2022-12-03_caustique.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Caustics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.002832Z",
     "iopub.status.busy": "2022-09-16T06:50:17.002540Z",
     "iopub.status.idle": "2022-09-16T06:50:17.009923Z",
     "shell.execute_reply": "2022-09-16T06:50:17.009225Z"
    }
   },
   "outputs": [],
   "source": [
    "figpath = '2022-12-03_caustique'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.012647Z",
     "iopub.status.busy": "2022-09-16T06:50:17.012413Z",
     "iopub.status.idle": "2022-09-16T06:50:17.665184Z",
     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.668239Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
    }
   },
   "outputs": [],
   "source": [
    "PRECISION = 4 # the higher, the bigger the file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.673182Z",
     "iopub.status.busy": "2022-09-16T06:50:17.672981Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.674999Z"
    }
   },
   "outputs": [],
   "source": [
    "PRECISION = 10 # the higher, the bigger the file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.677775Z",
     "iopub.status.busy": "2022-09-16T06:50:17.677563Z",
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     "shell.execute_reply": "2022-09-16T06:50:17.685757Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import datetime\n",
    "import numpy as np\n",
    "\n",
    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
    "from dataclasses import dataclass, asdict, field\n",
    "\n",
    "@dataclass\n",
    "class init:\n",
    "    figpath: str = figpath # Folder to store images\n",
    "    fig_width: float = 12 # width of figure\n",
    "    phi: float = 1.61803 # beauty is gold\n",
    "    N_PG_show: float = 5 # number of PG to show in plot_PG\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 = 4 # relative bin density\n",
    "    bin_spectrum: int = 3 # bin spacing in spectrum\n",
    "    seed: int = 8601 # seed for RNG\n",
    "    H: float = 10.0 # depth of the pool\n",
    "    variation: float = .4 # 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 = .5*2**PRECISION # period in pixels\n",
    "    B_sf: float = 0.25 # 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",
    "    theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
    "    B_theta: float = np.pi/4 # bandwidth in theta\n",
    "    min_lum: float = .2 # diffusion level for the rendering\n",
    "    gamma: float = 2.8 # 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": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.688713Z",
     "iopub.status.busy": "2022-09-16T06:50:17.688504Z",
     "iopub.status.idle": "2022-09-16T06:50:17.691583Z",
     "shell.execute_reply": "2022-09-16T06:50:17.691125Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving our simulations in=2022-12-03_caustique\n"
     ]
    }
   ],
   "source": [
    "print(f'Saving our simulations in={figpath}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.722173Z",
     "iopub.status.busy": "2022-09-16T06:50:17.721924Z",
     "iopub.status.idle": "2022-09-16T06:50:17.725840Z",
     "shell.execute_reply": "2022-09-16T06:50:17.725292Z"
    }
   },
   "outputs": [],
   "source": [
    "opt = init()\n",
    "opt.figpath = figpath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    {
     "data": {
      "text/plain": [
       "init(figpath='2022-12-03_caustique', fig_width=12, phi=1.61803, N_PG_show=5, tag='caustique', ext='png', nx=5120, ny=5120, nframe=1, bin_dens=4, bin_spectrum=3, seed=8601, H=10.0, variation=0.4, scale=512.0, B_sf=0.25, V_Y=0.3, V_X=0.3, B_V=1.0, theta=2.399988291783386, B_theta=0.7853981633974483, min_lum=0.2, gamma=2.8, fps=18, multispectral=True, cache=True, verbose=False, do_display=False, do_recompute=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [],
   "source": [
    "if opt.nframe==1: opt.ext = 'png'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## utilities\n",
    "\n",
    "Transfoming a sequence of PNG frames into gif or mp4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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",
    "    import imageio\n",
    "\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": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
     "iopub.status.busy": "2022-09-16T06:50:17.743461Z",
     "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": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:17.760440Z",
     "iopub.status.busy": "2022-09-16T06:50:17.760224Z",
     "iopub.status.idle": "2022-09-16T06:50:17.823069Z",
     "shell.execute_reply": "2022-09-16T06:50:17.822569Z"
    }
   },
   "outputs": [],
   "source": [
    "import shutil\n",
    "import hashlib\n",
    "# from tqdm.notebook import tqdm, trange\n",
    "from tqdm import tqdm, trange\n",
    "import MotionClouds as mc\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\n",
    "\n",
    "    def transform(self, z_, modulation=1.):\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",
    "        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=50):\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_, edge_x, edge_y = 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",
    "                        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",
    "                        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_, edge_x, edge_y = 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",
    "                    ax.imshow(image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma), 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 ** .61803\n",
