1 Introduction

It is widely accepted that an "aged'' star of low to medium mass ( $1.0~M_\odot<M_{\rm MS} <8.0~M_\odot$) which is evolving toward the white dwarf region of the H-R diagram, first expels and then ionizes the surface layers, thus generating the Planetary Nebula (PN) phenomenology (Paczynski 1970; Aller 1984; Pottasch 1984; Osterbrock 1989).

Figure 1: WFPC2 archive images of NGC 6818 in [O III] (left) and [N II] (right). The binary nature of the central star is shown in the enlargement at the bottom. North is up and East to the left.

Thanks to the advent of sophisticate photo-ionization codes (Harrington 1989; Pequignot 1997; Ferland et al. 1998), we now know in detail the physical effects produced by any UV flux on any gas distribution and composition. Conversely, the situation is quite disappointing for a true nebula, due to projection limitations: on the one hand the HST imagery has strongly enhanced the ground-based evidences of the PNe complexity, on the other hand the observational data are still interpreted in terms of approximate structures and unrealistic assumptions for the physical conditions, like $T{\rm e}=\rm constant$ and $N{\rm e}=$ constant all over the object (more comments are in Aller 1984, 1990, 1994).

In order to overcome the wide gap between theory and practice, the apparent, bi-dimensional nebular image should be de-projected, and the accurate spatial distribution of the gas recovered.

To this end we have developed an original procedure based on high dispersion spectra: the PN being an extended and expanding plasma, the position, thickness and density of each elementary volume can be, in principle, obtained from the radial velocity, width and flux of the corresponding emission. We first apply a tomographic analysis, which reconstructs the ionic distribution in the nebular slices covered by the spectrograph slit, and then assemble all the tomographic maps by means of a 3-D rendering procedure for studying the morphology, physical conditions, ionization, spatial structure and evolutionary status.

The rationale of the method and the earliest, rough results based on plate echellograms go back to Sabbadin et al. (1985, 1987). More recent, "quantitative'' observations (i.e. using a linear detector) concern NGC 40 and NGC 1501, both objects covered at moderate spectral resolution, $R\simeq 20~000{-}25~000$, with the Echelle + 1.82 m telescope of Padua Observatory at Asiago, Cima Ekar (Sabbadin et al. 2000a,b; Ragazzoni et al. 2001; hereafter Papers I to III, respectively).

At the same time we have carried out a survey of two dozen PNe and proto-PNe in both hemispheres with ESO NTT+EMMI (spectral range $\lambda\lambda$3900-7900 Å, R=60 000, spatial resolution $\simeq$1.0 arcsec) and the Telescopio Nazionale Galileo (TNG)+SARG (spectral range $\lambda\lambda$4600-8000 Å, R=115 000, spatial resolution $\simeq$0.7 arcsec). The observed sample covers a variety of morphologies, kinematics and evolutionary phases, including NGC 2392 (the Eskimo nebula), NGC 3132 (the Eight-Burst n.), NGC 3242 (the Ghost of Jupiter n.), NGC 6210 (the Turtle n.), NGC 6543 (the Cat's Eye n.), NGC 6751 (the Glowing Eye n.), NGC 6826 (the Blinking n.), NGC 7009 (the Saturn n.), NGC 7662 (the Blue Snowball n.), IC 418 (the Spirograph n.), He 2-47 (the Starfish n.), MyCn 18 (the Hourglass n.), MZ 3 (the Ant n.), and as many un-dubbed, but equally exciting targets.

The 3-D ionization structure of NGC 6565 has been presented by Turatto et al. (2002, Paper IV); here we discuss the case of NGC 6818 (PNG 025.8-17.9, Acker et al. 1992).

The paper is structured as follows: Sect. 2 introduces the nebula, Sect. 3 presents the observational material and the reduction procedure, Sect. 4 is dedicated to the gas kinematics, Sect. 5 concerns the radial profile of the physical conditions (electron temperature and electron density from forbidden line ratios), in Sect. 6 the ionization structure and the overall gas distribution are discussed, in Sect. 7 we derive the nebular distance, mass and age, in Sect. 8 the central star parameters are given, Sect. 9 contains the application of the photo-ionization model (CLOUDY), Sect. 10 describes the 3-D structure of the nebula in different ions, and Sect. 11 presents a short discussion and the conclusions.