As of Fri Jul 19 9:03:56 2024

PBCOR: Task to apply the primary beam correction


INNAME                             Input image name (name)
INCLASS                            Input image name (class)
INSEQ           0.0      9999.0    Input image name (seq. #)
INDISK          0.0         9.0    Input image disk drive #
BLC             0.0      4096.0    Bottom Left Corner
TRC             0.0      4096.0    Top Right Corner
OUTNAME                            Output image name (name)
OUTCLASS                           Output image name (class)
OUTSEQ         -1.0      9999.0    Output image name (seq. #)
OUTDISK         0.0         9.0    Output disk drive #
PBPARM                             Beam parameters:
                                   (1) Cutoff 0 -> 0.023
                                   (2) > 0 -> Use (3)-(7)
                                   (3)-(7) Beam shape
COORDINA                           RA and DEC in form:
                                      HH MM SS.SS, DD MM SS.S
                                   ** used if not all 0 **
DOINVERS        -1.0        1.0    > 0 => multiply image by beam
OPCODE                             'GAUS' -> use APARM(1)
                                   'POLY' -> use all of APARM
APARM                              (1) Gaussian FWHM arc min
                                       at header frequency
                                   (1)-(10) Polynomial coeffs


Type: Task
Use:  PBCOR will apply a primary beam correction (divide by the primary
      beam gain factor) to images.  It can also multiply an image by a
      primary beam pattern to, for example, compare an optical or
      single-dish image with an interferometer image.  (One multiplies
      the former by the beam of the latter rather than raising the
      appearance of noise in the latter by dividing by its beam.)  The
      image is required to have RA, DEC and FREQ axes in order to
      compute the correction.  However, they may be in any order and
      "cubes" are fully supported.
  INNAME......Input name of image(name).     Standard defaults.
  INCLASS.....Input name of image(class).    Standard defaults.
  INSEQ.......Input name of image(seq. #).   0 => highest.
  INDISK......Disk drive # of image.         0 => any.
  BLC.........The bottom left-hand pixel of the input image
              which becomes the bottom left corner of the
              corrected subimage.  The value (0,0) means (1,1).
  TRC.........The top right-hand pixel of the input image
              which becomes the top right corner of the correct-
              ed subimage.  The value (0,0) means take the top
              right hand corner of the image.
  OUTNAME.....Output name of image(name).   Standard defaults.
  OUTCLASS....Output name of image(class).  Standard defaults.
  OUTSEQ......Output name of image(seq. #). 0 => highest unique.
  OUTDISK.....Disk drive # of Output image. 0 => highest w room.
  PBPARM......Primary beam parameters:
              (1) Lowest beam value to believe: <= 0.001 -> 0.023
                  Image pixels outside this range are blanked.
              (2) > 0 => Use beam parameters from PBPARM(3)-PBPARM(7)
                  Otherwise use default parameters for the VLA (or
                  ATCA where appropriate)
              (3-7)..For all wavelengths, the beam is described by the
                   1.0 + X*PBPARM(3)/(10**3) + X*X*PBPARM(4)/(10**7) +
                   X*X*X*PBPARM(5)/(10**10) + X*X*X*X*PBPARM(6)/(10**13)
                where X is (distance from the pointing position in arc
                minutes times the frequency in GHz)**2.
                See explain for details
  COORDINA....The RA and DEC coordinates for the pointing position are
              found as:
              RA = abs(CO(1)) + abs(CO(2))/60 + abs(CO(3))/3600
                 if any of CO(1), CO(2), CO(3) < 0: Xpos = -Xpos
              DEC = abs(CO(4)) + abs(CO(5))/60 + abs(CO(6))/3600
                 if any of CO(4), CO(5), CO(6) < 0: Ypos = -Ypos
              RA is in hours, minutes, seconds of time
              DEC is in degrees, minutes, seconds of arc
              WARNING: if any of these 6 are not zero, then COORDINA
              defines the pointing direction for the image.  Otherwise
              the pointing position in the header (or if that is 0,
              the source coordinate in the header) is used.
  DOINVERS....> 0 Multiply the image by the beam pattern.
              <= 0 Divide the image by the beam pattern.
  OPCODE......'GAUS' => use APARM(1) as the FWHM in arc minutes at
                        the reference frequency of a Gaussian primary
              'POLY; => Use APARM(1) - APARM(10) as coefficients of a
                        polynomial in r, the radius in arcmin  *
              other => use PBPARM
  APARM.......If GAUS: APARM(1) is the full width at half maximum at the
                       header frequency in arc minutes.
              If POLY: F(r) = 1.0 + APARM(1)*r + APARM(2)*r*r +
                       APARM(3)*r*r*r + ...
                       where r is is the distance from the pointing
                       center in arc minutes times the frequency in GHz.


