direct_imaging.ipynb

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    "<h1>Direct imaging: the planet around beta-Pictoris</h1>\n",
    "    \n",
    "In this example we take a look at data obtained with the [NACO](https://www.eso.org/sci/facilities/paranal/decommissioned/naco.html) instrument on the [Very Large Telescope (VLT)](https://www.eso.org/public/unitedkingdom/teles-instr/paranal-observatory/vlt/). This data was described in a paper by [Bonnefoy et al. (2013)](https://arxiv.org/abs/1302.1160); we will be looking at data taken at $4.78~\\mu {\\rm m}$ (known as the $M'$ band). We will follow the example of the [`pynpoint`](https://pynpoint.readthedocs.io/en/latest/index.html) package and look at the planet around beta-Pictoris. This notebook is intended to give you an idea of what is involved; **you will not be examined on the techniques discussed here!** \n",
    "\n",
    "<h2>Angular Differential Imaging</h2>\n",
    "\n",
    "The brightness contrast between star and planet is the main concern with direct imaging. In the lecture notes, we covered coronographs as a possible solution. In this notebook, we cover a different technique called Angular Differential Imaging ([Marois et al. 2006](https://arxiv.org/abs/astro-ph/0512335)). This is a technique that can be used to subtract the light from the central star to very high accuracy. The central star is a point source, and the response of the optics system to a point source is called the Point Spread Function (PSF).\n",
    "\n",
    "<h3>Field rotation</h3>\n",
    "\n",
    "When taking long exposures while tracking an object, the field of view will rotate during the exposure; this is called [field rotation](https://themcdonalds.net/richard/wp/astrophotography-field-rotation/). Normally, this is corrected for during an observation using a field derotator. However, when looking for faint objects around a bright star, turning the derotator off can be advantageous. Since the telescope now does not rotate, any feature in the image introduced by the optics of the telescope will not rotate and can therefore be more easily subtracted. \n",
    "\n",
    "<h3>Accurate Point Spread function</h3>\n",
    "\n",
    "We now take **many** short observations during one night, so that field rotation can be ignored for a single exposure. Atmospheric turbulence as well as thermal effects are likely to change the PSF during the night, but we can use the large number of observations to track these changes and construct *very* accurate PSFs. These can then be subtracted from each observation.     \n",
    "\n",
    "<h2>Original image set</h2>\n",
    "\n",
    "Below is an image set of 263 observations of beta-Pictoris. The star is in the middle of each image and completely dominates: no planet in sight! You can move the slider to look at different images, and you will see subtle changes. These are all artificial, possibly caused by atmospheric turbulence. "
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    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'pynpoint'",
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      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-2-29df1341d05e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mipywidgets\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mwidgets\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mpynpoint\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mPypeline\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m                      \u001b[0mHdf5ReadingModule\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m                      \u001b[0mPSFpreparationModule\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'pynpoint'"
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   "source": [
    "%%capture\n",
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widgets\n",
    "\n",
    "from pynpoint import Pypeline, \\\n",
    "                     Hdf5ReadingModule, \\\n",
    "                     PSFpreparationModule, \\\n",
    "                     PcaPsfSubtractionModule\n",
    "\n",
    "pipeline1 = Pypeline(working_place_in='./',\n",
    "                    input_place_in='./',\n",
    "                    output_place_in='./')\n",
    "\n",
    "\n",
    "module = Hdf5ReadingModule(name_in='read',\n",
    "                           input_filename='data/betapic_naco_mp.hdf5',\n",
    "                           input_dir=None,\n",
    "                           tag_dictionary={'stack': 'stack'})\n",
    "\n",
    "pipeline1.add_module(module)\n",
    "\n",
    "pipeline1.run()\n",
    "\n",
    "#print(pipeline.get_tags())\n",
    "raw_data = pipeline1.get_data('stack')\n",
    "pixscale = pipeline1.get_attribute('stack', 'PIXSCALE')\n",
    "\n",
    "size = pixscale*raw_data.shape[-1]/2.\n"
   ]
