{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Tutorial 1a - Optiland for Beginners"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {
                "tags": [
                    "nbsphinx-toctree"
                ]
            },
            "source": [
                "### May 2024"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "This tutorial describes the basics of Optiland. In particular, the following topics are covered:\n",
                "\n",
                "- Basic lens entry\n",
                "- Material definition and selection\n",
                "- Aperture, field and wavelength selection\n",
                "- Drawing a lens in 2D and 3D"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T09:48:40.131691Z",
                    "iopub.status.busy": "2026-03-24T09:48:40.131535Z",
                    "iopub.status.idle": "2026-03-24T09:48:43.052115Z",
                    "shell.execute_reply": "2026-03-24T09:48:43.051665Z"
                }
            },
            "outputs": [],
            "source": [
                "import numpy as np\n",
                "\n",
                "from optiland import optic"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Building a Lens - an Overview\n",
                "\n",
                " This shows the full code to generate a singlet lens. In the next section, we will go into each part of this code in more detail."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T09:48:43.054044Z",
                    "iopub.status.busy": "2026-03-24T09:48:43.053795Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.318188Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.316084Z"
                }
            },
            "outputs": [],
            "source": [
                "singlet = optic.Optic()\n",
                "\n",
                "# define surfaces\n",
                "singlet.surfaces.add(index=0, radius=np.inf, thickness=np.inf)\n",
                "singlet.surfaces.add(index=1, radius=20, thickness=7, is_stop=True, material=\"N-SF11\")\n",
                "singlet.surfaces.add(index=2, radius=np.inf, thickness=18)\n",
                "singlet.surfaces.add(index=3)\n",
                "\n",
                "# define aperture\n",
                "singlet.set_aperture(aperture_type=\"EPD\", value=25)\n",
                "\n",
                "# define fields\n",
                "singlet.fields.set_type(field_type=\"angle\")\n",
                "singlet.fields.add(y=0)\n",
                "\n",
                "# define wavelengths\n",
                "singlet.wavelengths.add(value=0.5, is_primary=True)\n",
                "\n",
                "# view in 3D - Note this opens a new window, but we add a photo below to\n",
                "# show the visualization\n",
                "singlet.draw3D()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "<figure style=\"text-align: left;\">\n",
                "  <img src=\"../images/singlet.png\" alt=\"Singlet\" style=\"width: 500px;\">\n",
                "</figure>"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.323675Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.323244Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.421414Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.420950Z"
                }
            },
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(<Figure size 1000x400 with 1 Axes>, <Axes: xlabel='Z [mm]', ylabel='Y [mm]'>)"
                        ]
                    },
                    "execution_count": 3,
                    "metadata": {},
                    "output_type": "execute_result"
                },
                {
                    "data": {
                        "image/png": 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c7S07BN1ITztYSpNdIxPgZo/Pbh6Nj/48jP/9ckANdXjliiEYHKTZkEdkjhhsiYjotPz555+wtLTU22ptd3k4WGFSpKs6RHVDM/blaTovyMruws35aGhuhYO1hZqKpg26Ta0wqqEON00Ix8QoL8xbuhuXvvUn7j4nCndOiYSVEY8zJjpTDLZERNRt1dXVqrZWNowZymptdznaWGJUiLM6RENzCw4U1OpWdBfvLsJ7WwtgiWDEVbYiaEgphodqVn8NXZSvM5b9fTxe/yMdr/6ehj9SC/DK3AREeGs23xGZCwZbIiI6rSlj8rS/tPgydjaWFm0lCTLRyxvNbaOAF/++Hfvq3HDZ239iZJg7bk+MxDmxPmp11NCHOtx/XozqnnDfl7tx/mvr8cj5A/C3MaFGXVNMdDr4PAUREXVLfX09tm3bhujoaJMcVS51ttHe9hjpUomHE5qx6LoRqib3lk+2q96xX23PRkNTCwzdsBB3/HzPRFw+PEh1Trjug63IK6/T92kR9QkGWyIi6hYZad7Y2GgSq7V/RRZnp8X54pu/j8PXd4xFqKcjHvh6DyY+/wfeXZeByrpGGDIHGyv85+J4fHTjSKTmVapg/kPSMX2fFlGvY7AlIqK/JGNzpQwhMjISjo7y1L35GBHmgfeuH4Hf7kvEpGhvvPBrKsY9+weeW3EABRWGvRI6OUYz1GFClBf+b/Eu3L14F8pqGvR9WkS9hsGWiIj+0t69e1FVVdUrU8aMRX8fZzx/eQLWP3gOrh4Tgs83Z2HC/1bjoa/34GBBFQyVu6MN3rhqKF69cgjWphao1dt1aYX6Pi2iXsFgS0REpyTDD6TFV1BQENzc2CPVz9UO82cOwMb55+C+86KxOrUA015Zi9s+2Y4dWaUwRLJ57KIhgfh1XiKifJxV3e3j3+9FbUOzvk+NqEcx2BIR0SkdPnwYBQUFZlFbezpc7Kxxx6RIrH9oCv536WBkFFapTgpz3vkTv6Xko0V2nhkYf1d7fHLTKDw5Ow5fbsvGBa+tR1J2mb5Pi6jHMNgSEdEpSW2tu7s7/P399X0qBsnWyhJzRwZj1bxJqpNCa1snhfMWrMPS7dmobzKsVVFpW3bD+HAs/7+JcLKzwqVv/4lXVqWhsdnwOz4Q/RUGWyIiOqnS0lKkpaWpKWPshfrXgVE6KXzd1kkhzNMRD369B4nPr8bCtRmoMLBOCv19nFTXh7um9Mcbqw+q1WZDrhUm6g4GWyIiOqmtW7eqnrURERH6PhWj7qTw4spUjH/2Dzy7Yr9BdVKwtrTAvGnRKuBW1TWp0oSPNh4yyDIKou5gsCUioi5Jz9rdu3ejf//+sLLioMqz6aSw4SFNJ4UvNh8xyE4KQ4LdVGnClSOD8eSPKWpzWW55rb5Pi+i0MdgSEdFJW3zV1dUhNjZW36di9HxdjndSuL+tk8LUl9fiVtVJoQSGwN7GEk9dNEhtLksvqMT0V9bh+905qisGkbFgsCUiopNOGgsMDISzs7O+T8WkOinc3tZJ4fnLByNTdVLYhMvf/hOrDKSTQmK0txrqMCnGB/cs2Y27ONSBjAiDLRERnSAvLw/Hjh1DdHS0vk/FdDspjDjeSUHcakCdFNwcbPD6VUPx2lVDsT6tEOe9sg5rUgv0ek5E3cFgS0REJ9ixYwccHBwQHBys71Mxq04K4V7tOimsy0RlXZNez+/ChACsnDcJMX7OuOHDbfjXd8moadDvORGdCncDEBHRCZvGkpOTERMTAwsLrn/0ZScFOQ4WVGLRukN4aWUq3vjDAteMDsVNE8JVna6+Jq1J3e1nm7Pw35/3Y+PBYrw0NwHDQtz1cj5Ep8J7LCIi6mD//v2or69X3RBIP50U/nf5YKx/cArmDPPHF1uOYKKeOylID+O/jQ1TnRNc7K1VTbAEbw51IEPDYEtERB3s2rULfn5+cHFx0fepmDVZob3vnAhseHiK6qSwJk3/nRQivZ3wzR1jcc+50XhrTQYueWsj0vMr9XIuRF1hKYIeZZfU4J9fJcHUNTc3w9LSUt+nQWeI1894lRxOQXNLC7xTbbv9NU1NTTiWY4Nof19U7SlCqLsdQt1t4e1oxcljeu6kcMP4MHy/+5iaYiadFEaEuqv3nxvro2p1+4qVpQXumRqFKbHemPflblzw+gY8NCMWN44L69PzIOoKg60eWVn2g7+rfmqm+kpr2x9Kae7Ouzvjw+tn3Po52aKpuVnVSHb3+hUUFMDOogXZtVbYtDkfDc2a9lMO1hYq4GqPsLaXfs42sGSY6dNOCpcPC8IfBwrwztoMtXob6e2I2xMjcdHQAPU5fWVwkGaow3MrDuDfP6Xg9/35eGFOAgLd7PvsHIg6Y7DVI39Xeyy4cihMmTT2rqqqgpOTE1d7jBCvn3HburURNTU1mDRpSLeun1zvN998E64xrkhMjEJzSytyKxuQVVKPrLJ6HC6px+HSeqzNrEBto6a20sayH0LcTgy8ga42alwr9TxZFZ0a56uO7YdLVPeEB7/Zo8b2yiazq0eHqFXevmBnbYknLxyIqQN88cDXSZixYB2evmggLh4SyPsM0gsGWyIiUnJzc1FcXIxhw4apt2UlNsjVVh3jOwXgwupGFXSzSjVhV15uy65CRb2m/6pk2kCX40FXe0gItrNm4O35TgpVWLQuEy+vTMObfxxU43tvGt93nRQmRHnhl3sT8cT3ezHvyyQ1bOK/F8fD3dGmT74/kRaDLRERKdLiy97eHv7+/qf8PFmJ83GyUceoEOcOgbesthmHS+t0gfdIaT1+PlCK4hpN71NZw/NztkaYh90Jq7yONqzlPlP9fZxUJ4X7zovGhxsP4/