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Name Designation Affiliation Signature Authored by: T.J. Cornwell, SKA Architect Date: Owned by: A.M. MacPherson, Head of Project Date: Approved by: P.J. Diamond, Director General Date: Released by: P.J. Diamond, Director General SKA1 TELESCOPE CALIBRATION FRAMEWORK Document number........................................................................ SKATELSKO0000000 Context ........................................................................................................ AGCALFRM Revision........................................................................................................................ DE Author .......................................................................................................... T.J. Cornwell Date ............................................................................................................... 20150408 Document Classification .......................................................................... UNRESTRICTED Status ....................................................................................................................... Draft

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Name   Designation   Affiliation   Signature  

Authored  by:  

      T.J.  Cornwell,  SKA  Architect  

Date:    Owned  by:  

      A.M.  MacPherson,  Head  of  Project  

Date:    Approved  by:  

      P.J.  Diamond,  Director  General  

Date:    Released  by:  

      P.J.  Diamond,  Director  General  

SKA1  TELESCOPE  CALIBRATION  FRAMEWORK      

Document  number  ........................................................................  SKA-­‐TEL-­‐SKO-­‐0000000  Context  ........................................................................................................  AG-­‐CAL-­‐FRM  Revision  ........................................................................................................................  DE  Author  ..........................................................................................................  T.J.  Cornwell  Date  ...............................................................................................................  2015-­‐04-­‐08  Document  Classification  ..........................................................................  UNRESTRICTED  Status  .......................................................................................................................  Draft  

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

  UNRESTRICTED  Author:  T.J.  Cornwell  

Page  2  of  28      

     

Date:      

DOCUMENT  HISTORY  

Revision   Date  Of  Issue   Engineering  Change    Number  

Comments  

A   2014-­‐11-­‐10   -­‐   First  draft  release  for  internal  review  

       

       

   

DOCUMENT  SOFTWARE  

  Package   Version   Filename  

Wordprocessor   MsWord   Word  2007   SKA-­‐TEL-­‐SKO-­‐0000000-­‐Telescope_CalibrationD.docx  

Block  diagrams        

Other        

   

ORGANISATION  DETAILS  Name   SKA  Organisation  

Registered  Address   Jodrell  Bank  Observatory  

Lower  Withington  

Macclesfield  

Cheshire  

SK11  9DL  

United  Kingdom  

 Registered  in  England  &  Wales  Company  Number:  07881918  

Fax.   +44  (0)161  306  9600  Website   www.skatelescope.org  

 

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

  UNRESTRICTED  Author:  T.J.  Cornwell  

Page  3  of  28      

CONTENTS    

1   Introduction  ................................................................................................................  7  1.1   Purpose  of  the  document  .................................................................................................  7  1.2   Scope  of  the  document  .....................................................................................................  7  

2   References  ...................................................................................................................  8  2.1   Applicable  documents  ......................................................................................................  8  2.2   Reference  documents  .......................................................................................................  8  

3   Calibration  requirements  .............................................................................................  9  3.1   L1  Requirements  ..............................................................................................................  9  3.2   Analysis  ...........................................................................................................................  13  

4   Calibration  framework  ...............................................................................................  14  

5   Centralisation  of  Calibration  Framework  ....................................................................  19  

6   Telescope  Calibration  Framework  ..............................................................................  20  6.1   Design  and  development  .................................................................................................  20  6.2   Commissioning  and  operations  ........................................................................................  20  

7   Calibration  of  SKA1  Telescopes  ..................................................................................  21  7.1   Calibration  of  SKA1_Low  .................................................................................................  22  7.2   Calibration  of  SKA1_Mid  ..................................................................................................  24  

8   Modifications  to  Statements  of  Work  ........................................................................  26  

9   Additional  L1  requirements  .......................................................................................  27  9.1   Missing  L1  requirements  .................................................................................................  27  

10   The  Way  Forward  ....................................................................................................  28  

 LIST  OF  FIGURES  

Figure  1  Project  documentation  structure.  ............................................................................  14  Figure  2  Operations  documents  .............................................................................................  14  Figure  3  Conceptual  map  of  calibration  framework  ...............................................................  17  Figure  4  Conceptual  map  of  imaging  framework  ...................................................................  17  Figure  6  SKA1  Context  diagram  ..............................................................................................  21  Figure  7  Low  Product  Tree  ......................................................................................................  22  Figure  8  Mid  Product  Tree  ......................................................................................................  24  Figure  9  Plan  for  a  Calibration  Consultation  for  SKA1-­‐Low,  showing  the  input  topics  and  the  

output  models.  ..............................................................................................................  28          

LIST  OF  TABLES  Table  6-­‐1  Element  responsibility  for  calibration  .....................................................................  20          

