Interferometric Spectral  Line Imaging <ul><li>Martin Zwaan </li></ul><ul><ul><li>(Chapters 11+12 of synthesis imaging boo...
Topics <ul><li>Calibration </li></ul><ul><li>Gibbs phenomenon </li></ul><ul><li>Continuum subtraction </li></ul><ul><li>Fl...
Why Spectral Line Interferometry? <ul><li>Spectroscopy </li></ul><ul><ul><li>Important spectral lines </li></ul></ul><ul><...
Calibration <ul><li>Continuum data: determine complex gain solutions as function of time </li></ul><ul><li>Spectral line d...
 
Calibration <ul><li>Determine bandpass  B i,j   (    ) once per observation </li></ul><ul><li>Pcal-Scal-target-Scal-targe...
Calibration procedure <ul><li>Create pseudo-continuum (inner 75% of channels) </li></ul><ul><li>Determine complex gains  G...
Check bandpass calibration <ul><li>Smooth variation with frequency </li></ul><ul><li>Apply BP solution to Scal: should be ...
Gibbs Phenomenon <ul><li>Wiener-Khintchine theorem:   Spectral content I(  ) of stationary signal is Fourier transform of...
 
Solutions <ul><li>Observe with more channels than necessary </li></ul><ul><li>Remove first channels </li></ul><ul><li>Tape...
Continuum Subtraction <ul><li>Every field contains several continuum sources </li></ul><ul><li>Separate line and continuum...
Continuum Subtraction
IMLIN   <ul><li>Fit low-order polynomials to selected channels (free from line emission) at every pixel in image cube and ...
UVLIN <ul><li>Linear fits to real and imaginary components versus channel number for each visibility and subtracts the app...
UVLIN (cont’d) <ul><li>Allows to shift visibilities to move single strong source to image center    do fitting    shift ...
UVSUB   <ul><li>Subtract Fourier transform of specified model from visibility data set. Input model may consist of the  CL...
A procedure for continuum subtraction <ul><li>Make large continuum map to find far field sources </li></ul><ul><li>UVLIN o...
Flagging of Spectral Line Data <ul><li>Remove interfering signals from sun, satellites, TV, radio, mobile phones, etc </li...
Basic Reduction Steps <ul><li>Read data </li></ul><ul><li>Check quality and edit (flag) </li></ul><ul><li>Make pseudo-cont...
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Interferometric Spectral Line Imaging Martin Zwaan

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Interferometric Spectral Line Imaging Martin Zwaan

