{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "81b4222f",
   "metadata": {},
   "source": [
    "# Tutorial 1 - System with Rotation\n",
    "\n",
    "This notebok shows how to setup an optical system and how to do some irradiance calculations with diffinytrace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "88d88edf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "import gc\n",
    "import tqdm\n",
    "sys.path.insert(0, os.path.abspath(\"..\"))\n",
    "device = \"cuda:0\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e4eda394",
   "metadata": {},
   "outputs": [],
   "source": [
    "import diffinytrace as dit\n",
    "import torch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da4b472a",
   "metadata": {},
   "source": [
    "Diffinytrace implements multiple refractive indices from the RefractiveIndex.Info database; however, it is also possible to define custom materials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d37d9dce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "NBK7 = dit.materials[\"NBK7\"]\n",
    "dit.plotting.wavelength.plot(NBK7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1381e2e",
   "metadata": {},
   "source": [
    "Defining a light source is very straightforward. All objects in Diffinytrace need to be initialized with a transform. One simple transform is the offset transform, which sets the position relative to the origin or a parent transform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ef4702e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "z_pos = 0.0\n",
    "lens_thickness = 3.0\n",
    "\n",
    "wave_len = 1.024\n",
    "light_transforms = dit.transforms.Offset(torch.tensor([0.0,0.0,0.0]))\n",
    "light_source = dit.source.CollimatedMonochromatic(light_transforms,8.0,wave_len)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b2bfce1",
   "metadata": {},
   "source": [
    "This code defines a lens element in the optical system:\n",
    "\n",
    "- `plane_surface = dit.Plane()`: Creates a planar surface for the front of the lens.\n",
    "- `surface2 = dit.Aspheric(-1/50.)`: Creates an aspheric surface for the back of the lens with a specified curvature.\n",
    "- `transf1 = dit.transforms.Distance(10.0, parent_transform=light_transforms)`: Positions the lens 10 units away from the light source using a distance transform.\n",
    "- `lens1 = dit.Lens(transf1, lens_thickness, plane_surface, surface2, NBK7, 13.0)`: Constructs the lens object with the specified transform, thickness, surfaces, material (`NBK7`), and aperture radius.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5d17c3cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "plane_surface = dit.Plane()\n",
    "surface2 = dit.Aspheric(-1/50.)\n",
    "transf1 = dit.transforms.Distance(10.0,parent_transform=light_transforms)\n",
    "lens1 = dit.Lens(transf1,lens_thickness,plane_surface,surface2,NBK7,13.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "702905a5",
   "metadata": {},
   "source": [
    "It is also possible to set a lens as the `parent_transform`. In this case, the \"real\" parent transform will be the last transform of the back surface of the lens. This allows to easily chain optical elements together in a sequence, ensuring that each new element is positioned relative to the previous one in the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1f754a6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "surface3 = dit.Aspheric(-1/50.)\n",
    "surface4 = dit.Aspheric(0.0)#Plane()\n",
    "transf2 = dit.transforms.Distance(10.0,parent_transform=lens1)\n",
    "lens2 = dit.Lens(transf2,lens_thickness,surface3,surface4,NBK7,17.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69935bdc",
   "metadata": {},
   "source": [
    "This code adds a mirror and a detector to the optical system:\n",
    "\n",
    "- `transf3 = dit.transforms.Compose([dit.transforms.Distance(30., parent_transform=lens2), dit.transforms.Rotation(45., axis=0)])`: Creates a composite transform that first positions the mirror 30 units away from `lens2`, then rotates it 45 degrees around the x-axis.\n",
    "- `surface5 = dit.Aspheric(-1/75.)`: Defines an aspheric surface for the mirror.\n",
    "- `mirror = dit.Mirror(transf3, surface5, 25.0)`: Creates a mirror object with the specified transform, surface, and aperture radius.\n",
    "- `transf4 = dit.transforms.Compose([transf3, dit.transforms.Rotation(45., axis=0), dit.transforms.Distance(-40.0)])`: Creates a composite transform for the detector by applying an additional 45-degree rotation and then moving it -40 units from the mirror.\n",
    "- `detector = dit.Detector(transf4, plane_surface, 8.0)`: Creates a detector object with the specified transform, planar surface, and aperture radius.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3cb8b0ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "transf3 = dit.transforms.Compose([dit.transforms.Distance(30.,parent_transform=lens2),dit.transforms.Rotation(45.,axis=0)])\n",
