Gradient WFS - Pixel Scale.ipynb

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   "source": [
    "import numpy\n",
    "import bokeh.plotting as bplot\n",
    "bplot.output_notebook()\n",
    "from matplotlib import pyplot\n",
    "%matplotlib notebook\n",
    "import seaborn"
   ]
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     "text": [
      "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/IPython/qt.py:13: ShimWarning: The `IPython.qt` package has been deprecated. You should import from qtconsole instead.\n",
      "  \"You should import from qtconsole instead.\", ShimWarning)\n"
     ]
    }
   ],
   "source": [
    "from soapy import WFS, confParse\n",
    "from aotools import circle"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "SOAPY_CONF = \"conf/test_conf.py\""
   ]
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   "source": [
    "# load Soapy config\n",
    "config = confParse.Configurator(SOAPY_CONF)\n",
    "config.loadSimParams()\n",
    "config.wfss[0].pxlsPerSubap = 30\n",
    "config.wfss[0].subapThreshld = 1.\n",
    "mask = circle.circle(config.sim.pupilSize/2., config.sim.simSize)"
   ]
  },
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   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "35.25917680796625"
      ]
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     "execution_count": 5,
     "metadata": {},
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    }
   ],
   "source": [
    "# One arcec in tilt Amp across scope\n",
    "tilt_rad = 1./3600 * numpy.pi/180\n",
    "tilt_amp = tilt_rad*config.tel.telDiam/2.\n",
    "tilt_amp/(550e-9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "PXL_SCALE = 1 #asec/pxl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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   "source": [
    "# Measure current pixel scale\n",
    "maxTilt = 4*PXL_SCALE # arcsecs\n",
    "tilts_asec = numpy.linspace(-maxTilt, maxTilt, 10)\n",
    "\n",
    "tilts_rad = (tilts_asec/3600.) * (numpy.pi/180)\n",
    "# Must convert arcsecs of tilt to amp in nm\n",
    "tiltAmps = 1e9 * (tilts_rad * config.tel.telDiam/2.)# in nm amp\n",
    "\n",
    "# Make a unit tilt to multiply\n",
    "coords = numpy.linspace(-1, 1, config.sim.pupilSize)\n",
    "coords = numpy.pad(coords, pad_width=[config.sim.simPad,]*2, mode=\"constant\")\n",
    "tilt = numpy.meshgrid(coords, coords)[0]\n",
    "\n",
    "measuredTilts = numpy.zeros((tiltAmps.shape[0]))\n",
    "for i, A in enumerate(tiltAmps):\n",
    "    config.wfss[0].subapFOV = config.wfss[0].pxlsPerSubap*PXL_SCALE\n",
    "    wfs = WFS.Gradient(config.sim, config.wfss[0], config.atmos, config.lgss[0], mask)\n",
    "    \n",
    "    aTilt = tilt*A\n",
    "    slopes = wfs.frame(aTilt)\n",
    "    measuredTilts[i] = slopes[:wfs.activeSubaps].mean()\n",
    "    \n",
    "    # Check tilt is what I think it is\n",
    "    dAmp = (aTilt.max() - aTilt.min())*1e-9\n",
    "    angle = (dAmp/config.tel.telDiam) * (180./numpy.pi) * 3600"
   ]
  },
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   "execution_count": 8,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measured Pixel Scale: 4.20903598889 pxls/arcsec\n"
     ]
    }
   ],
   "source": [
