  When measuring diameters of partially resolved sources like planetary
nebulae, H II regions or galaxies, often a technique called gaussian
deconvolution is used. This technique yields a gaussian diameter which
subsequently has to be multiplied with a conversion factor to obtain the true
angular diameter of the source. This conversion factor is a function of the
Full Width at Half Maximum (FWHM) of the beam. It also depends on the intrinsic
surface brightness distribution of the source.
  In this paper the theory behind this technique will be studied. This study
will be restricted to circularly symmetric geometries and beams. First an
implicit equation will be derived, from which the conversion factor for a given
surface brightness distribution and beam size can be solved. Explicit
expressions for the conversion factor will be derived from this equation which
are valid in cases where the beam size is larger than the intrinsic size of the
source. A more detailed discussion will be given for two simple geometries: a
circular constant surface brightness disk and a spherical constant emissivity
shell with arbitrary inner radius. The theory is subsequently used to construct
a new technique for determining the FWHM of an arbitrary observed surface
brightness distribution.
  Usually the FWHM of the source and beam are measured using gaussian fits, but
second moments can also be used. The alternative use of second moments in this
context is studied here for the first time and it is found that in this case
the conversion factor has a different value which is independent of the beam
size. In the limit for infinitely large beam sizes, the values of the
conversion factors for both techniques are equal.
