RHESSI Visibilities

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RHESSI Visibilities
Gordon Hurford, Ed Schmahl, Richard
Schwartz 1 April 2005
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What are Visibilities?

• A visibility is the calibrated measurement of a
  single Fourier component of the source.
• Measured spatial frequency (arcsec-1)
• Magnitude determined by the angular pitch of
  the grid.
• Azimuth determined by the grid orientation at
  the time of measurement.
• The measured visibility is a complex number
• Has amplitude and phase OR sine and cosine
  components

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Properties of visibilities (1)

• Represent an intermediate step between
  modulated light curves and images.
• Represent an (almost) noise-free transformation
  of input imaging data, containing all the
  imaging info required for mapping
• Fully calibrated.
• No remaining instrument dependence (other than
  spatial frequencies)

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Properties of visibilities (2)

• Statistical errors are well-determined because
  visibilities are linear combinations of
  binned counts.
• Redundancy provides indication of systematic
  errors.
• Amplitudes for visibility azimuths differing
  by 180 deg should be same.
• Phases for visibility azimuths differing by 180
  deg should be equal and opposite.
• 3rd harmonic visibilities from grid n should
  match fundamental visibility from grid n-2.
• Redundancy is independent of source.

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Properties of visibilities (3)

• Visibilities depend linearly on both the data and
  the source.
• gt Visibilities of a multi-component source
• sum of visibilities of its components
• Very helpful in directly interpreting
  visibilities
• Facilitates a visibility forward-fit routine
• gt Visibility measurements can be linearly
  combined.
• Can add or subtract energy bands
• Can add or subtract data over time
• Can weight data in energy and/or time.

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How are visibilities measured ?

• Visibility observations correspond to the
  modulation amplitude and phase
• Can be measured from light curves directly
• Problem of data gaps
• Statistical issues
• Normalization and sampling issues
• Most easily determined from stacked data

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Stacker Output as the Starting Point for
Measuring Visibilitesly
Subcollimator 5
Measure amplitude phase in each of 24 roll bins
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Example of measured visibilities for
subcollimator 5
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Polar plots of amplitude vs roll angle
Subcollimators 1 2 3 4 5
6 7 8 9 Aug 20, 2002 12-25 keV
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How can visibilities be used? (1)

• IMAGING
• Provide a compact representation of input
  imaging data
• Can provide starting point for imaging
  algorithms
• Useful for iterative processing
• Ease statistical and chi2 issues
• Background is automatically removed.
• Can be used with any radio astronomy imaging
  package

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How can visibilities be used? (2)

• Can infer quantitative source properties
  without mapping.
• Source diameter
• Source ellipticity
• Source position
• Statistical errors can be well-determined.
• Provides a very sensitive tool for refining
  grid calibration

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Status of Visibility Software

• Currently testing a fragile version of software
  to calculate, display and exploit visibilities
• Available offline to venturesome volunteers
• Many features to be implemented
• Testing for compatibility with latest version of
  hsi_phz_stacker
• Handling of missing visibilities
• Better shell routine for convenient execution
• Testing with use of automatic calculation of
  time and roll bins
• Convenient tools for exploiting visibilities
• Improved grid calibration
• Calculation and application of statistical
  errors
• Testing with harmonics
• Integration of visibility analysis routines

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