tritemio/Decoding PTU files.ipynb

## Decoding PTU files.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decoding PTU files\n",
    "\n",
    "Reference:\n",
    "\n",
    "- https://github.com/PicoQuant/PicoQuant-Time-Tagged-File-Format-Demos/blob/master/PTU/cc/ptudemo.cc\n",
    "\n",
    "See also [this github issue](https://github.com/Photon-HDF5/phconvert/issues/12) for discussion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "filename = 'data/Cy3+Cy5_diff_PIE-FRET.ptu'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "filename = 'data/ncodina/20161027_DM1_1nM_pH7_20MHz1.ptu'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell will check if the `filename` location is correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data file found, you can proceed.\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "try: \n",
    "    with open(filename): pass\n",
    "    print('Data file found, you can proceed.')\n",
    "except IOError:\n",
    "    print('ATTENTION: Data file not found, please check the filename.\\n'\n",
    "          '           (current value \"%s\")' % filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initial imports and definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "phconvert version: 0.7.2\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import phconvert as phc\n",
    "print('phconvert version: ' + phc.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from collections import OrderedDict, namedtuple\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Constants\n",
    "TTTRTagTTTRRecType = \"TTResultFormat_TTTRRecType\"\n",
    "TTTRTagNumRecords  = \"TTResult_NumberOfRecords\"  # Number of TTTR Records in the File;\n",
    "TTTRTagRes         = \"MeasDesc_Resolution\"       # Resolution for the Dtime (T3 Only)\n",
    "TTTRTagGlobRes     = \"MeasDesc_GlobalResolution\" # Global Resolution of TimeTag(T2) /NSync (T3)\n",
    "FileTagEnd         = \"Header_End\"                # Always appended as last tag (BLOCKEND)\n",
    "\n",
    "# Tag Types\n",
    "tag_type = dict(\n",
    "    tyEmpty8      = 0xFFFF0008,\n",
    "    tyBool8       = 0x00000008,\n",
    "    tyInt8        = 0x10000008,\n",
    "    tyBitSet64    = 0x11000008,\n",
    "    tyColor8      = 0x12000008,\n",
    "    tyFloat8      = 0x20000008,\n",
    "    tyTDateTime   = 0x21000008,\n",
    "    tyFloat8Array = 0x2001FFFF,\n",
    "    tyAnsiString  = 0x4001FFFF,\n",
    "    tyWideString  = 0x4002FFFF,\n",
    "    tyBinaryBlob  = 0xFFFFFFFF,\n",
    "    )\n",
    "\n",
    "# Record Types\n",
    "rec_type = dict(\n",
    "    rtPicoHarpT3     = 0x00010303,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $03 (T3), HW: $03 (PicoHarp)\n",
    "    rtPicoHarpT2     = 0x00010203,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $02 (T2), HW: $03 (PicoHarp)\n",
    "    rtHydraHarpT3    = 0x00010304,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $03 (T3), HW: $04 (HydraHarp)\n",
    "    rtHydraHarpT2    = 0x00010204,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $02 (T2), HW: $04 (HydraHarp)\n",
    "    rtHydraHarp2T3   = 0x01010304,  # (SubID = $01 ,RecFmt: $01) (V2), T-Mode: $03 (T3), HW: $04 (HydraHarp)\n",
    "    rtHydraHarp2T2   = 0x01010204,  # (SubID = $01 ,RecFmt: $01) (V2), T-Mode: $02 (T2), HW: $04 (HydraHarp)\n",
    "    rtTimeHarp260NT3 = 0x00010305,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $03 (T3), HW: $05 (TimeHarp260N)\n",
    "    rtTimeHarp260NT2 = 0x00010205,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $02 (T2), HW: $05 (TimeHarp260N)\n",
    "    rtTimeHarp260PT3 = 0x00010306,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $03 (T3), HW: $06 (TimeHarp260P)\n",
    "    rtTimeHarp260PT2 = 0x00010206,  # (SubID = $00 ,RecFmt: $01) (V1), T-Mode: $02 (T2), HW: $06 (TimeHarp260P)\n",
    "    )\n",
    "\n",
    "# Reverse mappings\n",