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       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = 'image/png';\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data']);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id='ade52794-fada-43ad-af71-b118588514ad'></div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "ename": "NameError",
     "evalue": "name 'raw_data' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-aa211af70507>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[0max1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgca\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 21\u001b[0;31m \u001b[0mim\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0max1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mraw_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m260\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0morigin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'lower'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextent\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     22\u001b[0m \u001b[0max1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_title\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'beta Pic b - NACO M\\' - original data'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0max1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_xlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'R.A. offset [arcsec]'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfontsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'raw_data' is not defined"
     ]
    }
   ],
   "source": [
    "w_raw_index=widgets.IntSlider(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=262,\n",
    "    step=1,\n",
    "    description='Image index:',\n",
    "    disabled=False,\n",
    "    continuous_update=False,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='d',\n",
    ")\n",
    "\n",
    "# Display button\n",
    "output = widgets.Output()\n",
    "display(w_raw_index, output)\n",
    "\n",
    "fig1 = plt.figure(figsize=(6,4),num='Raw data')\n",
    "ax1 = plt.gca()\n",
    "\n",
    "im=ax1.imshow(raw_data[260, ], origin='lower', extent=[size, -size, -size, size])\n",
    "ax1.set_title('beta Pic b - NACO M\\' - original data')\n",
    "ax1.set_xlabel('R.A. offset [arcsec]', fontsize=12)\n",
    "ax1.set_ylabel('Dec. offset [arcsec]', fontsize=12)\n",
    "plt.colorbar(im);\n",
    "\n",
    "def on_value_change(change):\n",
    "    with output:\n",
    "        im.set_data(raw_data[w_raw_index.value])\n",
    "\n",
    "        #ax3.set_title(name)\n",
    "        #ax1.relim()\n",
    "        #ax1.autoscale()\n",
    "\n",
    "w_raw_index.observe(on_value_change, names='value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Subtracting the saturated centre</h2>\n",
    "\n",
    "The exposure time was chosen so that the central pixels are completely saturated. If we mask these out, the changes from frame to frame become much more apparent. You can now clearly see the ringed structure of the PSF (normal for circular apertures). Still no planet to be seen..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "pipeline2 = Pypeline(working_place_in='./',\n",
    "                     input_place_in='./',\n",
    "                     output_place_in='./')\n",
    "\n",
    "\n",
    "module = Hdf5ReadingModule(name_in='read',\n",
    "                           input_filename='data/betapic_naco_mp.hdf5',\n",
    "                           input_dir=None,\n",
    "                           tag_dictionary={'stack': 'stack'})\n",
    "\n",
    "pipeline2.add_module(module)\n",
    "\n",
    "module = PSFpreparationModule(name_in='prep',\n",
    "                              image_in_tag='stack',\n",
    "                              image_out_tag='prep',\n",
    "                              mask_out_tag=None,\n",
    "                              norm=False,\n",
    "                              resize=None,\n",
    "                              cent_size=0.15,\n",
    "                              edge_size=1.1)\n",
    "\n",
    "pipeline2.add_module(module)\n",
    "\n",
    "pipeline2.run()\n",
    "\n",
    "psf_prep = pipeline2.get_data('prep')\n",
    "pixscale = pipeline2.get_attribute('stack', 'PIXSCALE')\n",
    "\n",
    "size = pixscale*psf_prep.shape[-1]/2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_psf_index=widgets.IntSlider(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=262,\n",
    "    step=1,\n",
    "    description='Image index:',\n",
    "    disabled=False,\n",
    "    continuous_update=False,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='d',\n",
    ")\n",
    "\n",
    "# Display button\n",
    "output = widgets.Output()\n",
    "display(w_psf_index, output)\n",
    "\n",
    "fig2 = plt.figure(figsize=(6,4),num='PSF')\n",
    "ax2 = plt.gca()\n",
    "\n",
    "im2=ax2.imshow(psf_prep[0, ], origin='lower', extent=[size, -size, -size, size])\n",
