2024-07-25_caustique.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.668239Z",
     "iopub.status.busy": "2022-09-16T06:50:17.667940Z",
     "iopub.status.idle": "2022-09-16T06:50:17.670759Z",
     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import imageio, cv2\n",
    "\n",
    "# the higher PRECISION, the bigger the file\n",
    "# PRECISION = 4  # debugging\n",
    "# PRECISION = 10 # good quality\n",
    "PRECISION = 12 # very good quality\n",
    "# PRECISION = 14 # for production\n",
    "\n",
    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
    "from dataclasses import dataclass\n",
    "\n",
    "@dataclass\n",
    "class init:\n",
    "    figpath: str = '2024-07-25_caustique' # Folder to store images\n",
    "    phi: float = 1.61803 # beauty is gold\n",
    "    tag: str = 'caustique' # Tag\n",
    "    ext: str = 'png' # Extension for output\n",
    "    nx: int = 5*2**PRECISION # number of pixels (vertical)\n",
    "    ny: int = 5*2**PRECISION # number of pixels (horizontal)\n",
    "    nframe: int = 1 # number of frames\n",
    "    bin_dens: int = 2 # relative bin density\n",
    "    bin_spectrum: int = 1 # bin spacing in spectrum (lower is more CPU)\n",
    "    seed: int = 2024 # seed for RNG\n",
    "    H: float = 20.0 # depth of the pool\n",
    "    variation: float = .20 # variation of diffraction index: http://www.philiplaven.com/p20.html 1.40 at 400 nm and 1.37 at 700nm makes a 2% variation\n",
    "    scale: float = .95*2**PRECISION # period in pixels\n",
    "    B_sf: float = 1.00 # bandwidth in sf\n",
    "    V_Y: float = 0.3 # horizontal speed\n",
    "    V_X: float = 0.3 # vertical speed\n",
    "    B_V: float = 1.0 # bandwidth in speed\n",
    "    zmin: float = 0.10 # gradient of wave height\n",
    "    # theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
    "    theta: float = np.pi/2 # angle with the horizontal\n",
    "    B_theta: float = 60*np.pi/180 # bandwidth in theta\n",
    "    min_lum: float = .01 # global diffusion level for the rendering giving the pedestal value\n",
    "    n_bits: int = 16 # bits to save images\n",
    "    gamma: float = 2.4 # Gamma exponant to convert luminosity to luminance\n",
    "    fps: float = 18 # frames per second\n",
    "    multispectral: bool = True # Compute caustics on the full spectrogram.\n",
    "    cache: bool = True # Cache intermediate output.\n",
    "    verbose: bool = False # Displays more verbose output.\n",
    "    do_display: bool = False # Displays images in notebook.\n",
    "    do_recompute: bool = False # Restart each computation    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.688713Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.691125Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving our simulations in=2024-07-25_caustique\n"
     ]
    }
   ],
   "source": [
    "opt = init()\n",
    "print(f'Saving our simulations in={opt.figpath}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# if opt.nframe==1: opt.ext = 'png'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
     "iopub.status.idle": "2022-09-16T06:50:17.734829Z",
     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "init(figpath='2024-07-25_caustique',\n",
      "     phi=1.61803,\n",
      "     tag='caustique',\n",
      "     ext='png',\n",
      "     nx=20480,\n",
      "     ny=20480,\n",
      "     nframe=1,\n",
      "     bin_dens=2,\n",
      "     bin_spectrum=1,\n",
      "     seed=2024,\n",
      "     H=20.0,\n",
      "     variation=0.2,\n",
      "     scale=3891.2,\n",
      "     B_sf=1.0,\n",
      "     V_Y=0.3,\n",
      "     V_X=0.3,\n",
      "     B_V=1.0,\n",
      "     zmin=0.1,\n",
      "     theta=1.5707963267948966,\n",
      "     B_theta=1.0471975511965976,\n",
      "     min_lum=0.01,\n",
      "     n_bits=16,\n",
      "     gamma=2.4,\n",
      "     fps=18,\n",
      "     multispectral=True,\n",
      "     cache=True,\n",
      "     verbose=False,\n",
      "     do_display=False,\n",
      "     do_recompute=True)\n"
     ]
    }
   ],
   "source": [
    "from pprint import pprint\n",
    "pprint(opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Screen size=100cm, dpi=260dpi\n"
     ]
    }
   ],
   "source": [
    "screen_size = 100 # cm\n",
    "cm_by_inch = 2.54\n",
    "inches = screen_size/cm_by_inch\n",
    "dpi = opt.nx // opt.bin_dens / inches\n",
    "print(f'Screen size={screen_size}cm, dpi={dpi:.0f}dpi')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## utilities\n",
    "\n",
    "Transfoming a sequence of PNG frames into gif or mp4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.737334Z",
     "iopub.status.busy": "2022-09-16T06:50:17.737126Z",
