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 = True # 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=2024-07-24_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='2024-07-24_caustique',\n",
      "     phi=1.61803,\n",
      "     tag='caustique',\n",
      "     ext='png',\n",
      "     nx=5120,\n",
      "     ny=5120,\n",
      "     nframe=1,\n",
      "     bin_dens=2,\n",
      "     bin_spectrum=1,\n",
      "     seed=2024,\n",
      "     H=20.0,\n",
      "     variation=0.2,\n",
      "     scale=870.4,\n",
      "     B_sf=1.25,\n",
      "     V_Y=0.3,\n",
      "     V_X=0.3,\n",
      "     B_V=1.0,\n",
      "     zmin=0.2,\n",
      "     theta=1.5707963267948966,\n",
      "     B_theta=1.0471975511965976,\n",
      "     min_lum=0.1,\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=65dpi\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_21826/1923257970.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": [
       "(5120, 5120, 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 [03:21<00:00,  2.49s/it]\n",
      "100%|██████████| 1/1 [03:21<00:00, 201.80s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.68it/s]\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=\"2024-07-24_caustique/caustique_bb52fe1f.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": 14,
   "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": [
      "100%|██████████| 81/81 [03:13<00:00,  2.39s/it]\n",
      "100%|██████████| 1/1 [03:13<00:00, 193.86s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.94it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 10.000 -> output_filename='2024-07-24_caustique/caustique_H_10.000_f71b6441.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:15<00:00,  2.42s/it]\n",
      "100%|██████████| 1/1 [03:15<00:00, 195.63s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.89it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 11.892 -> output_filename='2024-07-24_caustique/caustique_H_11.892_7d5a54d5.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:15<00:00,  2.41s/it]\n",
      "100%|██████████| 1/1 [03:15<00:00, 195.07s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 14.142 -> output_filename='2024-07-24_caustique/caustique_H_14.142_1bf6c15d.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:16<00:00,  2.43s/it]\n",
      "100%|██████████| 1/1 [03:16<00:00, 196.53s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.85it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 16.818 -> output_filename='2024-07-24_caustique/caustique_H_16.818_1417ee42.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:16<00:00,  2.42s/it]\n",
      "100%|██████████| 1/1 [03:16<00:00, 196.24s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 20.000 -> output_filename='2024-07-24_caustique/caustique_H_20.000_ca9a3260.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:17<00:00,  2.44s/it]\n",
      "100%|██████████| 1/1 [03:17<00:00, 197.60s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.67it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 23.784 -> output_filename='2024-07-24_caustique/caustique_H_23.784_6025daa7.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:23<00:00,  2.51s/it]\n",
      "100%|██████████| 1/1 [03:23<00:00, 203.32s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.51it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 28.284 -> output_filename='2024-07-24_caustique/caustique_H_28.284_8aca5dce.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:26<00:00,  2.55s/it]\n",
      "100%|██████████| 1/1 [03:26<00:00, 206.34s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.44it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 33.636 -> output_filename='2024-07-24_caustique/caustique_H_33.636_1676bd58.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:28<00:00,  2.57s/it]\n",
      "100%|██████████| 1/1 [03:28<00:00, 208.37s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.32it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 40.000 -> output_filename='2024-07-24_caustique/caustique_H_40.000_14b4f753.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\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, 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": 15,
   "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": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:20<00:00,  2.48s/it]\n",
      "100%|██████████| 1/1 [03:20<00:00, 200.79s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.75it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.010  -> output_filename='2024-07-24_caustique/caustique_variation_0.010_3b7030f9.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:14<00:00,  2.40s/it]\n",
      "100%|██████████| 1/1 [03:14<00:00, 194.59s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.90it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.017  -> output_filename='2024-07-24_caustique/caustique_variation_0.017_bdd57b3e.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:15<00:00,  2.41s/it]\n",
      "100%|██████████| 1/1 [03:15<00:00, 195.15s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.87it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.028  -> output_filename='2024-07-24_caustique/caustique_variation_0.028_c7bf47b3.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:16<00:00,  2.42s/it]\n",
      "100%|██████████| 1/1 [03:16<00:00, 196.29s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.046  -> output_filename='2024-07-24_caustique/caustique_variation_0.046_bbcb11bd.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:14<00:00,  2.41s/it]\n",
      "100%|██████████| 1/1 [03:14<00:00, 194.97s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.82it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.077  -> output_filename='2024-07-24_caustique/caustique_variation_0.077_73aa2331.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:14<00:00,  2.40s/it]\n",
      "100%|██████████| 1/1 [03:14<00:00, 194.29s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.129  -> output_filename='2024-07-24_caustique/caustique_variation_0.129_7ecd7924.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:14<00:00,  2.40s/it]\n",
      "100%|██████████| 1/1 [03:14<00:00, 194.78s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.79it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.215  -> output_filename='2024-07-24_caustique/caustique_variation_0.215_992964a2.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:13<00:00,  2.39s/it]\n",
      "100%|██████████| 1/1 [03:13<00:00, 193.82s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.76it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.359  -> output_filename='2024-07-24_caustique/caustique_variation_0.359_273fe732.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:13<00:00,  2.39s/it]\n",
      "100%|██████████| 1/1 [03:13<00:00, 193.84s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.69it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variation = 0.599  -> output_filename='2024-07-24_caustique/caustique_variation_0.599_4482c49c.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\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, 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": 16,
   "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"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:27<00:00,  2.57s/it]\n",
      "100%|██████████| 1/1 [03:27<00:00, 207.79s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.20it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*0.500=4.352E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.500_a13a0f8e.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:24<00:00,  2.52s/it]\n",