    "tag_type_r = {v: k for k, v in tag_type.items()}\n",
    "rec_type_r = {v: k for k, v in rec_type.items()}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Open file and read magic and version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open(filename, 'rb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "s = f.read() # reads all file in memory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(b'PQTTTR', b'1.0.00')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "magic = s[:8].rstrip(b'\\0')\n",
    "version = s[8:16].rstrip(b'\\0')\n",
    "magic, version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "if magic != b'PQTTTR':\n",
    "    raise IOError(\"This file is not a valid PTU file. \"\n",
    "                  \"Magic: '%s'.\" % header['Magic'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read header\n",
    "\n",
    "Header is made of \"tags\" on unequal sizes. The following function\n",
    "decodes a single tag:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import struct\n",
    "\n",
    "def _ptu_read_tag(s, offset):\n",
    "    tagdata = None\n",
    "    # Get the header struct as a tuple\n",
    "    # Struct fields: 32-char string, int32, uint32, int64\n",
    "    tag_struct = struct.unpack('32s i I q', s[offset:offset+48])\n",
    "    offset += 48\n",
    "    # and save it into a dict\n",
    "    tagname = tag_struct[0].rstrip(b'\\0').decode()\n",
    "    keys = ('idx', 'type', 'value')\n",
    "    tag = {k: v for k, v in zip(keys, tag_struct[1:])}\n",
    "    # Recover the name of the type (a string)\n",
    "    tag['type'] = tag_type_r[tag['type']]\n",
    "    \n",
    "    # Some tag types need conversion\n",
    "    if tag['type'] == 'tyFloat8':\n",
    "        tag['value'] = np.int64(tag['value']).view('float64')\n",
    "    elif tag['type'] == 'tyBool8':\n",
    "        tag['value'] = bool(tag['value'])\n",
    "    elif tag['type'] == 'tyTDateTime':\n",
    "        TDateTime = np.uint64(tag['value']).view('float64')\n",
    "        t = time.gmtime(_ptu_TDateTime_to_time_t(TDateTime))\n",
    "        tag['value'] = time.strftime(\"%Y-%m-%d %H:%M:%S\", t)\n",
    "        \n",
    "    # Some tag types have additional data\n",
    "    if tag['type'] == 'tyAnsiString':\n",
    "        tag['data'] = s[offset: offset + tag['value']].rstrip(b'\\0').decode()\n",
    "        offset += tag['value']\n",
    "    elif tag['type'] == 'tyFloat8Array':\n",
    "        tag['data'] = np.frombuffer(s, dtype='float', count=tag['value']/8)\n",
    "        offset += tag['value']\n",
    "    elif tag['type'] == 'tyWideString':\n",
    "        # WideString use type WCHAR in the original C++ demo code.\n",
    "        # WCHAR size is not fixed by C++ standard, but on windows \n",
    "        # is 2 bytes and the default encoding is UTF-16.\n",
    "        # I'm assuming this is what the PTU requires.\n",
    "        tag['data'] = s[offset: offset + tag['value']*2].decode('utf16')\n",
    "        offset += tag['value']\n",
    "    elif tag['type'] == 'tyBinaryBlob':\n",
    "        tag['data'] = s[offset: offset + tag['value']]\n",
    "        offset += tag['value']\n",
    "        \n",
    "    return tagname, tag, offset\n",
    "\n",
    "def _ptu_TDateTime_to_time_t(TDateTime):\n",
    "    EpochDiff = 25569  # days between 30/12/1899 and 01/01/1970\n",
    "    SecsInDay = 86400  # number of seconds in a day\n",
    "    return (TDateTime - EpochDiff) * SecsInDay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decode the header and put data in an (ordered) dictionary (`tags`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "offset = 16\n",
    "tag_end_offset = s.find(FileTagEnd.encode())\n",
    "\n",
    "tags = OrderedDict()\n",
    "tagname, tag, offset = _ptu_read_tag(s, offset)\n",
    "tags[tagname] = tag\n",
    "while offset < tag_end_offset:\n",
