The physical parameters of Herbig-Haro (HH) jets are usually determined from emission-line ratios, obtained from spectroscopy or narrowband imaging, assuming that the emitting region is homogeneous along the line of sight. Under the more general hypothesis of axisymmetry, we apply tomographic reconstruction techniques to the analysis of HH jets. We use data of the HH30 jet taken by Hartigan and Morse with the Hubble Space Telescope using the slitless spectroscopy technique. Using a non-parametric Tikhonov regularization technique, we determine the volumetric emission-line intensities of the [S II]λλ6716,6731, [O I]λ6300, and [N II]λ6583 forbidden emission lines. From our tomographic analysis of the corresponding line ratios, we produce "three-dimensional" images of the physical parameters. The reconstructed density, temperature, and ionization fraction present much steeper profiles than those inferred using the assumption of homogeneity. Our technique reveals that the reconstructed jet is much more collimated than the observed one close to the source (a width ~5 AU versus ~20 AU at a distance of 10 AU from the star), while they have similar widths at larger distances. In addition, our results show a much more fragmented and irregular jet structure than the classical analysis, suggesting that the ejection history of the jet from the star-disk system has a shorter timescale component (~some months) superimposed on a longer, previously observed timescale (of a few years). Finally, we discuss the possible application of the same technique to other stellar jets and planetary nebulae.