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

  UNRESTRICTED  Author:  T.J.  Cornwell  

Page  6  of  28      

 LIST  OF  ABBREVIATIONS  

Acronym   Definition  AA   Aperture  Array  ACM   Auto  Correlation  Matrix  AG   Architecture  Group  CSP   Central  Signal  Processing  DSH   Dish  Consortium  ECP   Engineering  Change  Proposal  ICD   Interface  Control  Document  INFRA   Infrastructure  Consortium  LFAA   Low  Frequency  Aperture  Array  LINFRA   Local  Infrastructure  LMC   Local  Monitor  and  Control  LOW   Low  frequency  component  of  SKA1  MID   Mid  frequency  component  of  SKA1  MRO   Murchison  Radio  Observatory  OPS   Operations  RBS   Rebaselining  RFI   Radio  Frequency  Interference  SADT   Signals  and  Data  Transport  SAT   Synchronisation  And  Timing  SCI   Science  SDP   Science  Data  Processing  SKA   Square  Kilometre  Array  SKADC   SKA  Design  Consortium  SKAO   Square  Kilometre  Array  Organisation  (or  Office)  SKO   SKA  Office  TBA   To  Be  Advised  TBC   To  Be  Confirmed  TBD   To  Be  Decided  TM   Telescope  Manager  WBS   Work  Breakdown  Structure  

   

1 Introduction  

1.1 Purpose  of  the  document  

The  purpose  of  this  document  is  to  describe  the  SKA1  system  level  framework  for  calibration  of  SKA1  telescopes.   The   word   “framework”   is   taken   to   mean   a   set   of   coherently   defined   processes   and  procedures  that  may  be  adapted  for  one  of  a  small  set  of  related  purposes  –  specifically  calibration  of   SKA1-­‐Low   and   SKA1-­‐Mid.  One   assumption   is   therefore   that   calibration   of   these   telescopes   has  much   in   common   –   conceptually   and   practically.   This   is   a   system   framework   because   it   specifies  responsibilities  for  all  Elements.    Calibration   necessarily   includes   information   flow   from   all   Project   Elements,   but   the   two   Elements  most  directly  involved  are  TM  and  SDP.  Indeed  calibration  would  be  ideally  designed  by  an  Element  that   combined   TM   and   SDP   functions.   Unfortunately   since   TM   and   SDP   are   separate   Elements   in  SKA,  much  of  the  architecture  and  design  of  calibration  has  to  be  done  at  the  system  level.  We  urge  readers  to  bear  that  fact  in  mind.    

1.2 Scope  of  the  document  

This  document  presents  a  unified  view  of  the  system  calibration  of  all  aspects  of  an  SKA1  telescope,  and  aspects  of  calibration  of  the  individual  telescopes,  Low  and  Mid.  The  context  is  post  2015  RBS.    System  calibration  includes  all  aspects  of  the  measurement  process,  not  just  those  directly  related  to  astronomical   observations.   “System”   denotes   that   the   operation   of   the   entire   telescope   is  considered,   even   though   only   one   component   may   be   the   subject   of   the   calibration   process.  Calibration  of  a  single  component,  such  as  antenna  pointing  model,  is  considered  to  be  a  special  case  of  system  calibration.    This  document  will  be  of  direct  relevance  to  all  elements,  to  SCI  and  OPS.    The  scope  includes  the  design  and  use  of  the  framework  but  not  the  implementation  in  any  of  the  elements.  Therefore  this  is  not  a  software  design  document.    By  the  very,  system-­‐focused,   level  of  this  document,  we  provide  only  a  sketch  of  the  calibration  of  the  two  SKA  Telescopes,  SKA1-­‐Mid  and  SKA1-­‐Low.  Specifically  we  do  not  examine  the  details  of  the  calibration  required.  Detailed  accounts  are  given  elsewhere.    

2 References  

2.1 Applicable  documents  

The  following  documents  are  applicable  to  the  extent  stated  herein.  In  the  event  of  conflict  between  the  contents  of  the  applicable  documents  and  this  document,  the  applicable  documents  shall  take  precedence.    

[AD1] Cornwell,   T.,   Turner,  W.,   et   al,   2014,   “SKA   PHASE   1   SYSTEM   (LEVEL   1)   REQUIREMENTS  SPECIFICATION”  SKA-­‐OFF.SE.ARC-­‐SKO-­‐SRS-­‐001_3  

[AD2] Cornwell,   T.,   “SKA   Telescope   Calibration   Template”,   SKA-­‐TEL-­‐SKO-­‐0000000-­‐Telescope_Calibration  TemplateA  

2.2 Reference  documents  

The   following   documents   are   referenced   in   this   document.   In   the   event   of   conflict   between   the  contents  of  the  referenced  documents  and  this  document,  this  document  shall  take  precedence.    There  are  currently  no  Reference  Documents.            

3 Calibration  requirements  

3.1 L1  Requirements  

Here  we  list  the  L1  requirements[AD1]  that  touch  on  calibration  activities.  

ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2621  

Spectral  stability:  The  spectral  stability,  on  a  time  scale  of  600  sec.,of  the  station  beam  bandpass,  post  station  calibration  and  RFI-­‐mitigation,  shall  be  within  1.3  %,  0.4  %,  0.6  %  and  1.1  %  at  50  MHz,  100  MHz,  160  MHz,  and  220  MHz  respectively  compared  to  the  full  polarization,  parameterized  beam  model.    