PNWfhgwyFcMjQQtyVGqE4Lvc3V3lo9Czktzg+Pfpeshk08f9lgTIn16fXvTaTFYEtERCqU7t27F6GhoWfcu1YCr7uDFdwdnDA00KnDxyrrm1XY1Rya4Lsmoxx5lY26z5ENaiEq6Np1CLxu9vxT1V2yQvvwzFjcOSVStQn7YOMhLN1+VJUK3DEpQq3u9rYLBvtjRJi7GjRx40fbVGnEo+cPgKMtryP1Pv6UERERjhw5ouqpIyIieuXfd7a1xCA/B3W0J7W62VK/2xZ6ZbV3W3YlvttbjLZ9a3C1s+wQdNmp4a85d+qk8O66TFz+ziYMD3XHHX3QSUEC9kc3jsTnW47gv8tlqEMRXp47RH1/ot7EYEtERNi3bx8cHR3h7e3dp9/X3toC0d726mivobkFOeUNusArx778WvySWsZODWfRSWHhur7rpCAPOq4dE4rx/b1UW7A57/yJv0+OVD1wbaxYZ029g8GWiMjMtbS0ICUlRZUhGMoKqI2lBcI97NTRHjs1nH0nBRnusHBt33VSCPdyxNd3jMXbazLw6u/pWJNaiFeuGIJo396v+yXzw2BLRGTmsrOzUV1djbCwMBg6dmo4e8NDPfDudZpOCu+t13RSeOOPg7hmdIgKub3RSUGGOtx9bhQmx/hg3tLdmPX6Bjw4PUZ1buBQB+pJDLZERGZu//79cHBw6PMyhJ7UY50a3GxRXuUIy1rN1xrKCnZvdVJ47rLBmDetXSeFjb3bSSE+yBU/3T0BL/yaiv8s34/f9ufjxTkJCHLvWHtNdKYYbImIzJiEtwMHDiA4ONgkQ1z3OjUcD71rMqVTgydWFANfZK/BuQN8ce4AH4wM8zDZMob2nRQWbz2C9zf0bicFGerw2Kw4tYFNxsrPXLAeT1w4EJcN41AHOnsMtkREZiw/Px/l5eUYPXo0zM3JOjV899MKVDkGoMrFCz8mHVNBz8XOSj2NLiF3crQPXB36ZrJXX3dSuC0xEjeMC8f3u3PURDNtJ4XbEyNU0O3JsoFx/b2w4t5EPPXDPhVwV6Xk4ZlL4uHpZNtj34PMD4MtEZEZk9VaGxsb+Pr66vtUDIaNRSsGubfioovi0dIyCHuPleO3/QX4fX8+fkg6pup8R4a5q6AnK7qyOcqUSMeCOSOCcVm7Tgq3fbqjVzopyFCHl68Ygmlxvnjk22RMX7Ae/7ssXt2uRGeCwZaIyIylpaUhICAAlpac+tUVWaEcHOSmjvumRSO3vBa/7y9QtaHPt9WJRng7YlpbyB0W4qY2SplqJ4WHlvVOJ4WZ8f5qZfihb/bg5o+348qRwfjXrDg4cagDnSb+xBARmanKykrk5uZi4sSJ+j4Vo+Hvaq96s8pR09CE9elFaiX3m51H1VP3bg7WmNJWspAY7d1rLbQMqZPCjePD4ed69p0UfFzs8MENI7F4azb+szwFf2YU4+W5CX0yLY1MB4MtEZGZOnjwoHoZGBio71MxSg42Vpg+0E8dLS2tSDpaplvN/XZXDqws+mF0hIcqWZAj2MPBZDspXDxE00kh6ix708rmMVkJHt/fE/ctTcLchZvUBLV5UznUgbqHwZaIyEylp6erFl92dj3ft9TcyNP2Q0Pc1fHP6TE4WlqjC7nP/LwfT/2YgmhfJ1WuMHWAD4YEuxv1dLSuOil8tUM6KfioICpdJM5GqKcjlt4+Fu+szcCC39LahjokINbPpcf+D2SaGGyJiMx02lhmZiZiY2P1fSomSfqyXj8uTB1V9U1Yn1aoNqB9uS1bTeDydLRRXRamxflgYpQ3HI20lrRzJ4V312ViTg91UpDgf+eU/pgc461G8l74+kb8c3o0bp4QYdQPCqh3Gedv0kksXLgQixYt6vA+GRH5zTff6O2ciIgMUU5ODurr61mG0AdkA5RsjpJDRgLvOlKq67IgtbkyPnhMpKda7ZQV3UA3exhzJ4XVqQVqo5l0UpCNdRJwLx4aeMadFAYGuOKHuybgpZWpeHbFAXXbvTQnwSRKO6jnmVSwFREREXjrrbd0b1tZmdx/kYjorGVkZKg2X15eXvo+FbMiK42yGUoOeSo/q7halSz8fiAfT/+Ygse/34dYP2fV/uqcWB9EuBlXtwpZndUMtZBOCqVYuDYDDy9Lxksr09Qms2vGnFknBRnq8OgFcTgn1lcz1OHV9Xh8dhzmDA/iUAfqwORSnwRZ3lETEZ3aoUOH4OfnBwsLbsjRJ6klldZZclTUNWJtaqFayf1kUxZe/+MgvBxtcM4AH/WU/oQoL7VhzVhIOcK7143QdVJ4ZVUa3lx9dp0UxkZ6YsW9E/HUDyl48Os9WJWSj2cvjYcXhzpQG+P5DemmI0eOYMaMGbC1tUV8fDzuuusuded9Mg0NDerQkqfmtGMm5aCzo70deVsaJ14/07x+cp8npQgjRozgtT2Fvr5tnG2tMGuwvzqamlvUiueKPUexPqNUjbi1tbLAOFWyoFnN7YkWW31BBjtI+Jw3NQof/XkYn205ouukcOvE8NPupCC304tzBqv65Ee+3YvpC9bh2Uvi1Sq3IeH9Z8/q7u3Yr9WEbvGNGzeitrZW1dUWFRWpetuCggJ8+eWXcHR07FZdrqz4zpw5E3feeacKx3R25MdLrom9vT2fLjJCvH7Gbfv27erB+rhx4zpcPwm1v/32G8aPHw8nJye9nqMh2rJli3rmT24fQ/n9yyqpxdr0EqxJL8au7HI0twID/JwwOcoDk6I8EefnZDS/o7KZ7ptdefhk61EUVDao/8ONY4MxLNj1tP+toqoGPPVzGtakl+CSBF88OC3SYIY68P6zZ8l92ZtvvomHH374lPnMMK5+D2l/JxQVFYVBgwZh1qxZWLVqFS6++OIuv+bGG2/ENddc0+GGe+ONN9SdPYPt2dM+bpLbk7/YxofXz7g5ODh0ef2OHj2q/uC6ubnxup5kcIWzs7PeQ3/7379Bzs4YFOqDO6cCZTUNWNvWZeGzbcfw9voj8HWxVau4sporq7pSk2qo5Ga9c6obbp0cjR+TjqnBFtd/kqRKF6QX7tRYn253UpB/64MbR+PL7Ufxn59SsO1IhdpYNipc/0MdeP/Zs6ytu1ebbVLBtjO5Y5LVW7kTPxnZPCFH5xtOfgj5g9gztLclb0/jxOtnGteu/fXLysqCj4+EB9bXnooh/Mx3df3cHW1x8dAgdTQ2t2DboRJNl4UD+Wpql521BSb091ZdFqQ+18fZMEsWbK0tcfmIYFzarpPC7WfQSUFum6tGhWB8pBfuW7obVy7ajNsmRuC+86LPuBNDT+H9Z8/p7m1o0sG2pqZGhdrzzz9f36dCRGQQGhsbcezYMYwaNUrfp0I9wNrSAuP6e6njsVkDkFFYpULubyn5eOTbZLQsAxKCXNsGQ/higL+zwYWszp0U3l2n6aTw4so03DQ+XE0ic7X/69W6EE8HfHn7WNVL9+VVqWpV+5UrhmCAP4c6mBOTCrYLFixQM8/9/f1RWFio6mdlRWL69On6PjUiIoMg9bUynEFWbMm0SGDt7+OsjjsmRaKkugGrD2hWcjVhLw0BrnZtIdJHdRjQ94pmZ1KOsPBvI1RAX7TueCcFCbcScv9qw5y0U/v75EhMivZWq7cXvrEB902LUSUOHOpgHkwq2Obn5+PRRx9FeXk53N3dkZCQgI8++ki9TkREms4xUn7F+0XT5+Fog8uGB6mjoakFWw4Vq5650iLr081ZcLCxxMQoL7WSOyXWx6BaZkV6O+G5ywbjvmnR+FA6KWzOwocbD+GiIYGqTOGvOinEBbjg+7vG4+WVaXj+1wP440A+Xp47hEMdzIBJBdtnn31W36dARGTQsrOz4e3tbXBPR1PvTwaT0b1yPDE7Dqn5lSrk/rY/Hw9+s0d9ztBgN13JQrSvYWx48nGxw0MzYvGPyZFYsjUb7284hK93HMW5sT64Y3IkRoS6n/Q8ZTV6/vkD1Ka6+79KwowF69RQh7kjgg3i/0a9w6SCLRERnXqXtuw7iI2N1fepkB5JqIv1c1HHnVP6o7CyXm3eksEQb/xxEC/8moogd3sVcOWQDgMSjPXJ2c4atyZG4PpxYfhBOimszcCcdzZhWIgbbp8UiWkDfE/aSWF0hCdW3DMR//4pBQ99k9w21GEwvJ0NZ4Waeg6DrR7lltfifysOwJRJs5OmpibVH5iPj40Pr59xy8tIQ1NzM77N262uX319A9Iq/HCkwBGpu4vg4WDV4XCxteRKlhmSgCermHLUNTZjU6aULOTj1315aqCCDERIjPZWdblTYnzg7ni8k1Bfk4B9+fAgXDo0EGvSCvDOmuOdFKQTwiXDuu6kIMH4+csTVFCfvyxZDXV45pJ4zBh08gFOZJwYbPWoqbkVueV1MHXNzc2wtGzS92nQGeL1M14lVfVobmmBZdv9THV1FSpb7bC7sAWrjxSgprGlw+dbWfSDu70lPB2t4WHfMfR6qpfW6qW7vZVqKUWmR/rfSniV498XtSIlt0JXsnDf0iTIoqhs8NKWLMhUMX08GJLV2XNiZQLb8U4K879Nxkur0nDj+DBcMzq0y04K5w30w7BQdxVu7/hshwrJUpohwZdMA4OtHkkRu7QmMfWnPquqqtig2kjx+hm3rVstVdvDSZPGqOu3YsUKHDhwDJdeOkZ9vLaxBaW1TSiubkRJTRNKapvUy2J5vaYJ6UV1KKlpVO9v7piB4Whj0Sn8akJv51VgNzsr7kY3UvIzMzDAVR3/d24U8ivq8Id0WdifjwW/peG5FQcQ5umg67IwMsxDtR/TZyeF99ZnYsGqdLy1OkN1UpCQ6+9q3+HzZZPcu38bjq92HMVTP+zDpoxivDQ3AWMiPPv83KnnMdgSEZkJ6V/r6Xn8j7e9tQXsrW0Q4HLqp5ZbWltRUdfcIfxqAnBbIK5pwqGSevWyor65w9dKpnXTBuC2l54nCcMO1hZ8AGXAfF3s1CAEOWobmvFnRpHqmSvTw2RTl4udFSbFyPQzH0yO9oGrg3Wfd1KQ2tl5U6NVCcWnp+ikID9nUnoxNsIT9y9NwlWLNuOWCeG4/7wYg57aRn+NwZaIyAxI79q8vDwMGTLktL/Wol8/FU7liPiLz21obkGZWgVuC7/tgrAcR8rqsftYtXq9oVkzclTL1qpfu1XgrleAtaUQ+lgZpOPsbSx1QxVaWgZh77FyzfSz/fm4J+mYWqUfGeauyhXkc8K9HPu0k8KD0klhSn8s2XoE760/3klBNprJeWkfQMkzp4tvG4P3N2TixV/TsC6tCC9fkaBWqck4MdgSEZmB4uJitRGw/Yptb7CxtICPk406/qrMpbqhpWMJhJREtAvCe/Nq1Espl+gYgQFXO8sT6oAlDHdcEeaGuL6qdx0c5KYO6TsrG6N/bwu5z/+aiv8s3682d6mQG+ujSges+uCBiZOtFW6ZGIHrxh7vpDB34YmdFCSE35YYqTbIzfsyCRe/uRH3To1WQy5YRmN8GGyJiMxAbm6ueunh4QFDIGHTydZSHSHup2671NTSinJZBdau/HZYBW5EflUj9hfUqrdPtiGuq9Cr3RCnLZPghrieITWt144JVUdNQxPWpxepkLts51E1Ac3NwVptTpO6XAmTLr28ceuETgpr2zopeDmqiWQXDw1U5QfS/uy7O8fhlVXpeHFlqqonfnluAkI9+261mc4egy0RkRmQyYyyCdDW1vh6d0o4lU4NcvwV7YY4bejVhuHT2RCHOh/411igYF0mov2cEePrDF8XW678ngEHGytMH+injpaWViQdLdN1Wfh2V466tqMjPHBurKbLQoinQ590Uth5pBTvrs3sspPCwzNjVeiWkbwzX12Pf10Qh6tGcaiDsWCwJSIyk2BrDmN0z3ZDnITe5PRS5NX0w8ur0lDbqNkMJxujon2ddUFXXo/xc1Zja6n7wXJoiLs6/jk9BkdLa3Qh99kV+/H0Tylq4pmmlZgPhgS791opwLAQd7zzt+EdOim8+cdB1UnhpgnhqsPDinsS8Z+fUvDIt8nqHJ+7LB4+zna9cj7UcxhsiYjMJNhGRPzV1i/zcaoNcT+X7UJAgC1mz74AR0tr1fjZtPxKpOZVYmdWKb7ano3Gto1v0joqxs9JE3Tbgq+8LvWddGpB7g5qkpgcVfVNWJ9WqDagfbktG2+vyVAPGqRkQULuxGjvXrlNdZ0UpkXjo42aTgrSUUE6KUiZwnOXDVYryQ8v24Ppr2iGOsyM9+/x86Cew988IiITV1dXp/oRu7m56ftUjG6FUZ4al2NanK/u/Y3NLThcVN0WeKuQlleJtamF+PjPw2hp2+UW6GavVnQ1K7ua4Cshiq2kuiahVQKjHM0trdh1pFTXZeGbnUfVpsQxkZ4q5MqKrty+PUlWYk/VSeGXeybi0e/24u+f78SlwwLx5IUDe702mM4Mgy0RkYkrKChQLxlse4a0GpOeqO37ogoZR3uwoEqzuiuhN69S9Xh9Z22t+rg8qx7m5dihlEFeypCDvugSYCyk/GBEmIc6pN71SHGNKgX4/UA+nv4xBY9/vw+xfs5trcR8kBDkph6E9EYnBZloJp0Uhoa4qZG98j2f+jEFWzJL8MKcwRgX6dUj35d6DoMtEZGJKyoqUhtfXFxc9H0qJk1WYwcFuqqjvYq6RqTLym5bOYO8/HxLFoqqGtTHZTUy