  We performed resonant soft X-ray diffraction on known charge density wave
(CDW) compounds, rare earth tri-tellurides. Near the $M_5$ (3d - 4f) absorption
edge of rare earth ions, an intense diffraction peak is detected at a
wavevector identical to that of CDW state hosted on Te$_2$ planes, indicating a
CDW-induced modulation on the rare earth ions. Surprisingly, the temperature
dependence of the diffraction peak intensity demonstrates an exponential
increase at low temperatures, vastly different than that of the CDW order
parameter. Assuming 4f multiplet splitting due to the CDW states,we present a
model to calculate X-ray absorption spectrum and resonant profile of the
diffraction peak, agreeing well with experimental observations. Our results
demonstrate a situation where the temperature dependence of resonant X-ray
diffraction peak intensity is not directly related to the intrinsic behavior of
the order parameter associated with the electronic order, but is dominated by
the thermal occupancy of the valence states.