Accepted   Derived  from  science  requirements  

Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2629  

Station  beam  stability.  The  difference  between  the  parameterized  station  beam  model  and  the  actual  station  beam  shall  remain  smaller  than  1.3  %,  0.4  %,  0.6  %  and  1.1  %  relative  to  the  main  beam  peak  power,  after  calibration,  at  50  MHz,  100  MHz,  160  MHZ  and  220  MHz  respectively    

Accepted   Derived  from  Science  Requirements  

Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2634  

Calibration  update  rate.  Calibration  measurements  shall  be  necessary  at  a  rate  of  no  more  than  10seconds.    

Accepted   References  [16],  [17]   Demonstration  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2635  

Real-­‐time  calibration.  The  LFAA  reception  system  at  station  level  shall  provide  on-­‐line  instrumental  calibration  functions  with  an  update  rate  of  10  minutes    

Accepted   Derived  from  DRM   Demonstration  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2675  

Polarisation  purity.  The  SKA1_Low  station  beams  shall  have  an  Intrinsic  Cross  Polarization  Ratio  (IXR)  at  the  zenith  better  than  -­‐15  dB  before  calibration  

Accepted   Baseline  Design  section  6.1  item  3  

Analysis  

 

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

  UNRESTRICTED  Author:  T.J.  Cornwell  

Page  10  of  28    

The   polarisation   purity   of   reflector   antenna   shall   be   expressed   by   using   the   intrinsic   polarisation  ratio   (IXR).   It  will   give  coordinate   system   independent  FoM  of   the  polarisation  purity  and  quantify  the  polarimetric  performances  even  after  the  calibration.  

ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2630  

Station  Beam  stability.  Station  beams  shall  have  a  maximal  RMS  stability  within  TBD  %  RMS  of  a  TBD  mask  over  the  calibration  period  of    10s  TBC  with  a  zenith  pointing  direction  across  the  full  frequency  band  with  one  failed  signal  path  

Accepted   TBJ   Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2805  

SKA1_Mid  fine  frequency  channel  amplitude  variation.  The  fine  frequency  channels  for  the  SKA1_Mid  channeliser  shall  have  a  total  amplitude  variation  as  a  function  of  frequency  of  less  than  0.01  dB  after  bandpass    calibration  

Accepted   Signal  processing  chain  performance  document  in  preparation  

Test  

 The  VLBI   community   indicate   there   should  be  at   least   4  beams  generated   for  VLBI  usage:  one   for  target  and  three  for  calibrators  to  establish  calibration  plane.  

ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2633  

Beam  polarization  stability.  The  polarisation  properties  of  the  beams  shall  be  stable  enough  to  allow  their  calibration  to  be  better  than  TBD  %  

Accepted   TBJ   Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2280  

System  status.  The  system  shall  extract  information  about  the  current  condition  of  the  system  from  the  science  and  calibration  data  streams,  and  log  this  information  along  with  other  relevant  system  and  environmental  status  information.  Based  on  this  information,  it  shall  be  possible  to  monitor,  save,  and  analyse  the  technical  performance  of  the  system.    

Accepted   ConOps  5.2   Demonstration  

 The   Forensic   tool   for   telescope   behaviour   will   draw   upon   the   monitor   data   archive,   the   System  Configuration  database,  Alarm  Log,  Calibration  data,  and  other  related  sources  of  information.  

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

  UNRESTRICTED  Author:  T.J.  Cornwell  

Page  11  of  28    

ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2729  

Calibration  and  imaging  formalism.  The  Calibration  and  Imaging  formalism  shall  be  based  upon  the  Rau  framework  [14].    

Accepted   Reference  [1]   Demonstration  

   ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2319  

Closed  loop  calibration.  The  telescope  calibration  shall  be  solved  by  comparison  of  observed  with  GSM  predictions  with  a  time  scale  appropriate  to  the  component  and  physical  effect  being  calibrated  and  fed  back  to  the  telescope.    

Accepted   ConOps  4.3   Demonstration  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2322  

Global  sky  model.  Calibration  and  continuum  subtraction  shall  use  a  Local  Sky  Model,  derived  from  a  Global  Sky  Model  or  previous  Local  Sky  Model.    

Accepted   ConOps  9.8   Demonstration  

 

ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2724  

Aperture  Array  DDE.  There  shall  be  a  direction  dependent  model  for  the  aperture  array  primary  beam  to  be  used  in  calibration  and  imaging.    

Accepted   SKA1-­‐SYS_REQ-­‐2321   Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2727  

Dish  DDE.  There  shall  be  a  direction  dependent  model  for  the  dish  primary  beam  to  be  used  in  calibration  and  imaging.    

Accepted   SKA1-­‐SYS_REQ-­‐2321   Test  

   ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2725  

Faraday  rotation  DDE.  There  shall  be  a  direction  dependent  Faraday  Rotation  model  for  use  in  calibration  and  imaging.    

