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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 the program IMPOL to make the position angle images and position angle error images.

*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.
*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.
*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 above. See also options=guess where it is used slightly differently. Default is 0
*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.
*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.
*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
*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.
*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.
*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.
*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.

*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
*csize*- PGPLOT character height. Default is 1.0
*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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Time: 18:35:38 GMT, July 05, 2011