     "iopub.status.idle": "2022-09-16T06:50:17.741165Z",
     "shell.execute_reply": "2022-09-16T06:50:17.740716Z"
    }
   },
   "outputs": [],
   "source": [
    "def make_gif(gifname, fnames, fps, do_delete=True):\n",
    "    with imageio.get_writer(gifname, mode='I', fps=fps) as writer:\n",
    "        for fname in fnames:\n",
    "            writer.append_data(imageio.imread(fname))\n",
    "\n",
    "    from pygifsicle import optimize\n",
    "    optimize(str(gifname))\n",
    "    if do_delete: \n",
    "        for fname in fnames: os.remove(fname)\n",
    "    return gifname\n",
    "\n",
    "# https://moviepy.readthedocs.io/en/latest/getting_started/videoclips.html#imagesequenceclip\n",
    "def make_mp4(mp4name, fnames, fps, do_delete=True):\n",
    "    import moviepy.editor as mpy\n",
    "    clip = mpy.ImageSequenceClip(fnames, fps=fps)\n",
    "    clip.write_videofile(mp4name, fps=fps, codec='libx264', verbose=False, logger=None)\n",
    "    if do_delete: \n",
    "        for fname in fnames: os.remove(fname)\n",
    "    return mp4name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Utilities to compute the spectrum of the blue sky and convert them later to RGB values (check out https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for details)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
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     "iopub.status.idle": "2022-09-16T06:50:17.757701Z",
     "shell.execute_reply": "2022-09-16T06:50:17.757282Z"
    }
   },
   "outputs": [],
   "source": [
    "from lambda2color import Lambda2color, xyz_from_xy\n",
    "\n",
    "# borrowed from https://github.com/gummiks/gummiks.github.io/blob/master/scripts/astro/planck.py\n",
    "def planck(wav, T):\n",
    "    import scipy.constants as const\n",
    "    c = const.c # c = 3.0e+8\n",
    "    h = const.h # h = 6.626e-34\n",
    "    k = const.k # k = 1.38e-23\n",
    "    a = 2.0*h*c**2\n",
    "    b = h*c/(wav*k*T)\n",
    "    intensity = a / ( (wav**5) * (np.exp(b) - 1.0) )\n",
    "    return intensity\n",
    "\n",
    "def scattering(wav, a=0.005, p=1.3, b=0.45):\n",
    "    \"\"\"\n",
    "    b is  proportionate  to  the  column  density  of  aerosols\n",
    "    along  the  path  of  sunlight,  from  outside  the  atmosphere\n",
    "    to  the  point  of  observation\n",
    "    \n",
    "    see https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for more details\n",
    "\n",
    "    \"\"\"\n",
    "    # converting wav in µm:\n",
    "    intensity = np.exp(-a/((wav/1e-6)**4)) # Rayleigh extinction by nitrogen\n",
    "    intensity *= (wav/1e-6)**-4\n",
    "    intensity *= np.exp(-b/((wav/1e-6)**p)) # Aerosols\n",
    "    return intensity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## computing the caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.012647Z",
     "iopub.status.busy": "2022-09-16T06:50:17.012413Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:193: SyntaxWarning: invalid escape sequence '\\>'\n",
      "<>:193: SyntaxWarning: invalid escape sequence '\\>'\n",
      "/var/folders/3p/m0g52j9j69z3gj8ktpgg1dm00000gn/T/ipykernel_37768/1923257970.py:193: SyntaxWarning: invalid escape sequence '\\>'\n",
      "  html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n"
     ]
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from tqdm import tqdm, trange\n",
    "import shutil\n",
    "import hashlib\n",
    "import MotionClouds as mc\n",
    "\n",
    "class Caustique:\n",
    "    def __init__(self, opt):\n",
    "        \"\"\"\n",
    "        Image coordinates follow 'ij' indexing, that is,\n",
    "        * their origin at the top left,\n",
    "        * the X axis is vertical and goes \"down\",\n",
    "        * the Y axis is horizontal and goes \"right\".\n",
    "\n",
    "        \"\"\"\n",
    "        self.mc = mc\n",
    "        self.ratio = opt.ny/opt.nx # ratio between height and width (>1 for portrait, <1 for landscape)\n",
    "        X = np.linspace(0, 1, opt.nx, endpoint=False) # vertical\n",
    "        Y = np.linspace(0, self.ratio, opt.ny, endpoint=False) # horizontal\n",
    "        self.xv, self.yv = np.meshgrid(X, Y, indexing='ij')\n",
    "        self.opt = opt\n",
    "        # https://stackoverflow.com/questions/16878315/what-is-the-right-way-to-treat-python-argparse-namespace-as-a-dictionary\n",
    "        self.d = vars(opt)\n",
    "        os.makedirs(self.opt.figpath, exist_ok=True)\n",
    "        self.cachepath = os.path.join('/tmp', self.opt.figpath)\n",
    "        if opt.verbose: print(f'{self.cachepath=}')\n",
    "        os.makedirs(self.cachepath, exist_ok=True)\n",
    "\n",
    "        # a standard white:\n",