    "                        ax.imshow(image_L[:, :, None]*image_rgb, vmin=0, vmax=1)\n",
    "\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",
    "                fig.savefig(fname, dpi=dpi)\n",
    "                fnames.append(fname)\n",
    "                plt.close('all')\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",
    "        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": 13,
   "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": [
       "(5120, 5120, 1)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = Caustique(opt)\n",
    "z = c.wave()\n",
    "z.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [],
   "source": [
    "c = Caustique(opt)\n",
    "output_filename = c.plot(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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=\"2022-12-03_caustique/caustique_7e43f342.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": 16,
   "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": 17,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "H = 5.000 -> output_filename='2022-12-03_caustique/caustique_H_5.000_6a1a8f45.png' \n",
      "H = 5.946 -> output_filename='2022-12-03_caustique/caustique_H_5.946_d7481454.png' \n",
      "H = 7.071 -> output_filename='2022-12-03_caustique/caustique_H_7.071_b21fc95d.png' \n",
      "H = 8.409 -> output_filename='2022-12-03_caustique/caustique_H_8.409_23125a2d.png' \n",
      "H = 10.000 -> output_filename='2022-12-03_caustique/caustique_H_10.000_189ae81a.png' \n",
      "H = 11.892 -> output_filename='2022-12-03_caustique/caustique_H_11.892_27403fd1.png' \n",
      "H = 14.142 -> output_filename='2022-12-03_caustique/caustique_H_14.142_a2cf125e.png' \n",
      "H = 16.818 -> output_filename='2022-12-03_caustique/caustique_H_16.818_8767bdba.png' \n",
      "H = 20.000 -> output_filename='2022-12-03_caustique/caustique_H_20.000_eecab46d.png' \n"
     ]
    }
   ],
   "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)\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": 18,
   "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.010  -> output_filename='2022-12-03_caustique/caustique_variation_0.010_044cf470.png'\n",
      "variation = 0.017  -> output_filename='2022-12-03_caustique/caustique_variation_0.017_72c3d748.png'\n",
      "variation = 0.028  -> output_filename='2022-12-03_caustique/caustique_variation_0.028_bb0f0729.png'\n",
      "variation = 0.046  -> output_filename='2022-12-03_caustique/caustique_variation_0.046_47650743.png'\n",
      "variation = 0.077  -> output_filename='2022-12-03_caustique/caustique_variation_0.077_06a7b693.png'\n",
      "variation = 0.129  -> output_filename='2022-12-03_caustique/caustique_variation_0.129_72b3a868.png'\n",
      "variation = 0.215  -> output_filename='2022-12-03_caustique/caustique_variation_0.215_129b9559.png'\n",
      "variation = 0.359  -> output_filename='2022-12-03_caustique/caustique_variation_0.359_f4973aeb.png'\n",
      "variation = 0.599  -> output_filename='2022-12-03_caustique/caustique_variation_0.599_f69f3f9b.png'\n"
     ]
    }
   ],
   "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)\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": 19,
   "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": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "======scale======\n",
      "scale=scale(default)*0.500=2.560E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_0.500_957a94fc.png'\n",
      "scale=scale(default)*0.595=3.044E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_0.595_764db4d6.png'\n",
      "scale=scale(default)*0.707=3.620E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_0.707_242782e1.png'\n",
      "scale=scale(default)*0.841=4.305E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_0.841_2a2fbbd6.png'\n",
      "scale=scale(default)*1.000=5.120E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_1.000_c46e4b44.png'\n",
      "scale=scale(default)*1.189=6.089E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_1.189_ecba796d.png'\n",
      "scale=scale(default)*1.414=7.241E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_1.414_2733594b.png'\n",
      "scale=scale(default)*1.682=8.611E+02 -> output_filename='2022-12-03_caustique/caustique_scale_modul_1.682_0c5d6f16.png'\n",
      "scale=scale(default)*2.000=1.024E+03 -> output_filename='2022-12-03_caustique/caustique_scale_modul_2.000_7a47fbd6.png'\n",
      "======B_sf======\n",
      "B_sf=B_sf(default)*0.500=1.250E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_0.500_ee3014ad.png'\n",
      "B_sf=B_sf(default)*0.595=1.487E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_0.595_81e34436.png'\n",
      "B_sf=B_sf(default)*0.707=1.768E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_0.707_9aff4697.png'\n",
      "B_sf=B_sf(default)*0.841=2.102E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_0.841_14720da2.png'\n",
      "B_sf=B_sf(default)*1.000=2.500E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_1.000_c9c7269e.png'\n",
      "B_sf=B_sf(default)*1.189=2.973E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_1.189_4e0f028a.png'\n",
      "B_sf=B_sf(default)*1.414=3.536E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_1.414_6d3bb86b.png'\n",
      "B_sf=B_sf(default)*1.682=4.204E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_1.682_02141297.png'\n",
      "B_sf=B_sf(default)*2.000=5.000E-01 -> output_filename='2022-12-03_caustique/caustique_B_sf_modul_2.000_692b448c.png'\n",
      "======theta======\n",
