  An electronic nematic state spontaneously breaks a point-group symmetry of an
underlying lattice. As a result, the nematic-isotropic transition accompanies a
Fermi surface distortion. However, the anisotropic nature of the nematic state
at a macroscopic scale can be easily wiped out when domains of different
orientations of nematic order exist. We suggest that a spatial pattern of local
density of states (LDOS) in the presence of a non-magnetic impurity can be a
direct probe of the nematic order. We study various patterns of LDOS across the
quantum phase transition between the isotropic and nematic phases. Especially
the Fourier transformed local density of states (FT-LDOS), which can be deduced
from scanning tunneling microscope images, represent a transparent symmetry of
an electronic structure. The application of our results to the bilayer
ruthenate, Sr$_3$Ru$_2$O$_7$ is also discussed.
