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

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 ‘x’ and ‘y’ components

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

Properties of visibilities (2) Statistical errors are well-determined. 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 visibilties 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 multicomponent source = sum of visibilities of its components Very helpful in directly interpreting visibilities => 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 Visibilites ly Measure amplitude & phase in each of 24 roll bins Subcollimator 5

Example of measured visibilities for subcollimator 5

Polar plots of amplitude vs roll angle Subcollimators Aug 20, 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 chi^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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