    "        # illuminant_D65 = xyz_from_xy(0.3127, 0.3291), \n",
    "        illuminant_sun = xyz_from_xy(0.325998, 0.335354)\n",
    "        # color conversion class\n",
    "        self.cs_srgb = Lambda2color(red=xyz_from_xy(0.64, 0.33),\n",
    "                               green=xyz_from_xy(0.30, 0.60),\n",
    "                               blue=xyz_from_xy(0.15, 0.06),\n",
    "                               white=illuminant_sun)\n",
    "        self.wavelengths = self.cs_srgb.cmf[:, 0]*1e-9\n",
    "        self.N_wavelengths = len(self.wavelengths)\n",
    "        # multiply by the spectrum of the sky\n",
    "        intensity5800 = planck(self.wavelengths, 5800.)\n",
    "        scatter = scattering(self.wavelengths)\n",
    "        self.spectrum_sky = intensity5800 * scatter\n",
    "        self.spectrum_sky /= self.spectrum_sky.max()\n",
    "\n",
    "    def wave(self):\n",
    "        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'\n",
    "        if os.path.isfile(filename) and not(self.opt.do_recompute):\n",
    "            z = np.load(filename)\n",
    "        else:\n",
    "            # A simplistic model of a wave using https://github.com/NeuralEnsemble/MotionClouds\n",
    "            fx, fy, ft = mc.get_grids(self.opt.nx, self.opt.ny, self.opt.nframe)\n",
    "            env = mc.envelope_gabor(fx, fy, ft, V_X=self.opt.V_Y, V_Y=self.opt.V_X, B_V=self.opt.B_V,\n",
    "                                    sf_0=1./self.opt.scale, B_sf=self.opt.B_sf/self.opt.scale,\n",
    "                                    theta=self.opt.theta, B_theta=self.opt.B_theta)\n",
    "            z = mc.rectif(mc.random_cloud(env, seed=self.opt.seed))\n",
    "            if self.opt.cache: np.save(filename, z)\n",
    "        return z * np.linspace(self.opt.zmin, 1., self.opt.nx)[:, None, None]\n",
    "\n",
    "    def transform(self, z_, modulation=1., edge_order=2):\n",
    "        xv, yv = self.xv.copy(), self.yv.copy()\n",
    "\n",
    "        # dzdx = z_ - np.roll(z_, 1, axis=0)\n",
    "        # dzdy = z_ - np.roll(z_, 1, axis=1)\n",
    "\n",
    "        # https://numpy.org/doc/stable/reference/generated/numpy.gradient.html\n",
    "        # dzdx = np.gradient(z_, axis=0, edge_order=edge_order)\n",
    "        # dzdy = np.gradient(z_, axis=1, edge_order=edge_order)\n",
    "        dzdx, dzdy = np.gradient(z_, edge_order=edge_order)\n",
    "\n",
    "        xv = xv + modulation * self.opt.H * dzdx\n",
    "        yv = yv + modulation * self.opt.H * dzdy\n",
    "\n",
    "        xv = np.mod(xv, 1)\n",
    "        yv = np.mod(yv, self.ratio)\n",
    "\n",
    "        return xv, yv\n",
    "\n",
    "    def plot(self, z, image=None, do_color=True, dpi=dpi):\n",
    "        \"\"\"\n",
    "        \n",
    "        dpi: output resolution - sets the figure size as we ensure there is a one to one correspondance between pixels in the data and the output image\n",
    "        \"\"\"\n",
    "\n",
    "        # output filename        \n",
    "        md5 = hashlib.sha224((self.opt.figpath + self.opt.tag).encode()).hexdigest()[:8] # an unique identifier for future tagging\n",
    "        output_filename = f'{self.opt.figpath}/{self.opt.tag}_{md5}.{self.opt.ext}'\n",
    "        if os.path.isfile(output_filename) and not(self.opt.do_recompute):\n",
    "            return output_filename\n",
    "        else:\n",
    "            # 1/ do the raytracing of image through z:\n",
    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
    "\n",
    "            # a fixed image in degree of contrast (from 0=black to 1=white)\n",
    "            if image is None: image = np.ones((self.opt.nx, self.opt.ny))\n",
    "\n",
    "            #hist = self.do_raytracing(z)\n",
    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
    "\n",
    "            subplotpars = matplotlib.figure.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)\n",
    "\n",
    "            if self.opt.multispectral:\n",
    "\n",
    "                #image_rgb = self.cs_srgb.spec_to_rgb(hist)\n",
    "                image_rgb = np.zeros((self.opt.nx//self.opt.bin_dens,  self.opt.ny//self.opt.bin_dens, 3, self.opt.nframe))\n",
    "                for i_frame in trange(self.opt.nframe):\n",
    "                    for i_wavelength in trange(self.opt.bin_spectrum//2, self.N_wavelengths, self.opt.bin_spectrum):\n",
    "                        modulation = 1. + self.opt.variation/2 - self.opt.variation*i_wavelength/self.N_wavelengths\n",
    "                        xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)\n",
    "                        hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                     bins=[binsx, binsy],\n",