Accepted   SKA1-­‐SYS_REQ-­‐2321   Test  

   ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2338  

Calibration  pipeline.  There  shall  be  a  Calibration  pipeline  that  derives  current  telescope  parameters  using  a  recent  observation  and  a  Global  Sky  Model,  either  a  known  GSM  or  

Accepted   ConOps  4.4   Test  

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

  UNRESTRICTED  Author:  T.J.  Cornwell  

Page  12  of  28    

the  most  recent  GSM.      ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2339  

Continuum  imaging  pipeline.  There  shall  be  a  Continuum  Imaging  pipeline  that  shall  have  the  goal  of  constructing  noise-­‐limited  wide-­‐band  images  for  observations  up  to  1000h  integration  time.  Polarisation  shall  be  available  if  requested  or  necessary  for  calibration  or  quality  assurance.    

Accepted   SKA1-­‐SYS_REQ-­‐2128   Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2692  

Coherence  loss  1min.  The  SKA  frequency  reference  system  shall  provide  a  2%  maximum  coherence  loss,  equivalent  to  0.2  radians,  within  a  maximum  solution  interval  for  in-­‐beam  calibration  of  1  minute.    

Accepted   Baseline  Design  Addendum  SKA-­‐TEL-­‐SKO-­‐DD-­‐003  

Demonstration  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2693  

Frequency  reference  phase  drift.  The  SKA  Frequency  Reference  System  shall  have  a  phase  drift  of  less  than  1  radian,  over  calibration  intervals  of  up  to  10  minutes,  when  using  out  of  beam  calibration  sources.    

Accepted   Baseline  design  addendum  SKA-­‐TEL.SKO-­‐DD-­‐003  

Demonstration  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2695  

Pulse  per  second  phase  relative  to  UTC.  The  SKA  synchronisation  and  timing  system  shall  provide  a  1PPS  heartbeat  signal  with  phase  relative  to  UTC  that  over  a  10  minute  calibration  interval  shall  survive  synchronisation  loss.  

Accepted   Baseline  design  addendum  SKA-­‐TEL-­‐SKO-­‐DD-­‐003  

Demonstration  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2337  

Ingest  pipeline.  There  shall  be  an  Ingest  pipeline  that  ingests  data  from  the  Correlator  and  Telescope  Manager,  applies  known  correction,  flags  known  RFI,  applies  known  calibration,  and  averages  in  time  and  frequency  as  required.  

Accepted   TBJ   Test  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2694  

Frequency  reference  rms.  The  SKA  Frequency  Reference  

Accepted   Baseline  design  addendum  SKA-­‐TEL.SKO-­‐

Demonstration  

Document  No.:  Revision:  Date:    

SKA-­‐TEL-­‐SKO-­‐0000000  D  2015-­‐04-­‐08  

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System  shall  have  phase  variability  about  a  linear  slope  calibration,  of  less  than  0.05  radians  RMS,  for  calibration  intervals  of  up  to  10  minutes,  using  out  of  beam  calibration  sources.  

DD-­‐003  

 ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐2542  

Training  A  plan  detailing  the  training  required  for  maintenance,  calibration  and  repair  shall  be  generated.    

Accepted   SKA1-­‐SYS_REQ-­‐2802   Inspection  

3.2 Analysis  

The  overall  calibration  capabilities  as  constrained  by  the  L1  Requirements  can  be  summarised  as:    

• Telescope   calibration   is   closed-­‐loop,   no   faster   than   10   seconds;   there   are   currently   no  requirements  on  how  quick  calibration  needs  to  be  applied.  

• Station  calibration  is  closed-­‐loop,  no  faster  than  10  minutes.  • A  Global  Sky  Model  is  used  for  Telescope  calibration  • Application   of   calibration   corrections   occurs   at   the   beamformers   and   at   ingest   to   SDP   for  

imaging.  • There  are  relatively  few  performance  requirements  • Direction-­‐dependent  effects  must  be  handled  • Telescope  self-­‐calibration  may  be  needed  in  the  SDP  pipelines  

 

4 Calibration  framework  The   calibration   framework   is   part   of   the   documentation   to   be   delivered  with   telescope   definition  (see  Figure  1)  

 Figure  1  Project  documentation  structure.    

 

 Figure  2  Operations  documents  

 • We  will  define  Calibration  as  the  ability  to  predict  the  data  received  for  a  given  observation,  

such  as  a  long  track,  or  a  sequence  of  point  observations.  This  is  the  forward  problem.    For  visibility  plane  effects  this  is  straightforward  but  for  image  plane  effects,  such  as  the  primary  beam,  a  propagation  of  the  model  sky  through  the  appropriate  telescope  description  must  be  performed.  The  inverse  problem  of  determining  the  input  signal  that  produced  given,  measured  data  is  much  harder  and  often  not  feasible.  Imaging  provides  an  example  of  an  

Observatory requirements documents structure V2Observatory_Requirementspackage [ ]

Level 0 (Science)

Level 0 verification documents

Level 0 requirements

Level 1 (System)

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Level 1 requirements

Level 1 verification documents

Level 1 supporting documents

Operations documents

Level 3 (Subelement)

Level 3 requirements

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inverse  problem.  We  will  therefore  not  consider  imaging  or  other  inverse  aspects  in  this  memo.  

