  The first image of black hole in M87 galaxy taken by Event Horizon Telescope
shows that directed observation of supermassive black holes would be a
promising way to test general relativity in strong gravity field regime. In
order to calculate shadow of rotating black holes with respect to observers
located at finite distance, orthonormal tetrads have been introduced in
previous works. However, it is noticed that different choice of tetrads does
not lead to the same shape of shadow for observers in near regions. In this
paper, we alternatively use formula of astrometric observables for calculating
the shadow of a general rotating black hole with respect to these observers.
For the sake of intuitive, we also consider Kerr-de Sitter black holes as a
representative example. In this space-time, size and shape of Kerr-de Sitter
black hole shadows are expressed as functions of distance between the black
hole and observer. It is forecasted that the distortion of shadow would
increase with distance.