      "theta=theta(default)*0.500=1.200E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_0.500_65c37562.png'\n",
      "theta=theta(default)*0.595=1.427E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_0.595_ad0226f9.png'\n",
      "theta=theta(default)*0.707=1.697E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_0.707_68f59106.png'\n",
      "theta=theta(default)*0.841=2.018E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_0.841_e2b602df.png'\n",
      "theta=theta(default)*1.000=2.400E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_1.000_7734fe81.png'\n",
      "theta=theta(default)*1.189=2.854E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_1.189_9f01b3a9.png'\n",
      "theta=theta(default)*1.414=3.394E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_1.414_3daa0287.png'\n",
      "theta=theta(default)*1.682=4.036E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_1.682_4e6b1cdb.png'\n",
      "theta=theta(default)*2.000=4.800E+00 -> output_filename='2022-12-03_caustique/caustique_theta_modul_2.000_fdd3cd28.png'\n",
      "======B_theta======\n",
      "B_theta=B_theta(default)*0.500=3.927E-01 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_0.500_0bc5581d.png'\n",
      "B_theta=B_theta(default)*0.595=4.670E-01 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_0.595_86d76893.png'\n",
      "B_theta=B_theta(default)*0.707=5.554E-01 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_0.707_7114c277.png'\n",
      "B_theta=B_theta(default)*0.841=6.604E-01 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_0.841_822ff8ab.png'\n",
      "B_theta=B_theta(default)*1.000=7.854E-01 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_1.000_0a858033.png'\n",
      "B_theta=B_theta(default)*1.189=9.340E-01 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_1.189_3389f1c0.png'\n",
      "B_theta=B_theta(default)*1.414=1.111E+00 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_1.414_26ae7871.png'\n",
      "B_theta=B_theta(default)*1.682=1.321E+00 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_1.682_cdfdd338.png'\n",
      "B_theta=B_theta(default)*2.000=1.571E+00 -> output_filename='2022-12-03_caustique/caustique_B_theta_modul_2.000_7963ffbf.png'\n",
      "======gamma======\n",
      "gamma=gamma(default)*0.500=1.400E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_0.500_c8241e1e.png'\n",
      "gamma=gamma(default)*0.595=1.665E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_0.595_08026a17.png'\n",
      "gamma=gamma(default)*0.707=1.980E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_0.707_05fb4d76.png'\n",
      "gamma=gamma(default)*0.841=2.355E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_0.841_1510817d.png'\n",
      "gamma=gamma(default)*1.000=2.800E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_1.000_7856a4e4.png'\n",
      "gamma=gamma(default)*1.189=3.330E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_1.189_f8872d88.png'\n",
      "gamma=gamma(default)*1.414=3.960E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_1.414_0b8f8861.png'\n",
      "gamma=gamma(default)*1.682=4.709E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_1.682_0dcadf8b.png'\n",
      "gamma=gamma(default)*2.000=5.600E+00 -> output_filename='2022-12-03_caustique/caustique_gamma_modul_2.000_48b2d378.png'\n"
     ]
    }
   ],
   "source": [
    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', ]: #  '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)\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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = (image>=1) * 1.\n",
    "    image *= ((X**2 + Y**2) < radius**2) * 1.\n",
    "    return image\n",
    "image = grid_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": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_grid-image_7eaab721.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_grid-image'\n",
    "\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.100 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.100_015b86e0.png' \n",
      "threshold=0.200 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.200_5b11b935.png' \n",
      "threshold=0.300 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.300_01c17739.png' \n",
      "threshold=0.400 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.400_1853a025.png' \n",
      "threshold=0.500 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.500_a1a8dbb7.png' \n",
      "threshold=0.600 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.600_89943780.png' \n",
      "threshold=0.700 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.700_0e70dc9a.png' \n",
      "threshold=0.800 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.800_85fdca33.png' \n",
      "threshold=0.900 -> output_filename='2022-12-03_caustique/caustique_grid-image_threshold=0.900_29444535.png' \n"
     ]
    }
   ],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grid-image_{threshold=:.3f}'\n",
    "    image = grid_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": 23,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.000 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=1.000_c273d018.png' \n",
      "periods=1.334 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=1.334_6bbfb25d.png' \n",
      "periods=1.778 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=1.778_de3d6f7c.png' \n",
      "periods=2.371 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=2.371_d366c450.png' \n",
      "periods=3.162 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=3.162_4b62cf2a.png' \n",
