the properties of the core sample and explain observational details. In Sect. 3, we show our ISOCAM absorption maps and analyze the associated absorption profiles in terms of column density structure. In Sect. 4, we compare our results with various theoretical models of core structure and discuss possible implications for our understanding of the pre-stellar stage of star formation. Our main conclusions are summarized in Sect. 5.

Observations and Data Reduction
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Starless core sample
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The 24 starless fields of the present survey were selected from various dark cloud and nebula catalogs (e.g. Parker 1988, Benson & Myers 1989, Bourke, Hyland & Robinson 1995, Schneider & Elmegreen 1979), on the grounds that they contained no IRAS point sources associated with a young stellar object and had an estimated mid-infrared (mid-IR) background stronger than $\sim
1$ MJy/sr at $\sim$ 7 $\mu$m. We also included a map of the dark cloud Oph D (also called L1696A) situated in the $\rho$ Ophiuchi complex, and already observed in absorption by ISOCAM (Abergel et al. 1998). The background at 7 $\mu$m was originally estimated from IRAS images, as were the 7 $\mu$m flux densities of the IRAS sources appearing in the fields. Fields containing 