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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

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 the program 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 of the algorithm
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 10x10

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.
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# User Guide References to imrm

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Generated by smamiriad@cfa.harvard.edu on 09 Jul 2012