    "    tagname, tag, offset = _ptu_read_tag(s, offset)\n",
    "    tags[tagname] = tag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's print a table of all tags in the header:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "File_GUID                                        40       -1  tyAnsiString {CB047DA3-C1BE-4BCA-BFC9-60A31E50A8BA}\n",
      "File_CreatingTime               2016-10-27 15:31:42       -1  tyTDateTime  \n",
      "Measurement_SubMode                               1       -1  tyInt8       \n",
      "File_Comment                                    168       -1  tyAnsiString coat cover-slip with BSA previously, to avoid surface adsorption\r\n",
      "Laser 485 nm: 50000 au, 20MHz\r\n",
      "objective: 60x/1.2NA\r\n",
      "50 um pinhole\r\n",
      "585 dichroic, 525/50, 645/75\n",
      "TTResult_StopReason                               0       -1  tyInt8       \n",
      "Fast_Load_End                                     0       -1  tyEmpty8     \n",
      "CreatorSW_Name                                   16       -1  tyAnsiString SymPhoTime 64\n",
      "CreatorSW_Version                                 8       -1  tyAnsiString 2.1\n",
      "CreatorSW_SVNBuild                             3813       -1  tyInt8       \n",
      "CreatorSW_Modules                                 0       -1  tyInt8       \n",
      "ImgHdr_Dimensions                                 1       -1  tyInt8       \n",
      "ImgHdr_Ident                                      6       -1  tyInt8       \n",
      "ImgHdr_X0                                        40       -1  tyFloat8     \n",
      "ImgHdr_Y0                                        40       -1  tyFloat8     \n",
      "UsrPulseCfg                                      16       -1  tyAnsiString Standard\n",
      "UsrPulseCfgIdx                                    0       -1  tyInt8       \n",
      "UsrHeadName                                      24        1  tyAnsiString 594.0nm (LDH-D-TA-595)\n",
      "Sep2_SerialNo                               1027452  1304064  tyInt8       \n",
      "Sep2_FirmwareVersion                              1  1304064  tyInt8       \n",
      "Sep2_SCM_000_SerialNo                       1026939  1304064  tyInt8       \n",
      "Sep2_SOM_100_SerialNo                       1027866  1304064  tyInt8       \n",
      "Sep2_SOM_100_BaseOscFreq                   80000000  1304064  tyInt8       \n",
      "Sep2_SOM_100_Divider                              4  1304064  tyInt8       \n",
      "Sep2_SOM_100_PreSync                              0  1304064  tyInt8       \n",
      "Sep2_SOM_100_SyncMask                             1  1304064  tyInt8       \n",
      "Sep2_SOM_100_InvSyncMask                         -1  1304064  tyInt8       \n",
      "Sep2_SOM_100_Seq_BurstLen                         0        7  tyInt8       \n",
      "Sep2_SOM_100_Seq_EnaOutput                       -1        7  tyInt8       \n",
      "Sep2_SOM_100_Seq_EnaSync                          0        7  tyInt8       \n",
      "Sep2_SLM_200_SerialNo                       1028447        0  tyInt8       \n",
      "Sep2_SLM_200_TriggerIndex                         7        0  tyInt8       \n",
      "Sep2_SLM_200_FineIntensity                       60        0  tyInt8       \n",
      "Sep2_SLM_200_CW_PulseDisable                      0        0  tyInt8       \n",
      "Sep2_SLM_200_HeadType                             0        0  tyInt8       \n",
      "Sep2_SLM_300_SerialNo                       1028448        1  tyInt8       \n",
      "Sep2_SLM_300_TriggerIndex                         7        1  tyInt8       \n",
      "Sep2_SLM_300_FineIntensity                        0        1  tyInt8       \n",
      "Sep2_SLM_300_CW_PulseDisable                      0        1  tyInt8       \n",
      "Sep2_SLM_300_HeadType                             0        1  tyInt8       \n",
