go_05_chief_marginal_ray.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#### Chief ray and marginal ray"
      ],
      "metadata": {
        "id": "av05X0bcP2dP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import sympy as smp\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.patches import Arc, Rectangle, Ellipse, Circle\n",
        "import numpy as np\n",
        "\n",
        "np.random.seed(42)\n",
        "np.set_printoptions(formatter={'float': '{: 0.4f}'.format})\n",
        "\n",
        "plt.style.use('dark_background')\n",
        "\n",
        "# color: https://matplotlib.org/stable/gallery/color/named_colors.html"
      ],
      "metadata": {
        "id": "Ju6hrXHLa1l-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def chief_marginal_ray(ax, title=None, title_loc='center', fontsize=12):\n",
        "    # Distances\n",
        "    d = 0.05\n",
        "    f = 0.4\n",
        "\n",
        "    # lens 1\n",
        "    lens_1 = Ellipse((-2*f,0), 0.1, 0.7, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    ax.add_patch(lens_1)\n",
        "\n",
        "    # lens 2\n",
        "    eyepiece = Ellipse((2*f,0), 0.1, 0.7, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    ax.add_patch(eyepiece)\n",
        "\n",
        "    # Ray 1 (start from center)\n",
        "    ax.plot([-4*f, 5*f], [0, 0], 'r', linewidth=2)\n",
        "    ax.plot([-4*f, -2*f],[0, f/4], 'r', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-4*f, -2*f],[0, -f/4], 'r', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-2*f, 2*f],[f/4, f/4], 'r', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-2*f, 2*f],[-f/4, -f/4], 'r', linewidth=2, alpha=0.2)\n",
        "    ax.plot([2*f, 5*f],[f/4, -f/8], 'r', linewidth=2, alpha=0.2)\n",
        "    ax.plot([2*f, 5*f],[-f/4, f/8], 'r', linewidth=2, alpha=0.2)\n",
        "    ax.arrow(-3*f, 0, 0.001, 0,  head_width=0.04, head_length=0.06, fc='r', ec='none', zorder=5)\n",
        "    source_red = Circle((-4*f,0), 0.02, edgecolor='none', facecolor='red', zorder=-6)\n",
        "    ax.add_patch(source_red)\n",
        "    focus_red = Circle((4*f,0), 0.02, edgecolor='none', facecolor='red', zorder=-6)\n",
        "    ax.add_patch(focus_red)\n",
        "\n",
        "    # Ray 2 (start from top)\n",
        "    ax.plot([-4*f, -2*f], [f/4, f/4], 'c', linewidth=2)\n",
        "    ax.plot([-4*f, -2*f],[f/4, f/2], 'c', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-4*f, -2*f],[f/4, 0], 'c', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-2*f, 2*f],[f/4, -f/4], 'c', linewidth=2)\n",
        "    ax.plot([2*f, 5*f],[-f/4, -f/4], 'c', linewidth=2)\n",
        "    ax.plot([-2*f, 5*f],[f/2, -3*f/8], 'c', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-2*f, 2*f],[0, -f/2], 'c', linewidth=2, alpha=0.2)\n",
        "    ax.plot([2*f, 5*f],[-f/2, -f/8], 'c', linewidth=2, alpha=0.2)\n",
        "    ax.arrow(-3*f, f/4, 0.001, 0,  head_width=0.04, head_length=0.06, fc='c', ec='none', zorder=5)\n",
        "    source_green = Circle((-4*f,f/4), 0.02, edgecolor='none', facecolor='c', zorder=-6)\n",
        "    ax.add_patch(source_green)\n",
        "    focus_green = Circle((4*f,-f/4), 0.02, edgecolor='none', facecolor='c', zorder=-6)\n",
        "    ax.add_patch(focus_green)\n",
