4, -0.4, length, 0, width=width, color=\"g\")\n",
    "axs.arrow(-0.4, -0.4, 0, length, width=width, color=\"g\")\n",
    "axs.text(-0.18, -0.48, \"$X_L$\", c=\"g\", fontsize=\"x-large\")\n",
    "axs.text(-0.38, -0.18, \"$Y_L$\", c=\"g\", fontsize=\"x-large\")\n",
    "axs.text(-0.35, -0.35, \"Lab reference frame\")\n",
    "dx = length * np.cos(np.deg2rad(phi1))\n",
    "dy = length * np.sin(np.deg2rad(phi1))\n",
    "axs.arrow(0, 0, dx, dy, width=width, color=\"b\")\n",
    "axs.text(dx+0.08, dy-0.03, \"$X_c$\", c=\"b\", fontsize=\"x-large\")\n",
    "dx = length * np.cos(np.deg2rad(phi1+90))\n",
    "dy = length * np.sin(np.deg2rad(phi1+90))\n",
    "axs.arrow(0, 0, dx, dy, width=width, color=\"b\")\n",
    "axs.text(dx-0.1, dy+0.04, \"$Y_c$\", c=\"b\", fontsize=\"x-large\")\n",
    "axs.text(0.02, 0.2, \"Crystal reference frame\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0aa682aa-83a2-440d-9095-c0d7c7cb9b61",
   "metadata": {},
   "source": [
    "Pyxem uses the same conventions as illustrated by this `diffsims.sims.Simulation.plot()` plot.\n",
    "Arrows are added to the plot to show the orientation reference frames. The lab reference frame (shown in green, $Z_L$ pointing out of the screen) is fixed with respect to the edges of the diffraction pattern. The crystal reference frame (shown in blue) is fixed to the <100> directions of the cubic unit cell.\n",
    "\n",
    "We see that the lab reference frame must be rotated 10&deg; counter-clockwise around\n",
    "$Z_L$ to align the lab reference frame with the crystal reference frame. Hence, the orientation of the diffraction pattern is (10&deg;, 0&deg;, 0&deg;) in Euler angles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dfd0712c-90dd-443f-b7d1-28d015cb03a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diff_gen = DiffractionGenerator(accelerating_voltage=200,\n",
    "                                precession_angle=0,\n",
    "                                scattering_params='xtables',\n",
    "                                shape_factor_model=\"linear\",\n",
    "                                minimum_intensity=0.001,\n",
    "                                )\n",
    "sim2 = diff_gen.calculate_ed_data(structure_matrix, reciprocal_radius=rec_rad,\n",
    "                                rotation=(0, 2, 0), with_direct_beam=True,\n",
    "                                max_excitation_error=0.04)\n",
    "fig, axs = plt.subplots()\n",
    "axs.set_aspect(\"equal\"); axs.set_xlim(-1.6, 1.6); axs.set_ylim(-1.6, 1.6)\n",
    "axs.set_title(\"$(0\\degree, 2\\degree, 0\\degree)$\")\n",
    "sim2.plot(size_factor=30, show_labels=True, ax=axs);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a397304-8e5b-4dda-ab65-735d63177006",
   "metadata": {},
   "source": [
    "Above is the simulated diffraction pattern for the Euler angle orientation (0&deg;, 2&deg;, 0&deg;).\n",
    "`minimum_intensity` was decreased to include more diffraction spots. We see that a 2&deg; counter-clockwise rotation around $X_L$ (pointing to the right) gives stronger spots in the upper part of the diffraction pattern, since the corresponding reciprocal lattice rods (relrods) are closer to the Ewald sphere there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11865fe8-0d74-4069-bf4d-a108e4e97c8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sim3 = diff_gen.calculate_ed_data(structure_matrix, reciprocal_radius=rec_rad,\n",
    "                                rotation=(0, 45, 3), with_direct_beam=True,\n",
    "                                max_excitation_error=0.04)\n",
    "fig, axs = plt.subplots()\n",
    "axs.set_aspect(\"equal\"); axs.set_xlim(-1.6, 1.6); axs.set_ylim(-1.6, 1.6)\n",
    "axs.set_title(\"$(0\\degree, 45\\degree, 3\\degree)$\")\n",
    "sim3.plot(size_factor=30, show_labels=True, ax=axs);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b71bc88f-7670-4554-8553-ced2b9bee99a",
   "metadata": {},
   "source": [
    "Above is the simulated diffraction pattern for the Euler angle orientation (0&deg;, 45&deg;, 3&deg;). We can find the approximate zone axis (the direction pointing along $Z_L$) of this diffraction pattern by taking the cross product of two of the reflections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9479b4fe-18db-4103-b280-730766ede816",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 2])"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross([2, 0, 0], [1, 1, -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "249df1aa-390c-4807-982d-a7dfe65e9299",