    "                                                     weights=image.ravel(),\n",
    "                                                     range=[[0, 1], [0, self.ratio]],\n",
    "                                                     density=True)\n",
    "\n",
    "                        # we convert the spectrum into a color\n",
    "                        spec = np.zeros((self.N_wavelengths))\n",
    "                        spec[i_wavelength] = 1\n",
    "                        rgb = self.cs_srgb.spec_to_rgb(spec)\n",
    "                        rgb *= self.spectrum_sky[i_wavelength]\n",
    "                        # we add the color to the image\n",
    "                        image_rgb[:, :, :, i_frame] += hist_[:, :, None] * rgb[None, None, :]\n",
    "\n",
    "                image_rgb -= image_rgb.min()\n",
    "                image_rgb /= image_rgb.max()\n",
    "            else:\n",
    "                hist = np.zeros((binsx, binsy, self.opt.nframe))\n",
    "                for i_frame in trange(self.opt.nframe):\n",
    "                    xv, yv = self.transform(z[:, :, i_frame])\n",
    "                    hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
    "                                                        bins=[binsx, binsy],\n",
    "                                                        range=[[0, 1], [0, self.ratio]],\n",
    "                                                        density=True)\n",
    "                #hist /= hist.max()\n",
    "\n",
    "            # 2/ transform light into image:\n",
    "            fnames = []\n",
    "            for i_frame in trange(self.opt.nframe):\n",
    "                fig, ax = plt.subplots(figsize=(self.opt.ny/self.opt.bin_dens/dpi, self.opt.nx/self.opt.bin_dens/dpi), subplotpars=subplotpars)\n",
    "                if self.opt.multispectral:\n",
    "                    image_array = image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma)\n",
    "                    ax.imshow(image_array, vmin=0, vmax=1)\n",
    "                else:\n",
    "                    if do_color:\n",
    "                        bluesky = np.array([0.268375, 0.283377]) # xyz\n",
    "                        sun = np.array([0.325998, 0.335354]) # xyz\n",
    "                        # ax.pcolormesh(edge_y, edge_x, hist[:, :, i_frame], vmin=0, vmax=1, cmap=plt.cm.Blues_r)\n",
    "                        # https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram\n",
    "                        L1 = 1 - hist[:, :, i_frame]\n",
    "                        L2 = hist[:, :, i_frame]\n",
    "                        image_denom = L1 / bluesky[1] + L2 / sun[1]\n",
    "                        image_x = (L1 * bluesky[0] / bluesky[1] + L2 * sun[0] / sun[1]) / image_denom\n",
    "                        image_y = (L1 + L2) / image_denom \n",
    "                        image_xyz = np.dstack((image_x, image_y, 1 - image_x - image_y))\n",
    "                        image_rgb = self.cs_srgb.xyz_to_rgb(image_xyz)\n",
    "                        image_L = (self.opt.min_lum + (1-self.opt.min_lum)* L2) ** (1/self.opt.gamma)\n",
    "                        image_array = image_L[:, :, None]*image_rgb\n",
    "                        ax.imshow(image_array, vmin=0, vmax=1)\n",
    "                    else:\n",
    "                        ax.imshow(1-image_L, vmin=0, vmax=1)\n",
    "\n",
    "                fname = f'{self.cachepath}/{self.opt.tag}_frame_{i_frame:04d}.png'\n",
    "                \n",
    "                # fig.savefig(fname, dpi=dpi)\n",
    "                np_dtype = np.uint8 if self.opt.n_bits==8 else np.uint16\n",
    "                # imageio.imsave(fname, image_array.astype(np_dtype), dpi=dpi, extension=opt.ext)\n",
    "                cv2.imwrite(fname, (image_array*(2**self.opt.n_bits-1)).astype(np_dtype))\n",
    "                fnames.append(fname)\n",
    "                plt.close(fig)\n",
    "\n",
    "            if self.opt.nframe==1:\n",
    "                shutil.copyfile(fname, output_filename)\n",
    "                return output_filename\n",
    "            else:\n",
    "                if self.opt.ext == 'gif':\n",
    "                    return make_gif(output_filename, fnames, fps=self.opt.fps)\n",
    "                else:\n",
    "                    return make_mp4(output_filename, fnames, fps=self.opt.fps)\n",
    "\n",
    "    def show(self, output_filename, width=1024):\n",
    "        from IPython.display import HTML, Image, display\n",
    "        if self.opt.nframe==1:\n",
    "            # display(Image(url=output_filename.replace(self.opt.ext, 'png'), width=width))\n",
