  This study establishes a reduction formula for nonstationary cross-spectrally
pure vector light fields with any spectral bandwidth. The formation of a
reduction formula, analogous to that for stationary fields, does not apply to
the normalized two-time Stokes parameters of a nonstationary field that is
cross-spectrally pure. The current formula incorporates time-integrated
coherence parameters to ensure cross-spectral purity. The reduction formula
derived for nonstationary vector light fields with arbitrary spectral bandwidth
shares a similar mathematical structure to that of reduction formulas used for
stationary vector fields. Additionally, we examine the requirement of strict
cross-spectral purity for using a time-integrated coherence function, which
exhibits a mathematical expression similar to that of strict cross-spectral
purity in stationary vector fields. This investigation sheds light on the
cross-spectral purity of pulse-type fields, which holds potential applications
in the field of statistical optics.
