A radio interferometer is an indirect imaging device that samples the spatial Fourier transform of the sky brightness distribution being observed. It consists of a collection of spatially separated electromagnetic-wave detectors. The signals from each pair of N detectors are correlated and integrated over some finite time and frequency range to form N(N-1)/2 measurements in the spatial-frequency domain. An image is formed by taking the inverse spatial Fourier transform of the accumulated measurements.
The measurement process of an imaging interferometer can be written as a linear system of equations.
represents an image of the sky,
represents a 2D Fourier transform,
represents a spatial frequency sampling function that includes direction dependent instrumental effects,
represents direction independent instrumental gains for each measured correlation, and
represents the observed data. In a typical observation,
are unknown, whereas
is known and can be computed for any instrumental setup.
The main data analysis steps are :
: Discard data points that are contaminated by sources other than sky radiation or instrumental effects that can be calibrated out.
: Use observations of a known region of sky to solve for the elements of
, calculate its inverse, and apply it to the observed data. A typical observation consists of observations that switch between a science target and a calibrator source, with calibration solutions being interpolated across stretches of time when the target is observed.
: Use the calibrated data along with the known
to solve for
. For a practical interferometer with a finite number of array elements, the spatial frequency plane sampling is incomplete and
has no unique inverse. Therefore, an iterative least squares method is used to reconstruct the final image.
: At all stages, data and images need to be examined...
: Astrophysically significant quantities must be extracted from the output images....
( Jim - if you need it, this is some background that could go at the beginning of the paper, to help connect the different stages of processing. Also, this is not the only way of describing this. There are more standard (in radio astronomy literature i.e.) analytical expressions that describes what the interferometer measures, but (IMO) that would need more words to connect to the analysis algorithms and software. )