Abstract:  Based on the generalized Huygens-Fresnel principle, we derive the cross-spectral
density function using the modified von Karmon spectrum and atmospheric refractive-index
structure constant issued by ITU-R. We also derive analytic expressions of intensity distribution
and beam width of partially coherent Gaussian-Schell beam propagating in the
atmosphere along slant and horizontal paths. The impact on the beam propagating in
the two ways due to turbulence intensity, zenith, coherence length of the beam and other
parameters are discussed. They are compared respectively from the perspective of normalized
intensity distribution and relative expansion. The results show that the normalized
intensity distribution of the beam in a free space along a horizontal path is the same as
that along a slant path. The normalized intensity distribution is more concentrated, with
the peak much stronger when zenith is smaller, while the effects of the turbulence become
weaker. Impact on the zenith expansion, turbulence, coherence of the beam is almost consistent
with the slant path.

Key words: partially coherent beam, slant path, normalized intensity distribution, relative beam width