        "\n",
        "    # Ray 3 (start from bottom)\n",
        "    ax.plot([-4*f, -2*f], [-f/4, -f/4], 'y', linewidth=2)\n",
        "    ax.plot([-4*f, -2*f],[-f/4, -f/2], 'y', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-4*f, -2*f],[-f/4, 0], 'y', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-2*f, 2*f],[-f/4, f/4], 'y', linewidth=2)\n",
        "    ax.plot([2*f, 5*f],[f/4, f/4], 'y', linewidth=2)\n",
        "    ax.plot([-2*f, 5*f],[-f/2, 3*f/8], 'y', linewidth=2, alpha=0.2)\n",
        "    ax.plot([-2*f, 2*f],[0, f/2], 'y', linewidth=2, alpha=0.2)\n",
        "    ax.plot([2*f, 5*f],[f/2, f/8], 'y', linewidth=2, alpha=0.2)\n",
        "    ax.arrow(-3*f, -f/4, 0.001, 0,  head_width=0.04, head_length=0.06, fc='y', ec='none', zorder=5)\n",
        "    source_blue = Circle((-4*f,-f/4), 0.02, edgecolor='none', facecolor='y', zorder=-6)\n",
        "    ax.add_patch(source_blue)\n",
        "    focus_blue = Circle((4*f,f/4), 0.02, edgecolor='none', facecolor='y', zorder=-6)\n",
        "    ax.add_patch(focus_blue)\n",
        "\n",
        "    # Aperture\n",
        "    aperture_top = Rectangle((-0.025, f/4+0.01), 0.05, f/2, linewidth=1, edgecolor='none', facecolor='w', alpha=0.9)\n",
        "    ax.add_patch(aperture_top)\n",
        "    aperture_bottom = Rectangle((-0.025, -f/4-0.01), 0.05, -f/2, linewidth=1, edgecolor='none', facecolor='w', alpha=0.9)\n",
        "    ax.add_patch(aperture_bottom)\n",
        "    ax.text(0, 3*f/4+0.07, 'aperture', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "\n",
        "    # Set limits and aspect ratio\n",
        "    ax.set_xlim(-1.7, 2)\n",
        "    ax.set_ylim(-0.5, 0.5)\n",
        "    ax.set_aspect('equal')\n",
        "    ax.grid(True)\n",
        "    ax.axis('off')\n",
        "\n",
        "    if title:\n",
        "        ax.set_title(title, loc=title_loc, fontsize=fontsize)"
      ],
      "metadata": {
        "id": "c-J0NJQTxSSY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots(figsize=(10, 3))\n",
        "\n",
        "chief_marginal_ray(ax, title='Chief and Marginal Rays')\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "QJrtBLoZ4Rfu",
        "outputId": "15249d3a-c59b-48ee-dd35-a3865dfee073"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Chief rays go through center of aperture \\\n",
        "Marginal rays go pass edge aperture"
      ],
      "metadata": {
        "id": "97aiEMkg3JAn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Aperture size and depth of focus"
      ],
      "metadata": {
        "id": "5J1EmqqEQT2T"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def depth_of_focus(ax, title=None, title_loc='center', fontsize=12):\n",
        "    # Distances\n",
        "    d = 0.05\n",
        "    f = 0.4\n",
        "\n",
        "    # lens 1\n",
        "    lens_1 = Ellipse((-2*f,0), 0.1, 0.7, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    ax.add_patch(lens_1)\n",
        "\n",
        "    # lens 2\n",
        "    eyepiece = Ellipse((2*f,0), 0.1, 0.7, edgecolor='none', facecolor='skyblue', zorder=-5)\n",
        "    ax.add_patch(eyepiece)\n",
        "\n",
        "    # Ray 1 (start from center)\n",
        "    ax.plot([-4*f, 5*f], [0, 0], 'r', linewidth=2)\n",