      "periods=4.217 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=4.217_10df54f4.png' \n",
      "periods=5.623 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=5.623_dba0a5bb.png' \n",
      "periods=7.499 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=7.499_8732cec4.png' \n",
      "periods=10.000 -> output_filename='2022-12-03_caustique/caustique_grid-image_periods=10.000_b61b6d49.png' \n"
     ]
    }
   ],
   "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}_grid-image_{periods=:.3f}'\n",
    "    image = grid_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": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_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": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_hole-image_627db918.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_hole-image'\n",
    "\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.100 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.100_16d4b0a7.png' \n",
      "threshold=0.200 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.200_41641e6a.png' \n",
      "threshold=0.300 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.300_b9884984.png' \n",
      "threshold=0.400 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.400_3da027cd.png' \n",
      "threshold=0.500 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.500_91eecbe1.png' \n",
      "threshold=0.600 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.600_76a8ac51.png' \n",
      "threshold=0.700 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.700_f7033192.png' \n",
      "threshold=0.800 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.800_c3ef3dd2.png' \n",
      "threshold=0.900 -> output_filename='2022-12-03_caustique/caustique_hole-image_threshold=0.900_c123ae10.png' \n"
     ]
    }
   ],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan+2)[1:-1]:\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_hole-image_{threshold=:.3f}'\n",
    "    image = grid_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": 27,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.000 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=1.000_32eddccb.png' \n",
      "periods=1.334 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=1.334_7f8e324c.png' \n",
      "periods=1.778 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=1.778_9a5e9fc8.png' \n",
      "periods=2.371 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=2.371_9f8a83e1.png' \n",
      "periods=3.162 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=3.162_7dcdd2c7.png' \n",
      "periods=4.217 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=4.217_9d83efdc.png' \n",
      "periods=5.623 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=5.623_07c46a4b.png' \n",
      "periods=7.499 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=7.499_d2018dfa.png' \n",
      "periods=10.000 -> output_filename='2022-12-03_caustique/caustique_hole-image_periods=10.000_7d43741b.png' \n"
     ]
    }
   ],
   "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}_hole-image_{periods=:.3f}'\n",
    "    image = grid_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": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d3SbJzp49+4HXMT4+br7vB9vAwIBJmpetqalprssEAEtGc3PzvH3+lWS+78/5mm77e3ZTU1Nqa2vTe++9p+rqap07d06pVEq1tbXBTDgc1qZNm9TV1SVJ6u3t1bVr1zJmotGoysvLg5nu7m55nqeqqqpgZuPGjfI8L5i5mXg8HnzZ0/M8rV69+nZvDQDgmFnHrq+vTx/72McUDof1+OOPq729XZ/97GeVSqUkSSUlJRnzJSUlwbFUKqXc3FwtX758xpni4uJpH7e4uDiYuZmmpib5vh9sAwMDs701AICjsmf7DmvWrFEymdTw8LBefvllPfzww+rs7AyOh0KhjHkzm7bvRjfO3Gz+z50nHA4rHA7f6m0AAJaQWT/Z5ebm6tOf/rQ2bNigeDyu9evX6zvf+Y4ikYgkTXv6GhoaCp72IpGIJicnlU6nZ5y5dOnStI97+fLlaU+NAADcijn/nJ2ZaWJiQqWlpYpEIuro6AiOTU5OqrOzUzU1NZKkyspK5eTkZMwMDg7q9OnTwUx1dbV839eJEyeCmePHj8v3/WAGAIDZmNWXMffu3av7779fq1ev1ujoqNra2nT06FElEgmFQiE1NjaqublZZWVlKisrU3Nzs+6++241NDRIkjzP0yOPPKI9e/ZoxYoVKioq0jPPPKOKigpt3bpVkrR27Vpt375djz76qF544QVJ0mOPPaa6ujqtWbNmnm8fALAUzCp2ly5dUiwW0+DgoDzP07p165RIJLRt2zZJ0rPPPquxsTE98cQTSqfTqqqq0pEjR1RQUBCc47nnnlN2drYeeughjY2NacuWLTp8+LCWLVsWzLz00kt66qmngldt1tfXq7W1dT7uFwCwBIXMzBb6Ij4MIyMj8jxvXs7V1NSk5ubmeTkXALguHo9r796983Y+3/dVWFg4p3PwuzEBAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgPGIHAHAesQMAOI/YAQCcR+wAAM4jdgAA5xE7AIDziB0AwHnEDgDgvDnFLh6PKxQKqbGxMdhnZtq/f7+i0ajy8vK0efNm9ff3Z7zfxMSEdu3apZUrVyo/P1/19fW6cOFCxkw6nVYsFpPnefI8T7FYTMPDw3O5XADAEnXbsTt58qS+//3va926dRn7Dxw4oIMHD6q1tVUnT55UJBLRtm3bNDo6Gsw0Njaqvb1dbW1tOnbsmK5evaq6ujpNTU0FMw0NDUomk0okEkokEkomk4rFYrd7uQCApcxuw+joqJWVlVlHR4dt2rTJdu/ebWZm169ft0gkYi0tLcHs+Pi4eZ5nhw4dMjOz4eFhy8nJsba2tmDm4sWLlpWVZYlEwszMzpw5Y5Ksp6cnmOnu7jZJdvbs2Zte0/j4uPm+H2wDAwMmaV62pqam21kmAFiSmpub5+3zryTzfX/O13RbT3ZPPvmkHnjgAW3dujVj/7lz55RKpVRbWxvsC4fD2rRpk7q6uiRJvb29unbtWsZMNBpVeXl5MNPd3S3P81RVVRXMbNy4UZ7nBTM3isfjwZc8Pc/T6tWrb+fWAAAOmnXs2tradOrUKcXj8WnHUqmUJKmkpCRjf0lJSXAslUopNzdXy5cvn3GmuLh42vmLi4uDmRs1NTXJ9/1gGxgYmO2tAQAclT2b4YGBAe3evVtHjhzRXXfd9YFzoVAo420zm7bvRjfO3Gx+pvOEw2GFw+EZPwYAYGma1ZNdb2+vhoaGVFlZqezsbGVnZ6uzs1Pf/e53lZ2dHTzR3fj0NTQ0FByLRCKanJxUOp2ecebSpUvTPv7ly5enPTUCAPDnzCp2W7ZsUV9fn5LJZLBt2LBBO3bsUDKZ1Kc+9SlFIhF1dHQE7zM5OanOzk7V1NRIkiorK5WTk5MxMzg4qNOnTwcz1dXV8n1fJ06cCGaOHz8u3/eDGQAAbtWsvoxZUFCg8vLyjH35+flasWJFsL+xsVHNzc0qKytTWVmZmpubdffdd6uhoUGS5HmeHnnkEe3Zs0crVqxQUVGRnnnmGVVUVAQveFm7dq22b9+uRx99VC+88IIk6bHHHlNdXZ3WrFkz55sGACwts4rdrXj22Wc1NjamJ554Qul0WlVVVTpy5IgKCgqCmeeee07Z2dl66KGHNDY2pi1btujw4cNatmxZMPPSSy/pqaeeCl61WV9fr9bW1vm+XADAEhAyM1voi/gwjIyMyPO8eTlXU1OTmpub5+VcAOC6eDyuvXv3ztv5fN9XYWHhnM7B78YEADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB52Qt9AXeCrq4uxePxhb4MALgjHD16dKEvYZqQmdlCX8SHYWRkRJ7nLfRlAADmyPd9FRYWzukcfBkTAOA8YgcAcB6xAwA4j9gBAJxH7AAAzptV7Pbv369QKJSxRSKR4LiZaf/+/YpGo8rLy9PmzZvV39+fcY6JiQnt2rVLK1euVH5+vurr63XhwoWMmXQ6rVgsJs/z5HmeYrGYhoeHb/8uAQBL2qyf7D73uc9pcHAw2Pr6+oJjBw4c0MGDB9Xa2qqTJ08qEolo27ZtGh0dDWYaGxvV3t6utrY2HTt2TFevXlVdXZ2mpqaCmYaGBiWTSSUSCSUSCSWTScVisTneKgBgybJZ2Ldvn61fv/6mx65fv26RSMRaWlqCfePj4+Z5nh06dMjMzIaHhy0nJ8fa2tqCmYsXL1pWVpYlEgkzMztz5oxJsp6enmCmu7vbJNnZs2dv+Vp93zdJbGxsbGx3+Ob7/mxSdVOzfrJ75513FI1GVVpaqq9//et69913JUnnzp1TKpVSbW1tMBsOh7Vp0yZ1dXVJknp7e3Xt2rWMmWg0qvLy8mCmu7tbnuepqqoqmNm4caM8zwtmbmZiYkIjIyMZGwAA0iy/jFlVVaWf/OQn+q//+i/94Ac/UCqVUk1Nja5cuaJUKiVJKikpyXifkpKS4FgqlVJubq6WL18+40xxcfG0j11cXBzM3Ew8Hg++x+d5nlavXj2bWwMAOGxWsbv//vv11a9+VRUVFdq6dat+9rOfSZJ+/OMfBzOhUCjjfcxs2r4b3Thzs/k/d56mpib5vh9sAwMDt3RPAAD3zelHD/Lz81VRUaF33nkneFXmjU9fQ0NDwdNeJBLR5OSk0un0jDOXLl2a9rEuX7487anxT4XDYRUWFmZsAABIc4zdxMSEfvOb3+iee+5RaWmpIpGIOjo6guOTk5Pq7OxUTU2NJKmyslI5OTkZM4ODgzp9+nQwU11dLd/3deLEiWDm+PHj8n0/mAEAYFZm82qWPXv22NGjR+3dd9+1np4eq6urs4KCAvvtb39rZmYtLS3meZ698sor1tfXZ9/4xjfsnnvusZGRkeAcjz/+uK1atcp++ctf2qlTp+y+++6z9evX2x/+8IdgZvv27bZu3Trr7u627u5uq6iosLq6ulm98oZXY7KxsbG5sc3HqzFnFbuvfe1rds8991hOTo5Fo1H7yle+Yv39/cHx69ev2759+ywSiVg4HLYvfelL1tfXl3GOsbEx27lzpxUVFVleXp7V1dXZ+fPnM2auXLliO3bssIKCAisoKLAdO3ZYOp2e1Y0ROzY2NjY3tvmIHX/PDgCwqPH37GbgaMMBYMmZj8/nzsbuypUrC30JAIB58Ke/cvJ2Zc/DdSxKRUVFkqTz58/z5cybGBkZ0erVqzUwMMCPaXwA1mhmrM/MWJ+Z3cr6mJlGR0cVjUbn/PGcjV1W1h8fWj3P4x/aDPiZxD+PNZoZ6zMz1mdmf2595uthxdkvYwIA8D5iBwBwnrOxC4fD2rdvn8Lh8EJfyqLE+vx5rNHMWJ+ZsT4z+6jXx9mfswMA4H3OPtkBAPA+YgcAcB6xAwA4j9gBAJxH7AAAznM2dt/73vdUWlqqu+66S5WVlfr1r3+90Jc0715//XV9+ctfVjQaVSgU0k9/+tOM42am/fv3KxqNKi8vT5s3b1Z/f3/GzMTEhHbt2qWVK1cqPz9f9fX1unDhQsZMOp1WLBaT53nyPE+xWEzDw8Mf8t3NXTwe1xe+8AUVFBSouLhYDz74oN5+++2MmaW8Rs8//7zWrVsX/AaL6upq/eIXvwiOL+W1uZl4PK5QKKTGxsZg31Jfo/379ysUCmVskUgkOL6o1mfOfyRoEWpra7OcnBz7wQ9+YGfOnLHdu3dbfn6+/e53v1voS5tXP//5z+3b3/62vfzyyybJ2tvbM463tLRYQUGBvfzyy9bX1xf8PcIb/5juX/zFX1hHR4edOnXK7r333pv+Md3y8nLr6uqyrq4uKy8vn/Uf010If/d3f2cvvviinT592pLJpD3wwAP2iU98wq5evRrMLOU1evXVV+1nP/uZvf322/b222/b3r17LScnx06fPm1mS3ttbnTixAn7y7/8S1u3bp3t3r072L/U12jfvn32uc99zgYHB4NtaGgoOL6Y1sfJ2P3N3/yNPf744xn7PvOZz9i3vvWtBbqiD9+Nsbt+/bpFIhFraWkJ9o2Pj5vneXbo0CEzMxseHracnBxra2sLZi5evGhZWVmWSCTMzOzMmTMmyXp6eoKZ7u5uk2Rnz579kO9qfg0NDZkk6+zsNDPW6GaWL19uP/zhD1mbPzE6OmplZWXW0dFhmzZtCmLHGv0xduvXr7/pscW2Ps59GXNyclK9vb2qra3N2F9bW6uurq4FuqqP3rlz55RKpTLWIRwOa9OmTcE69Pb26tq1axkz0WhU5eXlwUx3d7c8z1NVVVUws3HjRnmed8etp+/7kv7/L2KwRv9vampKbW1teu+991RdXc3a/Iknn3xSDzzwgLZu3ZqxnzX6o3feeUfRaFSlpaX6+te/rnfffVfS4lsf5/7qwe9//3tNTU2ppKQkY39JSYlSqdQCXdVH7/17vdk6/O53vwtmcnNztXz58mkz779/KpVScXHxtPMXFxffUetpZnr66af1xS9+UeXl5ZJYI0nq6+tTdXW1xsfH9bGPfUzt7e367Gc/G3wSWcprI0ltbW06deqUTp48Oe0Y/36kqqoq/eQnP9Ff//Vf69KlS/qXf/kX1dTUqL+/f9Gtj3Oxe18oFMp428ym7VsKbmcdbpy52fydtp47d+7UW2+9pWPHjk07tpTXaM2aNUomkxoeHtbLL7+shx9+WJ2dncHxpbw2AwMD2r17t44cOaK77rrrA+eW8hrdf//9wf+uqKhQdXW1/uqv/ko//vGPtXHjRkmLZ32c+zLmypUrtWzZsmnFHxoamvZfGC57/xVRM61DJBLR5OSk0un0jDOXLl2adv7Lly/fMeu5a9cuvfrqq3rttde0atWqYD9rJOXm5urTn/60NmzYoHg8rvXr1+s73/kOa6M/foltaGhIlZWVys7OVnZ2tjo7O/Xd735X2dnZwfUv5TW6UX5+vioqKvTOO+8sun9DzsUuNzdXlZWV6ujoyNjf0dGhmpqaBbqqj15paakikUjGOkxOTqqzszNYh8rKSuXk5GTMDA4O6vTp08FMdXW1fN/XiRMngpnjx4/L9/1Fv55mpp07d+qVV17Rr371K5WWlmYcZ42mMzNNTEywNpK2bNmivr4+JZPJYNuwYYN27NihZDKpT33qU0t+jW40MTGh3/zmN7rnnnsW37+hW34pyx3k/R89+NGPfmRnzpyxxsZGy8/Pt9/+9rcLfWnzanR01N5880178803TZIdPHjQ3nzzzeBHLFpaWszzPHvllVesr6/PvvGNb9z0Zb+rVq2yX/7yl3bq1Cm77777bvqy33Xr1ll3d7d1d3dbRUXFHfGy6H/8x380z/Ps6NGjGS+N/t///d9gZimvUVNTk73++ut27tw5e+utt2zv3r2WlZVlR44cMbOlvTYf5E9fjWnGGu3Zs8eOHj1q7777rvX09FhdXZ0VFBQEn2sX0/o4GTszs3/913+1T37yk5abm2uf//zng5ebu+S1114zSdO2hx9+2Mz++NLfffv2WSQSsXA4bF/60pesr68v4xxjY2O2c+dOKyoqsry8PKurq7Pz589nzFy5csV27NhhBQUFVlBQYDt27LB0Ov0R3eXtu9naSLIXX3wxmFnKa/QP//APwf9HPv7xj9uWLVuC0Jkt7bX5IDfGbqmv0fs/N5eTk2PRaNS+8pWvWH9/f3B8Ma0Pf88OAOA8575nBwDAjYgdAMB5xA4A4DxiBwBwHrEDADiP2AEAnEfsAADOI3YAAOcROwCA84gdAMB5xA4A4Lz/AwWG+ekaMGJyAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_image(nx=c.opt.nx, ny=c.opt.ny, radius=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_square-image_782449f6.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_square-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.000 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.000_386fb4c7.png' \n",
      "radius=0.125 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.125_36f4eeeb.png' \n",
      "radius=0.250 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.250_d1e6443f.png' \n",
      "radius=0.375 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.375_15288855.png' \n",
      "radius=0.500 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.500_fbdf5c7f.png' \n",
      "radius=0.625 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.625_330bd850.png' \n",
      "radius=0.750 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.750_cdb6de88.png' \n",
      "radius=0.875 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=0.875_308bbd70.png' \n",
      "radius=1.000 -> output_filename='2022-12-03_caustique/caustique_square-image_radius=1.000_1f2d46a9.png' \n"
     ]
    }
   ],
   "source": [
    "for radius in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_square-image_{radius=:.3f}'\n",
    "    image = grid_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": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_image(nx=c.opt.nx, ny=c.opt.ny, radius_out=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_disk-image_9c070e15.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_disk-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "0.000 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.000_c50f72cb.png' \n",
