This
routine finds the parameters of a one- or two-component Gaussian beam by doing a least squares fit to
a supplied 2D NDF containing an image of a compact source. The source need not be a point source -
the source is assumed to be a sharp-edged circular disc of specified radius (i.e. a simple model of a
planet). On each iteration of the fitting process, this source model is convolved with the candidate
beam and the residuals with the supplied image are then found. The parameters of the beam are
modified on each iteration to minimise the sum of the squared residuals. The beam consists of one or
two (see parameter FITTWO) concentric Gaussians added together. The first Gaussian
has a fixed amplitude of 1.0. Each candidate beam is normalised to a total data sum of
unity before being used. The following parameters are varied during the minimisation
process:
-
The FWHM of the first Gaussian.
-
The FWHM and amplitude of the second Gaussian (if used).
-
The centre position of the beam within the supplied image.
-
The peak value in the source.
-
The background level (but only if parameter FITBACK is TRUE).
Note, if the two components have the same FWHM, they become degenerate (i.e. indistinguishable),
which causes problems for the minimisation process. To avoid this, the cost function that is minimised
(i.e. the sum of the squared residuals between the smoothed source model and the supplied map) is
multiplied by a factor that increases the cost as the FWHM for the two beams becomes more
similar. Consequently the second component will always have a larger FWHM than the first
beam.
In addition, if parameter FITBACK is TRUE and the FWHM of the second component is similar in
size to (or larger than) the data array, it becomes difficult for the minimisation process to
distinguish between the second component and a constant background level, again making
minimisation difficult. For this reason very wide second components are discouraged by
increasing the cost if the second component FWHM is similar to (or larger than) the size of the
array.
In addition large amplitude second components are discouraged by increasing the cost for large
amplitude second components.
AMP2 = _DOUBLE (Write)
An output parameter
holding the amplitude of the second fitted Gaussian relative to the first. For instance, if AMP2 is 0.15 it
means that the amplitude of the second component is 15% of the amplitude of the first component.
BACK = _DOUBLE (Write)
An output parameter holding the fitted background level. This will be set
to zero if FITBACK is FALSE.
CENTRE = LITERAL (Write)
An output parameter holding the fitted
position of the beam centre, in the celestial co-ordinate frame of the NDF (which may or may not be
the current co-ordinate system). The string consists of a space separated list of two formatted
axis values.
FITBACK = _LOGICAL (Read)
If FALSE, the background level is fixed at
zero throughout the minimisation. If TRUE, the background level is included as one of the
free parameters in the fit. [TRUE]
FITTWO = _LOGICAL (Read)
If TRUE, the beam
consists of two Gaussians. Otherwise only one Gaussian is used. [TRUE]
FWHM1 =
_DOUBLE (Write)
An output parameter holding the FWHM of the first fitted Gaussian
in arc-sec.
FWHM2 = _DOUBLE (Write)
An output parameter holding the FWHM of
the second fitted Gaussian in arc-sec.
IN = NDF (Read)
Input image containing the
source to be fitted. Note, if parameter FITBACK is FALSE, the source should be on a zero
background. The WCS information must contain a pair of celestial axes, but they need not
be the current coordinate system.
INITCENTRE = LITERAL (Read)
An initial guess
at the position of the beam centre, in the celestial co-ordinate frame of the NDF (which
may or may not be the current co-ordinate system). A space or comma separated list of
formatted axis values should be supplied.
LOGFILE = LITERAL (Read)
Name of a log file in
which to store a table holding the beam parameters and cost function at each iteration
of the minimisation. This table is in TOPCAT " ascii" format. [!]
OUT = NDF (Write)
Output NDF containing the fitted model. This is the source model convolved with the final
beam.
RADIUS = _DOUBLE (Read)
The radius of the sharp-edge circular source, in
arc-seconds. Must be no smaller than 1.0 arcsec.
RMS = _DOUBLE (Write)
An output
parameter holding the RMS residual between the fitted model and the supplied image.