INNAME First image name Qpol INCLASS First image class INSEQ 0.0 9999.0 First image seq. # INDISK 1.0 9.0 First image disk drive # IN2NAME Second image name Upol IN2CLASS Second image class IN2SEQ 0.0 9999.0 Second image seq. # IN2DISK 1.0 9.0 Second image disk drive # OUTNAME First output image name OUTSEQ -1.0 9999.0 First output image seq. # OUTDISK 0.0 9.0 First output image disk # INFILE Input file of weights DOALIGN -2.0 1.0 Should images be coincident? (See HELP.) BLC 0.0 4096.0 Bottom left corner TRC 0.0 4096.0 Top right corner APARM Parameters for algorithm: 1 number of pixels at half of the Fourier transform output The whole number is 2*APARM(1)+1 2 cell size in 1/m^2 0 => PI/(4*(Lmax^2-Lmin^2)) Lmax,Lmin-max,min lambda at the data 3 0 => regular output 1 => output is RMTF 4 0=> CLEANed Fourier transform 1=> unCLEANed Fourier transform 5 0=>original(shifted back) RE/IM are sent out 1=>the shifted RE/IM are sent out 2=>amplitude and phase of the data are sent out 6 is not used 7 0=> convolve the clean components 1=> no convolve 8 0=> use the Gaussian as the convolve function 1=> use the Re of RMTF as the convolve function 9 full width of Gaussian convolve function, at 0.5 level, in 1/m^2 0 => 1 10 what send to output? 0 => sum of CLEAN and residual 1 => CLEAN result 2 => residual GAIN Gain in the CLEAN NITER Maximum number of clean components FLUX Minimum flux of clean component (Jy) DOHIST -3.0 1.0 -2 => copy 1st HI only -3 => copy no HI files

FARS Type: Procedure DOFARS is a procedure which reads in Q and U polarization cubes oriented with axes in the order RA, DEC, FREQID or FREQUENCY plus any more. The procedure optionally runs RSPEC to make a list of weights to be used for each channel. Then the procedure runs TRANS to re-order the axes so that FREQID/FREQUENCY is first as is required by the FARS task. It then runs FARS itself. Then it deletes the temporary transposed images which were the inputs to FARS. Finally, it transposes the two outputs of FARS into cubes in the normal axis order (RA, Dec, frequency). Note that, if you are going to run FARS multiple times, varying the input parameters, it would be more efficient to do the RSPEC and TRANS steps "by hand" once rather than re-running them each time with this procedure. *************************************************************** The help file for FARS follows: BUT note the changed meanings for INFILE, BLC, TRC *************************************************************** The measured brightness of images at a set of lambda^2 is related to the brightness distribution as a function of Faraday rotation depth through the Fourier transform. To solve the inverse problem: "Evaluation of the brightness distribution as a function of Faraday rotation depth using the measured brightness in the given set of lambda^2" has been called "Faraday Rotation Synthesis". The task FARS performs this operation. FARS now writes 4 slice files in each output image. They reresent the real part, imaginary part, amplitude, and phase of the RMTF or dirty beam of the synthesis. TVSLICE and other slice functions may be used to examine these parts of the beam. The units displayed are based on the image and so they do not really apply. The phase slice is in degrees and the others really in normalized beam units. Adverbs: INNAME......First image name. Q-polarization. Standard defaults. INCLASS.....First image class. Standard defaults. INSEQ.......First image seq. #. 0 => highest. INDISK......Disk drive # for the first image. 0 => not allowed IN2NAME.....Second image name. U-polarization. Standard defaults. IN2CLASS....Second image class. Standard defaults. IN2SEQ......Second image seq. #. 0 => highest. IN2DISK.....Disk drive # for the second image. 0 => not allowed OUTNAME.....Output image name. Real part. Standard defaults. Output image class for first image 'FARSre' or 'FARSam' Output image class for second image 'FARSim' or 'FARSph' OUTSEQ......Output image seq. #. 0 => highest unique. OUTDISK.....Output disk number. 