PBCOR: Task to apply the primary beam correction


     PBCOR corrects an image for the primary beam attenuation of
the ntennas.  The function used to model the primary beam for normal
VLA frequencies

            F(x) =  1.0
                   + parm(3) * 10E-3  * x
                   + parm(4) * 10E-7  * x*x
                   + parm(5) * 10E-10 * x*x*x
                   + parm(6) * 10E-13 * x*x*x*x
                   + parm(7) * 10E-16 * x*x*x*x*x

where x is proportional to the square of the distance from the
pointing position in units of [arcmin * freq (GHz)]**2, and F(x)
is the multiplicative factor to divide into the image intensity at the
distance parameter x.  For other antennas, the user may read
in appropraite constants in PBPARM(3) through PBPARM(7).  The
flag, PBPARM(2) must be set to a positive number to invoke this
option and PBPARM(3) must not be zero.
     This correction scales with frequency and has a cutoff
beyond which the map values are set to an undefined pixel value GIVEN
in PBPARM(1).  At the VLA frequencies the default cutoff is
                 1.485 GHz     29.8  arcmin
                 4.885 GHz      9.13 arcmin
                15     GHz      2.95 arcmin
                22.5   GHz      1.97 arcmin
and occurs at a primary beam sensitivity of 2.3 percent of the value at
the beam center.  Corrections factors < 1 are forced to be 1.
The estimated error of the algorithm is about 0.02 in (1/F(x))
and thus leads to very large errors for x>1500, or at areas
outside of the primary response of 20 percent.  The cutoff level
may be specified with DPARM(1).

Default values of PBPARM for the VLA are given by Perley's fits:
      0.0738 GHz  -0.897  2.71   -0.242
      0.3275      -0.935  3.23   -0.378
      1.465       -1.343  6.579  -1.186
      4.885       -1.372  6.940  -1.309
      8.435       -1.306  6.253  -1.100
     14.965       -1.305  6.155  -1.030
     22.485       -1.417  7.332  -1.352
     43.315       -1.321  6.185  -0.983
For the ATCA, these are by default:
      1.5 GHz     -1.049   4.238  -0.8473  0.09073  -5.004E-3
      2.35        -0.9942  3.932  -0.7772  0.08239  -4.429E-3
      5.5         -1.075   4.651  -1.035   0.12274  -6.125E-3
      8.6         -0.9778  3.875  -0.8068  0.09414  -5.841E-3
     20.5         -0.9579  3.228  -0.3807  0.0       0.0
For the Karl G Jansky VLA ("EVLA"), the defaults are frequency
dependent.  If the observing frequency is between two tabulated
frequencies, then the beam is computed for each of the tabulated
frequencies and then interpolated to the observing frequency.  The
values used are far too numerous to give here, see EVLA Memo 195,
"Jansky Very Large Array Primary Beam Characteristics" by Rick Perley,
revision dated June 2016.  Obtain it from

If OPCODE='POLY', then APARM gives the coefficients of a polynomial:

          F(r) = 1.0  +  APARM(1) * r  +  APARM(2) * r * r  +
                 APARM(3) * r * r * r  + ...

where r is is the distance from the pointing center in arc minutes times
the frequency in GHz.

                 RICK PERLEY'S (OLD) REPORT

	Polynomial Coefficients from LSQ Fit to VLA Primary
	Beam raster scans.

	Functional form fitted:

		1 + G1.X^2 + G2.X^4 + G3.X^6

	where X = r.F,

	and 	r = radius in arcminutes
		F = frequency in GHz.

	Fits were made to 3 percent cutoff in power for 24 antennas.
Poor fits, and discrepant fits were discarded, and the most
consistent subset of antennas had their fitted coefficients
averaged to produce the following 'best' coefficients.

Freq.		G1		G2		G3

1.285           -1.329E-3       6.445E-7        -1.146E-10  *
1.465           -1.343          6.579           -1.186 "
4.885           -1.372          6.940           -1.309
8.435           -1.306          6.253           -1.100
14.965          -1.305          6.155           -1.030
22.485 (old)    -1.350          6.526           -1.090      *
22.485 (new)    -1.417          7.332           -1.352
43.315          -1.321          6.185           -0.983

	The estimated errors (from the scatter in the fitted
coefficients) are generally very small:

	G1: .003 at all bands except Q (.014)
	G2: .03 to .07 at all bands except Q (.15)
	G3: .01 to .02 at all bands except Q (.04)

	R. Perley  21/Nov/00

* The 1.285 and 22.485 old feed values are not used.


     If COORDINA is all zero, the pointing position is taken to be
the pointing position given in the header or, if that is 0,
the position of the reference pixel (equal to the map making
position which is equal to the phase tracking position if the
map was made with no shift).  Any other pointing position can be
specified in COORDINA, an array of dimension 6 in the format


where the RA is HHh MMm SS.SSs and the DEC is DDd MM' SS.SS".
Set some or all of COORDINA to non-zero to have it used by the

     The accuracy of the correction is about 1 percent within the 50 percent
primary beam sensitivity and about 2 percent beyond this region.  Thus
the errors of the correction F(x) become quite large near the
edges of the primary beam response.

     Do NOT use PBCOR on the dirty map before running APCLN or
any of the other deconvolution processes.  PBCOR is usually
run near the end of data processing.  It may now be run on
data "cubes" but it does require that frequency, right
ascension, and declination axes appear in the header.

     The speed of the task is dependent on the axis order and
the accuracy of the position computations.  In general, with
linear computations, the RA-DEC-FREQ order of axes is faster.
With non-linear position computations (needed for 1-degree
fields and larger), the FREQ-RA-DEC order appears to be
significantly faster than RA-DEC-FREQ.  Any order will give
correct results, however, and non-linear is always rather
slower than linear.