  We explain why it is possible to detect directly X-ray emission from near the
surface of the neutron star (NS) in SAX J1808.4-3658 but not in most other
low-mass X-ray binaries (LMXBs), with the exception that emission from the
surface can be seen during bursts events. We show that the X-ray emission from
SAX J1808.4-3658 mostly originates in the Comptonization process in a
relatively optical thin hot region (with an optical depth $\tau_0$ around 4 and
temperature is around 20 keV). Such a transparent region does not prevent us
from detecting coherent X-ray pulsation due to hot spots on the NS surface.
When the characteristic scattering time in the region is of order of inverse
rotational frequency omega or higher then the amplitude of the harmonic
oscillation decays exponentially with (tau_0 x omega). We give a precise model
for the loss of modulation, such suppression of the QPO amplitude due to
scattering can explain the disappearance of kHz QPOs with increasing QPO
frequency. We also formulate general conditions under which the millisecond
X-ray pulsation can be detected in LMXBs.
  We demonstrate that the observed soft phase lag of the pulsed emission is a
result of the downscattering of the hard X-ray photons in the relatively cold
material near the NS surface. In the framework of this downscattering model we
propose a method to determine the atmosphere density in that region from
soft-lag measurements.