      "100%|██████████| 1/1 [03:24<00:00, 204.51s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.30it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*0.595=5.175E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.595_d13b1441.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:20<00:00,  2.47s/it]\n",
      "100%|██████████| 1/1 [03:20<00:00, 200.42s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.46it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale=scale(default)*0.707=6.155E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.707_7b95187e.png'\n"
     ]
    },
    {
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      "scale=scale(default)*0.841=7.319E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.841_c7477141.png'\n"
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      "scale=scale(default)*1.189=1.035E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_1.189_91183d43.png'\n"
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      "scale=scale(default)*1.414=1.231E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_1.414_7561f818.png'\n"
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      "scale=scale(default)*1.682=1.464E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_1.682_d3a01cd1.png'\n"
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      "scale=scale(default)*2.000=1.741E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_2.000_c38acc44.png'\n",
      "======B_sf======\n"
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      "B_sf=B_sf(default)*0.500=6.250E-01 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.500_2e25c9c6.png'\n"
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      "B_sf=B_sf(default)*0.595=7.433E-01 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.595_680311d9.png'\n"
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      "B_sf=B_sf(default)*0.841=1.051E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.841_a3f5b12f.png'\n"
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      "B_sf=B_sf(default)*1.000=1.250E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.000_5b595f4c.png'\n"
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      "B_sf=B_sf(default)*1.189=1.487E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.189_f2cc2bb1.png'\n"
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      "B_sf=B_sf(default)*1.414=1.768E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.414_df5a9ab1.png'\n"
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      "B_sf=B_sf(default)*1.682=2.102E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.682_df7d7055.png'\n"
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      "B_sf=B_sf(default)*2.000=2.500E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_2.000_46aa158d.png'\n",
      "======theta======\n"
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      "theta=theta(default)*0.500=7.854E-01 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.500_797ee560.png'\n"
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      "theta=theta(default)*0.595=9.340E-01 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.595_57ef1765.png'\n"
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      "theta=theta(default)*0.707=1.111E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.707_c728cd2a.png'\n"
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      "theta=theta(default)*0.841=1.321E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.841_f7950331.png'\n"
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      "theta=theta(default)*1.000=1.571E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.000_9338e312.png'\n"
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      "theta=theta(default)*1.189=1.868E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.189_6066711f.png'\n"
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      "theta=theta(default)*1.414=2.221E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.414_0c6f7927.png'\n"
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      "theta=theta(default)*1.682=2.642E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.682_fea7a4df.png'\n"
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      "theta=theta(default)*2.000=3.142E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_2.000_cf5d5ab6.png'\n",
      "======B_theta======\n"
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      "B_theta=B_theta(default)*0.500=5.236E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.500_c026242c.png'\n"
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      "B_theta=B_theta(default)*0.595=6.227E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.595_5f1f01bc.png'\n"
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      "B_theta=B_theta(default)*0.707=7.405E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.707_4f4ac9ea.png'\n"
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      "B_theta=B_theta(default)*0.841=8.806E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.841_e219eec0.png'\n"
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      "B_theta=B_theta(default)*1.000=1.047E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.000_363867b2.png'\n"
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      "B_theta=B_theta(default)*1.189=1.245E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.189_ffe819cf.png'\n"
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      "B_theta=B_theta(default)*1.414=1.481E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.414_828c9bbb.png'\n"
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      "B_theta=B_theta(default)*1.682=1.761E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.682_4b40e085.png'\n"
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      "B_theta=B_theta(default)*2.000=2.094E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_2.000_add66392.png'\n",
      "======gamma======\n"
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.500=1.200E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.500_49f79e4c.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.595=1.427E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.595_71396ff5.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.707=1.697E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.707_b6d698fb.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.841=2.018E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.841_2faf2034.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.000=2.400E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.000_a5a0d8ca.png'\n"
     ]
    },
    {
     "name": "stderr",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.189=2.854E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.189_f658bd09.png'\n"
     ]
    },
    {
     "name": "stderr",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.414=3.394E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.414_568cf5fe.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.682=4.036E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.682_af7134f6.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*2.000=4.800E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_2.000_ed8fc44b.png'\n",