    "            display(Image(url=output_filename, width=width))\n",
    "        else:\n",
    "            if self.opt.ext == 'gif':\n",
    "                return display(Image(url=output_filename, width=width))\n",
    "            else:\n",
    "                #import moviepy.editor as mpy\n",
    "                #return mpy.ipython_display(output_filename, width=width)\n",
    "                # https://github.com/NeuralEnsemble/MotionClouds/blob/master/MotionClouds/MotionClouds.py#L858\n",
    "                opts = ' loop=\"1\" autoplay=\"1\" controls '\n",
    "                html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n",
    "                html.reload()\n",
    "                return display(html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# a simple caustics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## generating the caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.864888Z",
     "iopub.status.busy": "2022-09-16T06:50:17.864663Z",
     "iopub.status.idle": "2022-09-16T06:50:19.896847Z",
     "shell.execute_reply": "2022-09-16T06:50:19.896285Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20480, 20480, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
    "    # image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
    "    # image = (image>=1) * 1.\n",
    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.899518Z",
     "iopub.status.busy": "2022-09-16T06:50:19.899287Z",
     "iopub.status.idle": "2022-09-16T06:50:19.902454Z",
     "shell.execute_reply": "2022-09-16T06:50:19.902008Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [4:50:45<00:00, 215.38s/it]\n",
      "100%|██████████| 1/1 [4:50:45<00:00, 17445.69s/it]\n",
      "100%|██████████| 1/1 [00:14<00:00, 14.41s/it]\n"
     ]
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "output_filename = c.plot(z, image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.904998Z",
     "iopub.status.busy": "2022-09-16T06:50:19.904782Z",
     "iopub.status.idle": "2022-09-16T06:50:19.908171Z",
     "shell.execute_reply": "2022-09-16T06:50:19.907731Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2024-07-25_caustique/caustique_9db4b5f9.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "# exploring parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.910794Z",
     "iopub.status.busy": "2022-09-16T06:50:19.910587Z",
     "iopub.status.idle": "2022-09-16T06:50:19.913072Z",
     "shell.execute_reply": "2022-09-16T06:50:19.912580Z"
    }
   },
   "outputs": [],
   "source": [
    "N_scan = 9\n",
    "base = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## water depth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1 [00:00<?, ?it/s]"
     ]
    }
   ],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## refraction index variation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:21.644704Z",
     "iopub.status.busy": "2022-09-16T06:50:21.644457Z",
     "iopub.status.idle": "2022-09-16T06:50:23.391217Z",
     "shell.execute_reply": "2022-09-16T06:50:23.390608Z"
    }
   },
   "outputs": [],
   "source": [
    "for variation_ in np.logspace(-2, 0, N_scan, base=10, endpoint=False):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.variation = variation_\n",
    "    c.opt.tag = f'{opt.tag}_variation_{variation_:.3f}'\n",
    "\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'variation = {variation_:.3f}  -> {output_filename=}')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## other variables on the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:23.394466Z",
     "iopub.status.busy": "2022-09-16T06:50:23.394219Z",
     "iopub.status.idle": "2022-09-16T06:50:23.686162Z",
     "shell.execute_reply": "2022-09-16T06:50:23.685512Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
    "    print(f'======{variable}======')\n",
    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
    "        opt = init()\n",
    "        c = Caustique(opt)\n",
    "        c.d[variable] *= modul\n",
    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
    "        \n",
    "        z = c.wave()\n",
    "        output_filename = c.plot(z, image)\n",
    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
    "        if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## shining a grating image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'grating'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
    "    # image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
    "    # image = (image>=1) * 1.\n",
    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, threshold=threshold)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{threshold:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.2e}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
