1 Introduction

Doppler imaging is an elaborate observational and computational technique similar to medical tomography wherein a series of high-resolution spectral line profiles are inverted into an "image'' of the stellar surface. A complex computer code - hereafter called TEMPMAP - was developed by Rice et al. (1989) for Ap stars and subsequently was applied to spectral-line data for numerous cool stars in a series of papers (e.g. Strassmeier & Rice 2000). With every application, our code continuously evolved and features were frequently added or removed and tested. The actual test results are extensive and could not be accommodated within the "regular'' astronomical papers. Following suggestions from previous referees who had questions about the behavior of Doppler imaging under less than ideal conditions, we felt now that the time was ripe to present an update of the TEMPMAP code and document the reliability (and weaknesses) of our code through a series of tests on artificial data.

The basic concepts of TEMPMAP were layed out in the original paper by Rice et al. (1989) and Doppler imaging with it was reviewed, among others, by Piskunov & Rice (1993), Rice (1996), and Strassmeier (2000). A brief description of the new features of TEMPMAP can be found in previous papers, e.g., Rice & Strassmeier (1998) and references therein. In the present paper, we will concentrate on the test results.

Other codes were developed in parallel and include the early efforts of Vogt et al. (1987) and Piskunov (1990). Many successful applications appeared in the literature and a comparison of these two codes with an early version of TEMPMAP was made using EI Eri as a test star (Strassmeier et al. 1991). Generally, the comparison was satisfactory given the state of Doppler imaging at that time. In 1990, Collier Cameron (1992) introduced his code which, in the meantime, has experienced numerous upgrades and successful applications to AB Dor (e.g. by Unruh et al. 1995). Also in that year, Kürster et al. (1990) presented an inversion code based on the CLEAN algorithm and later conducted extensive testing (Kürster 1993) along with an application to AB Dor. In 1992, the French group around M. Semel introduced their mapping version (Donati et al. 1992) which had been also continuously upgraded and tested since then (e.g. Donati 1999). Two more french groups presented papers on new computer codes, Jankov & Foing (1992) and Joncour et al. (1994). Testing was presented by the former while two applications were presented by the latter. Most recently, Berdyugina (1998) presented a code based on the Occamian principle and successfully applied it to the RS CVn star II Pegasii (Berdyugina et al. 1998).