  Superresolution has been demonstrated to overcome the limitation of the
Rayleigh's criterion and achieve significant improvement of the precision in
resolving the centroid separation of two incoherent optical point sources.
However, in recent years, it was found that if the photon numbers of the two
incoherent optical sources are unknown, the precision of superresolution
vanishes when the two photon numbers are actually different. In this work, we
analyze the estimation precision of the centroid separation between two
incoherent optical sources with the same point-spread functions and unknown
photon numbers in detail, and show that when the photon numbers of the two
optical sources are different but sufficiently close, the superresolution can
still realized but with different precisions. We find the condition on how
close the photons numbers of two optical sources need to be to realize the
superresolution, and derive the precision of superresolution in different
regimes of the photon number difference. We further consider the
superresolution for two incoherent optical sources with different point-spread
functions, and show that the competition between the difference of photon
numbers, the difference of the two point-spread functions and the centroid
separation of the two optical sources determines the precision of
superresolution. The results exhibit various precision limits of the centroid
separation distinct from that of two point sources with identical point-spread
functions and equal photon numbers. The results are finally illustrated by
Gaussian point-spread functions.
