We analyze instantaneous profiles of intense femtosecond optical pulses propagating in helium gas measured using femtosecond time-resolved optical polarigraphy (FTOP). Considering the characteristics of the optical Kerr effect, relations linking images obtained by FTOP with intensity distributions of optical pulses are derived under approximations applicable to a relatively wide range of experimental conditions. By inversely applying the derived equations, images proportional to instantaneous intensity distributions of propagating light pulses are constructed from snapshot images taken in the experiment. From an analysis of the images obtained, we discuss the temporal changes in the optical-pulse profiles. We can directly observe the energy reduction of the optical pulses after they pass through the simultaneously generated laser plasma. It is confirmed that each filament can be separately investigated by this method even under multifilament conditions. Furthermore, the images clearly reveal intensity distributions along the propagation axis as well as cross-section distributions of femtosecond-pulse filaments, and show temporal shape modulations shorter than the incident pulse width in the middle of the propagation. We specify the volume where the tight energy concentrates at a particular instant of time, and directly observe the cross-section expansion of the volume at the focal point brought about due to nonlinear effects.
