diff --git a/examples/demo_coordinate_system.ipynb b/examples/demo_coordinate_system.ipynb
index cd6fb0551..6a6dffb0c 100644
--- a/examples/demo_coordinate_system.ipynb
+++ b/examples/demo_coordinate_system.ipynb
@@ -99,7 +99,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "id": "7c7b2a1a-e59e-4f8e-a415-d957af0b4b0f",
    "metadata": {},
    "outputs": [],
@@ -109,7 +109,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "id": "11263d57-3e76-4fe1-adbc-9e1299e6900e",
    "metadata": {},
    "outputs": [],
@@ -127,7 +127,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "id": "20841454-8b80-4b8b-adb9-c1f189f03c78",
    "metadata": {},
    "outputs": [],
@@ -145,7 +145,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "id": "bb8e1555-565e-40c3-8d76-b5039bf6043d",
    "metadata": {},
    "outputs": [],
@@ -157,6 +157,7 @@
     "    \"photoz_sigma_unscaled\": 0.05,\n",
     "    \"ngals\": 1000,\n",
     "    \"pz_bins\": np.linspace(0, 10, 1001),\n",
+    "    \"shapenoise\": 0.05,\n",
     "}"
    ]
   },
@@ -170,7 +171,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "id": "4db4311b-7947-4089-b092-d69de52bff69",
    "metadata": {},
    "outputs": [],
@@ -184,7 +185,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "id": "e51cb813-c077-4d94-878e-0387e1b21801",
    "metadata": {},
    "outputs": [],
@@ -314,7 +315,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "id": "353b4dbb-6239-4763-9125-d5d53b2f7d4e",
    "metadata": {},
    "outputs": [],
@@ -330,7 +331,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": null,
    "id": "20c559a0-0ce2-411c-8d12-dbcb3fc42026",
    "metadata": {},
    "outputs": [],
@@ -346,7 +347,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": null,
    "id": "a275df25",
    "metadata": {},
    "outputs": [],
@@ -404,7 +405,7 @@
    "id": "789c6e25",
    "metadata": {},
    "source": [
-    "We will now compute the tangential and cross components of the ellipticity for all three clusters. We should get the same result for `cl_euclidean` and `cl_celestial`, but a completely different dataset for `cl_wrong`."
+    "We will now compute the tangential and cross components of the ellipticity for all three clusters. We should get the same $e_t$ and a flipped sign $e_x$ for `cl_euclidean` and `cl_celestial`, but a completely different dataset for `cl_wrong`."
    ]
   },
   {
@@ -449,17 +450,32 @@
    "source": [
     "f, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
     "\n",
-    "ax[0].hist(cl_euclidean.galcat[\"et\"], bins=50, color=\"tab:blue\", alpha=0.5)\n",
-    "ax[0].hist(cl_celestial.galcat[\"et\"], bins=50, color=\"tab:red\", alpha=0.5)\n",
-    "ax[0].hist(cl_wrong.galcat[\"et\"], bins=50, color=\"tab:orange\", alpha=0.5)\n",
-    "ax[0].set_xlabel(\"$\\\\epsilon_t$\", fontsize=\"xx-large\")\n",
-    "\n",
-    "ax[1].hist(cl_euclidean.galcat[\"ex\"], bins=50, color=\"tab:blue\", alpha=0.5)\n",
-    "ax[1].hist(cl_celestial.galcat[\"ex\"], bins=50, color=\"tab:red\", alpha=0.5)\n",
-    "ax[1].hist(cl_wrong.galcat[\"ex\"], bins=50, color=\"tab:orange\", alpha=0.5)\n",
-    "ax[1].set_xlabel(\"$\\\\epsilon_x$\", fontsize=\"xx-large\")\n",
+    "ax[0].hist(cl_euclidean.galcat[\"et\"], bins=50, color=\"tab:blue\", alpha=0.5, label=\"euclidean\")\n",
+    "ax[0].hist(cl_celestial.galcat[\"et\"], bins=50, color=\"tab:red\", histtype=\"step\", label=\"celestial\")\n",
+    "ax[0].hist(\n",
+    "    cl_wrong.galcat[\"et\"],\n",
+    "    bins=50,\n",
+    "    color=\"tab:orange\",\n",
+    "    alpha=0.5,\n",
+    "    histtype=\"stepfilled\",\n",
+    "    label=\"incorrect coordinate system\",\n",
+    ")\n",
+    "ax[0].set_xlabel(\"$\\epsilon_t$\", fontsize=\"xx-large\")\n",
+    "\n",
+    "ax[1].hist(cl_euclidean.galcat[\"ex\"], bins=50, color=\"tab:blue\", alpha=0.5, label=\"euclidean\")\n",
+    "ax[1].hist(cl_celestial.galcat[\"ex\"], bins=50, color=\"tab:red\", histtype=\"step\", label=\"celestial\")\n",
+    "ax[1].hist(\n",
+    "    cl_wrong.galcat[\"ex\"],\n",
+    "    bins=50,\n",
+    "    color=\"tab:orange\",\n",
+    "    alpha=0.5,\n",
+    "    histtype=\"stepfilled\",\n",
+    "    label=\"incorrect coordinate system\",\n",
+    ")\n",
+    "ax[1].set_xlabel(\"$\\epsilon_x$\", fontsize=\"xx-large\")\n",
     "ax[1].set_yscale(\"log\")\n",
     "\n",
+    "plt.legend()\n",
     "plt.show()"
    ]
   },
@@ -705,7 +721,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": null,
    "id": "2f61c348",
    "metadata": {},
    "outputs": [],
@@ -728,7 +744,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": null,
    "id": "8eb0581e",
    "metadata": {},
    "outputs": [],
@@ -780,7 +796,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": null,
    "id": "0f237ea0",
    "metadata": {},
    "outputs": [],
@@ -808,7 +824,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": null,
    "id": "2a8705d3",
    "metadata": {},
    "outputs": [],
@@ -827,7 +843,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": null,
    "id": "d76c9464",
    "metadata": {},
    "outputs": [],
@@ -944,7 +960,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": null,
    "id": "cba6862c",
    "metadata": {},
    "outputs": [],
@@ -971,7 +987,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": null,
    "id": "2657871a",
    "metadata": {},
    "outputs": [],