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We demonstrate a method for the calibration-free and quantitative analysis of small volumes of gaseous samples. A 10 m hollow-core photonic bandgap fiber is used as the sample cell (volume = 0.44 mu L) and is placed inside a linear resonator setup. The application of cavity ring-down spectroscopy and in consideration of rather small coupling losses, this leads to an increased effective optical path length of up to 70 m. This implies a volume per optical interaction path length of 6.3 nL.m(-1). We used tunable diode laser spectroscopy at 760 nm and scanned the absorption for oxygen sensing. The optical loss due to sample absorption is obtained by measuring the ring-down time of light propagating inside the cavity. The resultant absorption coefficient shows a discrepancy of only 5.1% comparing to the HITRAN database. This approach is applicable for sensitive measurements if only submicroliter sample volumes are available.