# Presentation: 177360

## RHESSI Visibilities

- <date/time>

- Gordon Hurford,  Ed Schmahl,  Richard Schwartz
- 1 April 2005

## What are Visibilities?

- <date/time>

-   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

## Properties of visibilities (1)

- <date/time>

-   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)

- <date/time>

-   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)

- <date/time>

**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 ?

- <date/time>

-   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 

- Stacker Output as the Starting Point
- for Measuring Visibilitesly

- Measure amplitude & phase in each of 24 roll bins

- Subcollimator 5

## Example of measured visibilities for subcollimator 5

- <date/time>

## Polar plots of amplitude vs roll angle

- <date/time>

- _Subcollimators_
- 1     2     3
- 4    5     6
- 7     8     9
- Aug 20, 2002
- 12-25 keV

## How can visibilities be used?  (1)

- <date/time>

-  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)

- <date/time>

-   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

- <date/time>

-   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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