  Surface and spatial radial density profiles in open clusters are derived
using a kernel estimator method. Formulae are obtained for the contribution of
every star into the spatial density profile. The evaluation of spatial density
profiles is tested against open-cluster models from N-body experiments with N =
500. Surface density profiles are derived for seven open clusters (NGC 1502,
1960, 2287, 2516, 2682, 6819 and 6939) using Two-Micron All-Sky Survey data and
for different limiting magnitudes. The selection of an optimal kernel
half-width is discussed. It is shown that open-cluster radius estimates hardly
depend on the kernel half-width. Hints of stellar mass segregation and
structural features indicating cluster non-stationarity in the regular force
field are found. A comparison with other investigations shows that the data on
open-cluster sizes are often underestimated. The existence of an extended
corona around the open cluster NGC 6939 was confirmed. A combined function
composed of the King density profile for the cluster core and the uniform
sphere for the cluster corona is shown to be a better approximation of the
surface radial density profile.The King function alone does not reproduce
surface density profiles of sample clusters properly. The number of stars, the
cluster masses and the tidal radii in the Galactic gravitational field for the
sample clusters are estimated. It is shown that NGC 6819 and 6939 are extended
beyond their tidal surfaces.
