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In this paper we present an approach to retrieve stratospheric aerosol number densities in the altitude range 10-40 km from SCIAMACHY limb radiance measurements in the spectral range of the O-2 A absorption band, near 760 nm. Here, the characteristic light paths differ for the measured light in the O-2 A-band and in the spectral continuum next to the absorption band. This difference is used to distinguish the effect of stratospheric aerosol scattering and ground reflection on the limb measurement. The capability to disentangle both effects is illustrated for SCIAMACHY limb observations over the Libyan desert, where the measurements are not affected by tropospheric clouds. Comparison of the SCIAMACHY retrieval and the SAGE II aerosol extinction product between 75 degrees southern and northern latitude shows the clear need for prior knowledge of the mean size of the stratospheric aerosol for the SCIAMACHY retrieval. We found best agreement between SCIAMACHY and SAGE II aerosol extinction for the period 2003-2005 for a prior choice of the mean aerosol size radius of 0.2 mu m. The overall agreement between both data sets is in the range <50% root mean square difference at 14-30 km with a minimum of 30% at 22 km.