Testing the Distance-Duality Relation with a Combination of Cosmological
  Distance Observations
  In this paper, we propose an accurate test of the distance-duality (DD)
relation, $\eta=D_{L}(z)(1+z)^{-2}/D_{A}(z)=1$ (where $D_{L}$ and $D_{A}$ are
the luminosity distances and angular diameter distances, respectively), with a
combination of cosmological observational data of Type Ia Supernave (SNe Ia)
from Union2 set and the galaxy cluster sample under an assumption of spherical
model. In order to avoid bias brought by redshift incoincidence between
observational data and to consider redshift error bars of both clusters and SNe
Ia in analysis, we carefully choose the SNe Ia points which have the minimum
acceptable redshift difference of the galaxy cluster sample ($|\Delta z|_{\rm
min} =\sigma_{z, \rm SN}+\sigma_{z, \rm cluster}$). By assuming $\eta$ a
constant and functions of the redshift parameterized by six different
expressions, we find that there exists no conceivable evidence for variations
in the DD relation concerning with observational data, since it is well
satisfied within $1\sigma$ confidence level for most cases. Further considering
different values of $\Delta z$ in constraining, we also find that the choosing
of $\Delta z$ may play an important role in this model-independent test of the
distance-duality relation for the spherical sample of galaxy clusters.