      "======min_lum======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:09<00:00,  2.34s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.500=5.000E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.500_dbef85a5.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.595=5.946E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.595_8e7ae54b.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.707=7.071E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.707_aa550a41.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.841=8.409E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.841_c29c6e37.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.000=1.000E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.000_f1d0bdab.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.189=1.189E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.189_5cd543a2.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.414=1.414E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.414_88fc2b4a.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.682=1.682E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.682_20ce93a6.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*2.000=2.000E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_2.000_ecf47e0c.png'\n",
      "======zmin======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:09<00:00,  2.33s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.500=1.000E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.500_fb8bb25a.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.595=1.189E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.595_3ca3d201.png'\n"
     ]
    },
    {
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     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.707=1.414E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.707_bf3c0e8d.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.841=1.682E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.841_f06ad317.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.000=2.000E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.000_5a2642d1.png'\n"
     ]
    },
    {
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     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.189=2.378E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.189_bf52ece1.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.414=2.828E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.414_5646fe1e.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.682=3.364E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.682_60a57eb1.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*2.000=4.000E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_2.000_1b0aa246.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:12<00:00, 192.18s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.79it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img src=\"2024-07-24_caustique/caustique_grating-image_d6c01183.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}_{type}-image'\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:06<00:00,  2.30s/it]\n",
      "100%|██████████| 1/1 [03:06<00:00, 186.29s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.88it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 10.000 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_10.000_784a462c.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:07<00:00,  2.31s/it]\n",
      "100%|██████████| 1/1 [03:07<00:00, 187.32s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.97it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 11.892 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_11.892_3909d292.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:08<00:00,  2.33s/it]\n",
      "100%|██████████| 1/1 [03:08<00:00, 188.89s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.88it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 14.142 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_14.142_21227dce.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:09<00:00,  2.35s/it]\n",
      "100%|██████████| 1/1 [03:09<00:00, 190.00s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.84it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 16.818 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_16.818_21319d52.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.81s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.75it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 20.000 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_20.000_681cf358.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:13<00:00,  2.39s/it]\n",
      "100%|██████████| 1/1 [03:13<00:00, 193.32s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.66it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 23.784 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_23.784_7b1090da.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:15<00:00,  2.41s/it]\n",
      "100%|██████████| 1/1 [03:15<00:00, 195.28s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.53it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 28.284 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_28.284_e5f3e67e.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:17<00:00,  2.44s/it]\n",
      "100%|██████████| 1/1 [03:17<00:00, 197.35s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.42it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 33.636 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_33.636_7561e551.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:18<00:00,  2.44s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H = 40.000 -> output_filename='2024-07-24_caustique/caustique_grating-image_H_40.000_140204a8.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\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}_{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": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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      "100%|██████████| 1/1 [00:00<00:00,  1.58it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.100 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.100_ef4b472a.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.200 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.200_21b96c33.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.300 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.300_a930bec9.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:10<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.400 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.400_88a562f1.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.500 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.500_f999bcd2.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.600 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.600_db03f147.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.700 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.700_221fa8d7.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.800 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.800_02695f59.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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      "100%|██████████| 1/1 [00:00<00:00,  2.30it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.900 -> output_filename='2024-07-24_caustique/caustique_grating-image_threshold=0.900_45da01db.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "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": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.61s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  3.50it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.111 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.111_4cabe6db.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.70s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  3.35it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.222 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.222_817fd394.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.333 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.333_a0510b84.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.444 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.444_62bfb655.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.38s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.556 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.556_01812285.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.667 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.667_1a5aada8.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.38s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.778 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.778_f66d93ed.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.37s/it]\n",
