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##### imagepol.rotationmeasure - Function

1.1.4 Find Rotation Measure (traditional approach)

Description

This function generates the rotation measure image from a collection of different frequencies. It will only work if the Imagepol tool is attached to an image containing Stokes Q and U, and a frequency axis (regular or irregular) with at least 2 pixels. It will work out the position angle images for you.

Rotation Measure algorithms that work robustly are not common. The main problem is in trying to account for the n - π ambiguity (see Leahy et al, Astronomy & Astrophysics, 156, 234 or Killeen et al; http://www.atnf.csiro.au/\$\sim\$nkilleen/rm.ps).

The algorithm that this function uses is that of Leahy et al. (see Appendix A.1). But as in all these algorithms, the basic process is that for each spatial pixel, a vector of position angles (i.e. at the different frequencies) is fit to determine the rotation measure and the position angle at zero wavelength (and their errors). An image containing the number of n - π turns that were added to the data at each spatial pixel and for which the best fit was found can be written. The reduced chi-squared image for the fits can also be written.

Note that no assessment of curvature (i.e. deviation from the simple linear position angle - λ2 functional form) is made.

Any combination of output images can be written.

The argument sigma gives the thermal noise in Stokes Q and U. By default it is determined automatically using the image data. But if it proves to be inaccurate (maybe not many signal-free pixels), it may be specified. This is used for calculating the error in the position angles (propagation of Gaussian errors).

The argument maxpaerr specifies the maximum allowable error in the position angle that is acceptable. The default is an infinite value. From the standard propagation of errors, the error in the linearly polarized position angle is determined from the Stokes Q and U images (at each spatial pixel for each frequency). At each spatial pixel we do a fit to the position angle vector (i.e. at the different frequencies) to determine the rotation measure. If the position angle error for any pixel in the vector exceeds the specified value, it is dropped from the fit. The process generates an error for the fit and this is used to compute the errors in the output images.

Note that maxpaerr is not used to specify that any pixel for which the output position angle error exceeds this value should be masked out.

The argument rmfg is used to specify a foreground RM value. For example, you may know the mean RM in some direction out of the Galaxy, then including this can aid the algorithm by reducing ambiguity.

The argument rmmax specifies the maximum absolute RM that should be solved for. This quite an important parameter. If you leave it at the default, zero, no ambiguity handling will be used. So some apriori information should be supplied; this is the basic problem with rotation measure algorithms.

Arguments

 Inputs rm Output Rotation Measure image file name. Default is unset. allowed: string Default: rmerr Output Rotation Measure error image file name. Default is unset. allowed: string Default: pa0 Output position angle (degrees) at zero wavelength image file name. Default is unset. allowed: string Default: pa0err Output position angle (degrees) at zero wavelength error image file name. Default is unset. allowed: string Default: nturns Output number of turns image file name. Default is unset. allowed: string Default: chisq Output reduced chi squared image file name. Default is unset. allowed: string Default: sigma Estimate of the thermal noise. Default is auto estimate. allowed: double Default: -1 rmfg Foreground Rotation Measure (rad/m/m) to subtract. allowed: double Default: 0.0 rmmax Maximum rotation measure (rad/m/m) to solve for. IMPORTANT TO SPECIFY. allowed: double Default: 0.0 maxpaerr Maximum input position angle error (degrees) to allow allowed: double Default: 1e30 plotter Name of plotter. Default is none. allowed: string Default: nx Number of plots in x direction allowed: int Default: 5 ny Number of plots in y direction allowed: int Default: 5
Returns
bool

Example

"""
#
print "\t----\t rotationmeasure Ex 1 \t----"
#im = ia.imageconcat(outfile=’stokes.image’,
#                    infiles="im.f1 im.f2 im.f3 im.f4 im.f5", axis=4)
po.open(’stokes.image’)
ok = po.rotationmeasure(rm=’rm’, rmerr=’rmerr’, rmmax=800, maxpaerr=10)
#
"""

Say we have 5 images, each with axes RA, DEC, Stokes, and Frequency in
that order.  We use the Image \tool\ to concatenate these images
along the frequency axis - you have ordered them in increasing or
decreasing frequency order.  We then compute the Rotation Measure
and Rotation Measure error images with the traditional method and
write them out to disk.

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