   "metadata": {},
   "source": [
    "We see that the orientation (0&deg;, 45&deg;, 3&deg;) corresponds approximately to the zone axis $[011]$ of aluminium.\n",
    "\n",
    "Alternatively, we can use orix to calculate the zone axis more precisely:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8be45f71-b0fa-44bc-9080-988ccee094d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Miller (1,), point group m-3m, uvw\n",
       "[[ 1. 19. 19.]]"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from orix.quaternion import Rotation\n",
    "from orix.vector import Vector3d, Miller\n",
    "from orix.crystal_map import Phase\n",
    "\n",
    "Al = Phase(point_group=\"m-3m\", structure=structure_matrix)\n",
    "rot = Rotation.from_euler([0, 45, 3], degrees=True)\n",
    "za_vec = rot * Vector3d.zvector()\n",
    "za = Miller(xyz=za_vec.data, phase=Al)\n",
    "za.coordinate_format=\"uvw\"\n",
    "za.round()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e180fdf-baa2-40fb-a702-d6a6a5e6e01a",
   "metadata": {},
   "source": [
    "## Interoperability"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c1947f2-9ade-4598-a66e-fde7d32a9864",
   "metadata": {},
   "source": [
    "### Importing into [MTEX](https://mtex-toolbox.github.io/)\n",
    "An ANG file created from an orix `CrystalMap` ([https://orix.readthedocs.io/en/stable/reference/generated/orix.io.save.html](https://orix.readthedocs.io/en/stable/reference/generated/orix.io.save.html)) can be imported into MTEX using a script such as the one shown below.\n",
    "Here the scan direction was the one typically used in scanning electron diffraction and STEM (scanning from left to right starting in the top-left corner). Since MTEX requires the lab reference frame and the scan reference frame to have the same orientation, the Euler angles are modified using `convertEuler2SpatialReferenceFrame`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e487978e-ca75-4232-889f-5ff1e0699f3b",
   "metadata": {},
   "source": [
    "```\n",
    "filename = 'example.ang';\n",
    "plotx2east;\n",
    "plotzIntoPlane;\n",
    "CS_Al = crystalSymmetry('432', [4 4 4], 'X||a*', 'Z||c', 'mineral', 'Al');\n",
    "CS = {'not_indexed', CS_Al};\n",
    "ebsd = EBSD.load(filename, CS, 'interface', 'ang', 'convertEuler2SpatialReferenceFrame', 'setting 3');\n",
    "ebsd.scanUnit = 'nm';\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5c7adbc-f2b2-4c3b-b4e3-29ed3ab21283",
   "metadata": {},
   "source": [
    "Instead of using `'convertEuler2SpatialReferenceFrame', 'setting 3'` when loading the ANG file, the following commands can be used:\n",
    "```\n",
    "rot = rotation.byAxisAngle(xvector, 180*degree);\n",
    "ebsd_rot = rotate(ebsd, rot, 'keepXY');\n",
    "```          "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f758eb2c-9a0c-4834-9972-4e9469095c66",
   "metadata": {},
   "source": [
    "#### Euler angle conventions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36106cc9-eb15-4692-8410-f14ff4529c3a",
   "metadata": {},
   "source": [
    "Taking the orientation (0&deg;, 45&deg;, 3&deg;) used above, we can again calculate the zone axis (now pointing in the negative $Z_L$ direction due to `plotzIntoPlane`):\n",
    "```\n",
    "ori = orientation.byEuler(0*degree, 45*degree, 3*degree, CS_Al);\n",
    "rot = rotation.byAxisAngle(xvector, 180*degree);\n",
    "new_ori = rot * ori;\n",
    "za = inv(new_ori) * -zvector;\n",
    "za.dispStyle = 'uvw';\n",
    "round(za, 'maxHKL', 50)\n",
    "\n",
    "ans = Miller (Al)\n",
    "  u  v  w\n",
    "  1 19 19\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c021c95c-f2f6-4f76-ab2e-1288032661fd",
   "metadata": {},
   "source": [
    "Note that MTEX uses the \"crystal2lab\" convention, but interprets Euler angles such that they coincide with the Euler angles of the \"lab2crystal\" convention ([https://mtex-toolbox.github.io/MTEXvsBungeConvention.html](https://mtex-toolbox.github.io/MTEXvsBungeConvention.html)). Therefore, the inverse orientation, `inv(new_ori)`, must be used above, but the Euler angles themselves do not need to be changed.\n"
   ]
  }
 ],
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