    "    print(f'======{variable}======')\n",
    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
    "        opt = init()\n",
    "        c = Caustique(opt)\n",
    "        c.d[variable] *= modul\n",
    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
    "        z = c.wave()\n",
    "        image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "        output_filename = c.plot(z, image)\n",
    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
    "        if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a grid image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'grid'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny, periods=10, threshold=0.45, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
    "    image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
    "    image = (image>=1) * 1.\n",
    "    image *= ((X**2 + Y**2) < radius**2) * 1.\n",
    "    return image\n",
    "    \n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=10, threshold=0.45, radius=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=10, threshold=threshold)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{threshold=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods, threshold=.2)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a hole image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'hole'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny, periods=6.5, threshold=0.45, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
    "    image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
    "    image = 1. - (image<=1)\n",
    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=6.5, threshold=0.45, radius=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=6.5, threshold=threshold)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{threshold=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods, threshold=.2)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a square image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'square'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny,  radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a disk image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'disk'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny, radius_in=0., radius_out=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image = ((X**2 + Y**2) < radius_out**2) * ((X**2 + Y**2) > radius_in**2) * 1.\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius_out=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for radius_out in np.linspace(0, 1, N_scan+1)[1:]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius_out=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius_out=radius_out)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{radius_out:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for radius_in in np.linspace(0, 1, N_scan+1)[1:]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius_in=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius_in=radius_in)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{radius_in=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a bi-grating image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_image(nx, ny, period1=2, period2=64, threshold=0.3, radius=.9):\n",
    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
    "    image  = (np.cos(2*np.pi*X*period1) > threshold) * 1.\n",
    "    image *= np.cos(2*np.pi*X*period2) > threshold\n",
    "    image *= (X**2 < radius**2) * (Y**2 < radius**2)\n",
    "    return image\n",
    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "type = 'bigrating'\n",
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "    c.opt.H = H_\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
    "    \n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, threshold=threshold)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{threshold:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for period1 in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{period1=:.2e}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, period1=period1)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{period1=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [],
   "source": [
    "for period2 in np.logspace(0, 1, N_scan, base=10):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{period2=:.3f}'\n",
    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, period2=period2)\n",
    "    output_filename = c.plot(z, image)\n",
    "    print(f'{period2=:.3f} -> {output_filename=} ')\n",
    "    if c.opt.do_display: c.show(output_filename)"
   ]
  }
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