      "0.125 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.125_c1bc6b84.png' \n",
      "0.250 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.250_2fe31f46.png' \n",
      "0.375 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.375_c719a34c.png' \n",
      "0.500 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.500_7410435c.png' \n",
      "0.625 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.625_0d4d76ce.png' \n",
      "0.750 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.750_fe521138.png' \n",
      "0.875 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.875_4f7f4981.png' \n",
      "1.000 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=1.000_25ee1611.png' \n"
     ]
    }
   ],
   "source": [
    "for radius_out in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_disk-image_{radius_out=:.3f}'\n",
    "    image = grid_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": 34,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "radius_in=0.000 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.000_080ddaa1.png' \n",
      "radius_in=0.113 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.113_1e9a0adb.png' \n",
      "radius_in=0.225 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.225_e79071ff.png' \n",
      "radius_in=0.338 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.338_bf75ca1b.png' \n",
      "radius_in=0.450 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.450_369e3461.png' \n",
      "radius_in=0.562 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.562_8995bf5a.png' \n",
      "radius_in=0.675 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.675_323b73ef.png' \n",
      "radius_in=0.787 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.787_1662b0e9.png' \n",
      "radius_in=0.900 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.900_2ddc35f3.png' \n"
     ]
    }
   ],
   "source": [
    "for radius_in in np.linspace(0, .9, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_disk-image_{radius_in=:.3f}'\n",
    "    image = grid_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 disk image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_image(nx=c.opt.nx, ny=c.opt.ny, radius_out=.9)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_disk-image_9c070e15.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_disk-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "0.000 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.000_c50f72cb.png' \n",
      "0.125 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.125_c1bc6b84.png' \n",
      "0.250 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.250_2fe31f46.png' \n",
      "0.375 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.375_c719a34c.png' \n",
      "0.500 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.500_7410435c.png' \n",
      "0.625 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.625_0d4d76ce.png' \n",
      "0.750 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.750_fe521138.png' \n",
      "0.875 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=0.875_4f7f4981.png' \n",
      "1.000 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_out=1.000_25ee1611.png' \n"
     ]
    }
   ],
   "source": [
    "for radius_out in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_disk-image_{radius_out=:.3f}'\n",
    "    image = grid_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": 38,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "radius_in=0.000 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.000_080ddaa1.png' \n",
      "radius_in=0.113 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.113_1e9a0adb.png' \n",
      "radius_in=0.225 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.225_e79071ff.png' \n",
      "radius_in=0.338 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.338_bf75ca1b.png' \n",
      "radius_in=0.450 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.450_369e3461.png' \n",
      "radius_in=0.562 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.562_8995bf5a.png' \n",
      "radius_in=0.675 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.675_323b73ef.png' \n",
      "radius_in=0.787 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.787_1662b0e9.png' \n",
      "radius_in=0.900 -> output_filename='2022-12-03_caustique/caustique_disk-image_radius_in=0.900_2ddc35f3.png' \n"
     ]
    }
   ],
   "source": [
    "for radius_in in np.linspace(0, .9, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_disk-image_{radius_in=:.3f}'\n",
    "    image = grid_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 grating image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_grating-image_7e526b9c.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_grating-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "0.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.000_31a59792.png' \n",
      "0.125 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.125_67794d7a.png' \n",
      "0.250 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.250_2d8cfb7a.png' \n",
      "0.375 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.375_202c37e8.png' \n",
      "0.500 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.500_c0b3da24.png' \n",
      "0.625 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.625_2f81f17a.png' \n",
      "0.750 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.750_3edc820d.png' \n",
      "0.875 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.875_7e8891d4.png' \n",
      "1.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=1.000_4d0f1795.png' \n"
