  Influences of a substrate below samples in imaging performances are studied
by reaching the solution to the dyadic Green's function, where the substrate is
modeled as half space in the sample region. Then, theoretical and numerical
analysis are performed in terms of magnification, depth of field, and
resolution. Various settings including positions of dipoles, the distance of
the substrate to the focal plane and dipole polarization are considered.
Methods to measure the resolution of $z$-polarized dipoles are also presented
since the modified Rayleigh limit cannot be applied directly. The silicon
substrate and the glass substrate are studied with a water immersion objective
lens. The high contrast between silicon and water leads to significant
disturbances on imaging.