    "surface5 = dit.Aspheric(-1/75.)#Plane()\n",
    "mirror = dit.Mirror(transf3,surface5,25.0)\n",
    "transf4 = dit.transforms.Compose([transf3,dit.transforms.Rotation(45.,axis=0),dit.transforms.Distance(-40.0)])\n",
    "detector = dit.Detector(transf4,plane_surface,8.0)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0208a31c",
   "metadata": {},
   "source": [
    "Last but not least, we need to set up a sequential optical system. This takes as input a dictionary of optical elements, which will later be used during ray tracing. When tracing rays, a sequence must be provided, and the sequential optical system will perform ray tracing according to the specified order of elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c6583f46",
   "metadata": {},
   "outputs": [],
   "source": [
    "system = dit.SequentialOpticalSystem({\"light_source\":light_source,\"lens1\":lens1,\"mirror\":mirror,\"detector\":detector,\"lens2\":lens2})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fa50fed",
   "metadata": {},
   "source": [
    "Diffinytrace also supports automated annotation of the optical system, making it easy to visualize and label each component in your setup."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a941223d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sequence = [\"light_source\",\"lens1\",\"lens2\",\"mirror\",\"detector\"]\n",
    "dit.plotting.system2D.plot(system,annotate=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09ad5f9c",
   "metadata": {},
   "source": [
    "Diffinytrace also supports visualization of rays—the ray tracing is always performed in 3D, and the rays are just projected onto the y-z plane. For this reason, in 2D these rays may sometimes appear unusual, since the lens surfaces are also plotted as slices of the surfaces in the y-z plane with x = 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "797ab9db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: ray_paths will project the ray position onto the y-z plane!\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\marti\\anaconda3\\envs\\dit\\Lib\\site-packages\\torch\\autograd\\graph.py:869: UserWarning: cudaGetDeviceCount() returned cudaErrorNotSupported, likely using older driver or on CPU machine (Triggered internally at C:\\actions-runner\\_work\\pytorch\\pytorch\\pytorch\\c10\\cuda\\CUDAFunctions.cpp:88.)\n",
      "  return Variable._execution_engine.run_backward(  # Calls into the C++ engine to run the backward pass\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_rays = 10\n",
    "x,weights = light_source.sample(num_rays)\n",
    "x.requires_grad = True\n",
    "O,D,wave_len,_,RayPaths = system(x,sequence)\n",
    "dit.plotting.system2D.plot(system,RayPaths)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2e9b527",
   "metadata": {},
   "source": [
    "Also 3D plotting is supported. Here rays always look correct since no projection is needed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a067635d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\marti\\anaconda3\\envs\\dit\\Lib\\site-packages\\torch\\functional.py:505: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at C:\\actions-runner\\_work\\pytorch\\pytorch\\pytorch\\aten\\src\\ATen\\native\\TensorShape.cpp:4383.)\n",
      "  return _VF.meshgrid(tensors, **kwargs)  # type: ignore[attr-defined]\n"
     ]
    },
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "colorscale": [
          [
           0,
           "rgb(248, 206, 204)"
          ],
          [
           1,
           "rgb(184, 84, 80)"
          ]
         ],
         "name": "light_source_0",
         "showscale": false,
         "type": "surface",
         "x": {
          "bdata": 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          "dtype": "f8",
          "shape": "24, 24"
         }
        },
        {
         "colorscale": [
          [
           0,
           "rgb(213, 232, 212)"
          ],
          [
           1,
           "rgb(130, 179, 102)"
          ]
         ],
         "name": "detector_0",
         "showscale": false,
         "type": "surface",
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          "shape": "24, 24"
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          "shape": "24, 24"
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   "source": [
    "\n",
    "dit.plotting.system3D.plot(system,RayPaths,resolution=24)"
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  },
  {
   "cell_type": "markdown",
   "id": "c2356938",
   "metadata": {},
   "source": [
    "Diffiny trace also supports the calculation of the nearest ray (index) with the target grid module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "88072386",
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      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "grid = dit.target_grid.GridSquare(detector.aperture_radius,64)\n",
    "\n",