0 => highest with space. INFILE......User-supplied text file defining weights for ALL spectral channels INCLUDING those < BLC(3). The sequence of the weights must correspond to the sequence of frequencies in the input cubes. The weights are read with a free format and more than one may occur on each line of the input text file. The weights are read as floating-point values and any value >= 0 is acceptable. *** In DOFARS (not FARS), INFILE = ' ' requests DOFARS to *** run RSPEC to find the desired weights (using the Q image *** cube). Also in DOFARS, INFILE = '1' means to use no *** INFILE in FARS and weight all frequencies equally. In *** DOFARS, any other value of INFILE is passed directly to *** FARS. DOALIGN.....Controls how the two input images are to be aligned True (>.1) means that the images must agree in their coordinates, though not necessarily in the reference pixel position. Alignment is by coordinate values (if DOALIGN > -0.1) or by offsets from the reference pixel positions (if DOALIGN <= -0.1). NOTE: all real axes (>1 point) are aligned. If DOALIGN = -2, the headers are ignored and the images are aligned at pixel (1,1,...). (see HELP DOALIGN). BLC.........Bottom left corner of the 1st input image. The other images really should be aligned before hand. BLC(1,2,4,5,6,7) and TRC(1,2,4,5,6,7) are applied in the TRANS step. BLC(3) and TRC(3) are applied in the FARS step (hence the comments about INFILE above). *** In DOFARS, the third axis must be the one with multiple *** frequencies (FQID or FREQ). The output data for the first axis is controlled by APARM(1,2,4) TRC.........Top right corner of input images. (See BLC.) APARM.......Parameters needed for algorithm: APARM(1) number of pixels for half of the Fourier transform output. The total number is 2*APARM(1)+1 with coordinate zero at the center. The value of APARM(1) should be chosen in accordance the expected range of Faraday rotation measure and value of CELL (APARM(2)) APARM(2) cell size of the outputs, in 1/m^2 The cell is recomended to be less or around the default value (pi)/4/(lambda^2max - lambda^2min) APARM(3) 0 => regular outputs 1 => outputs are RMTF ("1-D dirty beam") Note that the RMTF is now written as slice files so this option is normally not needed. APARM(4) 0=> CLEANed Fourier transform, using inputs: NITER, FLUX, GAIN. The CLEAN uses the shifed (at lambda^2) data but the cleaned components correspond to the original lambda^2 1=> the uncleaned Fourier transform is recorded RE/amp is recorded to the first output IM/phase is recorded to the second output APARM(5) 0=>original data (RE and IM) are used in the Fourier transform 1=> the shifted (to the center) data (RE, IM) are used in the Fourier transform. This option allows better discrimination of different features in the Fourier transform. 2=> amplitude and phase of the data are sent out. APARM(6) is not used APARM(7) 0=> convolve the clean components 1 => no convolution; so just the set of the clean components is sent to the output files No convolution is forced if uncleaned Fourier data are sent out (APARM(4)=1) APARM(8) 0=> use the Gaussian as the convolution function 1=> use the Re of RMTF as the convolution function APARM(9) full width at half maximumof the Gaussian convolution function, in 1/m^2 0 -> fit the real part of the RMTF. APARM(10) What send to the output? 0 => sum of CLEAN and residual 1 => CLEAN result 2 => residual GAIN........Gain in the CLEAN NITER.......Maximum number of clean components 0 => 1 FLUX........Minimum Clean component (Jy) The task can subtract the given number of complex components. On each iteration, the maximum (and its position) of the spectrum amplitude is determined. The complex function RMTF is multiplied by the complex value of the spectrum at the position of the found amplitude maximum and by GAIN. The found function(production) is put by its median on the position of found amplitude maximum, and is subtracted from the having evaluated spectrum. The process of the subtraction is terminated having achieved number of iterations NITER or the flux FLUX. DOHIST......Normally the HI file of input 1 is copied to the output history file and the HI file of the second input is appended. If you are doing many FARSs this can lead to immense history files of little use to anyone. Thus, DOHIST=-2 => copy the first HI file only. DOHIST=-3 => copy no HI file, write FARS HI only.