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      "100%|██████████| 1/1 [00:00<00:00,  1.80it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=0.889 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=0.889_a3f9a495.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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      "100%|██████████| 1/1 [00:00<00:00,  1.50it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "radius=1.000 -> output_filename='2024-07-24_caustique/caustique_grating-image_radius=1.000_e76caea3.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.45s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  2.15it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.000 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=1.00e+00_a8d80f2e.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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      "100%|██████████| 1/1 [00:00<00:00,  1.70it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.334 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=1.33e+00_c7ac651d.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=1.778 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=1.78e+00_204af4c1.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=2.371 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=2.37e+00_35298f76.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.38s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=3.162 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=3.16e+00_5dd1a7cd.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:13<00:00,  2.39s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=4.217 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=4.22e+00_0801226e.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.36s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=5.623 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=5.62e+00_8c8e8a2a.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=7.499 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=7.50e+00_7e51e58c.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "periods=10.000 -> output_filename='2024-07-24_caustique/caustique_grating-image_periods=1.00e+01_469dfca1.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\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}_{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": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "======scale======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:23<00:00,  2.52s/it]\n",
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      "100%|██████████| 1/1 [00:00<00:00,  1.20it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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      "scale=scale(default)*0.500=4.352E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.500_a13a0f8e.png'\n"
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      "scale=scale(default)*0.595=5.175E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.595_d13b1441.png'\n"
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      "scale=scale(default)*0.707=6.155E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.707_7b95187e.png'\n"
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      "scale=scale(default)*0.841=7.319E+02 -> output_filename='2024-07-24_caustique/caustique_scale_modul_0.841_c7477141.png'\n"
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      "scale=scale(default)*1.189=1.035E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_1.189_91183d43.png'\n"
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      "scale=scale(default)*1.414=1.231E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_1.414_7561f818.png'\n"
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      "scale=scale(default)*1.682=1.464E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_1.682_d3a01cd1.png'\n"
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      "scale=scale(default)*2.000=1.741E+03 -> output_filename='2024-07-24_caustique/caustique_scale_modul_2.000_c38acc44.png'\n",
      "======B_sf======\n"
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      "B_sf=B_sf(default)*0.500=6.250E-01 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.500_2e25c9c6.png'\n"
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      "B_sf=B_sf(default)*0.595=7.433E-01 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.595_680311d9.png'\n"
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      "B_sf=B_sf(default)*0.707=8.839E-01 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.707_59ce4d32.png'\n"
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      "B_sf=B_sf(default)*0.841=1.051E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_0.841_a3f5b12f.png'\n"
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      "B_sf=B_sf(default)*1.189=1.487E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.189_f2cc2bb1.png'\n"
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      "B_sf=B_sf(default)*1.414=1.768E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.414_df5a9ab1.png'\n"
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      "B_sf=B_sf(default)*1.682=2.102E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_1.682_df7d7055.png'\n"
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      "B_sf=B_sf(default)*2.000=2.500E+00 -> output_filename='2024-07-24_caustique/caustique_B_sf_modul_2.000_46aa158d.png'\n",
      "======theta======\n"
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      "theta=theta(default)*0.500=7.854E-01 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.500_797ee560.png'\n"
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      "theta=theta(default)*0.595=9.340E-01 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.595_57ef1765.png'\n"
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      "theta=theta(default)*0.707=1.111E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.707_c728cd2a.png'\n"
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      "theta=theta(default)*0.841=1.321E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_0.841_f7950331.png'\n"
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      "theta=theta(default)*1.000=1.571E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.000_9338e312.png'\n"
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      "theta=theta(default)*1.189=1.868E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.189_6066711f.png'\n"
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      "theta=theta(default)*1.414=2.221E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.414_0c6f7927.png'\n"
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      "theta=theta(default)*1.682=2.642E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_1.682_fea7a4df.png'\n"
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      "theta=theta(default)*2.000=3.142E+00 -> output_filename='2024-07-24_caustique/caustique_theta_modul_2.000_cf5d5ab6.png'\n",
      "======B_theta======\n"
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      "B_theta=B_theta(default)*0.500=5.236E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.500_c026242c.png'\n"
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      "B_theta=B_theta(default)*0.595=6.227E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.595_5f1f01bc.png'\n"
