Based on the second-order coherence function, we have studied a phase-conju
gate ultrafast modulation spectroscopy due to the interference between the
fifth- and fifth-order optical polarizations in cascade three-level Doppler
-broadened system. It is found that the temporal behaviour of the beat sign
al depends on the stochastic properties of the lasers and the transverse re
laxation rate of the transition. The beat signal depends on the second-orde
r coherence function, which is determined by the laser line shape. Since di
fferent stochastic models of the laser held only affect higher than second-
order coherence functions, they have little influence on the general tempor
al modulation behaviour of the beat signal. The cases that pump beams have
either narrow band or broadband linewidth are considered and it;has been fo
und that for both cases the overall accuracy for the energy-level differenc
e measurement is determined by the homogeneous linewidths of the optical tr
ansitions. Finally the spatial modulation behaviour of the beat signal has
also been discussed.