    "A = numpy.vstack([tilts_asec, numpy.ones(len(tilts_asec))]).T\n",
    "pxlScale, bias = numpy.linalg.lstsq(A, measuredTilts)[0]\n",
    "print(\"Measured Pixel Scale: {} pxls/arcsec\".format(1./pxlScale))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "6e-07\n"
     ]
    }
   ],
   "source": [
    "print(wfs.subapDiam)\n",
    "print(wfs.wfsConfig.wavelength)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
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       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    {\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.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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\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,\n",
       "                             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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"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\";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 overriden (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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\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).html('<img src=\"' + dataURL + '\">');\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\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",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-4, 4)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyplot.figure()\n",
    "pyplot.plot(tilts_asec, measuredTilts)\n",
    "pyplot.xlabel('Input Tilt (arcsecs)')\n",
    "pyplot.ylabel('Measurement')\n",
    "pyplot.ylim(-4,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def getMeasurePixelScale(maxTilt, config, samples=50):\n",
    "    \n",
    "    # Measure current pixel scale\n",
    "    tilts_asec = numpy.linspace(-maxTilt, maxTilt, samples)\n",
    "\n",
    "    tilts_rad = (tilts_asec/3600.) * (numpy.pi/180)\n",
    "    # Must convert arcsecs of tilt to amp in nm\n",
    "    tiltAmps = 1e9 * (tilts_rad * config.tel.telDiam/2.)# in nm amp\n",
    "\n",
    "    # Make a unit tilt to multiply\n",
    "    coords = numpy.linspace(-1, 1, config.sim.pupilSize)\n",
    "    coords = numpy.pad(coords, pad_width=[config.sim.simPad,]*2, mode=\"constant\")\n",
    "    tilt = numpy.meshgrid(coords, coords)[0]\n",
    "\n",
    "    measuredTilts = numpy.zeros((tiltAmps.shape[0]))\n",
    "    for i, A in enumerate(tiltAmps):\n",
    "        wfs = WFS.Gradient(config.sim, config.wfss[0], config.atmos, config.lgss[0], mask)\n",
    "\n",
    "        aTilt = tilt*A\n",
    "        slopes = wfs.frame(aTilt)\n",
    "        measuredTilts[i] = -1*slopes[:wfs.activeSubaps].mean()\n",
    "\n",
    "        # Check tilt is what I think it is\n",
    "        dAmp = (aTilt.max() - aTilt.min())*1e-9\n",
    "        angle = (dAmp/config.tel.telDiam) * (180./numpy.pi) * 3600\n",
    "\n",
    "    A = numpy.vstack([tilts_asec, numpy.ones(len(tilts_asec))]).T\n",
    "    grad, bias = numpy.linalg.lstsq(A, measuredTilts)[0]\n",
    "    measPxlScale = 1./grad\n",
    "    print(\"Measured Pixel Scale: {} pxls/arcsec\".format(measPxlScale))\n",
    "\n",
    "    return measPxlScale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measured Pixel Scale: -4.2090359866 pxls/arcsec\n",