FARS: Task to solve Faraday Rotation Synthesys problem DOCUMENTOR: L. Kogan RELATED PROGRAMS: The main ideas of the algorithm are described by B.J. Burn at: MNRAS, 133, 67, 1966 and M.A.Brentjens and A.G.de Bruyn at: Astronomy & Astrophysics, 441, 1217-1228(2005) FARS reads the two input cube images which should have identical structure. The first axis of the cubes must be FREQ or FQID. If not, the task 'TRANS' should be used to achieve this order. The first cube should correspond to the Q-linear polarization component. The second cube should correspond to the U-linear polarization component. The purpose of the task is to get the brightness distribution (for each pixel in the RA-DEC plane) corresponding to the given Fraday rotation depth. Multi-frequency observations are required to achieve this. The task forms complex function of wavelength squared (the first input image is the real part, the second input is the imaginary part). For each pixel of the RA-DEC plane, FARS carries out the Fourier transform along the wavelength squared axis. This Fourier transform converts the observed complex brightness as a function of the lambda^2 to the output complex function of the Faraday rotation depth. The Fourier transform can be directed to the outputs directly or it can be deconvolved with a complex Clean algorithm. The real part or amplitude of the output is recorded into the first output file and the imaginary part or phase of this output is recorded in the second output file. The input data are determined from the positive set of lambda^2. The output of the Fourier transform (complex function) is the convolution of the actual brightness (as a function of the Faraday depth) and the so called Rotation Measure Transfer Function (RMTF). The RMTF is a one dimensional Fourier transform of the lambda^2 sampling function and is recorded in slice files attached to the output images. The RMTF is similar to the dirty beam in aperture synthesis. The dirty beam is real function because the brightness distribution is a real function. RMTF is a complex function, but it's imaginary part can be zeroed at the vicinity of zero Faraday depth if we shift the origin of the lambda^2 set to the median. The more homogeneous the distribution of the lambda^2 the wider the area where the imaginary part of RMTF is near zero. FARS carries out all calculation with the centered data, and then rotates the outputs by the phase corresponded to the central lambda^2. The output (RE, IM) can be shifted back to the original lambda^2 distribution or not (or amplitude and phase can be sent to the output) under control of APARM(5). It is supposed the images for each of the frequencies are available The example of the typical image header is following: AIPS 1: ---------------------------------------------------------------- AIPS 1: Type Pixels Coord value at Pixel Coord incr Rotat AIPS 1: RA---SIN 2048 12 28 16.418 1024.00 -0.100000 0.00 AIPS 1: DEC--SIN 1024 12 39 58.294 513.00 0.100000 0.00 AIPS 1: FREQ 1 8.0851000E+09 1.00 5.0000000E+07 0.00 AIPS 1: STOKES 1 2.0000000E+00 1.00 1.0000000E+00 0.00 The images for different frequencies should be combined in the cube using the AIPS task MCUBE. The recommended inputs for MCUBE are following: AIPS 1: MCUBE: Task to collect a set of n-dim maps into a (n+1)-dim map AIPS 1: Adverbs Values Comments AIPS 1: ---------------------------------------------------------------- AIPS 1: INNAME 'M87X' Input name(name). AIPS 1: INCLASS 'Q-COS' Input name(class). AIPS 1: INSEQ 1 Input name(seq. #). 