AIPS HELP file for FTARS in 31DEC22
As of Wed Jan 19 12:37:14 2022
FTARS: Fits polarization spectrum to Q/U text file
Q/U spectrum input to TARS
RM spectrum output by TARS
NITER 0.0 4000.0 Max # fit iterations
0 -> 100.
NGAUSS 1.0 4.0 Max number components
DOSPIX -1.0 4.0 1 => fit spectral index
2,3,4 => fit thickness
else keep both at zero
RMSLIMIT RMS level above which a
solution is "bad"
Task: Fits a single polarization spectrum for one or more components
of total polarization, polarization angle at 0 wavelength, and
rotation measure. FTARS will be used on the Q and U text file
spectrum input to TARS and the rotation measure spectrum output
The task fits up to 4 polarization components the spectrum. It
is based on task RMFIT, but does only a single spectrum rather
than whole data cubes. Just as TARS is used to test isolated
real or model cases for FARS, FTARS is used to carry the test
through the RM fitting stage.
Color differentiates what is plotted. Graphics channel 1
(usually yellow) is used for axis labels and the data. The
FARS output is plotted in amplitude/phase initially. The
initial guess is shown as a large X in graphics channel 2
(usually green). This screen may be used to reset the initial
guess. Then the Q and U data are plotted. Since the Q and U
data may be on a FQID axis and so may not actually be in
frequency order, the Q and U data are plotted as small X's.
The initial guess is shown as a smooth curve in graphics
channel 2 (usually green). The fit is then shown as somewhat
large X's in graphics channel 4 (usually cyan).
Details of the interactive operation and options are described
in the EXPLAIN file. See also AIPS Memo 118, "Modeling
spectral cubes in AIPS", May 2020 for a more detailed
description of the use of RMFIT.
The model fit is:
Q(i) = SUM_j [ P_j cos ( 2 theta_j + 2 RM_j lambda(i)^2)
F (beta_j, lambda(i)^2) ]
U(i) = SUM_j [ P_j sin ( 2 theta_j + 2 RM_j lambda(i)^2)
F (beta_j, lambda(i)^2) ]
where P_j is the polarized flux at 1 GHz, theta_j is the
intrinsic polarization angle, and RM_j is the rotation measure
in radians/m/m. F(beta_j, lambda(i)^2) is an amplitude
function that solves for a spectral index or one of several
possible thickness parameters. The spectral index function
(lambda_1^2 / lambda(i)^2)^(beta_j/2)
while the thickness functions are ('SLAB' in MODIM) and ('GAUS'
in MODIM) and ('EXP ' in MODIM)
sin (beta_j lambda(i)^2) / (beta_j lambda(i)^2)
exp (-ln(2) * (beta_j lambda(i)^2 / 1.8954)^2)
exp (-ln(2) * beta_j lambda(i)^2 / 1.8954)
where lambda_1 is the wavelength at 1 GHz and beta_j is the
spectral index or the thickness parameter, the latter in
rad/m/m. Set DOSPIX(j) to 1 for spectral index or 2,3,4 for
SLAB, GAUS, or EXP. respectively, or set it to 0 to omit
fitting a thickness to component j. The 1.8954 was chosen to
make all functions have the same half-power point. Output
images are written of the P_j, theta_j, RM_j, beta_j, Q0_j, and
U0_j and their uncertainties, where
Q0_j = P_j cos ( 2 theta_j )
U0_j = P_j sin ( 2 theta_j )
are Q and U at 1 GHz with no rotation measure. The beta_j
images are only written when they have been fit.
INFILE.....The input file to TARS with three columns: frequency in Hz,
then Q in Jy/beam, then U in Jy/beam. A semi-colon in
column 1 means the line is a comment.
OUTFILE....The output file from TARS containing the rotation measure
spectrum. The 3 columns are RM, Real part, Imaginary part
or RM, amplitude, phase. A semi-colon in column 1 means
the line is a comment. NOTE: TARS can write many RM
spectra to a single file. Only the first of these is used
NITER......Maximum function evaluations during the fit of each row.
