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Deep multiband surface photometry on star forming galaxies: I. A sample of 24 blue compact galaxies

[Abridged] We present deep optical and near-infrared UBVRIHKs imaging data for 24 blue compact galaxies (BCGs). The sample contains luminous dwarf and intermediate-mass BCGs which are predominantly metal-poor, although a few have near-solar metallicities. We have analyzed isophotal and elliptical integration surface brightness and color profiles, extremely deep (mu_B<29 mag arcsec^{-2}) contour maps and RGB images for each galaxy in the sample. The colors are compared to different spectral evolutionary models. We detect extremely extended low surface brightness (LSB) components dominant beyond the Holmberg radius as well as optical bridges between companion galaxies at the mu_V~28th mag arcsec^{-2} isophotal level. The central surface brightness mu_0 and scale length h_r are derived from two radial ranges typically assumed to be dominated by the underlying host galaxy. We find that mu_0 and h_r of the BCGs host deviate from those of dwarf ellipticals (dE) and dwarf irregulars (dI) solely due to a strong burst contribution to the surface brightness profile almost down to the Holmberg radius. Structural parameters obtained from a fainter region, mu_B=26-28 mag arcsec^{-2}, are consistent with those of true LSB galaxies for the starbursting BCGs in our sample, and with dEs and dIs for the BCGs with less vigorous star formation.