0=>high AIPS 1: First sequence # in the set AIPS 1: INDISK 3 Input disk drive #. 0=>any AIPS 1: IN2SEQ 4 Last sequence # in set. AIPS 1: IN3SEQ 1 Sequence # increment. AIPS 1: OUTNAME 'M87XCUBE' Output name(name). AIPS 1: OUTCLASS 'Q-COS' Output name(class). AIPS 1: OUTSEQ 0 Output name(seq. #). AIPS 1: 0 => highest unique AIPS 1: OUTDISK 3 Output image disk drive # AIPS 1: 0 => highest with space AIPS 1: DOALIGN 0 Alignment control parm AIPS 1: AXREF 1 n+1 axis pixel of map INSEQ. AIPS 1: 0 => 1 AIPS 1: AX2REF 0 n+1 axis pixel of map IN2SEQ AIPS 1: 0 => opposite end from INSEQ AIPS 1: NPOINTS 4 Number of pixels on axis n+1 AIPS 1: DOCONCAT 2 > 1 => make a SEQ.NUM or AIPS 1: NPOINTS is the number of combined images, which should be prepared under the same NAME and CLASS but with different INSEQ=1,2,3,4 Use task FQUBE is the images are not distributed linearly in frequency. This task adds an FQ table to the output image listing the actual frequency of each plane in its cube. The output cube image should have the following axes in the image header: AIPS 1: ---------------------------------------------------------------- AIPS 1: Type Pixels Coord value at Pixel Coord incr Rotat AIPS 1: RA---SIN 2048 12 28 16.418 1024.00 -0.100000 0.00 AIPS 1: DEC--SIN 1024 12 39 58.294 513.00 0.100000 0.00 AIPS 1: FQID 4 1.0000000E+00 1.00 1.0000000E+00 0.00 AIPS 1: STOKES 1 2.0000000E+00 1.00 1.0000000E+00 0.00 AIPS 1: FREQ 1 8.0851000E+09 1.00 5.0000000E+07 0.00 AIPS 1: ---------------------------------------------------------------- The axis 'FQID' reports the number of frequencies at the cube. The axis 'FREQ' reports the reference frequency. The actual frequencies are the sum of the reference frequency and the offsets given in the FQ table created by MCUBE or FQUBE. FARS requires another order of the axes. So the AIPS task TRANS should be applied to get it. An example of TRANS inputs is: AIPS 1: TRANS: Task to transpose a subimage of an up to 7-dim. image AIPS 1: Adverbs Values Comments AIPS 1: ---------------------------------------------------------------- AIPS 1: INNAME 'M87XCUBE' Input name(name). AIPS 1: INCLASS 'Q-COS' Input name(class). AIPS 1: INSEQ 1 Input name(seq. #). 0=>high AIPS 1: INDISK 3 Input disk drive #. 0=>any AIPS 1: OUTNAME 'M87XTRANS' Output name(name). AIPS 1: OUTCLASS 'Q-COS' Output name(class). AIPS 1: OUTSEQ 0 Output name(seq. #). AIPS 1: 0 => highest unique AIPS 1: OUTDISK 3 Output image disk drive # AIPS 1: 0 => highest with room AIPS 1: BLC *all 0 Bottom left corner of image AIPS 1: 0 => entire image AIPS 1: TRC *all 0 Top right corner of image AIPS 1: 0 => entire image AIPS 1: TRANSCOD '31245' New axis order in terms of AIPS 1: input axis numbers AIPS 1: BADDISK *all 0 Disks to avoid for scratch So the final image cube should have the following axes in the image header: AIPS 1: ---------------------------------------------------------------- AIPS 1: Type Pixels Coord value at Pixel Coord incr Rotat AIPS 1: FQID 4 1.0000000E+00 1.00 1.0000000E+00 0.00 AIPS 1: RA---SIN 2048 12 28 16.418 1024.00 -0.100000 0.00 AIPS 1: DEC--SIN 1024 12 39 58.294 513.00 0.100000 0.00 AIPS 1: STOKES 1 2.0000000E+00 1.00 1.0000000E+00 0.00 AIPS 1: FREQ 1 8.0851000E+09 1.00 5.0000000E+07 0.00 AIPS 1: ---------------------------------------------------------------- The same set of steps should be carried out to get the second linear polarization input image for FARS.