  1. 1. Interferometric Spectral Line Imaging <ul><li>Martin Zwaan </li></ul><ul><ul><li>(Chapters 11+12 of synthesis imaging book) </li></ul></ul>
  2. 2. Topics <ul><li>Calibration </li></ul><ul><li>Gibbs phenomenon </li></ul><ul><li>Continuum subtraction </li></ul><ul><li>Flagging </li></ul><ul><li>First reduction steps </li></ul><ul><li>After imaging: B ärbel’s talk </li></ul>
  3. 3. Why Spectral Line Interferometry? <ul><li>Spectroscopy </li></ul><ul><ul><li>Important spectral lines </li></ul></ul><ul><ul><ul><li>HI hyperfine line </li></ul></ul></ul><ul><ul><ul><li>Recombination lines </li></ul></ul></ul><ul><ul><ul><li>Molecules (CO, OH, H 2 O, masers) </li></ul></ul></ul><ul><ul><li>Calculate column densities (physical state of ISM) and line widths (rotation of galaxies) </li></ul></ul><ul><li>Continuum </li></ul><ul><ul><li>Reduce bandwidth smearing </li></ul></ul><ul><ul><li>Isolate RFI </li></ul></ul>
  4. 4. Calibration <ul><li>Continuum data: determine complex gain solutions as function of time </li></ul><ul><li>Spectral line data: same, but also function of  </li></ul><ul><li>Bandpass: complex gain as function of frequency </li></ul><ul><li>Factors that affect the bandpass: </li></ul><ul><ul><li>Front-end system, IF transmission system (VLA 3 MHz ripple) , back-end filters, Correlator, atmosphere, standing waves </li></ul></ul><ul><li>Different for all antennas </li></ul><ul><li>Usually not time-dependent </li></ul>
  5. 6. Calibration <ul><li>Determine bandpass B i,j (  ) once per observation </li></ul><ul><li>Pcal-Scal-target-Scal-target-Scal-… </li></ul><ul><li>Pcal: strong (point) source with known S (  ), observe at same  as target </li></ul><ul><li>Observe Pcal more often for high spectral DR </li></ul><ul><li>Observe long enough so that uncertainties in BP do not contribute significantly to image </li></ul>Peak continuum/ rms noise image
  6. 7. Calibration procedure <ul><li>Create pseudo-continuum (inner 75% of channels) </li></ul><ul><li>Determine complex gains G i,j ( t ) </li></ul><ul><li>Determine B i,j (  ) </li></ul><ul><li>Effects of atmosphere and source structure are removed by dividing by pseudo-continuum </li></ul><ul><li>N unknowns, N ( N -1)/2 measurables </li></ul><ul><li>Compute separate solution for every observation of Pcal </li></ul>
  7. 8. Check bandpass calibration <ul><li>Smooth variation with frequency </li></ul><ul><li>Apply BP solution to Scal: should be flat </li></ul><ul><li>Compare BP solutions of different scans (for all antennas) </li></ul>
  8. 9. Gibbs Phenomenon <ul><li>Wiener-Khintchine theorem: Spectral content I(  ) of stationary signal is Fourier transform of the time cross-correlation function R(  ) </li></ul><ul><ul><li>Need to measure R(  ) from -  to  ! </li></ul></ul><ul><ul><li>In practice: only measure from -N/2B to N/2B </li></ul></ul><ul><ul><li> Multiply R(  ) with a window function (uniform taper) </li></ul></ul><ul><ul><li>In  domain: I(  ) convoluted with sinc(x) </li></ul></ul><ul><ul><li>Nulls spaced by channel separation </li></ul></ul><ul><ul><li>Effective resolution: 1.2 times channel separation </li></ul></ul><ul><ul><li>-22% spectral side lobes </li></ul></ul>
  9. 11. Solutions <ul><li>Observe with more channels than necessary </li></ul><ul><li>Remove first channels </li></ul><ul><li>Tapering sharp end of lag spectrum R(  ) </li></ul><ul><ul><li>Hanning smoothing: f(  )=0.5+0.5 cos (  /T) </li></ul></ul><ul><ul><li>In frequency space: multiplying channels with </li></ul></ul><ul><ul><li>0.25, 0.5, 0.25 </li></ul></ul><ul><ul><li>After Hanning smoothing: </li></ul></ul><ul><ul><li>Effective resolution: 2.0 times channel separation </li></ul></ul><ul><ul><li>-3% spectral side lobes </li></ul></ul>
  10. 12. Continuum Subtraction <ul><li>Every field contains several continuum sources </li></ul><ul><li>Separate line and continuum emission </li></ul><ul><li>Two basic methods: </li></ul><ul><li>Subtract continuum in map domain ( IMLIN ) </li></ul><ul><li>Subtract continuum in UV domain ( UVSUB , UVLIN ) </li></ul><ul><li>Know which channels are line free </li></ul><ul><li>Use maximum number of line free channels </li></ul><ul><li>Iterative process </li></ul>
  11. 13. Continuum Subtraction
  12. 14. IMLIN <ul><li>Fit low-order polynomials to selected channels (free from line emission) at every pixel in image cube and subtract the appropriate values from all channels </li></ul><ul><li>Don't have to go back to uv data </li></ul><ul><li>Can't flag data </li></ul><ul><li>Clean continuum in every channel </li></ul><ul><ul><li>Time consuming </li></ul></ul><ul><ul><li>Non-linear: noisy data cube </li></ul></ul><ul><ul><li>Noisy continuum map </li></ul></ul>
  13. 15. UVLIN <ul><li>Linear fits to real and imaginary components versus channel number for each visibility and subtracts the appropriate values from all channels </li></ul><ul><li>Visibilities: </li></ul><ul><li>V=cos (2  bl/c) + i sin (2  bl/c) </li></ul>b·l small b·l large Baseline length Distance from phase center
  14. 16. UVLIN (cont’d) <ul><li>Allows to shift visibilities to move single strong source to image center  do fitting  shift back </li></ul><ul><li>No need to deconvolve continuum sources in all channels (deconvolution is non-linear) </li></ul><ul><li>Yields better continuum image </li></ul><ul><li>Fast </li></ul><ul><li>Allows flagging (remove baselines with high residuals) </li></ul><ul><li>Corrects for spectral slope </li></ul><ul><li>Only works for restricted field of view </li></ul>
  15. 17. UVSUB <ul><li>Subtract Fourier transform of specified model from visibility data set. Input model may consist of the CLEAN components, input images, or specified model </li></ul><ul><li>Works well for strong sources far away from phase center </li></ul><ul><li>Non-linear: introduces errors in maps </li></ul><ul><li>Slow! </li></ul>
  16. 18. A procedure for continuum subtraction <ul><li>Make large continuum map to find far field sources </li></ul><ul><li>UVLIN on large number of channels </li></ul><ul><li>Do Fourier transform and find line emission </li></ul><ul><li>Look for artifacts from strong continuum sources </li></ul><ul><li>Use UVLIN if one source dominates </li></ul><ul><li>Use UVSUB if many sources dominate, then UVLIN </li></ul><ul><li>Quality of continuum subtraction depends on quality of bandpass calibration </li></ul>
  17. 19. Flagging of Spectral Line Data <ul><li>Remove interfering signals from sun, satellites, TV, radio, mobile phones, etc </li></ul><ul><li>Remove corrupted data due to equipment problems </li></ul><ul><li>Edit program sources and calibrators! </li></ul><ul><li>Time consuming for many channels, many baselines </li></ul><ul><li>First check pseudo-continuum </li></ul><ul><li>Try UVLIN </li></ul><ul><li>Try to maintain similar uv coverage in all channels </li></ul>
  18. 20. Basic Reduction Steps <ul><li>Read data </li></ul><ul><li>Check quality and edit (flag) </li></ul><ul><li>Make pseudo-continuum </li></ul><ul><li>Determine gain solutions </li></ul><ul><li>Determine bandpass </li></ul><ul><li>Split off calibrated program source </li></ul><ul><li>Subtract continuum </li></ul><ul><li>Make image cube </li></ul>

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