    "ax2.set_title('beta Pic b - NACO M\\' - PSF')\n",
    "ax2.set_xlabel('R.A. offset [arcsec]', fontsize=12)\n",
    "ax2.set_ylabel('Dec. offset [arcsec]', fontsize=12)\n",
    "plt.colorbar(im2);\n",
    "\n",
    "def on_value_change(change):\n",
    "    with output:\n",
    "        im2.set_data(psf_prep[w_psf_index.value,])\n",
    "\n",
    "        #ax3.set_title(name)\n",
    "        #ax1.relim()\n",
    "        #ax1.autoscale()\n",
    "\n",
    "w_psf_index.observe(on_value_change, names='value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Calculating and subtracting the PSF</h2>\n",
    "\n",
    "The PSF is fitted using Principle Component Analysis. It takes the global shapes of the PSF and its variation with time to obtain a very accurate representation of the PSF that can then be subtracted. You can see in the individual images that the algorithm did a good job: there is nothing left but noise! The exposure times for the individual frames are too short to reveal the planet.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "pipeline3 = Pypeline(working_place_in='./',\n",
    "                     input_place_in='./',\n",
    "                     output_place_in='./')\n",
    "\n",
    "\n",
    "module = Hdf5ReadingModule(name_in='read',\n",
    "                           input_filename='data/betapic_naco_mp.hdf5',\n",
    "                           input_dir=None,\n",
    "                           tag_dictionary={'stack': 'stack'})\n",
    "\n",
    "pipeline3.add_module(module)\n",
    "\n",
    "module = PSFpreparationModule(name_in='prep',\n",
    "                              image_in_tag='stack',\n",
    "                              image_out_tag='prep',\n",
    "                              mask_out_tag=None,\n",
    "                              norm=False,\n",
    "                              resize=None,\n",
    "                              cent_size=0.15,\n",
    "                              edge_size=1.1)\n",
    "\n",
    "pipeline3.add_module(module)\n",
    "\n",
    "module = PcaPsfSubtractionModule(pca_numbers=[20, ],\n",
    "                                 name_in='pca',\n",
    "                                 images_in_tag='prep',\n",
    "                                 reference_in_tag='prep',\n",
    "                                 res_median_tag='residuals',\n",
    "                                 res_arr_out_tag='res_array')\n",
    "\n",
    "pipeline3.add_module(module)\n",
    "\n",
    "pipeline3.run()\n",
    "\n",
    "res_array = pipeline3.get_data('res_array20')\n",
    "res_median = pipeline3.get_data('residuals')\n",
    "pixscale = pipeline3.get_attribute('stack', 'PIXSCALE')\n",
    "\n",
    "size = pixscale*res_median.shape[-1]/2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "w_res_index=widgets.IntSlider(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=262,\n",
    "    step=1,\n",
    "    description='Image index:',\n",
    "    disabled=False,\n",
    "    continuous_update=False,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='d',\n",
    ")\n",
    "\n",
    "# Display button\n",
    "output = widgets.Output()\n",
    "display(w_res_index, output)\n",
    "\n",
    "fig3 = plt.figure(figsize=(6,4),num='Residuals')\n",
    "ax3 = plt.gca()\n",
    "\n",
    "im3=ax3.imshow(res_array[0, ], origin='lower', extent=[size, -size, -size, size])\n",
    "ax3.set_title('beta Pic b - NACO M\\' - residuals')\n",
    "ax3.set_xlabel('R.A. offset [arcsec]', fontsize=12)\n",
    "ax3.set_ylabel('Dec. offset [arcsec]', fontsize=12)\n",
    "plt.colorbar(im3);\n",
    "\n",
    "fig4 = plt.figure(figsize=(6,4),num='Median Residuals')\n",
    "ax4 = plt.gca()\n",
    "\n",
    "im4=ax4.imshow(res_median[0, ], origin='lower', extent=[size, -size, -size, size])\n",
    "ax4.set_title('beta Pic b - NACO M\\' - median residuals')\n",
    "ax4.set_xlabel('R.A. offset [arcsec]', fontsize=12)\n",
    "ax4.set_ylabel('Dec. offset [arcsec]', fontsize=12)\n",
    "plt.colorbar(im4);\n",
    "\n",
    "def on_value_change(change):\n",
    "    with output:\n",
    "        im3.set_data(res_array[w_res_index.value,])\n",
    "\n",
    "w_res_index.observe(on_value_change, names='value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Combining all frames</h2>\n",
    "\n",
    "If we now combine all frames, we can finally see the planet! The projected separation is roughly 0.5 arcseconds. As it turns out, this technique is much more powerful than taking a single, very long exposure. This would mean only a single, average PSF can be obtained, which is much less accurate. Another drawback is that a longer exposure time would mean much more of the image would get saturated, possibly flooding the planet as well (the brightness contrast strikes again!).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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