From The Stacker to Visibilities

Gordon Hurford, Ed Schmahl, Richard Schwartz

18-April-2005 Revised by EJS 13-July-2005

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

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

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

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

Typical Modulation Profiles

Mapping Time Bins to Roll/Phase Bins

Phase (relative to map center)

Rol

l ang

le (

deg)

One Rotation

PHASE (relative to map center)

Rol

l ang

le (

deg)

Multiple Rotations

PHASE (relative to map center)

Rol

l ang

le (

deg)

Roll and Phase Bins

Rol

l ang

le (

deg)

PHASE (relative to map center)

Populated

Roll / Phase Bins

Subcollimators 1-9

23 July 2002

12-25 keV

80-second integration

Counts ____________________

livetime*gridtran*modamp

c

23 July

Profiles in

Roll Bins

Subcollimator 5

25 March 2002

12-25 keV

80-second integration

Counts/phase bin

c

23 July

Stacked Modulation Profile

Grid 8

7680 time bins

288 roll / phase bins

Comparison of Unstacked vs Stacked PIXON Maps

Unstacked Stacked

Comparison of Unstacked vs Stacked PIXON Fits

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

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.

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

RHESSI Visibilities

What they areTheir propertiesHow they are measuredAn exampleHow they can be usedStatus of software

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 )

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)

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.

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.

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

Stacker Output as the Starting Point

for Measuring Visibilitiesly

Measure amplitude & phase in each of 24 roll bins

Subcollimator 5

Example of measured visibilities for subcollimator 5

Polar plots of amplitude vs roll angleSubcollimators

1 2 3

4 5 6

7 8 9

Aug 20, 2002

12-25 keV

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

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

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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