{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "# Orthogonal Descent Optimization"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [],
            "source": [
                "import numpy as np\n",
                "\n",
                "from optiland import optic, optimization"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Define a starting lens:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 1000x400 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "lens = optic.Optic()\n",
                "\n",
                "# add surfaces\n",
                "lens.surfaces.add(index=0, thickness=np.inf)\n",
                "lens.surfaces.add(index=1, thickness=7, radius=1000, material=\"N-SF11\", is_stop=True)\n",
                "lens.surfaces.add(index=2, thickness=30, radius=-1000)\n",
                "lens.surfaces.add(index=3)\n",
                "\n",
                "# set aperture\n",
                "lens.set_aperture(aperture_type=\"EPD\", value=15)\n",
                "\n",
                "# add field\n",
                "lens.fields.set_type(field_type=\"angle\")\n",
                "lens.fields.add(y=0)\n",
                "\n",
                "# add wavelength\n",
                "lens.wavelengths.add(value=0.55, is_primary=True)\n",
                "\n",
                "# draw lens\n",
                "_ = lens.draw(num_rays=5)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Define optimization problem:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [],
            "source": [
                "problem = optimization.OptimizationProblem()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Add operands (targets for optimization):"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [],
            "source": [
                "\"\"\"\n",
                "Define RMS spot size properties for the optimization:\n",
                "    1. Surface number = -1, implying last surface (image surface)\n",
                "    2. Normalized field coordinates (Hx, Hy) = (0, 0)\n",
                "    3. Number of rays = 5, corresponds to number of rings in hexapolar distribution\n",
                "        (see distribution documentation)\n",
                "    4. Wavelength = 0.55 µm\n",
                "    5. Pupil distribution = hexapolar\n",
                "\"\"\"\n",
                "\n",
                "input_data = {\n",
                "    \"optic\": lens,\n",
                "    \"surface_number\": -1,\n",
                "    \"Hx\": 0,\n",
                "    \"Hy\": 0,\n",
                "    \"num_rays\": 5,\n",
                "    \"wavelength\": 0.55,\n",
                "    \"distribution\": \"hexapolar\",\n",
                "}\n",
                "\n",
                "# add RMS spot size operand\n",
                "problem.add_operand(\n",
                "    operand_type=\"rms_spot_size\",\n",
                "    target=0,\n",
                "    weight=1,\n",
                "    input_data=input_data,\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Define variables - let radius of curvature vary for both surfaces, at surface index 1 and 2:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [],
            "source": [
                "problem.add_variable(lens, \"radius\", surface_number=1)\n",
                "problem.add_variable(lens, \"radius\", surface_number=2)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Check initial merit function value and system properties:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "╒════╤════════════════════════╤═══════════════════╕\n",
                        "│    │   Merit Function Value │   Improvement (%) │\n",
                        "╞════╪════════════════════════╪═══════════════════╡\n",
                        "│  0 │                30.0924 │                 0 │\n",
                        "╘════╧════════════════════════╧═══════════════════╛\n",
                        "╒════╤════════════════╤══════════╤══════════════╤══════════════╤══════════╤═════════╤═════════╤════════════════╕\n",
                        "│    │ Operand Type   │   Target │ Min. Bound   │ Max. Bound   │   Weight │   Value │   Delta │   Contrib. [%] │\n",
                        "╞════╪════════════════╪══════════╪══════════════╪══════════════╪══════════╪═════════╪═════════╪════════════════╡\n",
                        "│  0 │ rms spot size  │        0 │              │              │        1 │   5.486 │   5.486 │            100 │\n",
                        "╘════╧════════════════╧══════════╧══════════════╧══════════════╧══════════╧═════════╧═════════╧════════════════╛\n",
                        "╒════╤═════════════════╤═══════════╤═════════╤══════════════╤══════════════╕\n",
                        "│    │ Variable Type   │   Surface │   Value │ Min. Bound   │ Max. Bound   │\n",
                        "╞════╪═════════════════╪═══════════╪═════════╪══════════════╪══════════════╡\n",
                        "│  0 │ radius          │         1 │    1000 │              │              │\n",
                        "│  1 │ radius          │         2 │   -1000 │              │              │\n",
                        "╘════╧═════════════════╧═══════════╧═════════╧══════════════╧══════════════╛\n"
                    ]
                }
            ],
            "source": [
                "problem.info()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Define optimizer (Orthogonal Descent):"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [],
            "source": [
                "optimizer = optimization.OrthogonalDescent(problem)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Run optimization:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [],
            "source": [
                "optimizer.optimize(max_iter=100, tol=1e-3)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Print merit function value and system properties after optimization:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "╒════╤════════════════════════╤═══════════════════╕\n",
                        "│    │   Merit Function Value │   Improvement (%) │\n",
                        "╞════╪════════════════════════╪═══════════════════╡\n",
                        "│  0 │             0.00188088 │           99.9657 │\n",
                        "╘════╧════════════════════════╧═══════════════════╛\n",
                        "╒════╤════════════════╤══════════╤══════════════╤══════════════╤══════════╤═════════╤═════════╤════════════════╕\n",
                        "│    │ Operand Type   │   Target │ Min. Bound   │ Max. Bound   │   Weight │   Value │   Delta │   Contrib. [%] │\n",
                        "╞════╪════════════════╪══════════╪══════════════╪══════════════╪══════════╪═════════╪═════════╪════════════════╡\n",
                        "│  0 │ rms spot size  │        0 │              │              │        1 │   0.043 │   0.043 │            100 │\n",
                        "╘════╧════════════════╧══════════╧══════════════╧══════════════╧══════════╧═════════╧═════════╧════════════════╛\n",
                        "╒════╤═════════════════╤═══════════╤════════════╤══════════════╤══════════════╕\n",
                        "│    │ Variable Type   │   Surface │      Value │ Min. Bound   │ Max. Bound   │\n",
                        "╞════╪═════════════════╪═══════════╪════════════╪══════════════╪══════════════╡\n",
                        "│  0 │ radius          │         1 │    28.0266 │              │              │\n",
                        "│  1 │ radius          │         2 │ -1000      │              │              │\n",
                        "╘════╧═════════════════╧═══════════╧════════════╧══════════════╧══════════════╛\n"
                    ]
                }
            ],
            "source": [
                "problem.info()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Draw final lens:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "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=5)"
            ]
        }
    ],
    "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
}