 • The  input  signal  is  always  an  electromagnetic  field,  which  might  be  referred  to  a  standard  

location  outside  the  Earth’s  ionosphere.  We  measure  the  EM  field  after  propagation  through  the  atmosphere,  at  the  focus  of  an  antenna.  The  output  data  can  be  spatial  and  temporal  correlations  of  these  inputs  or  time-­‐series.  

 • There  is  a  signal  path  composed  of  Products.  In  the  analogue  part  of  the  signal  path,  gains,  

delays,  non-­‐linear  effects,  addition,  etc.  affect  the  signal.  In  the  digital  part,  the  signal  should  not  be  affected,  except  by  some  error.  To  be  concrete,  we  will  take  the  signal  path  to  terminate  at  the  Ingest  phase  of  the  Imaging  Processor,  or  the  equivalent  for  the  Time  Series  Processor.  

 • Post-­‐ingest,  the  effects  of  the  known  calibration  terms  are  corrected.  We  will  call  this  step  

Calibration  Correction.  Note  that  Calibration  Correction  is  not  as  well  defined  as  Calibration  because  it  may  involve  an  inverse  problem.  

 • Successful  calibration  allows  a  null  experiment  –  the  differences  between  the  observed  data  

and  the  predicted  data  are  consistent  with  the  known  noise  processes.      

• The  calibration  state  is  captured  in  a  finite  set  of  Calibration  parameters.  These  calibration  parameters  may  be  determined  by  observing  a  known  calibration  source  and  then  using  a  procedure  to  determine  the  calibration  parameters  via  fitting  or  similar  process.  These  parameters  are  then  used  on  the  target  source.  Usually  a  model  of  the  target  source  will  be  constructed  in  some  way  and  compared  and  adjusted  iteratively  until  the  observed  and  predicted  data  are  consistent.  

 The  difficulty  with  calibration  comes  from  the  number,  complexity,  and  interrelatedness  of  physical  processes  that  must  be  calibrated.  The  SKA1  product  tree  shows  all  the  active  elements  in  the  telescopes  down  to  product  level  4.  Below  level  4  there  are  more  active  elements  requiring  calibration.  In  addition,  the  environment  must  also  be  calibrated  in  the  above  definition  of  calibration  –  we  must  be  able  to  predict  the  effects  of  a  given  component  of  the  environment  of  the  observed  data.      Some  elements  of  the  product  tree  can  be  calibrated  once  or  infrequently,  perhaps  using  a  non-­‐astronomical  approach,  and  then  the  calibration  parameters  used  thereafter.  The  pointing  model  of  a  dish  provides  an  excellent  example.  The  form  and  parameters  of  the  pointing  model  can  be  determined  at  DSH  qualification  and  thereafter  determined  during  AIV  and  changed  only  occasionally  during  special  pointing  calibration  observations.    There  are  three  cases  to  be  considered:    

• If  the  calibration  parameters  can  be  determined  by  stand-­‐alone,  non-­‐astronomical  or  non-­‐interferometric  measurements,  then  the  calibration  of  that  product  can  be  performed  in  isolation.    

• The  more  common  circumstance  is  that  a  telescope  has  many  products  or  environmental  factors  that  must  be  calibrated  purely  from  measured  data  and  assumptions  about  the  input  source.  Usually  there  will  be  degeneracies  in  the  effect  of  products  on  the  measured  data.  These  must  be  broken  by  a  carefully  designed  measurement  strategy  in  which  the  

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configuration  of  the  telescope  is  changed  sequentially.  The  complete  set  of  measured  data  can  then  be  used  to  determine  the  calibration  parameters  of  the  products  or  environmental  factors.  In  the  simplest  case,  this  corresponds  to  alternating  between  a  known,  point  source  calibrator,  and  the  target  source.  In  a  more  complex  observation,  one  might  want  to  untangle  the  various  gain  terms  –  the  phase  delay  of  the  atmosphere,  the  complex  gain  of  the  receiver  for  each  hand  of  polarisation,  the  leakage  between  polarisations,  and  the  band  passes.  These  effects  vary  on  different  timescales  and  so  estimation  of  the  calibration  parameters  must  take  that  into  account.  It  is  possible  to  do  a  global  solution  for  all  the  parameters,  but  often  it  is  easier  to  solve  incrementally  and  sequentially.  

• The  calibration  source  may  be  in  the  field  being  observed,  which  case  joins  smoothly  into  self-­‐calibration.  

• Finally  there  are  circumstances  in  which  a  standalone  calibration  is  possible  but  is  limited  in  accuracy  and  must  be  further  improved  by  calibration  on  astronomical  sources  of  known  properties.  