     ]
    }
   ],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grating-image_{threshold=:.3f}'\n",
    "    image = grid_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": 42,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.000_d5c69061.png' \n",
      "radius=0.113 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.113_40afe992.png' \n",
      "radius=0.225 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.225_c44306d0.png' \n",
      "radius=0.338 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.338_8506311d.png' \n",
      "radius=0.450 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.450_1710bbfe.png' \n",
      "radius=0.562 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.562_2b50e892.png' \n",
      "radius=0.675 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.675_59a008a6.png' \n",
      "radius=0.787 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.787_527e88c4.png' \n",
      "radius=0.900 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.900_328f619f.png' \n"
     ]
    }
   ],
   "source": [
    "for radius in np.linspace(0, .9, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grating-image_{radius=:.3f}'\n",
    "    image = grid_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": 43,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=1.000_0a25a5f6.png' \n",
      "periods=1.334 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=1.334_2e6e4551.png' \n",
      "periods=1.778 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=1.778_6c795443.png' \n",
      "periods=2.371 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=2.371_3dfe1a08.png' \n",
      "periods=3.162 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=3.162_f8a452a6.png' \n",
      "periods=4.217 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=4.217_3272d9c8.png' \n",
      "periods=5.623 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=5.623_edc0f8f5.png' \n",
      "periods=7.499 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=7.499_578ca927.png' \n",
      "periods=10.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=10.000_84c0f76c.png' \n"
     ]
    }
   ],
   "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}_grating-image_{periods=:.3f}'\n",
    "    image = grid_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": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a grating image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_grating-image_7e526b9c.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_grating-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "0.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.000_31a59792.png' \n",
      "0.125 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.125_67794d7a.png' \n",
      "0.250 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.250_2d8cfb7a.png' \n",
      "0.375 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.375_202c37e8.png' \n",
      "0.500 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.500_c0b3da24.png' \n",
      "0.625 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.625_2f81f17a.png' \n",
      "0.750 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.750_3edc820d.png' \n",
      "0.875 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=0.875_7e8891d4.png' \n",
      "1.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_threshold=1.000_4d0f1795.png' \n"
     ]
    }
   ],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grating-image_{threshold=:.3f}'\n",
    "    image = grid_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": 47,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.000_d5c69061.png' \n",
      "radius=0.113 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.113_40afe992.png' \n",
      "radius=0.225 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.225_c44306d0.png' \n",
      "radius=0.338 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.338_8506311d.png' \n",
      "radius=0.450 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.450_1710bbfe.png' \n",
      "radius=0.562 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.562_2b50e892.png' \n",
      "radius=0.675 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.675_59a008a6.png' \n",
      "radius=0.787 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.787_527e88c4.png' \n",
      "radius=0.900 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.900_328f619f.png' \n"
     ]
    }
   ],
   "source": [
    "for radius in np.linspace(0, .9, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grating-image_{radius=:.3f}'\n",
    "    image = grid_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": 48,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=1.000_0a25a5f6.png' \n",
      "periods=1.334 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=1.334_2e6e4551.png' \n",
      "periods=1.778 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=1.778_6c795443.png' \n",
      "periods=2.371 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=2.371_3dfe1a08.png' \n",
      "periods=3.162 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=3.162_f8a452a6.png' \n",
      "periods=4.217 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=4.217_3272d9c8.png' \n",
      "periods=5.623 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=5.623_edc0f8f5.png' \n",
      "periods=7.499 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=7.499_578ca927.png' \n",
      "periods=10.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_periods=10.000_84c0f76c.png' \n"
     ]
    }
   ],
