Surface (Doppler) imaging techniques for mapping the temperature distr
ibution of a single star are generalized to the case of an eclipsing s
pectroscopic binary. In this paper we study three main questions, cruc
ial for further application of the techniques: (a) Can we map both com
ponents of a binary system simultaneously and what are the consequence
s of an eclipse for the mapping? (b) What kind of mapping quality shou
ld we expect in different configurations and what observational data a
re required to get a reliable map? (c) What sort of distortion of the
map is produced by errors in the parameters of the binary system (in p
eriod, eccentricity, inclination, etc.)? We found that the method desc
ribed in this paper can be successfully used for imaging eclipsing bin
ary systems. The resulting map is more sensitive to the errors in the
parameters of the system than is the case of a single star. Characteri
stic distortions of the map can be used as indicators for fine tuning
of some of the parameters. We also found that a good phase coverage of
the observations is most important for reducing the artificial equato
rial symmetry, typical for the line profile inversion when used for hi
gh inclination binary systems.