      "Measurement_Mode                                  3       -1  tyInt8       \n",
      "HW_Type                                          16       -1  tyAnsiString HydraHarp\n",
      "HW_SerialNo                                       8       -1  tyAnsiString 1028074\n",
      "HW_Version                                        8       -1  tyAnsiString 3.11\n",
      "HW_ExternalRefClock                               0       -1  tyBool8      \n",
      "HW_Modules                                        4       -1  tyInt8       \n",
      "HWModule_TypeCode                              1040        3  tyInt8       \n",
      "HWModule_VersCode                          18153994        3  tyInt8       \n",
      "HW_Markers                                        4       -1  tyInt8       \n",
      "HWMarkers_Enabled                                 1        3  tyBool8      \n",
      "HWMarkers_RisingEdge                              0        3  tyBool8      \n",
      "HW_BaseResolution                             1e-12       -1  tyFloat8     \n",
      "MeasDesc_BinningFactor                           16       -1  tyInt8       \n",
      "MeasDesc_Resolution                         1.6e-11       -1  tyFloat8     \n",
      "HWSync_CFDLevel                                 150       -1  tyInt8       \n",
      "HWSync_CFDZeroCross                              10       -1  tyInt8       \n",
      "HWSync_Offset                                 89800       -1  tyInt8       \n",
      "HWSync_Divider                                    8       -1  tyInt8       \n",
      "HW_InpChannels                                    5       -1  tyInt8       \n",
      "HWInpChan_CFDLevel                              150        3  tyInt8       \n",
      "HWInpChan_CFDZeroCross                           10        3  tyInt8       \n",
      "HWInpChan_Offset                                420        3  tyInt8       \n",
      "HWInpChan_Enabled                                 1        3  tyBool8      \n",
      "HWInpChan_ModuleIdx                               3        3  tyInt8       \n",
      "TTResult_SyncRate                          20000000       -1  tyInt8       \n",
      "TTResult_InputRate                                0        3  tyInt8       \n",
      "MeasDesc_GlobalResolution                     5e-08       -1  tyFloat8     \n",
      "TTResult_NumberOfRecords                   24731887       -1  tyInt8       \n",
      "MeasDesc_AcquisitionTime                     600000       -1  tyInt8       \n",
      "TTResult_StopAfter                           600000       -1  tyInt8       \n",
      "TTResultFormat_TTTRRecType                 16843524       -1  tyInt8       \n",
      "TTResultFormat_BitsPerRecord                     32       -1  tyInt8       \n",
      "UsrPowerDiode                             2.383e+04       -1  tyFloat8     \n"
     ]
    }
   ],
   "source": [
    "line = '{:30s} %s {:8}  {:12} '\n",
    "for n in tags:\n",
    "    value_fmt = '{:>20}'\n",
    "    if tags[n]['type'] == 'tyFloat8':\n",
    "        value_fmt = '{:20.4g}'\n",
    "    endline = '\\n'\n",
    "    if tags[n]['type'] == 'tyAnsiString':\n",
    "        endline = tags[n]['data'] + '\\n'\n",
    "    print((line % value_fmt).format(n, tags[n]['value'], tags[n]['idx'], tags[n]['type']), \n",
    "          end=endline)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some useful metadata extracted from the header:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5e-08"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timestamps_unit = 1/tags['TTResult_SyncRate']['value']\n",
    "timestamps_unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5999999936067155e-11"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nanotimes_unit = tags['MeasDesc_Resolution']['value']\n",