 For  a  concrete  example,  consider  the  location  of  an  antenna,  which  is  involved  in  the  Point  function.  Theodolite  (too  time-­‐consuming),  laser  ranging  (possible),  or  GPS  (better)  may  be  used  to  determine  the   location.   These   measurements   provide   a   certain   accuracy   and   context   (or   reference   frame).  Measurement   of   a   set   of   radio   sources   using   the   entire   telescope  will   provide   holistic,   consistent  information   on   the   antenna   locations   with   a   certain   accuracy   and   reference   frame   (this   time  referred   to   that   used   for   the   radio   sources).   To   determine   the   antenna   locations   from   the  measurements  requires  a  model  of  the  measurement  process  that  is  parameterised  by  the  antenna  pointing.   In   the   case   of   antenna   pointing,   the   calibration   strategy  may   be,   for   example,   such   the  antennas  are  directed   to  move   in  a   cross  pattern  around  a   radio   source  while   the   strength  of   the  sources  is  monitored.  For  a  global  solution,  this  is  repeated  for  sources  all  across  the  sky  (in  azimuth  and   elevation).   For   a   local  model,   this   would   be   repeated   only   for   sources   nearby.   From   a   least-­‐squares  fit,  the  pointing  parameters  can  be  determined.      The  specific  way  in  which  the  observations  are  made  and  the  parameters  solved  is  just  as  important  as  the  equations  describing  the  model.  We  call  this  a  Calibration  strategy.  It  is  conceptualised  as  a  sequence  of  observations  and  data  reductions.    The  calibration  strategy  cannot  be  standalone  but  must  be  connected  to  the  architecture  of  the  telescope,  most  specifically  the  top-­‐level  descriptions  of  behaviour  (via  functional  analysis)  and  structure  (product  tree[AD1]and  other  diagrams).    Only  functions  of  the  telescope  can  be  used  to  calibrate  the  telescope  as  a  system,  and  to  then  use  the  telescope  for  observations.  Hence  the  functional  analysis  is  key.  The  functions  edged  by  a  black  box   impinge   upon   the   system   calibration,   either   by   producing   data   that   is   used   in   the   calibration  process  or  by  having  parameters  that  must  be  determined.  The  functions  in  the  functional  analysis  are  allocated  to  products  in  the  product  tree  (Figure  5).    We  call  this  model  of  the  telescope  a  Telescope  Model.  The  Telescope  Model  is  itself  a  collection  of  models,  one  or  more  for  each  product.  The  Telescope  Model  contains  Telescope  Parameters.    This   overall   conceptual   model   is   shown   in   Figure   3.   Although   we   do   not   discuss   imaging   in   this  memo,  for  clarity  we  show  the  complementary  imaging  strategy  in  Figure  4.    

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 Figure  3  Conceptual  map  of  calibration  framework  

 

 Figure  4  Conceptual  map  of  imaging  framework  

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 Figure  5  Product  tree  for  SKA1  

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5 Centralisation  of  Calibration  Framework      Calibration   must   be   performed   for   many   products   in   the   Telescopes.   The   overall   approach   for  development  of  the  calibration  framework  capabilities  is:    

1. The  Elements,  particularly  DSH  and  LFAA,  are  formally  responsible  (via  the  existing  SOW)  for  providing  models   to   the  SKAO   for   their  products.  The   term  “model”  here  means   functions  and  data  allowing  the  prediction  of  the  state  of  a  product.  

2. TM  will  incorporate  these  product  models  as  part  of  the  Telescope  Model.  In  some  cases,  it  might   be   appropriate   for   SDP   to   implement   these   within   a   high-­‐performance   computing  environment.  

3. TM  is  responsible  for  choreographing  observations  and  attaching  meta-­‐data  appropriately  to  the  measurements.  

4. SDP   is   responsible   for   converting   observational   data   and   meta-­‐data   into   science   data  products.  This  includes  visibility  calibration  solution  and  correction.  

 Calibration  approaches  may  evolve  over  time  in  response  to  the  existing  performance  requirements.  We   can   expect   that   station-­‐based   calibration  may   be   augmented   or   replaced   by   telescope-­‐based  calibration  using  the  entire  telescope  to  determine  calibration  of  each  station  in  a  holistic  approach.  This  would  probably  one  come  after  years  of  operation  and  optimisation.    In  addition,  on-­‐going  maintenance  will  be  necessary  after  operations  start.  Since  the  Elements  that  responsible   for   the   products   will   disappear   at   the   end   of   construction,   maintenance   and   further  development  are  assumed  to  be  the  responsibility  of  an  Operations  computing  team.    These  points  argue  for  centralisation  of  as  much  of  the  calibration  strategy  as  possible  into  the  single  TM   code   framework   and   away   from   the   multiple   and   possibly   divergent   LMC   code   frameworks.  Thus,   solution   of   Telescope  Model   parameters  will   be   centralised   in   either   TM   or   SDP,   and   away  from  the  product  LMCs.      This  centralisation  has  the  following  advantages:    

• Algorithm  resource  requirements  can  grow  without  having  to  upgrade  all  relevant  Telescope  LMCs.  For  example,  concurrent  processing  could  be  utilised  as  needed.  

