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Function: PRIBEAM

Purpose: Calculate primary beam correction
(after proper initialization)

Files: pribeam.shl

Author: M. Vogelaar

Category: RADIO DATA, HEADER

Use: REAL PRIBEAM( setname , Input CHARACTER*(*)
subset , Input INTEGER
axperm , Input INTEGER ARRAY
X , Input REAL
Y , Input REAL
option , I/O INTEGER
errtxt , O CHARACTER*(*)
)

PRIBEAM Returns correction value less than 1.0 (i.e.
a 'Antenna Power Spectrum' value) after
proper initialization. The setup needs to be
done only once and is achieved by calling the
function with option = 0.
If the function returns option <> 0 it is
ready for calculating the corrections.
setname Name of GDS set.
subset Subset coordinate word.
The subset can be 1- or 2-dimensional. If it
is one dimensional, the coordinates are to be
supplied in X.
axperm Axis permutation array.
X Grid position of point in longitude direction.
Y Grid position in latitude direction.
option INPUT:
option = 0 : Initialize PRIBEAM.
option = 1 : Return 0 if beyond cutoff.
option = 2 : Return min. allowed value beyond
cutoff. The function calculates
this value for different telescopes.
option = 3 : Disable cutoff, i.e. return values
that correspond to coordinates
outside the validity range of the
correction function.
option = 4 : Return blank if beyond cutoff.

Use option <> 4 very carefully!

OUTPUT:
option < 0 : Not a successful initialization.
'errtxt' contains the error message.

errtxt After an unsuccessful initialization, errtxt
contains a message about what went wrong.

Description: PRIBEAM looks in the set header for the instrument
used. Instruments recognized by PBCORR are: WSRT, VLA,
(VLAP), FST and the millimeter arrays IRAM-PdB, NMA (Nobeyama),
OVRO and BIMA. The VLAP beam shape comes from A. Rots.
The shape for the millimeter arrays are approximated by form.4
(F Viallefond)

RF is [D * freq (GHz)], where D is the distance
from the pointing position in minutes of arc for
the VLA and the ATCA antenna and in degrees for
other antennas. The distance D is computed using spherical
geometry except for the millimeter arrays for which
a flat geometry is a good approximation (small ratio
primary beam size/pixel size) to speed up the computations.

The shape of the primary beam then, is represented by the
following formulas (PBC is the correction factor):

form.1 : WSRT
PBC = COS(C*RF)**6
4995 Mhz (6 cm): C = 61.18
1415 Mhz (21 cm): C = 61.18
608.5 Mhz (50 cm): C = 66.4
327.25 Mhz (90 cm): C = 62.9 (After jan '89)


form.3 : VLA all frequencies
PBC = 1 / F(RF**2)
The VLA correction is described by the function:
( 1/correction=Power Spectrum )
F(RF2) = 0.9920378
+0.9956885 E-3 RF2
+0.3814573 E-5 RF2*RF2
-0.5311695 E-8 RF2*RF2*RF2
+0.3980963 E-11 RF2*RF2*RF2*RF2

F(FR2) = a0
+ a1*RF2
+ a2*RF2*RF2
+ a3*RF2*RF2*RF2
+ a4*RF2*RF2*RF2*RF2

------------------------------------------------------------------
Instru. VLA ATCA ATCA ATCA ATCA
Band all bands 20cm 13cm 6cm 3cm
------------------------------------------------------------------
a0 +0.9920378 +1. +1. +1. +1.
a1 +0.9956885 E-03 +8.99E-04 +1.02E-03 +1.08E-03 +1.04E-03
a2 +0.3814573 E-05 +2.15E-06 +9.48E-07 +1.31E-06 +8.36E-07
a3 -0.5311695 E-08 -2.23E-09 -3.68E-10 -1.17E-09 -4.68E-10
a4 +0.3980963 E-11 +1.56E-12 +4.88E-13 +1.07E-12 +5.50E-13
------------------------------------------------------------------

N.B. range for the ATCA [0-50] arcmin GHz for the
20, 13, 6 and 3cm bands (ref. "Measurement of the ATCA
primary beam" Sept. 8, 1992 by Wieringe and Kesteven.

form.4 : FST (Fleurs) and millimeter arrays
PBC = EXP(-T2*RF*RF) (T2 = 0.8031 for the FST)

T0, T2, T4 and T6 depend on the instrument used and in
some cases also on the frequency.

Outside the validity range, the correction is set to a
value depending on 'option'. For WSRT and VLA The cutoff
occurs at a primary beam sensitivity of 2.3% of the value
at the beam center, i.e. where the Antenna Power Spectrum
is equal to 2.3/100. For the ATCA the cutoff occurs for
RF = 50 arcmin GHz in all bands. For the Fleurs telescope
the cutoff is (at 21 cm) at a distance of 2.8 degrees.
The pointing position is obtained from the header items
PCRA and PCDEC. If these items are not available, the
reference values (CRVAL) of pixel 0 are used.

Note: If PRIBEAM cannot find a proper frequency, the frequency
is asked with FREQUENCY= The keyword accepts a number and a
unit. If no unit is given, the number is in Ghz. Otherwise
a conversion is done to Ghz. The possible units to convert
are for example MHz, Hz, but also cm. Only the first time
the keyword is asked unhidden. Documentation
about this keyword should be included in the documentation
of the application that calls 'PRIBEAM'.

Updates: Mar 27, 1990: MV, Document created.
Jan 14, 1992: MV, Cotrans to calculate distance.
Apr 8, 1992: MV, Other VLA formula.
Jul 23, 1992: MV, Made suitable for 1-dim. subsets.
Jul 24, 1992: MV, One formula for all WSRT frequencies.
Dec 31, 1992: FV, Millimeter arrays added
Mar 9, 1993: FV, Australia Telescope added