      "Measured Pixel Scale: -4.2090359866 pxls/arcsec\n",
      "Measured Pixel Scale: -4.20903598864 pxls/arcsec\n",
      "Measured Pixel Scale: -4.2090359866 pxls/arcsec\n",
      "Measured Pixel Scale: -4.20903603697 pxls/arcsec\n",
      "Measured Pixel Scale: -4.20903598864 pxls/arcsec\n",
      "Measured Pixel Scale: -4.20903595692 pxls/arcsec\n",
      "Measured Pixel Scale: -4.2090359866 pxls/arcsec\n",
      "Measured Pixel Scale: -4.20903606305 pxls/arcsec\n",
      "Measured Pixel Scale: -4.20903603697 pxls/arcsec\n"
     ]
    }
   ],
   "source": [
    "pxlScales = numpy.linspace(0.05, 0.5, 10)\n",
    "measPxlScales = numpy.zeros_like(pxlScales)\n",
    "for ip, p in enumerate(pxlScales):\n",
    "    config.wfss[0].subapFOV = config.wfss[0].pxlsPerSubap*p\n",
    "    measPxlScales[ip] = getMeasurePixelScale(4*p, config, samples=20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
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       "    var inline_js = [\n",
       "      function(Bokeh) {\n",
       "        Bokeh.$(function() {\n",
       "            var docs_json = {\"070fb47a-a1c3-45fc-bbeb-c47c8dac6c79\": {\"version\": \"0.11.0\", \"roots\": {\"root_ids\": [\"4722556b-a657-46c3-9496-4a5b16092dc5\"], \"references\": [{\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}, \"axis_label\": \"Input Pixel Scale\", \"formatter\": {\"type\": \"BasicTickFormatter\", \"id\": \"eb99ce04-f38e-42a6-a211-fd6759029a51\"}, \"ticker\": {\"type\": \"BasicTicker\", \"id\": \"e541ab5c-43ba-4406-916e-72187ff1bc3d\"}}, \"type\": \"LinearAxis\", \"id\": \"016a9825-712c-4b8d-ac61-fc8059b88108\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}}, \"type\": \"WheelZoomTool\", \"id\": \"54d1d279-80f8-4609-a963-f68f59901b80\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}, \"ticker\": {\"type\": \"BasicTicker\", 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\"x\": {\"field\": \"x\"}}, \"type\": \"Line\", \"id\": \"27a787dc-c37f-4a1e-9491-8c7419a8ab64\"}, {\"attributes\": {\"line_color\": {\"value\": \"#1f77b4\"}, \"x\": {\"field\": \"x\"}, \"y\": {\"field\": \"y\"}}, \"type\": \"Line\", \"id\": \"79ad39ec-ec7e-491f-8c22-48e2bfb506bc\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}, \"axis_label\": \"Measured Pixel Scale\", \"formatter\": {\"type\": \"BasicTickFormatter\", \"id\": \"ceb624d0-b08a-4153-a87f-b761e05fcb7d\"}, \"ticker\": {\"type\": \"BasicTicker\", \"id\": \"42cddf19-1a19-40ac-9a28-11d54664628f\"}}, \"type\": \"LinearAxis\", \"id\": \"80af74be-a3dd-47ad-be3e-ab82acaef3e8\"}, {\"attributes\": {\"callback\": null, \"column_names\": [\"y\", \"x\"], \"data\": {\"y\": [0.05, 0.1, 0.15000000000000002, 0.2, 0.25, 0.3, 0.35000000000000003, 0.4, 0.45, 0.5], \"x\": [0.05, 0.1, 0.15000000000000002, 0.2, 0.25, 0.3, 0.35000000000000003, 0.4, 0.45, 0.5]}}, \"type\": \"ColumnDataSource\", \"id\": \"7f391573-08af-421d-88b5-45d50db0ce51\"}, {\"attributes\": {}, \"type\": \"BasicTickFormatter\", \"id\": \"eb99ce04-f38e-42a6-a211-fd6759029a51\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}, \"ticker\": {\"type\": \"BasicTicker\", \"id\": \"42cddf19-1a19-40ac-9a28-11d54664628f\"}, \"dimension\": 