0scJMb5OHWp4A1xZzylkxVzqXuWQ21JWx2UlV8oG3lh9UJWDyMqqhNwJUV5qw1pvdFKQ1VrppPCPKZFYk1qIqxdtwc0TwvHAdA51MCQMtkREZtDDVjoiWFnxLl8f5Clr6d0qR3tFVfUq5MrKbmpb8JXNVJX1TerjDjaWiPRywIAAV90Kr4Reb2fz7dAgt+XshAB1NDW3YEdWKX4/oNmA9uX2bBVIx0d66sb8dh6n2xOdFF74NRWeqv7XG59uysK6tEK8csWQEx7QkH7wXo6IyAyCrasr/+gaGllplKP909kyuCK3vE6VMsjqbsrREqQcq8D3u4+hvknTn0z6wLbfrKZZ4XWCm4N5dWiQ8o3REZ7qeOT8AcgsrNJ1WXjih33413d7MSjQRddKTF4/mwcE2k4K8n0WrT+kan8t+wEl1Q246M2NmDc1Sg11YFmJfjHYEhGZQSmCr+/xzU9kuCR4BbjZq2NytDeqqnzUartsSssuqdHV7srLLYeKsXjrETXAQkiv3c6BN8rXqUeemjcGEd5O6rg1MQJlNQ1Y29Zl4YONh/Dq7+nq9pGVV9mANr6/1xmXD8j3ePbSeMybFqU6KXyy6bDq0fviyjQsT87F29cMV7XUpB/m8dNORGSmZAWwvLwcUVFR+j4VOssNVRKW5JBhB1oNTS04pO3Q0BZ4V+3Px/sbD6G1rUNDiIdDh+4MUtIQ4eWknrY3VbJ6LS275JAuFtsOlWi6LBzIVw8GZMrchP7eKuSeE+sDHxe7s+6kIC3K9udW4pyX1qh64PkzYnrl/0anxmBLRGTCamtr0dLSwo1jJkrCqaq99XMGEo6/X0bZSocG7WY1qeH9ZkcO8irq1Mdl4le4l6Om767P8dAr42N7ayiCPrtYjOvvpY7HZg1QQxm0rcRk+IIseCcEuerqcuP8T69koX0nha93ZON/vxxQ7cKWbsvG/eeE45rx/WElNQvUJxhsiYhMWE1NjXrp7NyxNRWZNik/GBzkpo72ymsakVZwvDuDvPzzYBFKaxrVx22tLNBfdWhoV7/rp+nQYAob1uT/0N/HWR1SDyv1sasPaFZy312XqabNyf9VG3LHRHh2u2RBHmRcPToUV40KUaUPb64+iCd+Tseb64+oARCXDA1k94Q+wGBLRGQGwdbRkTV/BLg6WKtxsXK0L1cplA4NeVW6kgYJv7/uy0N1Q7NuVVI2qOmGTrQFXtn8Zsxkutllw4PUIWUdUres3YAm7cSkM8XEKC8VdKVkoTv/XwnP906Nxt/GhOKOT7dhW1Y55i9LVt0UpD3YtWNC4WrP4Q69hcGWiMjESxEk1FpacqWITh7EpF5UDukDqyUboo6V17at7GrakSVll+ObnTkqBAppe9V+2ISUNMjgCmOcyiUrrhOjvNXxxOw4FfK1Ifehb/aozxkS7KY6LMghQf9Uq9gSmt+/ZjBWpVfg8e/3qgEer6xKw1urD+Lq0SGqDvds25HRiRhsiYhMPNg6ODjo+zTICEkP1yB3B3VINwEt6R+bVVKj26wmgXd9eqFa4ZRxuEKezm8/bEKCr5Q4GMtT8RJYY/1c1HHnlP6q5/AfUrKwP1+VGMjqa5C7vW762ehwzy4348m/IyN4ZRzwP5cmYVNmMeJ8nNRmsw83Hlab225LjNDUSFOPYLAlIjLxYOvhcfxpZ6KzJX1aI72d1DEz3l/3flmRzCys7jBSWNpfLVyXqT4ui5uhug4NxwOvbGKTDV6GTEoQ5o4IVof8PyWgSsiVco2P/jysSjUSo71U0J0S4wN3x449hQPd7PH5LaPx4Z+H1eYyeVsGPKzYm6f64UqZw+2JERgV7mEStcz6xGBLRGQGpQhEvU1WY+MCXNTRXlV9E9LbVna1JQ1LtmWjsLJefdzasp9qP6ZZ4T3ekizY3UGtGhvi/1PCqxz/vqgVKbkVqmRBgu59S5MgpyxT5iSsjgt1Rryjowqr8n+RGtvEKC/MW7obn2zKUqvBEnLf25CJK97drEod7pgUgWlxfibXncKggu3LL7982v/wzTffzEk3RER6JJuC6uvrWYpAeiWrmUND3NXRnnQkkJCbrlvhrcLa1AJU1GlGCttbW6oBE52HTsigBUNZ1ZTzGBjgqo7/OzcKBRV1asSvhFzpjPC/xha1Si2bz6bG+ahNe1KDvOzv4/H6H+nqkM4Vb18zDEdKavHO2gzc8dlORHg5qkET7KTQS8F28eLFiI+Ph7V194rBd+/ejblz5zLYEhHpUUNDg+phy2BLhkg2V0k7LTnaPxgrqKzv0I5MXi7fk4vaRk2HBhc7qw6lDPJSDvn39E0GPUi7LzlqG5rw+96j2Hi4AsuTj6kJaM52Vpgc46MGQ9wyIQJTYn1w35e7ccHrG/Do+QOw5LYx2J1dplqPSY/dl1am4cbxYbh2dKjqaEE9WIrw4osvdrtOKzExsbv/LBER9XKrL3t77rwm4yAroL4udupIjPbu0KHhaGmtbrOaBN4dWaVYuj0bjc2aDWvezrbtNqtpVnpldVRWjPVBVlonRXnigqGhagrcvmMVaiqcrObek3RMlRqMCHVXdbsH8irx2Pf7sDIlHy9cnoC3rx2OzMIqLFqvGQcsnRQkLEsnBRm3TCfXrav9xBNPqFnV3fXII4/A0/P4IzAiItJPfa2wszv9caFEhkTqU0M8HdQxLe54hwYZl3u400jh1akF+PDP4yOFpYa1fTsyeSkb3/ryKX45//ggV3XcNy0aueW1urrcBb+nq/Zpfq62Kqyf+/IaPHNxPC4aGohnL43HvGlR+PjPw/h0U5baqHbhkADcnhjJTgpnE2xnzZqF0zFjxozT+nwiIuq9YMsVWzJV0k1BVmXlwODj75fOBR1HClfix6RjeGet5ndC9mWFeTl2aEcmL8M8HVTXh94m/WtlUIMcMv54Q3qR6pcro36l9vieL3erlmL/N7U/ZgzyxwPTY/H3yf1Vm7D3NxzCsp057KRwElZn+zSX1G+1dzoru0RE1Hvq6upgYWEBKys2wCHzIquxgwJd1dFeRV0j0vM1nRm0offzLVkoqmpQH7eRVmZqpLC2S4Mm8Mqqb291aJDxx+cN9FOHlFzszi7F22sz1Wrug18n4+FvkjE20hPnxvrivDg/XD8uTIX0hWvZSaErp31vl5OTg+effx47duxQGxPaF3zLI4atW7ee7j9JRES9FGwl1HI1h0hDJqJJKy452pMBDGm6cgZN8JVSgcp6TYcGRxvp0NCxO0O0nxO8nXq2Q4OE52GhHlh0nYcqV7j7i13YnlWq+gNvzdyPp39KQZSPk+qy8N9LBqKstgmL1mWqTgrSD/jWiRFqIIQ5d1I47WD72GOPqZePP/642kzGO8wzJz38ZJekSWttRUNjI2ykowZ/VowPr59R25xZh/p6J3yyoxC2VhawseyneobKS5mSpF5atr200rxu2+517cflmVne15MpkwEMcoyL9OqwYJdbXtehfndfbjm+252D+raRwu4O1rquDNrAK0dPdDCQcoWlt4/FJ5sO49kVBxDk4YC5I4JwsKBabZqT1mDSCUL66U6K9sau7DI8+l0yXl5l3p0UTjvYpqen49NPP0VYWFjvnJEZkabVPyfnwqS1Ai2tLbDoJ38Z9X0ydNp4/YxafmkrWlptkbevRG1OaWhuVcfpkkvfMey2D8Zt72//cat+sLawgK1V54+3/5wT/y3rLoK29nMYrKmvyc+cdCCQQ8KjlowNPlJS06F+d3NmMb7YekQ3Ulh67UrYDfewxaAgD8T4uaievFJ2cLoruDeMD8eEKG/M+3I3XlyZhrum9MefD5+DfcfKVU3ubyn5anqZ/L4Mb+sV/Opv5ttJ4bSDbVxcHPLz8xlse4A8bbD2gSkwZfKIt6qqStVe8w+T8eH1M25PP71e9R+/6qoY3fWTa9rY0oqGJk3IbWhuUa9r3tfS4X312tebtZ+vff14SNZ9fdvr1Q1t72//b7X7+vqmVnm8dNpODNGa1627E7Q7fVw2HMlLTfA+MWiXNVrCqUGzAUlWuvmzT+1JHav8/ZZjxiA/3fvrm5pxSDo0tOvBuzqtGJ9uzVEdGuTHSKapte/OIJvWZOqa/PydSn8fJyz7xzi8/sdBvLH6oOr88PLcIXhoRqw6jhTXqM1nvx/Ix5bMEjS1tMLZzgafbs5SY3wvSgjA7ZPMo5PCGZUiPPPMMygsLERkZOQJmxKioqJ68vyIiOgMydSxzq2+JKRpApx+zkmCdXMLjgfediFaG45PCM9dBOkuA3dzKyrqm9HQ1NQpVHf8evn+pxYIHAMe2/GLCs7SB9XJzgrOttZtL61Uo3153cnWWr2u3pbPUx/TvM+p3efZWplvzaO5kGsc6+eijvYLAxY2dsgobBd486vwzY4c5FXUqc+zagvK7TerSQAN8XDosBlMHpBJq7BztEMdXluP+TNjcd3YMNUGTVZmb5oQrjbIrUsrVCu5fxwoQH1dkyqfWLYrB4MCXfDAeTGqR7CpPmA77WBbWlqqNpA99dRTuvfJjcPNY0REhkU2+BpaRwT5OyEZz8rSEvqahyarWboQ3S4Ya97XinUbN8HZ3QtxCcNUyVhlXVPby0ZUtb1+rLwOVfnH3y+fI//uycjK8PEwrA3CnUKxLjRbq7cdbS1h1dIIHw/5Ws3nSrgh4yLlBzI2V472ymsakVZwvDuDvNx4sAhlNY3q4/JsQeeRwvJ6QpArlv/fRDy7Yj+e/DFFlSO8MGewqsnVbpCbNThAHU3NLao37qqUfHyflIO9ORW4/sNt6mdp1mB/3DmlP4LcTWsy4Wnf4z399NOIjo7Gf//7X24eIyIyYI2NjbC05EphZ7JCJoe9ddch8Yh9PQI8WnHRsKBu/5uyuCMbirQhWAJwZb0m8GrDsArA2o+1vS+ntFatsKmvaQvR2jrNrkjY0YRhTfjVBeK2UOzU7mPHQ3Pnt636pFcrnZps7BoZ5qGO9j9HhdKhIa+qw6a1X/fmobpBM1JYrrMEXlnVvXZ0CJYn5+K8V9bhPxcPwkVDAjt8D7nOoyM81fGvWXFqmpmM65WvWbw1Wx3+rna4ZGigKqsYFODaa23NDDbY5ubm4uWXX0ZwcHDvnBEREfWIpqYmBts+Ios80mJJDhnteqYk2NQ1tmhCcW0jCkor0Wxhjar6Zs2KsS40Hw/HVXWNqsZSG4y1n3eKfAx7a0vdCrE2GGuCcsdVZBWSTyi/OF6Wwb6pPf9z5ONsp44JUcc7NEh/25yyWt1mNQm8u7PLkVFQpZ5xEPcs2Y2nf0zBeXG+iA9yU3W80qJMVnC1Iryd8Nxlg9WxPq0QL65MRdLRcry9JgNvrcmAt7MNpg7ww9QBPhjf3+ukbcPk53Tf0RK1gix1/Ia0yHnawXbkyJFIS0tjsCUiMoJgKwMayHhIQLC3sVSH9Ej1sdcMPjrd4CDBo7ZRwvCJpRQdV401IbiibWW5qKq64+fVN+lG03bFwcayXS2x9fEA3G71WBueO68i64KyjZXRrxL2Nrl9gj0c1CE9bLWk1OBwcY0KvD/sPqY2kC3dcRRLtmXrNmkGuNqdUL8rm9EmRnurQza8LVyboTorlFY34qc9x7B46xHYWVtgQn8v9f3OjfWBj4umXr+2oRnP/ZQMi+Tv1dvz58+HjY0NjDbYTpw4Ua3YHjx4EP379z+hfmvSpEk9eX5ERHQGmpubVbhhsDVPEoSltlMOX81epjMiK4U1jc1t5RSNugDcvrZYV4fc9rqUVsjGqOOfp3l5Kp3LKnQhuG1l+ITSii7KLxysLc0uIEupgYRUOc6P90deeR0e+DoJ69OLcEG8PxKjvTTBN69SlR8sXJepvk4eJ4V5OiJaShp8ndXq8KVDA7E6rRCfb85SK/GR3k6qj++j3yZjfitUbe/AAFesTStASWUNrjScLHt2wfbZZ59VL997770TPsbNY0REhrNaKwzpKUIyPhIUtaET6Nhh43QDcnVD+9Xj4yUTxwOx9nVNYJbjWFldh8/T1pl2RX7UZfW34ya946UUpyytaNfJQlahjfX3xs/VDp/cNEq1+Xrm5/1Iya3Ay3MTVEswIbdjer52s5pmwtribdlqYJSQLiBhHo6wsbZQvXrlGgwPdcOIUHe1SU169arv42QDnPxSGFew3bZtW++cCRER9XiwZY0tGUpA1oTHs5uEJRvrtBvtNOUUnTfkacooVEhue39ZTQOOSkhr93lSpnHSc5WA3K47xckCcIeVZe1mvnadLaRPsj7069dPtQCTGllpC3b5O5tw5+RI3H1ulDrHoSHu6mivpLpBM1K4rTuDvNTWoOzIKlOHCHCzU/9ueVUtkAWDZFh9YIiIqMdKEYSxrjwRdUWeIne1t1bH2ZDa1Or65k4dKbourdCuLkv4065iakO0bPQ71bk62ljCxd666wDcbiVZ1SefpLPFmQ4JifR2wjd/H4c3V2fgtT/SsTq1EK9ckYD+PicOaZDRvGMiPNWh1dzcgjdXH8Rrv6fDzkY6afRTK+hfbz8KSzTjb/YmFGz37duH7du3q562LS0dL+p9993XU+dGRERnSHvfzGBL1HVtqquDHGcXkGX4R3W7Vm26sgkprahtRHFFDRpaLTp0syiorENmUccSDPl3TuZsh4RcOyYE46M88dDXe3DBaxtUWcIN48JOWY+cW16LB77agw0Hi3D92FA8PHOA2tC4O7tMbTT7bW8ODNVpB9sPPvgAb7/9NkJDQ0/oY2sod6BLly7Fp59+iuLiYjUJ7YEHHsCgQYP0fVpERH2+YsvNY0S9R41itrKBu6PNWY0kl3G8soJ8wqpxF6UV2tVl2dhVVdCx60Vj88lbWFhb9FOryE//lIKXVqYi2s8Jno52J5RWZBZVY/meY2ql+JGZsRgf5aVqcCVEx/m74O1rhyMtNwKL390Fkwi2S5YsweOPP47Zs2fDEK1cuRKvvPKKaj8hYXbx4sW4++678c0336ggTkRkDuSPKhEZzzheOaQk4GzUSQeLdrXE0g+5c3eK/bkVatRu8tEKRPu2qnKJqoZmtcIsq8nacFzb2IJnVhwAVnQ+Vwu42fbD+YBpBFt51JGQkABD9fnnn+Piiy/GhRdeqN6WgLthwwb88MMPuOGGG/R9ekREfYLBlsj82LUNCfFyOvWQEBnn+/gPe/H97mM4P94P1w/yVyu5MrjjxTmDMH2g3wmdK46vGjeioroOpZu2wCSC7dVXX42vvvoK999/PwxxfOSBAwdw44036t4nT8ONGjUKe/bsOeksdTm06uvrdX8U+Ifh7GlvR96WxonXz3jJNZOFCDl4/c6Mvm83/v4ZN0O+fi72VlhwxRAkRnlh/rK9+Dk5DwMDXPDedSNUyzBh62QDL2nr1QXJTc9t0rzeV//H7n6P0w62f/vb33DvvffioosuQkRExAkDGl544QXoS1lZmaor61xyIG8fPny4y6/58MMPsWjRIt3b8v+ZOXOmqouRoExnR02/qa01qBps6j5eP+MlD9KdnZ07tP6i7pHbzdbWVv0d0Cf+/hk3Q79+e3IqVMeDfmhFhKcD9h2rwMu/7sc/p0aoXr6n+n9V1GgWAUV1dXWHBcLeol147PFgK8FVOiKMGDECrq6uBnmxToes7l5zzTUdbrg33nhDFXvLHRv1zCOsMxkJSfrH62e85A9qZWWluobygJ3Xr/vkdpNwKz/3+sTfP+NmaNevtbUV9U0tKK1pwFtrMvDFliNq+tj88weoOluZOvZtUh5+3V+I0eEeqguCpk63fZ9gzdGvpUnX7svR0bFPRupaW1v3TrBdvnw5nn/+eUyYMAGGxs3NTTUjLykp6fB+edvT83hvtvbkYrS/INobTvsUHp097W3J29M48foZJ7kv1P5h5fU7M4Zwm/H3z7j11PXrzqawzjWxldpQ2va58nZTS8en86UDwpM/pug2hUlnBJnutmp/AQLd7BHr74wQD4cT+us6WLUiebmmK0Jf/Xx293ucdrB1cXFBUFAQDJGE0tjYWDXWd/LkybpejjItbe7cufo+PSKiPqP9I2CI9X1E5qKxuUUNdugcQHVh84RhEJ3bfWk+1tB88j63NpYWnaajWanetoHu9rq3HW2tsDenHKtS8lXd7P+dG4WEYDddX1z5PGldph1e8faaDLz6ezrcHKxV39to3+NDHXZklWDh6jQEwjCddrC97bbbsHDhQjzxxBOwszvzudG9RcoKnnzyScTFxWHgwIH44osv1FNyhtqejIioN2hH6XYeokNE3QuknSeP6QYv6IJoWwht/3R9u5XUvxq8YKXGDJ84eMHf1a5bgxe0Xyttwk4lp0yGLSThz4xiNZjh4ZmxqnPCSc/L0kKN350c44N5S3dj1usbMO/cKNhaW+DTzUdwqKgazjbA5QY6rfuM+tjm5OTgvPPOg7+//wmbx6Tdlj7JeclEtHfeeUcNaIiOjsbrr79+0lIEIiJTDrZE5uSvRuW2rxXtHFhPZ1Ru+7DpIk/P21nB29kW4d6OutG4skpqg2Z4uTq2BdLjq6NnMyq3u1pbW/Hd7hw8/v0+9T0/u3k0JkR5nfJrmltakVVcjbT8SqTmVSHcyxE5pbX436+pus9xd7BGtLc9UADTCLbap/gN2RVXXKEOIiJzxRVbMiYSqLQBUxM+GzttWjr5BK72n1fbqJm41xWZINt51VOCpqeTLUI9jwfS9uFTW1OqqS/VrKzaWXcvkJ7O5LGeVlrdgEe/S1ZtvC4aEoCnLxzUYXywnNux8jqk5VUiNb9S9/JgQZXaYCakp21TS4sa2BDsbo+Smga1Ai2BfEdWKeLaNo+ZRCkCEREZNu2zaQy21JtaWlpR3XDyDUxdPnXfxefJhqWTkUyogmanDUwS1ILc7XU1pcfDZ8fP0z6dL0HNHDbhrU4twINf71HlFG9cPRRjIjyx71i5JsCqlVh5WaVueyG3UbSvEwYHuarBDPJ5aw4UqA1r8rVyW24/XKpWwqUON6+iHsOC3IBimEawJSIiw8dgS6ciK3YSJrWBs+JUG5i0r7d9rPNu/FM5Xht6fCVUnroPcLXXBdEuV0fbVlbldQdrS1jIciudUm5ZLR7/YZ/aICYdDaSbwRPf70NxtabHrITSKB8nxPg647yBfupltJ8zAlztkFFYhXfXZeK139NgaWGhyiryK+qwMaNYfc2cEcGYFueDIcHuWLkvD48t2w1DnUHbrWB7zjnnYNmyZaqdVndccMEFeO+991QNLhER9T1ZmZJwK0NryMSa/jc2t6sHPcVT9x1WS4+HUk0LqCacqmGG9DU9/pT88afu/Vxsj6+OdgqsnTc2OdpYMZD2gtqGZlUy0H4FVjoeaAOsRT+oHrR+LnZIjPJGjJ+T6mogQVc2hrW39VAx7l2yG9sOl6jNbJoqhFaEejrgpvHhmDrAFyGeDh2+Zma8PwYHOOK9N7bCaIOtNKveuHFjt5tVl5eX886UiEjPGGwNK5DKhiTtrvm/fOpevd2Isup61DS16sKrvL9TK9IO5On2E56St7VWK3Ca1VJtEG0LoV08dS+HbJAi/ZJSAulAoCkd0JYQVCKrpEb3oERKMSSQSqgN9XDAY7PjMDHK65SdEuTnStp5LdmejeKqBt3PzdQ4H1WKkBjtrVbVTyXAwxnz588/rcEJBleKIC20iIjIuIItSxF6ZlpTh9XRdm2eutrAdPzzOobWzs3x25MNSV21dwr2sIe7o53uafkun7pve3rf0dbyhBU5Mo465ezSmuMBNr9KbebKLKpSG7eEj7MtYvycce4AX10JgTz0eOTbZPV190+Lxt8nR570+ueV1+HXfblYvDVbfb78q3ZWFpge54sbx4djRJj7af3syDNCfTFtrNeCrQw4ICIi4yIrKaa0Yis75xua5WhBQ1PbS/V2q9qt3eXr2s/p/L6mrv8tCRJFpX5oybPEk0krVSjVhouuSN1iV0/Jy0ra8SCqCaVqtbQtiGre1gRTx3bN8Q1lVz31PLme+RX1HboQSJBNz6/SdXNwtbdWAXZkuDuuHROiSgjkcHe06RCEP9h4CM//mqrKC779x3jEB7me8L325lTgt/35WJmSh/25lbqPyUaxu6f0x+whhjpi4exw8xgRkYmSFZWmplNv7uku+UMpK47a8KcNhPVdBcWTBE3d16n3nSyYdvFvtb1+iuFLJ2Vt0Q82Vv1gY9kP1pYW6qU6rNq9bimrpZbqpbxtX1sAD2crDI2POPGp+3arpbJC+lfN8ck8ybSx1LwKJB8pRlZZg66UQMpMhIONJaJ8nRHr54wLEwJUmJWVWCkZOdWDmKOlNfjnV0nYnFmiamAfnBGjG7YgXQz+zCjCb/sL8Mf+AuRV1Kmf6ZbWVlj264fZCf6465wo9PfpXlmpsWKw1aOymgb8kHQMJv80Xn0DbG1tuOJghHj9jFtajSOaa4CWXYWQBSFtUKzvtEL5lyugbR8/k+G8JwbJ9uHy+Nuu9lYdgqY2jOo+v+3rrTu8r+Prtl18rsUZ/Nz+/HMSAgLscdGU/mfwPyZzIiv6aZ1WYGWwQVFVvfq41L9KkJTgKpO8JLzK69K14HQ21sl98bKdOXjyh33qgdUXt4zGuP5eKKisw3e7clSY3XiwSK38SpcD+ZzCKs3v37Vjw3Hj+DD4uhjetNjewGCrR4WV9fjPT/th6uTPYT9VDUTGiNfPeFUXWUOe4E7dXdwhKFqfECAt4GTTKSh2DqOdg2YXq56dg6aslvIBEZkCWQ2Vllja4KpdgZVxtUIyapinoyobuHp0iKYO1tcJnrYtcHd1OavfA1n9fWRZMn7Zl4dLhgTgqtGh2JJZrKaBJWWXqe89PNQdlw0LREZhNTZlFsPXxRYPzYjFVaNC1LML5qTbwbawsBDe3t69ezZmRp6GSPvvTJgy1ogZN14/4/b66wdRUFCAm2+M5fUj6uZI3sPFNR26EMhK7OGial03ClltldA6K8G/LcA6q1VZbUlA5/vPs/H7/nw1bKG+qRmJUV7YergU3+4+pkpiEqO9cN0YTTfZL7YewWdbjqjzeP7ywbh4SGCXddvmoNvBdu7cuXjooYcwY8aM3j0jIiLqEfb29j1WY0tkSmQDlqy2aoOrppSgChkFVar0Rng52ajQKr1gb50YoV6P8nX6y1ZYPeFIiaaWduuhElj2A2T/YmZRNabF+eLcATIowQ0/J+fizTUHkVlYjZFh7njvuhE4J9bH7HsHdzvY/uMf/8AzzzyD1atX45FHHoGra8cdeEREZFhsbW1VsJWWX5aW3ORE5kdWTaXsL7XdCqyMk03Pr9SN8ZV6VFl5HRrihitHBrd1InCCp5Ntn56nnJd0Mfh+d456XQS72+PKUcGYOsBPnZO0kPtiyxHcvzQJBZX1OC/OFy9cPhjDQz367FxNJtjOmTMH48aNw7///W+1evvoo48iMTGxd8+OiIjOasVW1NXVwdHRUd+nQ9SrymsaNQG202ausppGXa/gKB9N6cD58RIUNRu5ZEKXPkp1ZIOmrMhKmP39QD6yS2rbpn+1ItTDHguuGIqhoe66PrTPrTiAz7ccUV936bBA3DIxwuQ7HPT65rHAwEC88847+PLLL/HAAw8gPDz8hFWAzz///IxOhIiIepadnWYXdG1tLYMtmYyahibV+7VzgJUesULCYYS3ZiPXxP5eapiBrMgGezjofaJaaXUDVqcW4Pf9BViXVqhWYP1d7dTmL2k7klteiwemx+D2xAg1MEFWlt9dl4nvdufAzsoS144JNasOB33SFSE3N1eVI7i4uGDSpEl8eouIyEBpw6ys2BIZG1mZlOlbx0fKaroRSP2pkEVWGVAgAXbO8GBdgA33cjSYjVNSYiB1u78f0ITZ7VklahNaQpArbk2MwJQYH/yZUYiXVqYjzMsB3981AQMDXLHtcAkWrs1Qbbykw4GEXXPscNDrwfbbb7/FggULMGrUKCxduhTu7polciIiMtwV25oaTRAgMtSJchJW23chkJXYQ0XVujHEUi4gwXX6QF9dCYE8De9gY3hdSxubW1Qw/T0lH6tS8nCktE6VQUzo74X/XhKPc2N94ONih+ySGtz/VZL63FsmhGPe1GhsOFiEx7/fhx1Zper/J/WzF5lxh4Mz0e2fiLvvvhv79u1TJQizZs06o29GRER9R55Rk+ljDLZkKKuXx8rrjpcPtL08WFCF+iZNJwJ3B81I2XGRnrhhfJhagZXWmDJq1tDre9ekaVZl16QWqAljstI6MdIdj88OxIQob107MLkdlm7PxtM/pqj/18c3jlIlCLPe2MAOB30ZbGXe+OLFi+Hr69sT35eIiPpo1ba6ulrfp0FmRiZvdZzGVanqYqWmVDjaWKoV2PhAV1w2LEiFWVmJlRZbxtJzWVaUpc+sbP7adrhUrTwPDHDBDePDMW2AL+L8nVFTU92hD7jcLvOXJWNVSr4apSu1wNLWq7CqXn0NOxz0YbB96623euDbERFRX3dG4Iot9ZaKuka1wan9NC55WVzdoD4uT6H399aMlJ0W54cYPycVYGXIgbEE2PbDG3YeKVNhdtX+fLW6Kv+/8ZGeeOrCgaq/rL+rphOJdmW2PQmz85ftQVNzq+pH+8eBAvyylx0OeprhFacQEVGPBluu2FJPjJSVkoHOdbBSWiCk20CYp4MKsH8bG6qZyOXnjFAPB7W735iDu3QvkBID6WYgrcO8nGxxTqw3Hp4RiwlRXn9Z51tV34R//5SCpduPqg4IZTX12JxZrG6nG8eFqXpb6jkMtkREJh5s8/Ly1OqRsa2QkX42PslT7JrSAW0pQRUOF1dDuwAZ5G6vgutFQwN1I2XlKfXOI2WNlWzqkvICObZklqgNbLF+zrh2dKhalU0Icut27ev2rDI89P0BFFdpVrBbWlvx4Ax2OOhNDLZERCbMwcFBTR+Tll/agQ1EMlI2u7R9J4IqtQIr7bUaZX4rAB9nW7UCK5uYtCuwUT5OcLQ1reggtbG7s0tVay0pM5Agb23ZD2MiPPHYrDgVZoPcHU7r36xtaMI9S3ZjZUq+eltWs++c0p8dDvqAaf10EhHRCcFWVFZWMtiaIVmpl8EFnYcZyEau2kbNSFkXOyvE+rlgZLg7rh0T0jZS1hnujjYwVdX1TVifXohVKZouBlIT7OFoo/rKStutidHecDqDAF/f1Iy3Vmfg7TUZaGhuQaCrLZ64cBCmDvBlh4M+wmBLRGTCtGFWgq2Pj4++T4d6eapV+y4E2pfSekrYW1si2tdJrb7KjnxtP1hZmTWHMpWcstq2LgYF2JxRrIKnrEDPGRGMaXE+GBLsfsaTycprG/H55iy8ueYgquubVSh+5tJBmB7t1qErAvU+BlsiIhNmbW2tVm0l2JJpkM1IUv/afhqXBNrCSs1IWXkaPdJb031gcoyPJsD6OqvaWHNaNZRyiz055bowuz+3Qo3bHR3hgYdnxqpV1BDP0ysx6CyvvA4fbDyEzzZnobahWabi4ooRQXj64kGwsbRAVVVVj/1/qHsYbImITJyHhwcqKir0fRp0muobm3EgrwrZleVIL9DUwEqAPVpaqz4ui4Bhno5qFfaqkcdHyoZ5OcLaiDsRnI2ahiZsSC9SXQz+SC1QYV+GIEyJ8cadUyKRGO0Nlx7YtCUPLBauy8T3u3PUKm9zcyt8Xezw6pVDMDrCs8t2X9Q3GGyJiEycp6cnjh49qu/ToFP0Rz1cXNOxhCC/EoeLqtE2UVb1fY3ydcIF8f4dRsqaSieCs101/f1AvgqzGw8WqSlm0qXhkqGBanzt8FD3Hmk5JkFVBjEsXJuB3w8UqBIOeWAhDzrmjghSG83Y6UD/GGyJiEycl5eXGonOll/6f2pc6jzb94GVbgQZBVWq3lPI5C0JrolR3rhlQjiCXawwOMwbrvamu5HrdMnP8d6cCtWOSwKtvC6rpiNC3fHA9BicO8AX4V6OPXrdZCCDBFoZ0CB1uTeMC8MPu3NQUt2Ad/82HOcN9Oux70dnh8GWiMgMVmwbGxvVBDJHx577g08nD14yIjUtr6pDNwJ5+rq6QdOJwNnWSpUODAl2UzWZ0bqRsrYd/h2p0XTiKqAaEPFnRpGuJZd0enC2s1I1xLdOjMCkaG+4OfRs+JcOB9/uzMG76zKRWVSNUWEeeOOqoWpQw0d/HlbTw569NL7DNSP9Y7AlIjJx3t7e6mVZWRmDbQ8rr2lEWkHHLgTysrSmUX3c1spClRBIaJ05yE9XBysTqLh6fmoFlXX4Y3+BCrMbDhairrEFoZ4OuCA+AFPjfDAyzKNXaolVh4MtWfhw42EUVdXjvDhfvDAnQQ2vuH9pEspqGvD85YMxZ3gQr6EBYrAlIjJx7u7usLKyUsE2MDBQ36djtJuSpPdr536wsnIo5KnwCC9HFVzH9/fS1cGGeDiccQspcyMr1PtzK9u6GOQj6Wg55KaTGtl7p0Zj6gAf1e2ht8JkbnmtCrNfbDmChqYWXDY8ELdMjFD1zS+tTMV7Gw5hZKgHltw2BsEeZ9dNgXoPgy0RkYmTICCrtqWlpfo+FYPW1NyK0tom5NbbILeoH9J+PaBrpyVTumSTu2QqCatRPs64fHiQLsBKTaetFTdyncnT/ZsyitXGLwm0x8rrVA/YxGgvXD8uTJUayOCE3iTX9922DgeyGe9vY0Nx47gw+LjYYd+xclz0xkY1ZvjhGbEq6PKBimFjsCUiMgO+vr7Izs6GOa4CVtY3o6SmSR3F8rJW+3qj7v1ylNdp6l8BPyAP8MvPUSuw0wf6duhE4GDDP51nQ57eX31ASgzysT69CDUNzarHrmzAkvG1o8M9e33sbOcOB34udnhweiyuHBWsOhvImN03Vx/Egt/S1Crx93eNxwB/l149J+oZ/O0kIjKTYJucnIyWlhZYWBh/j1Np6dQhrGpDaltobX80antmtbG3toCHgxU87K3UyxA3W3jK2w7W6mXKzs2ICfLG1Zefq7f/nymREJmWX6XpYrA/H7uyy9T7ZePcnVP6qzArdcd9Ua8qHQ5WpuRj4boM7GrrcPDinAQ1iU0bprOKq3Hf0iTsPFKK2xMjMW9aFFfjjQiDLRGRGfDz80NzczPKy8tVza0hklUyWTXVhdQOq6vtwmtNE6oaNO2xtCz7Ae5tYdXT0RoRHnYYEaQJrp0Ph7/o/VqyrxGObERwVqRGdeuhEl1LruySWjjYWGJilBf+d9lgnBPr06fdBKSrwne72nU4CPfABzeMwORoH900Ngngi7dm4z/LU+DpZIOlt49VG9TIuDDYEhGZSbAVJSUlfRpsJSzUNrZ0KAMorm4LqZ1WV8tqm9DcaViTs62lbnXV08EaUV726m3tCqv2dRc7S1hwh7pelVY3qFZYUi+7Lq0QlfVNqvuDrMhKb9mxEZ59PlCic4eD6XF+eHFuAoaFuJ/QgeHhb5Lxx4ECXDkyGP+aFadqfcn48KoREZkBOzs7uLm5obi4GJGRkT2y0ep4MD2xDKD9CmtdU8e0amPZ73gpgKMVBvg4tAXVjoe7vZVql0WGSR60ZBRW60oMdmSVqklpCUGuuDUxQgXaOH8XvbTEkg4HH2w4pDocNDa36jocSL1sZyuSc/HIt8lqU9h7143A1DjfPj9f6jkMtkREZiIgIEAF29PaaKV9vfZkG600JLq42VvqVlEDXWwQ7+egC6ntV1idbCzY/9NISS/XbYdLdF0MZBSwnbUFJvT3wn8viVcjbKWbgL5Ih4OFazUdDuxtLFVnBZkS1tU5VdQ14skf9mHZzhy1QfCZS+LhyWELRo/BVo8q6xqxObMEpkz+UNbV1cHOrpp/yIwQr59xO5BZgoaGejSk5Kvrl2vhjT15+ahLLkJpbfMJK6yl3dhoFepu2/a6ZqOVNri62VnBSgpdySSHUKxJ0wxKWJtagIq6Jvi62OKcWF88NstH9e3t6xKDrjocvLM2Q5USSIeDh2dKh4OQk5YTyBSzB77ao0oVZPPYZcMCeR9nIhhs9Si3vA63frJd36dBRCaqPjdNvbRNaX9XH47VG/PaPeV/4kYrbWB178ZGKzJN0rdVOyhBQqNs7BsY4IIbxodj2gBf9bp205W+dO5wEO17YoeDrjaRvfBrKt7fcAhjIjzw5ZwxCHLnsAVTwmCrRzKlZse/psKUySPp6upqNcaTj4aND6+fcdu53RW1dbUYN36iun6NjY147bVXMWnsSMTGxOj79MiANDW3YOeRMhVk5cgsrFbhcHykJ566cKCql/V3tYchkHD67a4cLDpFh4Ou7M0px7wvdyOrpAb/umAAbhofrvdwTj2PwVaPrCwtTL6eR4KRLRrh5GTLYGSEeP2Mm6uDDazRpO5nNNfPFiG+nigqLAQYbM2e1JhK9wKpl5VuBmU1jfByslGtuB6aEatacxnSMIrudjjoKrRLmcKC39LVoI0f75qghm2QaTKcn1giIup1wcHBSE9P1/dpkJ4cKa7R9ZbdklmCppZWxPo549rRoWpVNiHIzeBWMU+nw0Fnh4uqMW/pbiRll+HvkyNxz7nRvT7VjPSLwZaIyMyC7fbt29s2Bepv9zr1DamN3Z1dqjZ+Sc2sTACztuyHMRGeeGxWnAqzhlpjmppXqQYqdOhwMD4MPs523Xq26fMtR/Df5fvh7WyLr+4Yi+GhHLZgDhhsiYjMSEhIiHpZUFCge51MS1V9E9anFaowuya1AMXVDfBwtMGUGB/MmxqNidHeBjt8QAKpTCxbuC5TdTiQAQ9/1eGgs4KKOjz4zR6sSS3EVaNCVD2to4H+f6nnmdSVnj17NnJzczu876677sINN9ygt3MiIjIkMqTBxcUF+fn5DLYmJKestq2LQQE2ZxSjobkFUT5OmDMiGNPifDAk2F0NIDDkleVVKXl4Z20mdmdrOhy8NCcBs0/R4aAry/fk4tHvkmFlYaE2lElLMjIvJhVsxR133IGLL75Y97bs5iYiouNCQ0Nx7NgxfZ8GnWWrq6SjZWrjl9TMHsirhJVFP4yO8FArnFMH+CLE0zBLDLrT4UBWl09nw6psLHvi+734bvcxzBzkp4ZFyCo1mR+TC7YODg7w8vLS92kQERmssLAw7N27Fw0NDbCx4R9/Y1HT0IQN6UWaqV8HClRnAFd7a0yJ8cZd5/RHYrQ3XOysYSxDHz5r63BQXN39Dgdd2XiwCP/8KglVdU14eW4CLhnKYQvmzOSC7ccff4z3338fvr6+mDFjBq6++mpYWZ38vyl37HJo1dfX6+p85KCzo70deVsaJ14/07x+EmxFXl6e2kxGXdP3z718fxnks2Vvsao3/TOjGPVNLYjwdsQlQwNw7gBfDA9xU60jDeWc/8qxslp8sPEwlmw9oqbcycSvWyaEI6Ktw8HpnL+s9v7vl1R89OdhjI3wxAtzBiPQzd5gbgfef/as7t6OJhVsr7jiCsTGxsLV1RVJSUl48803UVRUhPvuu++kX/Phhx9i0aJFurclBM+cORNVVVWqmTmd/Q9ibW2tep2PoI0Pr59xq6mpUQ/W5f6s/fWT+zkJtKWlpfDz89PrORoiZ2dn2NraqttNH79zKXlVWJtejDXpJdifVwWZVDw02BV3Tw7D5ChPhHocH5RQV1sDY5BeUI2PNmfj532FqsPB1SMCcPXIQNU3V5zubb3vWCXm/3AAOWV1eHBaBK4ZGQiLfs16uWYnw/vPnqVdeDT6YPv666+rVdhT+frrr9UKxLXXXqt7X1RUFKytrfHMM8+oDWQne7rtxhtvxDXXXNPhhnvjjTfg5OSk7tioZx5hye3JX2zjw+tn/KVZJ7t+Hh4eOHToEAYPHqynszNclZWVKtzK7dYXZOVRnk6X8gJZmc2vqIeznRUmRXvjutGBmB4fBHdH4/t7pDocHC7Fu2sz8Edqoa7DwRUjg8+4K4MMW3hrTQZe/+Og6r/7090jEOVrmMMWeP/ZsyTTmUSwlbAq3Q5OJTAwsMv3Dxo0CM3NzWqThPapt84k8LYPvdobTn4I+YPYM7S3JW9P48TrZxrXrvP1i4yMxO7du9WKkjYAU0e9+TNfUFmHP9TGrwJsOFiIusYWhHo64IL4AEyN88HIMA+1GUxWIJ0cjWvyX091OOgss7AK9y1Nwp6jZbhzSn/cfU6UwQ9b4P1nz+nubWjwwdbd3V0dZyItLQ0WFhZqZYKIiI6LiIhQL3NyctQzXNQHJQa5FZqNX/vzkXS0HNJ9a3ioO+6dGo2pA3zUJK32f7yNrTZTVp6X7czBovWZOFRUjdHhHvjwhpGYHON9VsFObofPNmfhvz/vh5+LHb7++7gz2mRG5sHgg2137dmzR+3yHTFihFp9SE5Oxssvv6zqZaVnIxERHSf3k/7+/gy2vai+qRmbMop1YfZYeZ16Cj4x2gvXjQ3DlFgfk2hJ1VWHA+lOMLQHwmd+RR0e+HoP1qUV4toxIXjk/AFwsDGZ6EK9wGR+OqScYOXKlXj33XfVpq+AgADVEaF9/SwRER0ngXbLli1oaWlRz27R2ZMWXFInK0F2fXoRahqaEeRuj/MG+qnxtaPDPQ3+6fPT6nCw4RAW6zocBOHWicc7HJytH5OO4V/f7YWtlQU+ulFWfn165N8l02YywVa6IXz00Uf6Pg0iIqMKtuvWrUNhYaFqkUhn9jR5Wn6VGpIgYXZXdpl6/5BgN1UHKmE2xtfZpGosU/MqsXBdBn7YfQwONpa4YXwYrh8XBh9nux5bAX7s+734IekYLoj3x38uHgR3E1jZpr5hMsGWiIhOjzyzZW9vj6NHjzLYnoaGphZsOaQpMZBAe7S0VgW8iVFe+N9lg3FOrA+8nIyvi8FfBfgth0qwcG0GVrfrcHDlqJAz7nDQlfXphXjgqz2obmjCgiuG4KIhASb1oIB6H4MtEZGZkvIDWbU9cuQIhg8fru/TMWil1Q1YnSolBgVYm1aIqvomFe5kRVYGJciAADtrS5gabYeDt9dmIim7TK0+S/2sdDiwbjcY4mzVNjTjuRX78fGmLIzv74kXLk9AQNuwBaLTwWBLRGTGYmJi1ObbiooKbrRtRxoSHCyoVO24pMRgR1YpWlqBhCBX3JYYoQJtnL+Lya4m9laHg65IYJ63dDdySmvxxOw4XD82DBbSMoLoDDDYEhGZMelna2lpiezsbAwcOBDmSJ5mL6puwuHSemSV1mNdsTty8i1RtHkd7KwtMKG/F/57STzOjfWBj0vP1JEaS4eDGQN7rsNBZ43NLXjjj4N4Y/VB9SBh+f9NQH8fwxy2QMaDwZaIyIzJhEXpaSvlCKYebFtaW5FX2ajC6+GSOmSV1SOrpF69rG5oUZ9jY9kPrha2iHZvxf+uGInx/b1MssSgqw4H77d1OGhqacXlw6XDQQTCvRx75fsdLKjC/Ut3Y++xirZhC/17tLSBzBeDLRGRmRswYAB++OEHNYVMNpMZu6bmVhytqMcRCbBtq7DyMrusHvVNmqEH9tYWCHW3RaibLSZGuKiXoR628He2wa+/rFAb66R21tQdyKvAu2szVQcC2QB30/hw1eHA27l3Nr+1tLTik02H8eyKAwh0s8c3fx+nOkgQ9RQGWyIiMyd1tlI3mZWVpVonGov6phYckVXXtvCqDbBHy+vRrFmAhYutpQqwsd72mBHtpl4P87CFt6O1ydbHGkqHg85yy2tVx4MNB4tw3dhQzJ85APY2pr8aTn2LwZaIyMzJFLLw8HCDDbbVDc0dgqvm9TrkVjRCO3TW08EKYe62GBboiEsHeWgCrLsd3OwtzTbAdtXhYOW+PLyzrnc7HHTl+905eOy7vSrIfnLTKCRGe/fq9yPzxWBLRESIi4vD8uXL9VqOUFbb1CnA1qnXC6ubdJ/j52ytAuzEcBeEuttpygncbeFsy5W/7nY4GBPhgQ9lkld0z3c46KyspkFND/tpT64K0P++aCDcHDhsgXoPgy0REak6259//hmHDx9Wr/dVBwJteJW3y+ua1edY9gMCXW1UcJ0e466CrITXYDdbVRtLp9vh4BCKqxt6tcNBV6Tf74NfJ6keta9dNRQXJgT0yfcl88ZgS0REqhxBuiMcOnSoR4JtdzsQSFiV0DosyEkXYINcbbhD/izklNXigz7scNBZTUMTnv35AD7dnKWmscmwBT9X026TRoaDwZaIiJT4+Hh8++23qKqqgpOTU+91IGgLsNKBwJKN+I22w0FXdh0pxX1Lk9RGsacvGoi/jQlljTP1KQZbIiJSZOOYtbU1MjMzMXjw4A4fYwcCw+5w8M7aDKxJLUSAqx3mnz8AV4wM7tUOB10NW3j993S8uSYDgwJc8N71ExHp3b0HR0Q9icFWzwX90qTa1O90a2pq4ODQzD9sRojXz7hlFFShrq4Onjnl3b5+TsEDsH5/Do5aByGrrIEdCAyUPjscdCajh+d9mYSU3Ao1aEEGLrCUhPSFwVaPjpTUYNbrG/R9GkRkoupz09RL2+3aSNodsmM9GFhzjB0IDHRB5JudR7FoXSYOF9f0aYeDroYtfPTnYfzvlwMIdLfHsr+PQwKHLZCeMdjqUYiHA366ewLMY8XPgSs5RojXz7gl77JXK7Yjxozr9vVraWnB4i8+R1ywNxLHj+n1c6Tut836bHOWCpLS4WDmID8suHKo3qZ2yQjeB75OwsaDxbhhXBgemhHLYQtkEBhs9Ujmjw8KdIWpB6OqKku1EYXByPjw+hm3mhwn1NRYqPuZ07l+BcNjsW3bNjSNHgErK/6Z0Kfc8josWXMES7Zlqw4Hc4YH4ZY+7HDQ1X3Cd7tz8Pj3++BoY4VPbx6FiVEctkCGg/dYRETUwZAhQ7Bx40YcOXJEtQAj/XQ4WLg2Ez/qscNBZ6XVDXj0u2T8nJyHi4YE4OkLB8HVwVpv50PUFQZbIiLqwMvLCyEhIUhPT2ew7ePV0M2ZJVi47niHg/vODcffxveHs51+A+Tq1AI8+PUeNDS14I2rh2LWYA5bIMPEYEtERCcYNmwYvvvuO1RUVMDFxUXfp2PyHQ5+3ZeHhWszkHS0HLF+znjligRcEO+P+tqaPm3b1Vl1fRP++/N+fLHlCBKjvfHC5YPh68JhC2S4GGyJiOgEcXFx+OWXX5CWloYRI0bo+3TMpsPBRzeOxKS2Dgeygluvx/PbkSXDFnajoKIe/754EK4dHcJaezJ4DLZERHQCGdSQkJCApKQkDB06FJaW3PFuqh0OOpNyg9d+T8dbaw5icJAbPrpxlN42qxGdLgZbIiLqkqzUbtmyBYcPH0ZkZKS+T8fo5ZTV4v31h7Bk2xFdh4NbJ0YgzIBCY3p+Je79cjdS8yoxb2o0/j45ElYctkBGhMGWiIhOuoksPDwcBw4cYLA9C/tzK/Duukz8kHRM1cvePCEc143Vb4eDroYtfLDxEJ7/NVX1WP/2H+MRH2Ta7SjJNDHYEhHRSY0aNQpffvklioqKVNCl0+tw8M7aDKxN03Q4eOT8AbhyZDAc9bgZrCtHS2vwz6+S1PlKW7EHZ8SoPutExsiwfruIiMigREdHw9XVFfv378fEiRP1fTpG2+FA2mNZG9hT+hK+l+3MwZM/7IOznRW+uGU0xvXngxcybgy2RER0UhYWFmrV9vfff8fw4cPVeGXqusPB1zuOYtH6TGQV12BshGeHDgeGpqS6AY8sS8Yv+/JwydBAPHnhQLjac9gCGT8GWyIi+suetmvWrEFqaqrqkEAdOxx8uknT4aC0Rjoc+OO1K4ciwUA6HHTljwP5ePDrZDS1tOCta4bh/Hh/fZ8SUY9hsCUiolOys7NTgVZaf8XHx8PKin86pMPBe+sz8eW2bIPtcNDVsIX/LE/B4q3ZmBzjjecvGwwfDlsgE8N7JyIi+ktjxozBtm3bcPDgQcTGxsJcGUOHg65sP1yC+5YmobCyHv+9ZBCuHsVhC2SaGGyJiOgvubu7Y8CAAdi3b5/aUCa1t+ZCNlltyizGwrWZqsNBoJs9Hj1/AK4wwA4HXQ1beOW3NLWZTQZAfHLTKINeVSY6W4b9G0lERAZj/PjxWLRoEbKyslR/W3PscLDgiiG4YLC/wXU46IoMWZBhCzJ04f7zYnB7YgSHLZDJY7AlIqJuCQgIUIE2OTkZYWFhJvtUdmNLP2zI64eXX1qj63Dw8U2jkBjlZRT/Zwnk72/IxIu/piHU0wHf3TkegwI5bIHMA4MtERF1m/Sy/eSTT5CTk4OgoCCYgpqGZuzLr8Ge3BokHavGvrxANLf2w/nxrgbf4aCz7JIa3P9VErYdLsHN48Pxz+kctkDmhcGWiIi6TVZqAwMDsWfPHvXSGFYwOyurbVIhdk9utToOFtWhuRVwtbPEYH9HJLqVY3yYM26+YhiMqQ5Y+ug+9WOK6kf7xS1jMDbSU9+nRdTnGGyJiKjbJMgmJiZi8eLFyM3NVeUJhi6vskGtxGrCbA2OlNWr9/s5WyPe3wGz4zxUoA1xs1H/v59/3gsvO2cYi+KqesxfloyVKfm4bFgQnrgwDi52HLZA5onBloiITktUVBT8/f1VX1t5aUirti2trcgqrW+3IluDgqpG9bEwd1sMCXDEdcO9kRDgAB8nGxi7VSn5mL9sD1pagXeuHY4Zg/z0fUpEesVgS0REp0WC7KRJk7BkyRLk5eWpcKsvTc2tSC+q1QXZ5LwalNc1w7IfEO1tjymRLmo1dpCfA9zsTedPXlV9E57+cR+Wbj+Kc2N98Oxl8fBx5rAFItP5LScioj4jvWwl0O7atQt+fn59tmpb19iClAJNScGeY9VIya9FbVMLbK36Ic7HARcP9MDgAEfE+drDwUQ3TW09VIL7v9qN4qoGPHdpvOqna0ir5kT6xGBLRESnTYLUlClT8MUXX/Rqh4TK+mYk51YjqW1FNq2wTo2wdbKxQLy/I64b4Y0Ef0dEe9sZRW/Zs1Hf1IyXV6WpyWfDQ9zx2c2jEerJYQtE7THYEhHRGenfvz+Cg4PVqm1PdUgorGrU1cbKy0Ml9WgF4OVopUoKzot2Uy/DPWxhYUarlDLKd96Xu5FRWIUHpsuwhUhYWpjP/5+ouxhsiYjojEiQPffcc/HRRx+paWTSCux0W1QdLW/oEGSPVWg2egW72qgAe0WClyot8He2Nsun22XYwjtrM/DKqnSEezmqYQsDAzhsgehkGGyJiOiMhYaGqpXbnTt3IiQkBBYWFqcMaRnFdcc3euXWoKS2CbLwGOlph7GhstHLQQVaDwf+eZJhC/cuScKuoxW4dWIE7psWzWELRH+B9xxERHRWZNV24cKFSEtLQ2xsrO79Dc0tOFBQe3yiV34NqhtaYG3RD7E+9pgZ64aEAEcM9HWAky0DW/uV7KXbs/G0GrZghcW3jsGYCA5bIOoOBls9ampuQXmt5mk3U76Drq5uQD3qzfJpRGPH62fcymsaUFvXqBr49+b1s3ZyR8SAwdi0ax9KbP2wr0D6yFarUNvQ3AoHawvVbuuqIV5qNVZCra2VaW/0OlOFlTJsYQ9+21+AOcODcN+UEPh5Gs9IXyJ9M5pg+/7772Pjxo1ITU2FtbU11qxZc8LnSD/FZ599Ftu3b4eDgwNmzZqFO++8E1ZWhvnfzCyqxnmvrNP3aRCRiarPTVMvbdc09MF3k2EHMcAvR+FurxlNe/sYX/VSygy40emv/bovD48sS1avv/u34ZgW54uqqip9nxaRUTHMxNeFpqYm9XRXfHw8vv/++xM+3tzcjHvuuQeenp744IMPUFRUhCeeeEKFWgm3hsjf1Q6LrhsBU1/xq6urg52dHVf8jBCvn3E7sMcSDQ31iB8+vE+uX1LSbuQfTMYNl86Ek5NTr38/U1FZ14infkzB1zuOYuoAXzx3WTy8nGzV7x8RmWiwvf3229XLH3/8scuPb968GYcOHcJbb72lwm1MTAzuuOMOvP7667jtttvUKq+hcbazVo/ITZncMcuKg/yRYzAyPrx+xs21ygM1NTWYFOfbJ9cvMXIyXnttj9pIlpiY2OvfzxRszizG/UuTUFbTgOcvG4w5I4L4u0ZkDsH2ryQnJ6uduRJqtcaOHYvnnnsOGRkZHTY0tNfQ0KAOrfr6et0fdD5aPnva25G3pXHi9TNufX39bGxscM4552D58uXqPtfb2xvGrDdvt/rGZry0Kg3vbTiEEaHuWHzraAR7OHT4vvz9M268fj2ru7ejyQTb4uJieHh4dHifNuTKx07mww8/xKJFi3RvS+nCzJkz1SpVY6Npb+zqqx/E2tpa9TpXIYwPr59xk9VaebAu92d9df1kgUGOAwcOwM3NODc9OTs7w9bWttfqWw/kVWH+DweQVVKLeVPCcd3oIFhatJzw/fj7Z9x4/XqWduHRoIOtlAl8/PHHp/ycr7/++rSbfp+OG2+8Eddcc02HG+6NN95QT73KHRv1zCMsPpVtnHj9jJtsotXH9Rs/fry6b/f391ch19hUVlaqcNvTdcLSx3fhugws+C0dkd5O+P7O8Rjg73LSz+fvn3Hj9etZ3S0p1WuwvfbaazF79uxTfo6MaewOWZ3dt29fh/dpV2rblyd09dSZHJ1vOPkh5A9iz9Delrw9jROvn2lcu768fjK0YdCgQdixY4ca2mCsiwQ9eZtlFVfjvqVJ2HmkVI3DnTctCrZWf927l79/xo3Xr+d09zbUa7B1d3dXR0+QbgnSDaGkpERXkrBlyxY4OjoiIiKiR74HERF1z7Rp01R7xl27dmHMmDEw51W7Jduy8e+fUuDpZIOlt4/FyLCOZXNE1HOMpkO29KiVO0l52dLSol6XQ2rIhNxxhoeH4/HHH1fTbzZt2oS3334bc+fO7bAiS0REvU+eyp8yZYqqtZX2i+aooLIOt3y8HfOXJWP24ACsuCeRoZaolxnN5rF33nkHP/30k+5tbV2svH/EiBGwtLTEggUL1IAGqZu1t7dXAxq0bcKIiKhvjRo1Crt371YLDRdccAEsLIxmLeWs/bI3VwVaGUwh/cpNvbUjkaEwmmD75JNPquNUZKPCa6+91mfnREREJydBVhYYZHLk/v37MXDgQJi6irpGPPnDPizbmYPz4nzx7KXx8HQyzhpjImNkNMGWiIiMT1BQEEaOHKlqbWVTmSlPJPszowgPfLUH5bWNeHFOAi4bFshNQ0R9zHyeFyIiIr2QoQ1SHiYlCabYrL6usVltDrt60RYEudtjxT0TcflwThAj0gcGWyIi6lV2dnaqxjYnJweZmZkwJXtzyjH79Q34dFMWHj1/ABbfOkY3QYyI+h5LEYiIqNfFxMSoGtutW7ciICBAreAas6bmFryzVjNsIcrXGT/ePQExfs76Pi0is8cVWyIi6hMyrlw2lG3evBnG7HBRNeYu3ISXV6XhtsQINUGMoZbIMDDYEhFRn5CBOVKSkJWVhUOHDsHYSH3w51uyMPPV9SiqalDDFh6cEQsbK/4pJTIULEUgIqI+I+UIKSkpatXW19cXDg7GUY9aUFGHB7/ZgzWphbhqVAj+dcEAONryTyiRoeHDTCIi6lOyamtlZYU///zTKLokLN+Ti/MWrMPenAp8cMMI1ZuWoZbIMDHYEhFRn5JV2gsvvBBHjx5VI9ANlfSjvXfJLtz5xU6MjfDEynmJOCeWE8SIDBkfchIRUZ+Ljo7GsGHDsG3bNvj5+cHV1RWGJLW8H55bsA5VdU14eW4CLhnKYQtExoArtkREpBfTp0+Hs7Mz1q9fj5aWFn2fDppaWrEtuwrLizzwVoolwjwd8cu8RFw6jMMWiIwFV2yJiEgvbGxscNlll+GDDz5QI3eHDx/e5+fQ1NyKXceqsDqjAhsOVaC8rhmuVna4NKwZL94yGhYWDLRExoTBloiI9CYwMBBTpkzB77//Dn9/fzW8oc/C7MEKbDisCbMBLta4YIA7Jke64uDW1Qj0D2CoJTJCDLZERKRX48ePV6N2pSRBNpX1xlQyCbM7c6qwJqMC6w9VoKL+eJidEumKKC87XblBBvMskdFisCUiIr2SQHnppZfi7bffVuF26tSpakJZT4TZHSrMlmPDoUoVZgNdbDA7TrMy2z7MEpFpYLAlIiK9c3JyUvW2n376KZKTk5GQkHDWYXb9oUpUSph1ZZglMhcMtkREZBAiIiKQmJioVm29vb27XW/b2NyCHUersSZTszKrDbMXxrljSn9X9PdkmCUyFwy2RERkMCZNmqQGN6xbtw6zZ8+Go6PjKcPs6oxybDysCbNBrja4aKAHJke6MMwSmSkGWyIiMhhSWyv1tgsXLsSaNWswY8YMWFpanhBmpTVXVUOLLsxOiXRBJMMskdljsCUiIoMiq7Rz587FRx99hD83b4V10KAOYTbY1QaXDPJUK7MMs0TUHoOtHqXnV+KC1zbA1LWiFf3APzzGitfPeNUc2Yt+VtawX1ULY9TSOhTNe1rRuicLrv3q0N+qFOH2ZXBvrEW/VOBPOXrj+7a0ICQkpBf+ZSLqbQy2euTtbIt/zRoAU9ba2or6+gbY2tpwVcUI8foZr+amJvzvnqdw2xOvwtPbx2ivX+6xY4hwAUJcLNGvX3Cffd/Bgwf32fciop7DYKtHbg42uG5sGEw9GFVVValWPsb6h9Wc8foZL2mblbprC5CxEdddOM+Ir59p30cSUc86+w7YRERkUJqamvDvf/9bvf7SSy+hvr5e36dERNQnGGyJiEzM4sWLkZ6erl4/duwY3n//fX2fEhFRn2CwJSIy0dVarWeffZartkRkFlhjS0RkQmpra/H666/raqTlbXt7e9TU1MDW1lbfp0dE1KsYbImITIizszOmT5+uXufmPyIyNyxFICIiIiKTwGBLRERERCaBwZaIiIiITAKDLRERERGZBAZbIiIiIjIJDLZEREREZBLY7qsTaY8j2My8525PuS2tra3ZbsgI8foZN14/48brZ9x4/XqWNpdpc9rJMNh20tDQoF6+8sor+j4VIiIiIuqU0+zs7HAy/Vr/KvqamZaWFtXQ3MbGho+weoDclhdccAGWL1+umsSTceH1M268fsaN18+48fr1LImrEmrltrSwOHklLVdsO5Eby8XFRd+nYTIaGxvV7HoZ5clxnsaH18+48foZN14/48br1/NOtVKrxc1jRERERGQSGGyJiIiIyCQw2FKvklrlW2+9Vb0k48PrZ9x4/Ywbr59x4/XTD24eIyIiIiKTwBVbIiIiIjIJDLZEREREZBIYbImIiIjIJDDYEhEREZFJ4IAG6nHHjh3De++9h+3bt6O4uBheXl44//zzcdNNN6mZ2Vrp6en43//+h5SUFLi7u2Pu3Lm4/vrr9XrupPH+++9j48aNSE1NVddszZo1J3xOXl4enn32WXWdHRwcMGvWLNx5552wsuLdiiFYunQpPv30U/U7GBUVhQceeACDBg3S92lRJzt37lTXaf/+/SgqKsKLL76IyZMn6z4u+7sXLlyIb7/9Vk2ySkhIwMMPP4yQkBC9njdpfPjhh1i9ejUOHz6shjAMHjwYd999N8LCwnSfU19fjwULFmDlypVqctaYMWPUNfT09NTruZsqrthSj5NfcLkzfuSRR/Dll1/ivvvuwzfffIM333xT9zlyB33XXXfB399f3an/3//9H959910sW7ZMr+dOGjIt59xzz8Xll1/e5cebm5txzz33qMk6H3zwAZ588kn8+OOP6g8w6Z/8AX3llVdUq6HPPvsM0dHR6o9tSUmJvk+NOqmtrVUPPB566KEuP/7xxx9jyZIlmD9/Pj766CM1eUmupYQlMowHJnPmzFEBV/7GyX2n/G2T66r18ssvY926dXjuuefU3zl5ACMPNKmXSLsvot728ccft1544YW6t7/66qvWKVOmtDY0NOje99prr7VeeumlejpD6soPP/zQOmnSpBPev2HDhtaRI0e2FhUVdbimiYmJHa4p6cd1113X+txzz+nebm5ubp0xY0brhx9+qNfzolMbPnx46+rVq3Vvt7S0tJ533nmtn3zyie59lZWVrWPHjm395Zdf9HSWdColJSXqOu7YsUN3vUaPHt26atUq3eccOnRIfc6ePXv0eKamiyu21CdkhdbFxUX39p49ezB06NAOpQljx45FVlYWKioq9HSW1F3Jycno379/h6fS5PpVV1cjIyNDr+dm7mQV/cCBAxg9erTufRYWFhg1apT6vSPjkZOTo0pJ5NppOTk5qZIS+R0kw/xbJ7R/76TERFZx2/8+SpmCn58ffx97CYMt9brs7GxVknDppZfq3id31h4eHh0+T/u2fIwMW1fXTxtyef30q6ysTJWKdPX7xWtjXLTXq3MtJq+lYWppacFLL72k6qDlgb+Q6yQLOM7Ozh0+l9ew93CXB3Xb66+/ruq9TuXrr7/uUDRfUFCg6sGmTp2KSy65pA/Oknry+hERUffIZmh5xko2T5P+MNhSt1177bWYPXv2KT8nMDBQ93phYSHuuOMOtUv00Ucf7fB5sgLReSOL9m3uFDWM63cqco327dvXrdUl6ltubm6wtLTs8veL18a4tH8WRLrLtL+WsiGQDCvUbtiwQW0O8/X17XANpTyosrKyw6otfx97D4MtdZu05JKjO2SlVkJtbGwsnnjiCVXj156E3bfeekvVHmnbQ23ZsgWhoaEdanFJP9fvr8THx6tuCHLnrH3KW66fo6MjIiIieuR70JmRpz3l927r1q26tlHyFOm2bdtUSz0yHvJAU8KPXLuYmBhdDefevXtx2WWX6fv0qK0d2/PPP69aIkpXmM6LAwMGDFB/4+T3UTrNaDsHSbtE+TtIPY/BlnqchNrbb79dtfK69957UVpaqvuYdtVhxowZWLRoEZ5++mnVu1aevlm8eLFqDUb6J3e65eXl6qWEIulnK4KDg1XPWunDGB4ejscff1y1apMVpbffflsFJxsbG32fvtm75pprVAu2uLg4DBw4EF988YVqP/RXK/bU92pqatQ+hPYbxuT3zdXVVW0wuuqqq1Rfafndk9Akv2fe3t4det2Sfldqf/nlF1VbK/eN0spLu8lPWrPJy4suuki135NrKg/+X3jhBRVqZYGAel4/aY3QC/8umTHpZ/rUU091+TFp5t/VgAZ5+lRC0Q033NCHZ0onI6Hop59+OuH977zzDkaMGKFez83NVQMaduzYAXt7ezWgQfo3ckCDYZANm9oBDfK0NQc0GCa5T5RntzqT3yf5PWw/oEGezh4yZIjqeSvPbpH+ae8PO5NnKrUPJLUDGn799Vc1oEE6yMg1bF9eQj2HwZaIiIiITALbfRERERGRSWCwJSIiIiKTwGBLRERERCaBwZaIiIiITAKDLRERERGZBAZbIiIiIjIJDLZEREREZBIYbImIjIw0fpfG8HJI0359DBXQfv/777+/z78/EdHJcEQQEZEBTZzSGj58uJo4dTLytRdffLEa2dnXEhISdGNEZZISEZGhYLAlItIDbTjsbN26dWpU8Zw5c0759TKXXl8jOa2trdX3trW1ZbAlIoPCUgQiIj2Gw/aHlBW8+uqruPHGGzF16tTT+vd+/PFHTJ48GevXr8ell16K8ePH48EHH0RdXR1++uknVb4wZcoUvPDCC2hubtZ9nbz/vffew+OPP46JEydi1qxZWLt2LUpLS3Hfffep91155ZVISUnphVuBiKhnMdgSERkACbVSrzps2DD8/e9/P6N/Q0LskiVL8Mwzz+D111/Hjh078M9//hMbN25Ugfnpp5/GsmXL8Pvvv3f4usWLF6sV5M8//xwTJkxQIfeJJ57A+eefj88++wxBQUHq7dbW1h763xIR9Q4GWyIiPWtpacGjjz4KS0tL/Oc//0G/fv3O6N9pamrC/PnzERsbqwLyueeei927d+Oxxx5DRESEWn2VDV9S39veuHHjcNlllyEkJAS33HILqqurERcXp1aNQ0NDcf311+PQoUMoLi7uof8xEVHvYLAlItKzN998E8nJyWozlqOj4xn/O3Z2dmp1VcvT0xMBAQGqHlfLw8NDlRm0FxUV1eFrRP/+/Tt8jej8dUREhoabx4iI9OjXX39VT/cvWLBArZieDSsrq798n6wGywrxyT5Hu1rc1fs6fx0RkaHhii0RkZ6kpqbi3//+N+666y6MHTtW36dDRGT0uGJLRKQHZWVlamOX9KudOXMmioqKOnxc6m3d3d31dn5ERMaIwZaISA82bNiA3NxcdcyYMeOEj/v7+6sWXkRE1H39Wtm/hYjIqEjv2auuugpXX321Xs/jySefVG3KZNMbEZEhYI0tEZERkj610r6rqqqqz7/3rl271PdesWJFn39vIqJT4YotEZGRkfIF6VkrAgMDYWHRt2sUMgiisLBQvW5vb6+30b5ERJ0x2BIRERGRSWApAhERERGZBAZbIiIiIjIJDLZEREREZBIYbImIiIjIJDDYEhEREZFJYLAlIiIiIpPAYEtEREREJoHBloiIiIhMAoMtEREREcEU/D8FBAvlBDY4fQAAAABJRU5ErkJggg==",
                        "text/plain": [
                            "<Figure size 1000x400 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# view in 2D\n",
                "singlet.draw(num_rays=10)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "> **Note:**  \n",
                "The `draw()` method returns the matplotlib figure and axes.  \n",
                "When running Optiland in a script, you must explicitly call `plt.show()` or `fig.show()` to display the plot.  \n",
                "\n",
                "In Jupyter notebooks, figures are displayed automatically."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {
                "vscode": {
                    "languageId": "plaintext"
                }
            },
            "source": [
                "## Defining a lens, in detail:\n",
                "\n",
                "### Create the optic:\n",
                "\n",
                "In Optiland, lenses are instances of the \"Optic\" class. The process for defining a lens starts with creating an empty \"Optic\" object as follows:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.423198Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.423024Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.425574Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.425069Z"
                }
            },
            "outputs": [],
            "source": [
                "lens = optic.Optic()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Add the object surface:\n",
                "\n",
                "We now want to populate the lens object with surfaces. Let's first add the object surface, which will be at infinity and will have a radius of infinity, i.e. it is a plane. We add the surface by calling the \"add_surface\" method. We must specify the index as 0 to indicate this is the first surface."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.427287Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.427113Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.430092Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.429706Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.surfaces.add(index=0, radius=np.inf, thickness=np.inf)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Add a lens:\n",
                "\n",
                "Let's now add a singlet lens. The lens will be defined as follows:\n",
                "\n",
                "- Material: N-SF11\n",
                "- Thickness: 7 mm\n",
                "- Radius side 1: 20 mm\n",
                "- Radius side 2: infinity\n",
                "- Stop surface: 1\n",
                "\n",