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      "B_theta=B_theta(default)*0.707=7.405E-01 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_0.707_4f4ac9ea.png'\n"
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      "B_theta=B_theta(default)*1.000=1.047E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.000_363867b2.png'\n"
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      "B_theta=B_theta(default)*1.189=1.245E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.189_ffe819cf.png'\n"
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      "B_theta=B_theta(default)*1.414=1.481E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.414_828c9bbb.png'\n"
     ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B_theta=B_theta(default)*1.682=1.761E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_1.682_4b40e085.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B_theta=B_theta(default)*2.000=2.094E+00 -> output_filename='2024-07-24_caustique/caustique_B_theta_modul_2.000_add66392.png'\n",
      "======gamma======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:10<00:00,  2.35s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.500=1.200E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.500_49f79e4c.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.595=1.427E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.595_71396ff5.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.707=1.697E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.707_b6d698fb.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*0.841=2.018E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_0.841_2faf2034.png'\n"
     ]
    },
    {
     "name": "stderr",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.000=2.400E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.000_a5a0d8ca.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.189=2.854E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.189_f658bd09.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.414=3.394E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.414_568cf5fe.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*1.682=4.036E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_1.682_af7134f6.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma=gamma(default)*2.000=4.800E+00 -> output_filename='2024-07-24_caustique/caustique_gamma_modul_2.000_ed8fc44b.png'\n",
      "======min_lum======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:10<00:00,  2.35s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.500=5.000E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.500_dbef85a5.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.595=5.946E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.595_8e7ae54b.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.707=7.071E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.707_aa550a41.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*0.841=8.409E-02 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_0.841_c29c6e37.png'\n"
     ]
    },
    {
     "name": "stderr",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.000=1.000E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.000_f1d0bdab.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.189=1.189E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.189_5cd543a2.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.414=1.414E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.414_88fc2b4a.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*1.682=1.682E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_1.682_20ce93a6.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min_lum=min_lum(default)*2.000=2.000E-01 -> output_filename='2024-07-24_caustique/caustique_min_lum_modul_2.000_ecf47e0c.png'\n",
      "======zmin======\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:08<00:00,  2.32s/it]\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.500=1.000E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.500_fb8bb25a.png'\n"
     ]
    },
    {
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     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.595=1.189E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.595_3ca3d201.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.707=1.414E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.707_bf3c0e8d.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*0.841=1.682E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_0.841_f06ad317.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.000=2.000E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.000_5a2642d1.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.189=2.378E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.189_bf52ece1.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.414=2.828E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.414_5646fe1e.png'\n"
     ]
    },
    {
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*1.682=3.364E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_1.682_60a57eb1.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "zmin=zmin(default)*2.000=4.000E-01 -> output_filename='2024-07-24_caustique/caustique_zmin_modul_2.000_1b0aa246.png'\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.38s/it]\n",
      "100%|██████████| 1/1 [03:12<00:00, 192.62s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.57it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<img src=\"2024-07-24_caustique/caustique_grid-image_fbb3cbe7.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}_{type}-image'\n",
    "\n",
    "output_filename = c.plot(z, image)\n",
    "c.show(output_filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "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": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.87s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.37it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.100 -> output_filename='2024-07-24_caustique/caustique_grid-image_threshold=0.100_742a7cfa.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:12<00:00,  2.38s/it]\n",
      "100%|██████████| 1/1 [03:12<00:00, 192.47s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.45it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.200 -> output_filename='2024-07-24_caustique/caustique_grid-image_threshold=0.200_6718c7c4.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.84s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.52it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.300 -> output_filename='2024-07-24_caustique/caustique_grid-image_threshold=0.300_2aec17f2.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 81/81 [03:11<00:00,  2.37s/it]\n",
      "100%|██████████| 1/1 [03:11<00:00, 191.87s/it]\n",
      "100%|██████████| 1/1 [00:00<00:00,  1.56it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "threshold=0.400 -> output_filename='2024-07-24_caustique/caustique_grid-image_threshold=0.400_bd251189.png' \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1 [00:00<?, ?it/s]"
     ]
    }
   ],
   "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,
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    "execution": {
     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
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   },
   "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",
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     "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": {
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   "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",
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   "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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