    "nanotimes_unit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "600.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acquisition_duration = tags['MeasDesc_AcquisitionTime']['value']*1e-3\n",
    "acquisition_duration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Read T3records\n",
    "\n",
    "Read and decode the \"T3records\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'rtHydraHarp2T3'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "record_type = rec_type_r[tags[TTTRTagTTTRRecType]['value']]\n",
    "record_type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24731887"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_records = tags[TTTRTagNumRecords]['value']\n",
    "num_records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t3records = np.frombuffer(s, dtype='uint32', count=num_records, offset=offset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24731887"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(t3records)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the proper parameters, phconvert's function `process_t3records` ([doc](http://phconvert.readthedocs.io/en/latest/pqreader.html#phconvert.pqreader.process_t3records))\n",
    "should be able to cover all cases. So far we handle only a few record types\n",
    "for which example files have been provided. \n",
    "\n",
    "If you want to add support for a new\n",
    "record type, please open an [issue on github](https://github.com/Photon-HDF5/phconvert/issues) and send and example data file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "if record_type == 'rtPicoHarpT3':\n",
    "    detectors, timestamps, nanotimes = \\\n",
    "        phc.pqreader.process_t3records(\n",
    "            t3records, time_bit=16, dtime_bit=12, ch_bit=4, special_bit=False)\n",
    "elif record_type == 'rtHydraHarp2T3':\n",
    "    detectors, timestamps, nanotimes = \\\n",
    "        phc.pqreader.process_t3records(\n",
    "            t3records, time_bit=10, dtime_bit=15, ch_bit=6, special_bit=True,)\n",
    "else:\n",
    "    raise NotImplementedError('Sorry, decoding \"%s\" record type is not implemented!' % \n",
    "                              record_type)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> **NOTE** Additional `record_types` may require using the proper parameters for `process_t3records`. You can find those paramenters in this [PicoQuant demo code](https://github.com/PicoQuant/PicoQuant-Time-Tagged-File-Format-Demos/blob/master/PTU/cc/ptudemo.cc)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  0,   1,  34,  50,  68, 127], dtype=uint8),\n",
       " array([ 6023938, 11473517,        1,        1,        2,  7234428]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(detectors, return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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C8OQkq4AnAfdOOQ8AVXUd8NCsm4dPGPw48CtLGmqEUTmr6pqqenRweD1w6JIHm2WOryfA\nhcDvLXGcOc2R83eA91TVDwdjHhg3z1KV+yQnQi0rSY4EVtP/BNBy89g343J+w+Qo4IEklwy2jy5K\n8hPTDjVbVd0L/DlwN3AP8N2quma6qeb1jKq6H/qLEeCnp5xnEr8NXD3tEKMkeQ2ws6punnaWMY4B\nTkxyfZIvJvn5cQ9YqnKf5ESoZSPJAfT/jMLbBiv4ZSPJq4H7B68wwuiv7XKwCjge+GBVHQ/8N/0t\nhWUlyUH0V8NHAM8CDkjyuummakeSdwO7q+qyaWeZbbDYeDdw3vDNU4ozzirgoKpaA/w+8PfjHrBU\n5b4LGP5LkYeyTF76zjZ4aX4F8Imq+sdp5xnhZcDpSe4EPg2clOTSKWcaZRf9FdG/DY6voF/2y80p\nwJ1V9Z3Bn874B+ClU840n/uTPBMgycHAf0w5z5ySnEF/+3C5/rJ8DnAk8I0k36bfS19PsscJmMvA\nTvrfm1TVFuDRJE+b7wFLVe6Pnwg1+CTCemC5fsrjo8A3q+r90w4ySlX9QVUdXlVH0f86XltVvznt\nXLMNtg52JjlmcNPJLM83gO8G1iT58SShn3M5vfE7+9XZlcBvDa6fASyXBcj/yZlkLf0V5ulV9YOp\npdrT4zmr6paqOriqjqqqZ9NfkBxXVcvhF+bs/+6fZfAHGQc/U0+sqgfnm2BJyn2wInrsRKhtwKaq\nWk4/QAAkeRnweuAVSW4c7BWvnXauFeytwKeSbKX/aZk/mXKePVTV1+i/qrgR+Ab9H6iLphpqIMll\nwJeBY5LcneRM4D3ALye5jf6rjrEfidvX5sj5V8ABwBcGP0cfmmpI5sw5rFgG2zJz5PwocFSSm4HL\ngLELOk9ikqQG+b/Zk6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ2y3CWpQZa7JDXofwGIN4RTDTn1\nygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115e5af28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(detectors, bins=np.arange(16));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LL8Oa2z17xh2RSPap8paSsXIlXHcd7LEH9OkTNgBW4pZSpcpbSsKIEaHa3nHHMIvk17+O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\niEgRUvIWESlCSt4iIkVIyVtEpAj9P6xXi+nRZFx3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13b8e37f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timestamps);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kk50ZSTMzC2438PyBfHXbVwD0/ldvHlr4UJgjFZFo5NokYC3Ee2tHOoygqFHDGUJ6/fXO\n+tixTi3B6y24Xdvkttx+7u0AjPlsDPd9fB/pmemIiISKa5OA13rxVPDmoMJmzHBuTpMj3s9UQi9d\n+RLz+s4D4IklT5DwSEKYohORaOTaJGAryLQRpWEMjBsHh51ZpsnOdsp+/bXgdn858y+8dtVrec8b\nZ9iwdwMiIsHm2iSQlW3Buja8cklIcJqHciQnF00EN519U4EhpKf/8/QwRSci0cS1n7IZx7xUrVK5\nagL5detWcI6h5OSCF5n5Y8YZfvr9p9AGJiJRJSRJwBjTzBjzvDHmLWPMwLLsw1pLtWqVNwkAnHAC\nfPVV3vpFF+XdqyDH4VGHWTV4Ve56i+da8MBn+ToWRETKISRJwFq72lo7CLgOuLAs+/Bai6cCThtR\nWm3bOsNFO3fOK/N44LnnnOWEuASaJTXjt3t+49yTnCvNxi8cz4qdKyIQrYhUNgF9yhpjphpjdhpj\nVhQq72qMWW2MWWuMGV7osSuBfwPzyxKYl8o3Oqg4sbHwySdw5pl5ZYMHw+n5ugFOrH4iC/otyF0/\n+4WzefDzB8MYpYhURoF+1Z4GdMlfYIzxAJN95S2AvsaYZjmPW2vnWWu7Af3KEpi1FuOJjiSQY80a\nqF8/b33DhryRRABJCUkMaD2Ans16AjA2bSxx4yv+BXUiEjkBJQFr7WJgb6HiNsA6a+0ma20mMAvo\nAWCMudgYM8kY8wLwQVkCs7ZiziJaXjt2QFZW3nqNGk4/wdKlzvrL3V/mneveYXQnZ06lLG8WZpxh\n6a9LIxCtiFR0fiY6DlhDYEu+9a04iQFr7efA58fbQf4Z8VJSUkhJScld91pvpbtOIFAxMfDGG3DD\nDXllbdo4k88tXAjVqzvTTDy8KO/+y22mtOHBlAcZ0XEEcTGqHYhUFmlpacXOthwMAc8iaoxpDMyz\n1rbyrfcC/myt/atvvR9wgbV2aID7K3EW0XMe7s3J+3oz/4lrA4qvMlqwALZuLXiXsvr1ndoCwHfb\nvmPdnnX0fbtv7uMLb1lIp8adwhypiISLm2YR3Qo0yreeDGwrzQ5Kup+AJTpGB5WkSxe47TZnEroc\nO3c6zUNr1sB5J59Hnz/2YUbPGbmPX/TqRew8tDMC0YpIKEX8fgLGmCY4NYGWvvUYYA3QGdgOfAP0\ntdauKm4fhfZXYk2gUWpHWqffw3uPXRVQfJXZ0aNOjeAPfyhY/uOPcMYZzhxE1lrOe+k8lu1YBsCc\n3nO45qxrIhCtiIRSRGoCxpiZwBLgTGPMZmNMf2ttNnAH8BHwIzAr0ASQo8SagNdD3eqVYxbR8qpa\n1fmwP3rUuYYgR4sWzk1r1qxx3hjTekzLfazXv3phxhkiddMgEQmuiNcEgn7g49QEkh/oRPeER3hu\nhNq3C/vvf+GyywqWrVnj1BSMgbjxcWR584YY5Z+DSEQqNjf1CYSUtV48UXadQKA6d4Zt2wpeTNa0\nKfTq5Sxnjsnk7Ppn5z5mxhnMOJ1LESnKtTeat1gM+uAqzkknwfr1BcveeSfvpvbLBy7n29u/LfB4\n37f7smjTIp795tkwRSkiwRJ1zUEnjWnPdYlPMfGe9mGMquIpfDP7HC+8AH/7G6zYuYKzXzi7yONq\nIhKpmNQcJAU4I4Ngz56C5QMHQsuW0LJeK78f+Gt3rw1ThCLiZq5uDoqWCeSCoXZt505l+f3wgzOa\nyBh4vn7BGxo3ndwUM87wwdoyzeohImEWdc1B9e6/gP4nPsdjQy8IY1SVx6xZ0Ldv0fIff/uJFs+1\nKFK+qP8iOjbqyPaD2znphJPCEKGIlEX0NAeh5qDy6NMH5swpWt6iXnP6VZldpLzTtE6s272Ok586\nWdcWiEQR1zYHZWVVvhvNh1u7dtCvyETehhkjr4VUy2k1CtYIzpzs3NBg1g+zwhOgiAQs6pqDEoe3\n5v4/vsK9N7YOY1SVU0YGxMU5s5MWYLwMufcA/0woemV22s1pXNzk4vAEKCIBi5rmIPASG6uaQDBU\nqeJ0EFsL3+a/dMB6+OfjtZzlrW1hZZ/ch1JeS2Hpr0ux1uK1BTuVRaTyKM/9BELKYomNURIItvPO\nc5KBtfnmIVrZB9Z1gxX9oGVeU1CbKW1yl9NHp1M1tmqYoxWRUHNtTSAzZh8xnsLtFxIsxjjNRLVq\nAW+/6SQAgCN1/G5f7eFqZGZnhi9AEQkL93YMew5Ru0pSeAOKMvHx8NVXznLrnK6XJ3fAo/vh1/OL\nbJ/4aG0mfTWJfen7wxekiABR2DEcP7oeMy78gWu71QtjVNFp61ZITnZmIm3WzJmMbs0aoPYG2H8K\nPBBf5DlnHxvE01ePYmeVxfT5Y5+iOxWRkIiejmHjJTbGveFVJsnJzu+mTZ2+gtWrYcgQYO9p4I2D\np7YUec738c9z6b9Poe/bffn+e0vjxjB+vK4vEKloXPspm22ziY9zbXiV3lNPOfMRTZ8OD96TDK8s\nKnbbc+Z62Ny+Jw+s6oFJ2I0xMH48fPMNHDjg9D0cPhzG4EUkYK5tDjKjElnzt82c2TgxjFFJcT77\nDC69Yi/VB6dw+IQVJW/82ifwS+fc1S5dYMECuPdeJznExRW8Q5qIBK5SNQeV1DGM8VKlij4p3OKS\nS8Cm1+bgE99zSs1TSt745svg1E9zVxcscH4/8QQkJjoXrZ15Jrz6qjNKyRh46KGCu9i3z2maWr7c\nqUksXeqsi0SrqOoYzsyE+NTqbL/7NxrUqR7myOR49h3dR+0a1bhrWAxP1YgrfsP/+xUGtIOXvoXW\nr8DRWrCsP2T7uQECsGwZPPMM/PwzfP45XHklzJsH11wDb78N27c7HdZDhsCnn8LXX8PgwfDLLyH6\nQ4thbd7Ne0TCrVLVBAqbPx9273amQMZ4qRrvqvDEp1bVWtStVYV2bWLZN3wfTao397/h3Q0hcQvc\nWx8uGwl/GQRjqsJF4yEmA669psDmrVvDK684CQCcBABOAgDnbmopKbBiBSQlwezZsHEjbN4MH38M\nw4Y5tYaMDHj+eVi5Ery+i50zMuDgwaLTbQM8+igsXnz8v/uXX5zZWT0eOHq04GPz5+cdK8eGDXm3\n/PTH64WZM30jsUohOxv27nWWBw1yvjSVJCvL+SnOokXOhIPp6c55kihjrY3ID2DXr7d2wQJrZ860\n9ptvcq5jtbbLFRmWVOyxrGNWKo5DGYcsqRz/Z0yspeZmZxkbsp8uXfyX33CDtXPnFi0fNcraZcus\nfemlvLIDB6zNyrL2u++s7do1r/zjj6199llrvV5