• Maintenance   and  development  of   the   Telescope  Model  will   not   require   knowledge  of   the  numerous  individual  LMC  code  frameworks.  

• Simulation   can   use   the   modelling   capabilities   directly   in   the   knowledge   that   there   is   no  version  or  code  mismatch.  

 For  example,  ACM  information  from  the  aperture  arrays  will  be  sent  to  TM  for  solution  of  antenna  gains,  and  weights  and  calibration  information  returned  as  needed.      The  disadvantages  to  centralisation  are:    

• Derivation  of  a  common  framework  • Possible  performance  overheads  

 This  centralisation  is  a  key  element  of  the  SKA1  Architecture.  Waivers  may  be  requested  and  will  be  reviewed  by  the  SKA  Architect.    

6 Telescope  Calibration  Framework  

6.1 Design  and  development  

The  Elements  will  be  responsible  as  follows:    

Table  6-­‐1  Element  responsibility  for  calibration  Element   Principal  responsibility  

AIV   • Verification  of  system  calibration  CSP   • Apply  calibration  and  weights  in  correlator  and  central  

beamformers  DSH   • Provide  primary  beam  models,  pointing  models,  calibration  

procedures,  etc.  for  Telescope  Model  • Provide  calibration  measurements  to  TM  • Apply  calibration  and  weights  in  PAF  beamformers  

INFRA   • Provide  input  information  for  calibration  e.g.  antenna  locations  LFAA   • Provide  antenna  primary  beam  models,  station  models,  

calibration  procedures,  etc.  for  Telescope  Model  • Provide  calibration  measurements  to  TM  • Apply  calibration  and  weights  in  AA  beamformers  

SADT   • Application  of  timing  corrections  SCI   • Provide  models  and  calibration  procedures  for  external  factors  

such  as  troposphere,  ionosphere,  Galactic  plane,  etc.  SDP   • Execution  of  calibration  strategy  and  consequent  processes  

• Calibration  solvers,  calibration  application,  and  calibration  correction  

TM   • Instantiation  of  calibration  strategy  and  processes  of  scheduling  blocks  

• Telescope  Model  

 The  SKAO  Architecture  Group  is  responsible  for:  

• Definition  of  SKA1  approach  to  system  calibration  (this  and  related  documents)  • Definition  of  contents  of  Telescope  Model,  Telescope  Parameters  • Initial  definition  of  operational  aspects  of  Calibration  Strategy  

 

6.2 Commissioning  and  operations  

During  commissioning  and  operations,  the  SKA  Operations  Group  is  assumed  to  be  responsible  for  execution  of  all  aspects  of  this  calibration  strategy  

7 Calibration  of  SKA1  Telescopes  The  SKA  Product  Tree  is  composed  of  SKA  Products.  These  are  identified  by  SysML  stereotype  <<SKA  Product>>.  <<SKA  Calibrated  Product>>  denotes  products  that  require  derivation  of  or  application  of  calibration   parameters.   Products   that   apply   calibration   parameters   only   have   no   special   notation.  The  detailed  product  trees  for  Low  (Figure  7),  and  Mid  (Figure  8).    The   SKA1   telescopes   are   calibrated  within   a   physical   context   (see   Figure  6).   The   physical   context  establishes  physical  effects  that  must  be  modelled  and  calculable  in  order  to  predict  the  measured  data.   <<SKA   Environment>>   denotes   physical   elements.   <<SKA   Calibrated   Environment>>   denotes  physical  elements  that  can  be  calibrated.    

 Figure  6  SKA1  Context  diagram  

 

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7.1 Calibration  of  SKA1_Low  

7.1.1 Overview  

 Figure  7  Low  Product  Tree  

 

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Products/Environments  to  be  calibrated:  • Ionosphere  • Lower  Inner  Station  

o Low  Antenna  o Low  frequency  LNA  o Low  Analog  Transmission  

• Lower  Outer  Station  o Low  Antenna  o Low  frequency  LNA  o Low  Analog  Transmission  

• Low  Synchronisation  and  Timing    Correction  of  calibration:  

• Low  Telescope  Manager  • Low  Station  Beamformer  • Low  Synchronisation  and  Timing  • Low  Science  Data  Processor  

 

