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# Basic Information on moment

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Purpose: Calculate moments of a Miriad image.
Categories: image analysis

MOMENT calculates the nth moment of a Miriad image.  The
spectral axis, which is determined automatically, must be on
axis 1, 2, or 3.  Moments may be computed for other axis types
by specifying the axis number, though the brightness units
recorded in the output image header will likely not be correct.
They can be fixed using PUTHD.

Key: in
The input image.  No default.

Key: region
Region of the input image to be used, only the bounding box is
supported.  See documentation for region on how to specify this.

Key: out
The output image.  No default.

Key: mom
-3: Velocity at peak intensity using a three-point quadratic fit
around the peak (km/s).
-2: Peak intensity using a three-point quadratic fit (units same
as individual channels).
-1: Average intensity (units same as individual channels).
0: 0th moment = sum(I) (integrated intensity, I x km/s).
1: 1st moment = sum(I*v)/sum(I), (velocity centroid, km/s),
where v is the velocity.
2: 2nd moment = sqrt(sum(I*(v-M1)**2)/sum(I)), (velocity
dispersion, km/s), where M1 is the first
moment.  If the line profile is Gaussian,
this produces a map of Gaussian sigma, and
FWHM = 2*sqrt(2*ln(2))*sigma = 2.355*sigma.

The moments are calculated independently for each pixel
using spectral channels with intensity satisfying the
specified clip range.

For frequency axes the radio velocity is computed from the
line rest frequency recorded in the header.  For velocity
axes the axis scale is used directly.

Key: axis
Axis for which the moment is calculated.  Moments may be
computed for non-spectral axes though brightness units recorded
in the output image header will usually be incorrect.  Defaults
to the spectral axis determined from the input image header.

Key: clip
Two values.  For mom >= -1, exclude spectral channels with
intensity in the range clip(1) to clip(2) inclusive.  If only
one value is given, then exclude -abs(clip) to +abs(clip).
Default = 0 which excludes nothing.

Key: span
For mom >= -1, exclude channels further than the specified
number of channels from the peak, hence using a total of
2*span + 1 channels to compute the moment.  If the peak is too
close to the first or last channel to allow the full span, then
the pixel will be blanked in the output map.  Please bear this
in mind when specifying the channel range (via 'region').
Default = 0 which means no restriction.

Key: rngmsk
For mom > 0, mask pixels in the output map when the 1st moment
lies outside the range of the spectral axis.  This can happen
because sum(I) can be arbitrarily small in emission-free
channels but with sum(I*v) non-vanishing.  Default: false.