r33zTKVu/3tq9e5338x13FN3/4sXWZmdbm5Fh\n7ZEj1g4Y4JR7PM7527HDKc+xZo21H31k7e+/W3vxxc62336bt7/sbOf3L7/kPcfrtfbnn63t39/a\n/futfestZ5tLL7V2xgxrb7stb9suXawdNsza4cOdbdq2tfbqq63dudN5nriT87EdvM/iiDYHQTHH\nrrIf7m6IffhQeIOScvv7B3/ngpMv4Nb3bw3sCRsvhm8Gw/quUO9H2NoutAEGWe3aed/Kg2XQIDj3\nXLj99sCfM2AATJkCzZvDqlUlb5vTzHY8jzwCI0cGHoOER7Cbg9yZBKruhaGnYScE+b9LwsJrvcQ8\nWMYpPx7MBK9rp7SKKtde6zS5ibtU6j6BXJ5ssO4MTY7PYzwcHX2Uhy5xhvxsGLIh8Cc/EAedR8Gg\nlpyc8m8efvkHiE2Hy4fAiT+FKGLx5yed7qjgzppAjR3UHN2U/SM0R01lsWjTIpolNaPxxMakZ6WX\nb2fLbsG8P61AR6wxULUq7N8P55yT1yRyww2wcCFsKXrRc9DceqvToV3ZNG3qXD0u7lKpagLnn5/K\nTTelFShbtgya/WMEBzIORCYoCYlOjTtxYvUTea/Pe0UeqxLjf8hosVq/ih1rWLx5MXN+mkP/9/pz\n7JgzuiU+HpavPMaKHSuh7lpOPdUZbbR6dV4X7aRJQNxhLmiTzRtvFNy11+tsv3Sps37HHUXb2AcM\ncH5feaWTXKZOddbnzIF//7vgtued54w+Anj9decnv1atoIXvBm/pvtzYoweMGOEsb95ccoKp43/S\n11x/+tPxt+/YsejIJoAOHUret4RXpb1OYNs2aJjspUZ1DzfeCM89B7e+dyvTlk/DjtXVQZVVtjeb\ntI1pjF84nrRb0pixYgY3vntjmfc3ofMEpi6byqDzB3HXR3fllj+cMoGz6jdl2IJhbNy3Mfc9ZcYZ\nJl32IruP/cqDva9nYN/GLP+2Kl9+6Twv/aiXsQ94ePxxZ71BA3j2WeeaheO55Rbn94ABUK+ec2Fc\ndnbend1yrjEo6V8vPR0SEpyhnTExziR/p5wCTz4JEyfC0KFOAkpKcobGrlwJF17ofHB/8YUz9LRv\n37z9HT3qDJF95RVnWO3gwfDHP8J//uMkgRo1nOHZSUlODaBzZzjrLGc7cZdK1TG8N30vVWOr0mRi\nE+Jj4tlyYAt2rKXLjC589PNHSgJRxGu97Du6j7qP16VmlZohqwn2bNaThy59iBbPtaBTo04s2uzM\niTT5kpm8teEF3u/zPnNXz2XMZ2PYcsBpQ5py5RRuO/e23H2kZzo32Bnz2RgeXvQwdqzlQMYB1u1e\nx5rda0hp1Jm6CXXoPvsvzL9+Pseyj1Etrhq7juzi018+JXHrtdSsCe3bF4zt2W+e5Y/1/shFjS8C\nnH/23w7/Rt1qdXPvrZHlzWLf0X0czTrK3vS9tKzf0u/faa0lIzsDay07D++kWmw16teoX2Abr/Uy\n5MMhbNq/idm9ZpMQl8DIkXDqH9L5/rtqNG8O//hHUE67BFGlSgLNJzenSmwVlu9Ynlu+57491Hnc\nqbMqCUSfXw/8SkJcAh+u/5AJiyew8reVkQ4JgLnXzWXS15P4bONnRR57v8/7dJ/VPXf9uhbXMftH\nZ1jN/hH7SZzgzH9VLbYa6VnpTO0+lTdWvsGb17zJlP9NYcC5A1iyZQk9Z/fM3Uf75PYsuW0JZpxh\n7MVjueIPVzDnpzkcyDjAi9+9mLudHWsZ8+kYHlr0UO7/y/6j+xn6n6Es3LSQX/blXU7935v+y8GM\ng6RtTKNl/ZY8u/RZ/rf9fwX+FjvWYsYZUg6+yDVN/qok4EKVKgmQWvI2SgIC0GlaJ05MOJGhbYeS\nkZ1BlxldIh2Sa2y+czONJjYKePukhCR2HdlV7OMvdHuBgR8MBOCfdSx33FHuECXIlAQk6lhrMfkm\n69m4byOnTjoVgLPrn833O7+PVGiV2uO1D3DvkBMiHYYUUqlGB4kEwhSara1JrSZsGeb0Hy0fuByP\nyXsbv9/n/XCHV2m9c/jOSIcgYeDaJPDn0/8c6RDExZJrJucub7pzEw1qNADgyqZX8ny35wHYfd/u\nEvcR68m7MnlC5wkcHHmQQyMPsWXYFp7681O8e927IYi84vjqWCW8+EGKCFkSMMb0MMa8ZIx50xjz\np+M/o6DpV00PRVhSCSXXTGb73dtzmw8Hnj8QO9ZSp1odXu/5Otvu2kbWmCyqxlblwAhn1NGjnR9l\n9eC8K6H+0eYf1IivQfX46iTXTGZY+2Fc1ewqJnaZ6PeYP/39J2ZePROAa5o740ZvP/d2Pr7xY7/J\n5/Tap5f675rWY1qpnxNMDTwtInp8CY+QJQFr7XvW2r8Cg4BrS9o251t/1diqAFSPq15kOJtIWfRr\n1Y+TTjiJGE8M6aPTOaHKCbQ4sQUXnHwBp9c5nfV3rOfQyENUj/d/34qh7YZydPRRzqhzBgCHRx1m\n3R3raH5ic/q27EvmmEzmXDuH3+/9nZeufInLTruMOtXqkDkmk4z7M7j8jMsBWD9kPZO6TmLj0I28\ndtVrHBx5kA1DNuQmrrd6vVWgdnPZaZdxyzm3sGKgcxe3/9zwHwxOs9jsXrNJuzmNNf9w5qBuVb9V\n7vNGdxoNwPzr57Oo/yKGtRtGjHGGl97d/m4Anrn8mQJ/Y6+zejHrmlkADO8wPLe8Q5WBpT7fUgEF\nOt0oMBXYCawoVN4VWA2sBYb7ed6TwDl+yu2RY3nz5r667FU74/sZllRszUdrlmOiVZGSeb3esB1r\nX/o+u3DjwhK3mfjlRHso45DddXiXrf5wdUsqdsj8IX639Xq9BeInFTv568m503T7k+3NtjHjYuyW\n/VvsC0vIBg7aAAAMuElEQVRfsNZa2/3N7rnP6Tunr/3k508sqeTuu+WIv9trHnumLH+yhBhBnkq6\nNNM1TgOeAXLbaYwxHmAy0BnYBiw1xrxnrV3te3wCMN9au9zP/qgWVy13+eZzbgacyceK+1YmEgyF\nO5pDKbFqIp0adypxm6HthgJQPb46h0YdYsmWJZxd/2y/2xaO/cW/vEjPZj3ZcmALVze/2u9zPMZD\n1gPOXWX+dv7fAHKn7zDjDA1PaJjbuZ6zf4PBFje3l1QqAScBa+1iY0zjQsVtgHXW2k0AxphZQA9g\ntTHmDpzkUNMYc4a19qVAjtO3Zd/jbyRSiV14yoUBb/vX8/4KwITLJpTpWDnNUZ9v/LzQI6bEaS2k\n8ijvxO0NgfzzM27FSQxYa5/BqTmIiMvlH2YL+HoflAWiQXmTgL96dcDvnPwz4qWkpJCSklLOcESk\nLBrWbEicJy5fiWoCbpGWlkZaWlrI9l+qK4Z9zUHzrLWtfOvtgFRrbVff+gicTovHAtiXLc2xRSS0\nbL4rs1uPGkKTmqfz7oihEY5KCov0FcOGgt/+lwJnGGMaG2PigT5AwJdspqamhjTDiUjgCnY6h6/z\nXAIT8fsJGGNmAilAXZyhomOttdOMMZcDE3ESylRrbUA9VKoJiLhX61FDaVzzNOaqJuA6wa4JlGZ0\n0PXFlH8IfFiWg6empqovQMS19CXNTULVNxDxO4uJiPucO+pOGtVswtwRmkTObSLdJxBU6hMQcS99\nSXOXiPcJBP3AqgmIuNZ5o4aRfEIj3hs5LNKhSCGVqiYgIu7lVZ9AVFBzkIgUEc75lSQwag4SkbA5\nf/RdnFQjmXkj74p0KFKImoNEJCz0JS06KAmIiB9qDooW6hMQEb9UE3AX9QmISNhccP891KvWgA9G\n3xPpUKQQ9QmISJjoS1o0UBIQkSKMNUoBUUJ9AiJSlAHVBNxFfQIiEjZt77+POlWT+PD++yIdihSi\nPgEREQkaJQERKYZq6tFASUBEijCoYzhaKAmISFHqGI4aGh0kIkUYDBq34S4aHSQiYdN+zAhqxiey\nYMzISIcihWh0kIiEnNEEclFDSUBE/FI9PTooCYhIUQas0kBUUBIQkSKMkwUkCigJiIhfqglEByUB\nEfFDHcPRQtcJiIhfqgm4i64TEJGw6Tj2fqrEVOW/D9wf6VCkEF0nICJhcSwj0hFIOCgJiEgRVeIh\nM0s19WigJCAiRcTEgDVZkQ5DwkBJQESKiDHxZJi9kQ5DwkBJQESKqGYS0TDR6KAkICL+qUsgKoQk\nCRhjTjXGTDHGvBWK/YuISHCEJAlYa3+x1g4Ixb5FRCR4AkoCxpipxpidxpgVhcq7GmNWG2PWGmOG\nhyZEEREJlUBrAtOALvkLjDEeYLKvvAXQ1xjTrNDz1LMkUkGpSyA6BJQErLWLgcLjxdoA66y1m6y1\nmcAsoAeAMaaOMeZ54BzVEEQqHqOvb1EjthzPbQhsybe+FScxYK3dAww63g7yT4aUkpJCSkpKOcIR\nEal80tLSQjrRZnmSgL/vCqWqQYZiRjwRkcqk8BfkcePGBXX/5RkdtBVolG89GdhWmh1oKmkRF1On\ngKtEfCppY0wTYJ61tqVvPQZYA3QGtgPfAH2ttasC3J+mkhZxqV5PTGLdrg18/9ikSIcihURkKmlj\nzExgCXCmMWazMaa/tTYbuAP4CPgRmBVoAsihmoCISGAiXhMI+oFVExBxLdUE3Es3lRGRsNBXtOig\newyLSFG6TsB11BwkImHT68lJrP19AyvUHOQ6ag4SEZGgUXOQiEgFoOYgEQkbNQe5l5qDRCTk1C8c\nPZQERESimPoEREQqAPUJiEjY9H5yEqt/28DKx9Un4DbqExCR0FOnQNRQEhARiWLqExARqQDUJyAi\nYdP7/yaxeqf6BNxIfQIiEnK60Xz0UBIQEYliSgIiIlFMSUBE/FOXXVTQ6CARkQpAo4NEJGyufWoS\nq7ZvYOUTGh3kNhodJCIiQaMkICISxZQERMQvNdZGByUBESlCF4tFDyUBEZEopiGiIiIVgIaIikjY\nXPf0JH78dQM/PKkhom6jIaIiEnLqEogeSgIiIlFMSUBEJIopCYiIX+qxiw5KAiJSlDoFooaSgIhI\nFFMSEBGJYrGh2KkxJgF4DsgAPrfWzgzFcUREpHxCVRO4GviXtfZvQPcQHSMk3HgFs2IKjGIK3PHi\nikSXgBvPlRtjCraAkoAxZqoxZqcxZkWh8q7GmNXGmLXGmOH5HkoGtviWs4MUa1i48UVXTIFRTIFz\nY1yKKTICrQlMA7rkLzDGeIDJvvIWQF9jTDPfw1twEgFonIGIiGsFlASstYuBvYWK2wDrrLWbrLWZ\nwCygh++xd4FexphngXnBClZEwkdTe0WHgCeQM8Y0BuZZa1v51q8Bulhr/+pb7we0sdYOCXB/eouJ\niJRBMCeQK8/oIH9BBPzBHsw/QkREyqY8o4O2Ao3yrScD28oXjoiIhFNpkoCh4Lf/pcAZxpjGxph4\noA/wfjCDExGR0Ap0iOhMYAlwpjFmszGmv7U2G7gD+Aj4EZhlrV0VulBFRCTorLVh/wG6AquBtcDw\nMB97I/A9sAz4xldWGyeZrQEWAIn5tv8nsA5YDpwTpBimAjuBFfnKSh0DcLPvHK4BbgpRXGNxmv7+\n5/vpmu+xkb64VgF/Dvbri9PE+CnwE7ASGOKGc+UnrjtccK6qAF/73tcrgbG+8ibAV76/+00g1lce\njzOibx3wJdDoeLEGMaZpwAZf+f+AVhF4r3t8x34/0uepUEzL8sX0ajjOU7mCLscfuh5oDMT5/ohm\nYTz+BqB2obLHgPt8y8OBCb7ly4EPfMttga+CFENH4BwKftiWKgacD8KfgUSgVs5yCOIaC9zlZ9vm\nvjdnrO8faD1Oc2HQXl+gQc4bHKjhe2M3i/S5KiGuiJ0r33ESfL9jcD7Q2gKzgd6+8ueBv/mWBwHP\n+Zavw6nJA5zlL9YgxzQNuNrPtuF8rw8DZpD3gRvR81RMTNOAnqE+T5GYQK6k6wvCIeefL78ewGu+\n5dfyxdMDmA5grf0aSDTG1C9vANb/dReljaEL8JG1dr+1dh/ON+OuIYgL/I8E64HzD5Flrd2I862k\nDUF8fa21O6y1y33Lh3C+cSUT4XNVTFwNfQ9H5Fz5YjniW6yC8+FkgUuAt33lrwFX5Ysp5xzOAS71\nLXcvJtZgxeT1rRd3nkL++hljkoErgCn5ii8lguepmJjAf5N9UM9TJJJAQ/KmlACn+tywmG1DwQIL\njDFLjTEDfGX1rbU7wfkHB+r5ygvH+iuhi7VegDHknK9wxjbYGLPcGDPFGJNYTFw5xw/J62uMaYJT\nS/mKwF+vkJ+rfHF97SuK2LkyxniMMcuAHcDHON8E91lrcz548+8/99jW6d/bb4ypU0KsQYnJWrvU\n99BDvvP0f8aYuMIxFYo32K/f08C9+Ia0G2PqAnsjeZ4Kx5RPyM9TJJJAua4vCIILrbXn42TdwcaY\nTiUcP9Kx+ovB+GIIV2zPAadba8/B+Uf+v2Liyjl+0OMyxtTA+RY21PfNO9DXK6Tnyk9cET1X1lqv\ntbY1Tm2pDU4zVHH7j0hMxpizgBHW2ubABUBdnCY9fzEF/fUzxnQDdvpqcjn7LTzyMf/+Q36eiokJ\nwnSeIpEEInp9ge+bI9ba34G5OP8sO3OaeYwxDYDf8sV6SphiLW0MYTmP1trfra/BEXiZvCpvWOIy\nxsTifNC+bq19z1cc8XPlL65In6sc1toDwOdAO6CWb56vwvvPjckYE4PTdry3hFiDFVPXfLW4TJx2\n73Cepw5Ad2PMBpwO4EuBiThNKpE6T0ViMsZMD9t5Kk9HRhk7P2LI6wyLx+kMax6mYycANXzL1YEv\ngD/jdDQO95WPIK+j8QryOmDaEaSOYd/+mgAr862XKgYKdgLlLNcKQVwN8i0PA2b6lnM6xuKBU8nr\n7Azq64vT9vlUobKIn6ti4orYuQKS8HUCAtWAhb7zMRu4zlf+PDDQt/x38jo8+1C0w7NArEGOqYGv\nzOA0gzwSoff6xRTsGI7IeSohprCcp6B8oJXhD+2KM6JiHU6VJ1zHPdX3j5YzZG2Er7wO8Ikvpo/z\nnzicmVLX4wwrPTdIcczEydAZwGagv+9FK1UMwC2+c7iW4Ayb8xfXdGCF77zNxWmPz9l+pC8uf8Me\ny/364nxDys73mv3Pt+9Sv17BPFclxBXJc9XSF8dyXwyj873nv/b93bOBOF95FeAt33G/ApocL9Yg\nxvRf3+uzwnfOEsL9XvftM/8HbsTOUwkxheU8BTyBnIiIVD66x7CISBRTEhARiWJKAiIiUUxJQEQk\niikJiIhEMSUBEZEopiQgIhLF/h9nnkV4OneHzAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13bdb4438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(nanotimes[detectors == 0], bins=np.arange(4096), histtype='step');\n",
    "plt.hist(nanotimes[detectors == 1], bins=np.arange(4096), histtype='step');\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It works!"
   ]
  }
 ],
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