Calculating the Telescope FWHM given the Observed FWHM of a Planet
File: kdata:[smt.doc]beamwidth.doc Updated 11/23/00 M. Dumke
The telescope beamwidth may be smaller than the observed beamwidth when
a the object observed is not a point source. Baars (1973) gives a formula
for approximately calculating the telescope beam width when the telescope
beamwidth is greater than the planet diameter and the planet emission is
well approximated by that of a uniform disk:
FWHM(telescope) = sqrt(FWHM(observed)**2-(ln 2/2)*diameter**2)
When the diameter is slightly larger than the the telescope beam width, this
formula overestimates the telescope beamwidth. A better formula can be derived
from an earlier paper by Baars et al (1965). When the observed beamwidth
is nearly the same as the planet diameter, the telescope beamwidth is not
well determined and may be very sensitive to the difference between the
observed FWHM and the planet diameter.
BEAMWIDTH is a program that will calculate the telescope beamwidth given
the observed FWHM and the planet diameter. It calculates the beamwidth
three ways: via the above approximation, via the somewhat more complicated
formula derived from the 1965 paper, and via numerical integration. The
last one is done by calculating the signal at the offset of the observed
FWHM offset varying the telescope beam size until the signal is half of the
signal at offset 0. To run BEAMWIDTH, type
RUN TEL$POINTING:BEAMWIDTH
Since 23 November 2000, a Unix version is also available at
/home/smtop/bin/beamwidth
Since this directory is in the path of the smtobs and smtop account,
just type "beamwidth" to run the program.