7.1.2 Sketch  of  calibration  

Of   these,   the   calibration   of   the   ionosphere   is   the  most   troublesome   at   the   frequencies   at   which  SKA1-­‐Low   operates.   From   LOFAR  we   know   that   the   ionosphere   above   each   station   changes   on   a  time  of  5  to  10s.  Fortunately  the  sky  is  bright  and  there  usually  exists  a  background  sky  composed  of  compact   sources   that   can   be   used   to   solve   for   the   phase   screen   in   some  parametric   or   pixelated  form.   This   screen   can   then   be   applied   to   the   visibility   data   using   AW-­‐Projection   and   related  techniques.  The  compute  load  is  very  high,  though,  and  for  LOFAR  one  cycle  of  calibration  can  take  many  months.  Anecdotally,  we  know  that  while  this  approach  works  for  LOFAR,  it  does  not  allow  the  noise   level   to  be   reached.   Since  SKA1-­‐Low   is  16   times   larger   than   LOFAR,   it   seems   that   successful  calibration   of   LOFAR   is   a   necessary   but   by   no   way   sufficient   condition   for   SKA1-­‐Low   to   be  calibrateable.   Calibration   of   Low   is   an   Extreme   risk   in   the   Project   risk   register.   In   addition,  computation  of  the  calibration  is  also  an  Extreme  risk.    The  calibration  of  the  stations  requires  solving  for  the  gains  of  the  256x2  LNAs  in  each  station.  This  is  done  in  two  stages:  

• Antenna-­‐to-­‐antenna  (including  LNA-­‐to-­‐LNA)  consistency  is  ensured  by  solving  for  gains  from  the  autocorrelation  matrix  of   the   signals,  measured  across   coarse   frequency   channels   in  a  round   robin   that   repeats   every   few   minutes.   It   is   not   known   currently   how   often   this  calibration  will  have  to  be  repeated.  The  data  and  compute  loads  are  moderate.  

• Station-­‐to-­‐station   consistency   is   assured  by   self-­‐calibration  of   the   station   scalar   gains  on  a  few  minute  timescale.  

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7.2 Calibration  of  SKA1_Mid  

7.2.1 Overview  

 Figure  8  Mid  Product  Tree  

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 Products/Environments  to  be  calibrated:  

• Troposphere  • Ionosphere  • MeerKATProxy  (the  notional  interface  to  a  MeerKAT  antenna)  • Mid  Antenna  Station  

o Mid  Dish  o SPF  and  LNAs  o Mid  Analog  Transmission  

• Mid  Synchronisation  and  Timing    

Correction  of  calibration:  • Mid  Telescope  Manager  • Mid  Dish  Station  

o Mid  Dish  • Mid  Array  Beamformer  • Mid  Synchronization  and  Timing  • Mid  Science  Data  Processor  

 

7.2.2 Sketch  of  calibration  

The  troposphere  can  be  solved  for  as  part  of  Mid  station-­‐to-­‐Mid  station  self-­‐calibration.  This  type  of  processing  is  very  familiar  from  JVLA  and  eMERLIN,  and  presents  little  risk.    

8 Modifications  to  Statements  of  Work  As  part  of  the  implementation  of  this  framework,  some  modifications  to  existing  Statements  of  Work  may  be  required.  These  will  be  negotiated  between  the  consortia  and  SKAO.

9 Additional  L1  requirements  This  calibration  framework  requires  additional  L1  requirements.  These  will  be  submitted  as  part  of  the  ECP  including  this  document  as  a  reference  document.  

9.1 Missing  L1  requirements  

ID   Requirement   Status   Parent  Requirement   Verification  SKA1-­‐SYS_REQ-­‐????  

Beamformer  calibration:    All  beamformers  shall  accept  calibration  parameters  for  application  during  beamforming.  

Proposed     Test  

10 The  Way  Forward    The  future  developments  are  planned:    

• Send  for  review  and  commentary  by  SDP  and  TM,  initially  (Done)  • Modify  and  send  for  review  and  commentary  by  all  Elements.  • Discuss  tentative  assignments  with  those  affected.  • Consider  if  revised  SOW’s  are  required.  • Develop  set  of  L1  requirements  to  be  submitted  as  ECP  • Connect   this   approach   to   the   SysML  model   of   the   telescopes,   including   functional  

and  product  level  aspects.  • Develop  approach  for  both  telescopes  in  more  detail.  

 To  develop  the  approach  for  each  telescope,  we  will  proceed  via  Calibration  Consultations,  inviting   those  with   topical   related   information   to   advise   on   Best   Practice.   An   example   of  how  this  works  is  given  for  SKA1-­‐Low  in  Figure  9.    

 Figure  9  Plan  for  a  Calibration  Consultation  for  SKA1-­‐Low,  showing  the  input  topics  and  the  output  models.    The   outcome   will   be   a   Calibration   Plan   for   each   telescope,   outlining   the   methods   for  establishing  context,  specifying  product  level  models,  and  defining  calibration  processes.    

Calibrateability Antenna,Characterisation

Station,calibration

Telescope,calibration

Pulsar Ionospheric,modeling

EOR,detection

Imaging

Low,Antenna X X X X X XLow,Frequency,LNA X X X XLow,Analog,Transmission X X X XLow,Station,Configuration X X X X

OUTPUTS Low,Synchronisation,and,Timing X X X XLow,Configuration X X X XLow,BeamformerLow,CorrelatorLow,Imaging,Processor X XIonosphere X X X X X XGalactic,Plane X X

Context Extragalactic,Sky X X XConfusion X X,RFI,, X X

INPUTS