1}, \"type\": \"Grid\", \"id\": \"7ec4dc14-425a-4fc7-b6eb-7d317794407c\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}}, \"type\": \"PreviewSaveTool\", \"id\": \"38c345d7-e78c-4b6f-b071-b1f479eab25e\"}, {\"attributes\": {\"nonselection_glyph\": {\"type\": \"Line\", \"id\": \"2a12834f-d1f2-4c93-9baf-939edbb98540\"}, \"data_source\": {\"type\": \"ColumnDataSource\", \"id\": \"7f391573-08af-421d-88b5-45d50db0ce51\"}, \"selection_glyph\": null, \"hover_glyph\": null, \"glyph\": {\"type\": \"Line\", \"id\": \"85aa6d4b-7522-46d1-8492-62281ec9bb1d\"}}, \"type\": \"GlyphRenderer\", \"id\": \"edf36eb6-b813-4a99-ad01-848a9e52ab24\"}, {\"attributes\": {\"line_color\": {\"value\": \"black\"}, \"line_alpha\": {\"value\": 1.0}, \"render_mode\": \"css\", \"bottom_units\": \"screen\", \"level\": \"overlay\", \"top_units\": \"screen\", \"fill_alpha\": {\"value\": 0.5}, \"plot\": null, \"left_units\": \"screen\", \"line_dash\": [4, 4], \"line_width\": {\"value\": 2}, \"right_units\": \"screen\", \"fill_color\": {\"value\": \"lightgrey\"}}, \"type\": \"BoxAnnotation\", \"id\": \"0bf25bf7-84c1-4796-bd8a-f5ebf005aa81\"}, {\"attributes\": {\"y\": {\"field\": \"y\"}, \"x\": {\"field\": \"x\"}}, \"type\": \"Line\", \"id\": \"85aa6d4b-7522-46d1-8492-62281ec9bb1d\"}, {\"attributes\": {}, \"type\": \"BasicTicker\", \"id\": \"42cddf19-1a19-40ac-9a28-11d54664628f\"}, {\"attributes\": {}, \"type\": \"BasicTicker\", \"id\": \"e541ab5c-43ba-4406-916e-72187ff1bc3d\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}}, \"type\": \"HelpTool\", \"id\": \"80c2b445-9619-4fa5-88a0-f0e50ac0f845\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}, \"overlay\": {\"type\": \"BoxAnnotation\", \"id\": \"0bf25bf7-84c1-4796-bd8a-f5ebf005aa81\"}}, \"type\": \"BoxZoomTool\", \"id\": \"901ae7aa-110d-4693-8e2b-596102a71b82\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}}, \"type\": \"PanTool\", \"id\": \"c614cfcf-e03b-4677-9fed-566110abe1c5\"}, {\"attributes\": {\"callback\": null, \"column_names\": [\"y\", \"x\"], \"data\": {\"y\": [-4.2090359865989075, -4.2090359865989075, -4.2090359886380195, -4.2090359865989075, -4.20903603696758, -4.2090359886380195, -4.209035956916629, -4.2090359865989075, -4.209036063045434, -4.2090360369675786], \"x\": [0.05, 0.1, 0.15000000000000002, 0.2, 0.25, 0.3, 0.35000000000000003, 0.4, 0.45, 0.5]}}, \"type\": \"ColumnDataSource\", \"id\": \"58c945af-8526-4ce6-a435-2d6451486937\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}}, \"type\": \"ResizeTool\", \"id\": \"ae90974f-bb94-4642-b6d7-0be46e9fefc0\"}, {\"attributes\": {\"plot\": {\"subtype\": \"Figure\", \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}}, \"type\": \"ResetTool\", \"id\": \"11df77ee-ea3a-49da-a122-5113e627e0e3\"}, {\"attributes\": {\"callback\": null}, \"type\": \"DataRange1d\", \"id\": \"32b8fddc-c970-426f-9eca-7fc299c442ed\"}, {\"attributes\": {}, \"type\": \"ToolEvents\", \"id\": \"6070cb6e-e52e-42a5-ac78-7ac651f92e56\"}, {\"attributes\": {\"x_range\": {\"type\": \"DataRange1d\", \"id\": \"32b8fddc-c970-426f-9eca-7fc299c442ed\"}, \"y_range\": {\"type\": \"DataRange1d\", \"id\": \"8e35d3b0-8385-42f7-8e70-f3d6c67e8152\"}, \"renderers\": [{\"type\": \"LinearAxis\", \"id\": \"016a9825-712c-4b8d-ac61-fc8059b88108\"}, {\"type\": \"Grid\", \"id\": \"d12eb3d0-3cb1-4f8a-a8c5-9374bfbba33d\"}, {\"type\": \"LinearAxis\", \"id\": \"80af74be-a3dd-47ad-be3e-ab82acaef3e8\"}, {\"type\": \"Grid\", \"id\": \"7ec4dc14-425a-4fc7-b6eb-7d317794407c\"}, {\"type\": \"BoxAnnotation\", \"id\": \"0bf25bf7-84c1-4796-bd8a-f5ebf005aa81\"}, {\"type\": \"GlyphRenderer\", \"id\": \"8266c13b-b28e-42ec-8f2a-4c25de963a8c\"}, {\"type\": \"GlyphRenderer\", \"id\": \"edf36eb6-b813-4a99-ad01-848a9e52ab24\"}], \"below\": [{\"type\": \"LinearAxis\", \"id\": \"016a9825-712c-4b8d-ac61-fc8059b88108\"}], \"tool_events\": {\"type\": \"ToolEvents\", \"id\": \"6070cb6e-e52e-42a5-ac78-7ac651f92e56\"}, \"tools\": [{\"type\": \"PanTool\", \"id\": \"c614cfcf-e03b-4677-9fed-566110abe1c5\"}, {\"type\": \"WheelZoomTool\", \"id\": \"54d1d279-80f8-4609-a963-f68f59901b80\"}, {\"type\": \"BoxZoomTool\", \"id\": \"901ae7aa-110d-4693-8e2b-596102a71b82\"}, {\"type\": \"PreviewSaveTool\", \"id\": \"38c345d7-e78c-4b6f-b071-b1f479eab25e\"}, {\"type\": \"ResizeTool\", \"id\": \"ae90974f-bb94-4642-b6d7-0be46e9fefc0\"}, {\"type\": \"ResetTool\", \"id\": \"11df77ee-ea3a-49da-a122-5113e627e0e3\"}, {\"type\": \"HelpTool\", \"id\": \"80c2b445-9619-4fa5-88a0-f0e50ac0f845\"}], \"left\": [{\"type\": \"LinearAxis\", \"id\": \"80af74be-a3dd-47ad-be3e-ab82acaef3e8\"}]}, \"type\": \"Plot\", \"id\": \"4722556b-a657-46c3-9496-4a5b16092dc5\", \"subtype\": \"Figure\"}, {\"attributes\": {\"callback\": null}, \"type\": \"DataRange1d\", \"id\": \"8e35d3b0-8385-42f7-8e70-f3d6c67e8152\"}]}, \"title\": \"Bokeh Application\"}};\n",
       "            var render_items = [{\"notebook_comms_target\": \"401c8ad5-1b41-4545-82cf-0999b2308a9e\", \"docid\": \"070fb47a-a1c3-45fc-bbeb-c47c8dac6c79\", \"elementid\": \"e45a84bb-c33e-426d-8295-49c6ca3f66c0\", \"modelid\": \"4722556b-a657-46c3-9496-4a5b16092dc5\"}];\n",
       "            \n",
       "            Bokeh.embed.embed_items(docs_json, render_items);\n",
       "        });\n",
       "      },\n",
       "      function(Bokeh) {\n",
       "      }\n",
       "    ];\n",
       "  \n",
       "    function run_inline_js() {\n",
       "      for (var i = 0; i < inline_js.length; i++) {\n",
       "        inline_js[i](window.Bokeh);\n",
       "      }\n",
       "    }\n",
       "  \n",
       "    if (window._bokeh_is_loading === 0) {\n",
       "      console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "      run_inline_js();\n",
       "    } else {\n",
       "      load_libs(js_urls, function() {\n",
       "        console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "        run_inline_js();\n",
       "      });\n",
       "    }\n",
       "  }(this));\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<bokeh.io._CommsHandle at 0x1052e9050>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt = bplot.figure(x_axis_label=\"Input Pixel Scale\", y_axis_label=\"Measured Pixel Scale\")\n",
    "plt.line(pxlScales, measPxlScales)\n",
    "plt.line(pxlScales, pxlScales, color=\"black\"\n",
    "    )\n",
    "bplot.show(plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00023148148148148146"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(wfs.wfsConfig.wavelength*1e9/(2*numpy.pi)) * (numpy.pi/180.) * (wfs.subapDiam/2.) * (1./3600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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