    "from matplotlib.colors import LogNorm\n",
    "num_rays = 2000\n",
    "x,weights = light_source.sample(num_rays)\n",
    "O,D,wave_len,_,RayPaths = system(x,sequence)\n",
    "O_local = detector.to_local_pos(O)\n",
    "O_local = O_local[:,[0,1]]\n",
    "nearest_ray = grid.get_nearest_ray(O_local)\n",
    "num_rays_on_grid = grid.sum(O_local,torch.ones((x.shape[0]),dtype=x.dtype,device=x.device))\n",
    "dit.plotting.quantity2D.plot(nearest_ray,\"\",[-detector.aperture_radius,detector.aperture_radius],show=False,cmap=\"Spectral\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c0bf596",
   "metadata": {},
   "source": [
    "Also, some functions for quickly calculating irradiance using the ray counting method are implemented.\n",
    "\n",
    "There are a couple of integration methods supported. Here, PyTorch's implementation of Sobol sampling is used by default. If `sobol_pow2` is provided as the ray tracing method, SciPy's implementation of Sobol is used, which is preferred."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7fa68ef5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = dit.target_grid.GridSquare(detector.aperture_radius,512)\n",
    "irr = dit.render.binned_irradiance(system,sequence,light_source,detector,grid,num_rays=[1000,1000],method_ray_tracing=\"sobol\")\n",
    "dit.plotting.quantity2D.plot(irr,\"Irradiance using Ray Counting\",[-detector.aperture_radius,detector.aperture_radius])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f62a12c2",
   "metadata": {},
   "source": [
    "It is also possible to calculate the irradiance distribution with differential ray tracing which is described in \"Using differential ray tracing in stray light analysis\". As one can see there is no noise at all. The reason is that derivatives are used for irradiance calculation. There actually only needs to be one ray per pixel to calculate the irradiance distribution for bijective mappings of the optical system with this method.\n",
    "\n",
    "Here another method of the target grid is also used: mean which calculates the mean over pixel of values associated with a ray"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "710e233c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mThe Kernel crashed while executing code in the current cell or a previous cell. \n",
      "\u001b[1;31mPlease review the code in the cell(s) to identify a possible cause of the failure. \n",
      "\u001b[1;31mClick <a href='https://aka.ms/vscodeJupyterKernelCrash'>here</a> for more info. \n",
      "\u001b[1;31mView Jupyter <a href='command:jupyter.viewOutput'>log</a> for further details."
     ]
    }
   ],
   "source": [
    "\n",
    "x,weights = light_source.sample(1000*1000)\n",
    "O,D,wave_len,_,RayPaths = system(x,sequence)\n",
    "O_local = detector.to_local_pos(O)\n",
    "_,org_args = grid.nearest(O_local[:,[0,1]],return_args=True)\n",
    "org_args = org_args.reshape(-1)\n",
    "mask = org_args==-1\n",
    "\n",
    "args = org_args[mask!=True]\n",
    "xb = x.detach()\n",
    "xb = xb[args]\n",
    "\n",
    "xb.requires_grad = True\n",
    "O,D,wave_len,_,RayPaths = system(xb,sequence)\n",
    "O_local = detector.to_local_pos(O)\n",
    "O1x, = dit.grad(O_local[:,0],xb,torch.ones_like(O_local[:,0]))\n",
    "O2x, = dit.grad(O_local[:,1],xb,torch.ones_like(O_local[:,1]))\n",
    "\n",
    "a = O1x[:,0]\n",
    "b = O1x[:,1]\n",
    "c = O2x[:,0]\n",
    "d = O2x[:,1]\n",
    "H = a*d-b*c\n",
    "\n",
    "Qval = light_source.get_flux(xb.detach())\n",
    "    \n",
    "I = grid.mean(O_local[:,[0,1]],Qval/torch.abs(H))\n",
    "I = I.detach()\n",
    "dit.plotting.quantity2D.plot(I,\"Irradiance with Differential Raytracing\",[-detector.aperture_radius,detector.aperture_radius])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64316f61",
   "metadata": {},
   "source": [
    "As a library for algorithmic differentiable ray tracing also gaussian measurement functions are supported for the calculation of smooth irradiance distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d0e965a",
   "metadata": {},
   "outputs": [],
   "source": [
    "smoother = dit.gaussian_smoother.GaussianSmootherSquare(aperture_radius=detector.aperture_radius,sigma=0.1,grid_size=128,desired_irradiance_fun=lambda p: p[:,0],smoothed_num_integration_points=2,smoothed_num_splits=1,device=device)\n",
    "smoothed_irr = dit.render.smoothed_irradiance(system,sequence,light_source,detector,smoother,num_rays=[256,256],method_ray_tracing=\"midpoint\")\n",
    "dit.plotting.quantity2D.plot(smoothed_irr,\"Irradiance with Gaussian Measurement Functions\",[-detector.aperture_radius,detector.aperture_radius])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff48b4da",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5389da08",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "dit",
   "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": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}