RHESSI Visibilities

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

2. 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 What are Visibilities?

3. 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)

4. 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.

5. 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. Properties of visibilities (3)

6. 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

7. Stacker Output as the Starting Point for Measuring Visibilitesly Subcollimator 5 Measure amplitude & phase in each of 24 roll bins

8. Example of measured visibilities for subcollimator 5

9. Subcollimators 1 2 3 4 5 6 7 8 9 Aug 20, 2002 12-25 keV Polar plots of amplitude vs roll angle

10. 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

11. 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

12. 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 Status of Visibility Software

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