In this paper conversion factors are presented for a number of simple geometries: a circular constant surface brightness disk and a spherical constant emissivity shell, using a range of values for the inner radius. Also more realistic geometries are studied, based on a spherically symmetric photo-ionization model of a planetary nebula. This enables a study of optical depth effects, a comparison between images in various emission lines and the use of power law density distributions. It is found that the conversion factor depends quite critically on the intrinsic surface brightness distribution, which is usually unknown. The uncertainty is particularly large if extended regions of low surface brightness are present in the nebula. In such cases the use of gaussian or second moment deconvolution is not recommended.

As an alternative, a new algorithm is presented which allows the determination of the intrinsic FWHM of the source using only the observed surface brightness distribution and the FWHM of the beam. Hence no assumptions concerning the intrinsic surface brightness distribution are needed. Tests show that this implicit deconvolution method works well in realistic conditions, even when the signal-to-noise is low, provided that the beam size is less than roughly 2/3 of the observed FWHM and the beam profile can be approximated by a gaussian. A code implementing this algorithm is available.

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Peter van Hoof
Royal Observatory of Belgium
Ringlaan 3
1180 Brussel
Belgium

email: p DOT vanhoof AT oma DOT be