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# Basic Information on imrm

```
Purpose: Compute rotation measure image from position angle images
Categories: image analysis

IMRM computes rotation measure and zero wavelength position
angle images from at least 2 position angle images at different
frequencies.  This is done via a linear least squares fit to:

PA = PA_0 + RM*LAMBDA**2

where RM is the rotation measure (rad/m**2) and PA_0 is the
position angle at zero wavelength.  The output rotation measure
image is in rad/m**2, and the output position angle image is in
degrees.  Optionally, plots of the fits can be made.

The more frequencies you have the better.  It is very important
to try and get at least two sufficiently close that there is no
ambiguity between them.

By default, IMRM attempts to remove N*pi ambiguities from the
data.  Its algorithm is (pixel by pixel)

0) First remove angle according to the amount given by the
user (keyword "rmi") and the equation PA = RM*LAMBDA**2

1) Put the position angles of the first two frequencies in the
range +/- 90 degrees.

2) Remove 180 degree ambiguity from the position angles given
by the FIRST TWO IMAGES (keyword in).  Thus, it modifies
the position angle of the second frequency by 180 degrees
so that the absolute value of the angle between the two
position angles is less than 90 degrees.

3) Compute the initial RM and PA_0 from these FIRST TWO
position angles.

4) This RM and PA_0 is used to predict the expected position
angle at the other frequencies according to the expression
PA = PA_0 + RM*LAMBDA**2.  Integer amounts of 180 degrees
are then added or subtracted to the position angles at the
remaining frequencies in order to make the position angle
as close as possible to the expected value.

5) Then a least squares fit is used to solve for the RM and
PA_0

6) Finally, the procedure is repeated from step 0) where the
initial guess is now the value just determined above in
step 5).

The order in which the images are given is thus very important.
You should generally give your images in order of decreasing
frequency, with the assumption being that the smallest angle
between the first two represents a rough guess for the RM
with no ambiguities.  However, if you are very certain abou
the lack of ambiguity between certain frequencies, or there
are some of particularly high S/N and likely lack of ambiguity,
you may like to try these.  Its a nasty business and it is VERY
important that you look at the results carefully.

The attempt to remove ambiguities can be turned off with keyword
"options=ambiguous".  In this case, its algorithm is

0) First remove angle according to the intial guess given by
the user (keyword "rmi").

1) Put all position angles in the range +/- 90 degrees.

2) Then a least squares fit is used to solve for the RM and
PA_0.

In principle, you should never need to use this option.  If
there are no ambiguities, the first algorithm shouldn't find
any!

There are also a variety of methods offered with which to
blank the output images.  Most of these require error images
associated with the input position angle images.  Use IMPOL to
make the position angle images and position angle error images.

Key: in
Up to 5 input position angle (positive N -> E) images (in
degrees) at different frequencies.  Generally, you should give
the images in order of decreasing frequency.  Wild card
expansion is supported, no default.

Key: inerr
Up to 5 position angle error images (in degrees) used for
weighting the data during the least squares fit.  They are
assumed to be in one-to-one association with the position angle
images.  If no error images are given, each position angle image
is given equal weight and we must assume a goodness of fit of
unity in order to find the output image errors.  Wild card
expansion is supported, default is no error images.

Key: rmi
An amount of rotation measure to remove from the data before
fitting.  If you have a good idea of this, it helps enormously
in removing ambiguities.  See the detailed use in the discussion
slightly differently.  Default is 0.

Key: rm
Two values. The output fitted rotation measure image in
rad/m**2, and optionally, its associated error image.
The default is no output RM images.

Key: pa0
The output fitted (at zero wavelength) position angle image in
degrees, and optionally, its associated error image.
The default is no output PA images.

Key: qcut
Blank the output image (RM or PA) pixels if the goodness of fit
(Q) is less than this value.  If Q is larger than about 0.1 say,
the fit is believable.  If it is greater than 0.001, the fit may
be acceptable if the errors are non-normal or too small.  If Q
is less than 0.001 the model can be called into question.  The
probability distribution for position angle images approximates
a Gaussian at high S/N ratios.  At low S/N ratios (roughly, when
P/sigma < 2) it is non-Gaussian.  If you don't specify error
images, Q cannot be determined and is assumed to be one.  This
is also true if you give IMRM position angle images at two
frequencies only.  Default is 0.001

Key: errcut
Blank the output image (RM or PA) pixels if ANY of the input PA
image pixels has an error greater than this value (degrees).
Default is no input error based blanking.

Key: rmcut
Blank pixels in BOTH the output RM and PA_0 images when the
error in the fitted RM is greater than this value (rad/m**2).
Errors can be worked out if you give input error images, or if
you input images at more than two frequencies AND we assume the
goodness of fit is unity.  Default is no fitted RM error based
blanking.

Key: pacut
Blank pixels in BOTH the output RM and PA_0 images when the
error in the fitted PA_0 is greater than this value (degrees).
Errors can be worked out if you give input error images, or if
you input images at more than two frequencies AND we assume the
goodness of fit is unity.  Default is no fitted PA_0 error based
blanking.

Key: device
PGPLOT plotting device to see the fits to the data.  The
absolute pixel numbers in x and y are also written into the
corner of the plot (unless options=accumulate).  No default.

Key: nxy
Number of subplots per page in the x and y directions, to put on
the plotting device.  See options=accumulate.  The default is
2,2 (i.e. 2x2).

Key: csize
PGPLOT character height.  Default is 1.0.

Key: options
Task enrichment options.  Minimum match is active,
"relax"      issue warnings instead of a fatal error when image
axis descriptors are inconsistent with each other,
and when the input image headers do not indicate
that they are position angle images
(btype=position_angle).
"guess"      when removing ambiguities, this option causes IMRM
to use the rotation measure input through the
keyword "rmi" in step 3 above (on the first pass
only), rather than working it out from the first
two frequencies.  By default, angle is removed from
the data according to the value of "rmi" and then
the first guess made from the first two
frequencies.  The angle is not removed in this way
with this option.  This may prove useful if you
have two close but perhaps noisy frequencies which
is causing the initial guess of the RM to be wrong
(because of noise) and driving the subsequent turn
removal off.
"ambiguous"  Do not try to remove ambiguites.
"accumulate" means put all the plots on one sub-plot, rather
than the default, which is to put the plot for each
spatial pixel on a spearate subplot.
"yindependent"
By default, the sub-plots are all drawn with the
same Y-axis scale, that embraces all sub-plots.
This option forces each sub-plot to be scaled
independently.

Revision: 1.11, 2021/06/02 04:45:09 UTC
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Generated by miriad@atnf.csiro.au on 02 Jun 2021