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.
"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.