Spectroscopic observations of planetary nebulae are presently the only way to measure the chemical abundances of individual elements in old and intermediate age stars at distances of ~ 1 Mpc or greater. Although the nebular abundances of He, C, N, and S are enhanced by nucleosynthesis in the parent star (e.g. Dopita et al. 1997), comparisons can be made of relative abundances from one part of a galaxy to another, and between galaxies.
In the LMC, [O/H] in bright PNe has the same value as [O/H] in HII regions (Richer 1993); consequently, the oxygen abundance measured in PNe is a good measure of the oxygen abundance in the gas from which the parent stars formed.
With the exception of the He/H ratio, direct abundance determinations require the measurement of the electron temperature Te, the electron density ne, and line intensities in two or more ionization stages. Because the crucial temperature diagnostic line [OIII] 4363 is 50 to 200 times weaker than [OIII] 5007, the measurement of this faint line sets the distance limit for abundance determinations. To date, direct abundance measurements have not been made in galaxies more distant than M31. Indirect PNe abundance determinations based on diagnostic line ratios have been made in NGC 5128 (Walsh et al. 1999).
Jacoby & Ciardullo (1999) measured the chemical abundances in 15 M31 PNe. Their paper, which finds a wide range in [O/H] in M31's old stellar populations, is a model for these difficult observations.