  Imaging point sources in heterogeneous environments from boundary or
far-field measurements has been extensively studied in the past. In most
existing results, the environment, represented by the refractive index function
in the model equation, is assumed known in the imaging process. In this work,
we investigate the impact of environment uncertainty on the reconstruction of
point sources inside it. Following the techniques developed by El Badia and El
Hajj (C. R. Acad. Sci. Paris, Ser. I, 350 (2012), 1031-1035), we derive
stability of reconstructing point sources in heterogeneous media with respect
to measurement error as well as smooth changes in the environment, that is, the
refractive index. Numerical simulations with synthetic data are presented to
further explore the derived stability properties.