   "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}_grating-image_{periods=:.3f}'\n",
    "    image = grid_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": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## shining a bigrating image to the wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def grid_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 = grid_image(nx=c.opt.nx, ny=c.opt.ny)\n",
    "plt.imshow(image, cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"2022-12-03_caustique/caustique_bigrating-image_43b87222.png\" width=\"1024\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = Caustique(init())\n",
    "c.opt.tag = f'{c.opt.tag}_bigrating-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "0.000 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.000_964fa715.png' \n",
      "0.125 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.125_04d54c07.png' \n",
      "0.250 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.250_c2d84cb7.png' \n",
      "0.375 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.375_8b254ee1.png' \n",
      "0.500 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.500_6ae698ad.png' \n",
      "0.625 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.625_4ed0265c.png' \n",
      "0.750 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.750_a37d5fac.png' \n",
      "0.875 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=0.875_4da90088.png' \n",
      "1.000 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_threshold=1.000_2e9b5ff6.png' \n"
     ]
    }
   ],
   "source": [
    "for threshold in np.linspace(0, 1, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_bigrating-image_{threshold=:.3f}'\n",
    "    image = grid_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": 52,
   "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": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.000 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.000_d5c69061.png' \n",
      "radius=0.113 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.113_40afe992.png' \n",
      "radius=0.225 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.225_c44306d0.png' \n",
      "radius=0.338 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.338_8506311d.png' \n",
      "radius=0.450 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.450_1710bbfe.png' \n",
      "radius=0.562 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.562_2b50e892.png' \n",
      "radius=0.675 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.675_59a008a6.png' \n",
      "radius=0.787 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.787_527e88c4.png' \n",
      "radius=0.900 -> output_filename='2022-12-03_caustique/caustique_grating-image_radius=0.900_328f619f.png' \n"
     ]
    }
   ],
   "source": [
    "for radius in np.linspace(0, .9, N_scan):\n",
    "    opt = init()\n",
    "    c = Caustique(opt)\n",
    "\n",
    "    c.opt.tag = f'{c.opt.tag}_grating-image_{radius=:.3f}'\n",
    "    image = grid_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": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
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     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "period1=1.000 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=1.000_69e84a1e.png' \n",
      "period1=1.334 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=1.334_22ecdf75.png' \n",
      "period1=1.778 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=1.778_483d62d1.png' \n",
      "period1=2.371 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=2.371_311c8b48.png' \n",
      "period1=3.162 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=3.162_638c71d1.png' \n",
      "period1=4.217 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=4.217_8d108344.png' \n",
      "period1=5.623 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=5.623_9b6173f2.png' \n",
      "period1=7.499 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=7.499_14cc474c.png' \n",
      "period1=10.000 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period1=10.000_15b32c03.png' \n"
     ]
    }
   ],
   "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}_bigrating-image_{period1=:.3f}'\n",
    "    image = grid_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": 54,
   "metadata": {
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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "period2=1.000 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=1.000_fb06acad.png' \n",
      "period2=1.334 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=1.334_00af18eb.png' \n",
      "period2=1.778 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=1.778_e5044700.png' \n",
      "period2=2.371 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=2.371_b7602664.png' \n",
      "period2=3.162 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=3.162_8815be9f.png' \n",
      "period2=4.217 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=4.217_e4e0829d.png' \n",
      "period2=5.623 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=5.623_d93d2b75.png' \n",
      "period2=7.499 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=7.499_06c65336.png' \n",
      "period2=10.000 -> output_filename='2022-12-03_caustique/caustique_bigrating-image_period2=10.000_3df9b650.png' \n"
     ]
    }
   ],
   "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}_bigrating-image_{period2=:.3f}'\n",
    "    image = grid_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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