  In this paper, we present a new model, hollow Gaussian-Schell model beams
(HGSMBs), to describe the practical dark hollow beams. An analytical
propagation formula for HGSMBs passing through a paraxial first-order optical
system is derived based on the theory of coherence. Based on the derived
formula, an application example showing the influence of spatial coherence on
the propagation of beams is illustrated. It is found that the beam propagating
properties of HGSMBs will be greatly affected by their spatial coherence. Our
model provides a very convenient way for analyzing the propagation properties
of partially coherent dark hollow beams.
