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.