        "    ax.plot([-4*f, -2*f],[0, f/4], 'r', linewidth=2)\n",
        "    ax.plot([-4*f, -2*f],[0, -f/4], 'r', linewidth=2)\n",
        "    ax.plot([-2*f, 2*f],[f/4, f/4], 'r', linewidth=2)\n",
        "    ax.plot([-2*f, 2*f],[-f/4, -f/4], 'r', linewidth=2)\n",
        "    ax.plot([2*f, 5*f],[f/4, -f/8], 'r', linewidth=2)\n",
        "    ax.plot([2*f, 5*f],[-f/4, f/8], 'r', linewidth=2)\n",
        "    ax.plot([-4*f, -2*f], [0, f/2], 'r', linewidth=2, alpha=0.4)\n",
        "    ax.plot([-4*f, -2*f], [0, -f/2], 'r', linewidth=2, alpha=0.4)\n",
        "    ax.plot([-2*f, 2*f],[f/2, f/2], 'r', linewidth=2, alpha=0.4)\n",
        "    ax.plot([-2*f, 2*f],[-f/2, -f/2], 'r', linewidth=2, alpha=0.4)\n",
        "    ax.plot([2*f, 5*f],[f/2, -f/4], 'r', linewidth=2, alpha=0.4)\n",
        "    ax.plot([2*f, 5*f],[-f/2, f/4], 'r', linewidth=2, alpha=0.4)\n",
        "    ax.arrow(-3*f, 0, 0.001, 0,  head_width=0.04, head_length=0.06, fc='r', ec='none', zorder=5)\n",
        "    source_red = Circle((-4*f,0), 0.02, edgecolor='none', facecolor='red', zorder=-6)\n",
        "    ax.add_patch(source_red)\n",
        "    focus_red = Circle((4*f,0), 0.02, edgecolor='none', facecolor='red', zorder=-6)\n",
        "    ax.add_patch(focus_red)\n",
        "\n",
        "    # Aperture\n",
        "    aperture_top = Rectangle((-0.025, f/4+0.01), 0.05, f/2, linewidth=1, edgecolor='none', facecolor='w', alpha=0.9)\n",
        "    ax.add_patch(aperture_top)\n",
        "    aperture_bottom = Rectangle((-0.025, -f/4-0.01), 0.05, -f/2, linewidth=1, edgecolor='none', facecolor='w', alpha=0.9)\n",
        "    ax.add_patch(aperture_bottom)\n",
        "    ax.text(0, 3*f/4+0.07, 'aperture', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "\n",
        "    # f_t distance\n",
        "    ax.plot([5.1*f, 5.2*f], [f/4, f/4], 'w-', linewidth=1)\n",
        "    ax.plot([5.1*f, 5.2*f], [-f/4, -f/4], 'w-', linewidth=1)\n",
        "    ax.plot([5.15*f, 5.15*f], [f/4, -f/4], 'w-', linewidth=1)\n",
        "    ax.arrow(5.15*f, f/4-0.06, 0, 0,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.arrow(5.15*f, -f/4+0.06, 0, -0.001,  head_width=0.04, head_length=0.06, fc='w', ec='none')\n",
        "    ax.text(6*f, 0, 'larger aperture \\nsmaller DoF', horizontalalignment='center', verticalalignment='center', fontsize=fontsize, color='w')\n",
        "\n",
        "    # Set limits and aspect ratio\n",
        "    ax.set_xlim(-1.7, 2.5)\n",
        "    ax.set_ylim(-0.5, 0.5)\n",
        "    ax.set_aspect('equal')\n",
        "    ax.grid(True)\n",
        "    ax.axis('off')\n",
        "\n",
        "    if title:\n",
        "        ax.set_title(title, loc=title_loc, fontsize=fontsize)"
      ],
      "metadata": {
        "id": "l9PbqOli34-y"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig_2, ax_2 = plt.subplots(figsize=(12, 3))\n",
        "\n",
        "depth_of_focus(ax_2, title='Depth of Focus')\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        },
        "id": "i3a5AUs-4TjG",
        "outputId": "03a01290-1098-4ea3-d521-93db94beedbb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x300 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "uXc_LPxz6dKs"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}