The optical Sagnac effect sets fundamentals of the operating principle for ring laser and fiber optic gyroscopes, which are preferred instruments for inertial guidance systems, seismology, and geodesy. Operating at both high bias stability and angular velocity resolutions demands special precautions like dithering or multimode operation to eliminate frequency lock-in or similar effects introduced due to synchronization of counterpropagating channels. Recently, to circumvent these limitations, ultrashort pulsed radiation was suggested to supersede conventional continuous wave operation. Despite the ultrafast nature of ultrashort pulse generation, the interrogation of the Sagnac effect relies on highly averaging measurement methods. Here, we demonstrate the novel approach to the optical Sagnac effect visualization by applying real-time spatiooral intensity processing and time-resolved spectral domain measurements of ultrashort pulse dynamics in rotating the bidirectional ring fiber laser cavity. Our results reveal the high potential of application of novel methods of optical Sagnac effect measurements, allowing enhancement of rotation sensitivity and resolution by several orders of magnitude.