                "Optiland defines lenses one surface at a time, so we define each side of the lens separately. The material always corresponds to the material after interaction with a surface (refraction or reflection). Likewise, the thickness corresponds to the thickness after the surface and it is positive for surfaces to the right. This also implies that we must define the distance from the second surface to the next surface, which we'll define as 18 mm.\n",
                "\n",
                "Note that we specify the indices of the two surfaces as 1 and 2, after we already specified the object plane with index 0. Also note that Optiland uses millimeters by default."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.431847Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.431661Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.442045Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.441550Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.surfaces.add(index=1, thickness=7, radius=20, is_stop=True, material=\"N-SF11\")\n",
                "lens.surfaces.add(index=2, radius=np.inf, thickness=18)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Add image plane:\n",
                "\n",
                "Lastly, let's add the image plane. By default, the radius is infinity, so we can exclude it. We also can omit thickness, as there are no surfaces beyond the image. We need only to define the index, which is 3."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.443770Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.443592Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.446824Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.446476Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.surfaces.add(index=3)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Define aperture:\n",
                "\n",
                "Now, we can define the aperture of the system. Let's choose entrance pupil diameter (EPD) as the aperture type with a value of 25 mm.\n",
                "\n",
                "The options for aperture type are:\n",
                "\n",
                "- 'EPD' - entrance pupil diameter\n",
                "- 'imageFNO' - image-space F-number\n",
                "- 'objectNA' - object-space numerical aperture\n",
                "- 'float_by_stop_size' - the aperture size _floats_ with the size of the stop _diameter_, which is defined by the `value` argument."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.449126Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.448555Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.451582Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.451186Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.set_aperture(aperture_type=\"EPD\", value=25)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Define fields:\n",
                "\n",
                "Let's add the fields of the lens. We'll keep it simple and add a single field of type \"angle\" with a value of 0.\n",
                "\n",
                "The options for field types are:\n",
                "\n",
                "- 'angle' - the angle of the field in object space\n",
                "- 'object_height' - the height of the object\n",
                "- 'paraxial_image_height' - the image height of a paraxial chief ray\n",
                "- 'real_image_height' - the image height of a real chief ray"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.453319Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.453147Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.455516Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.455154Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.fields.set_type(field_type=\"angle\")\n",
                "lens.fields.add(y=0)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Define wavelengths:\n",
                "\n",
                "Lastly, let's define the wavelengths of the system. We define a single wavelength at 0.5 \u00b5m. Similar to fields, wavelengths can be assigned a weight to emphasize specific spectral regions."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.457129Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.456963Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.459690Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.459235Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.wavelengths.add(value=0.5, is_primary=True)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### View the lens:\n",
                "\n",
                "Let's view the lens in 2D. We can do this by calling the `draw` method.\n",
                "\n",
                "Note that you can also pass a `projection` argument, allowing you to plot in the `\"YZ\"` plane (default), `\"XZ\"` plane, or `\"XY\"` plane.\n",
                "\n",
                "The 2D visualization is now interactive! You can hover over surfaces, lenses, and ray bundles to get more information. You can also customize the look and feel of the plots using themes. See the gallery for an example of how to use themes."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.461595Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.461379Z",
                    "iopub.status.idle": "2026-03-24T10:11:57.534768Z",
                    "shell.execute_reply": "2026-03-24T10:11:57.534269Z"
                }
            },
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(<Figure size 1000x400 with 1 Axes>, <Axes: xlabel='Z [mm]', ylabel='Y [mm]'>)"
                        ]
                    },
                    "execution_count": 11,
                    "metadata": {},
                    "output_type": "execute_result"
                },
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 1000x400 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "lens.draw(num_rays=10)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {
                "tags": [
                    "nbsphinx-toctree"
                ]
            },
            "source": [
                "Finally, we view the lens in 3D using the \"draw3D\" function. Note that this opens a new window."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "metadata": {
                "execution": {
                    "iopub.execute_input": "2026-03-24T10:11:57.536757Z",
                    "iopub.status.busy": "2026-03-24T10:11:57.536579Z",
                    "iopub.status.idle": "2026-03-24T10:11:59.921302Z",
                    "shell.execute_reply": "2026-03-24T10:11:59.920406Z"
                }
            },
            "outputs": [],
            "source": [
                "lens.draw3D()"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": ".venv",
            "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": "3.13.2"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}