(< 10 -> 100 for NGAUSS > 1, < 100 -> 150 for 1
NGAUSS.....Number of Components to fit (between 1 and 4).
DOSPIX.....If 0.5 < DOSPIX < 1.5, solve for spectral index in the
corresponding component, otherwise take the spectral
index to be zero.
If 1.5 < DOSPIX < 2.5, solve for the thickness parameter
in the corresponding component with sin(x)/x form, or,
if 2.5 < DOSPIX < 3.5, solve for the thickness parameter
in the corresponding component with Gaussian form, or,
if 3.5 < DOSPIX < 4.5, solve for the thickness parameter
in the corresponding component with Exponential form.
Otherwise take the thickness parameter to be zero.
NOTE: all values of DOSPIX must be either 0 or indicate
the same functional form.
RMSLIMIT...If the RMS exceeds this, the solution is reported as
"bad". 0 -> 1000.0
FTARS: One-dimensional polarization fitting of image cubes
Documenter: E. W. Greisen NRAO
Related Programs: IMFIT, JMFIT, SAD, SLFIT, ZEMAN, XGAUS
Initial guesses for the fit are found from the TARS output data.
When NGAUSS = 1 this can happen automatically from the row data.
For the spectrum, the first step in the fitting process is to
determine an initial guess non-interactively. the next steps are
1. The input FARS RM data are plotted on the TV as amplitude
and phase. The task initially skips step 2 and goes to step
3 for an interactive initial guess.
2. If either NGAUSS > 1 or a fitting has been forced, FTARS asks
in a TV menu for instructions. If your answer is RE-GUESS on
the TV, FTARS will ask you to enter a new initial guess
(step 3). If your answer is DO FIT, then DARS goes on to step
4. If the answer is QUIT, the task prints its best fit and
3. To enter a new initial guess, you will be prompted to position
the TV cursor at the rotation measure of each Component (note
that only the X position matters). To mark each point, hit any
button (A, B, C, or D). FTARS then returns to step 1 above to
plot the new guess and ask again.
4. Once an acceptable initial guess has been found, FTARS proceeds
to call a non-linear least squares fitting routine to determine
the polarization parameters that appear to fit the data best.
The answers are then checked to see if they are "reasonable" -
negative and very large components and components with rotation
measures outside the input data are unreasonable.
6. The final model is added to the plot. In the input terminal,
you are then told if the answers are "unreasonable" and are
shown the answers, reasonable or not. You are then offered a
variety of choices. If your selected option is
QUIT - FTARS exits cleanly
RE-GUESS - FTARS returns to step 1 to try again with the
current number of components (<= NGAUSS)
1, 2, 3, or 4 - FTARS returns to step 1 to try again with
the specified number of Components (note that
only numbers <= NGAUSS are respected)
HAND - FTARS prompts you to enter the polarization
parameters for each component (HAND on the TV).
You enter in the input terminal window, the
total polarization in input image units, the
polarization position angle at zero wavelength
in degrees (-90 to +90), the rotation measure in
radians per meter squared and, if appropriate,
the spectral index (unitless) or RM thickness
(radians per meter squared). All 3 or 4 numbers
must appear in one line. It will prompt for all
NGAUSS components, but will change the prompt if
the current number of Components is < NGAUSS.
If you enter something besides 0 in that case,
then the current number of Components is
increased appropriately. FTARS then returns to
the start of this step 6 to allow you to see if
you made a good guess.
DO FIT - After a HAND operation, a DO FIT option is
available. It loops back using the hand-entered
parameters as the initial guess to the fitting
PIXRANGE - FTARS prompts you for the Q and U display
ranges to re-display the data
Enter Qmin, Qmax, Umin, Umax in that order in
one line. If you enter only two values, then
Umin and Umax are taken to equal Qmin and Qmax.
If you enter no values, then the plot reverts to
self-scaling. The Q plot self-scales if Qmin >=
Qmax; the U plot self-scales if Umin >= Umax.
Note that on the re-plot, the smooth "initial
guess" line is now actually the result of the
SHOW P&A - FTARS will switch the display between Q plus U
SHOW Q&U and total polarization and polarization angle.
The plotted "initial guess" becomes the actual