We use seeing-free high spatial resolution Ca II H data obtained by the SUNRISE observatory to determine properties of slender fibrils in the lower solar chromosphere. In this work we use intensity images taken with the SUFI instrument in the Ca II H line during the second scientific flight of the SUNRISE observatory to identify and track elongated bright structures. After the identification, we analyze theses structures in order to extract their morphological properties. We identify 598 slender Ca II H fibrils (SCFs) with an average width of around 180 km, a length between 500 km and 4000 km, an average lifetime of ~400 s, and an average curvature of 0.002 arcsec^-1. The maximum lifetime of the SCFs within our time series of 57 minutes is ~2000 s. We discuss similarities and differences of the SCFs with other small-scale, chromospheric structures such as spicules of type I and II, or Ca II K fibrils.
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