From The Stacker to Visibilities
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Transcript of From The Stacker to Visibilities
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From The Stacker to Visibilities
Gordon Hurford, Ed Schmahl, Richard Schwartz
18-April-2005 Revised by EJS 13-July-2005
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What is the Stacker?
Current imaging algorithms based on time-binned event lists
• Time bins must be very short (~1-100ms) to preserve modulation
-- Few events per bin (statistics, display, Forward Fit issues)
-- Large number of bins (long integrations impractical)
• Stacker is a form of superimposed epoch analysis
• Compresses data from an arbitrarily long interval into the equivalent of a 1-rotation integration
• Almost no loss of imaging information
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How does the Stacker help?
• Makes long integrations feasibleBut… solar rotation ~ 10 arcsec/hour at disk center
• Some improvement to image quality
• Improved 2
• Improved Forward Fit performance
• Helps with background and flare-variability issues
• Improvements in imaging speed
• fewer time bins to fit
• reuse stacked data (future)
• Opens the way to visibilities
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How does the Stacker work? (1)• Pointing changes
Phases are not duplicated rotation-to-rotation Cannot just stack data with rotation period
• Count rate in each time bin depends on:
• Source geometry and location
• Grid transmission and slit depth
• The occurrence time of the bin is not relevant.
• Roll angle & phase (relative to map center) are relevant
Substitute roll angle / phase bins for time bins
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How does the Stacker work? (2)
•Stacker associates each time bin with a roll / phase bin
• Accumulates counts and live time in each phase bin
• Calculates average grid transmission and modulation amplitude for each roll / phase bin
• Converts populated roll/phase bins back to equivalent time bins
Existing mapping algorithms can be used as is
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Typical Modulation Profiles
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Mapping Time Bins to Roll/Phase Bins
Phase (relative to map center)
Rol
l ang
le (
deg)
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One Rotation
PHASE (relative to map center)
Rol
l ang
le (
deg)
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Multiple Rotations
PHASE (relative to map center)
Rol
l ang
le (
deg)
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Roll and Phase Bins
Rol
l ang
le (
deg)
PHASE (relative to map center)
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Populated
Roll / Phase Bins
Subcollimators 1-9
23 July 2002
12-25 keV
80-second integration
Counts ____________________
livetime*gridtran*modamp
c
23 July
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Profiles in
Roll Bins
Subcollimator 5
25 March 2002
12-25 keV
80-second integration
Counts/phase bin
c
23 July
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Stacked Modulation Profile
Grid 8
7680 time bins
288 roll / phase bins
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Comparison of Unstacked vs Stacked PIXON Maps
Unstacked Stacked
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Comparison of Unstacked vs Stacked PIXON Fits
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Using the Stacker (1)
• Default is not to use the stacker
• No advantage if integration time is < ~ 3 rotations
• Invoke with switch, /use_phz_stacker
• Number of phase bins
• Reduces S/N if too small.
• Default=12 (99% efficient)
• Obj -> set, phz_n_phase_bins = nnn
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Using the Stacker (2)
• Number of roll bins
• Reduces s/n near edge of FOV is too small• Minimum value is determined by (max source offset) / (angular pitch)
• Default: Number of roll bins is calculated automatically assumingsource offset = 60 arcsec or image_dim * pixel_size/2
• To set source offset explicitly,phz_n_roll_bins_control = 0phz_radius = nnn (arcsec)
•To define number of roll bins explicitly,phz_n_roll_bins_control = [n1,n2,,,,n9] or n
• Should the number of roll bins be even or odd? Even = conservative choice.
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Status of the Stacker
• Basic capability is in SSW in the atest subdirectory
• Not yet systematically tested with all algorithms/options But seems to work fine with Clean and Pixons
• No known bugs
• To be implemented:
• Better handling of variable flux & background
• Features to support saving / retrieving / combining stacked counts from different intervals
• Correction for solar rotation
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RHESSI Visibilities
What they areTheir propertiesHow they are measuredAn exampleHow they can be usedStatus of software
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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 (e.g. 100*ei)
• Has amplitude and phase OR ‘sine’ and cosine’ components (e.g. A cos , A sin )
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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.
=> Visibilities of a multi-component source
= sum of visibilities of its components
• Very helpful in directly interpreting visibilities
• Facilitates a visibility forward-fit routine
=> 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 Visibilitiesly
Measure amplitude & phase in each of 24 roll bins
Subcollimator 5
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Example of measured visibilities for subcollimator 5
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Polar plots of amplitude vs roll angleSubcollimators
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 2 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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The end
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